Project 47: Guaranteed Accuracy arithmetic
At present this project is working on Interval Arithmetic and Complete
Arithmetic.
Pasadena 1984:
==============
Reid has received a letter of excuse from Kulisch who intended to
talk on ACRITH, the IBM new program package based on Kulisch-Miranker
arithmetic and the system 4361 which performs it in hardware.
Sophia-Antipolis 1985:
======================
Accurate arithmetic and ACRITH (Kulisch)
----------------------------------------
After a short discussion of Kulisch's presentation, the topic was
widened to include ACRITH (see document IFIP/WG 2.5 (Sophia-
Antipolis-07) 1207), which raised a technical discussion.
Cody made the following statement: "We must distinguish between
our roles as individuals, and our roles as members of this
committee. As committee members, we should be concerned if and when
the committee's actions are improperly used, or are misrepresented.
Such transgressions are best quietly handled whenever possible.
But this committee is not a judicial body; it is not charged with
the responsibility of sitting in technical judgement of anyone's
work. In my opinion, the technical dispute involving ACRITH does
not involve WG 2.5, and is none of our business. I do not believe
it is a proper matter for discussion here."
Kulisch said that he intended to reply personally to Kahan's
remarks. The group decided that we owe an answer to Kahan written
by Reid (see document IFIP/WG 2.5 (Sophia-Antipolis-06) 1206).
Como 1987:
==========
Document: IFIP/WG 2.5 (Como-26) 1426, 1 page.
Kulisch described the guaranteed accuracy effort pursued by GAMM
through their proposal that elementary compound operations be
implemented in such a way that guaranteed bounds are delivered for the
deviation of the floating-point result from the exact result.
During the discussion Gentleman noted that his experience with
interval arithmetic was less than encouraging. Kulisch said that,
while it is not easy to use, interval arithmetic may be very useful.
The GAMM effort is not aimed at producing a new standard but at
enabling computation of error propagation for vector processors. It
was noted that there are currently problems with arithmetic on some
supercomputers, and that perhaps WG 2.5 should encourage manufacturers
to consider the GAMM proposal (Ford, Dekker).
Stanford 1988:
==============
Activities on the project include the work on Pascal-SC and
FORTRAN-SC, there is an annual conference on guaranteed accuracy
arithmetic, the DIAMOND project is a continuing, etc.
B. Ford offered to prepare a paper on Prof. Kahan's work for the next
meeting.
Beijing 1989:
=============
Kulisch reported on the recent developments with Pascal-SC and
Fortran-SC.
Jerusalem 1990:
===============
Kulisch reported on the recent developments with Pascal-SC and
Fortran-SC with emphasis on the work of moving Pascal-SC into Unix
environment. Bercovier noted that CAS CAM projects could benefit from
interval arithmetic.
Project [61] was merged into [47] on Vouk's suggestion.
Oxford 1996:
===========
This will remain active, Kulisch and Walter will prepare a descriptive
paragraph with input from Ford. Consider pointers to related work in
symbolic systems. Delete Vouk and add Walter to people list.
Amsterdam 2001:
===============
Walter led a brief discussion of this project. There is a need for
improved hardware that is not being addressed by industry. Market
forces are driving HW developments and the current focus of these
forces is on faster chips with more cache (and not on better
features).
Portland 2002:
==============
Some discussion of activity in this area took place. Boisvert gave
examples of the need for such facilities that arose in the NIST
mathematical handbook project. In this project some physical constants
needed to be computed to very high accuracy (over a range of parameter
values) and there was a need to provide this project with facilities
to compute accurate solutions with guaranteed error bars.
Kulisch gave a presentation "Hardware support for interval arithmetic
and basic features of mathematical software".
Strobl 2003:
============
While there was no new information presented, Kulisch assured the group
that it was still an active area and several members of the group were
participating in related activities.
Washington 2004:
================
Ulrich Kulisch is writing a new book on computer arithmetic and other
members are also participating in this active research area.
Hong Kong 2005:
===============
Ulrich Kulisch's new book on computer arithmetic appeared earlier this
year.
Prescott 2006:
==============
There was no report although the project remains active with Kulisch
and others involved in recent activities. Einarsson's review of the
revised IEEE floating point standard is a report on a related activity
(see project 25).
Uppsala 2007:
=============
The technical talks by Kulisch "Hardware Support for Interval
Arithmetic" and Einarsson "Revised IEEE 754 Floating Point Standard"
are reports of recent activities. Kulisch has published a new book on
interval arithmetic. Einarsson reported the status of the latest
draft of the revised IEEE 754 standard. Some of our earlier
suggestions have been ignored and Kulisch and others have written to
ask for changes. It was agreed that the WG would send a letter from
Boisvert to the standards committee providing support for some of the
specific suggestions of Kulisch and others.
The proposed revision of IEEE 754 was discussed in Uppsala and it was
decided to send a letter expressing the views of the working group to
the IEEE Microprocessor Standards Committee.
The final letter is available on the internal pages as
http://www.nsc.liu.se/%7Eboein/ifip/intern/IFIPWG-IEEE754R.pdf
Toronto 2008:
=============
The technical talk by Kulisch and Einarsson "Computer Arithmetic
Standards" is a report of recent activities. Kulisch has published a
new book on computer arithmetic. Einarsson discussed a new floating
point standard combining binary and decimal standards and extending
the coverage to quadruple precision. Some members are also active in
the new IEEE group now working on standards for interval arithmetic.
Snyder, Kulisch and Einarsson are very active and are contributing to
the developments in this important area. Members endorsed their work
and passed a motion strongly supporting the initiatives they are
advocating.
Raleigh 2009:
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The technical talk by Snyder "Complete Arithmetic" is a report of
recent activities. Three members (Kulisch, Snyder, Einarsson) are
active in the IEEE working group P1788 on standards for interval
arithmetic. It was decided to send a letter to this group supporting
the idea of including complete arithmetic in the standard.
The final letter is available on the internal pages as
http://www.nsc.liu.se/~boein/ifip/intern/IFIPWG-IEEE-P1788.pdf
The letter has been well received, including suggestions not only
to provide an exact dot product but also variants like exact sum
and exact sum of squares and exact sum of absolute values.
The motion 5.02 "Arithmetic operations for intervals" from Kulisch and
Einarsson has been passed by the IEEE P1788 group.
The motion 9.01 "Exact Dot Product" from Kulisch and
Einarsson has been passed by the IEEE P1788 group.
Leuven 2010:
============
Ulrich Kulisch spoke on "Interval Arithmetc Standardization Activity",
that is IEEE P1788. The work is progressing slowly but the views of
IFIP WG 2.5 are usually accepted.
In particular, Kulisch reported that the recommendation of WG 2.5 for the
inclusion of an exact dot product was accepted by the IEEE Interval
Arithmetic Working Group for inclusion in their draft standard.
A text document is available as
http://www.nsc.liu.se/~boein/ifip/projects/Leuven1.pdf
and a poster as
http://www.nsc.liu.se/~boein/ifip/projects/Poster22.pdf
Boulder 2011:
=============
Some members remain active in the IEEE 1788 on-going effort to develop a
standard for interval arithmetic.
Santander 2012:
===============
Kulisch reported that he is revising his 2008 book (se below in Documents).
The activities of IEEE 1788 was also discussed by Nathalie Revol
"Tradeoffs between Accuracy and Efficiency for Interval Matrix Multiplication"
at the workshop and "IEEE 1788 standardization of interval arithmetic:
work in progress (a personal view)" at the meeting.
Shanghai 2013:
===============
Recent report by Siegfried M. Rump
Verification methods: Rigorous results using floating-point
arithmetic
The paper Siegfried sent (the Acta Numerica version with corrections)
is available via his webpage as
www.ti3.tu-harburg.de/paper/rump/Ru10.pdf
From the abstract:
A classical mathematical proof is constructed using pencil and
paper. However, there are many ways in which computers may be used in
a mathematical proof. But 'proof by computer', or even the use of
computers in the course of a proof, is not so readily accepted. In
the following we introduce verification methods and discuss how they
can assist in achieving a mathematically rigorous result. In
particular we emphasize how floating-point arithmetic is used.
The activities of IEEE 1788 standardization of interval arithmetic was
discussed by Bo Einarsson, it is making slow progress and will probably
not support complete arithmetic.
Documents:
==========
U. Kulisch, "GAMM-IMACS Proposal for Accurate Floating-Point
Vector Arithmetic", Mathematics and Computers in Simulation, Vol. 35,
No. 4, pp. 375-382, 1993. Also IFIP/WG 2.5 Kyoto-2214.
Ulrich Kulisch, "Computer Arithmetic and Validity", de Gruyter Studies
in Mathematics 33, ISBN 978-3-11-020318-9, Berlin 2008.