On the Lattice Structure of a Special Class of Multiple Recursive Random Number Generators
Published Online:21 Mar 2014https://doi.org/10.1287/ijoc.2013.0576
References
- (1999) Sphere Packings, Lattices and Groups 3rd ed. Grundlehren der Mathematischen Wissenschaften 290, (Springer-Verlag, New York).Crossref, Google Scholar
- (2004) Generalized Mersenne prime number and its application to random number generation. Niederreiter H, ed. Monte Carlo and Quasi-Monte Carlo Methods 2002 (Springer-Verlag, Berlin), 167–180.Crossref, Google Scholar
- (2005) Efficient and portable multiple recursive generators of large order. ACM Trans. Modeling Comput. Simulation 15:1–13.Crossref, Google Scholar
- (2008) Issues on computer search for large-order multiple recursive generators. Keller A, Heinrich S, Niederreiter H, eds. Monte Carlo and Quasi-Monte Carlo Methods 2006 (Springer-Verlag, Berlin), 251–261.Crossref, Google Scholar
- (2000) Random number generation for the new century. Amer. Statistician 54:145–150.Crossref, Google Scholar
- (2003) A system of high-dimensional, efficient, long-cycle and portable uniform random number generators. ACM Trans. Modeling Comput. Simulation 13:299–309.Crossref, Google Scholar
- (2009) Scalable parallel multiple recursive generators of large order. Parallel Comput. 35:29–37.Crossref, Google Scholar
- (2012) Large-order multiple recursive generators with modulus 231 – 1. INFORMS J. Comput. 24:636–647.Link, Google Scholar
- (2008) Design and implementation of efficient and portable multiple recursive generators with few zero coefficients. Keller A, Heinrich S, Niederreiter H, eds. Monte Carlo and Quasi-Monte Carlo Methods 2006 (Springer-Verlag, Berlin), 263–273.Crossref, Google Scholar
- (1998) The Art of Computer Programming, Volume 2: Seminumerical Algorithms, 3rd ed. (Addison-Wesley, Reading, MA).Google Scholar
- (1997) Bad lattice structures for vectors of non-successive values produced by some linear recurrences. INFORMS J. Comput. 9:57–60.Link, Google Scholar
- (1999a) Good parameters and implementations for combined multiple recursive random number generators. Oper. Res. 47:159–164.Link, Google Scholar
- (1999b) Tables of maximally equidistributed combined LFSR generators. Math. Comput. 68:261–269.Crossref, Google Scholar
- (2006) Uniform random number generation. Henderson SG, Nelson BL, eds. Simulation. Handbooks in Operations Research and Management Science, Chap. 3 (Elsevier, Amsterdam), 55–81.Google Scholar
- (1997) An implementation of the lattice and spectral tests for multiple recursive linear random number generators. INFORMS J. Comput. 9:206–217.Link, Google Scholar
- (2001) On the performance of birthday spacings tests for certain families of random number generators. Math. Comput. Simulation 55:131–137.Crossref, Google Scholar
- (2007) TestU01: A C library for empirical testing of random number generators. ACM Trans. Math. Software 33:Article 22.Crossref, Google Scholar
- (2000) Fast combined multiple recursive generators with multipliers of the form a = ±2q ± 2r. Joines JA, Barton RR, Kang K, Fishwick PA, eds. Proc. 2000 Winter Simulation Conf. (IEEE Press, Piscataway, NJ), 683–689.Google Scholar
- (2004) On the Deng-Lin random number generators and related methods. Statist. Comput. 14:5–9.Crossref, Google Scholar
- (2002) An object-oriented random-number package with many long streams and substreams. Oper. Res. 50:1073–1075.Link, Google Scholar
- (1985) A current view of random number generators. Billard L, ed. Comput. Sci. Statist., Sixteenth Sympos. Interface (Elsevier Science Publishers, North-Holland, Amsterdam), 3–10.Google Scholar
- (1999) Random numbers for C: The END? Posted to the electronic billboard sci.math.num-analysis. https://groups.google.com/forum/#!search/marsaglia$20random$20numbersA$20222/sci.math.num-analysis/yoaCpGWKEk0/UXCxgufdTesJ.Google Scholar
- (2007) Common defects in initialization of pseudorandom number generators. ACM Trans. Modeling Comput. Simulation 17:Article 15.Crossref, Google Scholar
- (2010) Boost random number library. http://www.boost.org/libs/random/index.html.Google Scholar
- (1992) Random Number Generation and Quasi-Monte Carlo Methods. SIAM CBMS-NSF Regional Conf. Ser. Appl. Math., Vol. 63 (SIAM, Philadelphia).Crossref, Google Scholar
- (1958) On the distribution mod 1 of the sequence nα. Ann. Univ. Sci. Budap. Rolando Eötvös, Sect. Math. 1:127–134.Google Scholar
- (1988) The three gap theorem (Steinhaus conjecture). J. Australian Math. Soc., Ser. A 45:360–370.Crossref, Google Scholar

