How to generate random numbers with standard distribution or Gaussian distribution

Here's one by  Marsaglia  Initiate  Knuth  Recommended method :

    #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;
	}

The above code is based on Box-Muller Method , The basic idea is to generate two groups of independent random numbers U and V, These two groups of numbers are in (0,1] Evenly distributed , use U and V Generate two sets of independent standard normal distribution random variables X and Y:

.

This equation is proposed because of two degrees of freedom Chi square distribution （ See nature 4） It's easy to make exponential random variables （ In the equation lnU） Generate . So through random variables V You can choose an angle that evenly surrounds the circle , Use the exponential distribution to select the radius and then transform it into （ Normal distribution ）x,y coordinate .