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Verified Validation for Affine Scheduling in Polyhedral Compilation

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Theoretical Aspects of Software Engineering (TASE 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14777))

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Abstract

Structural nested loops can be abstracted into polyhedral models, based on which one can perform aggressive loop optimizations; however, the optimizations are often heuristic and complex, and therefore error-prone. Meanwhile, verified compilers, though rigorously correct, still miss powerful optimizing transformations and therefore produce less efficient code than industrial ones. To bridge this gap, this work provides a general verified validation framework based on Bernstein’s conditions for affine scheduling, the core component of polyhedral optimization techniques. It is parameterized over the concrete definitions and proofs of the instruction language to be reusable. As shown in our evaluation, the framework is flexible enough to support both existing verified compilers like CompCert and existing polyhedral compilers like Pluto. The result is fully mechanized in the Coq proof assistant.

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Notes

  1. 1.

    https://compcert.org/doc/html/compcert.cfrontend.Csyntax.html.

  2. 2.

    https://github.com/bondhugula/pluto.

  3. 3.

    Please note that P-Time and V-Time for each test are not comparable, as they pertain to implementations of different algorithms in different programming languages.

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Acknowledgments

We thank anonymous referees for their suggestions and comments on earlier versions of this paper. This work is supported in part by National Natural Science Foundation of China (NSFC) under Grant No. 62232015.

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Authors and Affiliations

  1. State Key Laboratory for Novel Software Technology, Nanjing University, Nanjing, 210023, Jiangsu, China

    Xuyang Li, Hongjin Liang & Xinyu Feng

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Correspondence to Xinyu Feng .

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  1. National University of Singapore, Singapore, Singapore

    Wei-Ngan Chin

  2. Shenzhen University, Guangdong, China

    Zhiwu Xu

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Li, X., Liang, H., Feng, X. (2024). Verified Validation for Affine Scheduling in Polyhedral Compilation. In: Chin, WN., Xu, Z. (eds) Theoretical Aspects of Software Engineering. TASE 2024. Lecture Notes in Computer Science, vol 14777. Springer, Cham. https://doi.org/10.1007/978-3-031-64626-3_17

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  • DOI: https://doi.org/10.1007/978-3-031-64626-3_17

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