Provide a simple, efficient, and correct implementation to sample Gaussian random variables

[gkronber]

We currently use the Ziggurat method which is fast but not straight-forward. abeham made some tests and found significant deviations of the empirical distributions of samples generated with our implementation compared to other implementations.

In this image an offset is added to the probability values to prevent overlapping of points. The issue is that the blue line stops at approx. -3.5 and 3.5. So the current implementation does not produce correct distributions in the tails.

[gkronber]

Code from Sim#:

    const double NormalMagicConst = 4 * Math.Exp(-0.5) / Math.Sqrt(2.0);
    public double RandNormal(double mu, double sigma) {
      double z, zz, u1, u2;
      do {
        u1 = Random.NextDouble();
        u2 = 1 - Random.NextDouble();
        z = NormalMagicConst * (u1 - 0.5) / u2;
        zz = z * z / 4.0;
      } while (zz > -Math.Log(u2));
      return mu + z * sigma;
    }

[gkronber]

Performance comparison (1mio samples, release build):

FastRandom:
N(0,1)-hl: 28,7
N(0,1)-Sim#: 53,9
N(0,1)-alglib: 69,7

MersenneTwister:
N(0,1)-hl: 92,3
N(0,1)-Sim#: 174,1