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

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 Glen Low Posts: 41 Registered: 12/13/04
Re: Fast exponent and logarithm, given initial estimate
Posted: Oct 19, 2004 10:47 PM

&gt; take a polynomial approximation. sources:
&gt; abramowitz-stegun: handbook of mathematical functions has some for
&gt; rather low precision, may be these suffice already.
&gt; you could also use Clenshaws tables for the approxiamtion by
&gt; series in chebyshev polynomials of the first kind (hopefully avaliable
&gt; for you from NIST (formerly Nat. Bureau of Standards)
&gt;
&gt; or better:
&gt; <a href="http://www.netlib.org/cephes/cmath.tgz">http://www.netlib.org/cephes/cmath.tgz</a>
&gt; <a href="http://www.netlib.org/elefunt">http://www.netlib.org/elefunt</a>
&gt; <a href="http://www.netlib.org/fn">http://www.netlib.org/fn</a>
&gt; literature:
&gt; <a href="http://www/netlib.org/bibnet/journals/elefunt.bib">http://www/netlib.org/bibnet/journals/elefunt.bib</a>

Thanks for the URLs, I will look them up, since I don't have
Mathematica or Maple handy for the coefficients. Any sources for

&gt; (taylor series is a bad idea, since these approximate good only near the point of
&gt; development)

For exponents they aren't too bad. A Taylor polynomial of a small
positive number converges fast and is close to the number zero, so the
main thing is to analyze small numbers. The exponent laws comes in
handy, since you can split off the integral part and the fractional
part, then multiply the fractional part by 2^-n to get that small
number, do the Taylor thing and afterward raise to power 2^n to
recover the actual exponent.

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