Verified tensor-program optimization via high-level scheduling rewrites

• Main Authors: Liu, Amanda (Author), Bernstein, Gilbert Louis (Author), Chlipala, Adam (Author), Ragan-Kelley, Jonathan (Author)
• Format: Article
• Language: English
• Published: Association for Computing Machinery (ACM), 2022-07-19T13:14:37Z.
• Subjects: Article
• Online Access: Get fulltext

 <jats:p>We present a lightweight Coq framework for optimizing tensor kernels written in a pure, functional array language. Optimizations rely on user scheduling using series of verified, semantics-preserving rewrites. Unusually for compilation targeting imperative code with arrays and nested loops, all rewrites are source-to-source within a purely functional language. Our language comprises a set of core constructs for expressing high-level computation detail and a set of what we call reshape operators, which can be derived from core constructs but trigger low-level decisions about storage patterns and ordering. We demonstrate that not only is this system capable of deriving the optimizations of existing state-of-the-art languages like Halide and generating comparably performant code, it is also able to schedule a family of useful program transformations beyond what is reachable in Halide.</jats:p>