/**

* Shared numeric helpers (no color semantics).

*/

/**

* 3×3 matrix (row-major, 9 elements) times a 3-vector.

* @param {number[]} m row-major [m00,m01,m02, m10,m11,m12, m20,m21,m22]

* @returns {[number,number,number]}

*/

export const mat3 = (m, x, y, z) => [

x * m[0] + y * m[1] + z * m[2],

x * m[3] + y * m[4] + z * m[5],

x * m[6] + y * m[7] + z * m[8]

];

/**

* Inverse of a 3×3 matrix (row-major). Lets a color space declare one forward

* matrix as the single source of truth and derive its exact inverse, so the

* round-trip is bit-exact (no transcription drift from a separately-rounded inverse).

* @param {number[]} m row-major 9-element matrix

* @returns {number[]} row-major inverse

*/

/**

* Product of two 3×3 row-major matrices — A·B applies B first, then A.

* Lets a space pre-combine a fixed pipeline of linear steps into one matrix.

* @param {number[]} A row-major 3×3

* @param {number[]} B row-major 3×3

* @returns {number[]} row-major 3×3

*/

export const mul3 = (A, B) => [

A[0] * B[0] + A[1] * B[3] + A[2] * B[6], A[0] * B[1] + A[1] * B[4] + A[2] * B[7], A[0] * B[2] + A[1] * B[5] + A[2] * B[8],

A[3] * B[0] + A[4] * B[3] + A[5] * B[6], A[3] * B[1] + A[4] * B[4] + A[5] * B[7], A[3] * B[2] + A[4] * B[5] + A[5] * B[8],

A[6] * B[0] + A[7] * B[3] + A[8] * B[6], A[6] * B[1] + A[7] * B[4] + A[8] * B[7], A[6] * B[2] + A[7] * B[5] + A[8] * B[8],

];

export const inv3 = (m) => {

const [a, b, c, d, e, f, g, h, i] = m;

const A = e * i - f * h, B = f * g - d * i, C = d * h - e * g;

const det = a * A + b * B + c * C;

return [

A / det, (c * h - b * i) / det, (b * f - c * e) / det,

B / det, (a * i - c * g) / det, (c * d - a * f) / det,

C / det, (b * g - a * h) / det, (a * e - b * d) / det

];

};

/**

* Signed power: keeps the sign, raises the magnitude. The standard way every

* appearance model / gamma curve extends a fractional exponent to negative

* (out-of-gamut) inputs without producing NaN.

* @returns {number} sign(a)·|a|^b

*/

export const spow = (a, b) => Math.sign(a) * Math.abs(a) ** b;

/**

* Cartesian opponent pair (a,b) -> cylindrical (chroma, hue°). The lightness L

* passes straight through. Below `t` the colour is achromatic and the hue is

* undefined → 0 (avoids a ghost hue from float-noise residuals, and atan2(-0,-0)).

* @returns {[number,number,number]} [l, c, h] with h in [0,360)

*/

export const cartToPolar = (l, a, b, t = 1e-8) => {

const c = Math.sqrt(a * a + b * b);

const h = c < t ? 0 : Math.atan2(b, a) * 180 / Math.PI;

return [l, c, h < 0 ? h + 360 : h];

};

/**

* Cylindrical (chroma, hue°) -> Cartesian opponent pair (a,b); inverse of

* {@link cartToPolar}. Lightness L passes through.

* @returns {[number,number,number]} [l, a, b]

*/

export const polarToCart = (l, c, h) => {

const hr = h * Math.PI / 180;

return [l, c * Math.cos(hr), c * Math.sin(hr)];

};