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SPRNG: A Scalable Library for Pseudorandom Number Generation
"... 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 conside ..."
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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 leapfrog or blocking methods. We describe in detail
parameterized versions of the following pseudorandom number generators: (i) linear congruential
generators, (ii) shiftregister generators, and (iii) laggedFibonacci 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.
Testing Parallel Random Number Generators
"... . A parallel random number generator (PRNG) must be tested for two types of correlations  (i) Intrastream correlation, as for any serial generator, and (ii) Interstream correlation for correlations between random number streams on different processes. Since bounds on these correlations are diffi ..."
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Cited by 23 (1 self)
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. A parallel random number generator (PRNG) must be tested for two types of correlations  (i) Intrastream correlation, as for any serial generator, and (ii) Interstream correlation for correlations between random number streams on different processes. Since bounds on these correlations are difficult to prove mathematically, large empirical tests are necessary. Many of the popular RNGs in use today were tested when computational power was much lower, and hence they were evaluated with much smaller. This paper describes several tests of PRNGs, both statistical and physicallybased tests. We show defects in several popular generators. We then present the results for the tests conducted on the SPRNG generators. These generators have passed some of the largest empirical random number tests ever undertaken. 1 Introduction Monte Carlo (MC) computations have, currently do, and will continue to consume a large fraction of all available highperformance computing cycles. MC methods can be de...
Parallel Pseudorandom Number Generation Using Additive LaggedFibonacci Recursions
, 1995
"... . We study the suitability of the additive laggedFibonacci pseudorandom number generator for parallel computation. This generator has a relatively short period with respect to the size of its seed. However, the short period is more than made up for with the huge number of fullperiod cycles it cont ..."
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. We study the suitability of the additive laggedFibonacci pseudorandom number generator for parallel computation. This generator has a relatively short period with respect to the size of its seed. However, the short period is more than made up for with the huge number of fullperiod cycles it contains. We call these different fullperiod cycles equivalence classes. We show how to enumerate the equivalence classes and how to compute seeds to select a given equivalence class. The use of these equivalence classes gives an explicit parallelization suitable for a fully reproducible asynchronous MIMD implementation. To explore such an implementation we introduce an exponential sum measure of quality for the additive laggedFibonacci generators used in serial or parallel. We then prove the first nontrivial results we are aware of on this measure of quality. 1. Introduction. In Knuth's well known exposition on pseudorandom number generation [5], several methods of generation are considered...
Random Number Generators for Parallel Applications
 in Monte Carlo Methods in Chemical Physics
, 1998
"... 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 ntuples of random numbers and/or the equivalent property that random numbers be uncorrelated. The quality aspect i ..."
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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 ntuples 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 welldefined 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
Random Number Generation and Simulation on Vector and Parallel Computers
 LECTURE NOTES IN COMPUTER SCIENCE 1470
, 1998
"... Pseudorandom 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 rand ..."
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Cited by 14 (10 self)
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Pseudorandom 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
Parameterizing parallel multiplicative laggedfibonacci generators
 Parallel Computing
, 2004
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Some Methods Of Parallel Pseudorandom Number Generation
 in Proceedings of the IMA Workshop on Algorithms for Parallel Processing
, 1997
"... . 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 cong ..."
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Cited by 10 (1 self)
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. 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. shiftregister generators 4. laggedFibonacci 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, laggedFibonacci, inversive congruential, shiftregister AMS(MOS) subject classifications....
Techniques for Empirical Testing of Parallel Random Number Generators
 Proc. International Conference on Supercomputing (ICS'98
, 1998
"... Parallel computers are now commonly used for computational science and engineering, and many applications in these areas use random number generators. For some applications, such as largescale Monte Carlo simulations, it is crucial that the random number generator have good randomness properties. M ..."
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Parallel computers are now commonly used for computational science and engineering, and many applications in these areas use random number generators. For some applications, such as largescale Monte Carlo simulations, it is crucial that the random number generator have good randomness properties. Many programs are available for testing the quality of sequential random number generators, but very little work has been done on testing parallel random number generators. We present some techniques for empirical testing of random number generators on parallel computers, using tests based on computational science applications as examples. In particular, we focus on tests based on parallel algorithms developed for Monte Carlo simulations of the two dimensional Ising model, for which exact results are known. Preliminary results of these tests are presented for several parallel random number generators. Current address. 1 Introduction Parallel computers are now commonly used for computatio...