Adaptation of a long-period composite random number generator for parallel processing

An efficient and statistically reliable random number generator is one of the most important requirements for effective Monte Carlo simulation. The latest trend in supercomputing being towards parallelization, a random number generator was designed that will allow the generation of several uncorrelated streams of random numbers in parallel. This is achieved by the division of one period of a good serial random number generator into intervals of uniform length, one interval per processor. The serial random number generator chosen was the Marsaglia - Zaman random number generator which is a long period composite random number generator combining a linear congruential sequence with a lagged Fibonacci sequence. The mathematical relation between distantly separated seed values in each of the sequences was considered and a method was developed to obtain values from the Marsaglia - Zaman sequence spaced from each other by the length of a specified interval called the jump distance. Program\u27s implementing the algorithm were written in C and Fortran. Seed values obtained from the programs can be used to initialize different processors to use different portions of the Marsaglia - Zaman sequence. The seed values obtained by looping through all the random numbers in a section of the Marsaglia - Zaman sequence were shown to be identical to the seed values obtained from the developed algorithm. The execution time for the developed method was shown to increase only as the order of log2(jump distance)

Random number generation with multiple streams for sequential and parallel computing

International audienceWe provide a review of the state of the art on the design and implementation of random number generators (RNGs) for simulation, on both sequential and parallel computing environments. We focus on the need for multiple streams and substreams of random numbers, explain how they can be constructed and managed, review software libraries that offer them, and illustrate their usefulness via examples. We also review the basic quality criteria for good random number generators and their theoretical and empirical testing

Distribution of Random Streams for Simulation Practitioners

International audienceThere is an increasing interest in the distribution of parallel random number streamsin the high-performance computing community particularly, with the manycore shift. Even ifwe have at our disposal statistically sound random number generators according to the latestand thorough testing libraries, their parallelization can still be a delicate problem. Indeed, aset of recent publications shows it still has to be mastered by the scientific community. Withthe arrival of multi-core and manycore processor architectures on the scientist desktop, modelerswho are non-specialists in parallelizing stochastic simulations need help and advice in distributingrigorously their experimental plans and replications according to the state of the art in pseudo-random numbers parallelization techniques. In this paper, we discuss the different partitioningtechniques currently in use to provide independent streams with their corresponding software. Inaddition to the classical approaches in use to parallelize stochastic simulations on regular processors,this paper also presents recent advances in pseudo-random number generation for general-purposegraphical processing units. The state of the art given in this paper is written for simulationpractitioners

Random Number Generators for Parallel Computers

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

Pseudo-Random Streams for Distributed and Parallel Stochastic Simulations on GP-GPU

International audienceRandom number generation is a key element of stochastic simulations. It has been widely studied for sequential applications purposes, enabling us to reliably use pseudo-random numbers in this case. Unfortunately, we cannot be so enthusiastic when dealing with parallel stochastic simulations. Many applications still neglect random stream parallelization, leading to potentially biased results. In particular parallel execution platforms, such as Graphics Processing Units (GPUs), add their constraints to those of Pseudo-Random Number Generators (PRNGs) used in parallel. This results in a situation where potential biases can be combined with performance drops when parallelization of random streams has not been carried out rigorously. Here, we propose criteria guiding the design of good GPU-enabled PRNGs. We enhance our comments with a study of the techniques aiming to parallelize random streams correctly, in the context of GPU-enabled stochastic simulations

Pseudo-Random Number Generators for Vector Processors and Multicore Processors

Large scale Monte Carlo applications need a good pseudo-random number generator capable of utilizing both the vector processing capabilities and multiprocessing capabilities of modern computers in order to get the maximum performance. The requirements for such a generator are discussed. New ways of avoiding overlapping subsequences by combining two generators are proposed. Some fundamental philosophical problems in proving independence of random streams are discussed. Remedies for hitherto ignored quantization errors are offered. An open source C++ implementation is provided for a generator that meets these needs