Mathematics

Mathematics here is split the way mathematical software conventionally splits it, not the way the packages are. Where a function lives on npm is an engineering detail; what it is for is what you came looking for.

Basic features

What the machine’s own numbers can and cannot promise, and how to generate numbers on purpose.

• Floating point and tolerance — why 0.1 + 0.2 !== 0.3, what an ulp is, and how to compare two results that should be equal but are not. (@ac-kit/math-scalar)
• Random number generation — fast seedable generators for simulation, and the separate, slower ones you must use for anything a person could attack. (@ac-kit/math-random, @ac-kit/crypto-random)

Number representations

When binary64 is the wrong container.

• Integers and modular arithmetic (@ac-kit/math-integer)
• Arbitrary precision, decimals and fractions (@ac-kit/math-numbers)
• Complex numbers (@ac-kit/math-complex)
• Algebraic structures — groups, rings and fields as values you pass to an algorithm (@ac-kit/math-algebra)

Mathematical functions

The named functions that statistics, physics and engineering are written in. Everything in this group takes numbers and returns a number.

• The gamma and beta functions — the factorial, extended to every real number, and the ratio built from it
• The error function — how much of a bell curve lies within a given distance of its centre
• Incomplete gamma and beta — cumulative distributions and the quantiles that invert them

Numerical calculus

Answering a question about a function you can only evaluate, one sample at a time. Everything in this group takes a function and calls it repeatedly.

• Root finding — where does this cross zero?
• Numerical integration — what is the area under it?
• Continued fractions — how do you evaluate an expression that never ends?
• Convergence and iteration limits — how every routine here decides it is done, and what it does when it is not

Structured spaces and applied areas

• Linear algebra — vectors, matrices and rotations (@ac-kit/math-linear)
• Discrete grids — lattices, tiling and pixel conversion (@ac-kit/math-grid)
• Geometry — shapes, coordinate systems and meshes (@ac-kit/math-geometry)
• Curves — Bézier curves, splines and arc length (@ac-kit/math-curves)
• Statistics — descriptive statistics, distributions and regression (@ac-kit/math-stats)
• Combinatorics — factorials, binomial coefficients and generators (@ac-kit/math-combinatorics)
• Signal processing — transforms, convolution, filters and windows (@ac-kit/math-signal)
• Colour — colour spaces, gamut mapping and perceptual difference (@ac-kit/math-color)