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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 |