High-radix logarithm with selection by rounding

Abstract

A high-radix digit-recurrence algorithm or the computation of the logarithm is presented in this paper. Selection by rounding is used in iterations j/spl ges/2, and selection by table in the first iteration is combined with a restricted digit-set for the second one, in order to guarantee the convergence of the algorithm. A sequential architecture is proposed. and the execution time and hardware requirements of this architecture are estimated, for a target precision of n=32 bits and a radix r=256. These estimates are obtained according to a rough model for the delay and area cost of the main logic blocks employed, and show the achievement of a speed-up by over 4 times with regard to a conventional radix-2 implementation with redundant arithmetic.