scholarly journals Review of High-Quality Random Number Generators

2020 ◽  
Vol 4 (1) ◽  
Author(s):  
Frederick James ◽  
Lorenzo Moneta
Keyword(s):  
Monte Carlo ◽  
Random Number ◽  
Mechanical Systems ◽  
Pseudorandom Number ◽  
High Quality ◽  
Random Number Generators ◽  
Monte Carlo Calculations ◽  
Pseudorandom Number Generators ◽  
Number Sequences ◽  
The Ideal

AbstractThis 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.

Pseudorandom Number Generators

2017 ◽  
pp. 1-25
Keyword(s):  
Random Number ◽  
Pseudorandom Number ◽  
Random Numbers ◽  
Pseudorandom Sequences ◽  
Random Number Generators ◽  
Random Sequences ◽  
Pseudorandom Number Generators ◽  
Pseudo Random Number

In this chapter, the author considers existing methods and means of forming pseudo-random sequences of numbers and also are described the main characteristics of random and pseudorandom sequences of numbers. The main theoretical aspects of the construction of pseudo-random number generators are considered. Classification of pseudorandom number generators is presented. The structures and models of the most popular pseudo-random number generators are considered, the main characteristics of generators that affect the quality of the formation of pseudorandom bit sequences are described. The models of the basic mathematical generators of pseudo-random numbers are considered, and also the principles of building hardware generators are presented.

scholarly journals On pseudorandom number generators

ACTA IMEKO ◽  
2020 ◽  
Vol 9 (4) ◽  
pp. 128
Author(s):  
Daniel Chicayban Bastos ◽  
Luis Antonio Brasil Kowada ◽  
Raphael C. S. Machado
Keyword(s):  
Programming Languages ◽  
Random Number ◽  
Statistical Tests ◽  
Statistical Test ◽  
Pseudorandom Number ◽  
Pseudorandom Number Generator ◽  
Statistical Sampling ◽  
Simple Task ◽  
Random Number Generators ◽  
Pseudorandom Number Generators

<p class="Abstract">Statistical sampling and simulations produced by algorithms require fast random number generators; however, true random number generators are often too slow for the purpose, so pseudorandom number generators are usually more suitable. But choosing and using a pseudorandom number generator is no simple task; most pseudorandom number generators fail statistical tests. Default pseudorandom number generators offered by programming languages usually do not offer sufficient statistical properties. Testing random number generators so as to choose one for a project is essential to know its limitations and decide whether the choice fits the project’s objectives. However, this study presents a reproducible experiment that demonstrates that, despite all the contributions it made when it was first published, the popular NIST SP 800-22 statistical test suite as implemented in the software package is inadequate for testing generators.</p>

Methods and Models for the Formation of Pseudo-Random Number Sequences Based on Cellular Automata

2021 ◽  
pp. 99-193
Keyword(s):  
Cellular Automata ◽  
Statistical Tests ◽  
Variable Number ◽  
Pseudorandom Number ◽  
High Quality ◽  
Hybrid Cellular Automata ◽  
Pseudorandom Number Generators ◽  
Asynchronous Cellular Automata ◽  
Number Sequences

The chapter describes well-known models and implementation options for pseudorandom number generators based on cellular automata. Pseudorandom number generators based on synchronous and asynchronous cellular automata are briefly reviewed. Pseudorandom number generators based on one-dimensional and two-dimensional cellular automata, as well as using hybrid cellular automata, are described. New structures of pseudorandom number generators based on asynchronous cellular automata with a variable number of active cells are proposed. Testing of the proposed generators was carried out, which showed the high quality of the generators. Testing was conducted using graphical and statistical tests.

Pseudorandom Number Generators Based on Cellular Automata

2017 ◽  
pp. 52-65
Keyword(s):  
Cellular Automata ◽  
Random Number ◽  
Pseudorandom Number ◽  
Random Numbers ◽  
Random Number Generators ◽  
One Dimensional ◽  
Pseudorandom Number Generators ◽  
Pseudo Random Number ◽  
The Creation

In this chapter, the author considers the main theoretical solutions for the creation of pseudo-random number generators based on one-dimensional cellular automata. A Wolfram generator is described on the basis of rule 30. The main characteristics of the Wolfram generator is presented. The analysis of hybrid pseudo-random number generators based on cellular automata is carried out. Models of such generators and their realization with various forms of neighborhoods are presented. Also in the chapter is presented the analysis of the basic structures and characteristics of pseudo-random number generators using additional sources of pseudo-random numbers. As such additional sources the LFSR is used.

Improving Random Number Generators in the Monte Carlo simulations via twisting and combining

2008 ◽  
Vol 178 (6) ◽  
pp. 401-408 ◽  
Author(s):  
Lih-Yuan Deng ◽  
Rui Guo ◽  
Dennis K.J. Lin ◽  
Fengshan Bai
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Random Number ◽  
Random Number Generators

scholarly journals TESTS OF RANDOM NUMBER GENERATORS USING ISING MODEL SIMULATIONS

1996 ◽  
Vol 07 (03) ◽  
pp. 295-303 ◽  
Author(s):  
P. D. CODDINGTON
Keyword(s):  
Monte Carlo ◽  
Ising Model ◽  
Monte Carlo Simulations ◽  
High Performance ◽  
Large Scale ◽  
Random Number ◽  
Random Number Generators ◽  
Lattice Monte Carlo ◽  
High Performance Computers

Large-scale Monte Carlo simulations require high-quality random number generators to ensure correct results. The contrapositive of this statement is also true — the quality of random number generators can be tested by using them in large-scale Monte Carlo simulations. We have tested many commonly-used random number generators with high precision Monte Carlo simulations of the 2-d Ising model using the Metropolis, Swendsen-Wang, and Wolff algorithms. This work is being extended to the testing of random number generators for parallel computers. The results of these tests are presented, along with recommendations for random number generators for high-performance computers, particularly for lattice Monte Carlo simulations.

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