An Explainable Machine Learning Framework for Adaptive Multi-Mode CORDIC Iteration Optimization and Hardware-Efficient Computation

Abstract

The Coordinate Rotation Digital Computer (CORDIC) algorithm is widely employed in digital signal processing and hardware accelerators because it computes a broad range of elementary functions using iterative shift-and-add operations. Conventional CORDIC implementations, however, execute a fixed number of iterations irrespective of the input characteristics or the precision required, resulting in unnecessary computational overhead and increased execution latency. This work presents an explainable machine learning framework for adaptive iteration optimization in a multi-mode CORDIC architecture supporting circular, hyperbolic, and linear operating modes. A unified prediction framework for calculating the optimal number of iterations is made possible by the developing a generic feature representation to describe the numerical behavior of CORDIC computations across various modes. We systematically evaluated eight regression models, including Linear Regression, Decision Tree, Random Forest, Extra Trees, Support Vector Regression, Multi-Layer Perceptron, and Extreme Gradient Boosting (XGBoost) and LightGBM. Among the models evaluated, the Decision Tree achieved the best performance on an independent test set of 2305 samples from 461 previously unseen input groups, with a MAE of 0.9160 iterations, RMSE of 1.9671, and R2 of 0.6076. Predictions were within one and two iterations of the reference value for 80.26% and 90.07% of the test samples, respectively. Since prediction accuracy alone does not guarantee that the required numerical tolerance will be satisfied, the predicted iteration count was further evaluated using the actual CORDIC error, followed by a safety-correction procedure. The safety-corrected approach achieved 100% tolerance satisfaction on the independent test set, reducing the mean number of iterations from 20 to 11.739, corresponding to a 41.31% reduction in iterations. Model behavior was further interpreted using feature importance analysis, permutation importance, and feature ablation studies to examine the contribution of individual features to iteration prediction. Statistical robustness is established using bootstrap confidence intervals, the Friedman test, and Holm-corrected Wilcoxon signed-rank tests.