Issue No.07 - July (2000 vol.49)
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/12.863046
<p><b>Abstract</b>—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 <tmath>$G_m$</tmath> the Goldschmidt algorithm with <tmath>$m$</tmath> iterations, our variants allow us to reach an accuracy that is between that of <tmath>$G_3$</tmath> and that of <tmath>$G_4$</tmath>, with a number of cycle equal to that of <tmath>$G_3$</tmath>.</p>
Division, square root, square root reciprocal, convergence division, computer arithmetic, Goldschmidt iteration.
Laurent Imbert, David W. Matula, Jean-Michel Muller, Milos D. Ercegovac, "Improving Goldschmidt Division, Square Root, and Square Root Reciprocal", IEEE Transactions on Computers, vol.49, no. 7, pp. 759-763, July 2000, doi:10.1109/12.863046