Fixed Angle of Rotation Using CORDIC Designs

Rotation of vectors through fixed and known angles has wide applications in robotics, digital signal processing, graphics, games, and animation. But, we do not find any optimized coordinate rotation digital computer (CORDIC) design for vector-rotation through specific angles. Therefore, in this paper, we present optimization schemes and CORDIC circuits for fixed and known rotations with different levels of accuracy. For reducing the areaand time-complexities, we have proposed a hardwired pre-shifting scheme in barrel-shifters of the proposed circuits. Two dedicated CORDIC cells are proposed for the fixed-angle rotations. In one of those cells, micro-rotations and scaling are interleaved, and in the other they are implemented in two separate stages. Pipelined schemes are suggested further for cascading dedicated single-rotation CORDIC units for high-throughput and reduced latency implementations. We have the optimized set of micro-rotations for fixed and known angles. The derived optimized scale-factors from a set of micro rotations and dedicated shift-add circuits are used to implement the scaling. We have synthesized the proposed CORDIC cells using Xilinx field programmable gate array platform and shown that the proposed design offer higher throughput and less area-delay product than the reference CORDIC design for fixed and known angles of rotation.