PoissonRandom.jl: Fast Poisson Random Numbers
Tutorials and Documentation
For information on using the package, see the stable documentation. Use the in-development documentation for the version of the documentation, which contains the unreleased features.
Usage
Pkg.add("PoissonRandom")
# Simple Poisson random
pois_rand(λ)
# Using another RNG
using RandomNumbers
rng = Xorshifts.Xoroshiro128Plus()
pois_rand(rng,λ)Implementation
It mixes two methods. A simple count method and a method from a normal approximation. See this blog post for details.
Benchmark
using RandomNumbers, Distributions, BenchmarkTools, StaticArrays,
RecursiveArrayTools, Plots, PoissonRandom
labels = ["count_rand","ad_rand","pois_rand","Distributions.jl"]
rng = Xorshifts.Xoroshiro128Plus()
function n_count(rng,λ,n)
tmp = 0
for i in 1:n
tmp += PoissonRandom.count_rand(rng,λ)
end
end
function n_pois(rng,λ,n)
tmp = 0
for i in 1:n
tmp += pois_rand(rng,λ)
end
end
function n_ad(rng,λ,n)
tmp = 0
for i in 1:n
tmp += PoissonRandom.ad_rand(rng,λ)
end
end
function n_dist(λ,n)
tmp = 0
for i in 1:n
tmp += rand(Poisson(λ))
end
end
function time_λ(rng,λ,n)
t1 = @elapsed n_count(rng,λ,n)
t2 = @elapsed n_ad(rng,λ,n)
t3 = @elapsed n_pois(rng,λ,n)
t4 = @elapsed n_dist(λ,n)
@SArray [t1,t2,t3,t4]
end
# Compile
time_λ(rng,5,5000000)
# Run with a bunch of λ
times = VectorOfArray([time_λ(rng,n,5000000) for n in 1:20])'
plot(times,labels = labels, lw = 3)
So this package ends up about 30% or so faster than Distributions.jl (the method at the far edge is λ-independent so that goes on forever).