Abstract
A method of analysis of uniform random number generators is developed, applicable to almost all practical methods of generation. The method is that of Fourier analysis of the output sequences of such generators. With this tool it is possible to understand and predict relevant statistical properties of such generators and compare and evaluate such methods. Many such analyses and comparisons have been carried out. The performance of these methods as implemented on differing computers is also studied. The main practical conclusions of the study are: (a) Such a priori analysis and prediction of statistical behavior of uniform random number generators is feasible. (b) The commonly used multiplicative congruence method of generation is satisfactory with careful choice of the multiplier for computers with an adequate (≥ ∼ 35-bit) word length. (c) Further work may be necessary on generators to be used on machines of shorter word length.
- 1 CERTAIN. J. E. On sequences of pseudo-random numbers of maximal length. J. ACM 5 (1958), 353-356. Google Scholar
- 2 MACLAREN, M. D., AND MARSAGLIA, G. Uniform random number generators. J . ACM 12 (1965), 83-89. Google Scholar
- 3 MOIRDELL, L.J. Observation on the minimum of a quadratic form in eight variables. J. London Math. Soc. 19 (1944), 3-6.Google Scholar
- 4 CASSLS, J. W: S. An Introduction to the Geometry of Numbers. Springer-Verlag, Berlin, 1959, pp. 31,332. (This contains proofs of theorems referred to in the text.)Google Scholar
- 5 COVEYOU, R.R. Serial correlation in the generation of pseudo-random numbers. J. ACM 5 (1960), 72-74. Google Scholar
- 6 GREENBERGER, M. Method in randomness. Comm. ACM 8 (1965), 177-179. Google Scholar
- 7 HULL, W.E., AND DOBELL, A.R. Random number generators. SIAM Rev. 4 (1962), 229- 254. (This contains a good survey of the field and a comprehensive bibliography.)Google Scholar
- 8 JANSSON, B. Autocorrelations between pseudo-random numbers. NordisK Tidskr. Informations-Behandling 4 (1964), 6-27.Google Scholar
- 9 WEYL, H. Uber die Gleichverteilung yon Zahlen rood Eins. Math. Ann. 77 (1916); also Selecta Hermann Weyl. Birkhauser Verlag, Basel, 1956, p. 111. (This contains proofs of theorems referred to in the text.)Google Scholar
Index Terms
Fourier Analysis of Uniform Random Number Generators
Recommendations
Bit-Wise Behavior of Random Number Generators
In 1985, G. Marsaglia proposed the m-tuple test, a runs test on bits, as a test of nonrandomness of a sequence of pseudorandom integers. We try this test on the outputs from a large set of pseudorandom number generators and discuss the behavior of the ...
Resolution-stationary random number generators
Besides speed and period length, the quality of uniform random number generators (RNGs) is usually assessed by measuring the uniformity of their point sets, formed by taking vectors of successive output values over their entire period length. For F"2-...
Uniform Random Number Generator Using Leap Ahead LFSR Architecture
ICCCS '09: Proceedings of the 2009 International Conference on Computer and Communications SecurityUniform Random Number Generator (URNG) is a key element in most applications which run on FPGA based hardware accelerators. As multi-bits is required and a normal LFSR could only generate one bit per cycle, more than one LFSR is needed in a URNG. In ...






Comments