Foundations of Exact Rounding

Authors:
Chee K. Yap;Jihun Yu
Affiliations:
Department of Computer Science Courant Institute of Mathematical Sciences, New York University, New York, NY 10012;Department of Computer Science Courant Institute of Mathematical Sciences, New York University, New York, NY 10012
Venue:
WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
Year:
2009

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Abstract

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 these rounding problems. Our conclusions are derived from results in transcendental number theory.