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Compute Bound and I/O Bound Cellular Automata Simulations on FPGA Logic

Published:01 January 2009Publication History
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Abstract

FPGA-based computation engines have been used as Cellular Automata accelerators in the scientific community for some time now. With the recent availability of more advanced FPGA logic it becomes necessary to better understand the mapping of Cellular Automata to these systems. There are many trade-offs to consider when mapping a Cellular Automata algorithm from an abstract system to the physical implementation using FPGA logic. The trade-offs include both the available FPGA resources and the Cellular Automata algorithm's execution time. The most important aspect is to fully understand the behavior of the specified CA algorithm in terms of its execution times which are either compute bound or I/O bound. In this article, we present a methodology to categorize a specified CA algorithm as a compute bound or an I/O bound. We take the methodology further by presenting rigorous analysis for each of the two cases identifying the various parameters that control the mapping process and are defined both by the Cellular Automata algorithm and the given FPGA hardware specifications. This methodology helps to predict the performance of running Cellular Automata algorithms on specific FPGA hardware and to determine optimal values for the various parameters that control the mapping process. The model is validated for both compute and I/O bound two-dimensional Cellular Automata algorithms. We find that our model predictions are accurate within 7%.

References

  1. Boghosian, S. M. 1999. Lattice gas and cellular automata. Future Gen. Comput. Syst. 16, 0, 171--185. Google ScholarGoogle ScholarDigital LibraryDigital Library
  2. Bubak, M., Moscinski, J., and Slota, R. 1994. Parallel program for 2D FHP Lattice gas simulation on clusters of workstations. In Proceedings of the 10th Summer School on Computing Techniques in Physics: HPC in Science.Google ScholarGoogle Scholar
  3. Cappuccino, G. and Cocorullo, G. 2001. Custom Reconfigurable Computing Machine for High Performance Cellular Automata Processing. TechOnLine Publication.Google ScholarGoogle Scholar
  4. Chopard, B. and Droz, M. 1998. Cellular Automata Modeling of Physical Systems. Cambridge University Press.Google ScholarGoogle Scholar
  5. Deutsch, A. and Dormann, S. 2004. Cellular Automaton Modeling of Biological Pattern Formation. Birkhauser.Google ScholarGoogle Scholar
  6. Dubbeldam, D., Hoekstra, A. G., and Sloot, P. M. A. 2000. Dynamic structure factor in single- and two-species thermal GBL lattice gas. Comput. Phys. Comm. 129, 13--20.Google ScholarGoogle ScholarCross RefCross Ref
  7. Gutowitz, H. A. 1990. Cellular Automata. MIT Press.Google ScholarGoogle Scholar
  8. Hardy, P., Pommeau, Y., and de Pazzis, O. 1973. Time evolution of a two-dimensional model system. I. Invariant states and time correlation functions. J. Math. Phys. 1, 0, 1746--1759.Google ScholarGoogle ScholarCross RefCross Ref
  9. Ilachinski, A. 2001. Cellular Automata: A Discrete Universe. World Scientific. Google ScholarGoogle ScholarDigital LibraryDigital Library
  10. Kobori, T., Maruyama, T., and Hoshino, T. 2001. A cellular automata system with FPGA. In Proceedings of the 9th Annual IEEE Symposium on Field-Programmable Custom Computing Machines. 120--129. Google ScholarGoogle ScholarDigital LibraryDigital Library
  11. Murtaza, S., Hoekstra, A., and Sloot, P. 2007. Performance modeling of 2D Cellular Automata on FPGA. In Proceedings of the 17th International Conference on Field Programmable Logic and Applications. 74--78.Google ScholarGoogle Scholar
  12. Rivet, J. P. and Boon, J. P. 2001. Lattice Gas Hydrodynamics. Cambridge University Press.Google ScholarGoogle Scholar
  13. Rothman, D. H. and Zaleski, S. 1997. Lattice-Gas Cellular Automata, Simple Models of Complex Hydrodynamics. Cambridge University Press.Google ScholarGoogle Scholar
  14. Shand, D., Denning, D., and Chamberlain, R. 2005. Lattice gases - simple models of complex fluid dynamics. White Paper, NT309-0001. www.Nallatatech.com.Google ScholarGoogle Scholar
  15. Shaw, P., Cockshott, P., and Barrie, P. 1996. Implementation of lattice gases using FPGAs. J. VLSI Signal Process. 12, 1, 51--66.Google ScholarGoogle ScholarCross RefCross Ref
  16. Sloot, P. M. A., Chopard, B., and Hoekstra, A. G. 2004. Cellular automata. In Proceedings of the 6th International Conference on Cellular Automata for Research and Industry (ACRI'04). Springer Verlag.Google ScholarGoogle Scholar
  17. Sloot, P. M. A. and Hoekstra, A. G. 2001. Cellular Automata as a Mesoscopic Approach to Model and Simulate Complex Systems. Lecture Notes in Computer Science, vol. 518. Springer Verlag. Google ScholarGoogle ScholarDigital LibraryDigital Library
  18. Sloot, P. M. A. and Hoekstra, A. G. 2007. Modeling dynamic systems with cellular automata. In Handbook of Dynamic System Modeling, Ed. Paul A. Fishwick. CRC Press.Google ScholarGoogle Scholar
  19. Sloot, P. M. A., Kaandorp, J. A., Hoekstra, A. G., and Overeinder, B. J. 2001. Distributed cellular automata: Large scale simulation of natural phenomena. In Solutions to Parallel and Distributed Computing Problems, Lessons from Biological Sciences. 1--46.Google ScholarGoogle Scholar
  20. Sloot, P. M. A., Overeinder, B. J., and Schoneveld, A. 2001. Self-organized criticality in simulated correlated systems. Comput. Phys. Comm. 142, 76--81.Google ScholarGoogle ScholarCross RefCross Ref
  21. Succi, S. 2001. The Lattice-Boltzmann Equation. Oxford University Press.Google ScholarGoogle Scholar
  22. Toffoli, T. and Margolus, N. 1987. Cellular Automata Machines. MIT Press.Google ScholarGoogle Scholar
  23. Wolfram, S. 1994. Cellular Automata and Complexity. Perseus Book Group.Google ScholarGoogle Scholar

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  1. Compute Bound and I/O Bound Cellular Automata Simulations on FPGA Logic

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