A Digit-Recurrence Algorithm for Cube Rooting

Naofumi TAKAGI  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E84-A   No.5   pp.1309-1314
Publication Date: 2001/05/01
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: VLSI Design Technology and CAD
computer arithmetic,  cube rooting,  hardware algorithm,  digit-recurrence algorithm,  VLSI,  

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A digit-recurrence algorithm for cube rooting is proposed. In cube rooting, the digit-recurrence equation of the residual includes the square of the partial result of the cube root. In the proposed algorithm, the square of the partial result is kept, and the square, as well as the residual, is updated by addition/subtraction, shift, and multiplication by one or two digits. Different specific versions of the algorithm are possible, depending on the radix, the digit set of the cube root, and etc. Any version of the algorithm can be implemented as a sequential (folded) circuit or a combinational (unfolded) circuit, which is suitable for VLSI realization.