Range of Random.nextGaussian()

Recently I had a look at the source code of a language detection library. The library internally uses Random.nextGaussian to determine its behavior, but uses it in such a way that any value lower than -10 would result in incorrect calculations. I was curious if getting such a value is even possible.


The implementation of nextGaussian in Java 8 is as follows:

 private double nextNextGaussian;
 private boolean haveNextNextGaussian = false;

 public double nextGaussian() {
   if (haveNextNextGaussian) {
     haveNextNextGaussian = false;
     return nextNextGaussian;
   } else {
     double v1, v2, s;
     do {
       v1 = 2 * nextDouble() - 1;   // between -1.0 and 1.0
       v2 = 2 * nextDouble() - 1;   // between -1.0 and 1.0
       s = v1 * v1 + v2 * v2;
     } while (s >= 1 || s == 0);
     double multiplier = StrictMath.sqrt(-2 * StrictMath.log(s)/s);
     nextNextGaussian = v2 * multiplier;
     haveNextNextGaussian = true;
     return v1 * multiplier;
   }
 }

The function used to generate next values has extremes when both v1 and v2 are as close to zero as possible, without being both equal to zero.

Quick check of nextDouble indicates that the function generates only multiples of 1 / (double)(1L << 53). This means that nextGaussian will return extreme values for v1 = +/- 2 / (double)(1L << 53)and v2 = 0.

For these values nextGaussian would return +/- 12.00727336061225.

That does not mean that it is possible to get these values. There's a limited number of values that can be returned by nextDouble. But it does mean that nextGaussian (in its Oracle Java 8 implementation) will never return a value outside of the range between -12.00727336061225 and 12.00727336061225.