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Topic:
Fast exponent and logarithm, given initial estimate
Replies:
29
Last Post:
Nov 8, 2004 2:31 AM




Re: Fast exponent and logarithm, given initial estimate
Posted:
Oct 22, 2004 10:24 AM


> Some advice: try to eliminate the link in your head between "approximation" > and "taylor expansion" and replace it by "approximation" and "orthogonal > polynomials" :) Taylor is good in a small neighbourhood around the point > of interest. Orthogonal polynomials are good in quite a large interval to > which you can almost always reduce your initial interval to.
OK. Link eliminated :)
> > Qn: what tool did you use to generate the minimax polynomial? > > > Maple 9.51. The numapprox package, minimax function. The classical algorithm > associated with minimax approximations is the Remez algorithm (2nd version > of 1934, I don't have the exact reference at hand).
Looks like I have to continue to rely on the kindness of strangers :) , at least until next year when I might be in a position to purchase one. Or I might have a look at yacas.
Could you or someone else supply the following minimax polynomials
* sin(pi*x/2) for x in [0,1] OR in [0,1/2] and [1/2,1], 6 degrees up to 10e7 or 8 relative error * log(x) for x in [0,1], either 6 degrees polynomial or 3/2 or 4/1 rational (Pade?) polynomial with 10e7 or 8 relative error
I had used <a href="http://www.iancgbell.clara.net/maths/funcs.htm">http://www.iancgbell.clara.net/maths/funcs.htm</a> as a source for the coefficients but the error terms aren't what I wanted and I still can't get down to the # of ulps I need.
Cheers, Glen Low, Pixelglow Software www.pixelglow.com



