Random number generators are used in many applications, from slot machines to simulations of nuclear reactors. For many computational science applications, such as Monte Carlo simulation, it is crucial that the generators have good randomness properties. This is particularly true for large-scale simulations done on high-performance parallel computers. Good random number generators are hard to find, and many widely-used techniques have been shown to be inadequate. Finding high-quality, efficient algorithms for random number generation on parallel computers is even more difficult. Here we present a review of the most commonly-used random number generators for parallel computers, and evaluate each generator based on theoretical knowledge and empirical tests. In conclusion, we provide recommendations for using random number generators on parallel computers. Outline This review is organized as follows: A brief summary of the findings of this review is first presented, giving an overview of the use of parallel random number generators and a list of recommended algorithms. Section 1 is an introduction to random number generators and their use in computer simulations on parallel computers. Section 2 is a summary of the methods used to test and evaluate random number generators, on both sequential and parallel computers. Section 3 gives an overview of the main algorithms used to implement random number generators on sequential computers, provides examples of software implementations of the algorithms, and states any known problems with the algorithms or implementations. Section 4 gives a description of the most common methods used to parallelize the sequential algorithms, provides examples of software implementing these algorithms, and states any known problems ...

ing with credit is permitted. To copy otherwise, to republish, to post on servers, to redistribute to lists, or to use any component of this work in other works, requires prior specific permission and/or a fee. Permissions may be requested from Publications Dept, ACM Inc., 1515 Broadway, New York, NY 10036 USA fax +1 (212) 869-0481, or permissions@acm.org. Parallel Streams of Linear Random Numbers in the Spectral Test Karl Entacher Austrian Science Fund (FWF projects no. P11143-MAT and P12441-MAT) This paper reports analyses of subsequences of linear congruential pseudorandom numbers by means of the spectral test. Such subsequences occur in particular simulation setups or as methods to obtain parallel streams of pseudorandom numbers for parallel and distributed simulation. Especially in the latter case, two kinds of sub-streams are of special interest: lagged random numbers with step sizes k, and consecutive streams of random numbers of length l. We show how to analyze correlations ...

this report we shall present the fundamentals of random number generation on parallel processors. We shall exhibit how the practical task of carrying out stochastic simulation on a parallel machine leads deeply into number theory and algebra. We shall see that some classical algorithms which have proved to be excellent for single-processor machines, are either useless or require greatest care in the case of parallel processors. Stochastic simulation is one of the important tasks for single- as well as multiprocessor machines. Computer simulations of real-life processes based on stochastic models have become one of the most interesting -- and demanding -- applications of mathematics. Due to the computational complexity of the problems, parallelization of the underlying algorithms is receiving increasing attention. As a basic condition to any research, we should be able to reproduce and to verify a scientific experiment. These two requirements and, further, considerations of storage and computational effectiveness rule out physical sources for random numbers, such as radioactive decay or electronic noise. The efficient generation of random numbers of high statistical quality is an absolute necessity for stochastic simulation. In his well-known monograph, Ripley [19, p.2] writes: "The first thing needed for a stochastic simulation is a source of randomness. This is often taken for granted but is of fundamental importance. Regrettably many of the so-called random functions supplied with the most widespread computers are far from random, and many simulation studies have been invalidated as a consequence." D5H-1/Rel 1.0/April 27, 1994 Random number generators for parallel processors PACT The following statement from Ripley[19, p.14] does not exaggerate the actual situation:...

In a set of stochastic simulations, which we collectively call the digit test, we compare the widely used linear congruential with the new inversive random number generators. The inversive generators are found to perform always at least as good as any of the linear congruential generators; in some simulation runs, they perform significantly better.

. We use an empirical study based on simple Monte Carlo integrations to exhibit the well known long-range correlations between linear congruential random numbers. In contrast to former studies, our long-range correlation test is carried out to asses more than only two parallel streams. The results show that critical distances derived from earlier papers have to be updated. In addition we performed our test also with explicit inversive generators which from the theoretical point of view have to be stable against long-range correlations. 1 Introduction The well known concept of longe-range correlations between consecutive blocks of random numbers is due to a series of papers written by DeMatteis, Pagnutti, Eichenauer-Herrman and Grothe [5--11, 15]. Consecutive blocks of random number provide an easy method to get parallel streams of random numbers for parallel and distributed simulation [1, 3, 6] and such blocks are supported by various simulation languages [25, 23]. Additional papers w...