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<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Integer Real World Tests</title>
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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>
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