Hi I want to multiply 2 big integer in a most timely optimized way. I am currently using karatsuba algorithm. Can anyone suggest more optimized way or algo to do it.
Thanks
public static BigInteger karatsuba(BigInteger x, BigInteger y) {
// cutoff to brute force
int N = Math.max(x.bitLength(), y.bitLength());
System.out.println(N);
if (N <= 2000) return x.multiply(y); // optimize this parameter
// number of bits divided by 2, rounded up
N = (N / 2) + (N % 2);
// x = a + 2^N b, y = c + 2^N d
BigInteger b = x.shiftRight(N);
BigInteger a = x.subtract(b.shiftLeft(N));
BigInteger d = y.shiftRight(N);
BigInteger c = y.subtract(d.shiftLeft(N));
// compute sub-expressions
BigInteger ac = karatsuba(a, c);
BigInteger bd = karatsuba(b, d);
BigInteger abcd = karatsuba(a.add(b), c.add(d));
return ac.add(abcd.subtract(ac).subtract(bd).shiftLeft(N)).add(bd.shiftLeft(2*N));
}