Issue No. 10 - October (2000 vol. 49)

ISSN: 0018-9340

pp: 1074-1082

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/12.888043

ABSTRACT

<p><b>Abstract</b>—A digit-recurrence algorithm for computing the Euclidean norm of a three-dimensional (3D) vector which often appears in 3D computer graphics is proposed. One of the three squarings required for the usual computation is removed and the other two squarings, as well as the two additions, are overlapped with the square rooting. The Euclidean norm is computed by iteration of carry-propagation-free additions, shifts, and multiplications by one digit. Different specific versions of the algorithm are possible, depending on the radix, the redundancy factor of the digit set, and etc. Each version of the algorithm can be implemented as a sequential (folded) circuit or a combinational (unfolded) circuit, which has a regular array structure suitable for VLSI.</p>

INDEX TERMS

Computer arithmetic, Euclidean norm, VLSI algorithm, digit-recurrence algorithm, computer graphics.

CITATION

Naofumi Takagi, Seiji Kuwahara, "A VLSI Algorithm for Computing the Euclidean Norm of a 3D Vector",

*IEEE Transactions on Computers*, vol. 49, no. , pp. 1074-1082, October 2000, doi:10.1109/12.888043