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ARITH
2003
IEEE

SRT Division Algorithms as Dynamical Systems

11 years 5 months ago
SRT Division Algorithms as Dynamical Systems
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. In this paper, 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.
Mark McCann, Nicholas Pippenger
Added 04 Jul 2010
Updated 04 Jul 2010
Type Conference
Year 2003
Where ARITH
Authors Mark McCann, Nicholas Pippenger
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