Pseudo-random trees in Monte Carlo

Frederickson, Paul O.; Hiromoto, Robert E.; Jordan, Thomas; Smith, Burton; Warnock, Tony

doi:10.1016/s0167-8191(84)90072-3

Cited by 44 publications

(20 citation statements)

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“…Thus the output is reproducible. Frederickson et al (1984) give conditions for avoiding overlapping sequences. Frederickson, Hiromoto, and Larson (1987) discuss an example of applying this form of pseudorandom trees, which they call Lehmer trees, to a photon transport problem.…”

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confidence: 99%

Random Number Generators on Vector Supercomputers and Other Advanced Architectures

Anderson¹

1990

SIAM Rev.

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mentioning

confidence: 99%

Random Number Generators on Vector Supercomputers and Other Advanced Architectures

Anderson¹

1990

SIAM Rev.

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“…LCGMIX is related to the "Lehmer tree" DPRNG scheme of [19]. LCGMIX uses a family of compression functions for pedigrees that generalize linear congruential generators (LCG's) [29,32].…”

Section: The Lcgmix Dprngmentioning

confidence: 99%

Deterministic parallel random-number generation for dynamic-multithreading platforms

Leiserson¹,

Schardl²,

Sukha³

2012

Proceedings of the 17th ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming

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Existing concurrency platforms for dynamic multithreading do not provide repeatable parallel random-number generators. This paper proposes that a mechanism called pedigrees be built into the runtime system to enable efficient deterministic parallel randomnumber generation. Experiments with the open-source MIT Cilk runtime system show that the overhead for maintaining pedigrees is negligible. Specifically, on a suite of 10 benchmarks, the relative overhead of Cilk with pedigrees to the original Cilk has a geometric mean of less than 1%.We persuaded Intel to modify its commercial C/C++ compiler, which provides the Cilk Plus concurrency platform, to include pedigrees, and we built a library implementation of a deterministic parallel random-number generator called DOTMIX that compresses the pedigree and then "RC6-mixes" the result. The statistical quality of DOTMIX is comparable to that of the popular Mersenne twister, but somewhat slower than a nondeterministic parallel version of this efficient and high-quality serial random-number generator. The cost of calling DOTMIX depends on the "spawn depth" of the invocation. For a naive Fibonacci calculation with n = 40 that calls DOTMIX in every node of the computation, this "price of determinism" is about a factor of 2.3 in running time over the nondeterministic Mersenne twister, but for more realistic applications with less intense use of random numbers -such as a maximalindependent-set algorithm, a practical samplesort program, and a Monte Carlo discrete-hedging application from QuantLib -the observed "price" was at most 21%, and sometimes much less. Moreover, even if overheads were several times greater, applications using DOTMIX should be amply fast for debugging purposes, which is a major reason for desiring repeatability.

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“…Separate tasks sample asynchronously from this sequence, and different calcula tions from the same input will agree only statistically. A systematic approach to achieving exact reproducibility between calculations is to use trees of pseudo-random numbers, called Lehmer trees [10]. Two linear congruentia!…”

Section: The Problem Of Reproducibilitymentioning

confidence: 99%

Vectorizing and macrotasking Monte Carlo neutral particle algorithms

Heifetz¹

1987

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Monte Carlo algorithms for computing neutral particle transport in plasmas have been vectorized and macrotasked. The techniques used are directly applicable to Monte Carlo calculations of neutron and photon transport, and Monte Carlo integration schemes in general. A highly vectorized code was achieved by calculating test flight trajectories in loops over arrays of flight data, isolating the conditional branches to as few a number of loops as possible. A number of solutionis are discussed to the problem of gaps appearing in the arrays due to completed flights, which impede vectorization. A simple and effective implementation of macrotasking is achieved by dividing the calculation of the test flight profile among several processors. A tree of random numbers is used to ensure reproducible results. The additional memory required for each task may preclude using a large number of tasks. In future machines, the limit of macrotasking may be possible, with each teat flight, and split test flight, being a separate task. DISCLAIMER T»>is report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Governir -it nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsi bility lor the accuracy, completeness, or usefulness of ar.y ioformatioti. apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Refer ence herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its eodoracmcat, recom mendation, or favoring by the United Slates Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect thoie or the Ui.ited States Government or any agency thereof- MASTER

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Pseudo-random trees in Monte Carlo

Cited by 44 publications

References 2 publications

Random Number Generators on Vector Supercomputers and Other Advanced Architectures

Random Number Generators on Vector Supercomputers and Other Advanced Architectures

Deterministic parallel random-number generation for dynamic-multithreading platforms

Vectorizing and macrotasking Monte Carlo neutral particle algorithms

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