fast-arithmetic

This is a library for fast arithmetical functions using ATS, with a Haskell wrapper.

It is intended to supplement (but not replace) arithmoi and combinat where speed is important. In particular, this library provides a fast primality check and fast computation of basic combinatorial functions.

Benchmarks

Computation	Version (ATS/Haskell)	Time
isPrime 2017	ATS	117.2 ns
isPrime 2017	Haskell	425.0 ns
φ(2016)	ATS	191.5 ns
φ(2016)	Haskell	384.8 ns
τ(3018)	ATS	337.0 ns
τ(3018)	Haskell	660.2 ns
σ(115)	ATS	45.41 ns
σ(115)	Haskell	322.4 ns
ω(91)	ATS	65.52 ns
ω(91)	Haskell	345.2 ns
160!	ATS	2.363 μs
160!	Haskell	6.134μs
79!!	ATS	556.2 ns
79!!	Haskell	1.355 μs
322 `choose` 16	ATS	467.6 ns
322 `choose` 16	Haskell	956.7 ns
catalan 300	ATS	13.74 μs
catalan 300	Haskell	28.76 μs
permutations 20 10	ATS	202.8 ns
permutations 20 10	Haskell	362.6 ns
maxRegions 45000	ATS	624.1 ns
maxRegions 45000	Haskell	1.064 μs
stirling2 25 8	ATS	3.108 μs
stirling2 25 8	Haskell	9.494 μs

Building

The Haskell library comes with the C bundled, however you will likely want to build from source if you are hacking on the library. To that end, you can install atspkg and build with

atspkg build --pkg-args "./source.dhall"
cabal build

Documentation

You can find documentation for the Haskell library on Hackage. Unfortunately, there is no documentation for the ATS library, however, the bundled source code is commented.