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Am 21.04.2015 um 22:36 schrieb Oliver
Heimlich:
The only place, where IEEE 754 specific arithmetic is actually used in the standard document, is in chapter 12.12.12 (reduction operations on IEEE 754 data types), where arithmetic with NaNs and signed zeros is required. Again, this only applies if the implementation supports IEEE 754 data types.Oliver Heimlich Comment: The entire section 12.12.12. Reduction operations would be superfluous if in the section 12.13.5 Exact reduction operations the should would be replaced by shall. All operations in 12.12.12. would then be simple consequences. The logic behind all this: We have two problems: Problem A: compute dot products exactly, Problem B: compute dot products correctly rounded. Evidently a method that solves A also solves B. The opposite is not true! Problem B looks simpler than problem A. So P1788 requires B. But in fact solving A is much simpler and faster than all known solutions of B that ignore A. In the document P1788 the dot product should already be mentioned in 4.2 Definitions, in particular in: 4.2.6. arithmetic operations. A basic arithmetic operation is one of the seven fuctions +, -, ×, ÷, fused multiply add (fma), dot product (dot), and square root (sqrt). There is no reason why the dot product should be given less weight than fused multiply-add, and there are good reasons for listing it under basic arithmetic operations (speed and accuracy). In an early draft of P1788 it was indeed listed here. The dot product is a fundamental operation in Numerical Analysis. It allows a simple and very fast implementation on computers. The exact dot product is the key operation for variable precision interval and floating-point arithmetic. It would be a highlight of P1788. Best wishes Ulrich -- 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 |