Popova, E. D.: Extended Interval Arithmetic in IEEE
Floating-Point Environment.
Interval Computations, No 4, 1994, pp. 100-129.
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
- extension of the set of normal intervals by improper intervals;
- extension of the set of arithmetic operations
for normal intervals by nonstandard operations;
- 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.