A Novel Implementation of CORDIC Algorithm Using Backward Angle Recoding (BAR)

We propose a backward angle recoding (BAR) method to eliminate redundant CORDIC elementary rotations and hence expedite the CORDIC rotation computation. We prove that for each of the linear, circular, and hyperbolic CORDIC rotations, the use of BAR guarantees more than 50% reduction of elementary CORDIC rotations provided the scaling factor needs not be kept constant. The proposed BAR algorithm is simple, and amenable to VLSl implementation. Taking practical applications into consideration, we discuss how to incorporate convergence range enhancement procedure with BAR, and how easy it is to devise a constant-scaling-factor BAR algorithm while still enjoying 25% reduction of CORDIC elementary rotations.