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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 19 (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 generator’s period length, before the generator starts to fail the test systematically.
Fast and reliable random number generators for scientific computing, Lecture
 Proc. PARA'04 Workshop on the StateoftheArt inScientific Computing
"... Abstract. Fast and reliable pseudorandom number generators are required for simulation and other applications in Scientific Computing. We outline the requirements for good uniform random number generators, and describe a class of generators having very fast vector/parallel implementations with exce ..."
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Cited by 6 (2 self)
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Abstract. Fast and reliable pseudorandom number generators are required for simulation and other applications in Scientific Computing. We outline the requirements for good uniform random number generators, and describe a class of generators having very fast vector/parallel implementations with excellent statistical properties. We also discuss the problem of initialising random number generators, and consider how to combine two or more generators to give a better (though usually slower) generator. 1
A Nonempirical Test on the Weight of Pseudorandom Number Generators” 381–395 in: Monte Carlo and QuasiMonte Carlo methods 2000, SpringerVerlag 2002
"... Abstract. We introduce a theoretical test, named weight discrepancy test, on pseudorandom number generators. This test measures the χ 2discrepancy between the distribution of the number of ones in some specified bits in the generated sequence and the binomial distribution, under the assumption that ..."
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Cited by 5 (2 self)
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Abstract. We introduce a theoretical test, named weight discrepancy test, on pseudorandom number generators. This test measures the χ 2discrepancy between the distribution of the number of ones in some specified bits in the generated sequence and the binomial distribution, under the assumption that the initial value is randomly selected. This test can be performed for most generators based on a linear recursion over the twoelement field �2, and predicts with high precision for which sample size the generator will be rejected by a classical statistical test called the weight distribution test. This test may be considered as a theoretical version of a onedimensional random walk test. Differently from the empirical tests which can reject only very bad generators, this test assigns a ranking to generators. Thus it is useful to select good generators, similarly to the spectral tests and the kdistribution tests. This test rejects practically all generators linear over �2 that are known to fail in some physical tests although they pass kdistribution tests.
Ninth and Tenth Order Virial Coefficients for Hard Spheres
 in D Dimensions – Collection of
"... We evaluate the virial coefficients Bk for k ≤ 10 for hard spheres in dimensions D = 2, · · ·,8. Virial coefficients with k even are found to be negative when D ≥ 5. This provides strong evidence that the leading singularity for the virial series lies away from the positive real axis when D ≥ 5. ..."
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Cited by 4 (0 self)
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We evaluate the virial coefficients Bk for k ≤ 10 for hard spheres in dimensions D = 2, · · ·,8. Virial coefficients with k even are found to be negative when D ≥ 5. This provides strong evidence that the leading singularity for the virial series lies away from the positive real axis when D ≥ 5. Further analysis provides evidence that negative virial coefficients will be seen for some k> 10 for D = 4, and there is a distinct possibility that negative virial coefficients will also eventually occur for D = 3.
Quantum Simulations of Complex ManyBody Systems: From Theory to Algorithms, Lecture Notes,
"... Permission to make digital or hard copies of portions of this work for personal or classroom use is granted provided that the copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise requires pri ..."
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Cited by 3 (1 self)
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Permission to make digital or hard copies of portions of this work for personal or classroom use is granted provided that the copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise requires prior specific permission by the publisher mentioned above.
Pseudo random coins show more heads than tails
 J. Stat. Phys
"... Tossing a coin is the most elementary MonteCarlo experiment. In a computer the coin is replaced by a pseudo random number generator. It can be shown analytically and by exact enumerations that popular random number generators are not capable of imitating a fair coin: pseudo random coins show more ‘ ..."
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Cited by 2 (1 self)
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Tossing a coin is the most elementary MonteCarlo experiment. In a computer the coin is replaced by a pseudo random number generator. It can be shown analytically and by exact enumerations that popular random number generators are not capable of imitating a fair coin: pseudo random coins show more ‘‘heads’ ’ than ‘‘tails.’ ’ This bias explains the empirically observed failure of some random number generators in random walk experiments. It can be traced down to the special role of the value zero in the algebra of finite fields. KEY WORDS: Random number generator; MonteCarlo simulation; random walk; shift register sequences. 1. MANUFACTURING RANDOMNESS ‘‘After 40 years of development, one might think that the making of random numbers would be a mature and troublefree technology, but it seems the creation of unpredictability is ever unpredictable.’ ’ These words, written ten years ago by Brian Hayes, (9) allude to the ‘‘Ferrenberg affair:’’ In 1992, Ferrenberg, Landau, and Wong (4) had shown that a well established family of pseudo random number generators produces wrong results in MonteCarlo simulations based on the Wolff algorithm. Since then, deficiencies in pseudo random number generators have been detected in various other simulations, like simulations with the Swendsen–Wang algorithm, (1) 3d self avoiding random walks, (7) the Metropolis algorithm on the Blume–Capel model (17) and 2d random walks. (18, 19) Certainly this list is incomplete (see the references in ref. 19), but the message is clear: Hayes’
22 TestU01: A C Library for Empirical Testing of Random Number Generators
"... 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
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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 widely used 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 article 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.
Weighted Integration over IR d
, 2002
"... Abstract We present and analyze a new randomized algorithm for numerical computation of weighted integrals over the unbounded domain IR d. The algorithm and its desirable theoretical properties are derived based on certain stochastic assumptions about the integrands. It is easy to implement, enjoys ..."
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Abstract We present and analyze a new randomized algorithm for numerical computation of weighted integrals over the unbounded domain IR d. The algorithm and its desirable theoretical properties are derived based on certain stochastic assumptions about the integrands. It is easy to implement, enjoys O(n \Gamma 1=2 convergence rate, and uses only standard random number generators. Numerical results are also included.
IMPLIED WARRANTY, RELATING TO SALE AND/OR USE OF INTEL PRODUCTS INCLUDING LIABILITY OR WARRANTIES RELATING TO FITNESS FOR A PARTICULAR PURPOSE, MERCHANTABILITY, OR INFRINGEMENT
, 2003
"... This document as well as the software described in it is furnished under license and may only be used or copied in accordance with the terms of the license. The information in these Notes is furnished for informational use only, is subject to change without notice, and should not be construed as a c ..."
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This document as well as the software described in it is furnished under license and may only be used or copied in accordance with the terms of the license. The information in these Notes is furnished for informational use only, is subject to change without notice, and should not be construed as a commitment by Intel Corporation. Intel Corporation assumes no responsibility or liability for any errors or inaccuracies that may appear in this document or any software that may be provided in association with this document.