Fast and reliable random number generators for scientific computing

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 3732 LNCS, Issue , 2006, Pages 1-10

  Brent, Richard P ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; NATURAL SCIENCES COMPUTING; PROBLEM SOLVING; STATISTICAL METHODS; VECTORS;

RANDOM NUMBER GENERATORS; VECTOR/PARALLEL IMPLEMENTATIONS;

RANDOM NUMBER GENERATION;

EID: 33745318674     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/11558958_1     Document Type: Conference Paper

References (41)

1. Anonymous, Random number generation and testing, NIST, December 2000. http://csrc.nist.gov/rng/.
2. Anonymous, True randomness on request, University of Geneva and id Quantique, May 2004, http://www.randomnumber.info.
3. R. P. Brent, Some uniform and normal random number generators, ranut version 1.03 (January 2002) and xorgens version 2.01 (August 2004). Available from http://www.comlab.ox.ac.uk/oucl/work/richard.brent/random.html.
4. R. P. Brent, On the periods of generalized Fibonacci recurrences, Math. Comp. 63 (1994), 389-401.
5. R. P. Brent, Random number generation and simulation on vector and parallel computers, LNCS 1470, Springer-Verlag, Berlin, 1998, 1-20.
6. R. P. Brent, Note on Managlia's xorshift random number generators, J. of Statistical Software 11, 5 (2004), 1-4. http://www.jstatsoft.org.
7. R. P. Brent, Some comments on C. S. Wallace's random number generators, Computer J., to appear. Preprint at http://www.comlab.ox.ac.uk/oucl/work/ richard.brent/pub/pub213.html.
8. m, Discrete Mathematics 66 (1987), 35-49. ⋯/pub094.html.
9. R. P. Brent and P. Zimmermann, Random number generators with period divisible by a Mersenne prime, LNCS 2667, Springer-Verlag, Berlin, 2003, 1-10. Preprint at ⋯/pub211.html.
10. R. P. Brent and P. Zimmermann, Algorithms for finding almost irreducible and almost primitive trinomials, in Primes and Misdemeanours: Lectures in Honour of the Sixtieth Birthday of Hugh Cowie Williams, Fields Institute, Toronto, 2004, 91-102. Preprint at ⋯/pub212.html.
11. P. D. Coddington, Random number generators for parallel computers, The NHSE Review 2 (1996). http://nhse.cs.rice.edu/NHSEreview/RNG/PRNGreview.ps.
12. D. Coppersmith, H. Krawczyk and Y. Mansour, The shrinking generator, Advances in Crpyptology - CRYPTO'93, LNCS 773, Springer-Verlag, Berlin, 1994, 22-39.
13. A. M. Ferrenberg, D. P. Landau and Y. J. Wong, Monte Carlo simulations: hidden errors from "good" random number generators, Phys. Review Letters 69 (1992), 3382-3384.
14. P. Gimeno, Problem with ran_array, personal communication, 10 Sept. 2001.
15. M. Jakobsson, E. Shriver, B. K. Hillyer and A. Juels, A practical secure physical random bit generator, Proc. Fifth ACM Conference on Computer and Communications Security, November 1998. http://www.bell-labs.com/user/shriver/ random.html.
16. A. Juels, M. Jakobsson, E. Shriver and B. K. Hillyer, How to turn loaded dice into fair coins, IEEE Trans. on Information Theory 46, 2000, 911-921.
17. D. E. Knuth, The Art of Computer Programming, Volume 2: Seminumerical Algorithms (third edition), Addison-Wesley, Menlo Park, CA, 1998.
18. D. E. Knuth, A better random number generator, January 2002, http://www-cs-faculty.stanford.edu/~knuth/news02.html.
19. T. Kumada, H. Leeb, Y. Kurita and M. Matsumoto, New primitive t-normals (t = 3, 5) over GF(2) whose degree is a Mersenne exponent, Math. Comp. 69 (2000), 811-814.
20. Corrigenda: Math. Comp., ibid 71 (2002), 1337-1338.
21. P. L'Ecuyer, Random numbers for simulation, Comm. ACM 33, 10 (1990), 85-97.
22. P. L'Ecuyer, Tables of maximally equidistributed combined LFSR generators, Mathematics of Computation 68 (1999), 261-269.
23. P. L'Ecuyer, Random number generation, Chapter 2 of Handbook of Computational Statistics, J. E. Gentle, W. Haerdle, and Y. Mori, eds., Springer-Verlag, 2004, 35-70.
24. W. Knight, Prize draw uses heat for random numbers, New Scientist, 17 August 2004. http://www.newscientist.com/news/news.jsp?id=ns99996289.
25. M. Lüscher, A portable high-quality random number generator for lattice field theory simulations, Computer Physics Communications 79 (1994), 100-110.
26. G. Marsaglia, A current view of random number generators, in Computer Science and Statistics: The Interface, Elsevier Science Publishers B. V.,1985, 3-10.
27. G. Marsaglia, Diehard, 1995. Available from http://stat.fsu.edu/~geo/.
28. G. Marsaglia, Xorshift RNGs, J. of Statistical Software 8, 14 (2003), 1-9. http://www.jstatsoft.org.
29. G. Marsaglia and W. W. Tsang, Some difficult-to-pass tests of randomness J. of Statistical Software 7, 3 (2002), 1-9. http://www.jstatsoft.org.
30. M. Mascagni, M. L. Robinson, D. V. Pryor and S. A. Cuccaro, Parallel pseudorandom number generation using additive lagged-Fibonacci recursions, Lecture Notes in Statistics 106, Springer-Verlag, Berlin, 1995, 263-277.
31. M. Matsumoto and T. Nishimura, Mersenne twister: A 623-dimensionally equidistributed uniform pseudorandom number generator, ACM Transactions on Modeling and Computer Simulations 8, 1998, 3-30. Also http://www.math.keio.ac. jp/~matumoto/emt.html.
32. A. J. Menezes, P. C. van Oorschot and S. A. Vanstone, Handbook of Applied Cryptography, CRC Press, New York, 1997. http://cacr.math.uwaterloo.ca/hac/.
33. H. Niederreiter, Random Number Generation and Quasi-Monte Carlo Methods, CBMS-NSF Regional Conference Series in Applied Mathematics 63, SIAM, Philadelphia, 1992.
34. W. P. Petersen, Lagged Fibonacci series random number generators for the NEC SX-3, Internat. J. High Speed Computing 6 (1994), 387-398.
35. L. N. Shchur, J. R. Heringa and H. W. J. Blöte, Simulation of a directed random-walk-model: the effect of pseudo-random-number correlations, Physica A 241 (1997), 579.
36. S. Tezuka, P. L'Ecuyer, and R. Couture, On the add-with-carry and subtract-with-borrow random number generators, ACM Trans. on Modeling and Computer Simulation 3 (1993), 315-331.
37. I. Vattulainen, T. Ala-Nissila and K. Kankaala, Physical tests for random numbers in simulations, Phys. Review Letters 73 (1994), 2513-2516.
38. J. Walker, HotBits: Genuine random numbers, generated by radioactive decay, Fourmilab Switzerland, April 2004. http://www.fourmilab.ch/hotbits/.
39. C. S. Wallace, Physically random generator, Computer Systems Science and Engineering 5 (1990), 82-88.
40. C. S. Wallace, Fast pseudo-random generators for normal and exponential variates, ACM Trans. on Mathematical Software 22 (1996), 119-127.
41. R. M. Ziff, Four-tap shift-register-sequence random-number generators, Computers in Physics 12 (1998), 385-392.