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 ...

Pseudo-random numbers are often required for simulations performed on parallel computers. The requirements for parallel random number generators are more stringent than those for sequential random number generators. As well as passing the usual sequential tests on each processor, a parallel random number generator must give dierent, independent sequences on each processor. We consider the requirements for a good parallel random number generator, and discuss generators for the uniform and normal distributions. We also describe a new class of generators for the normal distribution (based on a proposal by Wallace). These

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In this work we discuss the use and possible abuse of linear and inversive pseudorandom numbers (PRNs) in parallel and distributed environments. After an investigation of properties of PRNs which determine how these may be applied in such environments we introduce a software package which provides an unified and easy-to-use approach to the generating and handling of parallel streams of such PRNs. Experimental results are conducted which describe the features of the software package and compare the performance of two selected types of pseudorandom number generators. 1 Introduction Parallel and distributed simulation of discrete event systems has received significant attention since the proliferation of massively parallel and distributed computing platforms [17]. Besides event processing, state update, statistics collection, and many more tasks, random number generation is an important element of every simulation experiment. Whereas the main objective in the parallel and distributed sim...

Solving the global illumination problem is equivalent to determining the intensity of ev-ery wavelength of light in all directions at every point inagiven scene. The complexity of the problem has led researchers to use approximation methods for solving the problem on serial computers. Rather than using an approximation method, such as backward ray tracing or radiosity, we have chosen to solve the Rendering Equation by direct sim-ulation of light transport from the light sources. This paper presents an algorithm that solves the Rendering Equation to any desired accuracy, and can be run in parallel on distributed memory or shared memory computer systems with excellent scaling prop-erties. It appears superior in both speed and physical correctness to recent published methods involving bidirectional ray tracing or hybrid treatments of di use and specu-lar surfaces. Like \progressive radiosity " methods, it dynamically re nes the geometry decomposition where required, but does so without the excessive storage requirements for \ray histories. " The algorithm, called Photon, produces a scene which converges to the global illumination solution. This amounts to a huge task for a 1997-vintage serial computer, but using the power of a parallel supercomputer signi cantly reduces

The paper explores the application of a lazy functional language, Haskell, to a series of grid-based scientific problems---solution of the Poisson equation and Monte Carlo simulation of two theoretical models from statistical and particle physics. The implementations introduce certain abstractions of grid topology, making extensive use of the polymorphic features of Haskell. Updating is expressed naturally through use of infinite lists, exploiting the laziness of the language. Evolution of systems is represented by arrays of interacting streams. 1 Introduction Lazy functional languages have not, to date, made an enormous impact in scientific computing. Partly, this has to do with performance---codes written in these languages often run an order of magnitude slower than imperative codes, which limits their appeal for numbercrunching production codes 1 . Apart from that, there is a suspicion that programming without assignments or side-effects is difficult, or restrictive. Evidently, ...

this article, the general design of RANEXP is outlined and the generators included are briefly described. The theoretical background for these generators is not discussed here, since various textbooks and review articles cover this field. For details on the algorithms, chapter 3 of Knuth[5], chapter 6 of Bratley/Fox/Schrage[2], chapter 7 of Press et.al[11, 12] and the review articles by James[4] and Marsaglia[7] may be referenced. The bibliography of the separate RANEXP manual contains further references. The generators are implemented in ANSI C[1], which is well-suited to efficiently implement those algorithms in a way fully conforming to the language standard, thus enhancing portability. A separate Fortran interface is provided which enables Fortran application programs to use the generators.

The quality of parallel substreams of pseudorandom numbers obtained from linear congruential generators as it is measured by the spectral test depends in a very sensitive and irregular way on the step size which is used. On the other hand, discrepancy estimates show that explicit inversive congruential pseudorandom number generators behave stable with respect to subsequences. The results of a sample Monte Carlo integration show the impact of these different theoretical findings on the reliability of the integration results.