Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
Drexel University or The Math Forum.
|
|
|
|
Re: Fast exponent and logarithm, given initial estimate
Posted:
Oct 19, 2004 10:47 PM
|
|
> take a polynomial approximation. sources:
> abramowitz-stegun: handbook of mathematical functions has some for
> rather low precision, may be these suffice already.
> you could also use Clenshaws tables for the approxiamtion by
> series in chebyshev polynomials of the first kind (hopefully avaliable
> for you from NIST (formerly Nat. Bureau of Standards)
>
> or better:
> <a href="http://www.netlib.org/cephes/cmath.tgz">http://www.netlib.org/cephes/cmath.tgz</a>
> <a href="http://www.netlib.org/elefunt">http://www.netlib.org/elefunt</a>
> <a href="http://www.netlib.org/fn">http://www.netlib.org/fn</a>
> literature:
> <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
rational or Pade approximants?
> (taylor series is a bad idea, since these approximate good only near the point of
> 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
|
|
|
|
