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Back in the 60's Goldschmidt presented a variation of Newton-Raphson iterations for division that is well suited for pipelining. The problem in using Goldschmidt's division algorithm is to present an error analysis that enables one to save hardware by using just the right amount of precision for intermediate calculations while still providing correct… (More)

One can naively view a computer number system as a pair (F, P) consisting of a finite set F of real numbers and a rounding rule P. One such number system is a hyperbolic rational number system which has as F a finite set of rational numbers and as P the so-called mediant rounding rule. In this paper we demonstrate how one can simulate a hyperbolic rational… (More)

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