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193 lines
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<title>Rounding Rules for Conversions</title>
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<div class="titlepage"><div><div><h3 class="title">
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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
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Conversions</a>
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</h3></div></div></div>
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<p>
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As a general rule, all conversions between unrelated types are performed
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using basic arithmetic operations, therefore conversions are either exact,
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or follow the same rounding rules as arithmetic for the type in question.
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</p>
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<p>
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The following table summarises the situation for conversions from native
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types:
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</p>
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<div class="informaltable"><table class="table">
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<colgroup>
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<col>
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</colgroup>
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<thead><tr>
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<th>
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<p>
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Backend
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</p>
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</th>
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<th>
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<p>
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Rounding Rules
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</p>
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</th>
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</tr></thead>
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<tbody>
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<tr>
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<td>
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<p>
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<a class="link" href="ints/cpp_int.html" title="cpp_int">cpp_int</a>
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</p>
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</td>
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<td>
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<p>
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Conversions from integer types are exact if the target has sufficient
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precision, otherwise they truncate to the first 2^MaxBits bits
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(modulo arithmetic). Conversions from floating-point types are
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truncating to the nearest integer.
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</p>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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<a class="link" href="ints/gmp_int.html" title="gmp_int">gmp_int</a>
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</p>
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</td>
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<td>
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<p>
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Conversions are performed by the GMP library except for conversion
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from <code class="computeroutput"><span class="keyword">long</span> <span class="keyword">double</span></code>
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which is truncating.
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</p>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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<a class="link" href="ints/tom_int.html" title="tom_int">tom_int</a>
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</p>
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</td>
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<td>
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<p>
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Conversions from floating-point types are truncating, all others
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are performed by libtommath and are exact.
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</p>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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<a class="link" href="floats/gmp_float.html" title="gmp_float">gmp_float</a>
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</p>
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</td>
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<td>
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<p>
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Conversions are performed by the GMP library except for conversion
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from <code class="computeroutput"><span class="keyword">long</span> <span class="keyword">double</span></code>
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which should be exact provided the target type has as much precision
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as a <code class="computeroutput"><span class="keyword">long</span> <span class="keyword">double</span></code>.
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</p>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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<a class="link" href="floats/mpfr_float.html" title="mpfr_float">mpfr_float</a>
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</p>
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</td>
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<td>
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<p>
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All conversions are performed by the underlying MPFR library.
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</p>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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<a class="link" href="floats/cpp_dec_float.html" title="cpp_dec_float">cpp_dec_float</a>
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</p>
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</td>
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<td>
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<p>
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All conversions are performed using basic arithmetic operations
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and are truncating.
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</p>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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<a class="link" href="rational/gmp_rational.html" title="gmp_rational">gmp_rational</a>
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</p>
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</td>
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<td>
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<p>
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See <a class="link" href="ints/gmp_int.html" title="gmp_int">gmp_int</a>
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</p>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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<a class="link" href="rational/cpp_rational.html" title="cpp_rational">cpp_rational</a>
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</p>
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</td>
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<td>
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<p>
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See <a class="link" href="ints/cpp_int.html" title="cpp_int">cpp_int</a>
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</p>
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</td>
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</tr>
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<tr>
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<td>
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<p>
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<a class="link" href="rational/tommath_rational.html" title="tommath_rational">tommath_rational</a>
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</p>
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</td>
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<td>
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<p>
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See <a class="link" href="ints/tom_int.html" title="tom_int">tom_int</a>
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</p>
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</td>
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</tr>
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</tbody>
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</table></div>
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</div>
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<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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<td align="left"></td>
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<td align="right"><div class="copyright-footer">Copyright © 2002-2019 John Maddock
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and Christopher Kormanyos<p>
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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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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</p>
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</div></td>
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</tr></table>
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<hr>
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<div class="spirit-nav">
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<a accesskey="p" href="import_export.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../tut.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="mixed.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
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