[Octave-bug-tracker] [bug #42071] complex trig functions differ from Matlab

[Michael Godfrey]

Follow-up Comment #5, bug #42071 (project octave):

John,

I agree that if this reveals problems in the math
library, including complex cases, it should be fixed
at the source.

However, it would also be useful if it could be
discovered why Matlab is more correct. Is it known
whether they use the math library?  I thought that they
did, but this is quite old information.

It would be very helpful if someone who is currently
working on numerical accuracy of the elementary
functions  (or at least has recently taken Kahan's 
or Muller's course)
could be convinced to work on this.

Finally, I very much doubt if the math library directly
produces non-monotonic convergence. This problem has
been known and solved many many years ago. Although,
if I recall correctly, the early solutions did not include
the complex case. Kahan dealt with that.

I could study this a bit more, but it would only be
luck if I got far enough to achieve a complete solution
even just for exp().

For instance, I have not even checked that Matlab is
monotonic even just for exp() with complex arg.



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