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<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_multiprecision.perf.int_real_world"></a><a class="link" href="int_real_world.html" title="Integer Real World Tests">Integer Real
      World Tests</a>
</h3></div></div></div>
<p>
        The first set of <a href="../../../../performance/voronoi_performance.cpp" target="_top">tests</a>
        measure the times taken to execute the multiprecision part of the Voronoi-diagram
        builder from Boost.Polygon. The tests mainly create a large number of temporaries
        "just in case" multiprecision arithmetic is required, for comparison,
        also included in the tests is Boost.Polygon's own partial-multiprecision
        integer type which was custom written for this specific task:
      </p>
<div class="informaltable"><table class="table">
<colgroup>
<col>
<col>
</colgroup>
<thead><tr>
<th>
                <p>
                  Integer Type
                </p>
              </th>
<th>
                <p>
                  Relative Performance (Actual time in parenthesis)
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  polygon::detail::extended_int
                </p>
              </td>
<td>
                <p>
                  1(0.138831s)
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  int256_t
                </p>
              </td>
<td>
                <p>
                  1.19247(0.165551s)
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  int512_t
                </p>
              </td>
<td>
                <p>
                  1.23301(0.17118s)
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  int1024_t
                </p>
              </td>
<td>
                <p>
                  1.21463(0.168628s)
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  checked_int256_t
                </p>
              </td>
<td>
                <p>
                  1.31711(0.182855s)
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  checked_int512_t
                </p>
              </td>
<td>
                <p>
                  1.57413(0.218538s)
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  checked_int1024_t
                </p>
              </td>
<td>
                <p>
                  1.36992(0.190187s)
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  cpp_int
                </p>
              </td>
<td>
                <p>
                  1.63244(0.226632s)
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  mpz_int
                </p>
              </td>
<td>
                <p>
                  5.42511(0.753172s)
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  tom_int
                </p>
              </td>
<td>
                <p>
                  29.0793(4.03709s)
                </p>
              </td>
</tr>
</tbody>
</table></div>
<p>
        Note how for this use case, any dynamic allocation is a performance killer.
      </p>
<p>
        The next <a href="../../../../performance/miller_rabin_performance.cpp" target="_top">tests</a>
        measure the time taken to generate 1000 128-bit random numbers and test for
        primality using the Miller Rabin test. This is primarily a test of modular-exponentiation
        since that is the rate limiting step:
      </p>
<div class="informaltable"><table class="table">
<colgroup>
<col>
<col>
</colgroup>
<thead><tr>
<th>
                <p>
                  Integer Type
                </p>
              </th>
<th>
                <p>
                  Relative Performance (Actual time in parenthesis)
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  cpp_int
                </p>
              </td>
<td>
                <p>
                  5.25827(0.379597s)
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  cpp_int (no Expression templates)
                </p>
              </td>
<td>
                <p>
                  5.15675(0.372268s)
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  cpp_int (128-bit cache)
                </p>
              </td>
<td>
                <p>
                  5.10882(0.368808s)
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  cpp_int (256-bit cache)
                </p>
              </td>
<td>
                <p>
                  5.50623(0.397497s)
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  cpp_int (512-bit cache)
                </p>
              </td>
<td>
                <p>
                  4.82257(0.348144s)
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  cpp_int (1024-bit cache)
                </p>
              </td>
<td>
                <p>
                  5.00053(0.360991s)
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  int1024_t
                </p>
              </td>
<td>
                <p>
                  4.37589(0.315897s)
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  checked_int1024_t
                </p>
              </td>
<td>
                <p>
                  4.52396(0.326587s)
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  mpz_int
                </p>
              </td>
<td>
                <p>
                  1(0.0721905s)
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  mpz_int (no Expression templates)
                </p>
              </td>
<td>
                <p>
                  1.0248(0.0739806s)
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  tom_int
                </p>
              </td>
<td>
                <p>
                  2.60673(0.188181s)
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  tom_int (no Expression templates)
                </p>
              </td>
<td>
                <p>
                  2.64997(0.191303s)
                </p>
              </td>
</tr>
</tbody>
</table></div>
<p>
        It's interesting to note that expression templates have little effect here
        - perhaps because the actual expressions involved are relatively trivial
        in this case - so the time taken for multiplication and division tends to
        dominate. Also note how increasing the internal cache size used by <code class="computeroutput"><span class="identifier">cpp_int</span></code> is quite effective in this case
        in cutting out memory allocations altogether - cutting about a third off
        the total runtime. Finally the much quicker times from GMP and tommath are
        down to their much better modular-exponentiation algorithms (GMP's is about
        5x faster). That's an issue which needs to be addressed in a future release
        for <a class="link" href="../tut/ints/cpp_int.html" title="cpp_int">cpp_int</a>.
      </p>
<p>
        Test code was compiled with Microsoft Visual Studio 2010 with all optimisations
        turned on (/Ox), and used MPIR-2.3.0 and <a href="http://www.mpfr.org" target="_top">MPFR</a>-3.0.0.
        The tests were run on 32-bit Windows Vista machine.
      </p>
</div>
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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>)
      </p>
</div></td>
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