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From: Phil Clayton <phil.clayton@lineone.net>
Newsgroups: comp.lang.ada
Subject: Re: Float conversion
Date: Wed, 4 Aug 2010 09:32:21 -0700 (PDT)
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Date: 2010-08-04T09:32:21-07:00
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On Aug 3, 11:38=A0am, Georg Bauhaus <rm.dash-bauh...@futureapps.de>
wrote:
> On 03.08.10 03:07, Phil Clayton wrote:
>
> >> Clearly to cover all cases, you
> >> need A < B, A =3D B, A > B, A < C, etc.
>
> > You make it sound easy... =A0Generally, how do you justify that tests
> > 'cover all cases' so giving you a 100% chance of finding an error?
>
> When {A, B, C} in (machine) Float, I guess "<", "=3D", and ">"
> won't tell the whole story in any case? (If they are assumed
> to mean what they usually mean in "mathematics".)

Yes.  Using a mathematical model where floating point values are
viewed as mathematical real numbers (i.e. having infinite precision)
and where operators have their standard mathematical meaning is an
approximation.  Reasoning with such a model of programs will detect a
useful and wide class of error but won't correctly predict the
behaviour of programs in absolutely every case.  It is easy to produce
examples that demonstrate this involving floating point equality and
values that cannot be represented exactly.

Phil