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

 Messages: [ Previous | Next ]
 Glen Low Posts: 41 Registered: 12/13/04
Re: Fast exponent and logarithm, given initial estimate
Posted: Oct 22, 2004 10:24 AM

&gt; and "taylor expansion" and replace it by "approximation" and "orthogonal
&gt; polynomials" :-) Taylor is good in a small neighbourhood around the point
&gt; of interest. Orthogonal polynomials are good in quite a large interval to
&gt; which you can almost always reduce your initial interval to.

&gt; &gt; Qn: what tool did you use to generate the minimax polynomial?
&gt; &gt;
&gt; Maple 9.51. The numapprox package, minimax function. The classical algorithm
&gt; associated with minimax approximations is the Remez algorithm (2nd version
&gt; 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 10e-7 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 10e-7 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

Date Subject Author
10/18/04 Glen Low
10/18/04 Jeremy Watts
10/19/04 Peter Spellucci
10/19/04 Glen Low
10/18/04 bv
10/19/04 Glen Low
10/19/04 George Russell
10/19/04 Glen Low
10/20/04 George Russell
10/20/04 Glen Low
10/21/04 Christer Ericson
10/21/04 Glen Low
10/22/04 Christer Ericson
10/19/04 Martin Brown
10/19/04 Glen Low
10/19/04 Richard Mathar
10/19/04 Glen Low
10/20/04 Gert Van den Eynde
10/20/04 Glen Low
10/20/04 Richard Mathar
10/21/04 Gert Van den Eynde
10/21/04 bv
10/22/04 Glen Low
10/22/04 Peter Spellucci
10/22/04 Glen Low
10/23/04 bv
10/24/04 Gert Van den Eynde
10/25/04 Peter Spellucci
10/20/04 Gert Van den Eynde
11/8/04 Glen Low