//================================================================
/**
 * @packageDocumentation
 * @module std
 */
//================================================================
/**
 * Gamma function.
 *
 * @reference https://en.wikipedia.org/wiki/Gamma_function, https://rosettacode.org/wiki/Gamma_function#JavaScript
 */
export function tgamma(x: number): number {
    if (x < 0.5) return Math.PI / (Math.sin(Math.PI * x) * tgamma(1 - x));
    /*else if (x >= 1 && x === Math.floor(x))
        return base.MathUtil.factorial(x - 1);*/

    x -= 1;
    let a: number = P[0];
    const t: number = x + G + 0.5;

    for (let i: number = 1; i < P.length; ++i) a += P[i] / (x + i);

    return Math.sqrt(2 * Math.PI) * Math.pow(t, x + 0.5) * Math.exp(-t) * a;
}

/**
 * Log gamma function.
 */
export function lgamma(x: number): number {
    return Math.log(tgamma(x));
}

const P: number[] = [
    0.99999999999980993, 676.5203681218851, -1259.1392167224028,
    771.32342877765313, -176.61502916214059, 12.507343278686905,
    -0.13857109526572012, 9.9843695780195716e-6, 1.5056327351493116e-7,
];
const G: number = 7;