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48
Mersenne Twister: A 623dimensionally equidistributed uniform pseudorandom number generator
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TestU01: A C library for empirical testing of random number generators
 ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
, 2007
"... We introduce TestU01, a software library implemented in the ANSI C language, and offering a collection of utilities for the empirical statistical testing of uniform random number generators (RNGs). It provides general implementations of the classical statistical tests for RNGs, as well as several ot ..."
Abstract

Cited by 80 (4 self)
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We introduce TestU01, a software library implemented in the ANSI C language, and offering a collection of utilities for the empirical statistical testing of uniform random number generators (RNGs). It provides general implementations of the classical statistical tests for RNGs, as well as several others tests proposed in the literature, and some original ones. Predefined tests suites for sequences of uniform random numbers over the interval (0, 1) and for bit sequences are available. Tools are also offered to perform systematic studies of the interaction between a specific test and the structure of the point sets produced by a given family of RNGs. That is, for a given kind of test and a given class of RNGs, to determine how large should be the sample size of the test, as a function of the generatorâ€™s period length, before the generator starts to fail the test systematically. Finally, the library provides various types of generators implemented in generic form, as well as many specific generators proposed in the literature or found in widelyused software. The tests can be applied to instances of the generators predefined in the library, or to userdefined generators, or to streams of random numbers produced by any kind of device or stored in files. Besides introducing TestU01, the paper provides a survey and a classification of statistical tests for RNGs. It also applies batteries of tests to a long list of widely used RNGs.
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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Cited by 38 (6 self)
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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.
TestU01: A Software Library in ANSI C for Empirical Testing of Random Number Generators
, 2007
"... This document describes the software library TestU01, implemented in the ANSI C language, and offering a collection of utilities for the (empirical) statistical testing of uniform random number generators (RNG). The library implements several types of generators in generic form, as well as many spec ..."
Abstract

Cited by 26 (2 self)
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This document describes the software library TestU01, implemented in the ANSI C language, and offering a collection of utilities for the (empirical) statistical testing of uniform random number generators (RNG). The library implements several types of generators in generic form, as well as many specific generators proposed in the literature or found in widelyused software. It provides general implementations of the classical statistical tests for random number generators, as well as several others proposed in the literature, and some original ones. These tests can be applied to the generators predefined in the library and to userdefined generators. Specific tests suites for either sequences of uniform random numbers in [0, 1] or bit sequences are also available. Basic tools for plotting vectors of points produced by generators are provided as well. Additional software permits one to perform systematic studies of the interaction between a specific test and the structure of the point sets produced by a given family of RNGs. That is, for a given kind of test and a given class of RNGs, to determine how large should be the sample size of the test, as a function of the generatorâ€™s period length, before the generator starts to fail the test systematically.
Maximum Likelihood Estimators for ARMA and ARFIMA Models: A Monte Carlo Study
, 1999
"... We analyze by simulation the properties of two time domain and two frequency domain estimators for low order autoregressive fractionally integrated moving average Gaussian models, ARFIMA (p; d; q). The estimators considered are the exact maximum likelihood for demeaned data, EML, the associated modi ..."
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Cited by 13 (0 self)
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We analyze by simulation the properties of two time domain and two frequency domain estimators for low order autoregressive fractionally integrated moving average Gaussian models, ARFIMA (p; d; q). The estimators considered are the exact maximum likelihood for demeaned data, EML, the associated modified profile likelihood, MPL, and the Whittle estimator with, WLT, and without tapered data, WL. Length of the series is 100. The estimators are compared in terms of pileup effect, mean square error, bias, and empirical confidence level. The tapered version of the Whittle likelihood turns out to be a reliable estimator for ARMA and ARFIMA models. Its small losses in performance in case of "wellbehaved" models are compensated sufficiently in more "difficult" models. The modified profile likelihood is an alternative to the WLT but is computationally more demanding. It is either equivalent to the EML or more favorable than the EML. For fractionally integrated models, particularly, it dominate...
Construction of Equidistributed Generators based on linear recurrences modulo 2
, 2000
"... Random number generators based on linear recurrences modulo 2 are widely used and appear in dierent forms, such as the simple and combined Tausworthe generators, the GFSR, and the twisted GFSR generators. Lowdiscrepancy point sets for quasiMonte Carlo integration can also be constructed based on t ..."
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Cited by 12 (5 self)
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Random number generators based on linear recurrences modulo 2 are widely used and appear in dierent forms, such as the simple and combined Tausworthe generators, the GFSR, and the twisted GFSR generators. Lowdiscrepancy point sets for quasiMonte Carlo integration can also be constructed based on these linear recurrences. The quality of these generators or point sets is usually measured by certain equidistribution criteria. Combining two or more recurrences and adding linear output transformations can be used to improve the equidistribution properties. In this
Random Generator Quality and GP Performance
, 1999
"... In previous studies, the authors found that pseudorandom number generator (PRNG) quality had little effect on the performance of a simple genetic algorithm (GA). This paper extends our work to the area of genetic programming (GP). We examine the effect of PRNG quality on the performance of GP techn ..."
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Cited by 10 (1 self)
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In previous studies, the authors found that pseudorandom number generator (PRNG) quality had little effect on the performance of a simple genetic algorithm (GA). This paper extends our work to the area of genetic programming (GP). We examine the effect of PRNG quality on the performance of GP techniques. We detail a set of PRNGs which generate random numbers through various techniques, and a method for evaluating the quality of these PRNGs. We explain the application of detailed statistical analysis to the results of many individual GP runs, over a set of four GP test problems. We found no evidence to support the notion that higher quality PRNGs caused improved GP performance.
Randomness and GA Performance, Revisited
"... Previous studies by the authors have indicated that pseudorandom number generator #PRNG# quality has little e#ect on the performance of a simple genetic algorithm #GA#. In this paper we examine this subject further, in the context of what we call the #granularityhypothesis. We detail a set of ..."
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Cited by 9 (1 self)
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Previous studies by the authors have indicated that pseudorandom number generator #PRNG# quality has little e#ect on the performance of a simple genetic algorithm #GA#. In this paper we examine this subject further, in the context of what we call the #granularityhypothesis. We detail a set of PRNG quality tests tailored speci#cally to the uses of randomness in a simple GA. We explain the application of detailed statistical analysis to the results of nearly tenthousand individual GA runs, for large and small populations, over an eleven function GA test suite. We conclude that, although there is no evidence to support the notion that higher quality PRNGs cause better GA performance than lessor quality PRNGs, there is statistical evidence that certain PRNGs can provide improved GA performance. 1
An Area Time Efficient Field Programmable Mersenne Twister Uniform Random Number Generator
 In Proc of International Conference on Engineering of Reconfigurabe Systems and Algorithms
, 2006
"... Reconfigurable computing offers an attractive solution to accelerating infrared scene simulations. In infrared scene simulations, the modeling of a number of atmospheric and optical phenomena like scintillation, refraction, blurring due to lens optics and photon noise may be implemented in parallel. ..."
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Cited by 6 (3 self)
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Reconfigurable computing offers an attractive solution to accelerating infrared scene simulations. In infrared scene simulations, the modeling of a number of atmospheric and optical phenomena like scintillation, refraction, blurring due to lens optics and photon noise may be implemented in parallel. All of these require simultaneous and continual generation of random numbers. Furthermore, random number generation is only a small component of all of these algorithms. Current software random number generators are too slow whilst current hardware random number generators are plagued by issues such correlations and are not area efficient. We describe a reconfigurable computing based uniform random number generator based on the mersenne twister algorithm that is area time efficient and that does not suffer from correlations. 1.