> >
> > Don't quote me on the "Taylor" part. Actually, upon closer inspection
> > there is a comment that simply says "polynomial of degree 13"
Well, it's "taylor" to first order anyway; first dozen odd significant
digits are plain ole Taylor Series around zero.
> One cannot be sure without running tests with an actual code in a
> "real life" situations, but I strongly suspect that a rational
> approximation of a degree 3 could fare better.
Digital doesn't seem to think so; there are no divisions in an objdump of
trigonometric portions of DPML (if this is against the rules; somebody
please tell me, because otherwise it's a nice way of getting hints on
fast AXP code).
I didn't look closely enough to see if they're using the same polynomial
coefficients as the fdlibm code, but my guess is that they probably are
(if the fdlibm guy did his homework correctly & got the "minimax"
polynomial right).
> > ---it doesn't say how they arrived at that polynomial.
>
> There are some ways. :-) Things like Chebyshev polynomials and Pade
> approximations should ring a bell. Manuals for Maple and Mathematica
> are likely not a bad place to look for hints of a use in practice.
> A venerable "Computer Approximations", by Hart, probably can also
> be consulted.
There's also Numerical Recipes, which is now online.
The relevant section (in Fortran; sorry)
http://cfatab.harvard.edu/nr/bookf.html
section 5.11 onwards
-SL
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