//***********************************************************************
        // Tests the correct implementation of sqrt() method.
        //***********************************************************************

        public static void SqrtTest(int rounds)
        {
            Random rand = new Random();
            for (int count = 0; count < rounds; count++)
            {
                // generate data of random length
                int t1 = 0;
                while (t1 == 0)
                    t1 = (int) (rand.NextDouble()*1024);

                Console.Write("Round = " + count);

                BigInteger a = new BigInteger();
                a.genRandomBits(t1, rand);

                BigInteger b = a.sqrt();
                BigInteger c = (b + 1)*(b + 1);

                // check that b is the largest integer such that b*b <= a
                if (c <= a)
                {
                    Console.WriteLine("\nError at round " + count);
                    Console.WriteLine(a + "\n");
                    return;
                }
                Console.WriteLine(" <PASSED>.");
            }
        }
        private bool LucasStrongTestHelper(BigInteger thisVal)
        {
            // Do the test (selects D based on Selfridge)
            // Let D be the first element of the sequence
            // 5, -7, 9, -11, 13, ... for which J(D,n) = -1
            // Let P = 1, Q = (1-D) / 4

            long D = 5, sign = -1, dCount = 0;
            bool done = false;

            while (!done)
            {
                int Jresult = BigInteger.Jacobi(D, thisVal);

                if (Jresult == -1)
                    done = true; // J(D, this) = 1
                else
                {
                    if (Jresult == 0 && Math.Abs(D) < thisVal) // divisor found
                        return false;

                    if (dCount == 20)
                    {
                        // check for square
                        BigInteger root = thisVal.sqrt();
                        if (root*root == thisVal)
                            return false;
                    }

                    //Console.WriteLine(D);
                    D = (Math.Abs(D) + 2)*sign;
                    sign = -sign;
                }
                dCount++;
            }

            long Q = (1 - D) >> 2;

            /*
        Console.WriteLine("D = " + D);
        Console.WriteLine("Q = " + Q);
        Console.WriteLine("(n,D) = " + thisVal.gcd(D));
        Console.WriteLine("(n,Q) = " + thisVal.gcd(Q));
        Console.WriteLine("J(D|n) = " + BigInteger.Jacobi(D, thisVal));
        */

            BigInteger p_add1 = thisVal + 1;
            int s = 0;

            for (int index = 0; index < p_add1.dataLength; index++)
            {
                uint mask = 0x01;

                for (int i = 0; i < 32; i++)
                {
                    if ((p_add1.data[index] & mask) != 0)
                    {
                        index = p_add1.dataLength; // to break the outer loop
                        break;
                    }
                    mask <<= 1;
                    s++;
                }
            }

            BigInteger t = p_add1 >> s;

            // calculate constant = b^(2k) / m
            // for Barrett Reduction
            BigInteger constant = new BigInteger();

            int nLen = thisVal.dataLength << 1;
            constant.data[nLen] = 0x00000001;
            constant.dataLength = nLen + 1;

            constant = constant/thisVal;

            BigInteger[] lucas = LucasSequenceHelper(1, Q, t, thisVal, constant, 0);
            bool isPrime = false;

            if ((lucas[0].dataLength == 1 && lucas[0].data[0] == 0) ||
                (lucas[1].dataLength == 1 && lucas[1].data[0] == 0))
            {
                // u(t) = 0 or V(t) = 0
                isPrime = true;
            }

            for (int i = 1; i < s; i++)
            {
                if (!isPrime)
                {
                    // doubling of index
                    lucas[1] = thisVal.BarrettReduction(lucas[1]*lucas[1], thisVal, constant);
                    lucas[1] = (lucas[1] - (lucas[2] << 1))%thisVal;

                    //lucas[1] = ((lucas[1] * lucas[1]) - (lucas[2] << 1)) % thisVal;

                    if ((lucas[1].dataLength == 1 && lucas[1].data[0] == 0))
                        isPrime = true;
                }

                lucas[2] = thisVal.BarrettReduction(lucas[2]*lucas[2], thisVal, constant); //Q^k
            }


            if (isPrime) // additional checks for composite numbers
            {
                // If n is prime and gcd(n, Q) == 1, then
                // Q^((n+1)/2) = Q * Q^((n-1)/2) is congruent to (Q * J(Q, n)) mod n

                BigInteger g = thisVal.gcd(Q);
                if (g.dataLength == 1 && g.data[0] == 1) // gcd(this, Q) == 1
                {
                    if ((lucas[2].data[maxLength - 1] & 0x80000000) != 0)
                        lucas[2] += thisVal;

                    BigInteger temp = (Q*BigInteger.Jacobi(Q, thisVal))%thisVal;
                    if ((temp.data[maxLength - 1] & 0x80000000) != 0)
                        temp += thisVal;

                    if (lucas[2] != temp)
                        isPrime = false;
                }
            }

            return isPrime;
        }