Boost C++ Libraries

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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

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



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