RE: [boost] Re: Floating Point comparisons

From: Paul A. Bristow (boost_at_[hidden])
Date: 2001-12-14 18:11:20

Thanks for this.

I found the refs on IEEE754 fascinating, but not greatly additionally
informative.

http://http.cs.berkeley.edu/~wkahan/

Gennadiy's floating_point_comparison looks to me what most testers need.
(Though I would express the tolerance in terms of number of epsilons as
some of operations might be expected to cancel (but see Prof Kahan's
examples "The Improbability of Probabilistic Error Analyses for numerical
computations", W. Kahan. in http://http.cs.berkeley.edu/~wkahan/improber.pdf
when it doesn't work out with a normal distribution, so it isn't always
sqrt(no_of_operations) as a random distribution might.

ieee754.ps gives a depressing view (from 1996) on using 754 hardware to the
full,
in that we seem to have made neglible progress in the five years since then!

Paul

> -----Original Message-----
> From: Fernando Cacciola [mailto:fcacciola_at_[hidden]]
> Sent: Friday, December 14, 2001 3:58 PM
> To: boost_at_[hidden]
> Subject: RE: [boost] Re: Floating Point comparisons
>
>
>
> ----- Original Message -----
> From: Paul A. Bristow <boost_at_[hidden]>
> To: <boost_at_[hidden]>
> Sent: Friday, December 14, 2001 7:02 AM
> Subject: RE: [boost] Re: Floating Point comparisons
>
>
> > I have tried to read up reference 3 on the Boost Test Library: Floating
> > Point Comparison.
> >
> > Knuth, D E, Vol III,
> >
> > in the hope that the jacket puff by Jonanthan Laventhol
> >
> > "It's always a pleasure when a problem is hard enough that you
> have to get
> > the Knuths of the shelf.  I find that merely opening one has a
> very useful
> > terrorising effect on computers."
> >
> > would work,
> >
> > but did not find anything in the index that looked relevant - only the
> Quote
> >
> > "If you don't find it in the index look very carefully through
> the entire
> > catalogue" - Consumers Guide, Sears, Roebuck & Co (1897)"
> >
> > Can you or Gennadiy give a more detailed reference please!
> >
> I recently found these papers on the web.
> I have only scanned them, not actually read them, but I think
> they can help
> us understand the issues about FP rounding.
>
> "Rounding Near Zero", U. Kulisch.
> "From Rounding Error Estimation to Automatic Correction with Automatic
> Differentiation", P. Langlois.
> "The Improbability of Probabilistic Error Analyses for numerical
> computations", W. Kahan.
> "Roundoff degrades an Idealized Cantilever", W. Kahan.
>
> I loose track of were I got them, though.
> If you and Gennadiy (or anyone else) want it I'll email them privately.
> (I got them from the public domain so I figure that it is OK to give them
> away).
>
> Fernando Cacciola
> Sierra s.r.l.
> fcacciola_at_[hidden]
> www.gosierra.com
>
>
>
>
>
>
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