Gaussian random number generators

Thomas, David B.; Luk, Wayne; Leong, Philip H. W.; Villasenor, John

doi:10.1145/1287620.1287622

Cited by 177 publications

(106 citation statements)

References 37 publications

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“…In digital domain, Gaussian samples are mostly generated by applying transformation methods on uniform random variables [3]. The rejection-acceptance methods include Ziggurat algorithm [6] and Polar method [7].…”

Section: Related Prior Workmentioning

confidence: 99%

“…Wallace algorithm is the class of recursion methods [3], that employs the linear transformations to previously generated Gaussian samples to produce new outputs. Due to inherent feedback nature, Wallace method suffers from correlations between successive samples [9].…”

Section: Related Prior Workmentioning

confidence: 99%

“…A variety of algorithms can be used to generate GRNs with a varying degree of computational complexity and accuracy [3]. A popular method is to convert uniformly distributed random numbers to Gaussian by some transformation like Box Muller and Monty Python [3].…”

Section: Introductionmentioning

confidence: 99%

“…A popular method is to convert uniformly distributed random numbers to Gaussian by some transformation like Box Muller and Monty Python [3]. These algorithms have been implemented both in software [3] and hardware [1].…”

Section: Introductionmentioning

confidence: 99%

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Generating high tail accuracy Gaussian Random Numbers in hardware using central limit theorem

Malik

Hemani

et al. 2011

2011 IEEE/IFIP 19th International Conference on VLSI and System-on-Chip

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Abstract-An efficient hardware implementation of Gaussian Random Number (GRN) generator based on Central Limit Theorem (CLT) is presented. CLT, although very simple to implement, is never used to generate high quality Gaussian numbers. This is due to the fact that direct implementation of CLT provides very poor accuracy in tail regions of the probability density function. In this work, we have shown that it is possible to achieve high tail accuracy by empirically computing the error in CLT, which can be compensated with a simple correction algorithm. The error has been modeled as first degree piece-wise polynomial approximation, using a novel non-uniform segmentation algorithm to compute the coefficients of polynomial segments. A novel hardware architecture of GRN generator is presented which requires only 420 slices and 1 DSP block of Xilinx Virtex-4 XC4VLX15 operating at 220 MHz. This resource utilization is better than any of the previously reported designs. Demonstrated for the tail accuracy of 6σ, the GRN generator design is scalable to achieve even higher accuracy with minimal increase in hardware resources. The accuracy of GRN generator is validated using statistical goodness of fit tests.

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Section: Related Prior Workmentioning

confidence: 99%

Section: Related Prior Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Generating high tail accuracy Gaussian Random Numbers in hardware using central limit theorem

Malik

Hemani

et al. 2011

2011 IEEE/IFIP 19th International Conference on VLSI and System-on-Chip

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show abstract

“…It is important to note that sampling from D σ is different to sampling from 1 In particular at https://www.cdc.informatik.tu-darmstadt.de/ ∼ pschmidt/ implementations/ziggurat/ziggurat-src.zip. a (continuous) normal distribution [TLLV07]. Another related problem is that of sampling from a Gaussian distribution over a generic lattice, a more complex problem, whose solutions often require sampling from D σ as a subroutine [GPV08,Pei10,DN12,AGHS12].…”

Section: Introductionmentioning

confidence: 99%

Discrete Ziggurat: A Time-Memory Trade-Off for Sampling from a Gaussian Distribution over the Integers

Buchmann

Cabarcas

Göpfert

et al. 2014

Selected Areas in Cryptography -- SAC 2013

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Abstract. Several lattice-based cryptosystems require to sample from a discrete Gaussian distribution over the integers. Existing methods to sample from such a distribution either need large amounts of memory or they are very slow. In this paper we explore a different method that allows for a flexible time-memory trade-off, offering developers freedom in choosing how much space they can spare to store precomputed values. We prove that the generated distribution is close enough to a discrete Gaussian to be used in lattice-based cryptography. Moreover, we report on an implementation of the method and compare its performance to existing methods from the literature. We show that for large standard deviations, the Ziggurat algorithm outperforms all existing methods.

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On the forward‐backward‐in‐time approach for Monte Carlo solution of Parker's transport equation: One‐dimensional case

et al. 2016

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The cosmic rays propagation inside the heliosphere is well described by a transport equation introduced by Parker in 1965. To solve this equation, several approaches were followed in the past. Recently, a Monte Carlo approach became widely used in force of its advantages with respect to other numerical methods. In this approach the transport equation is associated to a fully equivalent set of stochastic differential equations (SDE). This set is used to describe the stochastic path of quasi‐particle from a source, e.g., the interstellar space, to a specific target, e.g., a detector at Earth. We present a comparison of forward‐in‐time and backward‐in‐time methods to solve the cosmic rays transport equation in the heliosphere. The Parker equation and the related set of SDE in the several formulations are treated in this paper. For the sake of clarity, this work is focused on the one‐dimensional solutions. Results were compared with an alternative numerical solution, namely, Crank‐Nicolson method, specifically developed for the case under study. The methods presented are fully consistent each others for energy greater than 400 MeV. The comparison between stochastic integrations and Crank‐Nicolson allows us to estimate the systematic uncertainties of Monte Carlo methods. The forward‐in‐time stochastic integrations method showed a systematic uncertainty <5%, while backward‐in‐time stochastic integrations method showed a systematic uncertainty <1% in the studied energy range.

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Gaussian random number generators

Cited by 177 publications

References 37 publications

Generating high tail accuracy Gaussian Random Numbers in hardware using central limit theorem

Generating high tail accuracy Gaussian Random Numbers in hardware using central limit theorem

Discrete Ziggurat: A Time-Memory Trade-Off for Sampling from a Gaussian Distribution over the Integers

On the forward‐backward‐in‐time approach for Monte Carlo solution of Parker's transport equation: One‐dimensional case

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