article

TestU01: A C library for empirical testing of random number generators

Authors:

Pierre L'Ecuyer,

Richard SimardAuthors Info & Claims

ACM Transactions on Mathematical Software (TOMS), Volume 33, Issue 4

Article No.: 22, Pages 1 - 40

https://doi.org/10.1145/1268776.1268777

Published: 15 August 2007 Publication History

Abstract

We introduce TestU01, a software library implemented in the ANSI C language, and offering a collection of utilities for the empirical statistical testing of uniform random number generators (RNGs). It provides general implementations of the classical statistical tests for RNGs, as well as several others tests proposed in the literature, and some original ones. Predefined tests suites for sequences of uniform random numbers over the interval (0, 1) and for bit sequences are available. Tools are also offered to perform systematic studies of the interaction between a specific test and the structure of the point sets produced by a given family of RNGs. That is, for a given kind of test and a given class of RNGs, to determine how large should be the sample size of the test, as a function of the generator's period length, before the generator starts to fail the test systematically. Finally, the library provides various types of generators implemented in generic form, as well as many specific generators proposed in the literature or found in widely used software. The tests can be applied to instances of the generators predefined in the library, or to user-defined generators, or to streams of random numbers produced by any kind of device or stored in files. Besides introducing TestU01, the article provides a survey and a classification of statistical tests for RNGs. It also applies batteries of tests to a long list of widely used RNGs.

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Index Terms

TestU01: A C library for empirical testing of random number generators
1. Mathematics of computing
  1. Mathematical software
    1. Statistical software
  2. Probability and statistics
    1. Probabilistic reasoning algorithms
      1. Random number generation

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Numerical Methods and Applications
Abstract
In this paper, we study the Capacitated Vehicle Routing Problem (CVRP) and implemented a simulation-based algorithm with different random number generators. The Binary-CWS-MCS algorithm has been integrated with six different random number ...
Occupancy Numbers in Testing Random Number Generators

The classical occupancy problem where n balls are placed in N cells is used for testing of random number generators. We show that the statistics of appropriately chosen occupancy numbers are incompatible with the statistics of manypseudorandom number ...

Reviews

Reviewer: Charles Raymond Crawford

Algorithms and software for computing pseudorandom number sequences have a wide range of applications. There are many acceptable methods, but each has its drawbacks. This paper summarizes the published research on the testing of random sequences. The discussion is focused on specific statistical tests, and how they might expose weaknesses in a given random number generator (RNG). The software library that accompanies the paper addresses this problem directly. "The aim of [the library] is to provide a general and extensive set of software tools for statistical testing of RNGs." Although the library does include RNGs, the important modules allow the user to test sequences from generators, both those within the library and ones supplied by the user. The ANSI C source for the library is available for free on the Web, along with extensive documentation. The paper concludes with an application of the library tests to a large set of RNGs, including the default generators used by some popular software packages. The authors plan to maintain and update the Web files, which should provide software developers as well as researchers with rigorous tools to design dependable generators. Online Computing Reviews Service

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Published In

cover image ACM Transactions on Mathematical Software

ACM Transactions on Mathematical Software Volume 33, Issue 4

August 2007

147 pages

ISSN:0098-3500

EISSN:1557-7295

DOI:10.1145/1268776

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Copyright © 2007 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

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Publication History

Published: 15 August 2007

Published in TOMS Volume 33, Issue 4

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