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

[Lachlan Andrew]

Follow-up Comment #13, bug #48307 (project octave):

Colin, the initial bug report may not have been about sin, but sin is the
cause of the loss of relative precision you see.

Besselj is an interesting example.  In bug #48316, you pointed out that
Besselj is NaN after 1e10.  That seems to rule out its having low error.

You say that the example of comment #5 seems OK.  The error it has in sin(x
pi) is about 1e-10 (which is a relative error of infinity, but we'll let that
slide).  If sin (x pi) has an error of 1e-10 and we divide by (x pi) to get
sinc(x), then we'll divide both the value and error by (x pi), so the relative
error is unchanged.  That means that the errors observed in comment #5 are
about the same as those in your original post.

My reading of Marco's comment #8 is that sinc is doing the best we can expect,
given the limitations of the *input*.

Finally, the relative error of sin(10000000*pi) is not about eps.  The
relative error is


approximate sin(10000000*pi)
----------------------------
true sin(10000000*pi)

=

non-zero / 0

= inf


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