Rigorous High Precision Interval Arithmetic in COSY INFINITY

Abstract

In this paper we present our implementation of a complete multiple machine precision interval package in FORTRAN 77. The operations are designed to perform optimally with up to about 100 significant digits. The implementation only requires IEEE 754 compliant floating point operations, and thus is highly portable to virtually any modern computer platform.

Intervals are stored as unevaluated floating point sums. Elementary operations such as addition and multiplication are based on exact floating point operations, while higher level operations such as division and square root are implemented based on those elementary operations. While there are several other non-rigorous high precision libraries based on these concepts, to the best of our knowledge this implementation is the first fully rigorous interval package.

Besides basic operations on high precision intervals, the library also provides a wide range of verified intrinsic functions such as sin, arctan, and ln. The library is integrated into a sepcial version of the COSY INFINITY rigorous computation environment, providing fast and rigorous interval operations from within the COSY environment.

A. Wittig, M. Berz, Proceedings of the Fields Institute, in print

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