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Maximally Equidistributed Combined Tausworthe Generators
, 1996
"... Tausworthe random number generators based on a primitive trinomial allow an easy and fast implementation when their parameters obey certain restrictions. However, such generators, with those restrictions, have bad statistical properties unless we combine them. A generator is called maximally equidis ..."
Abstract

Cited by 92 (24 self)
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Tausworthe random number generators based on a primitive trinomial allow an easy and fast implementation when their parameters obey certain restrictions. However, such generators, with those restrictions, have bad statistical properties unless we combine them. A generator is called maximally equidistributed if its vectors of successive values have the best possible equidistribution in all dimensions. This paper shows how to find maximally equidistributed combinations in an efficient manner, and gives a list of generators with that property. Such generators have a strong theoretical support and lend themselves to very fast software implementations.
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
Randomized Polynomial Lattice Rules For Multivariate Integration And Simulation
 SIAM JOURNAL ON SCIENTIFIC COMPUTING
, 2001
"... Lattice rules are among the best methods to estimate integrals in a large number of dimensions. They are part of the quasiMonte Carlo set of tools. A new class of lattice rules, defined in a space of polynomials with coefficients in a finite field, is introduced in this paper, and a theoretical fra ..."
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Cited by 13 (3 self)
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Lattice rules are among the best methods to estimate integrals in a large number of dimensions. They are part of the quasiMonte Carlo set of tools. A new class of lattice rules, defined in a space of polynomials with coefficients in a finite field, is introduced in this paper, and a theoretical framework for these polynomial lattice rules is developed. A randomized version is studied, implementations and criteria for selecting the parameters are discussed, and examples of its use as a variance reduction tool in stochastic simulation are provided. Certain types of digital net constructions, as well as point sets constructed by taking all vectors of successive output values produced by a Tausworthe random number generator, turn out to be special cases of this method.
Tables of MaximallyEquidistributed Combined Lfsr Generators
, 1998
"... We give the results of a computer search for maximallyequidistributed combined linear feedback shift register (or Tausworthe) random number generators, whose components are trinomials of degrees slightly less than 32 or 64. These generators are fast and have good statistical properties. ..."
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Cited by 10 (0 self)
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We give the results of a computer search for maximallyequidistributed combined linear feedback shift register (or Tausworthe) random number generators, whose components are trinomials of degrees slightly less than 32 or 64. These generators are fast and have good statistical properties.
Recent Advances in Uniform Random Number Generation
"... This paper discusses certain classes of uniform random number generators which have been studied and better understood in the recent few years. Most of the attention is devoted to combined generators. We also mention others and point out some pitfalls. Combination is a good way to obtain fast and re ..."
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Cited by 1 (0 self)
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This paper discusses certain classes of uniform random number generators which have been studied and better understood in the recent few years. Most of the attention is devoted to combined generators. We also mention others and point out some pitfalls. Combination is a good way to obtain fast and reliable generators, but the structural properties of the combined generator should be carefully examined before it could be recommended. Nonlinear generators offer some promise, but still require deeper investigation before specific instances can be safely recommended. 1. INTRODUCTION Random numbers are the nuts and bolts of all stochastic simulations. Simple linear congruential generators (LCGs) (Bratley, Fox, and Schrage 1987; Knuth 1981) are still in widespread use for generating uniform random numbers, mainly because of their simplicity and ease of implementation. However, LCGs have several wellknown defects and no longer satisfy the requirements of today's computerintensive simulations...
Statement Of Contribution
, 1995
"... This paper studies the combination of generators of the latter class. It shows that such combination offers a good way of obtaining a fast and reliable generator, and improves significantly upon the combination of simple LCGs. We also provide a specific generator with its computer implementation ..."
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This paper studies the combination of generators of the latter class. It shows that such combination offers a good way of obtaining a fast and reliable generator, and improves significantly upon the combination of simple LCGs. We also provide a specific generator with its computer implementation
Resource Utilization
"... Abstract Computers ’ required random numbers initially, for simulations and numerical computations like Monte Carlo calculations. Random number generators offer an important contribution to many communication systems for security. They are critical components in computational science. However the t ..."
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Abstract Computers ’ required random numbers initially, for simulations and numerical computations like Monte Carlo calculations. Random number generators offer an important contribution to many communication systems for security. They are critical components in computational science. However the tradeoff between quality and computational performance is an issue for many numerical simulations. FPGA optimized RNGs are efficient in terms of resources than other types of softwarebased RNGs which means that they can take advantage of bitwise operations and FPGA based specific features. One of the types of FPGA based RNG called a LUTSR RNG is illustrated using an algorithm. Shift registers are used to improve mixing rate between numbers. Results will be misleading when correlations exist between the random numbers and hence permutations are used. The LUTs are configured into shift registers. The algorithm is simplified based on the architecture such that it ensures longer periods. A generator with a period of can be implemented and provides r random output bits. This provides a good quality balance compared to previous generators. The critical path between all registers is a single LUT. The program is run in ModelSim 6.4a and implementation is done using Xilinx
FAST RANDOM NUMBER GENERATORS BASED ON LINEAR RECURRENCES MODULO 2: OVERVIEW AND COMPARISON
"... Random number generators based on linear recurrences modulo 2 are among the fastest longperiod generators currently available. The uniformity and independence of the points they produce, over their entire period length, can be measured by theoretical figures of merit that are easy to compute, and t ..."
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Random number generators based on linear recurrences modulo 2 are among the fastest longperiod generators currently available. The uniformity and independence of the points they produce, over their entire period length, can be measured by theoretical figures of merit that are easy to compute, and those having good values for these figures of merit are statistically reliable in general. Some of these generators can also provide disjoint streams and substreams efficiently. In this paper, we review the most interesting construction methods for these generators, examine their theoretical and empirical properties, and make comparisons. 1