Implementation of a portable and reproducible parallel pseudorandom number generator

Pryor, Daniel V.; Cuccaro, Steven A.; Mascagni, Michael; Robinson, M. L.

doi:10.1145/602827.602829

Cited by 4 publications

(11 citation statements)

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“…The parallelization scheme we recommend is based on parameterization (see [23][24][25]28], for example). This provides independent full-period streams on each processor.…”

Section: Parallelizing Prngsmentioning

confidence: 99%

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Testing parallel random number generators

2003

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Monte Carlo computations are considered easy to parallelize. However, the results can be adversely affected by defects in the parallel pseudorandom number generator used. A parallel pseudorandom number generator must be tested for two types of correlations-(i) intrastream correlation, as for any sequential generator, and (ii) inter-stream correlation for correlations between random number streams on different processes. Since bounds on these correlations are difficult to prove mathematically, large and thorough empirical tests are necessary. Many of the popular pseudorandom number generators in use today were tested when computational power was much lower, and hence they were evaluated with much smaller test sizes. This paper describes several tests of pseudorandom number generators, both statistical and application-based. We show defects in several popular generators. We describe the implementation of these tests in the SPRNG [ACM Trans. Math. Software 26 (2000) 436; SPRNG-scalable parallel random number generators. SPRNG 1.0-http://www.ncsa.uiuc.edu/ Apps/SPRNG; SPRNG 2.0-http://sprng.cs.fsu.edu] test suite and also present results for the tests conducted on the SPRNG generators. These generators have passed some of the largest empirical random number tests.

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“…The parallelization scheme we recommend is based on parameterization (see [23][24][25]28], for example). This provides independent full-period streams on each processor.…”

Section: Parallelizing Prngsmentioning

confidence: 99%

“…The sequence obtained is determined by the ' initial values of the sequences X and Y . The seeding algorithm ensures that distinct streams are obtained during parallelization [23,24,28].…”

Section: Modified Lagged-fibonacci Generator: Lfgmentioning

confidence: 99%

Testing parallel random number generators

2003

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“…In a previous work we only considered full-period exponential sum cross-correlation for studying these issues for a different recursion [Pryor et al 1994]. We will take the same approach here.…”

Section: Linear Congruential Generatorsmentioning

confidence: 99%

“…It is known that certain sequences are more correlated than others as a function of the similarity in the least-significant bits in the template for parameterization [Mascagni et al 1995b]. However, it is easy to avoid all but the most uncorrelated pairs in a computation [Pryor et al 1994]. In this case there is extensive empirical evidence that the full-period exponential sum correlation between streams is O͑ ͱ͑2 k Ϫ1͒2 mϪ1 ͒, the square root of the full-period.…”

Section: Lagged-fibonacci Generatorsmentioning

confidence: 99%

Algorithm 806: SPRNG

Mascagni

Srinivasan

2000

ACM Trans. Math. Softw.

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207

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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 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 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. SPRNG was designed around the uniform implementation of different 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 http://sprng.cs.fsu.edu. 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 randomness to eliminate generators that show defects when used in scalable environments.The SPRNG software was developed with funding from DARPA Contract Number DABT63-95-C-0123 for ITO: Scalable Systems and Software, entitled A Scalable Pseudorandom Number

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“…One method is to split the full-period sequence into subsequences that are then used on individual parallel processors, [5]. Recently, certain pseudorandom numbergenerators have been parallelized using dierent seeds to select dierent full-period cycles, [15,19]. This is a form of parameterization of the full-period cycle.…”

Section: Parameterization Via the Multipliermentioning

confidence: 99%

Parallel linear congruential generators with prime moduli

Mascagni

1998

Parallel Computing

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Linear congruential generators (LCGs) remain the most popular method of pseudorandom number generation on digital computers. Ease of implementation has favored implementing LCGs with power-of-two moduli. However, prime modulus LCGs are superior in quality to power-of-two modulus LCGs, and the use of a Mersenne prime minimizes the computational cost of generation. When implemented for parallel computation, quality becomes an even more compelling issue. We use a full-period exponential sum as the measure of stream independence and present a method for producing provably independent streams of LCGs in parallel by utilizing an explicit parameterization of all of the primitive elements modulo a given prime. The minimization of this measure of independence further motivates an algorithm required in the explicit parameterization. We describe and analyze this algorithm and describe its use in a parallel LCG package.

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Implementation of a portable and reproducible parallel pseudorandom number generator

Cited by 4 publications

References 0 publications

Testing parallel random number generators

Testing parallel random number generators

Algorithm 806: SPRNG

Parallel linear congruential generators with prime moduli

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