[
https://issues.apache.org/jira/browse/RNG-154?page=com.atlassian.jira.plugin.system.issuetabpanels:all-tabpanel
]
Alex Herbert updated RNG-154:
-----------------------------
Description:
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}
The largest value x where 2y < x^2 is false is sqrt(2*36.74) = 8.571 and the
returned tail would be +/- 12.01. 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.
was:
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.
> Avoid infinite samples in the normalised Gaussian samplers
> ----------------------------------------------------------
>
> 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
> Fix For: 1.4
>
>
> 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}
> The largest value x where 2y < x^2 is false is sqrt(2*36.74) = 8.571 and the
> returned tail would be +/- 12.01. 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.
>
--
This message was sent by Atlassian Jira
(v8.3.4#803005)
