From: Ronald Bruck Subject: Re: Chebyshev Date: Wed, 12 Jul 2000 11:52:37 -0700 Newsgroups: sci.math Summary: [missing] In article <396CBC92.1489E54A@brutele.be>, Jean-Francois Challe wrote: :Hello, : :I'm writting multiprecision functions using the floating point :arithmetic. I can do add, sub, mul and div on floating point number. :Now, I would like to compute sin, cos, tg, ln, exp, arcsin, arccos, :arctg, sinh, cosh, tgh, etc ... :To do this I would like to use Chebyshev's polynomials and of course not :Taylor's series. : :I know : : :T(n,x)=cos(n arccos(x) for x in [-1,1] :T(0,x)=1; T(1,x)=x; ...; T(n,x)=2x T(n-1,x)-T(n-2,x) : :But I don't know what can I do with theses formulas to compute with a :good precision for example sin(x) ? : :rq : I know the CORDIC algorithm but I in my case I can't use it. RUN, don't walk, RUN to David Bailey's web site at As I recall he has an extensive discussion in his papers how to do multiprecision routines for varions transcendental functions. His library is in FORTRAN, but should be readable nonetheless. He also refers to other available multiprecision routines. Hmmm. I see Bailey is at Lawrence Berkeley Lab. With the current climate of hysteria in this country, I hope he's not charged with disseminating nuclear secrets to a foreign agent... ;-) --Ron Bruck -- Due to University fiscal constraints, .sigs may not be exceed one line.