@woosh/meep-engine/src/core/math/complex/complex_horner_eval.js

Pure JavaScript game engine. Fully featured and production ready.

/**
 * Evaluate a univariate polynomial with real coefficients at a complex point,
 * via Horner's method.
 *
 *   p(z) = coeffs[0] + coeffs[1] · z + ... + coeffs[degree] · z^degree
 *
 * The result is written into `result` as `[Re(p(z)), Im(p(z))]`.
 *
 * @param {number[]|Float32Array|Float64Array} result 2-element output buffer
 * @param {number[]|Float32Array|Float64Array} coeffs ascending-power, length ≥ degree + 1
 * @param {number} degree polynomial degree, ≥ 0
 * @param {number} zr real part of z
 * @param {number} zi imaginary part of z
 */
export function complex_horner_eval(result, coeffs, degree, zr, zi) {
    let pr = coeffs[degree];
    let pi = 0;

    for (let i = degree - 1; i >= 0; i--) {

        const new_pr = pr * zr - pi * zi + coeffs[i];
        const new_pi = pr * zi + pi * zr;

        pr = new_pr;
        pi = new_pi;

    }

    result[0] = pr;
    result[1] = pi;
}