A Random Number Generator Test Suite for the C++ ... - ETH ZÃ¼rich

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$Departments of Mathematics and Physics (D-MATH/D ... - RW/CSE$

5.11. Serial test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345.12. Blocking test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355.13. Repeating Time Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355.14. gcd test (greatest common divisor) . . . . . . . . . . . . . . . . . . . . . . 365.15. Gorilla test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365.16. Ising-model test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365.17. Random-walk test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375.18. n-block test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395.19. Random Walker on a line (S n test) . . . . . . . . . . . . . . . . . . . . . . 405.20. 2D Intersection test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405.21. 2D Height Correlation test . . . . . . . . . . . . . . . . . . . . . . . . . . 405.22. Sum of independent distributions test . . . . . . . . . . . . . . . . . . . . . 405.23. Fourier transform test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415.24. Universal statistical test . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415.25. The Diehard Test Suite . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415.25.1. Birthday Spacings test . . . . . . . . . . . . . . . . . . . . . . . . 425.25.2. The overlapping 5-permutation test . . . . . . . . . . . . . . . . . 425.25.3. Ranks of binary matrices . . . . . . . . . . . . . . . . . . . . . . . 425.25.4. The bitstream test . . . . . . . . . . . . . . . . . . . . . . . . . . . 435.25.5. The OPSO, OQSO and DNA tests . . . . . . . . . . . . . . . . . . 445.25.6. The count-the-1’s test . . . . . . . . . . . . . . . . . . . . . . . . . 455.25.7. The parking lot test . . . . . . . . . . . . . . . . . . . . . . . . . . 455.25.8. The overlapping sums test . . . . . . . . . . . . . . . . . . . . . . 465.25.9. Squeeze test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465.25.10.The Minimum Distance test . . . . . . . . . . . . . . . . . . . . . 475.25.11.Random Sphere test . . . . . . . . . . . . . . . . . . . . . . . . . 475.25.12.The runs test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485.25.13.Craps test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 486. Extending the Random Number Generator Test Suite 496.1. How to implement a test . . . . . . . . . . . . . . . . . . . . . . . . . . . 496.1.1. Implementing a χ 2 , Kolmogorov-Smirnov or a Gaussian test . . . . 516.1.2. χ 2 test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 526.1.3. Kolmogorov-Smirnov test . . . . . . . . . . . . . . . . . . . . . . 526.1.4. Gaussian test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 546.2. The multiple_test wrapper . . . . . . . . . . . . . . . . . . . . . . . 546.3. Useful sequence diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . 576.4. Demands on Random Number Generators . . . . . . . . . . . . . . . . . . 576.5. Foreign Random Number Generators . . . . . . . . . . . . . . . . . . . . . 576.6. The XML Schema . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61A. Collection of Test Parameters 64B. Examples 66C. Compiling the Test Suite 67ii
1. IntroductionHow random is random?In this diploma thesis a generic random number test suite (RNGTS) is developed. The testsuite framework is written in C++ with attention to modern generic programming paradigm.It is based on the Boost reference implementation of the forthcoming C++ standard randomnumber generator library. The aim of RNGTS is to assist in finding a suitable random numbergenerator for a specific purpose and in deciding between good and bad random numbergenerators. Through a generic interface the RNGTS makes a variety of different tests availableand provides the possibility to extending the suite with user defined tests. The test resultsare produced in XML format, which allows the transformation into summaries or detailedreports through the use of XSLT style sheets. The main purpose is to support the user in hisdecision about a random number generator, and in the question how random the numbersproduced by the random number generators are.In the second part of this paper there is a short discussion about the different types ofrandom numbers and their applications.Then, in the third part the involved statistical methods and their pertaining programminginterface are presented.The fourth part contains the handling of RNGTS. This part is a “must” for the user whowants to perform any tests. It also describes the core of the whole test suite.In the fifth part there is a presentation of the most popular random number generatortests, their parameters and programming interfaces. These tests are collected fromdifferent sources and authors.The sixth part is for “advanced” users who want to extend RNGTS and add new testsor different extensions.Finally, the appendix contains a collection of different lists with test parameters andother useful stuff.DownloadThe RNGTS framework is located on the www.comp-phys.org web server and may bedownloaded there. There are also some installation hints, some examples and the full documentationwith additional interface descriptions and the XSL schema.1
Page 1 and 2: ¡Institute for Theoretical Physics
Page 3: to my parentsUrs and Heidi
Page 7: Contents1. Introduction 12. What ar
Page 11 and 12: 2.1. Types of random numberspossibl
Page 13 and 14: ¥3.1. χ 2 test (“Chi-square”
Page 15 and 16: 3.2. Kolmogorov-Smirnov test (KS te
Page 17 and 18: 3.3. Gaussian TestExample: Ising mo
Page 19 and 20: 4.2. The rng_test_suite environment
Page 21 and 22: 4.2. The rng_test_suite environment
Page 23 and 24: 4.4. Iterating a testminstd_rand //
Page 25 and 26: 4.8. The XML outputOriginal18019489
Page 27 and 28: 5.2. Run testExample: Throwing a di
Page 29 and 30: 5.2. Run testTest Class Name Descri
Page 31 and 32: 5.2. Run testSplitting up in subseq
Page 33 and 34: 5.4. Poker testThe first value lies
Page 35 and 36: 5.5. Coupon-collectors testTo calcu
Page 37 and 38: 5.6. Permutation testn number of co
Page 39 and 40: £ bin range percentage # expected
Page 41 and 42: N £ 2X N X 2 £N£1¤1¨§X5.10. S
Page 43 and 44: §25.12. Blocking testApply a χ 2
Page 45: - Generate n random number in X¢0;
Page 48 and 49: 5. Tests for Studying Random Data5.
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6. Extending the Random Number Gene
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A. Collection of Test ParametersThe
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B. ExamplesTo point out the ease of
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Bibliography[1] Z. W. Birnbaum and
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Bibliography[26] A. Srinivasan, M.
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A Random Number Generator Test Suite for the C++ ... - ETH ZÃ¼rich

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