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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 ..."
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Cited by 35 (1 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 generator’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.
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 ..."
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Cited by 18 (1 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 generator’s period length, before the generator starts to fail the test systematically.
A Collection of Selected Pseudorandom Number Generators with Linear Structures
, 1997
"... This is a collection of selected linear pseudorandom number that were implemented in commercial software, used in applications, and some of which have extensively been tested. The quality of these generators is examined using scatter plots and the spectral test. In addition, the spectral test is app ..."
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Cited by 14 (2 self)
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This is a collection of selected linear pseudorandom number that were implemented in commercial software, used in applications, and some of which have extensively been tested. The quality of these generators is examined using scatter plots and the spectral test. In addition, the spectral test is applied to study the applicability of linear congruential generators on parallel architectures. Additional Key Words and Phrases: Pseudorandom number generator, linear congruential generator, multiple recursive generator, combined pseudorandom number generators, parallel pseudorandom number generator, lattice structure, spectral test. 0 0.0001 0 0.0001 0 0.0001 0 0.0001 0 0.0001 Research supported by the Austrian Science Foundation (FWF), project no. P11143MAT. Contents 1 Linear congruential generator: LCG 5 1.1 LCG(2 31 ; 1103515245; 12345; 12345) ANSIC : : : : : : : : : : : : : : : : 5 1.2 LCG(2 31 \Gamma1; a = 7 5 = 16807; 0; 1) MINSTD : : : : : : : : : : : : : : : : 5 1.3 LCG...
Uniform Random Number Generators: A Review
"... Thispapersummarizesthecurrentstateoftheart onuniformrandomnumbergenerationforstochasticsimulation. Itrecallsthebasicideas,discusses somelinearmethodsandtheirtheoreticalanalysis, andprovidespointerstofurtherdetailsandtorecommendedimplementations. 1 WHATISAGOODRNG? Withoutagoodrandomnumbergenerato ..."
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Cited by 8 (0 self)
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Thispapersummarizesthecurrentstateoftheart onuniformrandomnumbergenerationforstochasticsimulation. Itrecallsthebasicideas,discusses somelinearmethodsandtheirtheoreticalanalysis, andprovidespointerstofurtherdetailsandtorecommendedimplementations. 1 WHATISAGOODRNG? Withoutagoodrandomnumbergenerator(RNG), simulationresultsareoftenmeaningless.Andquestionablegeneratorsarestillallovertheplace, somany experimentsrestonshakyfoundations.Whythis problemwasnotsolvedlongago?Becauseitisnot soeasy.AsocalledRNGactuallyproducesatotally deterministicandperiodicsequenceofnumbers,once itsinitialstate(orseed)ischosen.Thisisintotal contradictionwiththeassumptionofasequenceofindependentandidenticallydistributed (i.i.d.)random variables,andthereisnocleanwaytocompletely reconcilethesetwooppositeaspects.Therefore,everythingwedointhiscontextisheuristic. Thisbeingsaid, theheuristicargumentsleadtocriteriathat needtheorytobeanalyzed.
Random Number Generators and Empirical Tests
"... We recall some requirements for "good" random number generators and argue that while the construction of generators and the choice of their parameters must be based on theory, a posteriori empirical testing is also important. We then give examples of tests failed by some popular generato ..."
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Cited by 5 (3 self)
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We recall some requirements for "good" random number generators and argue that while the construction of generators and the choice of their parameters must be based on theory, a posteriori empirical testing is also important. We then give examples of tests failed by some popular generators and examples of generators passing these tests.
What is a Random Sequence
 The Mathematical Association of America, Monthly
, 2002
"... there laws of randomness? These old and deep philosophical questions still stir controversy today. Some scholars have suggested that our difficulty in dealing with notions of randomness could be gauged by the comparatively late development of probability theory, which had a ..."
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Cited by 4 (1 self)
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there laws of randomness? These old and deep philosophical questions still stir controversy today. Some scholars have suggested that our difficulty in dealing with notions of randomness could be gauged by the comparatively late development of probability theory, which had a
The Algorithmic Theory of Randomness
, 2001
"... this paper we won't discuss this very important topic. We will focus instead on the admittedly less ambitious but more manageable question of whether it is possible at least to obtain a mathematically rigourous (and reasonable) denition of randomness. That is, in the hope of clarifying the conc ..."
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this paper we won't discuss this very important topic. We will focus instead on the admittedly less ambitious but more manageable question of whether it is possible at least to obtain a mathematically rigourous (and reasonable) denition of randomness. That is, in the hope of clarifying the concept of chance, one tries to examine a mathematical model or idealization, that might (or might not) capture some of the intuitive properties associated with randomness. In the process of rening our intuition and circunscribing our concepts, we might be able to arrive at some fundamental notions. With luck (no pun intended) , these might in turn bring some insight into the deeper problems mentioned before. At least it could help one to discard some of our previous intuitions or to decide for the need of yet another mathematical model.