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

More documents

Recommendations

Info

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

5. Tests for Studying Random Data5.19. Random Walker on a line (S n test)This test uses different random walkers in one dimension. This N random walker movesimultaneously without any interaction. At each step in a walk, they can jump left or rightwith the same probability. After t 1 steps for each walker, the number of visited sitesS ¡n t has an asymptotic form S n t f§N¨tγ where the scaling function §ln 2 and N¨1¡1 2 is the expected exponent as based on theory. The value of the exponent γ observedfrom simulations serves as a measure of correlations.A description is available in [27] and the appropriate implementation can be found at http://www.physics.helsinki.fi/~vattulai/codes/sn1d_test.fγ¥ ¥ f§N¨5.20. 2D Intersection testIn this test we use two random walkers in two dimensions. Their paths are given by twodifferent sequences of random numbers. After n steps of each random walker we calculatethe probability that they never meet the same place in plane (at the same time or not) exceptat their common starting point. For a random process it is known that the number of intersectionsI§n¨behave asymptotically like a power law α with an exponent 8.A description is available in [27] and the appropriate implementation can be found at http://www.physics.helsinki.fi/~vattulai/codes/intersections.fα¥ £ I§n¨5.21. 2D Height Correlation testThe Height Correlation test observes again the behavior of one-dimensional random walker.Here the correlation between the heights of two walkers are measured, where each randomwalker represents a stream of random numbers. To do this we construct two sequences ofrandom steps on a line (x 1 i x 2 i ), then the height is defined as h x 1 xt 2 .£¢The correspondingcorrelation function H h 0 t φ is known to decay asymptotically as a power lawwith a exponent 1 2.t¥A description is available in [27] and the appropriate implementation can be found at http://www.physics.helsinki.fi/~vattulai/codes/height.ft t¥ tφ¥n5Constructor in height_corr2d_testheight_corr2d_test(std::size_t n, std::size_t steps)¡hn number of samples with each two walkssteps number of steps per walk5.22. Sum of independent distributions testThis test is used in the SPRNG test suite [26]. It is designed to check multiple streams forindependence. This test builds n sums of groupsize random numbers from each stream andtests the distribution with a K-S statistic.40
5.23. Fourier transform test5.23. Fourier transform testFor this test I found only a really scanty description [26]. So, the only way to find out howthis test has to be implemented is looking into existing source code.For a short description the following can be said. It is a test for multiple streams, butmultiple streams can be built of multiple subsequences. A two-dimensional array has to befilled with random numbers, each row with n numbers from a different stream. Then thetwo-dimensional Fourier coefficients were calculated and compared with the expected ones.A related article can be found in [7].5.24. Universal statistical testThis test was designed to detect any significant deviation of a devices output statistics fromthe statistic of a truly random bit source. This test is done by measuring a parameter closelyrelated to the devices per-bit entropy. The fully description is in [23].5.25. The Diehard Test SuiteDiehard is the name of a battery of tests for random number sequences which was developedby George Marsaglia in 1995 [18]. The original Code was written in FORTRAN, but thereare two new implementations in C [19], [22]. A useful paper may also be [24].The tests contained in the Diehard battery are listed bellow.Birthday Spacings testOverlapping PermutationsRanks of 31 31 and 32 32 matrices testRanks of 68 matrices testCount the 1‘s in a Stream of BytesCount the 1‘s in Specific BytesMonkey tests on 20-bit WordsMonkey tests OPSO,OQSO,DNAParking Lot testOverlapping Sums testSqeeze testMinimum Distance testRandom Spheres test41
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 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

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?