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Ian, Richard and others:
Thank you for your mails.
Just have a look at one of the languages [2, 3, 6] in my mail
below. It shows how far it is reasonable to go. PASCL-XSC was the
first one. It served as a model for developing the other two.
As an example let's consider the central task of interval
analysis, computing close bounds for the solution of a system of
linear equations.
First an approximate solution is computed. Then the
Kravczyk-operator with epsilon-inflation for computig a verified
enclosure is applied. If the system has a large condition number
the verificaion step fails. But in contrast to conventional
floating-point arithmetic the routine detects this. Then it
automatically calls a more powerful operator which I call the
Rump-operator in my book. It has been shown by Rump, Oishi, Ogita
and Tanabe that this process even for very ill-conditioned
problems always leads to a highly accurate verified enclosure.
A look at the details (Chapter 9 in my book Computer
Arithmetic and Validity for instance) shows that the
essential ingredient of the entire process is an EDP. Recently two
students at Berkeley showed that the EDP can be computed in 1/6 of
the time that is needed for computing a possibly wrong dot product
in conventional floating-point arithmetic. So it is really worth
fighting to get this extremely useful and fast operation
standardized.
I have nothing against using software packages like MPFR or MPFI
in interval analysis. But for many applications an EDP suffices to
compute close bounds for the solution. In contrast to software
packages it brings accuracy at high speed to interval algorithms.
By the way: In my book interval arithmetic is developed over the
real and floating-point numbers. This leads to an exception-free,
closed calculus. It avoids all the exceptions of the IEEE 754
standard being pulled into interval arithmetic.
Best wishes
Ulrich
Am 21.01.2016 um 21:34 schrieb Ulrich Kulisch:
Am 19.01.2016 um 00:11 schrieb
Richard Fateman:
...................................
I think that niche standards such as 1788 have a limited
opportunity to alter
the computing environment. I expect 1788 to be visible in the
development
and distribution of standards-conforming software libraries. If
EDP is
such a valuable tool for such libraries, implementers should
include it as
an internal component for those routines that benefit from it.
Perhaps it should be made visible as an API to library users.
As far
as I can see, it would not fit neatly into conventional
programming languages.
Richard
Richard:
the problem how to include the EDP into conventional programming
languages has been solved more than 25 years ago. See the
literature listed below. ACRITH-XSC is a Fortran-77 exrension for
the S/370 architecture. [4] describes among others how the EDP is
implemented on the S/370 architecture.
You may find some of the literature in your library.
Best wishes
Ulrich
[1] R. Klatte, U. Kulisch, M. Neaga, D. Ratz and Ch. Ullrich,
PASCAL-XSC – Sprachbeschreibung mit Beispielen,
Springer, Berlin Heidelberg New York, 1991.
See also http://www2.math.uni-wuppertal.de/
xsc/ or http://www.xsc.de/.
[2] R. Klatte, U. Kulisch, M. Neaga, D. Ratz and Ch. Ullrich, PASCAL-XSC
– Language Reference with Examples, Springer,
Berlin Heidelberg New York, 1992.
See also http://www2.math.uni-wuppertal.de/
xsc/ or http://www.xsc.de/.
Russian translation MIR, Moscow, 1995, third edition 2006.
See also http://www2.math.uni-wuppertal.de/
xsc/ or http://www.xsc.de/.
[3] R. Klatte, U. Kulisch, C. Lawo, M. Rauch and A. Wiethoff, C-XSC
– A C++ Class Library for Extended Scientific
Computing, Springer, Berlin Heidelberg New York, 1993.
See also http://www2.math.uni-wuppertal.de/xsc/
or http://www.xsc.de/.
[4] IBM, IBM System/370 RPQ. High Accuracy Arithmetic, SA
22-7093-0, IBM Deutschland GmbH (Department 3282, Sch¨onaicher
Strasse 220, D-71032 B¨oblingen), 1984.
[5] IBM, IBM High-Accuracy Arithmetic Subroutine Library
(ACRITH), IBM Deutschland GmbH (Department 3282,
Sch¨onaicher Strasse 220, D-71032 B¨oblingen), 1983, third
edition, 1986.
1. General Information Manual, GC 33-6163-02.
2. Program Description and User’s Guide, SC 33-6164-02.
3. Reference Summary, GX 33-9009-02.
[6] IBM, ACRITH–XSC: IBM High Accuracy Arithmetic – Extended
Scientific Computation. Version 1, Release 1, IBM
Deutschland GmbH (Department 3282, Sch¨onaicher Strasse 220,
D-71032 B¨oblingen), 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.
--
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
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