Uniformly Distributed CORDIC

This paper presents the uniformly distributed (UD) coordinate rotation digital computer (CORDIC). It receives this name because the distance between its rotation angles is uniform. The paper presents two versions of the UD CORDIC: the binary UD CORDIC and the canonical signed digit (CSD) UD CORDIC. Both simplify the control part of the CORDIC by obtaining the micro-rotation directions straightforwardly from the binary representation of the rotation angle, with the particularity that, in the CSD UD CORDIC, the binary representation is transformed first into a CSD number. Compared to previous CORDIC approaches that simplify the control part, the proposed rotators further simplify the micro-rotation stages. This is achieved by using more efficient angles for the micro-rotations in the binary UD CORDIC and by merging consecutive micro-rotation stages in the CSD UD CORDIC. Thus, the simplification of the control part of the rotators, the careful selection of the micro-rotation angles, and their optimized shift-and-add implementation results in CORDIC architectures that require the smallest number of adders among pipelined CORDIC implementations for a given resolution so far. Additionally, experimental results of the proposed approach on field-programmable gate array (FPGA) and application-specific integrated circuit (ASIC) are provided, showing improvements with respect to previous approaches in multiple figures of merit, mostly area, clock frequency, and power consumption.