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<title>Rational Number Types</title>
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<div class="titlepage"><div><div><h3 class="title">
<a name="boost_multiprecision.tut.rational"></a><a class="link" href="rational.html" title="Rational Number Types">Rational Number Types</a>
</h3></div></div></div>
<div class="toc"><dl class="toc">
<dt><span class="section"><a href="rational/cpp_rational.html">cpp_rational</a></span></dt>
<dt><span class="section"><a href="rational/gmp_rational.html">gmp_rational</a></span></dt>
<dt><span class="section"><a href="rational/tommath_rational.html">tommath_rational</a></span></dt>
<dt><span class="section"><a href="rational/br.html">Use With Boost.Rational</a></span></dt>
<dt><span class="section"><a href="rational/rational_adaptor.html">rational_adaptor</a></span></dt>
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<p>
        The following back-ends provide rational number arithmetic:
      </p>
<div class="informaltable"><table class="table">
<colgroup>
<col>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
                <p>
                  Backend Type
                </p>
              </th>
<th>
                <p>
                  Header
                </p>
              </th>
<th>
                <p>
                  Radix
                </p>
              </th>
<th>
                <p>
                  Dependencies
                </p>
              </th>
<th>
                <p>
                  Pros
                </p>
              </th>
<th>
                <p>
                  Cons
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  <code class="computeroutput"><span class="identifier">cpp_rational</span></code>
                </p>
              </td>
<td>
                <p>
                  boost/multiprecision/cpp_int.hpp
                </p>
              </td>
<td>
                <p>
                  2
                </p>
              </td>
<td>
                <p>
                  None
                </p>
              </td>
<td>
                <p>
                  An all C++ Boost-licensed implementation.
                </p>
              </td>
<td>
                <p>
                  Slower than <a href="http://gmplib.org" target="_top">GMP</a>.
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  <code class="computeroutput"><span class="identifier">gmp_rational</span></code>
                </p>
              </td>
<td>
                <p>
                  boost/multiprecision/gmp.hpp
                </p>
              </td>
<td>
                <p>
                  2
                </p>
              </td>
<td>
                <p>
                  <a href="http://gmplib.org" target="_top">GMP</a>
                </p>
              </td>
<td>
                <p>
                  Very fast and efficient back-end.
                </p>
              </td>
<td>
                <p>
                  Dependency on GNU licensed <a href="http://gmplib.org" target="_top">GMP</a>
                  library.
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  <code class="computeroutput"><span class="identifier">tommath_rational</span></code>
                </p>
              </td>
<td>
                <p>
                  boost/multiprecision/tommath.hpp
                </p>
              </td>
<td>
                <p>
                  2
                </p>
              </td>
<td>
                <p>
                  <a href="http://libtom.net" target="_top">libtommath</a>
                </p>
              </td>
<td>
                <p>
                  All C/C++ implementation that's Boost Software Licence compatible.
                </p>
              </td>
<td>
                <p>
                  Slower than <a href="http://gmplib.org" target="_top">GMP</a>.
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  <code class="computeroutput"><span class="identifier">rational_adaptor</span></code>
                </p>
              </td>
<td>
                <p>
                  boost/multiprecision/rational_adaptor.hpp
                </p>
              </td>
<td>
                <p>
                  N/A
                </p>
              </td>
<td>
                <p>
                  none
                </p>
              </td>
<td>
                <p>
                  All C++ adaptor that allows any integer back-end type to be used
                  as a rational type.
                </p>
              </td>
<td>
                <p>
                  Requires an underlying integer back-end type.
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">rational</span></code>
                </p>
              </td>
<td>
                <p>
                  boost/rational.hpp
                </p>
              </td>
<td>
                <p>
                  N/A
                </p>
              </td>
<td>
                <p>
                  None
                </p>
              </td>
<td>
                <p>
                  A C++ rational number type that can used with any <code class="computeroutput"><span class="identifier">number</span></code> integer type.
                </p>
              </td>
<td>
                <p>
                  The expression templates used by <code class="computeroutput"><span class="identifier">number</span></code>
                  end up being "hidden" inside <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">rational</span></code>:
                  performance may well suffer as a result.
                </p>
              </td>
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<td align="right"><div class="copyright-footer">Copyright &#169; 2002-2019 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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