Presburger Arithmetic in Memory Access Optimization for Data-Parallel Languages

  • Ralf Karrenberg
  • Marek Košta
  • Thomas Sturm
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8152)

Abstract

Data-parallel languages like OpenCL and CUDA are an important means to exploit the computational power of today’s computing devices. We consider the compilation of such languages for CPUs with SIMD instruction sets. To generate efficient code, one wants to statically decide whether or not certain memory operations access consecutive addresses. We formalize the notion of consecutivity and algorithmically reduce the static decision to satisfiability problems in Presburger Arithmetic. We introduce a preprocessing technique on these SMT problems, which makes it feasible to apply an off-the-shelf SMT solver. We show that a prototypical OpenCL CPU driver based on our approach generates more efficient code than any other state-of-the-art driver.

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References

  1. 1.
    Barrett, C., Conway, C.L., Deters, M., Hadarean, L., Jovanović, D., King, T., Reynolds, A., Tinelli, C.: CVC4. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 171–177. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  2. 2.
    Betts, A., Chong, N., Donaldson, A., Qadeer, S., Thomson, P.: Gpuverify: a verifier for gpu kernels. In: Proceedings of the ACM International Conference on Object Oriented Programming Systems Languages and Applications, OOPSLA 2012, pp. 113–132. ACM, New York (2012)CrossRefGoogle Scholar
  3. 3.
    Cimatti, A., Griggio, A., Schaafsma, B.J., Sebastiani, R.: The MathSAT5 SMT Solver. In: Piterman, N., Smolka, S. (eds.) TACAS 2013. LNCS, vol. 7795, pp. 93–107. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  4. 4.
    Coutinho, B., Sampaio, D., Pereira, F.M.Q., Meira, W.: Divergence analysis and optimizations. In: 2011 International Conference on Parallel Architectures and Compilation Techniques (PACT), pp. 320–329 (2011)Google Scholar
  5. 5.
    de Moura, L., Bjørner, N.: Z3: An efficient SMT solver. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 337–340. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  6. 6.
    Diamos, G.F., Kerr, A.R., Yalamanchili, S., Clark, N.: Ocelot: a dynamic optimization framework for bulk-synchronous applications in heterogeneous systems. In: Proceedings of the 19th International Conference on Parallel Architectures and Compilation Techniques, PACT 2010, pp. 353–364. ACM, New York (2010)CrossRefGoogle Scholar
  7. 7.
    Gulwani, S., Jha, S., Tiwari, A., Venkatesan, R.: Synthesis of loop-free programs. In: Proceedings of the 32nd ACM SIGPLAN Conference on Programming Language Design and Implementation, PLDI 2011, pp. 62–73. ACM, New York (2011)CrossRefGoogle Scholar
  8. 8.
    Gummaraju, J., Morichetti, L., Houston, M., Sander, B., Gaster, B.R., Zheng, B.: Twin peaks: a software platform for heterogeneous computing on general-purpose and graphics processors. In: PACT, pp. 205–216. ACM, New York (2010)CrossRefGoogle Scholar
  9. 9.
    Jaskelainen, P.O., de La Lama, C.S., Huerta, P., Takala, J.: OpenCL-based Design Methodology for Application-Specific Processors. In: SAMOS 2010, pp. 223–230 (July 2010)Google Scholar
  10. 10.
    Karrenberg, R., Hack, S.: Whole function vectorization. In: CGO, pp. 141–150 (2011)Google Scholar
  11. 11.
    Karrenberg, R., Hack, S.: Improving Performance of OpenCL on CPUs. In: O’Boyle, M. (ed.) CC 2012. LNCS, vol. 7210, pp. 1–20. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  12. 12.
    Kim, Y., Shrivastava, A.: Cumapz: a tool to analyze memory access patterns in CUDA. In: Proceedings of the 48th Design Automation Conference, DAC 2011, pp. 128–133. ACM, New York (2011)Google Scholar
  13. 13.
    Lattner, C., Adve, V.: LLVM: A Compilation Framework for Lifelong Program Analysis & Transformation. In: CGO (March 2004)Google Scholar
  14. 14.
    Li, G., Gopalakrishnan, G.: Scalable smt-based verification of GPU kernel functions. In: Proceedings of the Eighteenth ACM SIGSOFT International Symposium on Foundations of Software Engineering, FSE 2010, pp. 187–196. ACM, New York (2010)CrossRefGoogle Scholar
  15. 15.
    Lv, J., Li, G., Humphrey, A., Gopalakrishnan, G.: Performance degradation analysis of gpu kernels. In: Proceedings of the Workshop on Exploiting Concurrency Efficiently and Correctly 2011, EC2 2011 (2011)Google Scholar
  16. 16.
    Presburger, M.: Über die Vollständigkeit eines gewissen Systems der Arithmetik ganzer Zahlen, in welchem die Addition als einzige Operation hervortritt. In: Comptes Rendus du Premier Congres de Mathematiciens des Pays Slaves, Warsaw, Poland, pp. 92–101 (1929)Google Scholar
  17. 17.
    Robinson, J.: Definability and decision problems in arithmetic. J. Symb. Log. 14(2), 98–114 (1949)CrossRefMATHGoogle Scholar
  18. 18.
    Stratton, J.A., Stone, S.S., Hwu, W.-M.W.: MCUDA: An efficient implementation of CUDA kernels for multi-core CPUs. In: Amaral, J.N. (ed.) LCPC 2008. LNCS, vol. 5335, pp. 16–30. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  19. 19.
    Tripakis, S., Stergiou, C., Lublinerman, R.: Checking equivalence of spmd programs using non-interference. Technical Report UCB/EECS-2010-11, EECS Department, University of California, Berkeley (January 2010)Google Scholar
  20. 20.
    Weispfenning, V.: The complexity of almost linear Diophantine problems. Journal of Symbolic Computation 10(5), 395–403 (1990)MathSciNetCrossRefMATHGoogle Scholar
  21. 21.
    Yang, Y., Xiang, P., Kong, J., Zhou, H.: A GPGPU compiler for memory optimization and parallelism management. In: Proceedings of the 2010 ACM SIGPLAN Conference on Programming Language Design and Implementation, PLDI 2010, pp. 86–97. ACM, New York (2010)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Ralf Karrenberg
    • 1
  • Marek Košta
    • 2
  • Thomas Sturm
    • 2
  1. 1.Saarland UniversitySaarbrückenGermany
  2. 2.Max-Planck-Institut für InformatikSaarbrückenGermany

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