Interval Arithmetic and Standardization

Abstract

Interval arithmetic is arithmetic for continuous sets. Floating-point intervals are intervals of real numbers with floating-point bounds.
Operations for intervals can be efficiently implemented. There is an unanimous agreement, how to define the basic operations,
if we exclude division by an interval containing zero. Hence, it should be standardized.
For division by zero, two options are possible, the clean exception free interval arithmetic or the containment arithmetic. 
They can be standardized as options.
Elementary functions for intervals can be defined. In some application areas loose evaluation of functions, 
i.e. evaluation over an interval which is not completely contained in the function domain, is recommended, 
In this case, however, a discontinuity flag has to be set to inform that Brouwer's fixed point theorem is no longer applicable in that case.