ModularArithmetic.js

import { extendedEuclideanGCD } from './ExtendedEuclideanGCD'

/**
 * https://brilliant.org/wiki/modular-arithmetic/
 * @param {Number} arg1 first argument
 * @param {Number} arg2 second argument
 * @returns {Number}
 */

export class ModRing {
 constructor(MOD) {
 this.MOD = MOD
 }

 isInputValid = (arg1, arg2) => {
 if (!this.MOD) {
 throw new Error('Modulus must be initialized in the object constructor')
 }
 if (typeof arg1 !== 'number' || typeof arg2 !== 'number') {
 throw new TypeError('Input must be Numbers')
 }
 }
 /**
 * Modulus is Distributive property,
 * As a result, we separate it into numbers in order to keep it within MOD's range
 */

 add = (arg1, arg2) => {
 this.isInputValid(arg1, arg2)
 return ((arg1 % this.MOD) + (arg2 % this.MOD)) % this.MOD
 }

 subtract = (arg1, arg2) => {
 this.isInputValid(arg1, arg2)
 // An extra MOD is added to check negative results
 return ((arg1 % this.MOD) - (arg2 % this.MOD) + this.MOD) % this.MOD
 }

 multiply = (arg1, arg2) => {
 this.isInputValid(arg1, arg2)
 return ((arg1 % this.MOD) * (arg2 % this.MOD)) % this.MOD
 }

 /**
 *
 * It is not Possible to find Division directly like the above methods,
 * So we have to use the Extended Euclidean Theorem for finding Multiplicative Inverse
 * https://github.com/TheAlgorithms/JavaScript/blob/master/Maths/ExtendedEuclideanGCD.js
 */

 divide = (arg1, arg2) => {
 // 1st Index contains the required result
 // The theorem may have return Negative value, we need to add MOD to make it Positive
 return (extendedEuclideanGCD(arg1, arg2)[1] + this.MOD) % this.MOD
 }
}