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58
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 ..."
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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 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.
On the Periods of Generalized Fibonacci Recurrences
, 1992
"... We give a simple condition for a linear recurrence (mod 2 w ) of degree r to have the maximal possible period 2 w 1 (2 r 1). It follows that the period is maximal in the cases of interest for pseudorandom number generation, i.e. for 3term linear recurrences dened by trinomials which are prim ..."
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Cited by 35 (11 self)
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We give a simple condition for a linear recurrence (mod 2 w ) of degree r to have the maximal possible period 2 w 1 (2 r 1). It follows that the period is maximal in the cases of interest for pseudorandom number generation, i.e. for 3term linear recurrences dened by trinomials which are primitive (mod 2) and of degree r > 2. We consider the enumeration of certain exceptional polynomials which do not give maximal period, and list all such polynomials of degree less than 15. 1.
Improved Algorithms via Approximations of Probability Distributions
 Journal of Computer and System Sciences
, 1997
"... We present two techniques for approximating probability distributions. The first is a simple method for constructing the smallbias probability spaces introduced by Naor & Naor. We show how to efficiently combine this construction with the method of conditional probabilities to yield improved NC ..."
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Cited by 28 (4 self)
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We present two techniques for approximating probability distributions. The first is a simple method for constructing the smallbias probability spaces introduced by Naor & Naor. We show how to efficiently combine this construction with the method of conditional probabilities to yield improved NC algorithms for many problems such as set discrepancy, finding large cuts in graphs, finding large acyclic subgraphs etc. The second is a construction of small probability spaces approximating general independent distributions, which is of smaller size than the constructions of Even, Goldreich, Luby, Nisan & Velickovi'c. Such approximations are useful, e.g., for the derandomization of certain randomized algorithms. Keywords. Derandomization, parallel algorithms, discrepancy, graph coloring, small sample spaces, explicit constructions. 1 Introduction Derandomization, the development of general tools to derive efficient deterministic algorithms from their randomized counterparts, has blossomed ...
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 generator’s period length, before the generator starts to fail the test systematically.
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 21 (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...
Ultraefficient (embedded) SOC architectures based on probabilistic
 CMOS (PCMOS) technology,” in Proc. Design Automation and Test in Europe (DATE
, 2006
"... Major impediments to technology scaling in the nanometer regime include power (or energy) dissipation and “erroneous” behavior induced by process variations and noise susceptibility. In this paper, we demonstrate that CMOS devices whose behavior is rendered probabilistic by noise (yielding probabili ..."
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Cited by 19 (4 self)
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Major impediments to technology scaling in the nanometer regime include power (or energy) dissipation and “erroneous” behavior induced by process variations and noise susceptibility. In this paper, we demonstrate that CMOS devices whose behavior is rendered probabilistic by noise (yielding probabilistic CMOS or PCMOS) can be harnessed for ultra low energy and high performance computation. PCMOS devices are inherently probabilistic in that they are guaranteed to compute correctly with a probability 1/2 < p < 1 and thus, by design, they are expected to compute incorrectly with a probability (1 − p). In this paper, we show that PCMOS technology yields significant improvements, both in the energy consumed as well as in the performance, for probabilistic applications with broad utility. These benefits are derived using an applicationarchitecturetechnology (A 2 T) codesign methodology introduced here, yielding an entirely novel family of probabilistic systemonachip (PSOC) architectures. All of our application and architectural savings are quantified using the product of the energy and the performance denoted (energy × performance): the PCMOS based gains are as high as a substantial multiplicative factor of over 560 when compared to a competing energyefficient CMOS based realization. 1.
Random Number Generators with Period Divisible by a Mersenne Prime
 Proc. ICCSA 2003
, 2003
"... Pseudorandom numbers with long periods and good statistical properties are often required for applications in computational finance. We consider the requirements for good uniform random number generators, and describe a class of generators whose period is a Mersenne prime or a small multiple of ..."
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Cited by 16 (5 self)
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Pseudorandom numbers with long periods and good statistical properties are often required for applications in computational finance. We consider the requirements for good uniform random number generators, and describe a class of generators whose period is a Mersenne prime or a small multiple of a Mersenne prime. These generators are based on "almost primitive" trinomials, that is trinomials having a large primitive factor. They enable very fast vector/parallel implementations with excellent statistical properties.