Verification of Polyhedral Optimizations with Constant Loop Bounds in Finite State Space Computations

  • Markus Schordan
  • Pei-Hung Lin
  • Dan Quinlan
  • Louis-Noël Pouchet
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8803)

Abstract

As processors gain in complexity and heterogeneity, compilers are asked to perform program transformations of ever-increasing complexity to effectively map an input program to the target hardware. It is critical to develop methods and tools to automatically assert the correctness of programs generated by such modern optimizing compilers.

We present a framework to verify if two programs (one possibly being a transformed variant of the other) are semantically equivalent. We focus on scientific kernels and a state-of-the-art polyhedral compiler implemented in ROSE. We check the correctness of a set of polyhedral transformations by combining the computation of a state transition graph with a rewrite system to transform floating point computations and array update operations of one program such that we can match them as terms with those of the other program. We demonstrate our approach on a collection of benchmarks from the PolyBench/C suite.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Pouchet, L.N.: PolyOpt/C 0.2.0: A Polyhedral Compiler for ROSE (2012), http://www.cs.ucla.edu/~pouchet/software/polyopt/
  2. 2.
    Bondhugula, U., Hartono, A., Ramanujam, J., Sadayappan, P.: A practical automatic polyhedral program optimization system. In: ACM SIGPLAN Conference on Programming Language Design and Implementation (June 2008)Google Scholar
  3. 3.
    Kong, M., Veras, R., Stock, K., Franchetti, F., Pouchet, L.N., Sadayappan, P.: When polyhedral transformations meet simd code generation. In: PLDI (June 2013)Google Scholar
  4. 4.
    Holewinski, J., Pouchet, L.N., Sadayappan, P.: High-performance code generation for stencil computations on gpu architectures. In: ICS (June 2012)Google Scholar
  5. 5.
    Pouchet, L.N., Zhang, P., Sadayappan, P., Cong, J.: Polyhedral-based data reuse optimization for configurable computing. In: FPGA (February 2013)Google Scholar
  6. 6.
    Pouchet, L.N.: PoCC 1.2: The Polyhedral Compiler Collection (2012), http://www.cs.ucla.edu/~pouchet/software/pocc/
  7. 7.
    Leroy, X.: The Compcert C compiler (2014), http://compcert.inria.fr/compcert-C.html
  8. 8.
    Verdoolaege, S., Janssens, G., Bruynooghe, M.: Equivalence checking of static affine programs using widening to handle recurrences. ACM Transactions on Programming Languages and Systems (TOPLAS) 34(3), 11 (2012)CrossRefGoogle Scholar
  9. 9.
    Feautrier, P.: Some efficient solutions to the affine scheduling problem, part II: Multidimensional time. Intl. J. of Parallel Programming 21(6), 389–420 (1992)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Irigoin, F., Triolet, R.: Supernode partitioning. In: ACM SIGPLAN Principles of Programming Languages, pp. 319–329 (1988)Google Scholar
  11. 11.
    Bastoul, C.: Code generation in the polyhedral model is easier than you think. In: IEEE Intl. Conf. on Parallel Architectures and Compilation Techniques (PACT 2004), Juan-les-Pins, France, pp. 7–16 (September 2004)Google Scholar
  12. 12.
    Pouchet, L.N., Bondhugula, U., Bastoul, C., Cohen, A., Ramanujam, J., Sadayappan, P., Vasilache, N.: Loop transformations: Convexity, pruning and optimization. In: POPL, pp. 549–562 (January 2011)Google Scholar
  13. 13.
    Girbal, S., Vasilache, N., Bastoul, C., Cohen, A., Parello, D., Sigler, M., Temam, O.: Semi-automatic composition of loop transformations. Intl. J. of Parallel Programming 34(3), 261–317 (2006)CrossRefMATHGoogle Scholar
  14. 14.
    Pouchet, L.N.: PolyBench/C 3.2 (2012), http://www.cs.ucla.edu/~pouchet/software/polybench/
  15. 15.
    Allen, J., Kennedy, K.: Optimizing Compilers for Modern Architectures. Morgan Kaufmann Publishers (2002)Google Scholar
  16. 16.
    Cytron, R., Ferrante, J., Rosen, B.K., Wegman, M.N., Zadeck, F.K.: Efficiently computing static single assignment form and the control dependence graph. ACM Transactions on Programming Languages and Systems 13(4), 451–490 (1991)CrossRefGoogle Scholar
  17. 17.
    Steffen (Organizer), B.: RERS Challenge: Rigorous Examination of Reactive Systems (2010, 2012, 2013, 2014), http://www.rers-challenge.org
  18. 18.
    Quinlan, D., Liao, C., Matzke, R., Schordan, M., Panas, T., Vuduc, R., Yi, Q.: ROSE Web Page (2014), http://www.rosecompiler.org
  19. 19.
    Karfa, C., Banerjee, K., Sarkar, D., Mandal, C.: Verification of loop and arithmetic transformations of array-intensive behaviors. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 32(11), 1787–1800 (2013)CrossRefGoogle Scholar
  20. 20.
    Klein, G.: A framework for formal verification of compiler optimizations. In: Kaufmann, M., Paulson, L. (eds.) ITP 2010. LNCS, vol. 6172, pp. 371–386. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  21. 21.
    Kalvala, S., Warburton, R., Lacey, D.: Program transformations using temporal logic side conditions. ACM Transactions on Programming Languages and Systems (TOPLAS) 31(4), 14 (2009)CrossRefGoogle Scholar
  22. 22.
    Paulson, L.C.: Isabelle Page, https://www.cl.cam.ac.uk/research/hvg/Isabelle

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Markus Schordan
    • 1
  • Pei-Hung Lin
    • 1
  • Dan Quinlan
    • 1
  • Louis-Noël Pouchet
    • 2
  1. 1.Lawrence Livermore National LaboratoryUSA
  2. 2.University of California Los AngelesUSA

Personalised recommendations