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

[Michael Godfrey]

URL:
  <http://savannah.gnu.org/bugs/?42071>

                 Summary: complex trig functions differ from Matlab
                 Project: GNU Octave
            Submitted by: godfrey
            Submitted on: Tue 08 Apr 2014 11:05:55 AM GMT
                Category: Octave Function
                Severity: 3 - Normal
                Priority: 5 - Normal
              Item Group: Inaccurate Result
                  Status: None
             Assigned to: None
         Originator Name: Godfrey
        Originator Email: 
             Open/Closed: Open
         Discussion Lock: Any
                 Release: dev
        Operating System: GNU/Linux

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Details:

I noticed the following:
exp(i*n*pi)
produces results which are significantly
different from and less accurate than Matlab.

For example:
function    Octave                    Matlab
exp(i*pi)  -1.0000e+00 + 1.2246e-16i    -1.0000 + 0.0000i

Using format hex shows the differences more clearly
And, the relative error increases for increasing n
in exp(i*n*pi)

The problem also shows up for sin(i*n*pi), but the
error is much less.

While I am reporting this as a bug, the issue deserves
systematic and careful study.  I do not know what math library
Matlab uses, but I would have expected the results between
Octave and Matlab to be quite close.

Note that in a number of cases, the signs of the results
differ between Octave and Matlab. This will, for
instance, affect iterative improvement type code at
values approaching multiples of i*pi.

So far I have only tried experiments with sin and exp.
And, for real arguments the results are much closer.





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