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

[Colin Macdonald]

Follow-up Comment #12, bug #48307 (project octave):

> Colin was initially assuming that the relative error should be of the order
of eps.
> However, that is only true of approximately linear functions. 

I'm not sure that is true.

> With something like sin(), 

But this bug is not about sin.  Sinc oscillates and decays.  Some other
special functions oscillate and decay.  For example, Besselj does and yet its
approximation has low relative error.

But anyway, regarding sin(): I don't think there is anything wrong with sin in
glibc (why are we even talking about that?!)  sin's implementation has great
relative error!  To me the example in comment #5 is fine.  I think Marco has
already said so in comment #8: but just in case, note that the relative error
is of size eps in the calculation of sin(10000000*pi).  This looks like
standard numerical analysis to me.

Of course maybe it is inherently hard to compute sinc for some reason---I said
initially that I'm no expert on special functions.

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