/*
 * TransformedLFSR.java
 * Created on Feb 22, 2005
 */
package random;


/**
 * Transforms a uniform random number generator according to
 *   y1 = sqrt(-2 ln(x1)) sin(x2)
 *   y2 = sqrt(-2 ln(x1)) cos(x2)
 */
public final class TransformedLFSR {
    
    private LFSR rng = new LFSR();
    private boolean haveY2 = false;
    private double y2;
    
    public double next() {
        double nextNum;
        
        if (haveY2) {
            nextNum = y2;
            haveY2 = false;
        } else {
	        double x1 = rng.nextDouble();
	        // can't take the log of zero
	        if (Double.compare(x1, 0.0) == 0) return next();
	        double x2 = rng.nextDouble();
	        double k = Math.sqrt(-2 * Math.log(x1));
	        nextNum = k * Math.sin(x2);
	        this.y2 = k * Math.cos(x2);
	        haveY2 = true;
        }
        
        return nextNum;
    }
    
    
    //
    // some stuff to numerically evaluate cumulants
    //
    
    public static void main(String args[]) {
        final int NUM_ITERS = 5000000;
        TransformedLFSR rng = new TransformedLFSR();
        
        double raw1Sum = 0, raw2Sum = 0, raw3Sum = 0;
        for (int i = 0; i < NUM_ITERS; i++) {
            double p = rng.next();
            raw1Sum += p;
            raw2Sum += p * p;
            raw3Sum += p * p * p;
        }
        
        double raw1 = raw1Sum / NUM_ITERS;
        double raw2 = raw2Sum / NUM_ITERS;
        double raw3 = raw3Sum / NUM_ITERS;
        
        double C1 = raw1;
        double C2 = raw2 - (raw1 * raw1);
        double C3 = raw3 - (3 * raw1 * raw2) + (2 * raw1 * raw1 * raw1);
        
        System.out.println("C1: " + C1);
        System.out.println("C2: " + C2);
        System.out.println("C3: " + C3);
    }

}