Thread Links Date Links
Thread Prev Thread Next Thread Index Date Prev Date Next Date Index

Re: IEEEP1788

Am 29.04.2015 um 17:49 schrieb Ulrich Kulisch:

Am 27.04.2015 um 20:09 schrieb Michel Hack:

On Mon, 27 Apr 2015 18:16:34 +0200 Ulrich Kulisch wrote:

The dot product is a fundamental operation in Numerical Analysis.  It
allows a simple and very fast implementation on computers. *The exact
dot product* is the key operation for variable precision interval and
floating-point arithmetic.  It would be a highlight of P1788.

Few people would disagree with the above.

As I see it, the issue is that simply including the exact dot product
would be woefully incomplete without also including a discussion of
the complete format as an arithmetic number format, and a couple of
other operations on complete numbers.  If the only operation is to
convert a complete-format number to a floating-point number, then
we would have achieved nothing more than what is already required,
namely a correctly-rounded dot product.

Unfortunately the group did not want to include a whole chapter on
Complete Arithmetic, as that would have gone beyond the approved PAR.
(If I remember correctly, there was an earlier proposal in 2008 that
did include Complete Arithmetic.)

Michel.
---Sent: 2015-04-27 18:23:30 UTC
Yes, I sometimes felt that there is some ghost behind the scene whose only interest is to keep essential tools for success of interval arithmetic out of P1788. Sharp evaluation of expressions or complete arithmetic are such tools. For a simple example see, for instance, Sample 1: Computing the Frobenius Norm, in IBM's little brochure "Sample Programs" pp. 6 and 7 in [33] in the references of the attached paper (not yet published). We provided such tools in Pascal-XSC since 1980 and also in C-XSC, see [9] to [14]. 

Best wishes
Ulrich




SORRY, I forgot the attachment.

--
Karlsruher Institut für Technologie (KIT)
Institut für Angewandte und Numerische Mathematik
D-76128 Karlsruhe, Germany
Prof. Ulrich Kulisch

Telefon: +49 721 608-42680
Fax: +49 721 608-46679
E-Mail: ulrich.kulisch@xxxxxxx
www.kit.edu
www.math.kit.edu/ianm2/~kulisch/

KIT - Universität des Landes Baden-Württemberg
und nationales Großforschungszentrum in der
Helmholtz-Gesellschaft

Attachment: UMath4.pdf
Description: Adobe PDF document