Optimizing Expression Selection for Lookup Table Program Transformation

Scientific programmers can speed up function evaluation by precomputing and storing function results in lookup table (LUTs), thereby replacing costly evaluation code with an inexpensive memory access. A code transform that replaces computation with LUT code can improve performance, however, accuracy is reduced because of error inherent in reconstructing values from LUT data. LUT transforms are commonly used to approximate expensive elementary functions. The current practice is for software developers to (1) manually identify expressions that can benefit from a LUT transform, (2) modify the code by hand to implement the LUT transform, and (3) run experiments to determine if the resulting error is within application requirements. This approach reduces productivity, obfuscates code, and limits programmer control over accuracy and performance. We propose source code analysis and program transformation to substantially automate the application of LUT transforms. Our approach uses a novel optimization algorithm that selects Pareto optimal sets of expressions that benefit most from LUT transformation, based on error and performance estimates. We demonstrate our methodology with the Mesa tool, which achieves speedups of 1.4-6.9× on scientific codes while managing introduced error. Our tool makes the programmer more productive and improves the chances of finding an effective solution.