Polyhedral Specification and Code Generation of Sparse Tensor Contraction with Co-Iteration
Document Type
Article
Publication Date
3-2023
Abstract
This article presents a code generator for sparse tensor contraction computations. It leverages a mathematical representation of loop nest computations in the sparse polyhedral framework (SPF), which extends the polyhedral model to support non-affine computations, such as those that arise in sparse tensors. SPF is extended to perform layout specification, optimization, and code generation of sparse tensor code: (1) We develop a polyhedral layout specification that decouples iteration spaces for layout and computation; and (2) we develop efficient co-iteration of sparse tensors by combining polyhedra scanning over the layout of one sparse tensor with the synthesis of code to find corresponding elements in other tensors through an SMT solver.
We compare the generated code with that produced by a state-of-the-art tensor compiler, TACO. We achieve on average 1.63× faster parallel performance than TACO on sparse-sparse co-iteration and describe how to improve that to 2.72× average speedup by switching the find algorithms. We also demonstrate that decoupling iteration spaces of layout and computation enables additional layout and computation combinations to be supported.
Publication Information
Zhao, Tuowen; Popoola, Tobi; Wolcott Hall, Mary Wolcott; Mills Olschanowsky, Catherine; and Mills Strout, Michelle. (2023). "Polyhedral Specification and Code Generation of Sparse Tensor Contraction with Co-Iteration". ACM Transactions on Architecture and Code Optimization, 20(1), 16. https://doi.org/10.1145/3566054