We give the results of our search for the worst cases for correct rounding of themajor elementary functions in double precision floating-point arithmetic. These results allow the design of reasonably fast routines that will compute these functions with correct rounding, at least in some interval, for any of the four rounding modes specified by the IEEE-754 standard. They will also allow one to ...

Exact rounding of numbers and functions is a fundamental computational problem. This paper introduces the mathematical and computational foundations for exact rounding. We show that all the elementary functions in ISO standard (ISO/IEC 10967) for Language Independent Arithmetic can be exactly rounded, in any format, and to any precision. Moreover, a priori complexity bounds can be given for the...

The aim of this paper is to study integer rounding properties of various systems of linear inequalities to gain insight about the algebraic properties of Rees algebras of monomial ideals and monomial subrings. We study the normality and Gorenstein property—as well as the canonical module and the a-invariant—of Rees algebras and subrings arising from systems with the integer rounding property. W...