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

[Colin Macdonald]

Follow-up Comment #2, bug #48307 (project octave):


>> sinc(x)
ans = (sym) 0
>> sinc(d) 
ans =    4.5268e-17


>  You'd need to come up with a more concrete comparison to establish there is
a numerical problem.

Without disagreeing with any of your points, I think its very common practice
to for a special function library to aim for 15 digits **relative accuracy**
(and document when it cannot do that).  Here it cannot.  As x gets large, we
lose relative accuracy, I think linearly with x.

I certainly agree its good to not blindly assume symbolic computed results are
correct.  Here is Maple (which doesn't seem to have a built-in sinc).


> x := 10000001/3;
                                x := 10000001/3

> Digits := 32;
                                 Digits := 32

> evalf ( sin(Pi*x) / (Pi*x) );
                                                         -7
                   -0.82699326043336203093078665439080 10


And pasting back into Octave:

>> Maple = -0.82699326043336203093078665439080e-7
Maple =   -8.2699e-08
>> Q = sinc(10000001/3)
Q =   -8.2699e-08
>> Q - Maple
ans =   -5.2279e-17
>> (Maple - Q) / Maple
ans =   -6.3216e-10

1.  These results match SymPy's (Symbolic pkg).
2.  Again, we see that the absolute error is fine (< eps), but that the
relative error is approx "2e6*eps".


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