The suboptimality of angle coding in the CORDIC algorithm

The CORDIC algorithm has enjoyed widespread recognition as an efficient, compact, and VLSI-suitable algorithm for planar vector rotation. Nevertheless, very little research is available on the finite-precision numerical effects of CORDIC, with a few notable exceptions. It is shown that CORDIC´s angle coding scheme is suboptimal, which results in nonminimal approximation-error statistics. The suboptimality is quantified by simulating both CORDIC angle coding and optimal coding across the entire ROC while incrementing the number of iterations. The variances of the resulting errors are compared. It is concluded that the suboptimality is significant over only a limited range of angles. However, it is plausible that a modified coding scheme could exploit this suboptimality to produce superior error performance