Integer Real World Tests

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.