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<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
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<div class="titlepage"><div><div><h2 class="title" style="clear: both">
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<a name="boost_multiprecision.perf"></a><a class="link" href="perf.html" title="Performance Comparison">Performance Comparison</a>
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</h2></div></div></div>
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<div class="toc"><dl class="toc">
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<dt><span class="section"><a href="perf/overhead.html">The Overhead in the
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Number Class Wrapper</a></span></dt>
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<dt><span class="section"><a href="perf/realworld.html">Floating-Point Real
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World Tests</a></span></dt>
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<dt><span class="section"><a href="perf/int_real_world.html">Integer Real
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World Tests</a></span></dt>
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<dt><span class="section"><a href="perf/rational_real_world.html">Rational
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Real World Tests</a></span></dt>
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<dt><span class="section"><a href="perf/float_performance.html">Float Algorithm
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Performance</a></span></dt>
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<dt><span class="section"><a href="perf/integer_performance.html">Integer
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Algorithm Performance</a></span></dt>
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<dt><span class="section"><a href="perf/rational_performance.html">Rational
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Type Performance</a></span></dt>
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</dl></div>
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<p>
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In the beginning of the project and throughout, many performance analyses,
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counts of multiprecision-operations-per-second and the like have been performed.
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Some of these are already listed in the ensuing sections.
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</p>
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<p>
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We will now provide some general notes on performance, valid for all of the
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multiprecision backends, before the detailed benchmarks of the following sections.
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</p>
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<p>
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The header-only, library-independent Boost-licenses integer and floating-point
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backends including <a class="link" href="tut/ints/cpp_int.html" title="cpp_int">cpp_int</a>
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for multiprecision integers, <a class="link" href="tut/floats/cpp_bin_float.html" title="cpp_bin_float">cpp_bin_float</a>
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and <a class="link" href="tut/floats/cpp_dec_float.html" title="cpp_dec_float">cpp_dec_float</a>
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for multiprecision floating-point types are significantly slower than the world's
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fastest implementations generally agreed to be found in GMP/MPIR, MPFR and
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MPC (which are based on GMP). Complex types <a class="link" href="tut/complex/cpp_complex.html" title="cpp_complex">cpp_complex</a>
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that are synthesized from these types share similar relative performances.
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</p>
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<p>
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The backends which effectively wrap GMP/MPIR and MPFR retain the superior performance
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of the low-level big-number engines. When these are used (in association with
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at least some level of optmization) they achieve and retain the expected low-level
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performances.
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</p>
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<p>
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At low digit counts, however, it is noted that the performances of <a class="link" href="tut/ints/cpp_int.html" title="cpp_int">cpp_int</a>,
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<a class="link" href="tut/floats/cpp_bin_float.html" title="cpp_bin_float">cpp_bin_float</a>
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and <a class="link" href="tut/floats/cpp_dec_float.html" title="cpp_dec_float">cpp_dec_float</a>
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can actually meet or exceed those encountered for GMP/MPIR, MPFR, etc. The
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reason for this is because stack allocation and/or the use of fast container
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storage can actually out-perform the allocation mechanisms in GMP/MPIR, which
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dominate run-time costs at low digit counts.
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</p>
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<p>
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As digit counts rise above about 50 or so, however, GMP/MPIR performance steadily
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increases, and simultaneously increases beyond (in relation to) the performances
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of the Boost-licensed, self-written backends. At around a few hundred to several
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thousands of digits, factors of about two through five are observed, whereby
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GMP/MPIR-based calculations are (performance-wise) supreior ones.
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</p>
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<p>
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At a few thousand decimal digits, the upper end of the Boost backends is reached.
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At the moment, advanced big-number multiplication schemes in the Boost-licensed,
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self-written backends is limited to school multiplication and Karatsuba multiplication.
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Higher-orders of Toom-Cook and FFT-based multiplication are not (yet) implemented.
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So it is not yet feasible to perform mega-digit calculations with the Boost-licensed,
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self-written backends, whereas these are readily possible with the GMP/MPIR
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and MPRF based backends.
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</p>
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</div>
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<div class="copyright-footer">Copyright © 2002-2020 John
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Maddock 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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