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24
A Comparison of CPUs, GPUs, FPGAs, and Massively Parallel Processor Arrays for Random Number Generation
"... The future of highperformance computing is likely to rely on the ability to efficiently exploit huge amounts of parallelism. One way of taking advantage of this parallelism is to formulate problems as “embarrassingly parallel ” MonteCarlo simulations, which allow applications to achieve a linear s ..."
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The future of highperformance computing is likely to rely on the ability to efficiently exploit huge amounts of parallelism. One way of taking advantage of this parallelism is to formulate problems as “embarrassingly parallel ” MonteCarlo simulations, which allow applications to achieve a linear speedup over multiple computational nodes, without requiring a superlinear increase in internode communication. However, such applications are reliant on a cheap supply of high quality random numbers, particularly for the three main maximum entropy distributions: uniform, used as a general source of randomness; Gaussian, for discretetime simulations; and exponential, for discreteevent simulations. In this paper we look at four different types of platform: conventional multicore CPUs (Intel Core2); GPUs (NVidia
2010. “Random variate generation by numerical inversion when only the density is known
 ACM Transactions on Modeling and Computer Simulation
"... ePubWU, the institutional repository of the WU Vienna University of Economics and Business, is provided by the University Library and the ITServices. The aim is to enable open access to the scholarly output of the WU. ..."
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Cited by 10 (3 self)
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ePubWU, the institutional repository of the WU Vienna University of Economics and Business, is provided by the University Library and the ITServices. The aim is to enable open access to the scholarly output of the WU.
Discrete Ziggurat: A TimeMemory Tradeoff for Sampling from a Gaussian Distribution over the Integers
"... Several latticebased 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 timem ..."
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Several latticebased 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 timememory tradeoff, 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 latticebased 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.
A parallel spiking neural network simulator
 Proceedings of the IEEE International Conference on FieldProgrammable Technology 2009
, 2009
"... Abstract—An FPGAbased systolic architecture for the high speed simulation of spiking neural networks is presented. The design is an implementation of Izhikevich’s neuron model and employs optimizations for the typical case where neuron activity is low. Since execution time required is related to th ..."
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Abstract—An FPGAbased systolic architecture for the high speed simulation of spiking neural networks is presented. The design is an implementation of Izhikevich’s neuron model and employs optimizations for the typical case where neuron activity is low. Since execution time required is related to the activity level, performance of the design can be improved by an order of magnitude. I.
A New Hardware Efficient Inversion Based Random Number Generator for NonUniform Distributions
 in Reconfigurable Computing and FPGAs (ReConFig), 2010 International Conference on
, 2010
"... Abstract—For numerous computationally complex applications, like financial modelling and Monte Carlo simulations, the fast generation of high quality nonuniform random numbers (RNs) is essential. The implementation of such generators in FPGAbased accelerators has therefore become a very active re ..."
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Abstract—For numerous computationally complex applications, like financial modelling and Monte Carlo simulations, the fast generation of high quality nonuniform random numbers (RNs) is essential. The implementation of such generators in FPGAbased accelerators has therefore become a very active research field. In this paper we present a novel approach to create RNs for different distributions based on an efficient transformation of floatingpoint inputs. For the Gaussian distribution we can reduce the number of slices needed by up to 48 % compared to the stateoftheart while achieving a higher output precision in the tail region. Our architecture produces samples up to 8.37 휎 and achieves 381MHz. We also present a comprehensive testing methodology based on stochastic analysis and verification in practical applications.
Subspace iteration randomization and singular value problems. arXiv preprint arXiv:1408.2208
, 2014
"... Abstract. A classical problem in matrix computations is the efficient and reliable approximation of a given matrix by a matrix of lower rank. The truncated singular value decomposition (SVD) is known to provide the best such approximation for any given fixed rank. However, the SVD is also known to b ..."
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Abstract. A classical problem in matrix computations is the efficient and reliable approximation of a given matrix by a matrix of lower rank. The truncated singular value decomposition (SVD) is known to provide the best such approximation for any given fixed rank. However, the SVD is also known to be very costly to compute. Among the different approaches in the literature for computing lowrank approximations, randomized algorithms have attracted researchers ’ recent attention due to their surprising reliability and computational efficiency in different application areas. Typically, such algorithms are shown to compute with very high probability lowrank approximations that are within a constant factor from optimal, and are known to perform even better in many practical situations. In this paper, we present a novel error analysis that considers randomized algorithms within the subspace iteration framework and show with very high probability that highly accurate lowrank approximations as well as singular values can indeed be computed quickly for matrices with rapidly decaying singular values. Such matrices appear frequently in diverse application areas such as data analysis, fast structured matrix computations and fast direct methods for large sparse linear systems of equations and are the driving motivation for randomized methods. Furthermore, we show that the lowrank approximations computed by these randomized algorithms are actually rankrevealing approximations, and the special case of a rank1 approximation can also be used to correctly estimate matrix 2norms with very high probability. Our numerical experiments are in full support of our conclusions. key words: lowrank approximation, randomized algorithms, singular values, standard Gaussian matrix. 1. Introduction. Randomized
Constantinides, “Multivariate gaussian random number generator targeting specific resource utilization in an FPGA
 in ARC ’08: Proceedings of the 4th international workshop on Reconfigurable Computing
, 2008
"... Abstract. Financial applications are one of many fields where a multivariate Gaussian random number generator plays a key role in performing computationally extensive simulations. Recent technological advances and today’s requirements have led to the migration of the traditional software based multi ..."
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Abstract. Financial applications are one of many fields where a multivariate Gaussian random number generator plays a key role in performing computationally extensive simulations. Recent technological advances and today’s requirements have led to the migration of the traditional software based multivariate Gaussian random number generator to a hardware based model. Field Programmable Gate Arrays (FPGA) are normally used as a target device due to their fine grain parallelism and reconfigurability. As well as the ability to achieve designs with high throughput it is also desirable to produce designs with the flexibility to control the resource usage in order to meet given resource constraints. This paper proposes an algorithm for a multivariate Gaussian random number generator implementation in an FPGA given a set of resources to be utilized. Experiments demonstrate the proposed algorithm’s capability of producing a design that meets any given resource constraints.
Sampling exactly from the normal distribution. arXiv preprint arXiv:1303.6257
, 2013
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The new iris data: modular data generators
 In KDD
, 2010
"... In this paper we introduce a modular, highly flexible, opensource environment for data generation. Using an existing graphical data flow tool, the user can combine various types of modules for numeric and categorical data generators. Additional functionality is added via the data processing framewor ..."
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In this paper we introduce a modular, highly flexible, opensource environment for data generation. Using an existing graphical data flow tool, the user can combine various types of modules for numeric and categorical data generators. Additional functionality is added via the data processing framework in which the generator modules are embedded. The resulting data flows can be used to document, deploy, and reuse the resulting data generators. We describe the overall environment and individual modules and demonstrate how they can be used for the generation of a sample, complex customer/product database with corresponding shopping basket data, including various artifacts and outliers.