A Fast Jump Ahead Algorithm for Linear Recurrences in a Polynomial Space

Haramoto, Hiroshi; Matsumoto, Makoto; L’Ecuyer, Pierre

doi:10.1007/978-3-540-85912-3_26

Cited by 11 publications

(6 citation statements)

References 9 publications

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“…Combining over-estimation and polylog jumps mitigates largely the overheads. This is similar to what is done, for instance, by SFMT [4] and RNGStreams [14].…”

Section: Discussionsupporting

confidence: 80%

“…Moreover, R can itself use counter-based generators (e.g., AES). The "re-seed through jump" strategy is also discussed by Haramoto et al [4], which argued in favor of parallel programs to build a fast jump-ahead algorithm over Mersenne Twister, what resulted in the implementation of SIMD-oriented Fast Mersenne Twister (SFMT). This is also the case of L'Ecuyer's RNGStreams library (on the top of its MRG32k3a generator [5]).…”

Section: Introductionmentioning

confidence: 99%

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Generic Deterministic Random Number Generation in Dynamic-Multithreaded Platforms

Mor

Roch

Maillard

2014

Lecture Notes in Computer Science

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International audienceOn dynamic multithreaded platforms with on-line scheduling such as work-stealing, randomized computations raise the issue of repro-ducibility. Compliant with de facto standard sequential Deterministic Random Number Generators (DRNGs) noted R, we propose a parallel DRNG implementation for finite computations that provides determinis-tic parallel execution. It uses the stateless sub-stream approach, enabling the use of efficient DRNG such as Mersenne Twister or Linear Congru-ential. We demonstrate that if R provides fast jump ahead in the random sequence, the re-seeding overhead is small, polylog in expectation, inde-pendently from the parallel computation's depth. Experiments bench-mark the performance of randomized algorithms employing our solution against the stateful DRNG DotMix, tailored to the Cilk Plus dynamic multithreading runtime. The overhead of our implementation ParDRNG compares favorably to the linear overhead of DotMix re-seedings

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“…Combining over-estimation and polylog jumps mitigates largely the overheads. This is similar to what is done, for instance, by SFMT [4] and RNGStreams [14].…”

Section: Discussionsupporting

confidence: 80%

Section: Introductionmentioning

confidence: 99%

Generic Deterministic Random Number Generation in Dynamic-Multithreaded Platforms

Mor

Roch

Maillard

2014

Lecture Notes in Computer Science

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“…The R 2 T 2 is written in Fortran and parallelized using the Message Parsing Interface (MPI). Pseudo-random numbers are generated with the Fast Mersenne Twister [28] and independent streams of random numbers for each MPI process are obtained by jumping ahead [29].…”

Section: Methodsmentioning

confidence: 99%

Radiative transfer with reciprocal transactions: Numerical method and its implementation

et al. 2019

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We present a numerical method for solving electromagnetic scattering by dense discrete random media entitled radiative transfer with reciprocal transactions (R2T2). The R2T2 is a combination of the Monte Carlo radiative-transfer, coherent-backscattering, and superposition T-matrix methods. The applicability of the radiative transfer is extended to dense random media by incorporating incoherent volume elements containing multiple particles. We analyze the R2T2 by comparing the results with the asymptotically exact superposition T-matrix method, and show that the R2T2 removes the caveats of radiative-transfer methods by comparing it to the RT-CB. We study various implementation choices that result in an accurate and efficient numerical algorithm. In particular, we focus on the properties of the incoherent volume elements and their effects on the final solution.

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“…They have a period of 2 19937 -1, a seed status made of 624 integers and an extra integer that stores the position in this array of integers. For each MT generator, we generated 1,000 seed statuses, spaced out with 2 50 PRNs, making use of the jump-ahead algorithm proposed by [21], slightly changed to allow bigger jumps in a limited computing time (around one second) using exponentiation with squaring method. This allows supplying substreams with approximately 1,000 billion PRNs, which is far more than what our simulation requires 7 .…”

Section: ) Distributed Computing For Tomusimmentioning

confidence: 99%

Proper parallel Monte Carlo for computed tomography of volcanoes

Schweitzer

Mazel

Fehr

et al. 2013

2013 International Conference on High Performance Computing &Amp; Simulation (HPCS)

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Most Monte Carlo simulations can be parallelized, or at least easily distributed. However, the parallelization of such programs is not mainstream. In this paper, we propose good practices to distribute a Monte Carlo simulation for computed tomography. We apply this to large edifices (such as volcanoes or pyramids) and give a particular focus on performances. The work included first the optimization of an existing sequential prototype and second the use of reliable parallel random streams. The optimized parallel version runs on a Symmetric Multi-Processor (SMP) and shows a fine and scalable speedup. The cumulated optimizations (sequential and parallel) enabled a speedup of 400X on a 32 cores SMP.

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A Fast Jump Ahead Algorithm for Linear Recurrences in a Polynomial Space

Cited by 11 publications

References 9 publications

Generic Deterministic Random Number Generation in Dynamic-Multithreaded Platforms

Generic Deterministic Random Number Generation in Dynamic-Multithreaded Platforms

Radiative transfer with reciprocal transactions: Numerical method and its implementation

Proper parallel Monte Carlo for computed tomography of volcanoes

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