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From: Gerhard Heinzel <ghh@mpq.mpg.de>
Subject: Re: floating point comparison
Date: 1997/08/08
Message-ID: <Pine.SOL.3.91.970808104726.13390B-100000@mpqgrav1.mpq.mpg.de>#1/1
X-Deja-AN: 262832308
References: <33E61497.33E2@pseserv3.fw.hac.com>
 <5sar4r$t7m$1@cnn.nas.nasa.gov> <5sbb90$qsc@redtail.cruzio.com>
Organization: Rechenzentrum der Max-Planck-Gesellschaft in Garching
Newsgroups: 
 comp.lang.ada,sci.math.num-analysis,comp.software-eng,comp.theory,sci.math
Date: 1997-08-08T00:00:00+00:00
List-Id: <comp.lang.ada>


On 7 Aug 1997 schlafly@bbs.cruzio.com wrote:

> In article <5sar4r$t7m$1@cnn.nas.nasa.gov>, fyodor@sally.nas.nasa.gov (Chris L. Kuszmaul) writes:
> >   Fair enough. There are two basic guidlines I follow:
> > 
> > 1: Do not test for equality between floating point values. If you do, then
> > you better get a numerical analysit, or figure out how to avoid using floating
> > point, or see if you can use a 'close to equal' check.
> 
> There is nothing inherently wrong with testing for equality,
> if that is what you really want.  It is a very easily
> understandable and reliable operation, except for some funny
> business involving NANs.
> 

Maybe it should be clarified WHY one would want to test for equality.
I can imagine two distinct situations:

First, to test whether two numbers that have not been computed, but only
entered and maybe stored back and forth, are the same. I rarely have that
case (It is usually much better to mark things with logical or integer
variables in that case, and test the integers). But I assume that testing
for equality may be ok in that case.

Second, if you want to compare two numbers that come from some algorithm
(i.e. is an eigenvalue zero? is a pivot zero? is a correlation coefficient
unity?) In these cases one must NEVER test for exact equality, but always
take into account rounding errors and devise some test such as

fabs(x-y)<EPSILON

or fabs((x-y)/y)<EPSILON

or something similar, depending on the situation.

=====================================================================
 Gerhard Heinzel                            E-mail:   ghh@mpq.mpg.de
 Max-Planck-Institut fuer Quantenoptik   Phone: +49(89)32905-268/252
 Hans-Kopfermann-Str. 1            Phone (30m Lab): +49(89)3299-3282
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 Germany                           http://www.geo600.uni-hannover.de
=====================================================================