skip to main content
10.1145/503048.503064acmconferencesArticle/Chapter ViewAbstractPublication PagesfpgaConference Proceedingsconference-collections
Article

FPGA implementation of neighborhood-of-four cellular automata random number generators

Published:24 February 2002Publication History

ABSTRACT

Random number generators (RNGs) based upon neighborhood-of-four cellular automata (CA) with asymmetrical, non-local connections are explored. A number of RNGs that pass Marsaglia's rigorous Diehard suite of random number tests have been discovered. A neighborhood size of four allows a single CA cell to be implemented with a four-input lookup table and a one-bit register which are common building blocks in popular field programmable gate arrays (FPGAs). The investigated networks all had periodic (wrap around) boundary conditions with either 1-d, 2-d, or 3-d interconnection topologies. Trial designs of 64-bit networks using a Xilinx XCV1000-6 FPGA predict a maximum clock rate of 214 MHz to 230 MHz depending upon interconnection topology.

References

  1. 1.N. Metropolis and S. Ulam, "The Monte Carlo method," Journal of American Statistical Association, vol. 44, pp. 335-341, 1949.Google ScholarGoogle ScholarCross RefCross Ref
  2. 2.M.A.KalosandP.A.Whitlock,Monte Carlo Methods, Volume I: Basics, Wiley Interscience, New York, 1986. Google ScholarGoogle ScholarDigital LibraryDigital Library
  3. 3.S. K. Park and K. W. Miller, "Random number generators: good ones are hard to find," Communications of the ACM, vol. 31, no. 10, pp. 1192-1201, October 1988. Google ScholarGoogle ScholarDigital LibraryDigital Library
  4. 4.D. E. Knuth, The Art of Computer Programming: Volume 2, Seminumerical Algorithms, 3rd ed., Addison-Wesley, ch. 3, 1998. Google ScholarGoogle ScholarDigital LibraryDigital Library
  5. 5.G. Marsaglia, "Remarks on choosing and implementing random number generators," Communications of the ACM, vol. 36, no. 7, pp. 105-110, July 1993.Google ScholarGoogle Scholar
  6. 6.G. Marsaglia, "A current view of random numbers," Computer Science and Statistics: The Interface,L.Billard,ed.,Elsevier Science Publishers B. V., pp. 3-10, 1985.Google ScholarGoogle Scholar
  7. 7.G. Marsaglia, DIEHARD, http://stat.fsu.edu/geo/diehard.html, 1996.Google ScholarGoogle Scholar
  8. 8.VR. C. Tausworthe, "Random numbers generated by linear recurrence modulo two," Mathematical Computing, vol. 19, pp. 201-209, 1965.Google ScholarGoogle ScholarCross RefCross Ref
  9. 9.S. W. Golomb, Shift Register Sequences, Holden-Day, San Francisco, 1967. Google ScholarGoogle ScholarDigital LibraryDigital Library
  10. 10.S. Wolfram, "Random sequence generation by cellular automata," Advances in Applied Mathematics, vol. 7, pp. 123-169, June 1986. (Also available in S. Wolfram, Cellular Automata and Complexity, Addison-Wesley, 1994.) Google ScholarGoogle ScholarDigital LibraryDigital Library
  11. 11.P.D.Hortensius,R.D.McLeod,andH.C.Card,"Parallel number generation for VLSI systems using cellular automata," IEEE Transactions on Computers, vol. 38, no. 10, pp. 1466-1473, October 1989. Google ScholarGoogle ScholarDigital LibraryDigital Library
  12. 12.B. Shackleford, G. Snider, R. J. Carter, E. Okushi, M. Yasuda, K. Seo, and H. Yasuura, "A high-performance, pipelined, FPGA- based genetic algorithm machine," Genetic Programming and Evolvable Machines, vol. 2, no. 1, pp. 33-60, March 2001. Google ScholarGoogle ScholarDigital LibraryDigital Library
  13. 13.P. D. Hortensius, H. C. Card, R. D. McLeod, and W. Pries, "Importance sampling for Ising Computers using one-dimensional cellular automata," IEEE Transactions on Computers, vol. 38, no. 6, pp. 769-774, June 1989. Google ScholarGoogle ScholarDigital LibraryDigital Library
  14. 14.Ph. Tsalides, T. A. York, and A. Thanailakis, "Pseudorandom number generators for VLSI systems based on linear cellular automata," IEE Proceedings-E, vol. 138, no. 4, pp. 241-249, July 1991.Google ScholarGoogle Scholar
  15. 15.S. Nandi, B. Vamsi, S. Chakraborty, and P. P. Chaudhuri, "Cellular automata as a BIST structure for testing CMOS circuits," IEE Proceedings-Computer Digital Technology, vol. 141, no. 1, pp. 41-47, January 1994.Google ScholarGoogle ScholarCross RefCross Ref
  16. 16.D. R. Chowdhury, I. Sengupta, and P. P. Chaudhuri, "A class of two-dimensional cellular automata and their applications in random pattern testing," Journal of Electronic Testing,vol.5,pp. 67-82, 1994. Google ScholarGoogle ScholarDigital LibraryDigital Library
  17. 17.M. Sipper and M. Tomassini, "Generating parallel random number generators by cellular programming," International Journal of Modern Physics C, vol. 7, no. 2, pp. 181-190, 1996.Google ScholarGoogle ScholarCross RefCross Ref
  18. 18.M. Tomassini, M. Sipper, M. Zolla, and M. Perrenoud, "Generating high-quality random numbers in parallel by cellular automata," Future Generation Computer Systems, vol. 16, pp. 291-305, 1999. Google ScholarGoogle ScholarDigital LibraryDigital Library
  19. 19.M. Tomassini, M. Sipper, and M. Perrenoud, "On the generation of high-quality random numbers by two-dimensional cellular automata," IEEE Transactions on Computers, vol. 49, pp. 1146- 1151, October 2000. Google ScholarGoogle ScholarDigital LibraryDigital Library
  20. 20.S. Wolfram, "Statistical mechanics of cellular automata," Reviews of Modern Physics, vol. 55, pp. 601-644, July 1983. (Also available in S. Wolfram, Cellular Automata and Complexity, Addison-Wesley, 1994.)Google ScholarGoogle Scholar
  21. 21.S. Ulam, "Random processes and transformations," Proceedings of the International Congress of Mathematics (1950),vol.2,pp. 264-275, 1952.Google ScholarGoogle Scholar
  22. 22.J. von Neumann, Theory of Self-Reproducing Automata,ed. Authur Burks, University of Illinois Press, 1966. Google ScholarGoogle ScholarDigital LibraryDigital Library
  23. 23.S. Wolfram (ed.), Theory and Applications of Cellular Automata, World Scientific, 1986.Google ScholarGoogle Scholar
  24. 24.S. Wolfram, A New kind of Science, Wolfram Media, January 2002. Google ScholarGoogle ScholarDigital LibraryDigital Library

Recommendations

Comments

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Sign in

PDF Format

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader
About Cookies On This Site

We use cookies to ensure that we give you the best experience on our website.

Learn more

Got it!