A nonlinear congruential pseudorandom number generator with power of two modulus

Eichenauer, Jürgen; Lehn, Jürgen; Topuzoğlu, Alev

doi:10.1090/S0025-5718-1988-0958641-1

A nonlinear congruential pseudorandom number generator with power of two modulus
HTML articles powered by AMS MathViewer

by Jürgen Eichenauer, Jürgen Lehn and Alev Topuzoğlu PDF

Math. Comp. 51 (1988), 757-759 Request permission

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.

References

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 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 10.1007/BF01169087

Metrika

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 10.1007/BF01174798
Donald E. Knuth, The art of computer programming. Vol. 2, 2nd ed., Addison-Wesley Series in Computer Science and Information Processing, Addison-Wesley Publishing Co., Reading, Mass., 1981. Seminumerical algorithms. MR 633878
George Marsaglia, Random numbers fall mainly in the planes, Proc. Nat. Acad. Sci. U.S.A. 61 (1968), 25–28. MR 235695, DOI 10.1073/pnas.61.1.25