Reduction of Look Up Tables for Computation of Reciprocal of Square Roots

TL;DR

This paper proposes methods to reduce the size of look-up tables used for initial approximations in algorithms computing reciprocal square roots, aiming to optimize hardware efficiency without compromising convergence speed and accuracy.

Contribution

The paper introduces novel techniques to minimize LUT size for reciprocal square root calculations, enhancing hardware efficiency and maintaining acceptable convergence performance.

Findings

Significant reduction in LUT size achieved

Maintained convergence speed with smaller LUTs

Improved hardware efficiency in reciprocal square root computation

Abstract

Among many existing algorithms, convergence methods are the most popular means of computing square root and the reciprocal of square root of numbers. An initial approximation is required in these methods. Look up tables (LUT) are employed to produce the initial approximation. In this paper a number of methods are suggested to reduce the size of the look up tables. The precision of the initial approximation plays an important role in the quality of the final result. There are constraints for the use of a LUT in terms of its size and its access time. Therefore, the optimization of the LUTs must be done in a way to minimize hardware while offering acceptable convergence speed and exactitude.