added-ModularArithmetic-code (#1217)

* added-ModularArithmetic-code

* fix-typo

* suggested changes

Maths/ModularArithmetic.js

@@ -0,0 +1,56 @@
+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
+  }
+}