AMPT: Automatic Mixed-Precision Tuning Based on Accuracy Gain

Mixed-precision tuning is a valuable approach for striking a balance between the accuracy and performance of floating-point computations. However, selecting suitable configurations from numerous mixed-precision configurations can be challenging. The discrete and finite nature of floating-point numbers introduces unavoidable rounding errors that are difficult to predict. To address these challenges, we propose an accuracy gain evaluation function for expressions. This evaluation function quantifies the extent of accuracy improvement achieved by adjusting the precision of the operations within the expression. This is achieved through a thorough examination of the impact of each operation's condition number and implementation error on the final error. Based on this evaluation function, we present AMPT, a mixed-precision tuning method specifically for expressions. AMPT not only identifies the optimal mixed-precision configuration but also automatically generates the corresponding code. Experimental results demonstrate that AMPT accurately assesses the accuracy gains of different mixed-precision configurations, and the mixed-precision code generated by AMPT can achieve low-error computation of expressions with low performance overhead.