[Ant79]   Antonov, I.A., and Saleev, V.M. An economic method of computing LPt-sequences. USSR Comput. Math. Math. Phys., 19, 252-256, 1979.

[Atkin79] Atkinson A.C. A family of switching algorithms for the computer generation of beta random variables, Biometrika, 66, 1, 141-145, 1979.

[AVX] Intel® Advanced Vector Extensions Programming Reference,

[BMT] Intel Bull Mountain Technology, Software Implementation Kit (SIK),

[Box58] Box, G. E. P. and Muller, M. E. A Note on the Generation of Random Normal Deviates. Ann. Math. Stat. 28, 610-611, 1958.

[Brat87] Bratley, P., Fox, B.L., and Schrage, L.E.. A Guide to Simulation, 2nd Edition, Springer-Verlag, New York, 1987.

[Brat88] Bratley, P. and Fox, B.L. ALGORITHM 659: Implementing Sobol’s Quasirandom Sequence Generator. ACM Transactions on Modeling and Computer Simulation, Vol. 14, No. 1, 88-100, March 1988.

[Brat92] Bratley, P., Fox, B.L., and Niederreiter, H. Implementation and Tests of Low-Discrepancy Sequences. ACM Transactions on Modeling and Computer Simulation, Vol. 2, No. 3, 195-213, July 1992.

[Cheng78] Cheng, R. C. H., Generating Beta variates with Nonintegral Shape Parameters, Communications of the ACM, 21, 4, 317-322, 1978.

[Cram46] Cramer, H. Mathematical Methods of Statistics. Cambridge, 1946.

[Dev86] Devroye, L. Non-Uniform Random Variate Generation, Springer-Verlag, New York, 1986.

[Ent98] Entacher, Karl. Bad Subsequences of Well-Known Linear Congruential Pseudorandom Number Generators. ACM Transactions on Modeling and Computer Simulation, Vol. 8, No. 1, 61-70, January 1998.

[Haram08] Haramoto H., Matsumoto M., Nishimura T., Panneton F., and L’Ecuyer P. Efficient Jump Ahead for F2-Linear Random Number Generators, INFORMS Journal on Computing, Vol.20, No 3, Summer 2008, pp 385-390.

[IntelSWMan] Intel® 64 and IA-32 Architectures Software Developer’s Manual. 3 vols.



[Jöhnk64] Jöhnk, M.D. Erzeugung von Betaverteilten und Gammaverteilten Zufallszahlen, Metrika, 8, 5-15, 1964.

[Jun99] Jun, B., and Kocher, P. The Intel Random Number Generator. White paper prepared for Intel Corp., Cryptography Research, Inc., April 1999.

[Kach88] Kachitvichyanukul, V. and Schmeiser, B.W. Binomial random variate generation. Communications of the ACM, Volume 31, Issue 2, February 1988.

[Kach85] Kachitvichyanukul, V. and Schmeiser, B.W. Computer generation of hypergeometric random variates. J. Stat. Comput. Simul. 22, 1, 127-145, 1985.

[KIM04] Song-Ju Kim, Ken Umeno, and Akio Hasegawa, Corrections of the NIST Statistical Test Suite for Randomness,

[Kirk81] Kirkpatrick, S., and E. Stoll. A Very Fast Shift-Register Sequence Random Number Generator. Journal of Computational Physics, V. 40, 517-526, 1981.

[Knuth81] Knuth, Donald E. The Art of Computer Programming, Volume 2, Seminumerical Algorithms, 2nd edition, Addison-Wesley Publishing Company, Reading, Massachusetts, 1981.

[L'Ecu94] L'Ecuyer, Pierre. Uniform Random Number Generators, Annals of Operations Research, 53, 77-120, 1994.

[L'Ecu99] L'Ecuyer, P. Good Parameter Sets for Combined Multiple Recursive Random Number Generators. Operations Research, 47, 1, 159-164, 1999.

[L'Ecuyer99] L'Ecuyer, Pierre. Tables of Linear Congruential Generators of Different Sizes and Good Lattice Structure. Mathematics of Computation, 68, 249-260, 1999.

[MacLaren89] MacLaren, N.M. The Generation of Multiple Independent Sequences of Pseudorandom Numbers. Applied Statistics, 38, 351-359, 1989.

[Mars95] Marsaglia, G. The Marsaglia Random Number CDROM, including the DIEHARD Battery of Tests of Randomness, Department of Statistics, Florida State University, Tallahassee, Florida, 1995.

[Mars2000] Marsaglia, G., and Tsang, W. W. A simple method for generating gamma variables, ACM Transactions on Mathematical Software, Vol. 26, No. 3, Pages 363-372, September 2000.

[Matsum92] Matsumoto, M., and Kurita, Y. Twisted GFSR generators, ACM Transactions on Modeling and Computer Simulation, Vol. 2, No. 3, Pages 179-194, July 1992.

[Matsum94] Matsumoto, M., and Kurita, Y. Twisted GFSR generators II, ACM Transactions on Modeling and Computer Simulation, Vol. 4, No. 3, Pages 254-266, July 1994.

[Matsum98] Matsumoto, M., and Nishumira T. Mersenne Twister: A 623-Dimensionally Equidistributed Uniform Pseudo-Random Number Generator, ACM Transactions on Modeling and Computer Simulation, Vol. 8, No. 1, Pages 3-30, January 1998.

[Matsum2000] Matsumoto, M., and Nishimura T. Dynamic Creation of Pseudorandom Number Generators, 56- 69, in: Monte Carlo and Quasi-Monte Carlo Methods 1998, Ed. Niederreiter, H. and Spanier, J., Springer 2000,

[Mikh2000] Mikhailov, G.A. Weight Monte Carlo Methods, Novosibirsk: SB RAS Publ., 2000 (In Russian).


[NAG] Numerical Algorithms Group,

[NIST800-22] NIST Special Publication 800-22 A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications.

[NIST800-90] NIST Special Publication 800-90 Recommendation for Random Number Generation Using Deterministic Random Bit Generators (Revised), March 2007.

[Ripley87] Ripley, B.D. Stochastic Simulation, Wiley, New York, 1987.

[Saito08] Saito, M., and Matsumoto, M. SIMD-oriented Fast Mersenne Twister: a 128-bit Pseudorandom Number Generator,Monte Carlo and Quasi-Monte Carlo Methods 2006, Springer, pp. 607-622, 2008,

[Schmeiser81] Schmeiser, Bruce, and Kachitvichyanukul, Voratas. Poisson Random Variate Generation. Research Memorandum 81-4, School of Industrial Engineering, Purdue University, 1981.

[Vad77] Vaduva, I. On computer generation of gamma random variables by rejection and composition procedures. Mathematische Operationsforschung und Statistik, Series Statistics, vol. 8, 545-576, 1977.

[Ziff98] Ziff, Robert M. Four-tap shift-register-sequence random-number generators. Computers in Physics, Vol. 12, No. 4, Jul/Aug 1998.

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