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<html>
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<title>Rounding Rules for Conversions</title>
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<div class="section boost_multiprecision_tut_rounding">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_multiprecision.tut.rounding"></a><a class="link" href="rounding.html" title="Rounding Rules for Conversions">Rounding Rules for
Conversions</a>
</h3></div></div></div>
<p>
As a general rule, all conversions between unrelated types are performed
using basic arithmetic operations, therefore conversions are either exact,
or follow the same rounding rules as arithmetic for the type in question.
</p>
<p>
The following table summarises the situation for conversions from native
types:
</p>
<div class="informaltable"><table class="table">
<colgroup>
<col>
<col>
</colgroup>
<thead><tr>
<th>
<p>
Backend
</p>
</th>
<th>
<p>
Rounding Rules
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
<a class="link" href="ints/cpp_int.html" title="cpp_int">cpp_int</a>
</p>
</td>
<td>
<p>
Conversions from integer types are exact if the target has sufficient
precision, otherwise they truncate to the first 2^MaxBits bits
(modulo arithmetic). Conversions from floating point types are
truncating to the nearest integer.
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="ints/gmp_int.html" title="gmp_int">gmp_int</a>
</p>
</td>
<td>
<p>
Conversions are performed by the GMP library except for conversion
from <code class="computeroutput"><span class="keyword">long</span> <span class="keyword">double</span></code>
which is truncating.
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="ints/tom_int.html" title="tom_int">tom_int</a>
</p>
</td>
<td>
<p>
Conversions from floating point types are truncating, all others
are performed by libtommath and are exact.
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="floats/gmp_float.html" title="gmp_float">gmp_float</a>
</p>
</td>
<td>
<p>
Conversions are performed by the GMP library except for conversion
from <code class="computeroutput"><span class="keyword">long</span> <span class="keyword">double</span></code>
which should be exact provided the target type has as much precision
as a <code class="computeroutput"><span class="keyword">long</span> <span class="keyword">double</span></code>.
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="floats/mpfr_float.html" title="mpfr_float">mpfr_float</a>
</p>
</td>
<td>
<p>
All conversions are performed by the underlying MPFR library.
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="floats/cpp_dec_float.html" title="cpp_dec_float">cpp_dec_float</a>
</p>
</td>
<td>
<p>
All conversions are performed using basic arithmetic operations
and are truncating.
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="rational/gmp_rational.html" title="gmp_rational">gmp_rational</a>
</p>
</td>
<td>
<p>
See <a class="link" href="ints/gmp_int.html" title="gmp_int">gmp_int</a>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="rational/cpp_rational.html" title="cpp_rational">cpp_rational</a>
</p>
</td>
<td>
<p>
See <a class="link" href="ints/cpp_int.html" title="cpp_int">cpp_int</a>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="rational/tommath_rational.html" title="tommath_rational">tommath_rational</a>
</p>
</td>
<td>
<p>
See <a class="link" href="ints/tom_int.html" title="tom_int">tom_int</a>
</p>
</td>
</tr>
</tbody>
</table></div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright &#169; 2002-2012 John Maddock and Christopher Kormanyos<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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