Some vectorized random number generators for uniform, normal, and poisson distributions for CRAY X-MP

Abstract

It is amusing to note how the initial pessimism about vector/parallel methods for Monte Carlo simulations has now been replaced with requests for better and faster vcctorizcd random number generators for those purposes. In fact, much of the impetus for establishing the NSF supercomputer centers came from Nobel Laureate Kenneth G. Wilson's significant interests in Monte Carlo simulations of quantum field theories. The generality and usefulness of stochastic simulations has only begun to be explored and will likely be driven by the power of vector/parallel computer architectures [Monte Carlo 1983]. As the scope of these simulations increases, the need for fast vectorized random number generators with excellent statistical properties becomes more crucial. I hope that the three functions described below will move toward satisfying that need. The three functions, with their distributions and syntax for usage, are:1. Uniform distribution. The function is called RANQ and an example of usage is real u(n) cdir$ vfunction RANQ doli= 1,n u(i) = RANQ() 1 continue giving a uniformly distributed sequence { uilO. < ui< 1. }.2. Normal distribution. The function is called GAUSSQ and an example of usage is rcalv(n) cdir$ vfunction GAUSSQ doli= 1, n

Some Comments on C. S. Wallace's Random Number Generators

“…Traditional normal RNGs are inefficient on vector processors. In 1993 the author compared various normal RNGs on vector processors and concluded that careful implementations of old methods such as the 1958 Polar method of Box, Muller and Marsaglia (see Knuth [21, Algorithm P]) and the 1959 Box-Muller method [21,28] were faster than more recent methods [22] on vector processors produced by companies such as Cray, Fujitsu, and NEC: see [8,30]. When Wallace's maximum-entropy idea appeared, it was clear that the landscape had changed, although the published implementation fastnorm was not intended to be efficient on vector processors.…”

Random Number Generation

“…In 1993 the author compared various normal RNGs on vector processors and concluded that careful implementations of old methods such as the 1958 Polar method of Box, Muller and Marsaglia (see Knuth [21,Algorithm P]) and the 1959 Box-Muller method [21,28] were faster than more recent methods [22] on vector processors produced by companies such as Cray, Fujitsu, and NEC: see [8,30]. When Wallace's maximum-entropy idea appeared, it was clear that the landscape had changed, although the published implementation fastnorm was not intended to be efficient on vector processors.…”

An introduction to numerical methods for stochastic differential equations

“…We mention also the papers by Box and Muller (1958), Marsaglia and Bray (1964), Brent (1974), Eichenauer and Lehn (1986), Niederreiter (1988), Sugita (1995) and Antipov (1995Antipov ( , 1996. Random number generation on supercomputers was considered by Petersen (1988), Anderson (1990), Petersen (1994a) and Entacher, Uhl and Wegenkittl (1998).…”