Skip to main content
SpringerLink
Log in

Performance analysis and comparison of cellular automata GPU implementations

  • Published:
Cluster Computing Aims and scope Submit manuscript

Abstract

Cellular automata (CA) models are of interest to several scientific areas, and there is a growing interest in exploring large systems which would need high performance computing. In this work a CA implementation is presented which performs well in five different NVIDIA GPU architectures, from Tesla to Maxwell, simulating systems with up to a billion cells. Using the game of life (GoL) and a more complex variation of GoL as examples, a performance of 5.58e6 evaluated cells/s is achieved. The two optimizations most often used in previous studies are the use of shared memory and Multicell algorithms. Here, these optimizations do not improve performance in Fermi or newer architectures. The GoL CA code running in an NVIDIA Titan X obtained a speedup of up to \(\sim \)85 x and up to \(\sim \)230 x for a more complex CA, compared to an optimized serial CPU implementation. Finally, the efficiency of each GPU is analyzed in terms of cell performance/transistors and cell performance/bandwidth showing how the architectures improved for this particular problem.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  1. Aaby, B.G., Perumalla, K.S., Seal, S.K.: Efficient simulation of agent-based models on multi-GPU and multi-core clusters. In: Proceedings of the 3rd International ICST Conference on Simulation Tools and Techniques p. 29:1 (2010). doi:10.4108/icst.simutools2010.8822

  2. Balasalle, J., Lopez, M.A., Rutherford, M.J.: Optimizing memory access patterns for cellular. In: Hwu, W. (ed.) GPU Computing Gems Jade Edition, pp. 67–75. Morgan Kaufmann, Amsterdam (2011)

    Google Scholar 

  3. Bauer, M., Cook, H., Khailany, B.: Cudadma. In: Proceedings of 2011 International Conference for High Performance Computing, Networking, Storage and Analysis on—SC 11 p. 12 (2011). doi:10.1145/2063384.2063400

  4. Blecic, I., Cecchini, A., Trunfio, G.A.: Fast and accurate optimization of a GPU-accelerated ca urban model through cooperative coevolutionary particle swarms. Proc. Comput. Sci. 29, 1631–1643 (2014). doi:10.1016/j.procs.2014.05.148

    Article  Google Scholar 

  5. Brodtkorb, A.R., Dyken, C., Hagen, T.R., Hjelmervik, J.M., Storaasli, O.O.: State-of-the-art in heterogeneous computing. Sci. Program. 18(1), 1–33 (2010)

    Google Scholar 

  6. Brown, W.M., Wang, P., Plimpton, S.J., Tharrington, A.N.: Implementing molecular dynamics on hybrid high performance computers—short range forces. Comput. Phys. Commun. 182(4), 898–911 (2011). doi:10.1016/j.cpc.2010.12.021

  7. Browne, S., Dongarra, J., Garner, N., London, K., Mucci, P.: A scalable cross-platform infrastructure for application performance tuning using hardware counters. In: ACM/IEEE 2000 Conference on Supercomputing, p. 42. IEEE (2000)

  8. Campos, R.S., Lobosco, M., dos Santos, R.W.: A GPU-based heart simulator with mass-spring systems and cellular automaton. J Supercomput 69(1), 1–8 (2014). doi:10.1007/s11227-014-1199-5

    Article  Google Scholar 

  9. Carozzani, T., Gandin, C.A., Digonnet, H.: Optimized parallel computing for cellular automaton finite element modeling of solidification grain structures. Modelling Simul. Mater. Sci. Eng. 22(1), 015,012 (2013). doi:10.1088/0965-0393/22/1/015012

    Article  Google Scholar 

  10. Caux, J., Hill David, R., Siregar, P.: Accelerating 3D Cellular automata computation with GP-GPU in the context of integrative biology. In: Cellular Automata—Innovative Modelling for Science and Engineering, pp. 411–426. InTech (2011). https://hal.archives-ouvertes.fr/hal-00679045

  11. Chen, S., Doolen, G.D.: Lattice Boltzmann method for fluid flows. Ann. Rev. Fluid Mech. 30(1), 329–364 (1998). doi:10.1146/annurev.fluid.30.1.329

    Article  MathSciNet  Google Scholar 

  12. CUDA C Programming Guide, vol. 4.2. NVIDIA (2012). http://docs.nvidia.com/cuda/cuda-c-programming-guide/index.html

  13. CUDA C Programming Guide, vol. 7.0. NVIDIA (2015). http://docs.nvidia.com/cuda/cuda-c-programming-guide/index.html

  14. CUDA from NVIDIA. http://www.nvidia.com/cuda

  15. Feichtinger, C., Habich, J., Kstler, H., Hager, G., Rde, U., Wellein, G.: A flexible patch-based lattice Boltzmann parallelization approach for heterogeneous GPU-CPU clusters. Parallal Comput. 37(9), 536–549 (2011). doi:10.1016/j.parco.2011.03.005

    Article  MathSciNet  Google Scholar 

  16. Ferrero, E.E., De Francesco, J.P., Wolovick, N., Cannas, S.A.: q-state potts model metastability study using optimized GPU-based Monte Carlo algorithms. Comput. Phys. Commun. 183(8), 1578–1587 (2012). doi:10.1016/j.cpc.2012.02.026

    Article  MathSciNet  Google Scholar 

  17. Ganguly, N., Sikdar, B.K., Deutsch, A., Canright, G., Chaudhuri, P.P.: A survey on cellular automata. Center for High Performance Computing, Dresden University of Technology (2003). http://citeseerx.ist.psu.edu/viewdoc/summary?, doi:10.1.1.107.7729

  18. Gardner, M.: Mathematical games: the fantastic combinations of John Conway new solitaire game life. Sci. Am. 223(4), 120–123 (1970)

    Article  Google Scholar 

  19. Gibson, M.J., Keedwell, E.C., Savi, D.: Understanding the efficient parallelisation of cellular automata on CPU and GPGPU hardware. In: Proceeding of the Fifteenth Annual Conference Companion on Genetic and Evolutionary Computation Conference Companion—GECCO 13 Companion pp. 171–172 (2013). doi:10.1145/2464576.2464660

  20. Gibson, M.J., Keedwell, E.C., Savi, D.A.: An investigation of the efficient implementation of cellular automata on multi-core CPU and GPU hardware. J. Parallel Distrib. Comput. 77, 11–25 (2014). doi:10.1016/j.jpdc.2014.10.011

  21. Hawick, K.A., Johnson, M.G.: Bit-packed damaged lattice potts model simulations with cuda and gpus. In: Proceedings of International Conferences on Modelling, Simulation and Identification, pp. 371–378 (2011)

  22. Hong, S., Kim, H.: An analytical model for a GPU architecture with memory-level and thread-level parallelism awareness. SIGARCH Comput. Archit. News 37(3), 152 (2009). doi:10.1145/1555815.1555775

    Article  Google Scholar 

  23. Kjolstad, F.B., Snir, M.: Ghost cell pattern. In: Proceedings of the 2010 Workshop on Parallel Programming Patterns, p. 4. ACM, New York (2010)

  24. LAMMPS: Lennard Jones Liquid Benchmark. http://lammps.sandia.gov/bench.html#lj

  25. Lee, C., Ro, W.W., Gaudiot, J.L.: Boosting CUDA applications with CPU-GPU hybrid computing. Int. J. Parallel Program. 42(2), 384–404 (2013). doi:10.1007/s10766-013-0252-y

    Article  Google Scholar 

  26. Lindholm, E., Nickolls, J., Oberman, S., Montrym, J.: Nvidia tesla: a unified graphics and computing architecture. IEEE Micro 28(2), 39–55 (2008)

    Article  Google Scholar 

  27. Maruyama, N., Aoki, T.: Optimizing stencil computations for NVIDIA Kepler GPUs. In: Größlinger, A., Köstler, H. (eds.) Proceedings of the 1st International Workshop on High-Performance Stencil Computations, pp. 89–95. Austria, Vienna (2014)

  28. Meng, J., Skadron, K.: Performance modeling and automatic ghost zone optimization for iterative stencil loops on GPUs. In: Proceedings of the 23rd International Conference on Conference on Supercomputing—ICS 09 pp. 256–265 (2009). doi:10.1145/1542275.1542313

  29. Millán, E.N., Bederian, C., Piccoli, M.F., García Garino, C., Bringa, E.M.: Performance analysis of cellular automata HPC implementations. Comput. Electr. Eng. 48, 12–24 (2015). doi:10.1016/j.compeleceng.2015.09.015

    Article  Google Scholar 

  30. Millán, E.N., Martínez, P.C., Gil Costa, G.V., Piccoli, M.F., Printista, A.M., Bederian, C., García Garino, C., Bringa, E.M.: Parallel implementation of a cellular automata in a hybrid CPU/GPU environment. In: A. De Giusti (ed.) XVIII Congreso Argentino de Ciencias de la Computación, pp. 184–193. Red de Universidades con Carreras en Informática RedUNCI (2013). ISBN 978-987-23963-1-2

  31. Moore, N.: Kernel specialization for improved adaptability and performance on graphics processing units (gpus). Ph.D. thesis, Northeastern University Boston, MA (2012)

  32. North, M.J., Collier, N.T., Ozik, J., Tatara, E.R., Macal, C.M., Bragen, M., Sydelko, P.: Complex adaptive systems modeling with repast simphony. Complex Adapt. Syst. Model. 1(1), 3 (2013). doi:10.1186/2194-3206-1-3

    Article  Google Scholar 

  33. NVIDIA: Whitepaper NVIDIA GeForce GTX 750 Ti, v1.1

  34. NVIDIA: Whitepaper NVIDIA GeForce GTX 980, v1.1

  35. NVIDIA: Whitepaper NVIDIAs Next Generation CUDA Compute Architecture: Fermi, v1.1

  36. NVIDIA: Whitepaper NVIDIAs Next Generation CUDA Compute Architecture: Kepler GK110, v1.0

  37. NVIDIA: Nvidia geforce 8800 gpu architecture overview. Technical brief, November 2006 (2006)

  38. NVIDIA: Tuning Cuda Applications for Kepler, v7.0 (2015)

  39. NVIDIA: Tuning Cuda Applications for Maxwell, v7.0 (2015)

  40. NVIDIA: Nvidia geforce gtx 200 gpu architectural overview. Technical brief, May (2008)

  41. Oxman, G., Weiss, S., Be’ery, Y.: Computational methods for conway’s game of life cellular automaton. J. Comput. Sci. 5(1), 24–31 (2014). doi:10.1016/j.jocs.2013.07.005

    Article  MathSciNet  Google Scholar 

  42. Papadopoulou, M.M., Sadooghi-Alvandi, M., Wong, H.: Micro-benchmarking the GT200 GPU. Computer Group, ECE, University of Toronto, Technical Report (2009)

  43. Perumalla, K.S., Aaby, B.G.: Data parallel execution challenges and runtime performance of agent simulations on gpus. In: Proceedings of the 2008 Spring Simulation Multiconference, SpringSim’08, pp. 116–123. Society for Computer Simulation International, San Diego, CA, USA (2008). http://dl.acm.org/citation.cfm?id=1400549.1400564

  44. Pohl, T., Deserno, F., Thurey, N., Rude, U., Lammers, P., Wellein, G., Zeiser, T.: Performance evaluation of parallel large-scale lattice boltzmann applications on three supercomputing architectures. In: Proceedings of the ACM/IEEE SC2004 Conference p. 21 (2004). doi:10.1109/sc.2004.37

  45. Preis, T., Virnau, P., Paul, W., Schneider, J.J.: GPU accelerated Monte Carlo simulation of the 2D and 3D ising model. J. Comput. Phys. 228(12), 4468–4477 (2009). doi:10.1016/j.jcp.2009.03.018

    Article  MATH  Google Scholar 

  46. RanjanNayak, D., Kumar Sahu, S., Mohammed, J.: A cellular automata based optimal edge detection technique using twenty-five neighborhood model. IJCA 84(10), 27–33 (2013). doi:10.5120/14614-2869

    Article  Google Scholar 

  47. Rapaport, D.: Enhanced molecular dynamics performance with a programmable graphics processor. Comput. Phys. Commun. 182(4), 926–934 (2011). doi:10.1016/j.cpc.2010.12.029

    Article  MATH  Google Scholar 

  48. Rauch, L., Madej, L., Spytkowski, P., Golab, R.: Development of the cellular automata framework dedicated for metallic materials microstructure evolution models. Arch. Civil Mech. Eng. 15(1), 48–61 (2015). doi:10.1016/j.acme.2014.06.006

    Article  Google Scholar 

  49. Russo, L., Russo, P., Vakalis, D., Siettos, C.: Detecting weak points of wildland fire spread: a cellular automata model risk assessment simulation approach. Chem. Eng. 36, 253–258 (2014)

    Google Scholar 

  50. Rybacki, S., Himmelspach, J., Uhrmacher, A.M.: Experiments with single core, multi-core, and GPU based computation of cellular automata. In: First International Conference on Advances in System Simulation, 2009. SIMUL’09, pp. 62–67. IEEE (2009)

  51. Ryoo, S., Rodrigues, C.I., Stone, S.S., Baghsorkhi, S.S., Ueng, S.Z., Stratton, J.A., Hwu, W.m.W.: Program optimization space pruning for a multithreaded gpu. In: Proceedings of the Sixth Annual IEEE/ACM International Symposium on Code Generation and Optimization—CGO 08 (2008). doi:10.1145/1356058.1356084

  52. Shimokawabe, T., Aoki, T., Takaki, T., Yamanaka, A., Nukada, A., Endo, T., Maruyama, N., Matsuoka, S.: Peta-scale phase-field simulation for dendritic solidification on the tsubame 2.0 supercomputer. In: 2011 International Conference for High Performance Computing, Networking, Storage and Analysis (SC), pp. 1–11 (2011)

  53. Smoller, J.: Shock waves and reaction-diffusion equations. In: Research Supported by the US Air Force and National Science Foundation, vol. 258. Springer, New York(Grundlehren der Mathematischen Wissenschaften, vol. 258), p. 600 (1983)

  54. Topa, P.: Cellular automata model tuned for efficient computation on GPU with global memory cache. In: 2014 22nd Euromicro International Conference on Parallel, Distributed, and Network-Based Processing, pp. 380–383 (2014). doi:10.1109/pdp.2014.97

  55. Topa, P., Młocek, P.: Using shared memory as a cache in cellular automata water flow simulations on gpus. Comput. Sci. 14, 3 (2013)

    Google Scholar 

  56. Top 500 supercomputers, list of june 2016. http://www.top500.org/lists/2016/06/

  57. Veerbeek, W., Pathirana, A., Ashley, R., Zevenbergen, C.: Enhancing the calibration of an urban growth model using a memetic algorithm. Comput. Environ. Urban Syst. 50, 53–65 (2015). doi:10.1016/j.compenvurbsys.2014.11.003

    Article  Google Scholar 

  58. Volkov, V.: Better performance at lower occupancy. In: Proceedings of the GPU Technology Conference, GTC, vol. 10 (2010)

  59. Volkov, V., Demmel, J.: Benchmarking GPUs to tune dense linear algebra. 2008 SC—International Conference for High Performance Computing, Networking, Storage and Analysis, pp. 1–11 (2008). doi:10.1109/sc.2008.5214359

  60. Wilensky, U.: Netlogo. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL (1999). http://ccl.northwestern.edu/netlogo/

  61. Williams, S., Waterman, A., Patterson, D.: Roofline: an insightful visual performance model for multicore architectures. Commun. ACM 52(4), 65 (2009). doi:10.1145/1498765.1498785

    Article  Google Scholar 

  62. Zhao, Y.: GPU accelerated computation and real-time rendering of cellular automata model for spatial simulation. J. Inform. Comput. Sci. 11(12), 4453–4465 (2014). doi:10.12733/jics20104445

    Article  Google Scholar 

Download references

Acknowledgements

The authors acknowledge support from CONICET, ANPCyT Grant PICT-2014-0696, and a SeCTyP UNCuyo Grant. This work used the clusters Mendieta from CCAD-UNC and ICB-ITIC from UNCuyo, which are part of the SNCAD network.

Author information

Authors and Affiliations

  1. CONICET and FCEN, Universidad Nacional de Cuyo, Mendoza, Argentina

    Emmanuel N. Millán & Eduardo M. Bringa

  2. Universidad Nacional de Córdoba, Córdoba, Argentina

    Nicolás Wolovick

  3. Universidad Nacional de San Luis, San Luis, Argentina

    María Fabiana Piccoli

  4. ITIC and FING, Universidad Nacional de Cuyo, Mendoza, Argentina

    Carlos García Garino

Authors
  1. Emmanuel N. Millán
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nicolás Wolovick
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. María Fabiana Piccoli
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Carlos García Garino
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Eduardo M. Bringa
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Emmanuel N. Millán.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Millán, E.N., Wolovick, N., Piccoli, M.F. et al. Performance analysis and comparison of cellular automata GPU implementations. Cluster Comput 20, 2763–2777 (2017). https://doi.org/10.1007/s10586-017-0850-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10586-017-0850-3

Keywords

Search

Navigation