Alex Herbert created NUMBERS-182:
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Summary: LogBeta overflows for tiny arguments
Key: NUMBERS-182
URL: https://issues.apache.org/jira/browse/NUMBERS-182
Project: Commons Numbers
Issue Type: Bug
Components: gamma
Affects Versions: 1.0
Reporter: Alex Herbert
Fix For: 1.1
LogBeta computes the log of the beta function using a log of a computation
using the Gamma function when the arguments are small (a < 1). The code
includes a comment that this is more accurate than using LogGamma:
{code:java}
// The original NSWC implementation was
// LogGamma.value(a) + (LogGamma.value(b) - LogGamma.value(a + b));
// but the following command turned out to be more accurate.
return Math.log(Gamma.value(a) * Gamma.value(b) /
Gamma.value(a + b)); {code}
However Gamma(x) -> 1/x when x -> 0. Thus this can overflow, e.g. this test
fails:
{code:java}
@Test
void testTinyAB() {
double a = 1.0e-155;
double b = 1.5e-155;
double beta = 2.5 / 1.5 * 1e155;
Assertions.assertEquals(Math.log(beta), LogBeta.value(a, b));
} {code}
This can be fixed by checking for overflow and reverting to the original NSWC
implementation:
{code:java}
final double beta = Gamma.value(a) * Gamma.value(b) / Gamma.value(a + b);
if (Double.isFinite(beta)) {
return Math.log(beta);
}
return LogGamma.value(a) + (LogGamma.value(b) - LogGamma.value(a + b)); {code}
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