Title :
A Digit-by-Digit Algorithm for mth Root Extraction
Author :
Montuschi, Paolo ; Bruguera, Javier D. ; Ciminiera, Luigi ; Pieiro, J.-A.
Author_Institution :
Politecnico di Torino, Torino
Abstract :
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 iteration- independent 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 :
convergence; digital arithmetic; iterative methods; convergence condition; digit-by-digit algorithm; digit-recurrence algorithm; mth root extraction; Algorithm design and analysis; Circuits; Computer architecture; Convergence; Digital arithmetic; Helium; Layout; Newton method; Performance analysis; Signal processing algorithms; computer arithmetic; digit-by-digit algorithms; higher radix; integer rooting;
Journal_Title :
Computers, IEEE Transactions on
DOI :
10.1109/TC.2007.70764
