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

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5. Tests for Studying Random DataTo perform a χ 2 -test, with 1 degrees of freedom, we have to know theexpected probabilities for each length. This are calculated by the following formulas:d¤ t k¥p r ¥d!dr r1d r ¡ t (5.3)p t ¥d!d t £ 11d 1¡for1d ¡ t(5.4)Once more the termrd¡ denotes the Stirling number of second kind.Example: Throwing a dieWe use the same data as in 5.4. We have integers from 1 to 5 and we define 13We first split up the sequence into “complete sets” and count the lengtht¥5¡¢¡¢¡complete setlength5 2 4 4 5 1 2 4 2 3 103 4 2 3 5 5 4 4 1 94 1 2 1 5 1 3 71 1 5 2 3 5 4 72 4 3 3 5 2 4 3 4 3 5 2 2 5 5 1 165 3 1 1 4 5 2 71 1 3 1 2 5 5 5 2 3 2 4 123 4 3 1 3 5 5 4 2 94 4 2 4 1 3 5 75 2 2 5 2 4 5 3 4 5 3 5 2 5 4 16We can calculate the expected length of sequences with equation (5.3), (5.4) and compareto the measured length.r p r # expected # counted245625=0.0384 0.38 0486625=0.0768 0.77 031273125=0.0998 1.00 433683125=0.1075 1.08 0408249390625=0.1045 1.05 2=0.0955 0.95 1=0.0838 0.84 0=0.0716 0.72 1=0.3220 3.22 210372963906251116370419531251227984390625>136289011953125Constructor in coupon_collector_test.hcoupon_collector_test(uint64_t n,std::size_t different_coupons,std::size_t maxSeq)28
5.6. Permutation testn number of coupon setsdifferent_coupons number of different couponsmaxSeq sequence length above this value will be cumulated5.6. Permutation testThe sequence of numbers is divided into n groups of t elements each, denoted as the vector§X it X ¢ t£ it¡ 1 it¡ for 0 i n. The elements in each group of t values can have t!possible orderings. The number of times each ordering appears is counted and a χ 2 -test witht! degrees of freedom and with probability 1 t! for each ordering. The theory and analgorithm may be found in [16].¢¡¢¡¢¡£ ¡ 1£¨k¥XDivide the input sequence into n groups of t elements eachCount the occurrence of each possible ordering in the groupDo a χ 2 -test with t! k¥degrees of freedom and with probability 1 t! for each orderingExample:We get 50 n¥groups of data with each three values out of 1 2 3.1-10 3 1 2 1 2 3 3 1 2 1 3 2 2 1 3 2 3 1 2 1 3 2 1 3 3 1 2 1 3 211-20 2 1 3 3 1 2 3 1 2 3 2 1 2 3 1 3 2 1 1 2 3 1 2 3 1 2 3 3 2 121-30 1 3 2 3 1 2 3 1 2 1 3 2 2 3 1 1 3 2 2 1 3 2 3 1 2 1 3 3 1 231-40 2 3 1 2 3 1 1 2 3 3 1 2 2 3 1 1 2 3 2 3 1 3 2 1 3 2 1 1 2 341-50 3 2 1 2 3 1 1 2 3 1 2 3 1 3 2 2 1 3 1 2 3 3 2 1 3 2 1 1 3 2For 3 there are d!¥ 6 different combinations. We count the occurrence of eachcombinationd¥sequence 1 2 3 1 3 2 2 1 3 2 3 1 3 1 2 3 2 1# sequences 10 7 7 9 9 8The expected value for every combination is n 508 6¥ d!¥1 3Constructor in permutation_test.hpermutation_test(uint64_t n, std::size_t nrOfElements)n number of permutations to generatenrOfElements number of elements to permute29
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: 5.5. Coupon-collectors testTo calcu
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 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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