Calculate square root of a BigInteger (System.Numerics.BigInteger)

Question

.NET 4.0 provides the System.Numerics.BigInteger type for arbitrarily-large integers. I need to compute the square root (or a reasonable approximation -- e.g.,

Answer 1

It has been almost 10 years but hopefully, this will help someone. Here is the one I have been using. It does not use any slow division.

    // Source: http://mjs5.com/2016/01/20/c-biginteger-square-root-function/  Michael Steiner, Jan 2016
    // Slightly modified to correct error below 6. (thank you M Ktsis D) 
    public static BigInteger Sqrt(BigInteger number)
    {
        if (number < 9)
        {
            if (number == 0)
                return 0;
            if (number < 4)
                return 1;
            else
                return 2;
        }

        BigInteger n = 0, p = 0;
        var high = number >> 1;
        var low = BigInteger.Zero;

        while (high > low + 1)
        {
            n = (high + low) >> 1;
            p = n * n;
            if (number < p)
            {
                high = n;
            }
            else if (number > p)
            {
                low = n;
            }
            else
            {
                break;
            }
        }
        return number == p ? n : low;
    }

Update: Thank you to M Ktsis D for finding a bug in this. It has been corrected with a guard clause.