A PRNG specialized in double precision floating point numbers using an affine transition

Monte Carlo and Quasi-Monte Carlo Methods 2008

Volumn , Issue , 2009, Pages 589-602

  Saito, Mutsuo ^a   Matsumoto, Makoto ^a  

^a HIROSHIMA UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

DIGITAL ARITHMETIC; NUMBER THEORY; RANDOM NUMBER GENERATION;

DOUBLE PRECISION; EQUIDISTRIBUTION; FLOATING POINT NUMBERS; LINEAR TRANSITIONS; MERSENNE TWISTERS; PSEUDO RANDOM NUMBER GENERATORS; PSEUDO RANDOM PATTERN; TRANSITION FUNCTIONS;

MONTE CARLO METHODS;

EID: 84875184245     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1007/978-3-642-04107-5_38     Document Type: Conference Paper

References (20)

1. R.P. Brent and P. Zimmermann. Random number generators with period divisible by a Mersenne prime. In Computational Science and its Applications - ICCSA 2003, volume 2667, pages 1-10, 2003.
2. R.P. Brent and P. Zimmermann. Algorithms for finding almost irreducible and almost primitive trinomials. Fields Inst. Commun., 41:91-102, 2004.
3. R. Couture, P. L'Ecuyer, and S. Tezuka. On the distribution of k-dimensional vectors for simple and combined Tausworthe sequences. Math. Comp., 60(202):749-761, 1993.
4. Agner Fog. Pseudo random number generators. http://www.agner.org/random/.
5. M. Fushimi. Random number generation with the recursion xt = xt-3p ⊕xt-3q. Journal of Computational and Applied Mathematics, 31:105-118, 1990.
6. IEEE standard for binary floating-point arithmetic 754, 2008. http://ieeexplore.ieee.org/servlet/opac?punumber=4610933.
7. D. E. Knuth. The Art of Computer Programming. Vol.2. Seminumerical Algorithms. Addison- Wesley, Reading, Mass., 3rd edition, 1997.
8. P. L'Ecuyer. Maximally equidistributed combined tausworthe generators. Math. Comp., 65(213):203-213, 1996.
9. P. L'Ecuyer and J. Granger-Piché. Combined generators with components from different families. Mathematics and Computers in Simulation, 62:395-404, 2003.
10. P. L'Ecuyer and F. Panneton. F2-linear random number generators. In Advancing the Frontiers of Simulation: A Festschrift in Honor of George Samuel Fishman, pages 175-200, 2009. C. Alexopoulos, D. Goldsman, and J. R. Wilson Eds.
11. P. L'Ecuyer and R. Simard. Test U01: A C library for empirical testing of random number generators. ACM Transactions on Mathematical Software, 15(4):346-361, 2006.
12. G. Marsaglia. TheMarsaglia Random Number CDROM, with the DIEHARD Battery of Tests of Randomness. Department of Statistics, Florida State University, (1996) http://www.stat.fsu.edu/pub/diehard/.
13. G. Marsaglia. Xorshift RNGs. Journal of Statistical Software, 8(14):1-6, 2003.
14. M. Matsumoto and T. Nishimura. Mersenne twister: A 623-dimensionally equidistributed uniform pseudorandom number generator. ACM Trans. on Modeling and Computer Simulation, 8(1):3-30, January 1998. http://www.math.sci.hiroshima- u.ac.jp/m-mat/MT/emt.html.
15. T. Nishimura. Tables of 64-bit mersenne twisters. ACM Trans. on Modeling and Computer Simulation, 10(4):348-357, October 2000.
16. F. Panneton and P. L'Ecuyer. On the Xorshift random number generators. ACM Transactions on Modeling and Computer Simulation, 15(4):346-361, 2005.
17. F. Panneton, P. L'Ecuyer, and M.Matsumoto. Improved long-period generators based on linear reccurences modulo 2. ACM Transactions on Mathematical Software, 32(1):1-16, 2006.
18. M. Saito and M. Matsumoto. SFMT Homepage. http://www.math.sci.hiroshima- u.ac.jp/̃m-mat/MT/SFMT/index.html.
19. M. Saito and M. Matsumoto. SIMD-oriented fast Mersenne twister : A 128-bit pseudorandom number generator. In Monte Carlo and Quasi-Monte Carlo Methods 2006, LNCS, pages 607-622. Springer, 2008.
20. SIMD From Wikipedia, the free encyclopedia. http://en.wikipedia.org/wiki/ SIMD.