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.