Alex Herbert created RNG-154:
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Summary: Avoid infinite samples in the
ZigguratNormalisedGaussianSampler
Key: RNG-154
URL: https://issues.apache.org/jira/browse/RNG-154
Project: Commons RNG
Issue Type: Improvement
Components: sampling
Affects Versions: 1.3
Reporter: Alex Herbert
The ZigguratNormalisedGaussianSampler uses the following method to sample the
tail of the Gaussian:
{code:java}
// Note
// R = 3.442619855899
// 1 / R = 0.2905...
double y;
double x;
do {
y = -Math.log(rng.nextDouble());
x = -Math.log(rng.nextDouble()) * ONE_OVER_R;
} while (y + y < x * x);
final double out = R + x;
return hz > 0 ? out : -out;
{code}
In the unlikely event the RNG produces 0 then Math.log(0) is infinity. Two
zeros in a row can result in an infinite sample for the tail. This is very
unlikely but would be unexpected for a user of the library since a sample
should be roughly within +/-3.
Note that if the RNG is sampling from the 2^53 dyadic rationals in [0, 1) then
the next value is:
{code:java}
Math.log(0x1.0p-53) == -36.7368005696771
{code}
Here the returned tail would be 3.44 + 36.7368005696771 / 3.44 = 14.11. This is
very far from the extreme of infinity.
To avoid infinity this can be fixed by:
1. Assuming the RNG is returning a value in [0, 1) and using Math.log(1.0 -
rng.nextDouble())
2. Generating the double u from a long to ensure the value is in [0, 1) and
using 1.0 - u.
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