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From: fin@norge.unet.umn.edu (Craig A. Finseth)
Newsgroups: comp.sys.handhelds
Subject: Interestring Property of HP-* Calculators
Keywords: 48SX,COS
Message-ID: <2821@uc.msc.umn.edu>
Date: 23 Oct 90 14:27:11 GMT
Sender: news@uc.msc.umn.edu
Organization: Univ Netw Serv, Univ of Minn
Lines: 38

This article describes an interesting *artifact*[1] of the mechanism
use for computing COS and ACOS.  It has been tested on an HP-48SX and
TI-PROCALC (don't ask).  It is *NOT* a bug report!

Type the following on an HP-48SX:

	DEG 0 COS COS COS COS

you should see (in the STD display mode):

	.999847741531

Repeated pressings of the COS key at this point will return the same
number.  All is well and good.  I can well believe that, with 12-digit
arithmetic, there is a "fixed" point at which COS(x) -> x.  Now do:

	ACOS

You will see:

	.99984774182

Obviously, the ACOS algorithm has a different fixed point if, indeed,
it has one at all.  The Solver reports a sign reversal for:

	'ACOS(X)=X'

at, oddly  enough, .9998447741531.

Again, this is not a bug report, just an observation.

Craig A. Finseth			fin@unet.umn.edu [CAF13]
University Networking Services		+1 612 624 3375 desk
University of Minnesota			+1 612 625 0006 problems
130 Lind Hall, 207 Church St SE		+1 612 626 1002 FAX
Minneapolis MN 55455-0134, U.S.A.

[1] Artifact: An unexpected property of a correct implementation.