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18
Improved longperiod generators based on linear recurrences modulo 2
 ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
, 2006
"... Fast uniform random number generators with extremely long periods have been defined and implemented based on linear recurrences modulo 2. The twisted GFSR and the Mersenne twister are famous recent examples. Besides the period length, the statistical quality of these generators is usually assessed v ..."
Abstract

Cited by 40 (6 self)
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Fast uniform random number generators with extremely long periods have been defined and implemented based on linear recurrences modulo 2. The twisted GFSR and the Mersenne twister are famous recent examples. Besides the period length, the statistical quality of these generators is usually assessed via their equidistribution properties. The hugeperiod generators proposed so far are not quite optimal in that respect. In this paper, we propose new generators of that form, with better equidistribution and “bitmixing ” properties for equivalent period length and speed. The state of our new generators evolves in a more chaotic way than for the Mersenne twister. We illustrate how this can reduce the impact of persistent dependencies among successive output values, which can be observed in certain parts of the period of gigantic generators such as the Mersenne twister.
Empirical Evidence concerning AES
 ACM TRANSACTIONS ON MODELING AND COMPUTER SIMULATION
, 2003
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An Improved Ziggurat Method to Generate Normal Random Samples
"... The ziggurat is an efficient method to generate normal random samples. It is shown that the standard Ziggurat fails a commonly used test. An improved version that passes the test is introduced. Flexibility is enhanced by using a plugin uniform random number generator. An efficient doubleprecision ..."
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Cited by 4 (0 self)
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The ziggurat is an efficient method to generate normal random samples. It is shown that the standard Ziggurat fails a commonly used test. An improved version that passes the test is introduced. Flexibility is enhanced by using a plugin uniform random number generator. An efficient doubleprecision version of the ziggurat algorithm is developed that has a very high period.
Software specifications for uncertainty evaluation
, 2004
"... Software specifications for uncertainty evaluation ..."
Monte carlo simulation with the gate software using grid computing
 In NOTERE ’08: Proc. of the 8th Int. Conf. on New Technologies in Distributed Systems
, 2008
"... Monte Carlo simulations needing many replicates to obtain good statistical results can be easily executed in parallel using the “Multiple Replications In Parallel ” approach. However, several precautions have to be taken in the generation of the parallel streams of pseudorandom numbers. In this pap ..."
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Cited by 1 (0 self)
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Monte Carlo simulations needing many replicates to obtain good statistical results can be easily executed in parallel using the “Multiple Replications In Parallel ” approach. However, several precautions have to be taken in the generation of the parallel streams of pseudorandom numbers. In this paper, we present the distribution of Monte Carlo simulations performed with the GATE software using local clusters and grid computing. We obtained very convincing results with this large medical application, thanks to the EGEE Grid (Enabling Grid for EsciencE), achieving in one week computations that could have taken more than 3 years of processing on a single computer. This work has been achieved thanks to a generic objectoriented toolbox called DistMe which we designed to automate this kind of parallelization for Monte Carlo simulations. This toolbox, written in Java is freely available on SourceForge and helped to ensure a rigorous distribution of pseudorandom number streams. It is based on the use of a documented XML format for random numbers generators statuses.
Abstract ResolutionStationary Random Number Generators
"... Besides speed and period length, the quality of uniform random number generators is usually assessed by measuring the uniformity of their point sets, formed by taking vectors of successive output values over their entire period length. For F2linear generators, the commonly adopted measures of unifo ..."
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Besides speed and period length, the quality of uniform random number generators is usually assessed by measuring the uniformity of their point sets, formed by taking vectors of successive output values over their entire period length. For F2linear generators, the commonly adopted measures of uniformity are based on the equidistribution of the most significant bits of the output. In this paper, we point out weaknesses of these measures and introduce generalizations that also give importance to the loworder (less significant) bits. These measures look at the equidistribution obtained when we permute the bits of each output value in a certain way. In a parameter search for good generators, a quality criterion based on these new measures of equidistribution helps avoiding generators that fail statistical tests targeting their loworder bits. We also introduce the notion of resolutionstationary generators, whose point sets are invariant under a multiplication by certain powers of 2, modulo 1. For such generators, less significant bits have the same equidistribution properties as the most significant ones. Tausworthe generators have this property. We finally show how an arbitrary F2linear generator can be made resolutionstationary by adding an appropriate linear transformation to the output. This provides new efficient ways of implementing highquality and longperiod Tausworthe generators. Key words: random number generation, linear recurrence modulo 2, uniformity,