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A general digit-recurrence algorithm for the computation of the m-th root (with <em>m</em> integer) is presented in this paper. Based on the concept of completing the <em>m</em>-th 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 <em>m</em>-th rooting is also studied, together with closed formulas for both the digit selection rules and the number of bits required to perform correct selections.
integer rooting, digit-by-digit algorithms, higher radix, computer arithmetic
Paolo Montuschi, Luigi Ciminiera, Javier D. Bruguera, José-Alejandro Piñeiro, "A Digit-by-Digit Algorithm for mth Root Extraction", IEEE Transactions on Computers, vol. 56, no. , pp. 1696-1706, December 2007, doi:10.1109/TC.2007.70764
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