A VLSI algorithm for computing the Euclidean norm of a 3D vector

Author

Takagi, Naofumi ; Kuwahara, Seiji

Author_Institution

Dept. of Inf. Eng., Nagoya Univ., Japan

Volume

49

Issue

10

fYear

2000

fDate

10/1/2000 12:00:00 AM

Firstpage

1074

Lastpage

1082

Abstract

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

Keywords

computer graphics; digital arithmetic; 3D vector; Euclidean norm; VLSI algorithm; carry-propagation-free; combinational; computer graphics; digit-recurrence algorithm; iteration; sequential; Acceleration; Circuits; Computer errors; Computer graphics; Difference equations; Digital arithmetic; Hardware; Redundancy; Roundoff errors; Very large scale integration;

fLanguage

English

Journal_Title

Computers, IEEE Transactions on

Publisher

ieee

ISSN

0018-9340

Type

jour

DOI

10.1109/12.888043

Filename

888043