Good Parameters and Implementations for Combined Multiple Recursive Random Number Generators

Combining parallel multiple recursive sequences provides an efficient way of implementing random number generators with long periods and good structural properties. Such generators are statistically more robust than simple linear congruential generators that fit into a computer word. We made extensive computer searches for good parameter sets, with respect to the spectral test, for combined multiple recursive generators of different sizes. We also compare different implementations and give a specific code in C that is faster than previous implementations of similar generators.

[1]  Pierre L'Ecuyer,et al.  Uniform random number generation , 1994, Ann. Oper. Res..

[2]  Pierre L'Ecuyer,et al.  Bad Lattice Structures for Vectors of Nonsuccessive Values Produced by Some Linear Recurrences , 1997, INFORMS J. Comput..

[3]  Brian D. Ripley,et al.  Stochastic Simulation , 2005 .

[4]  Pierre L'Ecuyer,et al.  Implementing a random number package with splitting facilities , 1991, TOMS.

[5]  Paul Bratley,et al.  A guide to simulation , 1983 .

[6]  A. Grube,et al.  Mehrfach rekursiv‐erzeugte Pseudo‐Zufallszahlen , 1973 .

[7]  Pierre L'Ecuyer,et al.  An Implementation of the Lattice and Spectral Tests for Multiple Recursive Linear Random Number Generators , 1997, INFORMS J. Comput..

[8]  Pierre L'Ecuyer,et al.  Tables of linear congruential generators of different sizes and good lattice structure , 1999, Math. Comput..

[9]  Harald Niederreiter,et al.  Random number generation and Quasi-Monte Carlo methods , 1992, CBMS-NSF regional conference series in applied mathematics.

[10]  Linus Schrage,et al.  A guide to simulation , 1983 .

[11]  Pierre L'Ecuyer,et al.  Efficient and portable combined random number generators , 1988, CACM.

[12]  Pierre L'Ecuyer,et al.  Combined Multiple Recursive Random Number Generators , 1995, Oper. Res..

[13]  A. Blokhuis.  SPHERE PACKINGS, LATTICES AND GROUPS (Grundlehren der mathematischen Wissenschaften 290) , 1989 .

[14]  Pierre L'Ecuyer,et al.  Random Number Generators: Selection Criteria and Testing , 1998 .

[15]  Jean-François Cordeau,et al.  Close-Point Spatial Tests and Their Application to Random Number Generators , 2000, Oper. Res..

[16]  N. J. A. Sloane,et al.  Sphere Packings, Lattices and Groups , 1987, Grundlehren der mathematischen Wissenschaften.

[17]  Donald Ervin Knuth,et al.  The Art of Computer Programming, Volume II: Seminumerical Algorithms , 1970 .