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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 |
9.52301(0.0422246s) |
|
cpp_int |
11.2194(0.0497465s) |
|
cpp_int (1024-bit cache) |
10.7941(0.0478607s) |
|
cpp_int (128-bit cache) |
11.0637(0.0490558s) |
|
cpp_int (256-bit cache) |
11.5069(0.0510209s) |
|
cpp_int (512-bit cache) |
10.3303(0.0458041s) |
|
cpp_int (no Expression templates) |
16.1792(0.0717379s) |
|
mpz_int |
1.05106(0.00466034s) |
|
mpz_int (no Expression templates) |
1(0.00443395s) |
|
tom_int |
5.10595(0.0226395s) |
|
tom_int (no Expression templates) |
61.9684(0.274765s) |
|
uint1024_t |
9.32113(0.0413295s) |
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
|
Version |
|
|---|---|
|
Compiler |
GNU C++ version 10.3.0 |
|
GMP |
6.2.0 |
|
MPFR |
262146 |
|
Boost |
107800 |
|
Run date |
Sep 30 2021 |