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

[Dan Sebald]

Follow-up Comment #1, bug #48307 (project octave):

One would have to look more closely at the trigonometric functions to see if
there is really an estimation problem here, or whether this is simply a matter
of numerical inaccuracies.  A couple things to keep in mind.  One is that the
comparison is between a numeric computation and symbolic computation.  It's
difficult to say which is correct.  We do know that sinc(x) where x is a whole
number should be zero accept for x = 0.  What type of values do you see for,
say,

x = sym(10000001)
d = double(x)
sinc(x)
sinc(d)

?

A second thing to keep in mind is that a double is not a real number, but a
floating point number, so there is always going to be inaccuracy that way
(i.e., that double(1/3) is not necessarily the same value as the rational
number 1/3).

I suppose a third point of question is that in your first example the
valuations are convergent to zero and dividing by a small number, i.e.,
(P1-Q)/P1 will tend to amplify inaccuracies while in the second example the
divisor is a large number, relatively speaking.

A lot of questions here.  You'd need to come up with a more concrete
comparison to establish there is a numerical problem.

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