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List:       kde-core-devel
Subject:    Re: PATCH: control size of image generated by kimgio_eps_read
From:       Bernd Gehrmann <bernd () physik ! hu-berlin ! de>
Date:       2002-02-16 16:28:18
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On Thu, 14 Feb 2002, Michael Matz wrote:

> Hi,
> 
> On Thu, 14 Feb 2002, Bernd Gehrmann wrote:
> 
> > > Be aware, that this isn't the issue here. 1.0 is exactly representable in
> > > IEEE, but it means nothing for the issue at hand.  Intermediate spilling
> > > might extend/narrow the actual representaion (slightly violating IEEE),
> > > which could lead to rounding errors (in different ways, because different
> > > representation), which make == fail in every case.  For 1.0 this _might_
> > > indeed not be a problem, but just substitute 'x' for 1.0 and you are
> > > screwed.
> >
> > "Pigeons can't fly. Look, pigs can't fly, and pigs are animals, so all
> > animals can't fly."
> 
> This too has nothing to do with the issue at hand, which you seem not to
> be able to understand.  Sorry.

In contrast to you, I understand the issues at hand well beyond
vague "floating point numbers are something inherently mystical and
uncontrollable" statements and condescending comments. One of the first
C++ programs I have written was a library with an interval type that
propagated all uncontrolled rounding errors in floating point numbers
through the arithmetic operators. Thereby, it was possible to give
rigorous bounds on the result of a computation. Such techniques are widely
used, and a central concept is that of representable numbers. A nice
consequence of this is that one can compute things like "the smallest
representable number greater than 1" in a portable manner by starting 
with integer numbers and applying operations which are known to be 
exact. For example, in [1] you can find a computer-assisted fixed point
proof of the Feigenbaum equation written in Prolog. For the reliability of
such proofs, it is essential that an implementation does not violate IEEE
in an elementary way like not being able to convert small integer numbers
to their IEEE number representations. I believe that such a violation
would not have gone unnoticed. General statements not related to this
issue are not helpful at all.

[1] SIAM Review, Vol. 38, No. 4, pp. 565-604, (1996)

Bernd.

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