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- <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>
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- <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 © 2002-2019 John Maddock
- and Christopher Kormanyos<p>
- Distributed under the Boost Software License, Version 1.0. (See accompanying
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