THE DIFFERENTIAL CORDIC ALGORITHM - CONSTANT SCALE FACTOR REDUNDANT IMPLEMENTATION WITHOUT CORRECTING ITERATIONS

The CORDIC algorithm is a well-known iterative method for the efficien t computation of vector rotations, and trigonometric and hyperbolic fu nctions. Basically, CORDIC performs a vector rotation which is not a p erfect rotation, since the vector is also scaled by a constant factor. This scaling has to be compensated for following the CORDIC iteration . Since CORDIC implementations using conventional number systems are r elatively slow, current research has focused on solutions employing re dundant number systems which make a much faster implementation possibl e. The problem with these methods is that either the scale factor beco mes variable, making additional operations necessary to compensate for the scaling, or additional iterations are necessary compared to the o riginal algorithm. In contrast we developed transformations of the usu al CORDIC algorithm which result in a constant scale factor redundant implementation without additional operations. The resulting ''Differen tial CORDIC Algorithm'' (DCORDIC) makes use of on-line (most significa nt digit first redundant) computation. We derive parallel architecture s for the radix-2 redundant number systems and present some implementa tion results based on logic synthesis of VHDL descriptions produced by a DCORDIC VHDL generator. We finally prove that, due to the lack of a dditional operations, DCORDIC compares favorably with the previously k nown redundant methods in terms of latency and computational complexit y.