Hardware Algorithm for Computing Reciprocal of Euclidean Norm of a 3-D Vector

Fumio KUMAZAWA  Naofumi TAKAGI  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E89-A   No.6   pp.1799-1806
Publication Date: 2006/06/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e89-a.6.1799
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: VLSI Design Technology and CAD
computer arithmetic,  hardware algorithm,  reciprocal of the Euclidean norm,  digit-recurrence,  computer graphics,  

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A hardware algorithm for computing the reciprocal of the Euclidean norm of a 3-dimensional (3-D) vector which appears frequently in 3-D computer graphics is proposed. It is based on a digit-recurrence algorithm for computing the Euclidean norm and an on-line division (on-line reciprocal computation) algorithm. These algorithms are modified, so that the reciprocal of the Euclidean norm is computed by performing on-line division where the divisor is the partial result of Euclidean norm computation. Division, square-rooting, and reciprocal square-root computation, which are important operations in 3-D graphics, can also be performed using a circuit based on the proposed algorithm.