mathfuse

A modern, zero-dependency TypeScript math utility library.
Tree-shakeable · ESM + CJS · Browser & Node.js · Fully typed

Features

| Module | What's included | |--------|----------------| | stats | Mean, median, mode, std dev, variance, percentiles, IQR, MAD, skewness, kurtosis, Pearson/Spearman correlation, covariance, z-score, min-max normalization, linear regression | | algebra | Vector ops (add, dot, norm, normalize, cosine similarity, cross product), matrix ops (multiply, determinant, inverse, rank, transpose, solve) | | number-theory | Miller-Rabin primality, Sieve of Eratosthenes, GCD/LCM, factorial, binomial, permutations, modular exponentiation, Euler's totient, Fibonacci, Collatz | | numerical | Bisection, Newton-Raphson, Brent's method, numerical derivative/gradient, adaptive Simpson integration, Gauss-Legendre quadrature, Lagrange interpolation, Kahan summation |

Install

npm install mathfuse
# or
yarn add mathfuse
# or
pnpm add mathfuse

Quick Start

import { mean, stdDev, linearRegression } from 'mathfuse';
// or tree-shake specific modules:
import { mean, stdDev } from 'mathfuse/stats';
import { isPrime, fibonacci } from 'mathfuse/number-theory';
import { newtonRaphson, integrate } from 'mathfuse/numerical';
import { mmul, mdet, msolve } from 'mathfuse/algebra';

API Reference

📊 Statistics (mathfuse/stats)

Central Tendency

import { mean, median, mode, geometricMean, harmonicMean, weightedMean } from 'mathfuse/stats';

mean([1, 2, 3, 4, 5])              // 3
median([3, 1, 4, 1, 5])            // 3
mode([1, 2, 2, 3, 3])              // [2, 3]
geometricMean([1, 2, 4, 8])        // 2.828...
harmonicMean([1, 2, 4])            // 1.714...
weightedMean([1, 2, 3], [1, 2, 3]) // 2.333...

Spread & Dispersion

import { variance, stdDev, range, iqr, mad } from 'mathfuse/stats';

variance([2, 4, 4, 4, 5, 5, 7, 9])           // 4.571 (sample)
variance([2, 4, 4, 4, 5, 5, 7, 9], true)      // 4.0   (population)
stdDev([2, 4, 4, 4, 5, 5, 7, 9], true)        // 2.0
iqr([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])          // 4.5
mad([1, 1, 2, 2, 4, 6, 9])                    // 1.0

Percentiles

import { percentile, fiveNumberSummary } from 'mathfuse/stats';

percentile([1,2,3,4,5,6,7,8,9,10], 90) // 9.1
fiveNumberSummary([1,2,3,4,5])          // [1, 1.5, 3, 4.5, 5]

Correlation & Regression

import { pearsonCorrelation, spearmanCorrelation, linearRegression } from 'mathfuse/stats';

const x = [1, 2, 3, 4, 5];
const y = [2, 4, 5, 4, 5];

pearsonCorrelation(x, y)   // 0.8320...
spearmanCorrelation(x, y)  // 0.8207...

const reg = linearRegression(x, y);
reg.slope      // 0.7
reg.intercept  // 1.7
reg.r2         // 0.6923
reg.predict(6) // 5.9

Normalization

import { zScore, minMaxNormalize } from 'mathfuse/stats';

zScore([1, 2, 3, 4, 5])          // [-1.41, -0.71, 0, 0.71, 1.41]
minMaxNormalize([1, 2, 3, 4, 5]) // [0, 0.25, 0.5, 0.75, 1]

🔢 Number Theory (mathfuse/number-theory)

import { isPrime, primesUpTo, nextPrime, primeFactors } from 'mathfuse/number-theory';

isPrime(999_983)       // true  (Miller-Rabin)
primesUpTo(20)         // [2, 3, 5, 7, 11, 13, 17, 19]
nextPrime(100)         // 101
primeFactors(360)      // [2, 2, 2, 3, 3, 5]

import { gcd, lcm, factorial, binomial, fibonacci } from 'mathfuse/number-theory';

gcd(48, 18)            // 6
lcm(4, 6)              // 12
factorial(10)          // 3_628_800
binomial(10, 3)        // 120
fibonacci(8)           // [0, 1, 1, 2, 3, 5, 8, 13]
nthFibonacci(50)       // 12586269025

🧮 Linear Algebra (mathfuse/algebra)

Vectors

import { vadd, vdot, vnorm, cosineSimilarity, cross3d } from 'mathfuse/algebra';

vadd([1,2,3], [4,5,6])              // [5, 7, 9]
vdot([1,2,3], [4,5,6])              // 32
vnorm([3, 4])                       // 5
cosineSimilarity([1,0], [1,1])      // 0.7071...
cross3d([1,0,0], [0,1,0])           // [0, 0, 1]

Matrices

import { mmul, mdet, minverse, msolve } from 'mathfuse/algebra';

const A = [[2,1], [-1,3]];
mdet(A)           // 7
minverse(A)       // [[0.428, -0.142], [0.142, 0.285]]
msolve(A, [5,0])  // [3, 1]  (solves Ax = b)

📐 Numerical Methods (mathfuse/numerical)

Root Finding

import { bisection, newtonRaphson, brent } from 'mathfuse/numerical';

const f = (x: number) => x ** 2 - 2;  // root at √2

bisection(f, 1, 2).root       // 1.4142135623...
newtonRaphson(f, 1.5).root    // 1.4142135623...
brent(f, 1, 2).root           // 1.4142135623...

Calculus

import { derivative, integrate } from 'mathfuse/numerical';

derivative(Math.sin, Math.PI / 4)   // ≈ cos(π/4) ≈ 0.7071
integrate(Math.sin, 0, Math.PI)     // ≈ 2.0  (exact: 2)
integrate(x => x ** 2, 0, 1)        // ≈ 0.333 (exact: 1/3)

Interpolation

import { lerp, tableInterpolate, lagrange } from 'mathfuse/numerical';

lerp(0, 100, 0.3)                         // 30
tableInterpolate([0,1,2,3], [0,1,4,9], 1.5) // 2.5
lagrange([0, 1, 2], [0, 1, 4], 1.5)       // 2.25

Tree Shaking

mathfuse is fully tree-shakeable. Import only what you need:

// ✅ Only the functions you import will be bundled
import { mean, stdDev } from 'mathfuse/stats';
import { isPrime } from 'mathfuse/number-theory';

Browser Support

mathfuse targets ES2020 and works in all modern browsers and Node.js ≥ 16.

Contributing

Contributions are welcome! Please read CONTRIBUTING.md and open an issue before submitting a PR for large changes.

git clone https://github.com/Avinashvelu03/mathfuse.git
cd mathfuse
npm install
npm test

License

MIT © Scientist Maths

➕ Back MathFuse

MathFuse is a one-person project — no VC funding, no corporate backing. Just clean math primitives built for TypeScript developers.

If it's saved you from writing sum or mean for the hundredth time, or handled edge cases you never thought of:

┌─────────────────────────────────────────────────────┐
│   Open source math deserves open source support.    │
│                                                     │
│   ☕  Ko-fi · GitHub Sponsors                       │
└─────────────────────────────────────────────────────┘

Zero cost, high impact:

• ⭐ Drop a star — it's free and it helps more than you think
• 📣 Mention MathFuse in your next tech post or talk
• 🛠️ Open an issue with missing math functions you need