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From: edp@jareth.enet.dec.com (Eric Postpischil (Always mount a scratch monkey.))
Newsgroups: comp.sys.handhelds
Subject: Re: Interestring Property of HP-* Calculators
Keywords: 48SX,COS
Message-ID: <16659@shlump.nac.dec.com>
Date: 25 Oct 90 12:22:59 GMT
References: <2830@uc.msc.umn.edu> <2821@uc.msc.umn.edu> <15610@mentor.cc.purdue.edu>
Sender: newsdaemon@shlump.nac.dec.com
Reply-To: edp@jareth.enet.dec.com (Eric Postpischil (Always mount a scratch monkey.))
Organization: Digital Equipment Corporation
Lines: 21

In article <2830@uc.msc.umn.edu>, fin@norge.unet.umn.edu (Craig A. Finseth)
writes:

> The obvservation was that COS(x) had a fixed point but ACOS(x) did not.

An intuitive explanation is that COS is pushing numbers closer together in the
region of the fixed point.  E.g., the cosines of two numbers in that vicinity of
the fixed point will be closer together than the original numbers.  So repeated
applications of COS move closer to the fixed point; the representable real
closest to the fixed point returns itself.

ACOS spreads numbers out; the inverse cosines of two numbers in that vicinity
will be farther apart.  So ACOS magnifies the difference between the
representable real closest to the fixed point and the fixed point.

It is like the difference between a smooth peak and a smooth valley.  Both have
flat points where one could theoretically place a ball and have it remain at
rest.  But it's a lot harder on the peak than in the valley.


				-- edp