268 research outputs found
A Portable High-Quality Random Number Generator for Lattice Field Theory Simulations
The theory underlying a proposed random number generator for numerical
simulations in elementary particle physics and statistical mechanics is
discussed. The generator is based on an algorithm introduced by Marsaglia and
Zaman, with an important added feature leading to demonstrably good statistical
properties. It can be implemented exactly on any computer complying with the
IEEE--754 standard for single precision floating point arithmetic.Comment: pages 0-19, ps-file 174404 bytes, preprint DESY 93-13
Review of High-Quality Random Number Generators
This is a review of pseudorandom number generators (RNG's) of the highest
quality, suitable for use in the most demanding Monte Carlo calculations. All
the RNG's we recommend here are based on the Kolmogorov-Anosov theory of mixing
in classical mechanical systems, which guarantees under certain conditions and
in certain asymptotic limits, that points on the trajectories of these systems
can be used to produce random number sequences of exceptional quality. We
outline this theory of mixing and establish criteria for deciding which RNG's
are sufficiently good approximations to the ideal mathematical systems that
guarantee highest quality. The well-known RANLUX (at highest luxury level) and
its recent variant RANLUX++ are seen to meet our criteria, and some of the
proposed versions of MIXMAX can be modified easily to meet the same criteria.Comment: 21 pages, 4 figure
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
Hurst's Rescaled Range Statistical Analysis for Pseudorandom Number Generators used in Physical Simulations
The rescaled range statistical analysis (R/S) is proposed as a new method to
detect correlations in pseudorandom number generators used in Monte Carlo
simulations. In an extensive test it is demonstrated that the RS analysis
provides a very sensitive method to reveal hidden long run and short run
correlations. Several widely used and also some recently proposed pseudorandom
number generators are subjected to this test. In many generators correlations
are detected and quantified.Comment: 12 pages, 12 figures, 6 tables. Replaces previous version to correct
citation [19
Sum-discrepancy test on pseudorandom number generators
We introduce a non-empirical test on pseudorandom number generators (prng), named sum-discrepancy test. We compute the distribution of the sum of consecutive m outputs of a prng to be tested, under the assumption that the initial state is uniformly randomly chosen. We measure its discrepancy from the ideal distribution, and then estimate the sample size which is necessary to reject the generator. These tests are effective to detect the structure of the outputs of multiple recursive generators with small coefficients, in particular that of lagged Fibonacci generators such as random() in BSD-C library, as well as add-with-carry and subtract-with-borrow generators like RCARRY. The tests show that these generators will be rejected if the sample size is of order 106. We tailor the test to generators with a discarding procedure, such as ran_array and RANLUX, and exhibit empirical results. It is shown that ran_array with half of the output discarded is rejected if the sample size is of the order of 4Ă1010. RANLUX with luxury level 1 (i.e. half of the output discarded) is rejected if the sample size is of the order of 2Ă108, and RANLUX with luxury level 2 (i.e. roughly 3/4 is discarded) will be rejected for the sample size of the order of 2.4Ă1018. In our previous work, we have dealt with the distribution of the Hamming weight function using discrete Fourier analysis. In this work, we replace the Hamming weight with the continuous sum, using a classical Fourier analysis, i.e. Poisson's summation formula and Levy's inversion formula
A Search for Good Pseudo-random Number Generators : Survey and Empirical Studies
In today's world, several applications demand numbers which appear random but
are generated by a background algorithm; that is, pseudo-random numbers. Since
late century, researchers have been working on pseudo-random number
generators (PRNGs). Several PRNGs continue to develop, each one demanding to be
better than the previous ones. In this scenario, this paper targets to verify
the claim of so-called good generators and rank the existing generators based
on strong empirical tests in same platforms. To do this, the genre of PRNGs
developed so far has been explored and classified into three groups -- linear
congruential generator based, linear feedback shift register based and cellular
automata based. From each group, well-known generators have been chosen for
empirical testing. Two types of empirical testing has been done on each PRNG --
blind statistical tests with Diehard battery of tests, TestU01 library and NIST
statistical test-suite and graphical tests (lattice test and space-time diagram
test). Finally, the selected PRNGs are divided into groups and are
ranked according to their overall performance in all empirical tests
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
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