Abstract
A new summation formula based on the orthogonal property of Walsh functions is devised. Using this formula, the k-dimensional discrepancy of the generalized feedback shift register (GFSR) pseudorandom numbers is derived. The relation between the discrepancy and k-distribution of GFSR sequences is also obtained. Finally the definition of optimal GPSR pseudorandom number generators is introduced.
- 1 BEAUCHAMP, K.G. Walsh Functions and Their Applications. Academic Press, London, 1975.Google Scholar
- 2 BOROSH, I., AND NIEDERREITER, H. Optimal multipliers for pseudorandom number generation by the linear congruential method. BIT 23 (1983), 65-74.Google Scholar
- 3 FUSmMI, M., AND TEZUKA, S. The k-distribution of generalized feedback shift register pseudorandom numbers. Commun. ACM 26, 7 (July 1983), 516-523. Google Scholar
- 4 KNtrrH, D. E. The Art of Computer Programming, vol. 2: Seminumerical Algorithms, 2nd ed. Addison-Wesley, Reading, Mass., 1981.Google Scholar
- 5 KuNz, H. O., AND RAMM-ARNFr, J. Walsh matrices. Arch. Elektron. Ubertragungstech. (Electron. Commun.) 32 (1978), 56-58.Google Scholar
- 6 LEwis, T. G., AND PAVNE, W. H. Generalized feedback shift register pseudorandom number algorithms. J. ACM. 20, 3 (July 1973), 456-468. Google Scholar
- 7 MARSAGLIA, G. Random number generator. In Encyclopedia of Computer Science, A. Ralston and C. L. Meek, Eds. Petrocelli/Charter, New York, 1976.Google Scholar
- 8 NIFDERREITER, H. Pseudorandom numbers and optimal coefficients. Adv. Math. 26 (1977), 99-181.Google Scholar
- 9 NIEDERREITER, H. Quasi-Monte Carlo methods and pseudorandom numbers. Bull. Amer. Math. Soc. 84 (1978), 957-1041.Google Scholar
- 10 NIEDFRRErrER, H. Applications des corps finis aux nombres pesudoaleatoires. Sere. Theorie des Nombres 1982-83, Exp. 38. Univ. de Bordeaux 1, Talence, France, 1983.Google Scholar
- 11 NIEDFRREIT~R, H. The performance of K-step pseudorandom number generators under the uniformity test. SIAM J. Sci. Statist. Comput. 5 (1984), 798-810.Google Scholar
- 12 TAUSWORTHE, R. C. Random numbers generated by linear recurrence modulo two. Math. Comput. 19 (1965), 201-209.Google Scholar
- 13 T~.zu~, S. Walsh-spectral test for GFSR pscudorandom numbers. Commun. ACM 30, 8 (Aug. 1987), 731-735. Google Scholar
Index Terms
On the discrepancy of GFSR pseudorandom numbers
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