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

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5. Tests for Studying Random DataRuns testCraps testThe following sections describes tests from the Diehard battery. In most cases there is theoriginal (converted to LATEX style) test description quoted.5.25.1. Birthday Spacings testThis test is described in 5.8. The parameters used in Diehard areruns 500birthdays 2 9 512days 2 24 16777216maxCollisions = “not used” 45.25.2. The overlapping 5-permutation testThe following description is the original text from the Diehard test suite.This is the OPERM5 test. It looks at a sequence of one million 32-bit randomintegers. Each set of five consecutive integers can be in one of 120 states, forthe 5! possible orderings of five numbers. Thus the 5th, 6th, 7th,¡¢¡¢¡numberseach provide a state. As many thousands of state transitions are observed, cumulativecounts are made of the number of occurrences of each state. Then thequadratic form in the weak inverse of the 120 120 covariance matrix yieldsa test equivalent to the likelihood ratio test that the 120 cell counts came fromthe specified (asymptotically) normal distribution with the specified 120 120covariance matrix (with rank 99). This version uses 1 000 000 integers, twice.5.25.3. Ranks of binary matricesThe Diehard test suite implements three binary matrix tests for different matrix dimensions.The aim of all these test are the same, namely to check the rank of the constructed randommatrix against the expected rank.This implemented binary rank test is more flexible, it is possible to specify the dimensionof the matrix to construct from random numbers. In the test each random number is splitinto bits 0¡¢¡¢¡n, and so on, until n reaches the bit length of the random number.Matrices are constructed from each of these sequences and over each sequence we performa χ 2 test. At the end we make a K-S test over all χ 2 values. The probabilities for rank k in am n matrix is given in [32].In the Diehard test suite the result of the 6 8 and the 31 31 or 32 32 matrices test1¡¢¡¢¡§n¤are analysed in a different way. For the 6 8 matrix the χ 2 probability of all sub-matrices1¨is calculated and then a Kolmogorov-Smirnov test is performed over the values. For the4 In section 5.8 we wrote the expected value as birthdays days. The maxCollisions valueshould be much bigger than this value. In this example we get so 3¡§4¢ we can choose 16.µ¥ µ¥422,
5.25. The Diehard Test Suitebigger matrices, only the χ 2 value for matrix is reported. To accommodate to this differentmeanings, there are two different tests implemented, a bin_rank_ks_test and abin_rank_chisqr_test. The usage of both classes is exactly the same, only the statisticsare different.Constructors in bin_rank_test.hbin_rank_ks_test(uint64_t n,std::size_t rows,std::size_t columns,std::size_t minRankCount)bin_rank_chisqr_test(uint64_t n,std::size_t rows,std::size_t columns,std::size_t minRankCount)n number of matrices to buildrows number of rows in matrixcolumns number of columns in matrixminRankCount count ranks down to this rank, if a rank is smaller cumulate itIn the original implementation the following parameters were used:Ranks of 31 31 matrices testbin_rank_chisqr_testn 40000rows 31columns 31minRankCount 28Ranks of 32 32 matrices testbin_rank_chisqr_testn 40000rows 32columns 32minRankCount 29Ranks of 6 8 matrices testbin_rank_ks_testn 100000rows 6columns 8minRankCount 45.25.4. The bitstream testThe following description is the original text from the Diehard test suite.43
Page 1 and 2: ¡Institute for Theoretical Physics
Page 3: to my parentsUrs and Heidi
Page 7 and 8: Contents1. Introduction 12. What ar
Page 9 and 10: 1. IntroductionHow random is random
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.
Page 52 and 53: 5. Tests for Studying Random DataTh
Page 54 and 55: 5. Tests for Studying Random Dataat
Page 56 and 57: 5. Tests for Studying Random DataCo
Page 58 and 59: 6. Extending the Random Number Gene
Page 72 and 73: A. Collection of Test ParametersThe
Page 74 and 75: B. ExamplesTo point out the ease of
Page 76 and 77: Bibliography[1] Z. W. Birnbaum and
Page 78: Bibliography[26] A. Srinivasan, M.

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