Re: implementation of cos,sin,tan,etc.

*To*: mathgroup at smc.vnet.net*Subject*: [mg3927] Re: implementation of cos,sin,tan,etc.*From*: fateman at peoplesparc.cs.berkeley.edu (Richard J. Fateman)*Date*: Fri, 10 May 1996 03:29:13 -0400*Organization*: University of California, Berkeley*Sender*: owner-wri-mathgroup at wolfram.com

In article <4m7qed$k5h at dragonfly.wolfram.com>, Nicholas S Fogelson <nfogelso at ix.cs.uoregon.edu> wrote: > >Does anyone know exactly how MM calculates cos,sin,etc. Presumably someone does I know that its >not by expansion of a Taylor series because it makes the answer too >darn fast to be doing that (ie - if you went through the taylor calculation >of sin1000000 it would take quite a few seconds before it started outputting. >Just doing sin1000000 will cause instant output). Most likely it IS done by Taylor series, but after reducing the argument to a region near zero (e.g. -pi/4 to pi/4 ) You need to have a way of computing pi to arbitrary precision, not a big deal. >I know that the MM implementations are not public, but I thought maybe >somebody knows this anyway. bigfloat implementations of elementary functions are described in various places. >Also - does anyone know how an HP calculator does these calculations? >Is is the same way? No. Cordic transformations, I believe. Look it up.. >-- >Nicholas Fogelson >University of Oregon >Department of Computer and Information Science >nfogelso at cs.uoregon.edu (503)683-7885 > > > -- Richard J. Fateman fateman at cs.berkeley.edu http://http.cs.berkeley.edu/~fateman/ ==== [MESSAGE SEPARATOR] ====