skip to main content
article
Free Access

On the discrepancy of GFSR pseudorandom numbers

Published:01 October 1987Publication History
Skip Abstract Section

Abstract

A new summation formula based on the orthogonal property of Walsh functions is devised. Using this formula, the k-dimensional discrepancy of the generalized feedback shift register (GFSR) pseudorandom numbers is derived. The relation between the discrepancy and k-distribution of GFSR sequences is also obtained. Finally the definition of optimal GPSR pseudorandom number generators is introduced.

References

  1. 1 BEAUCHAMP, K.G. Walsh Functions and Their Applications. Academic Press, London, 1975.Google ScholarGoogle Scholar
  2. 2 BOROSH, I., AND NIEDERREITER, H. Optimal multipliers for pseudorandom number generation by the linear congruential method. BIT 23 (1983), 65-74.Google ScholarGoogle Scholar
  3. 3 FUSmMI, M., AND TEZUKA, S. The k-distribution of generalized feedback shift register pseudorandom numbers. Commun. ACM 26, 7 (July 1983), 516-523. Google ScholarGoogle Scholar
  4. 4 KNtrrH, D. E. The Art of Computer Programming, vol. 2: Seminumerical Algorithms, 2nd ed. Addison-Wesley, Reading, Mass., 1981.Google ScholarGoogle Scholar
  5. 5 KuNz, H. O., AND RAMM-ARNFr, J. Walsh matrices. Arch. Elektron. Ubertragungstech. (Electron. Commun.) 32 (1978), 56-58.Google ScholarGoogle Scholar
  6. 6 LEwis, T. G., AND PAVNE, W. H. Generalized feedback shift register pseudorandom number algorithms. J. ACM. 20, 3 (July 1973), 456-468. Google ScholarGoogle Scholar
  7. 7 MARSAGLIA, G. Random number generator. In Encyclopedia of Computer Science, A. Ralston and C. L. Meek, Eds. Petrocelli/Charter, New York, 1976.Google ScholarGoogle Scholar
  8. 8 NIFDERREITER, H. Pseudorandom numbers and optimal coefficients. Adv. Math. 26 (1977), 99-181.Google ScholarGoogle Scholar
  9. 9 NIEDERREITER, H. Quasi-Monte Carlo methods and pseudorandom numbers. Bull. Amer. Math. Soc. 84 (1978), 957-1041.Google ScholarGoogle Scholar
  10. 10 NIEDFRRErrER, H. Applications des corps finis aux nombres pesudoaleatoires. Sere. Theorie des Nombres 1982-83, Exp. 38. Univ. de Bordeaux 1, Talence, France, 1983.Google ScholarGoogle Scholar
  11. 11 NIEDFRREIT~R, H. The performance of K-step pseudorandom number generators under the uniformity test. SIAM J. Sci. Statist. Comput. 5 (1984), 798-810.Google ScholarGoogle Scholar
  12. 12 TAUSWORTHE, R. C. Random numbers generated by linear recurrence modulo two. Math. Comput. 19 (1965), 201-209.Google ScholarGoogle Scholar
  13. 13 T~.zu~, S. Walsh-spectral test for GFSR pscudorandom numbers. Commun. ACM 30, 8 (Aug. 1987), 731-735. Google ScholarGoogle Scholar

Index Terms

  1. On the discrepancy of GFSR pseudorandom numbers

      Recommendations

      Reviews

      Taghi J. Mirsepassi

      .abstract A new summation formula based on the orthogonal property of Walsh functions is devised. Using this formula, the k-dimensional discrepancy of the generalized feedback shift register (GFSR) pseudorandom numbers is derived. The relation between the discrepancy and k-distribution of GFSR sequences is also obtained. Finally the definition of optimal GFSR pseudorandom number generators is introduced. — Author's Abstract For the reader who needs additional background information, I recommend [1,2].

      Access critical reviews of Computing literature here

      Become a reviewer for Computing Reviews.

      Comments

      Login options

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

      Sign in

      Full Access

      • Published in

        cover image Journal of the ACM
        Journal of the ACM  Volume 34, Issue 4
        Oct. 1987
        254 pages
        ISSN:0004-5411
        EISSN:1557-735X
        DOI:10.1145/31846
        Issue’s Table of Contents

        Copyright © 1987 ACM

        Publisher

        Association for Computing Machinery

        New York, NY, United States

        Publication History

        • Published: 1 October 1987
        Published in jacm Volume 34, Issue 4

        Permissions

        Request permissions about this article.

        Request Permissions

        Check for updates

        Qualifiers

        • article

      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!