Project 47: Guaranteed Accuracy arithmetic At present this project is working on Interval Arithmetic and Complete Arithmetic. ----------------------------------------------------------------------- Oxford 2016: ============ ADDENDUM The standard for interval arithmetic has been made available as "1788-2015 - IEEE Standard for Interval Arithmetic" on http://standards.ieee.org/findstds/standard/1788-2015.html A subset of that standard is in preparation. ----------------------------------------------------------------------- ----------------------------------------------------------------------- Information from meetings before 2016 (in chronological order): ----------------------------------------------------------------------- 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 https://wg25.taa.univie.ac.at/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: ============= 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 https://wg25.taa.univie.ac.at/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 https://wg25.taa.univie.ac.at/ifip/projects/Leuven1.pdf and a poster as https://wg25.taa.univie.ac.at/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. Vienna 2014: ============ There was a technical presentation "Computer-assisted proofs in floating-point" by Rump at the Workshop associated with the WG 2.5 business meeting. Amsterdam 2023: =============== 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.