### Question 13.20

How can I generate random numbers with a normal or Gaussian distribution?

Here is one method, by Box and Muller, and recommended by Knuth:

    #include <stdlib.h>
    #include <math.h>

    double gaussrand()
    {
    	static double V1, V2, S;
    	static int phase = 0;
    	double X;

    	if(phase == 0) {
    		do {
    			double U1 = (double)rand() / RAND_MAX;
    			double U2 = (double)rand() / RAND_MAX;

    			V1 = 2 * U1 - 1;
    			V2 = 2 * U2 - 1;
    			S = V1 * V1 + V2 * V2;
    			} while(S >= 1 || S == 0);

    		X = V1 * sqrt(-2 * log(S) / S);
    	} else
    		X = V2 * sqrt(-2 * log(S) / S);

    	phase = 1 - phase;

    	return X;
    }

See the extended versions of this list (see question 20.40) for other ideas.

References: Knuth Sec. 3.4.1 p. 117
Box and Muller, ``A Note on the Generation of Random Normal Deviates''
Press et al., Numerical Recipes in C Sec. 7.2 pp. 288-290

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