The following URL is less likely to be mangled by e-mail readers: http://www.jsoftware.com/jwiki/Essays/Logarithm_and_Exponential_%28Extended_Precision%29
----- Original Message ----- From: Roger Hui <[EMAIL PROTECTED]> Date: Tuesday, December 12, 2006 10:20 am Subject: Re: [Jgeneral] exp(y). sin(y) and accuracy. > See also the essay in the J Wiki > http://www.jsoftware.com/jwiki/Essays/Logarithm_and_Exponential_(Extended_Precision) ----- Original Message ----- From: John Randall <[EMAIL PROTECTED]> Date: Tuesday, December 12, 2006 8:49 am Subject: Re: [Jgeneral] exp(y). sin(y) and accuracy. > Anyone interested in the gory details of how elementary functions are > calculated in floating-point arithmetic might take a look at > fdlibm, in > particular > > http://netlib.org/fdlibm/e_exp.c > > which is the source for exp. This demonstrates two common techniques: > argument reduction, and using interpolation based on polynomials with > precomputed coefficients. The polynomials tend not to be Taylor > polynomials (which minimize error near a point) but Chebyshev > polynomials(which minimize mean square error over an interval). > > The code here claims to have error less than 1 ulp (unit in the > last place). ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
