Radix-4 Vectoring CORDIC Algorithm and Architectures

In this work we extend the radix-4 CORDIC algorithm to the vectoring mode (the radix-4 CORDIC algorithm was proposed recently by the authors for the rotation mode). The extension to the vectoring mode is not straightforward, since the digit selection function is more complex in the vectoring case than in the rotation case; as in the rotation mode, the scale factor is not constant. Although the radix-4 CORDIC algorithm in vectoring mode has a similar recurrence as the radix-4 division algorithm, there are specific issues concerning the vectoring algorithm that demand dedicated study. We present the digit selection for nonredundant and redundant arithmetic (following two different approaches: arithmetic comparisons and table look-up), the computation and compensation of the scale factor, and the implementation of the algorithm (with both types of digit selection) in a word-serial architecture. When compared with conventional radix-2 (redundant and non-redundant) architectures, the radix-4 algorithms present a significant speed up for angle calculation. For the computation of the magnitude the speed up is very slight, due to the nonconstant scale factor in the radix-4 algorithm.