//================================================================
/**
 * @packageDocumentation
 * @module std.internal
 */
//================================================================
export namespace MathUtil {
    export function factorial(k: number): number {
        if (FACTORIALS.length <= k)
            for (let i: number = FACTORIALS.length; i <= k; ++i)
                FACTORIALS.push(FACTORIALS[i - 1] * i);

        return FACTORIALS[k];
    }

    export function integral(
        formula: (x: number) => number,
        first: number,
        last: number,
        segment_count: number = 100 * 1000,
    ): number {
        if (first > last) [first, last] = [last, first];
        else if (first === last) return 0;

        const interval: number = (last - first) / segment_count;
        let ret: number = 0.0;

        for (; first < last; first += interval)
            ret += formula(first) * interval;

        return ret;
    }

    export function sigma(
        formula: (k: number) => number,
        first: number,
        last: number,
    ): number {
        let ret: number = 0.0;
        for (; first <= last; ++first) ret += formula(first);

        return ret;
    }

    const FACTORIALS: number[] = [1, 1];
}