Abstract Interpretation of FIFO Replacement

  • Daniel Grund
  • Jan Reineke
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5673)


In hard real-time systems, the execution time of programs must be bounded by static timing analysis. For today’s embedded systems featuring caches, static analyses must predict cache hits and misses with high precision to obtain useful bounds. For caches with least-recently-used (LRU) replacement policy, efficient and precise cache analyses exist. However, for other widely-used policies like first-in first-out (FIFO), current cache analyses are much less precise.

This paper discusses challenges in FIFO cache analysis and advances the state of the art. We identify a generic framework for cache analysis that couples may- and must-analyses by means of domain cooperation. Our main contribution is a more precise may-analysis for FIFO. It not only increases the number of predicted misses, but also—due to the domain cooperation—the number of predicted hits. We instantiate the framework with a canonical must-analysis and three different may-analyses, including our new one, and compare the resulting three analyses to the collecting semantics. Our evaluation results characterize the progress achieved by our new may-analysis and reveal room for further improvement.


Cache Analysis FIFO Replacement Domain Cooperation May/Must Reasoning 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Wilhelm, R., Engblom, J., Ermedahl, A., Holsti, N., Thesing, S., Whalley, D., Bernat, G., Ferdinand, C., Heckmann, R., Mitra, T., Mueller, F., Puaut, I., Puschner, P., Staschulat, J., Stenström, P.: The worst-case execution-time problem—overview of methods and survey of tools. Transactions on Embedded Computing Systems 7(3), 1–53 (2008)CrossRefGoogle Scholar
  2. 2.
    Alt, M., Ferdinand, C., Martin, F., Wilhelm, R.: Cache behavior prediction by abstract interpretation. In: Cousot, R., Schmidt, D.A. (eds.) SAS 1996. LNCS, vol. 1145, pp. 52–66. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  3. 3.
    Ferdinand, C., Wilhelm, R.: Efficient and precise cache behavior prediction for real-time systems. Real-Time Systems 17(2-3), 131–181 (1999)CrossRefGoogle Scholar
  4. 4.
    White, R.T., Healy, C.A., Whalley, D.B., Mueller, F., Harmon, M.G.: Timing analysis for data caches and set-associative caches. In: RTAS 1997: Proceedings of the 3rd IEEE Real-Time Technology and Applications Symposium, Washington, DC, USA, p. 192. IEEE Computer Society, Los Alamitos (1997)Google Scholar
  5. 5.
    Ghosh, S., Martonosi, M., Malik, S.: Precise miss analysis for program transformations with caches of arbitrary associativity. In: ASPLOS-VIII: Proceedings of the Eighth International Conference on Architectural Support for Programming Languages and Operating Systems, pp. 228–239. ACM Press, New York (1998)CrossRefGoogle Scholar
  6. 6.
    Chatterjee, S., Parker, E., Hanlon, P.J., Lebeck, A.R.: Exact analysis of the cache behavior of nested loops. In: PLDI 2001: Proceedings of the ACM SIGPLAN 2001 Conference on Programming Language Design and Implementation, pp. 286–297. ACM Press, New York (2001)CrossRefGoogle Scholar
  7. 7.
    Reineke, J., Grund, D., Berg, C., Wilhelm, R.: Timing predictability of cache replacement policies. Real-Time Systems 37(2), 99–122 (2007)CrossRefMATHGoogle Scholar
  8. 8.
    Reineke, J., Grund, D.: Relative competitive analysis of cache replacement policies. In: LCTES 2008: Proceedings of the 2008 ACM SIGPLAN-SIGBED Conference on Languages, Compilers, and Tools for Embedded Systems, pp. 51–60. ACM Press, New York (2008)CrossRefGoogle Scholar
  9. 9.
    Jacob, B., Ng, S.W., Wang, D.T.: Memory Systems: Cache, DRAM, Disk. Morgan Kaufmann Publishers, San Francisco (2008)Google Scholar
  10. 10.
    Cousot, P., Cousot, R.: Basic Concepts of Abstract Interpretation. In: Building the Information Society, pp. 359–366. Kluwer Academic Publishers, Dordrecht (2004)CrossRefGoogle Scholar
  11. 11.
    Ferdinand, C.: Cache Behaviour Prediction for Real-Time Systems. PhD thesis, Saarland University (1997)Google Scholar
  12. 12.
    Cousot, P., Cousot, R., Feret, J., Mauborgne, L., Miné, A., Monniaux, D., Rival, X.: Combination of abstractions in the ASTRÉE static analyzer. In: Okada, M., Satoh, I. (eds.) ASIAN 2006. LNCS, vol. 4435, pp. 272–300. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  13. 13.
    Ghosh, S., Martonosi, M., Malik, S.: Cache miss equations: An analytical representation of cache misses. In: ICS 1997: Proceedings of the 11th International Conference on Supercomputing, pp. 317–324. ACM Press, New York (1997)Google Scholar
  14. 14.
    Ghosh, S., Martonosi, M., Malik, S.: Cache miss equations: A compiler framework for analyzing and tuning memory behavior. ACM Transactions on Programming Languages and Systems 21(4), 703–746 (1999)CrossRefGoogle Scholar
  15. 15.
    Mueller, F., Whalley, D.B., Harmon, M.: Predicting instruction cache behavior. In: LCTRTS 1994: Proceedings of the ACM SIGPLAN Workshop on Language, Compiler, and Tool Support for Real-Time Systems (1994)Google Scholar
  16. 16.
    Li, Y.T.S., Malik, S., Wolfe, A.: Cache modeling for real-time software: Beyond direct mapped instruction caches. In: RTSS 1996: Proceedings of the 17th IEEE Real-Time Systems Symposium, Washington, DC, USA, p. 254. IEEE Computer Society, Los Alamitos (1996)Google Scholar
  17. 17.
    Brand, D., Zafiropulo, P.: On communicating finite-state machines. Journal of the ACM 30(2), 323–342 (1983)MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Peng, W., Iyer, S.P.: Data flow analysis of communicating finite-state machines. ACM Transactions on Programming Languages and Systems 13(3), 399–442 (1991)CrossRefGoogle Scholar
  19. 19.
    Bouajjani, A., Habermehl, P.: Symbolic reachability analysis of FIFO-channel systems with nonregular sets of configurations. Theoretical Computer Science 221(1-2), 211–250 (1999)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Daniel Grund
    • 1
  • Jan Reineke
    • 1
  1. 1.Saarland UniversitySaarbrückenGermany

Personalised recommendations