> >>
> >> /**
> >> - * Sinc function.
> >> + * Sinc function, defined by <pre><code>
> >> + *
> >> + * sinc(x) = 1 if abs(x) < 1e-9;
> >> + * sin(x) / x; otherwise
> >> + * </code></pre>
> >
> > I would not document the first part of the alternative since it is an
> > implementation detail. "1e-9" was chosen just because, with "double"
> > precision, the function value will be indistinguishable from 1. Strictly
> > speaking it is not part of the definition of "sinc". [This part of the
> > implementation could even be removed if it is deemed that we lose more time
> > doing the check than we gain when the user asks the value of points below
> > 1e-9.]
> >
> > Also, there probably should not be a ";" after the statements.
>
> If it a) makes a difference in the returned result and b) is correct (up to
> double equality),
I don't understand what you write here.
What I meant above is:
For values < 1e-9, it does not make a difference at double precision whether
the computation is done in full (sin(x) / x) or by assigning "1" directly.
> I think we should leave the check in
Yes, of course; the suggestion to remove it was a mistake (see below).
> and document it. We should always document top-coding or other departures
> from the formulas we define things by.
I don't see why give a wrong definition since it makes no difference. The
definition of "sinc" is[1]:
sinc(x) = sin(x) / x
To compute it, care must be taken to not divide by zero, thus the simplest
operational definition is[2]:
sinc(x) = 1 if x = 0
sin(x) / x otherwise
The one in CM is an efficiency improvement (to avoid evaluation of a sine
and a division when the result is indistinguishable from the known result).
The rationale for the shortcut could be a code comment, but as a user-level
comment, it is confusing.
Gilles
>
> I am fine changing the semicolons (which are being used as punctuation) to
> commas or even dropping them altogether.
>
> Phil
[1] http://en.wikipedia.org/wiki/Sinc_function
[2] http://mathworld.wolfram.com/SincFunction.html
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