Random Number Generation

L’Ecuyer, Pierre

doi:10.1007/978-3-642-21551-3_3

Cited by 124 publications

(43 citation statements)

References 99 publications

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“…The resulting binary generator was used on the National Bureau of Standards Western Automatic Computer (SWAC). Interestingly, this combination principle to obtain long-period RNGs from shorter-period components has been rediscovered and reused in the RNG literature and is still used in some of the best RNGs currently available; see Wichmann and Hill (1982) and L'Ecuyer (1986, 1999a, 1999c, 2012, for example,…”

Section: Algorithmic Generatorsmentioning

confidence: 99%

“…They also found an asymptotically random Tausworthe generator with period 2 607 − 1, based on the recurrence x i = (x i−607 + x i−273 ) mod 2, s = 512, and w = 23. Asymptotically random is also called maximally equidistributed (ME) in many articles and books; e.g., Tezuka (1995), L'Ecuyer (1996b), L'Ecuyer (2012, and is seen as a highly-desirable property. Lewis and Payne (1973) proposed a fast way to run a generalized version of a Tausworthe generator with two nonzero coefficients a k = a r = 1, by using a large circular array of bits of size w × k for the state, and called it a generalized feedback shift register (GFSR).…”

Section: Linear Recurrences Modulo a Large Primementioning

confidence: 99%

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History of uniform random number generation

L’Ecuyer¹

2017

2017 Winter Simulation Conference (WSC)

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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.

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Section: Algorithmic Generatorsmentioning

confidence: 99%

Section: Linear Recurrences Modulo a Large Primementioning

confidence: 99%

History of uniform random number generation

L’Ecuyer¹

2017

2017 Winter Simulation Conference (WSC)

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“…A high-quality PRNG is commonly defined as a generator that passes a number of numerical tests and is found suitable for intended uses (L'Ecuyer, 1988;Press and others, 1992;Hellekalek, 1998;L'Ecuyer, 1998. Statistical theory dictates that random numbers are independent and identically distributed, but PRNGs have several characteristics that are at odds with statistical theory.…”

Section: Generating Random Numbers From a Uniform Distributionmentioning

confidence: 99%

Hydrologic Drought Decision Support System (HyDroDSS)

Granato¹

2014

Open-File Report

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For more information on the USGS-the Federal source for science about the Earth, its natural and living resources, natural hazards, and the environment, visit http://www.usgs.gov or call 1-888-ASK-USGS.For an overview of USGS information products, including maps, imagery, and publications, visit http://www.usgs.gov/pubprodTo order this and other USGS information products, visit http://store.usgs.gov Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the U.S. Government.Although this information product, for the most part, is in the public domain, it also may contain copyrighted materials as noted in the text. Permission to reproduce copyrighted items must be secured from the copyright owner.Suggested citation: Granato, G.E., 2014, Hydrologic Drought Decision Support System (HyDroDSS): U.S. Geological Survey Open-File Report 2014-1003. ISSN 2331ISSN -1258 iii AcknowledgmentsThe author thanks Carl Carlson, David Bjerklie, Mary Ashman, and Kevin Breen of the U.S. Geological Survey (USGS) and Kathleen Crawley of the Rhode Island Water Resources Board for providing thoughtful and thorough technical and editorial reviews of this report, the HyDroDSS program, and accompanying digital media. Richard Vogel of Tufts University identified the position analysis approaches developed by Hirsch (1981b) as a potential method for drought-projection analyses and provided information on use of the probability-plot correlation coefficient method for evaluating the distribution of the random numbers generated by the HyDroDSS. Robert Hirsch of the USGS provided information on the application of position analysis, and Gary Tasker of the USGS provided background information on the use of bootstrap methods in the application of position analysis (Tasker and Dunne, 1997). Altitude, as used in this report, refers to distance above the vertical datum.Withdrawal rates from some production wells are reported in million gallons per month (Mgal/mo) and in million gallons per year (Mgal/yr). Hydrologic Drought Decision Support System (HyDroDSS)By Gregory E. Granato AbstractThe hydrologic drought decision support system (HyDroDSS) was developed by the U.S. Geological Survey (USGS) in cooperation with the Rhode Island Water Resources Board (RIWRB) for use in the analysis of hydrologic variables that may indicate the risk for streamflows to be below userdefined flow targets at a designated site of interest, which is defined herein as data-collection site on a stream that may be adversely affected by pumping. Hydrologic drought is defined for this study as a period of lower than normal streamflows caused by precipitation deficits and (or) water withdrawals. The HyDroDSS is designed to provide water managers with risk-based information for balancing water-supply needs and aquatic-habitat protection goals to mitigate potential effects of hydrologic drought.This report describes the theory and methods for retrospective streamflow-depletion analysis, rank correlation analysis, and drough...

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“…Most common methods for non-uniform RN generation are based on a first stage in which U[0, 1] samples are generated [6]. Let u i be a sample of the U[0, 1] distribution, X the target distribution and ICDF its Inverse Cumulative Distribution Function.…”

Section: Monte-carlo Simulationsmentioning

confidence: 99%

“…For each simulation path, stock prices are updated by using Equation (6) and accumulated in order to compute the mean value until the maturity time T . The payoff is evaluated as the profit involved in the transaction.…”

Section: Option Price Calculationmentioning

confidence: 99%

FPGA acceleration using high-level languages of a Monte-Carlo method for pricing complex options

Sanchez-Roman

Moreno

López-Buedo

et al. 2013

Journal of Systems Architecture

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Esta es la versión de autor de la comunicación de congreso publicada en: This is an author produced version of a paper published in: AbstractIn this paper we present an FPGA implementation of a Monte-Carlo method for pricing Asian Options using Impulse C and floating-point arithmetic. In an Altera Stratix-V FPGA, a 149x speedup factor was obtained against an OpenMP-based solution in a 4-core Intel Core i7 processor. This speedup is comparable to that reported in the literature using a classic HDL-based methodology, but the development time is significantly reduced. Additionally, the use of a HLL-based methodology allowed us to implement a highquality gaussian random number generator, which produces more precise results than those obtained with the simple generators usually present in HDL-based designs.

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Random Number Generation

Cited by 124 publications

References 99 publications

History of uniform random number generation

History of uniform random number generation

Hydrologic Drought Decision Support System (HyDroDSS)

FPGA acceleration using high-level languages of a Monte-Carlo method for pricing complex options

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