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26
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 ..."
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Cited by 59 (8 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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Software specifications for uncertainty evaluation
, 2004
"... Software specifications for uncertainty evaluation ..."
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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 5 (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.
A pseudo random numbers generator based on chaotic iterations. application to watermarking
 In WISM 2010, Int. Conf. on Web Information Systems and Mining, volume 6318 of LNCS
, 2010
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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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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.