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

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0¡1111 0¡672;0¡449£5. Tests for Studying Random DataA correlation coefficient between always and¤lies 1 1. When it is zero or very small, itindicates that X i and X j are independent of each other. A “good” value of C will be betweenµ N and µ N which means 95%, whereN¤ Nµ N¥11σ1 N N¥ N 2 (5.6)2σGenerate a sequence of N random numbers X 0 X 1 ¢¡¢¡¢¡N £ 12σ1 13¨ N¤Calculate the “serial correlation coefficient” C with formula (5.5)N§N NCalculate the mean and the standard deviation and check if C lies between the two σlimit (µ N¡ 2σ N ) which denotes the 95% limitXExample:Lets take the same sequence of ten random number as in section 3.2 {0.809, 0.465, 0.151,0.628, 0.318, 0.824, 0.394, 0.968, 0.179, 0.458}.We have to calculate C as shown in equation (5.5)10 0¡465¤§0¡809 0¡465 0¡151¡¢¡¢¡¨20¡465¤10 §0¡809 0¡465 2¤ 2¤ 2¡¢¡¢¡¨ §0¡809¤0¡465¤ 0¡5153760¡151¡¢¡¢¡¨2 §0¡809¤To check if the calculated C coefficient lies between the 2σ bounds. Use the formulasgiven in (5.6) 0¡151¡¢¡£¡¨ C¥¥11 70µ 10¥ σ 10¥9 11¥ 0¡28039We see that the valid interval for this test is . The calculated coefficientC lies between these bounds. (The interval is so large because we only tested tennumbers)¢ ¥Constructor in serial_correlation_test.hserial_correlation_test(uint64_t n)n number of random numbers to calculate correlation for5.11. Serial testThis test checks if not only particular numbers are uniformly distributed but also two, three ord-dimensional points. To make this test, count the number of times the tuple§X di X di¡ 1 di¡ ¢ d£ 1£¨ ¢¡¢¡¢¡£Xthe test is the same as the “Equidis-occurs, for 0 i n and the dimension d 0. If 1tribution test”. The tuples should be χ 2 distributed.d¥ ¡Generate n d-tuples§X di X di¡ 1 X ¢¡¢¡¢¡di¡ ¢ d£ 1£¨, where d0 and 0 X j¡k34
§25.12. Blocking testApply a χ 2 test to these k d categories with probability 1 k d in each category.To get a valid χ 2 test n should be large compared to k d ,say nk dA more detailed description is given in [16].Example:Lets generateare:§2 §2 2¨ 1¨ n¥pairs of random numbers (d¥ between zero and two 3), the pairs§1 §0 §1 §1 §2 §1 §0 1¨ 2¨ 2¨ 1¨1¨ 1¨ 2¨ 0¨Then we count the appearing of each tuple10pairs §0count 0 2 0 0 2 2 1 1 22¨ 1¨ 0¨ 2¨ 1¨ 0¨ 2¨ 1¨ 0¨§0§0§1§1§1§2§2§2The expected number of pairs for each class is 1 d 3 n¥9¥1¡11Constructor in serial_test.hserial_test(uint64_t n, std::size_t gridSize, std::size_t dimension)10n number of random numbers to placegridSize edge length of the griddimension dimension of the grid5.12. Blocking testFor this test I found only a really scanty description in [26] . So, the only way to find outhow this test has to be implemented is looking into existing source code.The Blocking test tests a proposition of the central limit theorem. This says that, the thesum of k independent variables with zero mean and unit variance approaches the normaldistribution with mean zero and variance equal to k. To test the proposition n sums of suchgroups or blocks will be built and checked for normality.5.13. Repeating Time TestThis test checks if a uniform§0 random number generator starts to repeat its sequencewhen it is expected to. If the repetition occurs to soon, the test fails because the generatordoes not generate all possible number but only a subset of all values. If the first repetitionoccurs to late after the expected value, this means that the numbers are unusually uniformlyspread. The implementation and included description can be found in [10]1¨35
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: N £ 2X N X 2 £N£1¤1¨§X5.10. S
Page 45: - Generate n random number in X¢0;
Page 48 and 49: 5. Tests for Studying Random Data5.
Page 50 and 51: 5. Tests for Studying Random DataRu
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.

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

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