A random number generator for parallel computers

Abstract Running huge simulational computations on a system of parallel processors requires the generation of uniform random sequences on each processor. Various techniques useful for the generation of parallel random sequences are analyzed for their suitability to parallel architectures. An efficient parallelization of the Generalized Feedback Shift Register (GFSR) algorithm for generating pseudorandom numbers is presented. The algorithm works on any parallel computer where the number of processors is a power of two and requires the same amount of memory per processor as required by the sequential GFSR algorithm.

[1]  G. Marsaglia The Structure of Linear Congruential Sequences , 1972 .

[2]  C. H. Still,et al.  Random Number Generation in the Parallel Environment , 1990, Proceedings of the Fifth Distributed Memory Computing Conference, 1990..

[3]  Neal Zierler,et al.  Primitive Trinomials Whose Degree is a Mersenne Exponent , 1969, Inf. Control..

[4]  István Deák,et al.  Uniform random number generators for parallel computers , 1990, Parallel Comput..

[5]  Mark A. Johnson,et al.  Solving problems on concurrent processors. Vol. 1: General techniques and regular problems , 1988 .

[6]  Stuart L. Anderson,et al.  Random Number Generators on Vector Supercomputers and Other Advanced Architectures , 1990, SIAM Rev..

[7]  G. Marsaglia,et al.  Matrices and the structure of random number sequences , 1985 .

[8]  George Marsaglia,et al.  Regularities in congruential random number generators , 1970 .

[9]  Ted G. Lewis,et al.  Generalized Feedback Shift Register Pseudorandom Number Algorithm , 1973, JACM.

[10]  David H. Bailey,et al.  The Nas Parallel Benchmarks , 1991, Int. J. High Perform. Comput. Appl..

[11]  R. Tausworthe Random Numbers Generated by Linear Recurrence Modulo Two , 1965 .

[12]  Ora E. Percus,et al.  Random Number Generators for MIMD Parallel Processors , 1989, J. Parallel Distributed Comput..

[13]  Bruce Jay Collings,et al.  Initializing generalized feedback shift register pseudorandom number generators , 1986, JACM.

[14]  G. Marsaglia Random numbers fall mainly in the planes. , 1968, Proceedings of the National Academy of Sciences of the United States of America.

[15]  Solomon W. Golomb,et al.  Shift Register Sequences , 1981 .

[16]  Harald Niederreiter,et al.  A statistical analysis of generalized feedback shift register pseudorandom number generators , 1987 .

[17]  K. O. Bowman,et al.  Studies of random number generators for parallel processing , 1986 .

[18]  Neal Zierler,et al.  On Primitive Trinomials (Mod 2) , 1968, Inf. Control..