Latest Developments on the IEEE 1788 Effort for the Standardization of Interval Arithmetic

(Standardization effort supported by the INRIA D2T.)International audienceInterval 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

Dagstuhl News January - December 2008

"Dagstuhl News" is a publication edited especially for the members of the Foundation "Informatikzentrum Schloss Dagstuhl" to thank them for their support. The News give a summary of the scientific work being done in Dagstuhl. Each Dagstuhl Seminar is presented by a small abstract describing the contents and scientific highlights of the seminar as well as the perspectives or challenges of the research topic

Discussions on an Interval Arithmetic Standard at Dagstuhl Seminar 08021

Efforts have been made to standardise interval arithmetic 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 interval arithmetic (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 interval arithmetic. One such study is [3], a systematization of the options. Another, with a particular point of view, is Prof. Kulisch’s contribution to this volume. Extended arithmetic remain