On a nonlinear congruential pseudorandom number generator

Kato, Takashi; Wu, Li-Ming; Yanagihara, Niro

doi:10.1090/S0025-5718-96-00694-1

On a nonlinear congruential pseudorandom number generator
HTML articles powered by AMS MathViewer

by Takashi Kato, Li-Ming Wu and Niro Yanagihara PDF

Math. Comp. 65 (1996), 227-233 Request permission

Abstract:

A nonlinear congruential pseudorandom number generator with modulus $M = 2^w$ is proposed, which may be viewed to comprise both linear as well as inversive congruential generators. The condition for it to generate sequences of maximal period length is obtained. It is akin to the inversive one and bears a remarkable resemblance to the latter.

References

Jürgen Eichenauer-Herrmann, Inversive congruential pseudorandom numbers avoid the planes, Math. Comp. 56 (1991), no. 193, 297–301. MR 1052092, DOI 10.1090/S0025-5718-1991-1052092-X
Jürgen Eichenauer-Herrmann, Statistical independence of a new class of inversive congruential pseudorandom numbers, Math. Comp. 60 (1993), no. 201, 375–384. MR 1159168, DOI 10.1090/S0025-5718-1993-1159168-9
Jürgen Eichenauer-Herrmann, On generalized inversive congruential pseudorandom numbers, Math. Comp. 63 (1994), no. 207, 293–299. MR 1242056, DOI 10.1090/S0025-5718-1994-1242056-8
J. Eichenauer-Herrmann, H. Grothe, H. Niederreiter, and A. Topuzoğlu, On the lattice structure of a nonlinear generator with modulus $2^\alpha$, J. Comput. Appl. Math. 31 (1990), no. 1, 81–85. Random numbers and simulation (Lambrecht, 1988). MR 1068151, DOI 10.1016/0377-0427(90)90338-Z
Jürgen Eichenauer, Jürgen Lehn, and Alev Topuzoğlu, A nonlinear congruential pseudorandom number generator with power of two modulus, Math. Comp. 51 (1988), no. 184, 757–759. MR 958641, DOI 10.1090/S0025-5718-1988-0958641-1
Jürgen Eichenauer-Herrmann and Harald Niederreiter, Lower bounds for the discrepancy of inversive congruential pseudorandom numbers with power of two modulus, Math. Comp. 58 (1992), no. 198, 775–779. MR 1122066, DOI 10.1090/S0025-5718-1992-1122066-X
Tosihusa Kimura, On the iteration of analytic functions, Funkcial. Ekvac. 14 (1971), 197–238. MR 302876
Tosihusa Kimura, On meromorphic solutions of the difference equation $y(x+1)=y(x)+1+(\lambda /y(x) )$, Symposium on Ordinary Differential Equations (Univ. Minnesota, Minneapolis, Minn., 1972; dedicated to Hugh L. Turrittin), Lecture Notes in Math., Vol. 312, Springer, Berlin, 1973, pp. 74–86. MR 0399684
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
Harald Niederreiter, The serial test for congruential pseudorandom numbers generated by inversions, Math. Comp. 52 (1989), no. 185, 135–144. MR 971407, DOI 10.1090/S0025-5718-1989-0971407-2
Harald Niederreiter, Recent trends in random number and random vector generation, Ann. Oper. Res. 31 (1991), no. 1-4, 323–345. Stochastic programming, Part II (Ann Arbor, MI, 1989). MR 1118905, DOI 10.1007/BF02204856
Harald Niederreiter, Random number generation and quasi-Monte Carlo methods, CBMS-NSF Regional Conference Series in Applied Mathematics, vol. 63, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1992. MR 1172997, DOI 10.1137/1.9781611970081
Kyoichi Takano, On the hypertranscendency of solutions of a difference equation of Kimura, Funkcial. Ekvac. 16 (1973), 241–254. MR 352587
Niro Yanagihara, Meromorphic solutions of the difference equation $y(x+1)=y(x)+1+\lambda /y(x)$. I, Funkcial. Ekvac. 21 (1978), no. 2, 97–104. MR 518294
Niro Yanagihara, Meromorphic solutions of the difference equation $y(x+1)=y(x)+1+\lambda /y(x)$. II, Funkcial. Ekvac. 21 (1978), no. 3, 223–240. MR 540392