Redundant and Online CORDIC for Unitary Transformations

Abstract

Two-sided unitary transformations of arbitrary 2 x 2 matrices are needed in parallel algorithms based on Jacobi-like methods for eigenvalue and singulare value decompositions of complex matrices. This paper presents a two-sided unitary transformation structured to facilitate the integrated evaluation of parameters and application of the typically required tranformations using only the primitives afforded by CORDIC; thus enabling significant speedup in the computation of these transformations on special-purpose processor array architectures implementing Jacobi-like algorithms. We discuss implementation in (nonredundant) CORDIC to motivate and lead up to implementation in the redundant and on-line enhancements to CORDIC. Both variable and constant scale factor redundant (CFR) CORDIC approaches are detailed and it is shown that the transformations may be computed in 10n+<i>o</i> time, where n is the data precision in bits and <i>o</i> is a constant accounting for accumulated on-line delays. A more area-intesive approach uisng a novel on-line CORDIC encode angle summation/difference scheme reduces computation time to 6n+<i>o</i>. The area/time complexities involved in the various approaches are detailed.