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This paper presents our work toward correct and efficient automaticdifferentiation of OpenMP parallel worksharing loops in forward and reversemode. Automatic differentiation is a method to obtain gradients of numericalprograms, which are crucial in optimization, uncertainty quantification, andmachine learning. The computational cost to compute gradients is a commonbottleneck in practice. For applications that are parallelized for multicoreCPUs or GPUs using OpenMP, one also wishes to compute the gradients inparallel. We propose a framework to reason about the correctness of thegenerated derivative code, from which we justify our OpenMP extension to thedifferentiation model. We implement this model in the automatic differentiationtool Tapenade and present test cases that are differentiated following ourextended differentiation procedure. Performance of the generated derivativeprograms in forward and reverse mode is better than sequential, although ourreverse mode often scales worse than the input programs.

Source-to-Source Automatic Differentiation of OpenMP Parallel Loops