High speed bit-level pipelined architectures for redundant CORDIC implementation

The CORDIC algorithm is well known as an efficient method for the computation of trigonometric/hyperbolic functions and vector rotations. The achievable throughput and the latency of CORDIC processors using conventional arithmetic are determined by the carry propagation occurring in additions/subtractions, since the CORDIC iterations are directed by the signs of intermediate results. Using a redundant number system, much higher throughput is possible due to the elimination of carry propagation, but an exact sign detection can not be implemented efficiently. The authors derive transformations of the original CORDIC algorithm which result in partially fixed iteration sequences no longer dependent on intermediate signs for the CORDIC vectoring mode as well as the rotation mode. Very fast and efficient carry-save architectures using redundant absolute value computation resulting from the transformed algorithms are described. A CORDIC processor (rotation mode) is presented as an implementation example which to the best of the authors knowledge is the fastest CMOS CORDIC realization today