Uniform Random Rational Number Generation

  • Thomas Morgenstern
Conference paper
Part of the Operations Research Proceedings book series (ORP, volume 2006)


Classical floating point random numbers fail simple tests when considered as rational numbers.


Random Number Rational Number Random Number Generator Period Length Generator Pseudorandom Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Knuth D E (1998) The art of computer programming. Vol. 2: Seminumerical algorithms. third edition, Addison-Wesley, Reading, Mass.Google Scholar
  2. 2.
    L’Ecuyer P (1994) Uniform random number generation. Annals of Operations Research 53:77–120CrossRefGoogle Scholar
  3. 3.
    L’Ecuyer P (1998) Random number generation. In: Banks J (ed) Handbook on Simulation. John Wiley, Hoboken, NJ.Google Scholar
  4. 4.
    L’Ecuyer P (2004) Random number generation. In: Gentle J E, Härdle W, Mori Y, (eds) Handbook of computational statistics. Concepts and methods. Springer, Berlin Heidelberg New YorkGoogle Scholar
  5. 5.
    L’Ecuyer P (2001) Software for uniform random number generation: Distinguishing the good and the bad. In: Proceedings of the 2001 Winter Simulation Conference. Pistacaway NJ., IEEE PressGoogle Scholar
  6. 6.
    L’Ecuyer P, Hellekalek P (1998) Random number generators: Selection criteria and testing. In: Hellekalek P (ed) Random and quasi-random point sets. Springer Lecture Notes in Statistics 138. Springer, New YorkGoogle Scholar
  7. 7.
    L’Ecuyer P, Simard R (2001) On the performance of birthday spacings tests with certain families of random number generators. Mathematics and Computers in Simulation 55(1–3): 131–137CrossRefGoogle Scholar
  8. 8.
    L’Ecuyer P, Simard R, Wegenkittl S (2002) Sparse serial tests of uniformity for random number generators. SIAM Journal on Scientific Computing 24(2): 652–668CrossRefGoogle Scholar
  9. 9.
    Maple 10 (2005) Maplesoft, a division of Waterloo Maple Inc., www.maplesoft.comGoogle Scholar
  10. 10.
    MuPAD Pro 3.1 (2005) SciFace Software GmbH& Co.KG, www.sciface.comGoogle Scholar
  11. 11.
    Morgenstern T (2006) Uniform Random Binary Floating Point Number Generation. In: Proceedings of the 2. Wernigeröder Automatisierungs-und Informatiktage. Hochschule Harz, WernigerodeGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Thomas Morgenstern
    • 1
  1. 1.FB Automatisierung und InformatikHochschule HarzWernigerodeGermany

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