Sound Approximation of Programs with Elementary Functions [chapter]

Eva Darulova, Anastasia Volkova
2019 Lecture Notes in Computer Science  
Elementary function calls are a common feature in numerical programs. While their implementations in mathematical libraries are highly optimized, function evaluation is nonetheless very expensive compared to plain arithmetic. Full accuracy is, however, not always needed. Unlike arithmetic, where the performance difference between for example single and double precision floating-point arithmetic is relatively small, elementary function calls provide a much richer tradeoff space between accuracy
more » ... nd efficiency. Navigating this space is challenging, as guaranteeing the accuracy and choosing correct parameters for good performance of approximations is highly nontrivial. We present a fully automated approach and a tool which approximates elementary function calls inside small programs while guaranteeing overall user given error bounds. Our tool leverages existing techniques for roundoff error computation and approximation of individual elementary function calls and provides an automated methodology for the exploration of parameter space. Our experiments show that significant efficiency improvements are possible in exchange for reduced, but guaranteed, accuracy.
doi:10.1007/978-3-030-25543-5_11 fatcat:6qhrhilwlvdhlckteoscor455q