JavaScript implementation of Karatsuba multiplication algorithm

Question

Hi I am trying to implement karatsuba algorithm in Javascript. As of now the algorithm works fine for certain cases like when the length of integer is 4 or 8.When the length of integer is 6 it prints out wrong result

Eg: 3141*2718=>8537238 (correct result)

Eg: 314*271=>84981.37398106341 (incorrect result)

Eg: 3141592653589793238462643383279502884197169399375105820974944592 * 2718281828459045235360287471352662497757247093699959574966967627 =>8.539734222673569e+126 (partially correct )

var firstnumber= 3141592653589793238462643383279502884197169399375105820974944592
var secondNumber=2718281828459045235360287471352662497757247093699959574966967627



Karatsuba(firstnumber,secondNumber)


function Karatsuba(x,y)
{

    if(x<10 || y<10)
    {

        return x*y
    }




var first=Math.ceil(Math.log(x + 1) / Math.LN10)
var  second=Math.ceil(Math.log(x + 1) / Math.LN10)





 var min=Math.min(first,second);






var a=Math.floor(x/Math.pow(10,min/2))
var b=Math.floor(x%Math.pow(10,min/2))
var c=Math.floor(y/Math.pow(10,min/2))
var d=Math.floor(y%Math.pow(10,min/2))


 var s=Math.pow(10,min/2)

 return ((Math.pow(10,min))*Karatsuba(a,c)+ s*(Karatsuba(a,d) +Karatsuba(b,c)) +  Karatsuba(b,d))
}

Maybe you will have to use a BigNumber library: https://github.com/MikeMcl/bignumber.js — mateleco, May 03 '20 at 12:47
Typing `Number.MAX_SAFE_INTEGER` gives me 9007199254740991. The numbers on lines 1 and 2 are unsafe. — ggorlen, May 03 '20 at 19:21

score 1 · Answer 1 · answered May 03 '20 at 12:37

1

This can be not the only reason for your results to be incorrect, but in javascript, all numbers are fixed-precision floating-point numbers, and with big numbers (more than 15 digits) you will meet the lack of precision, that will bring to incorrect results. But that not explains why it is incorrect for relatively small numbers (6 digits integer can be perfectly represented both as float and double)

answered May 03 '20 at 12:37

Roman Svistunov

1,069
6
11

But once we divide 6 or half it we get 3 .and i am unable to come up with logic to deal with odd number length – Sheildboy May 03 '20 at 13:08
3

@Sheildboy, JavaScript can't handle infinite number precision natively, for that you will have to use external libraries. See: https://mikemcl.github.io/bignumber.js/ – mateleco May 03 '20 at 13:21
Yup.i will give it a try. – Sheildboy May 03 '20 at 13:29

JavaScript implementation of Karatsuba multiplication algorithm

1 Answers1