A Digit-by-Digit Algorithm for mth Root Extraction
- 29 October 2007
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Computers
- Vol. 56 (12), 1696-1706
- https://doi.org/10.1109/tc.2007.70764
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.This publication has 12 references indexed in Scilit:
- Algorithm and architecture for logarithm, exponential, and powering computationIEEE Transactions on Computers, 2004
- Faithful bipartite ROM reciprocal tablesPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2002
- The Symmetric Table Addition Method for Accurate Function ApproximationJournal of Signal Processing Systems, 1999
- Approximating elementary functions with symmetric bipartite tablesIEEE Transactions on Computers, 1999
- Computation of √(x/d) in a very high radix combined division/square-root unit with scaling and selection by roundingIEEE Transactions on Computers, 1998
- High-radix division and square-root with speculationIEEE Transactions on Computers, 1994
- Higher radix square rootingIEEE Transactions on Computers, 1990
- Radix-4 square rot without initial PLAIEEE Transactions on Computers, 1990
- On-the-Fly Conversion of Redundant into Conventional RepresentationsIEEE Transactions on Computers, 1987
- A General Hardware-Oriented Method for Evaluation of Functions and Computations in a Digital ComputerIEEE Transactions on Computers, 1977