On Thu 07 Dec 06, 9:10 AM, Ken Bloom <[EMAIL PROTECTED]> said: > On Saturday 02 December 2006 14:19, Bill Kendrick wrote: > > Pete posted this from a non-subscribed address: > > > > > > Date: Fri, 1 Dec 2006 21:31:14 -0800 > > From: Peter Salzman <[EMAIL PROTECTED]> > > Subject: [OT] How do calculators work? > > To: [email protected] > > > > I've always heard that calculators use truncated Taylor series to > > approximate functions like trig and exp functions. > > > > Yet that can't be the whole story: > > > > Taylor approximations require more and more terms for convergence as > > you evaluate the series farther and farther away from the point of > > expansion. > > > > Second, we get into problems with singularities and the radius of > > convergence. The series converges on a complex disk (or a real > > interval) that contains no singularities. That presents a major > > obstacle for calculating logarithms. That's why you always expand > > log(x + k), rather than log(x). > > > > So saying that calculators use power series approximations can't be > > the whole story. It's a good zeroth order approxmation to the truth. > > What's the first order correction to the truth? > > Have you considered looking at the various open source libc's (both > glibc and BSD's libc) to see how they do this? The calculator probably > does something similar. > > --Ken I did, but realized it probably wouldn't be what I was after. Implementation is not commonly useful except to learn about the implementation.
For example, I could show you code that estimated the number Pi by superscribing and subscribing polygons around a circle. You would have NO idea what the program does and NO idea how the program generates Pi (unless I explained it to you). It would look like some weird kind of summation of a bunch of sines and cosines. I'm pretty sure that's what I would get. Besides, I got my answer. :-) Pete _______________________________________________ vox-tech mailing list [email protected] http://lists.lugod.org/mailman/listinfo/vox-tech
