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From: ok@cs.mu.oz.au (Richard O'Keefe)
Newsgroups: comp.lang.prolog
Subject: Re: Floating Point
Message-ID: <2524@munnari.oz.au>
Date: 25 Oct 89 06:11:15 GMT
References: <2491@munnari.oz.au> <36169@srcsip.UUCP>
Sender: news@cs.mu.oz.au
Lines: 31

In article <36169@srcsip.UUCP>, shankar@SRC.Honeywell.COM (Subash Shankar) writes:

> With all the talk about floating point in Prolog, I was wondering if
> there any Prolog's which unify "close" floating point numbers. 

At least two:  IBM's VM/Prolog and SB Prolog.

> Would this make sense?

In a word, ***NO***.   It would make a *great* deal of sense to have
an *additional* set of "fuzzy comparison" predicates (see Knuth Vol 2
for a good set).  But it makes no sense at all to pervert unification.
If you unify X with Y whenever |X-Y| < epsilon.max(|X|,|Y|), then the
effect of that is to *REDUCE* your precision to epsilon.  For example,
Stony-Brook Prolog has its own internal format for floating-point
numbers which buys it about 6 decimal digits of precision.  But it
uses fuzzy unification with epsilon = 1.0e-5.  That is, it throws
away one whole decimal digit.  Writing numeric code in such a dialect
is a nightmare.  Precise comparison is important in many numeric
applications.

From the logical point of view, the nasty thing about fuzzy comparison
is that it is not transitive.  Let epsilon be 1.0e-5, and compute
	Y is 1.0,
	X is Y-6.0e-6,
	Z is Y+6.0e-6
Now, using fuzzy unification, we would get
	X = Y		(relative error is 0.6e-5 < 1.0e-5)
	Y = Z		(relative error is 0.6e-5 < 1.0e-5)
BUT NOT X = Z		(relative error is 1.2e-5 > 1.0e-5)
Making unification non-transitive is not an improvement to the language.