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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.
A hardware Gaussian noise generator using the BoxMuller method and its error analysis
 IEEE Trans. on Computers
, 2006
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Parallel Pseudorandom Number Generation Using Additive LaggedFibonacci Recursions
, 1995
"... . We study the suitability of the additive laggedFibonacci pseudorandom number generator for parallel computation. This generator has a relatively short period with respect to the size of its seed. However, the short period is more than made up for with the huge number of fullperiod cycles it cont ..."
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Cited by 19 (4 self)
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. We study the suitability of the additive laggedFibonacci pseudorandom number generator for parallel computation. This generator has a relatively short period with respect to the size of its seed. However, the short period is more than made up for with the huge number of fullperiod cycles it contains. We call these different fullperiod cycles equivalence classes. We show how to enumerate the equivalence classes and how to compute seeds to select a given equivalence class. The use of these equivalence classes gives an explicit parallelization suitable for a fully reproducible asynchronous MIMD implementation. To explore such an implementation we introduce an exponential sum measure of quality for the additive laggedFibonacci generators used in serial or parallel. We then prove the first nontrivial results we are aware of on this measure of quality. 1. Introduction. In Knuth's well known exposition on pseudorandom number generation [5], several methods of generation are considered...
Combined Generators with Components from Different Families
 Mathematics and Computers in Simulation
, 2003
"... Most random number generators used in practice are based on linear recurrences, with linear output transformations. This gives long periods, fast implementations, and structures that are easy to analyze. But the points produced by these generators have very regular structures. Nonlinear generators c ..."
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Cited by 18 (5 self)
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Most random number generators used in practice are based on linear recurrences, with linear output transformations. This gives long periods, fast implementations, and structures that are easy to analyze. But the points produced by these generators have very regular structures. Nonlinear generators can have less regular structures, but they are generally slower and much harder to analyze when their period is long. In this paper, combined generators with one large linear component, and a second component of a different type (nonlinear or linear), are proposed and studied. The structure of vectors of successive and nonsuccessive output values produced by the combined generators is analyzed. Under mild conditions, these vector sets are proved to have at least as much uniformity than the corresponding sets for the linear component alone. In empirical statistical tests, these combined generators perform better than simple linear generator of comparable period lengths, because of their less regular structure. Efficient implementation methods are suggested.
Random Number Generators for Parallel Applications
 in Monte Carlo Methods in Chemical Physics
, 1998
"... this article is devoted, because these com1 putations require the highest quality of random numbers. The ability to do a multidimensional integral relies on properties of uniformity of ntuples of random numbers and/or the equivalent property that random numbers be uncorrelated. The quality aspect i ..."
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Cited by 18 (7 self)
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this article is devoted, because these com1 putations require the highest quality of random numbers. The ability to do a multidimensional integral relies on properties of uniformity of ntuples of random numbers and/or the equivalent property that random numbers be uncorrelated. The quality aspect in the other uses is normally less important simply because the models are usually not all that precisely specified. The largest uncertainties are typically due more to approximations arising in the formulation of the model than those caused by lack of randomness in the random number generator. In contrast, the first class of applications can require very precise solutions. Increasingly, computers are being used to solve very welldefined but hard mathematical problems. For example, as Dirac [1] observed in 1929, the physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are completely known and it is only necessary to find precise methods for solving the equations for complex systems. In the intervening years fast computers and new computational methods have come into existence. In quantum chemistry, physical properties must be calculated to "chemical accuracy" (say 0.001 Rydbergs) to be relevant to physical properties. This often requires a relative accuracy of 10
Random Number Generators: Selection Criteria and Testing
, 1998
"... this paper, we shall assume that the sequence is purely periodic, in the sense that the initial state s 0 is always revisited. In other words, the sequence has no transient part. The goal is to make it hard to distinguish between the output of the generator and a typical realization of an i.i.d. uni ..."
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Cited by 16 (8 self)
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this paper, we shall assume that the sequence is purely periodic, in the sense that the initial state s 0 is always revisited. In other words, the sequence has no transient part. The goal is to make it hard to distinguish between the output of the generator and a typical realization of an i.i.d. uniform sequence over U . In
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...
FPGA implementation of neighborhoodoffour cellular automata random number generators
 Proc. FPGA 2002
, 2002
"... random number generator, cellular automata, FPGA Random number generators (RNGs) based upon neighborhoodoffour cellular automata (CA) with asymmetrical, nonlocal connections are explored. A number of RNGs that pass Marsaglia's rigorous DIEHARD suite of random number tests have been discovered ..."
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Cited by 13 (0 self)
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random number generator, cellular automata, FPGA Random number generators (RNGs) based upon neighborhoodoffour cellular automata (CA) with asymmetrical, nonlocal connections are explored. A number of RNGs that pass Marsaglia's rigorous DIEHARD suite of random number tests have been discovered. A neighborhood size of four allows a single CA cell to be implemented with a fourinput lookup table and a onebit register which are common building blocks in popular field programmable gate arrays (FPGAs). The investigated networks all had periodic (wrap around) boundary conditions with either 1d, 2d, or 3d interconnection topologies. Trial designs of 64bit networks using a Xilinx XCV 10006 FPGA predict a maximum clock rate of 214 MHz to 230 MHz depending upon interconnection topology.