A Digit-by-Digit Algorithm for mth Root Extraction
A general digit-recurrence algorithm for the computation of the mth root (with an m integer) is presented in this paper. Based on the concept of completing the mth root, a detailed analysis of the convergence conditions is performed and iterationindependent digit-selection rules are obtained for any radix and redundant digit set. A radix-2 version for mth rooting is also studied, together with closed formulas for both the digit selection rules and the number of bits required to perform correct selections.
keywords: integer rooting, digit-by-digit algorithms, higher radix, computer arithmetic