Quality and Quantity

, Volume 39, Issue 4, pp 413–422 | Cite as

Modulus of Linear Congruential Random Number Generator

  • Hui-Chin Tang


This paper considers the problem of empirically analyzing the linear congruential generators (LCGs) with ten largest prime moduli smaller than 231. For each modulus, a computer exhaustive search is conducted to find the 20 good multipliers with respect to spectral value for the full period LCGs. Eleven two-level statistical tests are applied to evaluate and compare the local randomness behaviors of these good LCGs. It is shown that modulus does not significantly affect spectral value. The spectral value and the two-level statistical test are also uncorrelated.


linear congruential generators spectral test statistical test full period random number 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Cassels, J.W.S. 1959An Introduction to the Geometry of NumberSpringer-VerlagNew YorkGoogle Scholar
  2. Coveyou, R.R., MacPherson R, D. 1967Fourier analysis of uniform random number generatorsJournal of the ACM14100119CrossRefGoogle Scholar
  3. Fincke, U., Pohst, M. 1985Improved methods for calculating vectors of short length in a lattice, including a complexity analysisMathematics of Computation44463471Google Scholar
  4. Fishman, G.S. 1990Multiplicative congruential random number generators with modulus 2β: an exhaustive analysis for β=32 and a partial analysis for β=48Mathematics of Computation54331344Google Scholar
  5. Fishman, G.S. 1996Monte Carlo: Concepts, algorithms, and applications. Springer Series in Operations ResearchSpringer-VerlagNew YorkGoogle Scholar
  6. Fishman, G.S., Moore, L.R.,III 1986An exhaustive analysis of multiplicative congruential random number generators with modulus 231 − 1SIAM Journal on Scientific and Statistical Computing72445CrossRefGoogle Scholar
  7. Grube, A. 1973Mehrfach rekursiverzeugte pseudo-zufallszahlenZeitschrift für angewandte Math. Und Mechank53T223T225Google Scholar
  8. Knuth, D.E. 1997The Art of Computer Programming Vol 2: Semi-numerical Algorithms3Addison-WesleyReading, MAGoogle Scholar
  9. L’Ecuyer P. (1992). Testing random number generators. Proceeding of the 1992 Winter Simulation Conference 305–313Google Scholar
  10. L’Ecuyer, P. 1999Tables of linear congruential generators of different sizes and good lattice structureMathematics of Computation68249260CrossRefGoogle Scholar
  11. Lehmer, D.H. 1951Proceedings 2nd Symposium on Large-scale Digital Calculating MachineryHarvard University PressCambridge141146Google Scholar
  12. Marsaglia, , G., , Zaman, , A.,  1993Monkey tests for random number generatorsComputers and Mathematics with Applications26110CrossRefMathSciNetGoogle Scholar
  13. Niederreiter, H. (1992). Random Number Generation and Quasi-Monte Carlo Methods. SIAM CBMS-NSF Regional Conference Series in Applied Mathematics, 63, SIAM, PhiladelphiaGoogle Scholar
  14. SAS Institute Inc. (1991). SAS Procedures Guide. Release 6.03 Edition. Cary, NC, USAGoogle Scholar
  15. Sáanchez-Bruno, A., Luis-Costas, C.S. 1995A statistical analysis of seven multiples for linear congruential random number generators with modulus 231 − 1Quality & Quantity29331337Google Scholar
  16. Tang, H.C. 2000Implementing a multiple recursive generator with Mersenne prime modulusInternational Journal of Computer Mathematics763543Google Scholar
  17. Tang, H.C. 2001A statistical analysis of the screening measure of multiple recursive random number generators of orders one and twoJournal of Statistical Computation and Simulation71345356MathSciNetGoogle Scholar
  18. Tang, H.C. 2002aCombined random number generator via the generalized Chinese remainder theoremJournal of Computational and Applied Mathematics142377388CrossRefGoogle Scholar
  19. Tang, H.C. 2002bModified decomposition method for multiple recursive random number generatorMathematics and Computers in Simulation59451456CrossRefGoogle Scholar
  20. Tang, H.C., Kao, C. 2002Lower bounds in spectral tests for vectors of nonsuccessive values produced by multiple recursive generator with some zero multipliersComputers & Mathematics with Applications4311531159Google Scholar

Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Department of Industrial Engineering and ManagementNational Kaohsiung University of Applied SciencesKaohsiungTaiwan

Personalised recommendations