Exploiting fast hardware floating point in high precision computation

Authors:
Keith O. Geddes;Wei Wei Zheng
Affiliations:
University of Waterloo, Waterloo, ON, Canada;University of Waterloo, Waterloo, ON, Canada
Venue:
ISSAC '03 Proceedings of the 2003 international symposium on Symbolic and algebraic computation
Year:
2003

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Abstract

We apply an iterative refinement method based on a linear Newton iteration to solve a particular group of high precision computation problems. The method generates an initial solution at hardware floating point precision using a traditional method and then repeatedly refines this solution to higher precision, exploiting hardware floating point computation in each iteration. This is in contrast to direct solution of the high precision problem completely in software floating point. Theoretical cost analysis, as well as experimental evidence, shows a significant reduction in computational cost is achieved by the iterative refinement method on this group of problems.