> 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.