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

A digit-recurrence algorithm for computing the Euclidean norm of a three-di mensional (3D) vector which often appears in 3D computer graphics is propos ed. One of the three squarings required for the usual computation is remove d 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 ca rry-propagation-free additions, shifts, and multiplications by one digit. D ifferent 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 combina tional (unfolded) circuit, which has a regular array structure suitable for VLSI.