Latest Developments on the IEEE 1788 Effort for the Standardization of Interval ArithmeticReport as inadecuate




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* Corresponding author 1 ARIC - Arithmetic and Computing Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l-Informatique du Parallélisme

Abstract : Interval arithmetic undergoes a standardization effort started in 2008 by the IEEE P1788 working group. The structure of the proposed standard is presented: the mathematical level is distinguished from both the implementation and representation levels. The main definitions are introduced: interval, mathematical functions, either arithmetic operations or trigonometric functions, comparison relations, set operations. While developing this standard, some topics led to hot debate. Such a hot topic is the handling of exceptions. Eventually, the system of decorations has been adopted. A decoration is a piece of information that is attached to each interval. Rules for the propagation of decorations have also been defined. Another hot topic is the mathematical model used for interval arithmetic. Historically, the model introduced by R. Moore in the 60s covered only non-empty and bounded intervals. The set-based model includes the empty set and unbounded intervals as well. Tenants of Kaucher arithmetic also insisted on offering -reverse- intervals. It has eventually been decided that an implementation must provide at least one of these flavors of interval arithmetic. The standard provides hooks for these different flavors. As the preparation of the draft should end in December 2013, no chapter is missing. However, a reference implementation would be welcome.

Keywords : interval arithmetic standardization arithmetic operations set theory exception handling





Author: Nathalie Revol -

Source: https://hal.archives-ouvertes.fr/



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