Simplifying Dependent Reductions

Reductions combine multiple input values with an associative operator to produce (a single or multiple) result(s). When the same input value contributes to multiple outputs, there is an opportunity to reuse partial results, enabling reduction simplification. Gautam and Rajopadhye [6] showed how reductions in the polyhedral model could be simplified automatically and optimally. In this paper, we tackle the case when (some) input values depend on (some) outputs. This couples simplification with the classic scheduling problem. We show how to extend the Gautam-Rajopadhye algorithm to optimally simplify such dependent reductions. ACM Reference Format: Sanjay Rajopadhye. 2018. Simplifying Dependent Reductions. In IMPACT ’21: 11th International Workshop on Polyhedral Compilation Techniques. ACM, New York, NY, USA, 5 pages. https://doi.org/10. 1145/1122445.1122456