Sv: Re: Motion 31: V04.2 Revision of proposed Level 1 text
I totally agree with the opinion expressed by Ulrich Kulish!
Best regards,
Bo
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Bo Einarsson
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SWEDEN
Tel 013 - 151896
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----Ursprungligt meddelande----
Från: Ulrich.Kulisch@xxxxxxxxxxx
Datum: 2012-02-07 19:38
Till: "John Pryce"<j.d.pryce@xxxxxxxxxxxx>
Kopia: "stds-1788"<stds-1788@xxxxxxxxxxxxxxxxx>
Ärende: Re: Motion 31: V04.2 Revision of proposed Level 1 text
Am 07.02.2012 13:08, schrieb John Pryce:
> Ulrich, Vincent
>
> On 26 Jan 2012, at 13:02, Vincent Lefevre wrote:
>
>> On 2012-01-25 12:00:38 +0000, John Pryce wrote:
>>> I send herewith a revised draft of the proposed Level 1 text, less
>>> decorations, that I originally circulated on 5 Dec 2011.
>> About the basic arithmetic operations:
>> ...
>> But why is the dot product included in the basic arithmetic
operations?
>> I don't see it as important as +, -, *, /. And not more important
than
>> recip, sqr, case, pown, abs, and perhaps some other operations.
> Ulrich: on reflection I agree with Vincent. However useful the dot
product is, it is essentially more complicated than +, -, *, /. I think
calling it "basic" will cause more disagreement than agreement, so I
have removed it from those lists.
>
> John P
>
John,
I totally disagree with this decision. I am very busy with other
things
right now. But let me simply remind you that the IFIP Working Group on
Numerical Software required the exact dot product by a letter to the
standards committee IEEE 754R (dated Sept. 4, 2007) and by another
letter to IEEE P1788 (dated Sept. 9, 2009). I attach copies of these
letters to this mail.
I also disagree with the statement that the exact dot product is
essentially more complicated than +, -, *, /.
Actually the *simplest* and *fastest* way for computing a dot product
is
to compute it exactly! By pipelining, it can be computed in the time
the
processor needs to read the data, i.e., it comes with utmost speed. No
software simulation can compete with a simple and direct hardware
solution. I attach a copy of the poster that I prepared for the
SCAN-Meeting at Lyon in 2010.
let me finally mention that the following is shown in my book
'Computer
Arithmetic and Validity', de Gruyter 2008. With the two requirements
of
the IFIP Working Group letter to IEEE 754R: Fast hardware support for
interval arithmetic and the exact dot product, all operations in the
usual product spaces of computation, the complex numbers, the real and
complex intervals, the real and complex vectors and matrices, and the
real and complex interval vectors and interval matrices can be
computed
with least bit accuracy and at very high speed. These operations are
distinctly different from those traditionally available on computers.
This would boost both the speed of a computation and the accuracy of
its
result.
Best regards
Ulrich
--
Karlsruher Institut für Technologie (KIT)
Institut für Angewandte und Numerische Mathematik (IANM2)
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-Gemeinschaft