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<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="math_toolkit.high_precision"></a><a class="link" href="high_precision.html" title="Using Boost.Math with High-Precision Floating-Point Libraries">Using Boost.Math with High-Precision
    Floating-Point Libraries</a>
</h2></div></div></div>
<div class="toc"><dl class="toc">
<dt><span class="section"><a href="high_precision/why_high_precision.html">Why use
      a high-precision library rather than built-in floating-point types?</a></span></dt>
<dt><span class="section"><a href="high_precision/use_multiprecision.html">Using
      Boost.Multiprecision</a></span></dt>
<dt><span class="section"><a href="high_precision/float128.html">Using with GCC's
      __float128 datatype</a></span></dt>
<dt><span class="section"><a href="high_precision/use_mpfr.html">Using With MPFR
      or GMP - High-Precision Floating-Point Library</a></span></dt>
<dt><span class="section"><a href="high_precision/e_float.html">Using e_float Library</a></span></dt>
<dt><span class="section"><a href="high_precision/use_ntl.html">Using NTL Library</a></span></dt>
<dt><span class="section"><a href="high_precision/using_test.html">Using without
      expression templates for Boost.Test and others</a></span></dt>
</dl></div>
<p>
      The special functions, distributions, constants and tools in this library can
      be used with a number of high-precision libraries, including:
    </p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
          <a href="../../../../../libs/multiprecision/doc/html/index.html" target="_top">Boost.Multiprecision</a>
        </li>
<li class="listitem">
          <a href="http://calgo.acm.org/910.zip" target="_top">e_float (TOMS Algorithm 910)</a>
        </li>
<li class="listitem">
          <a href="http://www.shoup.net/ntl/" target="_top">NTL A Library for doing Number Theory</a>
        </li>
<li class="listitem">
          <a href="http://gmplib.org/" target="_top">GNU Multiple Precision Arithmetic Library</a>
        </li>
<li class="listitem">
          <a href="http://www.mpfr.org/" target="_top">GNU MPFR library</a>
        </li>
<li class="listitem">
          <a href="https://gcc.gnu.org/onlinedocs/gcc-9.1.0/libquadmath/index.html" target="_top">GCC
          128-bit floating-point type</a>
        </li>
<li class="listitem">
          Intel _Quad type
        </li>
</ul></div>
<p>
      The last four have some license restrictions; only <a href="../../../../../libs/multiprecision/doc/html/index.html" target="_top">Boost.Multiprecision</a>
      when using the <code class="computeroutput"><span class="identifier">cpp_float</span></code> backend
      can provide an unrestricted <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">Boost</a>
      license.
    </p>
<p>
      At present, the price of a free license is slightly lower speed.
    </p>
<p>
      Of course, the main cost of higher precision is very much decreased (usually
      at least hundred-fold) computation speed, and big increases in memory use.
    </p>
<p>
      Some libraries offer true <a href="http://en.wikipedia.org/wiki/Arbitrary-precision_arithmetic" target="_top">arbitrary-precision
      arithmetic</a> where the precision is limited only by available memory
      and compute time, but most are used at some arbitrarily-fixed precision, say
      100 decimal digits, like <a href="../../../../../libs/multiprecision/doc/html/index.html" target="_top">Boost.Multiprecision</a>
      <code class="computeroutput"><span class="identifier">cpp_dec_float_100</span></code>.
    </p>
<p>
      <a href="../../../../../libs/multiprecision/doc/html/index.html" target="_top">Boost.Multiprecision</a>
      can operate in both ways, but the most popular choice is likely to be about
      a hundred decimal digits, though examples of computing about a million digits
      have been demonstrated.
    </p>
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      Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
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      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
      Daryle Walker and Xiaogang Zhang<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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