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PatEC: Pattern-Based Equivalence Checking

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Model Checking Software (SPIN 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12864))

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Abstract

Program parallelization is a common software engineering task, in which parallel design patterns are applied. While the focus of parallelization is on performance, the functional behavior should be kept invariant, i.e., sequential and parallelized program should be functionally equivalent. Several verification techniques exist that analyze properties of parallel programs, but only a few approaches inspect functional equivalence between a sequential program and its parallelization. Even fewer approaches consider parallel design patterns when checking equivalence.

In this paper, we present PatEC, which checks equivalence between sequential programs and their OpenMP parallelizations. PatEC utilizes the knowledge about the applied parallel design pattern to split equivalence checking into smaller subtasks. Our experiments show that PatEC is effective, efficient, and often outperforms existing approaches.

This work was funded by the Hessian LOEWE initiative within the Software-Factory 4.0 project.

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Notes

  1. 1.

    We assume that sequential programs are deterministic. To deal with non-determinism caused by random methods or I/O functions, one can consider those inputs as part of the starting state.

  2. 2.

    This is sufficient because we do not support aliasing.

  3. 3.

    Nested pattern applications can be checked recursively when being careful with the data-sharing attributes, but it is inefficient and misses equivalences.

  4. 4.

    Note that we make the assumption because (i) it simplifies the sequential equivalence check and (ii) most parallelizations we have seen fulfill the assumption. One can easily get rid of this assumption by letting the sequential check inspect \(P_\mathrm {seg}\) and \(P_\mathrm {par^{-1}}\).

  5. 5.

    In our implementation, we rely on the unparse function of the AST to avoid that formatting differences influence the check.

  6. 6.

    There exists some corner cases in which those variables are not thread-local like static variables. However, we do not support these rare cases.

  7. 7.

    Since it is sufficient that an array access is independent in one dimension, we only extract the complete accesses, e.g., from x[i][j] > 0 we collect x[i][j] but not x[i].

  8. 8.

    Note that our check additionally requires that a variable with attribute private or lastprivate must be modified. Since we only check variables that occur in the loop body, variables that are not used before must be modified.

  9. 9.

    Also, one must use the modifier conditional to ensure that the last write is considered.

  10. 10.

    Again, our implementation relies on the unparse function of the AST.

  11. 11.

    Especially note that all semantics we are aware of do not support all data-sharing attributes [12] or do not cover the data aspect [3].

  12. 12.

    https://git.rwth-aachen.de/svpsys-sw/FECheck, revision PatEC-SPIN2021.

  13. 13.

    To limit PatEC ’s checking to DoAll patterns, use -type=DOALL.

  14. 14.

    https://asc.llnl.gov/coral-benchmarks.

  15. 15.

    https://git.rwth-aachen.de/svpsys-sw/FECheck.

  16. 16.

    An incorrectly detected equivalence is an inequivalent task reported as equivalent.

  17. 17.

    We use the following command line: autoPar -rose:unparse_tokens -rose:autopar:no_aliasing -rose:autopar:enable_diff -fopenmp program.c.

  18. 18.

    PatEC times out twice (2*300 s) and AutoPar only once (300 s).

  19. 19.

    Note that the reported time for status TO in PEQcheck can differ significantly because PEQcheck may generate multiple verification tasks and we use a time out per task instead of one global time out for all tasks.

  20. 20.

    The parsing problems occur in one of the MILCmk header files.

  21. 21.

    Parallelizations without the reduction clause are classified as DoAll.

  22. 22.

    For our experiments, we therefore classified it inequivalent, too.

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Authors and Affiliations

  1. Department of Computer Science, Technical University of Darmstadt, Darmstadt, Germany

    Marie-Christine Jakobs

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Correspondence to Marie-Christine Jakobs .

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  1. Leiden University, Leiden, The Netherlands

    Alfons Laarman

  2. University of Salzburg, Salzburg, Austria

    Ana Sokolova

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Jakobs, MC. (2021). PatEC: Pattern-Based Equivalence Checking. In: Laarman, A., Sokolova, A. (eds) Model Checking Software. SPIN 2021. Lecture Notes in Computer Science(), vol 12864. Springer, Cham. https://doi.org/10.1007/978-3-030-84629-9_7

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