Boost
C++ Libraries
...one of the most highly
regarded and expertly designed C++ library projects in the
world.
— Herb Sutter and Andrei
Alexandrescu, C++
Coding Standards
Boost
C++ Libraries
...one of the most highly
regarded and expertly designed C++ library projects in the
world.
— Herb Sutter and Andrei
Alexandrescu, C++
Coding Standards
The first set of tests 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:
|
Integer Type |
Relative Performance (Actual time in parenthesis) |
|---|---|
|
polygon::detail::extended_int |
1(0.138831s) |
|
int256_t |
1.19247(0.165551s) |
|
int512_t |
1.23301(0.17118s) |
|
int1024_t |
1.21463(0.168628s) |
|
checked_int256_t |
1.31711(0.182855s) |
|
checked_int512_t |
1.57413(0.218538s) |
|
checked_int1024_t |
1.36992(0.190187s) |
|
cpp_int |
1.63244(0.226632s) |
|
mpz_int |
5.42511(0.753172s) |
|
tom_int |
29.0793(4.03709s) |
Note how for this use case, any dynamic allocation is a performance killer.
The next tests 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:
|
Integer Type |
Relative Performance (Actual time in parenthesis) |
|---|---|
|
cpp_int |
5.25827(0.379597s) |
|
cpp_int (no Expression templates) |
5.15675(0.372268s) |
|
cpp_int (128-bit cache) |
5.10882(0.368808s) |
|
cpp_int (256-bit cache) |
5.50623(0.397497s) |
|
cpp_int (512-bit cache) |
4.82257(0.348144s) |
|
cpp_int (1024-bit cache) |
5.00053(0.360991s) |
|
int1024_t |
4.37589(0.315897s) |
|
checked_int1024_t |
4.52396(0.326587s) |
|
mpz_int |
1(0.0721905s) |
|
mpz_int (no Expression templates) |
1.0248(0.0739806s) |
|
tom_int |
2.60673(0.188181s) |
|
tom_int (no Expression templates) |
2.64997(0.191303s) |
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 cpp_int 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 cpp_int.
Test code was compiled with Microsoft Visual Studio 2010 with all optimisations turned on (/Ox), and used MPIR-2.3.0 and MPFR-3.0.0. The tests were run on 32-bit Windows Vista machine.