// CS 1538 Fall 2009
// This handout verifies that the Random number generator that is standard
// in Java meets the theoretical guidelines of a mixed linear congruential
// generator with period m as stated in the textbook.  Note that it does NOT
// actually test to see if the values generated are uniform and independent.

import java.util.*;
import java.math.*;
public class TestRandom
{
	public static void main(String [] args)
	{
		long a = 0x5DEECE66DL;
		long c = 0xBL;
		long mask = (1L << 48) - 1;

		// We will verify that these values fit with the first form
		// of the linear congruential generator from p. 280 of the text
		// (the mixed generator)

		// First we test to see if a = 1 + 4k for some k.  If this is
		// true, then a-1 = 4k for some k and thus (a-1)%4 = 0;

		long aMinus1 = a - 1;
		if (aMinus1 % 4 == 0)
		{
			long quot = aMinus1 / 4;
			System.out.println(a + " = 1 + 4(" + quot + ")");
		}
		else
			System.out.println("Not valid 1");

		// Now we want to make sure the c and m are relatively prime
		// The way the mask is defined is that it is 2^48 - 1, which will
		// give 1s in the rightmost 48 bits of the number and zeros in the
		// leftmost bits.  This in effect produces an m of 2^48, so that is
		// what we will test.  To be relatively prime, two numbers must have
		// a greatest common divisor of 0.  A predefined gcd function is not
		// defined in the Java Math class, but it is defined in the BigInteger
		// class.
		BigInteger bigC = new BigInteger(String.valueOf(c));
		BigInteger bigM = new BigInteger(String.valueOf(mask+1));
		BigInteger gcd = bigC.gcd(bigM);
		if (gcd.equals(new BigInteger("1")))
			System.out.println(c + " and " + (mask+1) + " are relatively prime");
		else
			System.out.println("Not valid 2");

		// The code below will test the period.  Note that if the theory is
		// correct, the period will be m = 2^48 which will clearly take a VERY
		// long time to circle through.  However, since we are limiting the values
		// to the range of 32-bit integers, we could get a duplicate
		// earlier (but a duplicate here does not mean that the period has
		// completed, since we are throwing away some of the bits).

		long count = 0;
		Random R = new Random();
		int i = R.nextInt();
		count = 1;
		int first = i;
		i = R.nextInt();
		while (i != first && count <= (1L << 32))
		{
			count++;
			if (count % 20000000 == 0)
				System.out.println(count + " tried ");
			i = R.nextInt();
		}
		if (i == first)
			System.out.println("Duplicate of first found after " + count + " numbers");
		else
			System.out.println("No duplicates found");
	}
}