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https://issues.apache.org/jira/browse/RNG-154?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=17377520#comment-17377520
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Alex Herbert commented on RNG-154:
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Reading some more about the Box Muller transform it appears that the uniform
deviate should be in (0, 1). The wikipedia article has a section about [tails
truncation|https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform#Tails_truncation]
due to the limitations of approaching but not reaching 0. So this could be
considered a bug.
I think it is worth fixing the following to avoid calling Math.log with a zero:
ZigguratNormalisedGaussianSampler
BoxMullerNormalizedGaussianSampler
BoxMullerGaussianSampler
> 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
> Priority: Minor
>
> 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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