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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)

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



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