Report Number: CSL-TR-96-700
Institution: Stanford University, Computer Systems Laboratory
Title: Fast IEEE Rounding for Division by Functional Iteration
Author: Oberman, Stuart F.
Author: Flynn, Michael J.
Date: July 1996
Abstract: A class of high performance division algorithms is functional
iteration. Division by functional iteration uses
multiplication as the fundamental operator. The main
advantage of division by functional iteration is quadratic
convergence to the quotient. However, unlike non-restoring
division algorithms such as SRT division, functional
iteration does not directly provide a final remainder. This
makes fast and exact rounding difficult. This paper clarifies
the methodology for correct IEEE compliant rounding for
quadratically-converging division algorithms. It proposes an
extension to previously reported techniques of using extended
precision in the computation to reduce the frequency of back
multiplications required to obtain the final remainder.
Further, a technique applicable to all IEEE rounding modes is
presented which replaces the final subtraction for remainder
computation with very simple combinational logic.