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<div class="titlepage"><div><div><h3 class="title">
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<a name="boost_multiprecision.tut.floats"></a><a class="link" href="floats.html" title="floating-point Numbers">floating-point Numbers</a>
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</h3></div></div></div>
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<div class="toc"><dl class="toc">
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<dt><span class="section"><a href="floats/cpp_bin_float.html">cpp_bin_float</a></span></dt>
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<dt><span class="section"><a href="floats/cpp_dec_float.html">cpp_dec_float</a></span></dt>
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<dt><span class="section"><a href="floats/gmp_float.html">gmp_float</a></span></dt>
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<dt><span class="section"><a href="floats/mpfr_float.html">mpfr_float</a></span></dt>
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<dt><span class="section"><a href="floats/float128.html">float128</a></span></dt>
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<dt><span class="section"><a href="floats/fp_eg.html">Examples</a></span></dt>
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<dd><dl>
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<dt><span class="section"><a href="floats/fp_eg/aos.html">Area of
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Circle</a></span></dt>
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<dt><span class="section"><a href="floats/fp_eg/jel.html">Defining
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a Special Function.</a></span></dt>
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<dt><span class="section"><a href="floats/fp_eg/nd.html">Calculating
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a Derivative</a></span></dt>
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<dt><span class="section"><a href="floats/fp_eg/gi.html">Calculating
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an Integral</a></span></dt>
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<dt><span class="section"><a href="floats/fp_eg/poly_eg.html">Polynomial
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Evaluation</a></span></dt>
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<dt><span class="section"><a href="floats/fp_eg/variable_precision.html">Variable
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Precision Newton Evaluation</a></span></dt>
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</dl></dd>
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</dl></div>
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<p>
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The following back-ends provide floating-point arithmetic:
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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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<col>
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<col>
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<col>
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<col>
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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 Type
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</p>
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</th>
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<th>
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<p>
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Header
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</p>
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</th>
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<th>
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<p>
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Radix
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</p>
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</th>
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<th>
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<p>
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Dependencies
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</p>
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</th>
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<th>
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<p>
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Pros
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</p>
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</th>
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<th>
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<p>
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Cons
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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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<code class="computeroutput"><span class="identifier">cpp_bin_float</span><span class="special"><</span><span class="identifier">N</span><span class="special">></span></code>
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</p>
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</td>
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<td>
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<p>
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boost/multiprecision/cpp_bin_float.hpp
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</p>
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</td>
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<td>
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<p>
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2
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</p>
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</td>
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<td>
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<p>
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None
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</p>
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</td>
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<td>
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<p>
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Header only, all C++ implementation. Boost licence.
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</p>
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</td>
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<td>
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<p>
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Approximately 2x slower than the <a href="http://www.mpfr.org" target="_top">MPFR</a>
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or <a href="http://gmplib.org" target="_top">GMP</a> libraries.
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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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<code class="computeroutput"><span class="identifier">cpp_dec_float</span><span class="special"><</span><span class="identifier">N</span><span class="special">></span></code>
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</p>
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</td>
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<td>
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<p>
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boost/multiprecision/cpp_dec_float.hpp
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</p>
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</td>
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<td>
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<p>
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10
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</p>
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</td>
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<td>
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<p>
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None
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</p>
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</td>
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<td>
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<p>
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Header only, all C++ implementation. Boost licence.
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</p>
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</td>
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<td>
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<p>
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Approximately 2x slower than the <a href="http://www.mpfr.org" target="_top">MPFR</a>
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or <a href="http://gmplib.org" target="_top">GMP</a> libraries.
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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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<code class="computeroutput"><span class="identifier">mpf_float</span><span class="special"><</span><span class="identifier">N</span><span class="special">></span></code>
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</p>
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</td>
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<td>
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<p>
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boost/multiprecision/gmp.hpp
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</p>
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</td>
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<td>
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<p>
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2
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</p>
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</td>
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<td>
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<p>
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<a href="http://gmplib.org" target="_top">GMP</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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Very fast and efficient back-end.
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</p>
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</td>
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<td>
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<p>
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Dependency on GNU licensed <a href="http://gmplib.org" target="_top">GMP</a>
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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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<code class="computeroutput"><span class="identifier">mpfr_float</span><span class="special"><</span><span class="identifier">N</span><span class="special">></span></code>
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</p>
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</td>
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<td>
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<p>
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boost/multiprecision/mpfr.hpp
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</p>
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</td>
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<td>
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<p>
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2
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</p>
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</td>
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<td>
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<p>
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<a href="http://gmplib.org" target="_top">GMP</a> and <a href="http://www.mpfr.org" target="_top">MPFR</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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Very fast and efficient back-end, with its own standard library
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implementation.
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</p>
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</td>
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<td>
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<p>
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Dependency on GNU licensed <a href="http://gmplib.org" target="_top">GMP</a>
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and <a href="http://www.mpfr.org" target="_top">MPFR</a> libraries.
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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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<code class="computeroutput"><span class="identifier">float128</span></code>
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</p>
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</td>
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<td>
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<p>
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boost/multiprecision/float128.hpp
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</p>
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</td>
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<td>
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<p>
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2
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</p>
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</td>
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<td>
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<p>
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Either <a href="http://gcc.gnu.org/onlinedocs/libquadmath/" target="_top">libquadmath</a>
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or the Intel C++ Math library.
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</p>
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</td>
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<td>
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<p>
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Very fast and efficient back-end for 128-bit floating-point values
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(113-bit mantissa, equivalent to FORTRAN's QUAD real)
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</p>
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</td>
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<td>
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<p>
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Depends on the compiler being either recent GCC or Intel C++ versions.
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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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