Abstract
By applying Weyl's criterion for k-distributivity to GFSR sequences, we derive a new theoretical test for investigating the statistical property of GFSR sequences. This test provides a very useful measure for examining the k-distribution, that is, the statistical independence of the k-tuple of successive terms of GFSR sequences. In the latter half of this paper, we describe an efficient procedure for performing this test and furnish experimental results obtained from applying it to several GFSR generators with prime period lengths.
- 1 Beauchamp. K.C. Walsh Functions and Their Applications. Academic Press. New York. 1975.Google Scholar
- 2 Coveyou. R.R. and MacPherson. R.D. Fourier analysis of uniform random number generators. J. ACM 14. 1 (Jan. 1967). 100-119. Google ScholarDigital Library
- 3 Franklin. J.N. Deterministic simulalion of random processes. Math. Compuf. 17.81 (1963). 28-59.Google ScholarCross Ref
- 4 Fushimi. M., and Tezuka. S. Pseudorandom number generators based on maximum length linearly recurring sequences. J. Fac. Eng. A-17 (1979). 42-43 (in Japanese).Google Scholar
- 5 Fushimi. M. and Tezuka. S. The K-distribution of generalized feedback shift rcgisler pseudorandom numbers. Commun. ACM 26. 7 (July 1983). 516-523. Google ScholarDigital Library
- 6 Kirkpatrik. S. and Sloll. E.P. A very fast shift register sequence random number generator. J. Compur. Phys. 40. 2 (1981). 517-526.Google Scholar
- 7 Knuth. D.E. The Art of Computer Programming. Vol. 2. Seminumerical Algorithms. 2nd ed. Addison-Wesley, Reading, Mass., 1981. Google ScholarDigital Library
- 8 Lewis. P.A.W. Goodman. A.S. and Miller. J.M. A pseudorandom number generator for the System/360. IBM Syst. J. 8, 2 (1969). 136- 146.Google ScholarDigital Library
- 9 Lewis. T.G. and Payne, W.H. Generalized feedback shift register pseudorandom number algorithm. J. ACM 20. 3 (July 1973). 456-466. Google ScholarDigital Library
- 10 Marsaglia. G. Random number generator. In Encyclopedia of Computer Science. A. Ralston and C.L. Meek. Eds. Petrocelli/Charter. New York. 1976.Google Scholar
- 11 Tausworthe. R.C. Random numbers generated by linear recurrence module two. Math. Cornput. 19. 90 (1965). 201-209.Google Scholar
- 12 Tezuka. S. The asymptotic randomness of GFSR pseudorandom numbers. Trans. Inf. Process. Soc. Japan 25. 4 (July 1984). 681-684 (in Japanese).Google Scholar
- 13 Tezuka. S. The theoretical comparison between cogruential methods and GFSR algorithms. jSI Res. Rep. TR87-0001. IBM japan. Tokyo. 1984.Google Scholar
- 14 Toolill. J.P.R. Robinson, W.D. and Adams. A.G. The runs up-anddown performance of Tausworthe pseudo-random number generators. J. ACM 18. 3 (July 1971). 381-399. Google ScholarDigital Library
- 15 Tootill. J.P.R. Robinson. W.D. and Eagle, D.J. A" asymptotically random Tausworthe sequence. I. ACM 20. 3 (July 1973). 469-481. Google ScholarDigital Library
- 16 Walsh. J.L. A closed set of orthogonal functions. Am. 1. Math. 45 (1923). 5-24.Google Scholar
- 17 Weyl. H. Uber die gleichverteilung van zahlen mod. eins. Math. Ann.Google Scholar
- 18 Whittlesey. J.R.B. A comparison of the correlational behavior of random number generators for the IBM 360. Cwvnrun. ACM II. 9 (Sept. 1968). 641-644. Google ScholarDigital Library
Index Terms
- Walsh-spectral test for GFSR pseudorandom numbers
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