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.

**[1]**W. A. Beyer, R. B. Roof & D. Williamson, "The lattice structure of multiplicative pseudo-random vectors,"*Math. Comp.*, v. 25, 1971, pp. 345-363. MR**0309263 (46:8373)****[2]**J. Eichenauer & J. Lehn, "A non-linear congruential pseudorandom number generator,"*Statist. Hefte*, v. 27, 1986, pp. 315-326. MR**877295 (88i:65014)****[3]**J. Eichenauer & J. Lehn, "On the structure of quadratic congruential sequences,"*Manuscripta Math.*, v. 58, 1987, pp. 129-140. MR**884989 (88h:65019)****[4]**J. Eichenauer, H. Grothe & J. Lehn, "Marsaglia's lattice test and non-linear congruential pseudorandom number generators,"*Metrika*, 1988. (To appear.)**[5]**J. Eichenauer, H. Grothe, J. Lehn & A. Topuzoglu, "A multiple recursive non-linear congruential pseudorandom number generator,"*Manuscripta Math.*, v. 59, 1987, pp. 331-346. MR**909849 (89f:65008)****[6]**D. E. Knuth,*The Art of Computer Programming*, vol. 2, 2nd ed., Addison-Wesley, Reading, Mass., 1981. MR**633878 (83i:68003)****[7]**D. E. Knuth, personal communication, 1986.**[8]**G. Marsaglia, "Random numbers fall mainly in the planes,"*Proc. Nat. Acad. Sci. U.S.A.*, v. 61, 1968, pp. 25-28. MR**0235695 (38:3998)**

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1988-0958641-1

Keywords:
Pseudorandom number generator,
nonlinear congruential sequence,
power of two modulus,
period length

Article copyright:
© Copyright 1988
American Mathematical Society