FsMath - Fast & Friendly Numerical Foundation for F#

FsMath is a lightweight maths library designed for modern F# workflows. It focuses on zero-friction interop with existing array-centric libraries ( FSharp.Stats, Math.NET Numerics, libtorch via TorchSharp, etc.) while giving you the performance head-room of SIMD-accelerated kernels and a clean, idiomatic F# API.

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Why another numeric library?

Goal	What it means in practice
Interop first	Core types are just aliases or thin wrappers around native F# 'T [] arrays -> you can pass data to any array-based .NET or C library without conversion or pinning.
Predictable memory layout	Matrices are stored row-major (C-style) to line up with libtorch / TorchSharp, modern BLAS back-ends, and GPU kernels.
SIMD out-of-the-box	Tight loops (dot, outer product, reductions ...) auto-detect hardware with SIMD support and pure-managed fallback otherwise.
F#-idiomatic API	Pipelining, module functions, inline operators (.+, .*, transpose) and SRTP “type-class” dispatch keep your notebooks & scripts concise.

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Key features

• Vector / RowVector / Matrix - minimal, generic, and structural-equality aware.
• High-level operators - .+, .-, .*, ./, outer product, Kronecker, hadamard, etc.
• SIMD optimizes - dot products, outer products, reductions, and more.
• Unsafe-free - everything is pure managed IL; no native dlls to ship.
• Perfect interop - drop-in arrays to FSharp.Stats, TorchSharp, DiffSharp, and any BLAS/LAPACK P/Invoke you like.

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Getting started

open FsMath
open FSharp.Stats.Distributions

// init vector
let v1  = vector [| 1.0; 2.0; 3.0 |]

// init vector with random samples (using FSharp.Stats)
let v2 = Array.init 3 (fun _ -> Continuous.ChiSquared.Sample 30.)

// SIMD-accelerated element-wise multiply
let result = v1 .* v2              

// interop: pass 'result' straight into e.g. TorchSharp tensor

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Documentation

Topic	Where
API reference	docs/ folder & generated markdown
Benchmarks	benchmarks/
Contributing guide	CONTRIBUTING.md

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build

Check the build project to take a look at the build targets.

# Windows
./build.cmd

# Linux/mac
build.sh

running and writing tests

# Windows
./build.cmd runtests

# Linux/mac
build.sh runtests

docs

The docs are contained in .fsx and .md files in the docs folder. To develop docs on a local server with hot reload, run the following in the root of the project:

# Windows
./build.cmd watchdocs

# Linux/mac
./build.sh watchdocs

pack nuget package(s)

# Windows
./build.cmd pack

# Linux/mac
build.sh pack