Improving Goldschmidt Division, Square Root, and Square Root Reciprocal

ÐThe aim of this paper is to accelerate division, square root, and square root reciprocal computations when the Goldschmidt method is used on a pipelined multiplier. This is done by replacing the last iteration by the addition of a correcting term that can be looked up during the early iterations. We describe several variants of the Goldschmidt algorithm, assuming 4-cycle pipelined multiplier, and discuss obtained number of cycles and error achieved. Extensions to other than 4-cycle multipliers are given. If we call Gm the Goldschmidt algorithm with m iterations, our variants allow us to reach an accuracy that is between that of G3 and that of G4, with a number of cycle equal to that of G3. Index TermsÐDivision, square root, square root reciprocal, convergence division, computer arithmetic, Goldschmidt iteration.