ImprovingGoldschmidtDivision,SquareRoot andSquareRootReciprocal

The 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 $G_m$ the Goldschmidt algorithm with $m$ iterations, our variants allow us to reach an accuracy that is between that of $G_3$ and that of $G_4$, with a number of cycle equal to that of $G_3$.