Random number generation parallelization

IV. Testing Random Number Generators A. Parallel Tests... 

We shall focus here on developments caused by widespread use of parallel computers to perform Monte Carlo calculations. Our impression is that individual users are porting random number generators to parallel computers in an ad hoc fashion, possibly unaware of some of the issues that come to the fore when massive calculations are performed. Parallel algorithms can probe other qualities of random number generators such as interprocess correlation. A recent review covers parallel random number generation in somewhat more depth [12]. The interested reader can also refer to Refs. 13-17 for work related to parallel random number generation and testing. 

We have recently developed a library implementing several of the parallel random number generators and statistical tests of them on the most widely available multiprocessor computers. Documentation and software are available at... 

In this section we discuss some of the desired properties of good random number generators. We shall then explain specific implications of these for parallel random number generation. 

We next mention the implications of correlation and cycle length on parallel pseudo-random number generators (PPRNGs). 

We now mention some tests of parallel random number generators. 

P. Coddington, Random Number Generators for Parallel Computers, April 28, 1997, http //www.npac.syr.edu/users/paulc/papers/NHSEreviewLl/PRNGreview.ps. 

E. Percus and M. H. Kalos, Random Number Generators for MIMD Parallel Processors, J. Par. Distr. Comp. 6,477-497 (1989). 

Afshar, Y., Schmid, R, Kshevar, A., Worley, S. Exploiting seeding of random number generators for efficient domain decomposition parallelization of dissipative particle dynamics. Comput. Phys. Commun. 184(4), 1119-1128 (2013). doi 10.1016/j.cpc.2012.12.003... 

Figure 2.17. It has been shown that track lengths between fineparticles in a random array are log-normally distributed, a) A random number table consists of the digits 0 through 9 chosen in random order to form a table, b) A simulated random field of view can be generated by turning every 9 in the random number table of (a) into a black square. The distance between black squares then generates various track lengths when examined with a series of parallel lines, c) Track length distribution generated firom the array of (b).

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