FLOATING POINT EXCEPTION HANDLING FOR INTERVAL ARITHMETIC

Abstract

This chapter describes the floating point exception handling for interval arithmetic. The requirement for rigorous bounds in interval arithmetic leads inevitably to the consideration of what should be done when floating point exceptions occur. An example of such a situation would be when the attempt to apply a directed rounding to a number fails for want of a valid bound in the set of machine representable numbers. The chapter presents a proposal for a scheme for floating point exception handling that seems to fall about midway between the two extremes. This proposal is relatively straightforward, and it allows for representation of signed infinitesimals and infinities as required for conventional interval arithmetic, and yet at the same time, it allows Kahans gradual underflow to be implemented if desired. This proposal does require a slight restriction on the range of floating point numbers. The chapter also describes the operations on the extended number set.