functionalscript/types/monoid/module.f.js

FunctionalScript is a purely functional subset of JavaScript

/**
 * Repeats a monoid operation `n` times on the given element `a`.
 * This function efficiently performs the operation using exponentiation by squaring.
 *
 * @template T The type of the elements in the monoid.
 * @param monoid The monoid structure, including the identity and binary operation.
 * @returns A function that takes an element `a` and a repetition count `n`,
 * and returns the result of applying the operation `n` times.
 *
 * See also {@link https://en.wikipedia.org/wiki/Exponentiation_by_squaring}.
 *
 * @example
 *
 * ```ts
 * const add: Monoid<number> = {
 *     identity: 0,
 *     operation: a => b => a + b,
 * };
 *
 * const resultAdd = repeat(add)(2)(10n) // 20
 *
 * const concat: Monoid<string> = {
 *     identity: '',
 *     operation: a => b => a + b,
 * };
 *
 * const resultConcat = repeat(concat)('ha')(3n) // 'hahaha'
 * ```
 */
export const repeat = ({ identity, operation }) => (a) => (n) => {
    let ai = a;
    let ni = n;
    let result = identity;
    while (true) {
        if ((ni & 1n) !== 0n) {
            result = operation(result)(ai);
        }
        ni >>= 1n;
        if (ni === 0n) {
            return result;
        }
        ai = operation(ai)(ai);
    }
};