[Octave-bug-tracker] [bug #65230] Poor accuracy of betaln for high ratios of a/b

[anonymous]

Follow-up Comment #9, bug #65230 (group octave):

OP here again.

Regarding the changeset mentioned in comment #6, it would probably be good to
make the same change allowing broadcasting in beta.m as well, and update the
"full list of functions and operators that broadcast" in the
[https://docs.octave.org/latest/Broadcasting.html documentation].

I have an implementation of betaln for positive arguments that I'm reasonably
happy with.  I'm seeing performance about 3 to 8 times worse than the existing
implementation.  Inaccuracy quantified as min(absolute_error, relative_error)
seems likely to be less than 32 * eps for the full input space.  Unfortunately
the relative error can be quite large when the result is near zero, and I
haven't thought of a way around this.

Some work remains to be done on the BISTs, and I'd appreciate some input on
this point.  I developed the implementation with the aid of several million
test cases where I computed (hopefully) correctly rounded values.  These test
cases amount to several tens of megabytes and took several CPU-hours to
generate, so I don't expect it will be desired to incorporate anywhere near
the full set into BISTs.  Reducing the set to 10000 test cases (which still
strikes me as a lot for BISTs) seems to leave a lot of room for issues to
hide.  Suggestions?



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