A radix-4 redundant CORDIC algorithm with fast on-line variable scale factor compensation

In this work, a fast radix-4 redundant CORDIC algorithm with variable scale factor is proposed. The algorithm includes an on-line scale factor decomposition algorithm that transforms the complicated variable scale factor into a sequence of simple shift-and-add operations and does the variable scale factor compensation in the same fashion. On the other hand, the on-line decomposition algorithm itself can be realized with a simple and fast hardware. The new CORDIC algorithm has the smallest number of 0.8n iterations among all the CORDIC algorithms, which requires only about two-third rotation number that of the existing best (hybrid radix-2 and radix-4) redundant algorithms. Therefore, the new algorithm achieves fast rotation iterations, high-speed and low-overhead scale factor compensations, which are hard to attain simultaneously for the existing algorithms. The on-line scale factor compensation can be also applied to the existing on-line CORDIC algorithms.