F2-Linear Random Number Generators

L’Ecuyer, Pierre; Panneton, François

doi:10.1007/b110059_9

Cited by 17 publications

(11 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…These F 2 -linear RNGs (linear in the finite field F 2 ) can be defined in the following general framework taken from L'Ecuyer and Panneton (2002Panneton ( , 2009):…”

Section: Linear Recurrences Modulo a Large Primementioning

confidence: 99%

See 1 more Smart Citation

History of uniform random number generation

L’Ecuyer¹

2017

2017 Winter Simulation Conference (WSC)

View full text Add to dashboard Cite

Random number generators were invented before there were symbols for writing numbers, and long before mechanical and electronic computers. All major civilizations through the ages found the urge to make random selections, for various reasons. Today, random number generators, particularly on computers, are an important (although often hidden) ingredient in human activity. In this article, we give a historical account on the design, implementation, and testing of uniform random number generators used for simulation.

show abstract

“…These F 2 -linear RNGs (linear in the finite field F 2 ) can be defined in the following general framework taken from L'Ecuyer and Panneton (2002Panneton ( , 2009):…”

Section: Linear Recurrences Modulo a Large Primementioning

confidence: 99%

“…See also Tezuka (1995). This method of combination actually applies to F 2 -linear generators in general, as explained in L'Ecuyer and Panneton (2009). L'Ecuyer and Panneton (2002) made concrete constructions of ME combined TGFSR generators with periods around 2 466 and 2 1250 .…”

Section: Linear Recurrences Modulo a Large Primementioning

confidence: 99%

History of uniform random number generation

L’Ecuyer¹

2017

2017 Winter Simulation Conference (WSC)

View full text Add to dashboard Cite

show abstract

“…Good RNGs are usually constructed based on a mathematical analysis of this uniformity, which is measured by a figure of merit that can be computed efficiently even when S is huge. These measures depend on the structure of the RNG; they include the spectral test and measures of equidistribution (Knuth 1998, L'Ecuyer and Panneton 2009, L'Ecuyer 2012. A larger Ψ s (larger S ) can potentially cover (0, 1) s more evenly, but a large S and large period are not sufficient for high quality.…”

Section: L'ecuyermentioning

confidence: 99%

“…The matrices A and B usually represent simple operations on blocks of bits such as AND, OR, exclusive-OR, shift, rotation, etc., that are fast to execute. They are also selected so that the sets Ψ s have good uniformity over some range of values of s. The uniformity is evaluated by verifying the equidistribution of the points over a collection of dyadic rectangular boxes (L 'Ecuyer 1996b, L'Ecuyer 1999b, L'Ecuyer and Panneton 2009). This is achieved efficiently (without generating the points) by exploiting the linear structure.…”

Section: Linear Recurrences Modulomentioning

confidence: 99%

Random number generation with multiple streams for sequential and parallel computing

L’Ecuyer¹

2015

2015 Winter Simulation Conference (WSC)

View full text Add to dashboard Cite

We provide a review of the state of the art on the design and implementation of random number generators (RNGs) for simulation, on both sequential and parallel computing environments. We focus on the need for multiple streams and substreams of random numbers, explain how they can be constructed and managed, review software libraries that offer them, and illustrate their usefulness via examples. We also review the basic quality criteria for good random number generators and their theoretical and empirical testing.

show abstract

“…We briefly recall the notion of F 2 -linear generators, in particular Mersenne Twister (MT) [17] generator, since MTGP is its variant. See [13] for a general theory on F 2 -linear generators.…”

Section: F 2 -Linear Generators and Mersenne Twistermentioning

confidence: 99%

Variants of Mersenne Twister Suitable for Graphic Processors

Saito

Matsumoto

2013

ACM Trans. Math. Softw.

View full text Add to dashboard Cite

This article proposes a type of pseudorandom number generator, Mersenne Twister for Graphic Processor (MTGP), for efficient generation on graphic processessing units (GPUs). MTGP supports large state sizes such as 11213 bits, and uses the high parallelism of GPUs in computing many steps of the recursion in parallel. The second proposal is a parameter-set generator for MTGP, named MTGP Dynamic Creator (MTG-PDC). MTGPDC creates up to 2 32 distinct parameter sets which generate sequences with high-dimensional uniformity. This facility is suitable for a large grid of GPUs where each GPU requires separate random number streams. MTGP is based on linear recursion over the two-element field, and has better high-dimensional equidistribution than the Mersenne Twister pseudorandom number generator. ACM Reference Format:Saito, M. and Matsumoto, M. 2013. Variants of Mersenne twister suitable for graphic processors.

show abstract

F2-Linear Random Number Generators

Cited by 17 publications

References 40 publications

History of uniform random number generation

History of uniform random number generation

Random number generation with multiple streams for sequential and parallel computing

Variants of Mersenne Twister Suitable for Graphic Processors

Contact Info

Product

Resources

About