No Access Submitted: 13 June 2005 Accepted: 01 December 2005 Published Online: 13 January 2006
Chaos 16, 013110 (2006); https://doi.org/10.1063/1.2159147
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Modern computer microprocessors are composed of hundreds of millions of transistors that interact through intricate protocols. Their performance during program execution may be highly variable and present aperiodic oscillations. In this paper, we apply current nonlinear time series analysis techniques to the performances of modern microprocessors during the execution of prototypical programs. Our results present pieces of evidence strongly supporting that the high variability of the performance dynamics during the execution of several programs display low-dimensional deterministic chaos, with sensitivity to initial conditions comparable to textbook models. Taken together, these results show that the instantaneous performances of modern microprocessors constitute a complex (or at least complicated) system and would benefit from analysis with modern tools of nonlinear and complexity science.
  1. 1. G. E. Moore, Electronics 38, 114 (1965). Google Scholar
  2. 2. M. Stephenson and S. Amarasinghe, in Proc. International Symposium on Code Generation and Optimization (CGO), 2005. Google Scholar
  3. 3. P. Kulkarni, S. Hines, J. Hiser, D. Whalley, J. Davidson, and D. Jones, in Proc. ACM SIGPLAN Conference on Programming Language Design and Implementation (PLDI), 2004. Google Scholar
  4. 4. G. Fursin, M. O’Boyle, and P. Knijnenburg, in Proc. Languages and Compilers for Parallel Computers (LCPC), 2002, pp. 305–315. Google Scholar
  5. 5. E. Duesterwald, C. Cascaval, and S. Dwarkadas, in Proc. 12th International Conference on Parallel Architectures and Compilation Techniques (PACT’03), New Orleans, Louisiana, 2003, pp. 220–231. Google Scholar
  6. 6. M. Annavaram, R. Rakvic, M. Polito, J. -Y. Bouguet, R. Hankins, and B. Davies, in Proc. 37th Annual IEEE ACM International Symposium on Microarchitecture (MICRO-37), Portland, OR, 2004, pp. 93–104. Google Scholar
  7. 7. N. T. Slingerland and A. J. Smith, in ICS ’01: Proceedings of the 15th International Conference on Supercomputing (ACM Press, New York, NY, 2001), pp. 204–217, ISBN 1-58113-410-X. Google ScholarCrossref
  8. 8. M. D. Lam, E. E. Rothberg, and M. E. Wolf, in ASPLOS-IV: Proceedings of the 4th International Conference on Architectural Support for Programming Languages and Operating Systems (ACM Press, New York, NY, 1991), pp. 63–74, ISBN 0-89791-380-9. Google ScholarCrossref
  9. 9. S. Coleman and K. McKinley, in Proc. PLDI, 1995, pp. 279–290. Google ScholarCrossref
  10. 10. I. Gluhovsky and B. O’Krafka, ACM Trans. Comput. Syst. 23, 111 (2005). Google ScholarCrossref
  11. 11. J. Abella, A. Gonzalez, J. Llosa, and X. Vera, “Near-optimal loop tiling by means of cache miss equations and genetic algorithms,” 2001, URL citeseer.csail.mit.edu/abella01nearoptimal.html. Google Scholar
  12. 12. D. Burger, T. M. Austin, and S. Bennett, Tech. Rep. CS-TR-1996-1308 (1996), URL citeseer.ist.psu.edu/burger96evaluating.html. Google Scholar
  13. 13. T. S. Karkhanis and J. E. Smith, in ISCA ’04: Proceedings of the 31st Annual International Symposium on Computer Architecture (IEEE Computer Society, Washington, DC, USA, 2004), p. 338, ISBN 0-7695-2143-6. Google Scholar
  14. 14. D. Burger, T. M. Austin, and S. W. Keckler, Perform. Eval. Rev 31, 4 (2004). Google ScholarCrossref
  15. 15. P. Koiran, M. Cosnard, and M. H. Garzon, Theor. Comput. Sci. 132, 113 (1994). Google ScholarCrossref
  16. 16. M. Cook, Complex Syst. 15, 1 (2004). Google Scholar
  17. 17. J. Kilian and H. Siegelmann, in Proceedings of the 6th Annual ACM Conference on Computational Learning Theory, Santa Cruz, CA, USA, 1993. Google Scholar
  18. 18. H. Siegelmann and E. Sontag, Appl. Math. Lett. 4, 77 (1991). Google ScholarCrossref
  19. 19. M. Branicky, Theor. Comput. Sci. 138, 67 (1995). Google ScholarCrossref
  20. 20. S. Omohundro, Physica D 10, 128 (1984). Google ScholarCrossref
  21. 21. J. Ŝíma and P. Orponen, Neural Comput. 15, 693 (2003). Google ScholarCrossref
  22. 22. R. Hegger, H. Kantz, and T. Schreiber, Chaos https://doi.org/10.1063/1.166424 9, 413 (1999). Google ScholarScitation
  23. 23. T. Schreiber, Phys. Rep. https://doi.org/10.1016/S0370-1573(98)00021-0 308, 2 (1999). Google ScholarCrossref
  24. 24. Y. Yamamoto, Modern Techniques in Neuroscience Research (Springer-Verlag, Berlin, 1999), pp. 669–687. Google ScholarCrossref
  25. 25. C. -K. Peng, S. Havlin, H. Stanley, and A. Goldberger, Chaos https://doi.org/10.1063/1.166141 5, 82 (1995). Google ScholarScitation
  26. 26. G. Rangarajan and M. Ding, Phys. Rev. E https://doi.org/10.1103/PhysRevE.61.4991 61, 4991 (2000). Google ScholarCrossref
  27. 27. F. Takens, in Dynamical Systems and Turbulence, Vol. 898 of Lecture Notes in Math., edited by D. Rand and L. -S. Young (Springer-Verlag, Berlin, 1981), pp. 366–381. Google ScholarCrossref
  28. 28. N. Packard, J. P. Crutchfield, J. D. Farmer, and R. S. Shaw, Phys. Rev. Lett. https://doi.org/10.1103/PhysRevLett.45.712 45, 712 (1980). Google ScholarCrossref
  29. 29. M. Casdagli, S. Eubank, J. D. Farmer, and J. Gibson, Physica D https://doi.org/10.1016/0167-2789(91)90222-U 51, 52 (1991). Google ScholarCrossref
  30. 30. M. Rosenstein, J. Collins, and C. D. Luca, Physica D https://doi.org/10.1016/0167-2789(93)90009-P 65, 117 (1993). Google ScholarCrossref
  31. 31. H. Abarbanel, Analysis of Observed Chaotic Data (Springer-Verlag, New York, 1996). Google ScholarCrossref
  32. 32. H. Kantz and T. Schreiber, Nonlinear Time Series Analysis (Cambridge University Press, Cambridge, 1996). Google Scholar
  33. 33. M. Kennel, R. Brown, and H. Abarbanel, Phys. Rev. A https://doi.org/10.1103/PhysRevA.45.3403 45, 3403 (1992). Google ScholarCrossref
  34. 34. J. -P. Eckmann, S. O. Kamphorst, and D. Ruelle, Europhys. Lett. 5, 973 (1987). Google ScholarCrossref
  35. 35. J. Zbilut, N. Thomasson, and C. Webber, Med. Eng. Phys. https://doi.org/10.1016/S1350-4533(01)00112-6 24, 53 (2002). Google ScholarCrossref
  36. 36. M. Thiel, M. Romano, J. Kurths, and P. Read, Chaos https://doi.org/10.1063/1.1667633 14, 234 (2004). Google ScholarScitation
  37. 37. J. Theiler, J. Opt. Soc. Am. A 7, 1055 (1990). Google ScholarCrossref
  38. 38. H. Kantz, Phys. Lett. A 185, 177 (1994). Google ScholarCrossref
  39. 39. T. Schreiber and A. Schmitz, Physica D https://doi.org/10.1016/S0167-2789(00)00043-9 142, 346 (2000). Google ScholarCrossref
  40. 40. S. V. Buldyrev, A. L. Goldberger, S. Havlin, R. N. Mantegna, M. E. Matsa, C. -K. Peng, M. Simons, and H. E. Stanley, Phys. Rev. E https://doi.org/10.1103/PhysRevE.51.5084 51, 5084 (1995). Google ScholarCrossref
  41. 41. C. Heneghan and G. McDarby, Phys. Rev. E https://doi.org/10.1103/PhysRevE.62.6103 62, 6103 (2000). Google ScholarCrossref
  42. 42. E. Bradley and R. Mantilla, Chaos https://doi.org/10.1063/1.1488255 12, 596 (2002). Google ScholarScitation
  43. 43. H. D. I. Abarbanel, R. Brown, and M. B. Kennel, J. Nonlinear Sci. 1, 175 (1991). Google ScholarCrossref
  44. 44. A. Wolf, J. Swift, H. Swinney, and J. Vastano, Physica D https://doi.org/10.1016/0167-2789(85)90011-9 16, 285 (1985). Google ScholarCrossref
  45. 45. S. Wolfram, A New Kind of Science (Wolfram Media, 2002), URL http://www.wolframscience.com. Google Scholar
  46. 46. A. Seznec and N. Sendrier, ACM Trans. Model. Comput. Simul. 13, 334 (2003). Google ScholarCrossref
  47. 47. R. E. Wunderlich, T. F. Wenisch, B. Falsafi, and J. C. Hoe, in ISCA ’03: Proceedings of the 30th Annual International Symposium on Computer Architecture (ACM Press, New York, NY, 2003), pp. 84–97, ISBN 0-7695-1945-8. Google Scholar
  48. 48. T. Sherwood, E. Perelman, G. Hamerly, and B. Calder, SIGOPS Oper. Syst. Rev. 36, 45 (2002). Google ScholarCrossref
  49. 49. E. Perelman, G. Hamerly, M. V. Biesbrouck, T. Sherwood, and B. Calder, in ACM SIGMETRICS the International Conference on Measurement and Modeling of Computer Systems, 2003. Google Scholar
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