dist-javascript-algorithms-and-data-structures/dist/algorithms/math/bits/multiply.js

Algorithms and data-structures implemented on JavaScript

"use strict";

Object.defineProperty(exports, "__esModule", {
  value: true
});
exports.default = multiply;

var _multiplyByTwo = _interopRequireDefault(require("./multiplyByTwo"));

var _divideByTwo = _interopRequireDefault(require("./divideByTwo"));

var _isEven = _interopRequireDefault(require("./isEven"));

var _isPositive = _interopRequireDefault(require("./isPositive"));

function _interopRequireDefault(obj) { return obj && obj.__esModule ? obj : { default: obj }; }

/**
 * Multiply two signed numbers using bitwise operations.
 *
 * If a is zero or b is zero or if both a and b are zeros:
 * multiply(a, b) = 0
 *
 * If b is even:
 * multiply(a, b) = multiply(2a, b/2)
 *
 * If b is odd and b is positive:
 * multiply(a, b) = multiply(2a, (b-1)/2) + a
 *
 * If b is odd and b is negative:
 * multiply(a, b) = multiply(2a, (b+1)/2) - a
 *
 * Time complexity: O(log b)
 *
 * @param {number} a
 * @param {number} b
 * @return {number}
 */
function multiply(a, b) {
  // If a is zero or b is zero or if both a and b are zeros then the production is also zero.
  if (b === 0 || a === 0) {
    return 0;
  } // Otherwise we will have four different cases that are described above.


  const multiplyByOddPositive = () => multiply((0, _multiplyByTwo.default)(a), (0, _divideByTwo.default)(b - 1)) + a;

  const multiplyByOddNegative = () => multiply((0, _multiplyByTwo.default)(a), (0, _divideByTwo.default)(b + 1)) - a;

  const multiplyByEven = () => multiply((0, _multiplyByTwo.default)(a), (0, _divideByTwo.default)(b));

  const multiplyByOdd = () => (0, _isPositive.default)(b) ? multiplyByOddPositive() : multiplyByOddNegative();

  return (0, _isEven.default)(b) ? multiplyByEven() : multiplyByOdd();
}