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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) |
|---|---|
|
checked_int1024_t |
1.53714(0.0415328s) |
|
checked_int256_t |
1.20715(0.0326167s) |
|
checked_int512_t |
1.2587(0.0340095s) |
|
cpp_int |
1.80575(0.0487904s) |
|
extended_int |
1.35652(0.0366527s) |
|
int1024_t |
1.36237(0.0368107s) |
|
int256_t |
1(0.0270196s) |
|
int512_t |
1.0779(0.0291243s) |
|
mpz_int |
3.83495(0.103619s) |
|
tom_int |
41.6378(1.12504s) |
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) |
|---|---|
|
checked_uint1024_t |
6.90638(0.0477963s) |
|
cpp_int |
8.63811(0.0597808s) |
|
cpp_int (1024-bit cache) |
7.4261(0.051393s) |
|
cpp_int (128-bit cache) |
8.88868(0.061515s) |
|
cpp_int (256-bit cache) |
8.83724(0.061159s) |
|
cpp_int (512-bit cache) |
7.53024(0.0521137s) |
|
cpp_int (no Expression templates) |
9.1372(0.0632349s) |
|
mpz_int |
1(0.00692059s) |
|
mpz_int (no Expression templates) |
1.08118(0.00748244s) |
|
tom_int |
4.16719(0.0288394s) |
|
tom_int (no Expression templates) |
4.1723(0.0288748s) |
|
uint1024_t |
6.82875(0.047259s) |
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. 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.
Table 1.17. Platform Details
|
Platform |
Linux 5.3.0-24-generic, version #26-Ubuntu SMP Thu Nov 14 01:33:18 UTC 2019, x86_64 |
|---|---|
|
Compiler |
GNU C++ version 9.2.1 20191008 |
|
GMP |
6.1.2 |
|
MPFR |
262146 |
|
Boost |
107200 |
|
Run date |
Dec 13 2019 |