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Dear
colleagues,
I apologize for repeating myself. But I view Ned Nedialkov's motion as a late chance to correct mistakes that have been made during the development of a standard for interval arithmetic. Interval arithmetic developed over the real and floating-point numbers R and F leads to a closed and exception-free calculus CIRF. An exact dot product (EDP) brings speed and accuracy to CIRF. 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 of floating-point numbers or floaating-point intervals can be faster. It is computed by fixed-point accumulation of the summands (products) into a small local register memory on the arithmetic unit. An implementation at Karlsruhe in 1993 computed the EDP 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. So let's add the requirement of an EDP to Ned's motion. In contrast to CIRF, IEEE 1788 develops interval arithmetic over the set of IEEE 754 numbers. Since these include R and F this leads to a superset SIRF of CIRF. But it pulls all the exceptions of IEEE 754 into interval arithmetic. Much of the recent discussion within IEEE 1788 deals with elements and operations of the set SIRF\CIRF. Since CIRF is a complete, closed calculus any discussion of elements and operations of SIRF\CIRF is questionable. They do not occur for computations in CIRF. So in my opinion developing interval arithmetic over SIRF is a mistake. It unnecessarily complicates interval analysis and carries a high potential of becoming a serious hindrance for its further development. For more details see my mail to Baker Kearfot of Nov 28, 2015, my vote on Motion P1788.1/M002 of Nov. 8, 2015 and my books [1] and [2], in particular Chapter 1 in the book [1] or Chapter 8 in the book [2]. For applications see Chapter 9 in [2] [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. With best regards Ulrich Kulisch Am 12.01.2016 um 15:37 schrieb Nathalie Revol: Dear Colleagues I am afraid I forgot to launch the discussion period before the Christmas break. I suggest a 2-weeks discussion period, as there seems to be no opposition to this amendment (seconded by Michel Hack). The discussion period starts now and ends Tuesday, January 26, when the voting period begins. Best wishes for a Happy New Year! Best regards Nathalie -- 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 |