Efficient Jump Ahead for 𝔽2-Linear Random Number Generators

Published Online:https://doi.org/10.1287/ijoc.1070.0251

References

  • Golub G. H., Van Loan C. F.Matrix Computations (1996) 3rd ed.(John Hopkins University Press, Baltimore) Google Scholar
  • Hellekalek P. Don't trust parallel Monte Carlo! Twelfth Workshop on Parallel and Distributed Simulation, Banff, Canada (1998) (IEEE Computer Society, Los Alamitos, CA) 82–89Crossref, Google Scholar
  • Kelton W. D., Henderson S. G., Nelson B. L. Implementing representations of uncertainty. Simulation. Handbooks in Operations Research and Management Science (2006) (Elsevier, Amsterdam) 181–191Chapter 7Google Scholar
  • Knuth D. E.The Art of Computer Programming, Seminumerical Algorithms (1998) 23rd ed.(Addison-Wesley, Reading, MA) Google Scholar
  • Law A. M., Kelton W. D.Simulation Modeling and Analysis (2000) 3rd ed.(McGraw-Hill, New York) Google Scholar
  • L'Ecuyer P. Random numbers for simulation. Comm. ACM (1990) 33:85–97Crossref, Google Scholar
  • L'Ecuyer P., CĂŽtĂ© S. Implementing a random number package with splitting facilities. ACM Trans. Math. Software (1991) 17:98–111Crossref, Google Scholar
  • L'Ecuyer P., Panneton F. Fast random number generators based on linear recurrences modulo 2: Overview and comparison. Proc. 2005 Winter Simulation Conf. (2005) (IEEE Press, Piscataway, NJ) 110–119Crossref, Google Scholar
  • L'Ecuyer P., Simard R., Chen E. J., Kelton W. D. An object-oriented random-number package with many long streams and substreams. Oper. Res. (2002) 50:1073–1075Link, Google Scholar
  • Matsumoto M., Nishimura T. Mersenne twister: A 623-dimensionally equidistributed uniform pseudo-random number generator. ACM Trans. Model. Comput. Simulation (1998) 8:3–30Crossref, Google Scholar
  • Möller B., van Tilborg H. C. A. Sliding window exponentiation. Encyclopedia of Cryptography and Security (2005) (Springer-Verlag, New York) 588–590Crossref, Google Scholar
  • Nishimura T. Tables of 64-bit Mersenne twisters. ACM Trans. Model. Comput. Simulation (2000) 10:348–357Crossref, Google Scholar
  • Panneton F., L'Ecuyer P. On the xorshift random number generators. ACM Trans. Model. Comput. Simulation (2005) 15:346–361Crossref, Google Scholar
  • Panneton F., L'Ecuyer P., Matsumoto M. Improved long-period generators based on linear recurrences modulo 2. ACM Trans. Math. Software (2006) 32:1–16Crossref, Google Scholar
  • Saito M., Matsumoto M., Heinrich S., Keller A., Niederreiter H. SIMD-oriented fast Mersenne twister: A 128-bit pseudorandom number generator. Monte Carlo and Quasi-Monte Carlo Methods 2006 (2008) (Springer-Verlag, Berlin) 617–632Crossref, Google Scholar
  • Savage C. A survey of combinatorial Gray codes. SIAM Rev. (1997) 39:605–629Crossref, Google Scholar
  • Strang G.Linear Algebra and Its Applications (1988) 3rd ed.(Saunders, Philadelphia) Google Scholar
  • Tezuka S.Uniform Random Numbers: Theory and Practice (1995) (Kluwer Academic Publishers, Norwell, MA) Crossref, Google Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.