Dear Sirs.
I agree with Motion P1788.1/M002.01.
Nevertheless, I considered the arguments given by prof. Ulrich Kulisch once again.
I find his remark about the dot product essential.
Hence, only because of this point I vote NO.
With kind regards
Malgorzata Jankowska
Od: "Ulrich Kulisch" <ulrich.kulisch@xxxxxxx>
Do: "stds-1788" <stds-1788@xxxxxxxxxxxxxxxxx>
Wysłane: niedziela, 8 listopad 2015 8:36:50
Temat: Motion P1788.1/M002.01: Required operations
My vote is NO.
I would vote YES if in Table 4.1 under Basic operations after fma(x,y,z) the dot product of two vectors woulld be added.
In Numerical and Interval Analysis the dot product is ubiquitous. It appears in matrix and matrix-vector multiplication. It is the key operation of defect correction or iteratve refinement methods as well as of fast long real and long interval arithmetic.
The dot product brings high speed and accuracy to Numerical and Interval Analysis. By pipelining it can be computed in the time the processor needs to read the data, i.e., it is computed at extreme speed. No other method accumulating products or numbers can be faster. It is computed by fixed-point accumulation of the summands (products) into a small local register memory on the arithmetic unit.
A VLSI implementation at Karlsruhe in 1993 computed the exact dot product in 1/4 of the time the Intel processor needed for computing a possibly wrong result in conventional floating-point arithmetic. A corresponding implementation at Berkeley in 2015 even reaches a speed increase by a factor of 6. High speed and accuracy are essential for acceptance and success of interval methods.
For more details on the implementation see Chapter 1 in the book [1] or Chapter 8 in the book [2]. For applications see Chapter 9 in [2] and/or the Toolbox Volumes of the XSC-Languages [3, 4, 5].
[1] U. Kulisch, Advanced Arithmetic for the Digital Computer -- Design of Arithmetic Units. Springer ISBN 3-211-83870-8, 2002. See Chapter 1, in particular.
[2]. U. Kulisch, Computer Arithmetic and Validity – Theory, Implementation, and Applications, de Gruyter, Berlin, 2008, ISBN 978-3-11-020318-9, second edition 2013, ISBN 978-3-11-030173-1. See Chapter 8, in particular.
[3] IBM, ACRITH–XSC: IBM High Accuracy Arithmetic – Extended Scientific Computation.
Version 1, Release 1, IBM Deutschland GmbH (Department 3282, Schoenaicher
Strasse 220, D-71032 Boeblingen), 1990.
1. General Information, GC33-6461-01.
2. Reference, SC33-6462-00.
3. Sample Programs, SC33-6463-00.
4. How To Use, SC33-6464-00.
5. Syntax Diagrams, SC33-6466-00.
[4] R. Hammer, M. Hocks, U. Kulisch and D. Ratz, Pascal-XSC Toolbox for Verified Computing
I: Basic Numerical Problems, Springer, Berlin Heidelberg New York, 1993.
[5] R. Hammer, M. Hocks, U. Kulisch and D. Ratz, C++ Toolbox for Verified Computing:
Basic Numerical Problems. Springer, Berlin Heidelberg New York, 1995.
Updated versions of [4] and [5] are freely available via: http://www.math.uni-wuppertal.de/˜xsc/ or http://www.xsc.de/.
--
Karlsruher Institut für Technologie (KIT)
Institut für Angewandte und Numerische Mathematik
D-76128 Karlsruhe, Germany
Prof. Ulrich Kulisch
KIT Distinguished Senior Fellow
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