Extended Interval Arithmetic in IEEE Floating-Point Environment

This paper describes an implementation of a general interval arithmetic extension, which comprises the following extensions of the conventional interval arithmetic: (1) extension of the set of normal intervals by improper intervals; (2) extension of the set of arithmetic operations for normal intervals by nonstandard operations; (3) extension by infinite intervals. We give a possible realization scheme of such an universal interval arithmetic in any programming environment supporting IEEE floating-point arithmetic. A PASCAL-XSC module is reported which allows easy programming of numerical algorithms formulated in terms of conventional interval arithmetic or of any of the enlisted extended interval spaces, and provides a common base for comparison of such numerical algorithms.