Design and Analysis of Extension-Rotation CORDIC Algorithms based on Non-Redundant Method

In this paper, rotation-extension CORDIC methods, i.e. double-rotation and triplerotation, are proposed for the objective of improving the performance and accuracy of the CORDIC computational algorithm in radix-2. In the double-rotation and triple-rotation methods, the convergences of the CORDIC computations are accelerated by duplicating and triplicating the micro-rotation angles to be 2θ and 3θ, respectively. The non-redundant mechanism, where a rotation direction δ is in a set of 1 and -1, depending on an intermediate converging parameter (either y or z), is applied to constant scaling factors. Convergence range and accuracy of elementary functions hardware performed by using the CORDIC methods in rotation mode and vectoring mode on the circular, hyperbolic, and linear coordinate systems are examined, investigated and compared to Matlab/Simulink simulation results. The comparison results show that the proposed CORDIC methods provide higher computational accuracy than the conventional one at the same number of iterations. A high precision CORDIC algorithm is introduced and evaluated for VLSI implementation. Finally, speed and area performance of the CORDIC hardware based on the pipeline (unfolded) digit-parallel architecture of the proposed CORDIC methods are compared to the CORDIC methods previously published in the literature.