[Octave-bug-tracker] [bug #48307] sinc loses precision for large arguments

[Dan Sebald]

Follow-up Comment #5, bug #48307 (project octave):

Experiment with this a little bit:


>> sprintf("%0.100g", 10000000)
ans = 10000000
>> x = [1 10 100 1000 10000 100000 1000000 10000000];
>> plot([0:7], abs(sin(pi*x)));


There's a definite loss of accuracy, and if I go to higher powers (e.g.,
[0:10]) the sin() function starts to fall apart.

Maybe it is a problem with the C math library Octave uses.

I've not seen the library code, but the sorts of questions would be how the
Taylor series is evaluated.  From what I'm recalling about series expansion is
that it is done about some type of centroid and is accurate within a certain
range, and for better accuracy one does an expansion about a different
centroid...that sort of thing.  For trig functions it would make sense to
bring that value, no matter how large it is, back within the canonical range
of [0,2*pi) or [-pi,pi).


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