Discussions on an Interval Arithmetic Standard at Dagstuhl Seminar 08021

R. Baker Kearfott 1 John D. Pryce 2 Nathalie Revol 3
3 ARENAIRE - Computer arithmetic
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : Efforts have been made to standardize interval arithmetic (IA) for over a decade. The reasons have been to enable more widespread use of the technology, to enable more widespread sharing and collaboration among researchers and developers of the technology, and to enable easier checking that computer codes have been correctly programmed. During the late 1990's, the first author of this report led such a project to introduce an interval data type into the Fortran language. One reason for failure of that effort was the Fortran language standardization committee's lack of familiarity with interval technology and consequent caution. Another was misunderstanding between the Fortran standardization committee's basic tenets on standardizing interline optimization and some views expressed by members of the interval analysis community. A third was confusion over how extended IA (arithmetic dealing with division by intervals that contain zero) should be handled. This was coupled with a heavy committee load associated with other projects, such as standardizing an interface for interoperability with "C" language programs. Since then, the interval analysis community has studied and gained additional understanding of extended IA. One such study is a systematization of the options (Pryce and Corliss, Computing 2006). Another, with a particular point of view, is Prof. Kulisch's contribution to this volume. Extended arithmetic remains a controversial part of efforts to standardize the arithmetic, particularly whether the underlying model should consider -infinity and +infinity to be numbers in their own right or if -infinity and +infinity should just be considered placeholders to describe unbounded sets of finite real numbers. A practical consequence is a difference in the value of 0 × X when X is an unbounded interval. Nonetheless, our understanding and thinking about this issue is clearer than a decade ago. This, coupled with the desire to have a standard, should lead to progress.
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R. Baker Kearfott, John D. Pryce, Nathalie Revol. Discussions on an Interval Arithmetic Standard at Dagstuhl Seminar 08021. Dagstuhl Seminar 08021: Numerical Validation in Current Hardware Architectures, Cuyt, Annie and Krämer, Walter and Luther, Wolfram and Markstein, Peter, Jan 2008, Dagstuhl, Germany. pp.1-6, ⟨10.1007/978-3-642-01591-5_1⟩. ⟨inria-00545059⟩

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