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From: dewar@merv.cs.nyu.edu (Robert Dewar)
Subject: Re: Equality operator overloading in ADA 83
Date: 1997/05/01
Message-ID: <dewar.862496714@merv>#1/1
X-Deja-AN: 238689266
References: <01bc4e9b$ac0e7fa0$72041dc2@lightning>
 <335E0B1F.12C9@elca-matrix.ch> <E93v4u.DG1@world.std.com>
 <335F5971.6375@elca-matrix.ch> <E95y9L.AK1@world.std.com>
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 <dewar.862005183@merv> <3365C5E0.57A1@elca-matrix.ch>
Organization: New York University
Newsgroups: comp.lang.ada
Date: 1997-05-01T00:00:00+00:00
List-Id: <comp.lang.ada>



<<Yes, I do. But given good definitions of "=" and "<" for a floating
point type, applying my definitions will yield ">", "<=" and "<=" that
are just as good. Defining "good" here is tricky, e.g. you are not
supposed to use "=" for floating point, but rather something like
   abs (a - b) < epsilon * (abs a + abs b)>>

That is a common myth, particularly among those who do not do serious
analysis of floating-point code.

The equality operation for floating-point values is well defined, and
is useful.

The expression you give above with epsilon is sometimes useful (though
dangerous because of intermediate overflow), but is a quite different
operation.

The notion that you should always use the epsilon approach is wrong.
There are lots of examples of numerical algorithms where plain equality
works fine (and is far more efficient), and there are cases of algorithms
where ONLY the plain equality will work!