60 research outputs found
A Comparative Study of Some Pseudorandom Number Generators
We present results of an extensive test program of a group of pseudorandom
number generators which are commonly used in the applications of physics, in
particular in Monte Carlo simulations. The generators include public domain
programs, manufacturer installed routines and a random number sequence produced
from physical noise. We start by traditional statistical tests, followed by
detailed bit level and visual tests. The computational speed of various
algorithms is also scrutinized. Our results allow direct comparisons between
the properties of different generators, as well as an assessment of the
efficiency of the various test methods. This information provides the best
available criterion to choose the best possible generator for a given problem.
However, in light of recent problems reported with some of these generators, we
also discuss the importance of developing more refined physical tests to find
possible correlations not revealed by the present test methods.Comment: University of Helsinki preprint HU-TFT-93-22 (minor changes in Tables
2 and 7, and in the text, correspondingly
Pseudo-Random Number Generators for Vector Processors and Multicore Processors
Large scale Monte Carlo applications need a good pseudo-random number generator capable of utilizing both the vector processing capabilities and multiprocessing capabilities of modern computers in order to get the maximum performance. The requirements for such a generator are discussed. New ways of avoiding overlapping subsequences by combining two generators are proposed. Some fundamental philosophical problems in proving independence of random streams are discussed. Remedies for hitherto ignored quantization errors are offered. An open source C++ implementation is provided for a generator that meets these needs
Periodic orbits of the ensemble of Sinai-Arnold cat maps and pseudorandom number generation
We propose methods for constructing high-quality pseudorandom number
generators (RNGs) based on an ensemble of hyperbolic automorphisms of the unit
two-dimensional torus (Sinai-Arnold map or cat map) while keeping a part of the
information hidden. The single cat map provides the random properties expected
from a good RNG and is hence an appropriate building block for an RNG, although
unnecessary correlations are always present in practice. We show that
introducing hidden variables and introducing rotation in the RNG output,
accompanied with the proper initialization, dramatically suppress these
correlations. We analyze the mechanisms of the single-cat-map correlations
analytically and show how to diminish them. We generalize the Percival-Vivaldi
theory in the case of the ensemble of maps, find the period of the proposed RNG
analytically, and also analyze its properties. We present efficient practical
realizations for the RNGs and check our predictions numerically. We also test
our RNGs using the known stringent batteries of statistical tests and find that
the statistical properties of our best generators are not worse than those of
other best modern generators.Comment: 18 pages, 3 figures, 9 table
Distribution of Random Streams for Simulation Practitioners
International audienceThere is an increasing interest in the distribution of parallel random number streamsin the high-performance computing community particularly, with the manycore shift. Even ifwe have at our disposal statistically sound random number generators according to the latestand thorough testing libraries, their parallelization can still be a delicate problem. Indeed, aset of recent publications shows it still has to be mastered by the scientific community. Withthe arrival of multi-core and manycore processor architectures on the scientist desktop, modelerswho are non-specialists in parallelizing stochastic simulations need help and advice in distributingrigorously their experimental plans and replications according to the state of the art in pseudo-random numbers parallelization techniques. In this paper, we discuss the different partitioningtechniques currently in use to provide independent streams with their corresponding software. Inaddition to the classical approaches in use to parallelize stochastic simulations on regular processors,this paper also presents recent advances in pseudo-random number generation for general-purposegraphical processing units. The state of the art given in this paper is written for simulationpractitioners
Pseudo-random number generators for Monte Carlo simulations on Graphics Processing Units
Basic uniform pseudo-random number generators are implemented on ATI Graphics
Processing Units (GPU). The performance results of the realized generators
(multiplicative linear congruential (GGL), XOR-shift (XOR128), RANECU, RANMAR,
RANLUX and Mersenne Twister (MT19937)) on CPU and GPU are discussed. The
obtained speed-up factor is hundreds of times in comparison with CPU. RANLUX
generator is found to be the most appropriate for using on GPU in Monte Carlo
simulations. The brief review of the pseudo-random number generators used in
modern software packages for Monte Carlo simulations in high-energy physics is
present.Comment: 31 pages, 9 figures, 3 table
Algorithms for randomness in the behavioral sciences: A tutorial
Simulations and experiments frequently demand the generation of random numbera that have
specific distributions. This article describes which distributions should be used for the most cammon
problems and gives algorithms to generate the numbers.It is also shown that a commonly used permutation algorithm (Nilsson, 1978) is deficient
Bias in Monte Carlo Simulations Due To Pseudo-Random Number Generator Initial Seed Selection
Pseudo-random number generators can bias Monte Carlo simulations of the standard normal probability distribution function with initial seeds selection. Five generator designs were initial-seeded with values from 10000HEX to 1FFFFHEX, estimates of the mean were calculated for each seed, the distribution of mean estimates was determined for each generator and simulation histories were graphed for selected seeds
- …