[Octave-bug-tracker] [bug #65230] Poor accuracy of betaln for most inputs due to catastrophic cancellation

[anonymous]

URL:
  <https://savannah.gnu.org/bugs/?65230>

                 Summary: Poor accuracy of betaln for most inputs due to
catastrophic cancellation
                   Group: GNU Octave
               Submitter: None
               Submitted: Tue 30 Jan 2024 04:38:42 PM UTC
                Category: Octave Function
                Severity: 3 - Normal
                Priority: 5 - Normal
              Item Group: Inaccurate Result
                  Status: None
             Assigned to: None
         Originator Name: 
        Originator Email: 
             Open/Closed: Open
                 Release: dev
         Discussion Lock: Any
        Operating System: Any
           Fixed Release: None
         Planned Release: None


    _______________________________________________________

Follow-up Comments:


-------------------------------------------------------
Date: Tue 30 Jan 2024 04:38:42 PM UTC By: Anonymous
The betaln(a, b) function is currently implemented as gammaln (a) + gammaln
(b) - gammaln (a + b).  This seems to have reasonable accuracy when the ratio
a/b is near 1, but all accuracy is lost due to catastrophic cancellation as
the ratio becomes more extreme.  For most inputs, such as betaln(2^62, 2^6), 0
is returned.

My current workaround is to use the gsl_sf_lnbeta function from the gsl
package.  This function can provide an error estimate in its second output
argument.  The error estimates seem reasonably small for most inputs I've
tried.








    _______________________________________________________

Reply to this item at:

  <https://savannah.gnu.org/bugs/?65230>

_______________________________________________
Message sent via Savannah
https://savannah.gnu.org/