BigInteger ExtensionMethods

BigIntegerExtensionMethods.cs

public static class BigIntegerExtensionMethods
{
    public static BigInteger Sum(this IEnumerable<BigInteger> source)
    {
        return source.Aggregate((accumulator, current) => accumulator + current);
    }
    
    public static BigInteger Product(this IEnumerable<BigInteger> source)
    {
        return source.Aggregate((accumulator, current) => accumulator * current);
    }
    
    public static BigInteger Mod(this BigInteger source, BigInteger mod)
    {
        BigInteger r = (source >= mod) ? source % mod : source;
        return (r < 0) ? BigInteger.Add(r, mod) : r.Clone();
    }
    
    public static BigInteger NthRoot(this BigInteger source, int root)
    {
        BigInteger remainder = new BigInteger();
        return source.NthRoot(root, out remainder);
    }

    public static BigInteger NthRoot(this BigInteger source, int root, out BigInteger remainder)
    {
        if (root < 1) throw new Exception("Root must be greater than or equal to 1");
        if (source.Sign == -1) throw new Exception("Value must be a positive integer");

        remainder = 0;
        if (source == BigInteger.One) { return BigInteger.One; }
        if (source == BigInteger.Zero) { return BigInteger.Zero; }
        if (root == 1) { return source; }

        BigInteger upperbound = source.Clone();
        BigInteger lowerbound = BigInteger.Zero;

        while (true)
        {
            BigInteger nval = (upperbound + lowerbound) >> 1;
            BigInteger testPow = BigInteger.Pow(nval, root);

            if (testPow > source) upperbound = nval;
            if (testPow < source) lowerbound = nval;
            if (testPow == source)
            {
                lowerbound = nval;
                break;
            }
            if (lowerbound == upperbound - 1) break;
        }
        remainder = source - BigInteger.Pow(lowerbound, root);
        return lowerbound;
    }

    public static bool IsSquare(this BigInteger source)
    {
        if (source == null || source == BigInteger.Zero)
        {
            return false;
        }

        BigInteger input = BigInteger.Abs(source);

        int base16 = (int)(input & Fifteen); // Convert to base 16 number
        if (base16 > 9)
        {
            return false; // return immediately in 6 cases out of 16.
        }

        // Squares in base 16 end in 0, 1, 4, or 9
        if (base16 != 2 && base16 != 3 && base16 != 5 && base16 != 6 && base16 != 7 && base16 != 8)
        {
            BigInteger remainder = new BigInteger();
            BigInteger sqrt = input.NthRoot(2, out remainder);

            return (remainder == 0);
            // - OR -
            //return (sqrt.Square() == input);
        }
        return false;
    }
    private static BigInteger Fifteen = new BigInteger(15);
}