SRT Division Algortihms as Dynamical Systems

Authors

Mark McCann, University of British Columbia
Nicholas J. Pippenger, Harvey Mudd CollegeFollow

Document Type

Conference Proceeding

Department

Mathematics (HMC)

Publication Date

6-2003

Abstract

SRT division, as it was discovered in the late 1950s represented an important improvement in the speed of division algorithms for computers at the time. A variant of SRT division is still commonly implemented in computers today. Although some bounds on the performance of the original SRT division method were obtained, a great many questions remained unanswered. The original version of SRT division is described as a dynamical system. This enables us to bring modern dynamical systems theory, a relatively new development in mathematics, to bear on an older problem. In doing so, we are able to show that SRT division is ergodic, and is even Bernoulli, for all real divisors and dividends. With the Bernoulli property, we are able to use entropy to prove that the natural extensions of SRT division are isomorphic by way of the Kolmogorov-Ornstein theorem. We demonstrate how our methods and results can be applied to a much larger class of division algorithms.

Rights Information

© 2003 IEEE

DOI

10.1109/ARITH.2003.1207659

Recommended Citation

McCann, Mark and Nicholas Pippenger. "SRT Division Algorithms as Dynamical Systems." Proc. IEEE Symp. on Comp. Arithmetic, 16 (2003), 46-53.