An Improved Three-Stage Cordic Algorithm

The Cordic algorithm is a widely used method for high-precision sine and cosine calculations. To further reduce the number of iterations and improve computational accuracy, we propose improvements to the three-stage Cordic algorithm. In the first stage, we enhance the lookup table by adopting a [Formula: see text]/60 interval partition. In the second stage, we simplify and merge the butterfly iteration and merging operations into a single stage. In addition, the iterative calculation process is scaled, effectively reducing the cumulative error associated with the traditional three-stage Cordic algorithm. We compare the improved algorithm against the traditional Cordic algorithm, the three-stage Cordic algorithm, and the iterative-free Cordic algorithm in terms of output delay, accuracy, maximum operating frequency and hardware resource consumption. The improved algorithm demonstrates an accuracy improvement of at least 48.3% for 16-bit data compared to the above three algorithms, and a reduction in Slice resource consumption of at least 17.08%. While it requires more iterations than the iterative-free Cordic algorithm, the improved algorithm performs significantly better in other metrics. Compared to the original three-stage Cordic algorithm, it achieves comparable or better performance across most indicators, except for LUT consumption. The results confirm that the improved algorithm offers enhanced precision, reduced resource usage and broad applicability, making it valuable for practical applications.