In this article we present background, rationale, and a description of the Scalable Parallel Random Number Generators (SPRNG) library. We begin by presenting some methods for parallel pseudorandom number generation. We will focus on methods based on parameterization, meaning that we will not consider splitting methods such as the leap-frog or blocking methods. We describe in detail parameterized versions of the following pseudorandom number generators: (i) linear congruential generators, (ii) shift-register generators, and (iii) lagged-Fibonacci generators. We briey describe the methods, detail some advantages and disadvantages of each method, and recount results from number theory that impact our understanding of their quality in parallel applications. SPRNG was designed around the uniform implementation of dierent families of parameterized random number generators. We then present a short description of SPRNG. The description contained within this document is meant only to outline the rationale behind and the capabilities of SPRNG. Much more information, including examples and detailed documentation aimed at helping users with putting and using SPRNG on scalable systems is available at the URL: http://sprng.cs.fsu.edu/RNG. In this description of SPRNG we discuss the random number generator library as well as the suite of tests of randomness that is an integral part of SPRNG. Random number tools for parallel Monte Carlo applications must be subjected to classical as well as new types of empirical tests of ran- domness to eliminate generators that show defects when used in scalable environments.

this article is devoted, because these com1 putations require the highest quality of random numbers. The ability to do a multidimensional integral relies on properties of uniformity of n-tuples of random numbers and/or the equivalent property that random numbers be uncorrelated. The quality aspect in the other uses is normally less important simply because the models are usually not all that precisely specified. The largest uncertainties are typically due more to approximations arising in the formulation of the model than those caused by lack of randomness in the random number generator. In contrast, the first class of applications can require very precise solutions. Increasingly, computers are being used to solve very well-defined but hard mathematical problems. For example, as Dirac [1] observed in 1929, the physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are completely known and it is only necessary to find precise methods for solving the equations for complex systems. In the intervening years fast computers and new computational methods have come into existence. In quantum chemistry, physical properties must be calculated to "chemical accuracy" (say 0.001 Rydbergs) to be relevant to physical properties. This often requires a relative accuracy of 10

The ns-2 is a widely used network simulation tool which implements a fairly old and weak random number generator (RNG). As the RNG component is used by a variety of other components, it can be seen as one of the most important core components of the ns-2. In this paper we explore weaknesses of this RNG and demonstrate its shortcomings in context with a simple simulation example (M/D/1) which produces severely wrong simulation results when this RNG is used in combination with specific seeds. We incorporate the modern Mersenne Twister RNG into the ns-2 and show how the insensitivity of this RNG regarding to the initial seeds leads to significant improvements in the simulation outputs and that this modern RNG has no bad effects with respect to the performance of random number generation.

. We detail several methods used in the production of pseudorandom numbers for scalable systems. We will focus on methods based on parameterization, meaning that we will not consider splitting methods. We describe parameterized versions of the following pseudorandom number generation: 1. linear congruential generators 2. linear matrix generators 3. shift-register generators 4. lagged-Fibonacci generators 5. inversive congruential generators We briefly describe the methods, detail some advantages and disadvantages of each method and recount results from number theory that impact our understanding of their quality in parallel applications. Several of these methods are currently part of scalable library for pseudorandom number generation, called the SPRNG package available at the URL: www.ncsa.uiuc.edu/Apps/CMP/RNG. Key words. pseudorandom number generation, parallel computing, linear congruential, lagged-Fibonacci, inversive congruential, shift-register AMS(MOS) subject classifications....

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Scientific computing has long been pushing the boundaries of computational requirements in computer science. An important aspect of scientific computing is the generation of large quantities of random numbers, especially in parallel to take advantage of parallel architectures. Many science and engineering programs require random numbers for applications like Monte Carlo simulation. Such an environment suitable for parallel computing is Java, though rarely used for scientific applications due to its perceived slowness when compared to complied languages like C. Through research and recommendations, Java is slowly being shaped into a viable language for such computational intense applications. Java has the potential for such large scale applications, since it is a modern language with a large programmer base and many well received features such as built-in support for parallelism using threads. With improved performance from better compilers, Java is becoming more commonly used for scientific computing but Java still lacks a number of features like optimised scientific software libraries. This project looks at the effectiveness and efficiency of implementing a parallel random number

erator Karl Entacher University of Salzburg Department of Mathematics Salzburg, Austria E-mail: Karl.Entacher@sbg.ac.at We present a theoretical and empirical analysis of the quality of the CRAY-system random number generator RANF in parallel settings. Subsequences of this generator are used to obtain parallel streams of random numbers for each processor. We use the spectral test to analyze the quality of lagged subsequences of RANF with step sizes 2 , l 1, appropriate for CRAY systems. Our results demonstrate that with increasing l, the quality of lagged subsequences is strongly reduced in comparison to the original sequence. The results are supported by a numerical Monte Carlo integration study. We also use the spectral test to exhibit the well known longrange correlations between consecutive blocks of random numbers obtained from RANF. Keywords: Random number ge

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Numerical simulations in computational physics, biology, and finance, often require the use of high quality and efficient parallel random number generators. We design and optimize several parallel pseudo random number generators on the Cell Broadband Engine, with minimal correlation between the parallel streams: the linear congruential generator (LCG) with 64-bit prime addend and the Mersenne Twister (MT) algorithm. As compared with current Intel and AMD microprocessors, our Cell/B.E. LCG and MT implementations achieve a speedup of 33 and 29, respectively. We also explore two normalization techniques, Gaussian averaging method and Box Mueller Polar/Cartesian, that transform uniform random numbers to a Gaussian distribution. Using these fast generators we develop a parallel implementation of Value at Risk, a commonly used model for risk assessment in financial markets. To our knowledge we have designed and implemented the fastest parallel pseudo random number generators on the Cell/B.E..