zbMATH — the first resource for mathematics

A nonlinear congruential pseudorandom number generator with power of two modulus. (English) Zbl 0701.65008
Summary: A nonlinear congruential pseudorandom number generator is studied where the modulus is a power of two. Investigation of this generator was suggested by D. E. Knuth. A simple necessary and sufficient condition is given for this generator to have the maximal period length.

65C10 Random number generation in numerical analysis
11K45 Pseudo-random numbers; Monte Carlo methods
Full Text: DOI
[1] W. A. Beyer, R. B. Roof, and Dorothy Williamson, The lattice structure of multiplicative congruential pseudo-random vectors, Math. Comp. 25 (1971), 345 – 363. · Zbl 0269.65003
[2] Jürgen Eichenauer and Jürgen Lehn, A nonlinear congruential pseudorandom number generator, Statist. Hefte 27 (1986), no. 4, 315 – 326. · Zbl 0607.65001
[3] Jürgen Eichenauer and Jürgen Lehn, On the structure of quadratic congruential sequences, Manuscripta Math. 58 (1987), no. 1-2, 129 – 140. · Zbl 0598.65004
[4] J. Eichenauer, H. Grothe & J. Lehn, ”Marsaglia’s lattice test and non-linear congruential pseudorandom number generators,” Metrika, 1988. (To appear.) · Zbl 0653.65006
[5] 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. · Zbl 0609.65005
[6] 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. · Zbl 0477.65002
[7] D. E. Knuth, personal communication, 1986.
[8] George Marsaglia, Random numbers fall mainly in the planes, Proc. Nat. Acad. Sci. U.S.A. 61 (1968), 25 – 28. · Zbl 0172.21002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.