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

[Ken Bloom]

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

-- 
Ken Bloom. PhD candidate. Linguistic Cognition Laboratory.
Department of Computer Science. Illinois Institute of Technology.
http://www.iit.edu/~kbloom1/
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