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
  }
}