High-radix iterative algorithm for powering computation

A high-radix composite algorithm for the computation of the powering function (X^Y) is presented. The algorithm consists of a sequence of overlapped operations: (i) digit-recurrence logarithm, (ii) left-to-right carry-free (LRCF) multiplications, and (iii) online exponential. A redundant number system is used, and the selection in (i) and (iii) is done by rounding except from the first iteration, when selection by table look-up is necessary to guarantee the convergence of the recurrences. A sequential implementation of the algorithm is proposed, and the execution times and hardware requirements are estimated for single and double-precision floating-point computations, for radix r=128, showing that powering can be computed with similar performance as high-radix CORDIC algorithms.