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 VLSI 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.

A novel, efficient implementation of the Toeplitz eigensystem solver using a doubly pipelined VLSI CORDIC array processor is presented. First, a backward CORDIC angle recoding scheme is proposed which is able to reduce the number of internal CORDIC iterations by at least 50%. It is shown how to apply this scheme to a family of feedforward algorithms for solving general linear systems, especially the Toeplitz systems. This leads to the implementation of a Toeplitz eigensystem solver with CORDIC-based array processors.>