Gaussian random number generator

Question

I'm trying to implement a gaussian distributed random number generator in the interval [0,1].

float rand_gauss (void) {
  float v1,v2,s;

  do {
    v1 = 2.0 * ((float) rand()/RAND_MAX) - 1;
    v2 = 2.0 * ((float) rand()/RAND_MAX) - 1;

    s = v1*v1 + v2*v2;
  } while ( s >= 1.0 );

  if (s == 0.0)
    return 0.0;
  else
    return (v1*sqrt(-2.0 * log(s) / s));
}

It's pretty much a straight forward implementation of the algorithm in Knuth's 2nd volume of TAOCP 3rd edition page 122.

The problem is that rand_gauss() sometimes returns values outside the interval [0,1].

Answer 1

Knuth describes the polar method on p 122 of the 2nd volume of TAOCP. That algorithm generates a normal distribution with mean = 0 and standard deviation = 1. But you can adjust that by multiplying by the desired standard deviation and adding the desired mean.

You might find it fun to compare your code to another implementation of the polar method in the C-FAQ.