Critically damped CORDIC algorithm

The COordinate Rotation DIgital Computer (CORDIC) algorithm has been widely used in evaluating elementary functions. It employs only basic arithmetic operations such as additions and shifts rather than multiplications. This attractive hardware property is achieved by restricting the operation at each iteration step to either positive or negative “pseudo rotations,” so that the scale factor is a constant. However, because of this restriction the angular error does not converge directly towards zero. Instead, it asymptotically oscillates about zero like an underdamped second-order control system responding to a step input. Multiple overshots may also be observed during the convergence. According to control theory, this kind of convergence is not fast. In this paper, we develop a CORDIC algorithm with a critically damped convergence process by changing the restriction to either {0,+1} (for positive angles) or {-1,0} (for negative angles). Theory and simulation show that this algorithm is faster than the conventional one