[vox-tech] Fwd: [OT] How do calculators work?

[p at dirac.org]

On Thu 07 Dec 06,  9:10 AM, Ken Bloom <kbloom at gmail.com> 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 <p at cbreak.com>
> > Subject: [OT] How do calculators work?
> > To: vox-tech at lists.lugod.org
> >
> > 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