Re: floating point comparison

[dewar@merv.cs.nyu.edu (Robert Dewar)]

Andrew says

<<        Strongly disagree. There ARE roundoff errors even in the IEEE 754
arithemtic model. Moreover, the standard clearly specifies rounding models.>>

You completely miss the point I am making.

There are no *errors*, the discrepancies between IEEE arithmetic and
real arithmetic are not errors, they are simply differences that come from
two different arithmetic models.

When we have integer arithmetic and we divide 10 by 3 to get 3, we do
not say this is an error. The result is different from the mathematical
value of 10.0/3.0, but there is no error here, just a different arithmetic 
model.

I know perfectly well that the phrase "rounding error" is well established,
but my point is that calling it an error leads people into the niave trap
of thinking of floating-point arithmetic as being real arithmetic.

In fact I received quite a few email messages, from some quite interesting
people :-) saying that they agreed that it was a pity that the term
rounding error had ever got into the literature, but of course
it is much too entrnched to get rid of.

But your repsonse tends to make me think that you are indeed fallling
into the trap of thinking of these xdiscepancies as errors. It's a mistake!

As for your comment about different register lengths etc. This is a matter of binding
of the language you are using to IEEE. The set of IEEE operatoins
contains no such uncertainty, and a decent binding of a high level language
to IEEE (e.g. SANE from Apple) must avoid such uncertainties.