Roundings in floating point arithmetic.

In this paper we discuss directed roundings and indicate how hardware might be designed to produce proper upward-directed, downward-directed, and certain commonly used symmetric roundings. Algorithms for the four binary arithmetic operations and for rounding are presented, together with proofs of their correctness; appropriate formulas for a priori error analysis of these algorithms are presented. Some of the basic applications of directed roundings are surveyed. [ABSTRACT FROM PUBLISHER]