skip to main content
article
Free Access

Normal Random Numbers: Using Machine Analysis to Choose the Best Algorithm

Authors Info & Claims
Published:01 December 1977Publication History
First page image

References

  1. 1 AHRENS, H.H., AND DIETER, U. Computer methods for sampling from the exponential and normal distributions. Comm. ACM 15, 10 (Oct. 1972), 873-882. Google ScholarGoogle Scholar
  2. 2 AHRENS, J.H., AND DIETER, U. Extension of Forsythe's method for random sampling from the normal distribution. Math. Comput. 27, 124 (1973), 927-937.Google ScholarGoogle Scholar
  3. 3 BELL, J.R. Algorithm 334: Normal random deviates. Comm. ACM 11, 7 (July 1968), 498. Google ScholarGoogle Scholar
  4. 4 BRENT, R.P. Algorithm 488: A Gaussian pseudo-random number generator. Comm. ACM 17, 12 (Dec. 1974), 704-706. Google ScholarGoogle Scholar
  5. 5 DE LuG1s~, B.G A class of algorithms for automatic evaluation of certain elementary functions in a binary computer. Rep. No. 399, Dept. Comptr. Sei., U. of Illinois at Urbana- Champaign, Urbana, Ill., 1970.Google ScholarGoogle Scholar
  6. 6 DIETER, U., AND A~RENS, J.H. A combinatorial method for the generation of normally distributed random numbers. Computing 11 (1973), 137-146.Google ScholarGoogle Scholar
  7. 7 EARLICH, G. Loopless algorithm for generating permutation, combination, and other combinatorial configurations. J.ACM 20, 3 (July 1973), 500-513. Google ScholarGoogle Scholar
  8. 8 FORSYT~IE, G.E. Von Neumann's comparison method for sampling from the normal and other distributions. Math. Comput. 26 (1972), 817-826.Google ScholarGoogle Scholar
  9. 9 IvEs, F.M. Permutation enumeration, four new permutation algorithms. Comm. A CM 19, 2 (Feb. 1976), 68-72. Google ScholarGoogle Scholar
  10. 10 KNUTH, D.E. The analysis of algorithms. Acres Congres Int. Math. 8 (1970), 269-274.Google ScholarGoogle Scholar
  11. 11 KNUTH, D.E. Mathematical analysis of algorithms. Information Processing 71, North- Holland Pub. Co., Amsterdam, 1972, pp. 19-27.Google ScholarGoogle Scholar
  12. 12 KNUT~I, D.E. The Art of Computer Programmzng, Vol. 2: Seminumerical Algorithms. Addison-Wesley, Reading, Mass., 1969. Google ScholarGoogle Scholar
  13. 13 MARSAOLIA, G., MAcLAI~EN, M.P., AND BRAY, T.A. A fast procedure for generating normal random variables. Comm. ACM 7, 1 (Jan. 1964), 4-10. Google ScholarGoogle Scholar
  14. 14 MARSAGLXA, G. Generating a variable from the tail of the normal distribution. Technometrics 6 (1964), 101-102.Google ScholarGoogle Scholar
  15. 15 MARSAOLIA, G., AND BRAY, T.A. A convenient method for generating normal variables. SIAM Rev. 6 (1964), 260-264.Google ScholarGoogle Scholar
  16. 16 M~GGITT, J.E. Pseudo division and pseudo multiplication processes. IBM J. Res. Develop. 6 (1962), 210-226.Google ScholarGoogle Scholar
  17. 17 MULLER, M.E. An inverse method for the generation of random variables on large-scale computers. Math. Tables Aids Comput. 12 (1958), 167-174 (now Math. Comput.).Google ScholarGoogle Scholar
  18. 18 Muller, M.E. A comparison of methods for generating normal deviates on digital computers. J. A CM 6 (1959), 376-383. Google ScholarGoogle Scholar
  19. 19 ORD-SMITH, R.J. Generation of permutation sequences, P. 2. Comptr. J. 14 (May 1971), 136-139.Google ScholarGoogle Scholar
  20. 20 TOCHER, K.D. The Art of Simulation. English Universities Press, London, 1963. Google ScholarGoogle Scholar
  21. 21 ZELEN, M., AND SEVEaO, N.C. Probability functions. In Handbook of Mathematical Functions, M. Abramowitz and I.A. Stegun, Eds., Nat. Bur. of Standards, Washington, D.C., 1964.Google ScholarGoogle Scholar

Index Terms

  1. Normal Random Numbers: Using Machine Analysis to Choose the Best Algorithm

        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

        Full Access

        • Published in

          cover image ACM Transactions on Mathematical Software
          ACM Transactions on Mathematical Software  Volume 3, Issue 4
          Dec. 1977
          108 pages
          ISSN:0098-3500
          EISSN:1557-7295
          DOI:10.1145/355759
          Issue’s Table of Contents

          Copyright © 1977 ACM

          Publisher

          Association for Computing Machinery

          New York, NY, United States

          Publication History

          • Published: 1 December 1977
          Published in toms Volume 3, 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!