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From: dewar@merv.cs.nyu.edu (Robert Dewar)
Subject: Re: floating point comparison
Date: 1997/07/31
Message-ID: <dewar.870386556@merv>#1/1
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 comp.lang.ada,sci.math.num-analysis,comp.software-eng,comp.theory,sci.math
Date: 1997-07-31T00:00:00+00:00
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Bob Binder says

<<I haven't followed the IEEE fp standard, but I can't imagine how
(without resorting to some kind of BCD representation) any floating
point scheme using a non-decimal radix gets around the fundamental fact
that there are non-terminal fractions in this radix which are not
point scheme using a non-decimal radix gets around the fundamental fact
that there are non-terminal fractions in this radix which are not
non-terminal in a decimal radix.
>>

There is nothing to "get around" here. The IEEE floating-point standard
is a well defined arithmetic system, with a well defined set of values
with well defined operations on them.

It is NOT, and never pretends to be, a representation of real arithmetic.
It has its own laws and axioms, but they are of course different from
those of real arithmetic.

There is nothing special about decimal arithmetic here. The laws of
physics are not made up by a deity with ten fingers. Real arithmetic
is of course independent of the chosen base, but so are observations
in the physical world. 

The IEEE fpt standard (IEEE-854) provides binary and decimal variations.
It is of course the binary version that is used on most modern
computers.