perf: sample Binomial via BINV/BTPE instead of n Bernoulli trials#409
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perf: sample Binomial via BINV/BTPE instead of n Bernoulli trials#409agene0001 wants to merge 1 commit into
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`Binomial::sample` ran one Bernoulli trial per trial, so a single draw was O(n). The reported case in statrs-dev#183 - 5 categories, n = 100_000, 100 samples via `Multinomial` - took 22.4 ms; numpy was measured at ~400x faster. Replaces it with Kachitvichyanukul & Schmeiser (1988): BINV inversion for `n * min(p, 1-p) < 10`, BTPE rejection from a triangle/parallelogram/two exponential tails envelope otherwise, plus exact shortcuts for p in {0, 1} and a Poisson-limit path when `1 - p` rounds to 1. Binomial(0.4, 1_000).sample() 3.6 us -> 56 ns Binomial(0.4, 100_000).sample() 361 us -> 39 ns Binomial(0.4, 1e9).sample() ~3.6 s -> 39 ns Multinomial(5 cats, n=1e5) x100 22.4 ms -> 22.8 us (981x) `Multinomial` benefits automatically, since it draws conditioned binomials per category - which is what the issue asked for. The implementation is adapted from `rand_distr` (MIT/Apache-2.0, attributed in-source). That matters for one detail: the final acceptance test uses the Stirling-series signs from GSL, which differ from the published paper and were verified by one of the algorithm's original designers. Correctness is checked by a chi-square goodness-of-fit test against the exact pmf over five parameter sets covering every code path (BINV, BTPE, and both flipped variants), with expected-count pooling and a 6-sigma threshold on fixed seeds - so it is deterministic and a failure means a real defect. Plus moment tests for n = 1e9 and the Poisson-limit path, and degenerate-parameter tests. Closes statrs-dev#183
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Binomial::sampleran one Bernoulli trial per trial, so a single draw was O(n). The case reported in #183 (5 categories, n = 100 000, sampled viaMultinomial) took 22.4 ms per 100 draws here; numpy was reported ~400x faster.This replaces it with Kachitvichyanukul & Schmeiser (1988): BINV inversion for
n·min(p,1−p) < 10, BTPE rejection otherwise, exact shortcuts for p ∈ {0, 1}, and a Poisson-limit path when1 − prounds to 1.0.Binomial(0.4, 1_000).sample()Binomial(0.4, 100_000).sample()Binomial(0.4, 1e9).sample()Multinomial(5 cats, n=1e5)×100Multinomialbenefits automatically since it draws conditioned binomials per category.The implementation is adapted from
rand_distr(MIT/Apache-2.0, attributed in-source). One detail worth review attention: the final acceptance test uses the Stirling-series signs from GSL, which differ from the published paper and were verified by one of the algorithm's original designers (see the in-source comment).Correctness: chi-square goodness-of-fit against the exact pmf over five parameter sets covering every code path (BINV, BTPE, both flipped variants), with expected-count pooling and a 6σ threshold on fixed seeds — deterministic, so a failure means a real defect, not chance. Plus moment tests for n = 1e9 and the Poisson-limit path, and degenerate-parameter tests. Relates to the sampling-verification wish list in #288.
Closes #183
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