Karatsuba Multiplication in JavaScript

karatsuba.js

/**
 * Karatsuba Multiplication
 * @param  {Number} x - first number
 * @param  {Number} y - second number
 * @return {Number} Multiply of x and y
 */
 
function karatsubaMulti(x, y) {

  let n = Math.min(('' + x).length, ('' + y).length);

  if(n == 1)
    return x * y;

  let tenpowhalfn = Math.pow(10, parseInt(n / 2));
  let tenpown = Math.pow(10, 2 * parseInt(n / 2));

  let a = parseInt(x / tenpowhalfn);
  let b = x % tenpowhalfn;
  let c = parseInt(y / tenpowhalfn);
  let d = y % tenpowhalfn;

  let caller = arguments.callee;

  return tenpown * caller(a, c) + tenpowhalfn * (caller(a, d) + caller(b, c)) + caller(b, d);
}

Usage

karatsubaMulti(1234, 56789) // return 70077626

could you please explain why you round down the exponent when calculating the tenpown and tenpowhalfn? and why you take the minimum digit length for n? I'm assuming this is for when either of the digits lengths are odd, I just can't figure out why this works. Thanks for sharing this gist!

IF you get the error

TypeError: 'caller', 'callee', and 'arguments' properties may not be accessed on strict mode functions or the arguments objects for calls to them

All you have to do is remove line 23, 'let caller = .... ' and change the return to

  return tenpown * karatsubaMulti(a, c)
    + tenpowhalfn * (karatsubaMulti(a, d)
    + karatsubaMulti(b, c))
    + karatsubaMulti(b, d)