Re: using linux instead of osf

Michal Jaegermann (michal@ellpspace.math.ualberta.ca)
Wed, 27 Nov 1996 09:23:38 -0700 (MST)

>
> Don't quote me on the "Taylor" part. Actually, upon closer inspection
> there is a comment that simply says "polynomial of degree 13"

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. For a sigle precision
a coarser (and faster) approximation can be used. Often, especially
for a single precision, a fast table lookup plus a "refinment" step,
or two, can trade some memory for cycles, but I do not know how this
would work on Alpha with problems of cache and scheduling and all
that jazz...

In development of things of that sort nearly all time is spent in
testing that what you got is what you really want and that border
cases behave in a rational manner. :-)

> ---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.

Now for a question: anybody run these libraries through Paranoia tests -
speed notwithstanding?

Michal

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