fastapprox

Rust version of a library by Paul Mineiro.

Fast approximate versions of certain functions that arise in machine learning.

E.g. in Vowpal Wabbit this is one of the many clever tricks used to reach it's incredible training speed.

Module names fast and faster come from the original work, and represent sets of the same algorithms with different speed-accuracy levels.

Although approximate functions could give you some speedup (but not necessarily!), some warnings should be provided:

• Run your own benchmarks
• Make sure math is a bottleneck in your algorithm
• Pay attention to convergence
• SIMD versions are not implemented (yet, until simd crate will graduate from the nursery)

Benchmarks

Running cargo bench on MacBook Pro (Late 2013), 2.6 GHz Intel Core i7, gives the following output:

test cos_fast            ... bench:       3,674 ns/iter (+/- 778)
test cos_faster          ... bench:       1,559 ns/iter (+/- 206)
test cos_std             ... bench:       7,329 ns/iter (+/- 104)
test cosfull_fast        ... bench:       6,880 ns/iter (+/- 1,021)
test cosfull_faster      ... bench:       4,238 ns/iter (+/- 183)
test cosh_fast           ... bench:       8,270 ns/iter (+/- 4,190)
test cosh_faster         ... bench:       2,451 ns/iter (+/- 175)
test cosh_std            ... bench:       4,407 ns/iter (+/- 798)
test digamma_fast        ... bench:       4,644 ns/iter (+/- 1,126)
test digamma_faster      ... bench:       3,770 ns/iter (+/- 417)
test digamma_special     ... bench:      16,260 ns/iter (+/- 1,374)
test digamma_statrs      ... bench:      14,401 ns/iter (+/- 3,198)
test erf_fast            ... bench:      54,401 ns/iter (+/- 20,448)
test erf_faster          ... bench:       2,359 ns/iter (+/- 426)
test erf_inv_fast        ... bench:       5,958 ns/iter (+/- 2,794)
test erf_inv_faster      ... bench:       2,113 ns/iter (+/- 153)
test erf_inv_statrs      ... bench:         769 ns/iter (+/- 83)
test erf_special         ... bench:       4,948 ns/iter (+/- 1,443)
test erf_statrs          ... bench:       6,287 ns/iter (+/- 246)
test erfc_fast           ... bench:      54,201 ns/iter (+/- 6,307)
test erfc_faster         ... bench:       2,052 ns/iter (+/- 112)
test erfc_special        ... bench:       4,887 ns/iter (+/- 362)
test exp_fast            ... bench:       3,774 ns/iter (+/- 235)
test exp_faster          ... bench:       1,400 ns/iter (+/- 260)
test exp_std             ... bench:       2,760 ns/iter (+/- 202)
test lambertw_fast       ... bench:      21,040 ns/iter (+/- 2,523)
test lambertw_faster     ... bench:      24,840 ns/iter (+/- 8,939)
test lambertwexpx_fast   ... bench:      13,240 ns/iter (+/- 858)
test lambertwexpx_faster ... bench:       8,857 ns/iter (+/- 1,439)
test ln_fast             ... bench:       2,087 ns/iter (+/- 528)
test ln_faster           ... bench:       1,214 ns/iter (+/- 447)
test ln_gamma_fast       ... bench:       6,193 ns/iter (+/- 901)
test ln_gamma_faster     ... bench:       2,952 ns/iter (+/- 211)
test ln_gamma_special    ... bench:      36,726 ns/iter (+/- 846)
test ln_gamma_statrs     ... bench:      56,295 ns/iter (+/- 973)
test ln_std              ... bench:       5,175 ns/iter (+/- 321)
test log2_fast           ... bench:       1,998 ns/iter (+/- 335)
test log2_faster         ... bench:       1,206 ns/iter (+/- 188)
test log2_std            ... bench:       5,087 ns/iter (+/- 1,736)
test pow2_fast           ... bench:       3,472 ns/iter (+/- 192)
test pow2_faster         ... bench:       1,069 ns/iter (+/- 356)
test pow2_std            ... bench:       2,942 ns/iter (+/- 172)
test pow_fast            ... bench:       6,769 ns/iter (+/- 1,460)
test pow_faster          ... bench:       2,365 ns/iter (+/- 293)
test pow_std             ... bench:      13,147 ns/iter (+/- 1,000)
test sigmoid_fast        ... bench:       4,818 ns/iter (+/- 428)
test sigmoid_faster      ... bench:       1,869 ns/iter (+/- 56)
test sigmoid_std         ... bench:       3,312 ns/iter (+/- 131)
test sin_fast            ... bench:       3,038 ns/iter (+/- 685)
test sin_faster          ... bench:       1,875 ns/iter (+/- 481)
test sin_std             ... bench:       7,215 ns/iter (+/- 39)
test sinfull_fast        ... bench:       6,483 ns/iter (+/- 405)
test sinfull_faster      ... bench:       3,973 ns/iter (+/- 874)
test sinh_fast           ... bench:       8,394 ns/iter (+/- 618)
test sinh_faster         ... bench:       2,588 ns/iter (+/- 286)
test sinh_std            ... bench:       4,434 ns/iter (+/- 329)
test tan_fast            ... bench:       5,165 ns/iter (+/- 174)
test tan_faster          ... bench:       3,423 ns/iter (+/- 1,083)
test tan_std             ... bench:       7,695 ns/iter (+/- 453)
test tanfull_fast        ... bench:      10,299 ns/iter (+/- 1,761)
test tanfull_faster      ... bench:       6,214 ns/iter (+/- 524)
test tanh_fast           ... bench:       5,598 ns/iter (+/- 709)
test tanh_faster         ... bench:       1,921 ns/iter (+/- 445)
test tanh_std            ... bench:       4,056 ns/iter (+/- 306)