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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> |
| <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> |
| <td align="left"></td> |
| <td align="right"><div class="copyright-footer">Copyright © 2002-2013 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> |
| </tr></table> |
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