import multiplyByTwo from './multiplyByTwo';

import divideByTwo from './divideByTwo';

import isEven from './isEven';

import isPositive from './isPositive';

/**

* 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}

*/

export default 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(multiplyByTwo(a), divideByTwo(b - 1)) + a;

const multiplyByOddNegative = () => multiply(multiplyByTwo(a), divideByTwo(b + 1)) - a;

const multiplyByEven = () => multiply(multiplyByTwo(a), divideByTwo(b));

const multiplyByOdd = () => (isPositive(b) ? multiplyByOddPositive() : multiplyByOddNegative());

return isEven(b) ? multiplyByEven() : multiplyByOdd();

}