Algorithm and Design of a Fully Parallel Approximate Coordinate Rotation Digital Computer (CORDIC)

This paper proposes a new approximate scheme for coordinate rotation digital computer (CORDIC) design. This scheme is based on modifying the existing Para-CORDIC architecture with an approximation that is inserted in multiple parts and made possible by relaxing the CORDIC algorithm itself. A fully parallel approximate CORDIC (FPAX-CORDIC) scheme is proposed. This scheme avoids the memory register of Para-CORDIC and makes the generation of the rotation direction fully parallel. A comprehensive analysis and the evaluation of the error introduced by the approximation together with different circuit-related metrics are pursued using HSPICE as the simulation tool. This error analysis also combines existing figures of merit for approximate computing (such as the Mean Error Distance (MED) and MED Power Product (MPP)) with CORDIC specific parameters. It is shown that a good agreement between expected and simulated error values is found. The Discrete Cosine Transformation (DCT) and the Inverse DCT (IDCT) transformations as case study of approximate computing to image processing are investigated by utilizing the proposed approximate FPAX-CORDIC architecture with different accuracy requirements. The results confirm the viability of the proposed scheme.