Alex Herbert created NUMBERS-209:
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Summary: Infinite loop for Trigamma function on large negative
values
Key: NUMBERS-209
URL: https://issues.apache.org/jira/browse/NUMBERS-209
Project: Commons Numbers
Issue Type: Bug
Components: gamma
Affects Versions: 1.3
Reporter: Alex Herbert
The Trigamma function increments the input argument by 1 until it exceeds the
threshold of 49. This is not suitable for large negative values (below -2^53)
as the increment does not increment the argument.
Note that double values above 2^53 in magnitude are integers. For negative
arguments any integer is a pole of the trigamma function and has the value
+infinity.
However smaller magnitude arguments may take prohibitively long to compute by
incrementing. In this case it is possible to use the reflection formula:
{noformat}
trigamma(x) + trigamma(1 - x) = pi^2 / sin^2(pi * x)
if x < 0:
trigamma(x) = pi^2 / sin^2(pi * x) - trigamma(1 - x){noformat}
Issue identified using a security scan.
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