A nonlinear congruential pseudorandom number generator with power of two modulus
Authors:
Jürgen Eichenauer, Jürgen Lehn and Alev Topuzoğlu
Journal:
Math. Comp. 51 (1988), 757-759
MSC:
Primary 65C10; Secondary 11K45, 65C05
DOI:
https://doi.org/10.1090/S0025-5718-1988-0958641-1
MathSciNet review:
958641
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Abstract | References | Similar Articles | Additional Information
Abstract: A nonlinear congruential pseudorandom number generator is studied where the modulus is a power of two. Investigation of this generator was suggested by Knuth [7]. A simple necessary and sufficient condition is given for this generator to have the maximal period length.
- W. A. Beyer, R. B. Roof, and Dorothy Williamson, The lattice structure of multiplicative congruential pseudo-random vectors, Math. Comp. 25 (1971), 345–363. MR 309263, DOI https://doi.org/10.1090/S0025-5718-1971-0309263-4
- Jürgen Eichenauer and Jürgen Lehn, A nonlinear congruential pseudorandom number generator, Statist. Hefte 27 (1986), no. 4, 315–326. MR 877295
- Jürgen Eichenauer and Jürgen Lehn, On the structure of quadratic congruential sequences, Manuscripta Math. 58 (1987), no. 1-2, 129–140. MR 884989, DOI https://doi.org/10.1007/BF01169087 J. Eichenauer, H. Grothe & J. Lehn, "Marsaglia’s lattice test and non-linear congruential pseudorandom number generators," Metrika, 1988. (To appear.)
- Jürgen Eichenauer, Holger Grothe, Jürgen Lehn, and Alev Topuzoğlu, A multiple recursive nonlinear congruential pseudo random number generator, Manuscripta Math. 59 (1987), no. 3, 331–346. MR 909849, DOI https://doi.org/10.1007/BF01174798
- Donald E. Knuth, The art of computer programming. Vol. 2, 2nd ed., Addison-Wesley Publishing Co., Reading, Mass., 1981. Seminumerical algorithms; Addison-Wesley Series in Computer Science and Information Processing. MR 633878 D. E. Knuth, personal communication, 1986.
- George Marsaglia, Random numbers fall mainly in the planes, Proc. Nat. Acad. Sci. U.S.A. 61 (1968), 25–28. MR 235695, DOI https://doi.org/10.1073/pnas.61.1.25
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Additional Information
Keywords:
Pseudorandom number generator,
nonlinear congruential sequence,
power of two modulus,
period length
Article copyright:
© Copyright 1988
American Mathematical Society
