PoissonRandom.jl: Fast Poisson Random Numbers

PoissonRandom.jl is a component of the SciML ecosystem which allows for fast generation of Poisson random numbers.

Installation

To install PoissonRandom.jl, use the Julia package manager:

using Pkg
Pkg.add("PoissonRandom")

Usage

# 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)

benchmark result

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).

Contributing

Please refer to the SciML ColPrac: Contributor's Guide on Collaborative Practices for Community Packages for guidance on PRs, issues, and other matters relating to contributing to SciML.
See the SciML Style Guide for common coding practices and other style decisions.
There are a few community forums:
- The #diffeq-bridged and #sciml-bridged channels in the Julia Slack
- The #diffeq-bridged and #sciml-bridged channels in the Julia Zulip
- On the Julia Discourse forums
- See also SciML Community page

Reproducibility

The documentation of this SciML package was built using these direct dependencies,

Status `~/work/PoissonRandom.jl/PoissonRandom.jl/docs/Project.toml`
  [e30172f5] Documenter v1.14.1
  [e409e4f3] PoissonRandom v0.4.5 `~/work/PoissonRandom.jl/PoissonRandom.jl`

and using this machine and Julia version.

Julia Version 1.11.6
Commit 9615af0f269 (2025-07-09 12:58 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 4 × AMD EPYC 7763 64-Core Processor
  WORD_SIZE: 64
  LLVM: libLLVM-16.0.6 (ORCJIT, znver3)
Threads: 1 default, 0 interactive, 1 GC (on 4 virtual cores)

A more complete overview of all dependencies and their versions is also provided.

Status `~/work/PoissonRandom.jl/PoissonRandom.jl/docs/Manifest.toml`
  [a4c015fc] ANSIColoredPrinters v0.0.1
  [1520ce14] AbstractTrees v0.4.5
  [944b1d66] CodecZlib v0.7.8
  [ffbed154] DocStringExtensions v0.9.5
  [e30172f5] Documenter v1.14.1
  [d7ba0133] Git v1.4.0
  [b5f81e59] IOCapture v0.2.5
  [92d709cd] IrrationalConstants v0.2.4
  [692b3bcd] JLLWrappers v1.7.0
  [682c06a0] JSON v0.21.4
  [0e77f7df] LazilyInitializedFields v1.3.0
  [2ab3a3ac] LogExpFunctions v0.3.29
  [d0879d2d] MarkdownAST v0.1.2
  [69de0a69] Parsers v2.8.3
  [e409e4f3] PoissonRandom v0.4.5 `~/work/PoissonRandom.jl/PoissonRandom.jl`
⌅ [aea7be01] PrecompileTools v1.2.1
  [21216c6a] Preferences v1.4.3
  [2792f1a3] RegistryInstances v0.1.0
  [3bb67fe8] TranscodingStreams v0.11.3
  [2e619515] Expat_jll v2.6.5+0
  [f8c6e375] Git_jll v2.50.1+0
  [94ce4f54] Libiconv_jll v1.18.0+0
  [9bd350c2] OpenSSH_jll v10.0.1+0
  [458c3c95] OpenSSL_jll v3.5.1+0
  [0dad84c5] ArgTools v1.1.2
  [56f22d72] Artifacts v1.11.0
  [2a0f44e3] Base64 v1.11.0
  [ade2ca70] Dates v1.11.0
  [f43a241f] Downloads v1.6.0
  [7b1f6079] FileWatching v1.11.0
  [b77e0a4c] InteractiveUtils v1.11.0
  [b27032c2] LibCURL v0.6.4
  [76f85450] LibGit2 v1.11.0
  [8f399da3] Libdl v1.11.0
  [37e2e46d] LinearAlgebra v1.11.0
  [56ddb016] Logging v1.11.0
  [d6f4376e] Markdown v1.11.0
  [a63ad114] Mmap v1.11.0
  [ca575930] NetworkOptions v1.2.0
  [44cfe95a] Pkg v1.11.0
  [de0858da] Printf v1.11.0
  [3fa0cd96] REPL v1.11.0
  [9a3f8284] Random v1.11.0
  [ea8e919c] SHA v0.7.0
  [9e88b42a] Serialization v1.11.0
  [6462fe0b] Sockets v1.11.0
  [f489334b] StyledStrings v1.11.0
  [fa267f1f] TOML v1.0.3
  [a4e569a6] Tar v1.10.0
  [8dfed614] Test v1.11.0
  [cf7118a7] UUIDs v1.11.0
  [4ec0a83e] Unicode v1.11.0
  [e66e0078] CompilerSupportLibraries_jll v1.1.1+0
  [deac9b47] LibCURL_jll v8.6.0+0
  [e37daf67] LibGit2_jll v1.7.2+0
  [29816b5a] LibSSH2_jll v1.11.0+1
  [c8ffd9c3] MbedTLS_jll v2.28.6+0
  [14a3606d] MozillaCACerts_jll v2023.12.12
  [4536629a] OpenBLAS_jll v0.3.27+1
  [efcefdf7] PCRE2_jll v10.42.0+1
  [83775a58] Zlib_jll v1.2.13+1
  [8e850b90] libblastrampoline_jll v5.11.0+0
  [8e850ede] nghttp2_jll v1.59.0+0
  [3f19e933] p7zip_jll v17.4.0+2
Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated -m`

You can also download the manifest file and the project file.