Revealing parallel scans and reductions in recurrences through function reconstruction

Abstract

Many sequential loops are actually recurrences and can be parallelized across iterations as scans or reductions. Many efforts over the past 2+ decades have focused on parallelizing such loops by extracting and exploiting the hidden scan/reduction patterns. These approaches have largely been based on a heuristic search for closed-form composition of computations across loop iterations. While the search-based approaches are successful in parallelizing many recurrences, they have a large search overhead and need extensive program analysis. In this work, we propose a novel approach called sampling-and-reconstruction, which avoids the search for closed-form composition and has the potential to cover more recurrence loops. It is based on an observation that many recurrences can have a pointvalue representation. The loop iterations are divided across processors, and where the initial value(s) of the recurrence variable(s) are unknown, we execute with several chosen (sampling) initial values. Then, correct final result can be obtained by reconstructing the function from the outputs produced on the chosen initial values. Our approach is effective in parallelizing linear, rectified-linear, finite-state and multivariate recurrences, which cover all of the test cases in previous works. Our evaluation shows that our approach can parallelize a diverse set of sequential loops, including cases that cannot be parallelized by a state-of-the-art static parallelization tool, and achieves linear scalability across multiple cores.