l i n u x - u s e r s - g r o u p - o f - d a v i s
L U G O D
 
Next Meeting:
September 2: Social gathering
Next Installfest:
TBD
Latest News:
Aug. 18: Discounts to "Velocity" in NY; come to tonight's "Photography" talk
Page last updated:
2006 Dec 07 07:10

The following is an archive of a post made to our 'vox-tech mailing list' by one of its subscribers.

Report this post as spam:

(Enter your email address)
Re: [vox-tech] Fwd: [OT] How do calculators work?
[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]

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



Bill Kendrick wrote:
Pete posted this from a non-subscribed address:


Date: Fri, 1 Dec 2006 21:31:14 -0800
From: Peter Salzman <p@cbreak.com>
Subject: [OT] How do calculators work?
To: vox-tech@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?

Thanks!

Pete
It appears that CORDIC approximations are an effective solution. [1]

I had heard of them, but had never worked through them myself until
prompted by this question.  I still don't quite follow the theoretical
basis [2]. Tracy Allen's explanation [3] is helpful, but doesn't
address the application of the algorithm to logarithms and square roots.

-------

[1] http://www.jacques-laporte.org/TheSecretOfTheAlgorithms.htm
[2] http://www.jacques-laporte.org/Welther-Unified%20Algorithm.pdf
[3] http://www.emesystems.com/BS2mathC.htm

--
---------------------------------------------------------------------------
Jeff Newmiller                        The     .....       .....  Go Live...
DCN:<jdnewmil@dcn.davis.ca.us>        Basics: ##.#.       ##.#.  Live Go...
                                      Live:   OO#.. Dead: OO#..  Playing
Research Engineer (Solar/Batteries            O.O#.       #.O#.  with
/Software/Embedded Controllers)               .OO#.       .OO#.  rocks...1k
---------------------------------------------------------------------------
_______________________________________________
vox-tech mailing list
vox-tech@lists.lugod.org
http://lists.lugod.org/mailman/listinfo/vox-tech



LinkedIn
LUGOD Group on LinkedIn
Sign up for LUGOD event announcements
Your email address:
facebook
LUGOD Group on Facebook
'Like' LUGOD on Facebook:

Hosting provided by:
Sunset Systems
Sunset Systems offers preconfigured Linux systems, remote system administration and custom software development.

LUGOD: Linux Users' Group of Davis
PO Box 2082, Davis, CA 95617
Contact Us

LUGOD is a 501(c)7 non-profit organization
based in Davis, California
and serving the Sacramento area.
"Linux" is a trademark of Linus Torvalds.

Sponsored in part by:
O'Reilly and Associates
For numerous book donations.