RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-03-27_19:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.53 30.2820 0.975618 2 to 25 15.87 21.2453 0.784492 3 to 26 15.84 9.9767 0.095414 4 to 27 15.72 30.2807 0.975610 5 to 28 15.74 14.5978 0.375575 6 to 29 15.81 24.5127 0.893839 7 to 30 15.97 25.2016 0.909712 8 to 31 15.65 20.4666 0.748940 9 to 32 15.54 22.4490 0.831939 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.010403 Tough bday spacings test for dh-ranFile-2018-03-27_19:31: 4096 birthdays, year=2^32 days Table of Expected vs. Observed counts: Duplicates 0 1 2 3 4 5 6 7 8 9 >=10 Expected 9.2 36.6 73.3 97.7 97.7 78.1 52.1 29.8 14.9 6.6 4.1 Observed 10 37 77 92 100 67 49 40 12 8 8 (O-E)^2/E 0.1 0.0 0.2 0.3 0.1 1.6 0.2 3.5 0.6 0.3 3.8 Birthday Spacings: Sum(O-E)^2/E= 10.602, p= 0.611 RESULTS OF GCD FOR dh-ranFile-2018-03-27_19:31 Euclid's algorithm: p-value, steps to gcd: 0.132529 p-value, dist. of gcd's: 0.511702 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-03-27_19:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.186 0.322 0.056 0.670 0.811 0.309 0.229 0.552 Bits 8 to 15---> 0.791 0.397 0.894 0.078 0.361 0.920 0.131 0.522 Bits 16 to 23---> 0.580 0.339 0.984 0.069 0.882 0.146 0.544 0.333 Bits 24 to 31---> 0.781 0.323 0.449 0.841 0.234 0.987 0.697 0.216 KS test for the above 32 p values: 0.085 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-03-27_19:31, p-values for 5 runs: 0.5576, 0.7835, 0.7608, 0.0522, 0.8878 Rank test for binary matrices (31x31) for dh-ranFile-2018-03-27_19:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 200 211.4 0.617 0.617 r= 29 5134 5134.0 0.000 0.617 r= 30 23213 23103.0 0.523 1.140 r= 31 11453 11551.5 0.840 1.980 chi-square = 1.980 with df = 3; p-value = 0.423 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-03-27_19:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 204 211.4 0.260 0.260 r= 30 5187 5134.0 0.547 0.807 r= 31 23042 23103.0 0.161 0.969 r= 32 11567 11551.5 0.021 0.989 chi-square = 0.989 with df = 3; p-value = 0.196 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-03-27_19:31 b-rank test for bits 1 to 8, p=0.51104 b-rank test for bits 2 to 9, p=0.26442 b-rank test for bits 3 to 10, p=0.49725 b-rank test for bits 4 to 11, p=0.13197 b-rank test for bits 5 to 12, p=0.65552 b-rank test for bits 6 to 13, p=0.09323 b-rank test for bits 7 to 14, p=0.08513 b-rank test for bits 8 to 15, p=0.16388 b-rank test for bits 9 to 16, p=0.16048 b-rank test for bits 10 to 17, p=0.73640 b-rank test for bits 11 to 18, p=0.97263 b-rank test for bits 12 to 19, p=0.02768 b-rank test for bits 13 to 20, p=0.02754 b-rank test for bits 14 to 21, p=0.09739 b-rank test for bits 15 to 22, p=0.86938 b-rank test for bits 16 to 23, p=0.86221 b-rank test for bits 17 to 24, p=0.82598 b-rank test for bits 18 to 25, p=0.83444 b-rank test for bits 19 to 26, p=0.88095 b-rank test for bits 20 to 27, p=0.43302 b-rank test for bits 21 to 28, p=0.33030 b-rank test for bits 22 to 29, p=0.05733 b-rank test for bits 23 to 30, p=0.52199 b-rank test for bits 24 to 31, p=0.41076 b-rank test for bits 25 to 32, p=0.89185 TEST SUMMARY, 25 tests, each on 100,000 random 6x8 matrices The above should be 25 uniform [0,1] random variables: The KS test for those 25 supposed UNI's yields p = 0.323988 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-03-27_19:31 (20 bits/word, 2097152 words 20 bitstreams. No. missing words should average 141909.33 with sigma=428.00.) ---------------------------------------------------------------- BITSTREAM test results. Bitstream No. missing words z-score p-value 1 141979 0.16 0.564654 2 142132 0.52 0.698558 3 142086 0.41 0.660116 4 141782 -0.30 0.383042 5 142700 1.85 0.967653 6 141273 -1.49 0.068540 7 142054 0.34 0.632324 8 141753 -0.37 0.357460 9 142111 0.47 0.681248 10 141506 -0.94 0.173004 11 141890 -0.05 0.481989 12 141318 -1.38 0.083545 13 141665 -0.57 0.284046 14 142314 0.95 0.827796 15 142395 1.13 0.871759 16 141161 -1.75 0.040194 17 141516 -0.92 0.179049 18 142562 1.52 0.936362 19 141539 -0.87 0.193449 20 141803 -0.25 0.401899 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-03-27_19:31 Bits used No. missing words z-score p-value 23 to 32 142078 0.5816 0.719589 22 to 31 141777 -0.4563 0.324083 21 to 30 142262 1.2161 0.888027 20 to 29 141664 -0.8460 0.198786 19 to 28 142074 0.5678 0.714924 18 to 27 141986 0.2644 0.604256 17 to 26 141865 -0.1529 0.439254 16 to 25 142555 2.2264 0.987008 15 to 24 142137 0.7851 0.783793 14 to 23 141440 -1.6184 0.052790 13 to 22 142009 0.3437 0.634460 12 to 21 142238 1.1333 0.871465 11 to 20 141806 -0.3563 0.360804 10 to 19 141765 -0.4977 0.309351 9 to 18 141796 -0.3908 0.347975 8 to 17 141926 0.0575 0.522920 7 to 16 142363 1.5644 0.941136 6 to 15 142264 1.2230 0.889335 5 to 14 142250 1.1747 0.879947 4 to 13 141726 -0.6322 0.263637 3 to 12 141844 -0.2253 0.410882 2 to 11 141607 -1.0425 0.148586 1 to 10 142228 1.0989 0.864086 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-03-27_19:31 Bits used No. missing words z-score p-value 28 to 32 141329 -1.9672 0.024579 27 to 31 142150 0.8158 0.792702 26 to 30 141861 -0.1638 0.434932 25 to 29 141928 0.0633 0.525232 24 to 28 142089 0.6091 0.728755 23 to 27 141661 -0.8418 0.199951 22 to 26 141837 -0.2452 0.403156 21 to 25 141915 0.0192 0.507667 20 to 24 141633 -0.9367 0.174453 19 to 23 141530 -1.2859 0.099245 18 to 22 141409 -1.6960 0.044940 17 to 21 142498 1.9955 0.977005 16 to 20 142160 0.8497 0.802262 15 to 19 141700 -0.7096 0.238978 14 to 18 142343 1.4701 0.929228 13 to 17 142412 1.7040 0.955806 12 to 16 141212 -2.3638 0.009044 11 to 15 141785 -0.4215 0.336711 10 to 14 142212 1.0260 0.847554 9 to 13 141970 0.2057 0.581472 8 to 12 142193 0.9616 0.831873 7 to 11 142423 1.7413 0.959181 6 to 10 142346 1.4802 0.930595 5 to 9 141810 -0.3367 0.368167 4 to 8 141999 0.3040 0.619423 3 to 7 142197 0.9752 0.835258 2 to 6 142122 0.7209 0.764519 1 to 5 141733 -0.5977 0.275010 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-03-27_19:31 Bits used No. missing words z-score p-value 31 to 32 142209 0.8840 0.811647 30 to 31 141442 -1.3786 0.084016 29 to 30 141996 0.2557 0.600895 28 to 29 141882 -0.0806 0.467872 27 to 28 142187 0.8191 0.793631 26 to 27 142174 0.7807 0.782522 25 to 26 142687 2.2940 0.989105 24 to 25 141760 -0.4405 0.329787 23 to 24 142052 0.4209 0.663070 22 to 23 142162 0.7453 0.771967 21 to 22 141959 0.1465 0.558244 20 to 21 141616 -0.8653 0.193443 19 to 20 141651 -0.7620 0.223019 18 to 19 141784 -0.3697 0.355801 17 to 18 142044 0.3973 0.654411 16 to 17 141863 -0.1367 0.445647 15 to 16 141692 -0.6411 0.260732 14 to 15 141760 -0.4405 0.329787 13 to 14 142295 1.1377 0.872371 12 to 13 141892 -0.0511 0.479615 11 to 12 142075 0.4887 0.687474 10 to 11 141771 -0.4081 0.341617 9 to 10 141292 -1.8210 0.034301 8 to 9 141631 -0.8210 0.205814 7 to 8 142203 0.8663 0.806833 6 to 7 142205 0.8722 0.808446 5 to 6 142274 1.0757 0.858974 4 to 5 141920 0.0315 0.512555 3 to 4 142162 0.7453 0.771967 2 to 3 141972 0.1849 0.573333 1 to 2 142570 1.9489 0.974345 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-03-27_19:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2645.72 2.061 0.980336 Test results for specific bytes for dh-ranFile-2018-03-27_19:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2421.02 -1.117 0.132021 2 to 9 2449.99 -0.707 0.239716 3 to 10 2599.70 1.410 0.920722 4 to 11 2450.20 -0.704 0.240619 5 to 12 2533.63 0.476 0.682820 6 to 13 2443.79 -0.795 0.213334 7 to 14 2548.36 0.684 0.753001 8 to 15 2553.08 0.751 0.773572 9 to 16 2486.76 -0.187 0.425751 10 to 17 2507.52 0.106 0.542344 11 to 18 2513.30 0.188 0.574601 12 to 19 2531.73 0.449 0.673197 13 to 20 2518.01 0.255 0.600542 14 to 21 2504.80 0.068 0.527067 15 to 22 2506.86 0.097 0.538646 16 to 23 2560.91 0.861 0.805497 17 to 24 2470.11 -0.423 0.336263 18 to 25 2501.62 0.023 0.509123 19 to 26 2403.95 -1.358 0.087171 20 to 27 2444.25 -0.788 0.215235 21 to 28 2415.46 -1.196 0.115929 22 to 29 2544.26 0.626 0.734319 23 to 30 2567.24 0.951 0.829185 24 to 31 2546.34 0.655 0.743893 25 to 32 2441.60 -0.826 0.204427 CDPARK for dh-ranFile-2018-03-27_19:31: result of 10 tests (Of 12000 tries, the average no. of successes should be 3523.0 with sigma=21.9) No. succeses z-score p-value 3521 -0.0913 0.463617 3549 1.1872 0.882429 3519 -0.1826 0.427537 3513 -0.4566 0.323972 3517 -0.2740 0.392053 3546 1.0502 0.853193 3493 -1.3699 0.085365 3528 0.2283 0.590298 3495 -1.2785 0.100530 3524 0.0457 0.518210 Square side=100, avg. no. parked=3520.50 sample std.=17.35 p-value of the KSTEST for those 10 p-values: 0.826109 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-03-27_19:31 0.9033,0.7521,0.3991,0.9836,0.5728,0.0919,0.0788,0.1893,0.2315,0.3960, The KS test for those 10 p-values: 0.827247 The 3DSPHERES test for dh-ranFile-2018-03-27_19:31 sample no r^3 equiv. uni. 1 26.504 0.586653 2 19.590 0.479513 3 16.200 0.417251 4 2.551 0.081506 5 35.859 0.697383 6 31.320 0.647957 7 9.337 0.267446 8 12.701 0.345163 9 10.170 0.287514 10 37.869 0.716994 11 139.028 0.990287 12 27.377 0.598514 13 79.641 0.929681 14 10.494 0.295167 15 24.321 0.555460 16 22.365 0.525509 17 20.880 0.501420 18 0.144 0.004799 19 21.736 0.515443 20 4.817 0.148344 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.609526 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-03-27_19:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 0.1 -1.6 0.3 0.3 -0.3 1.2 -1.3 -1.2 1.7 -0.8 0.1 0.0 0.6 0.0 -1.1 0.3 0.0 -1.2 -0.6 0.1 1.3 -0.1 0.5 1.1 0.1 -0.9 1.1 0.6 -0.2 0.8 0.1 -1.1 -1.5 -0.5 -0.8 -0.5 -0.4 1.3 -1.3 0.9 1.0 1.8 Chi-square with 42 degrees of freedom:33.895581 z-score=-0.884265, p-value=0.190925 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-03-27_19:31 Test no p-value 1 0.110436 2 0.051619 3 0.651064 4 0.021703 5 0.784911 6 0.001372 7 0.169333 8 0.359586 9 0.243790 10 0.446472 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.015071 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-03-27_19:31: (for k>=2, the prob. of a run of length k is 2*k/(k+1)!) Length Expected UpRuns (O-E)^2/E DownRuns (O-E)^2/E 2 66666.67 66772 0.17 66699 0.02 3 25000.00 24959 0.07 24861 0.77 4 6666.67 6594 0.79 6767 1.51 5 1388.89 1439 1.81 1397 0.05 6 238.10 197 7.09 233 0.11 7 34.72 34 0.01 35 0.00 8 4.96 4 0.19 7 0.84 p=0.88062 p=0.22913 Number of rngs required: 688952, p-value: 0.737 RESULTS OF CRAPS TEST for dh-ranFile-2018-03-27_19:31 No. of wins: Observed Expected 98570 98585.9 z-score=-0.071, pvalue=0.47173 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67023 66666.7 1.905 1.905 2 37527 37654.3 0.431 2.335 3 27012 26954.7 0.122 2.457 4 19306 19313.5 0.003 2.460 5 13605 13851.4 4.384 6.844 6 9790 9943.5 2.371 9.214 7 7135 7145.0 0.014 9.229 8 5162 5139.1 0.102 9.331 9 3715 3699.9 0.062 9.393 10 2615 2666.3 0.987 10.380 11 1939 1923.3 0.128 10.507 12 1373 1388.7 0.178 10.686 13 1015 1003.7 0.127 10.813 14 785 726.1 4.771 15.584 15 556 525.8 1.730 17.314 16 406 381.2 1.620 18.934 17 279 276.5 0.022 18.956 18 206 200.8 0.133 19.089 19 153 146.0 0.337 19.426 20 99 106.2 0.490 19.916 21 299 287.1 0.492 20.408 Chisq= 20.41 for 20 degrees of freedom, p= 0.56734 SUMMARY of craptest p-value for no. of wins: 0.471727 p-value for throws/game: 0.567342 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-03-27_19:31 No. of wins: Observed Expected 98536 98585.9 z-score=-0.223, pvalue=0.41177 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66692 66666.7 0.010 0.010 2 37750 37654.3 0.243 0.253 3 26811 26954.7 0.766 1.019 4 19279 19313.5 0.061 1.081 5 13694 13851.4 1.789 2.870 6 10010 9943.5 0.444 3.314 7 7173 7145.0 0.110 3.423 8 5143 5139.1 0.003 3.426 9 3808 3699.9 3.160 6.587 10 2714 2666.3 0.853 7.440 11 1844 1923.3 3.272 10.712 12 1389 1388.7 0.000 10.712 13 1047 1003.7 1.867 12.579 14 748 726.1 0.658 13.237 15 528 525.8 0.009 13.246 16 363 381.2 0.864 14.110 17 256 276.5 1.526 15.636 18 227 200.8 3.410 19.046 19 144 146.0 0.027 19.073 20 91 106.2 2.180 21.253 21 289 287.1 0.012 21.265 Chisq= 21.26 for 20 degrees of freedom, p= 0.61831 SUMMARY of craptest p-value for no. of wins: 0.411769 p-value for throws/game: 0.618313 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0014,0.0048,0.0090,0.0104,0.0151,0.0217,0.0246,0.0275,0.0277,0.0343, 0.0402,0.0449,0.0516,0.0522,0.0528,0.0563,0.0573,0.0685,0.0688,0.0782, 0.0788,0.0815,0.0835,0.0840,0.0847,0.0851,0.0854,0.0872,0.0919,0.0932, 0.0954,0.0974,0.0992,0.1005,0.1104,0.1159,0.1305,0.1320,0.1320,0.1325, 0.1457,0.1483,0.1486,0.1605,0.1639,0.1693,0.1730,0.1745,0.1790,0.1862, 0.1893,0.1909,0.1934,0.1934,0.1961,0.1988,0.2000,0.2044,0.2058,0.2133, 0.2152,0.2163,0.2230,0.2287,0.2291,0.2315,0.2338,0.2390,0.2397,0.2406, 0.2438,0.2607,0.2636,0.2644,0.2674,0.2750,0.2840,0.2875,0.2952,0.3087, 0.3094,0.3221,0.3235,0.3240,0.3240,0.3241,0.3298,0.3298,0.3303,0.3326, 0.3363,0.3367,0.3391,0.3416,0.3452,0.3480,0.3558,0.3575,0.3596,0.3608, 0.3609,0.3682,0.3756,0.3830,0.3921,0.3960,0.3974,0.3991,0.4019,0.4032, 0.4108,0.4109,0.4118,0.4173,0.4235,0.4258,0.4275,0.4330,0.4349,0.4393, 0.4456,0.4465,0.4490,0.4636,0.4679,0.4717,0.4795,0.4796,0.4820,0.4972, 0.5014,0.5077,0.5091,0.5110,0.5117,0.5126,0.5154,0.5182,0.5215,0.5220, 0.5229,0.5252,0.5255,0.5271,0.5386,0.5423,0.5440,0.5524,0.5555,0.5576, 0.5582,0.5647,0.5673,0.5728,0.5733,0.5746,0.5800,0.5815,0.5867,0.5903, 0.5985,0.6005,0.6009,0.6043,0.6095,0.6106,0.6183,0.6194,0.6323,0.6345, 0.6480,0.6511,0.6544,0.6555,0.6601,0.6631,0.6701,0.6732,0.6812,0.6828, 0.6875,0.6970,0.6974,0.6986,0.7149,0.7170,0.7196,0.7288,0.7343,0.7364, 0.7368,0.7439,0.7489,0.7521,0.7530,0.7608,0.7645,0.7720,0.7720,0.7736, 0.7806,0.7825,0.7835,0.7838,0.7845,0.7849,0.7910,0.7927,0.7936,0.8023, 0.8055,0.8068,0.8084,0.8109,0.8116,0.8260,0.8261,0.8272,0.8278,0.8292, 0.8319,0.8319,0.8344,0.8353,0.8412,0.8476,0.8532,0.8590,0.8622,0.8641, 0.8694,0.8715,0.8718,0.8724,0.8799,0.8806,0.8809,0.8816,0.8824,0.8878, 0.8880,0.8893,0.8919,0.8935,0.8938,0.9033,0.9097,0.9202,0.9207,0.9292, 0.9297,0.9306,0.9364,0.9411,0.9558,0.9592,0.9677,0.9726,0.9743,0.9756, 0.9756,0.9770,0.9803,0.9836,0.9838,0.9868,0.9870,0.9891,0.9903, Overall p-value after applying KStest on 269 p-values = 0.927735 In response to requests, we have provided a list of all the p-values produced by the tests you have chosen for this run. The individual p-values are supposed to be uniform in [0,1), but they are not necessarily independent. So even though we have applied a KSTEST to the accumulated p-values, the result is not necessarily---even if your file contains truly random bits---uniform in [0,1). But it is probably pretty close, so take that last p-value with a grain of salt. In particular, there may be some values so close to 0 or 1 that the tests they came from should be applied several more times, or new, related tests should be undertaken.