RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-03-29_04:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.63 18.9765 0.670117 2 to 25 15.87 9.3250 0.070488 3 to 26 15.42 29.8829 0.972798 4 to 27 15.81 12.7320 0.246064 5 to 28 15.84 13.3871 0.290087 6 to 29 15.81 15.3566 0.430190 7 to 30 15.90 11.6555 0.179465 8 to 31 15.89 17.9702 0.609274 9 to 32 15.92 17.1785 0.557660 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.863755 Tough bday spacings test for dh-ranFile-2018-03-29_04:31: 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 7 35 70 91 108 82 64 26 5 8 4 (O-E)^2/E 0.5 0.1 0.1 0.5 1.1 0.2 2.7 0.5 6.6 0.3 0.0 Birthday Spacings: Sum(O-E)^2/E= 12.515, p= 0.748 RESULTS OF GCD FOR dh-ranFile-2018-03-29_04:31 Euclid's algorithm: p-value, steps to gcd: 0.400951 p-value, dist. of gcd's: 0.728954 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-03-29_04:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.105 0.376 0.739 0.395 0.601 0.561 0.083 0.781 Bits 8 to 15---> 0.477 0.844 0.554 0.126 0.359 0.507 0.833 0.054 Bits 16 to 23---> 0.765 0.637 0.732 0.624 0.076 0.545 0.343 0.417 Bits 24 to 31---> 0.747 0.855 0.630 0.743 0.841 0.364 0.668 0.064 KS test for the above 32 p values: 0.660 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-03-29_04:31, p-values for 5 runs: 0.3917, 0.7017, 0.6632, 0.4397, 0.5620 Rank test for binary matrices (31x31) for dh-ranFile-2018-03-29_04:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 226 211.4 1.006 1.006 r= 29 5129 5134.0 0.005 1.011 r= 30 23175 23103.0 0.224 1.235 r= 31 11470 11551.5 0.575 1.810 chi-square = 1.810 with df = 3; p-value = 0.387 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-03-29_04:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 204 211.4 0.260 0.260 r= 30 5121 5134.0 0.033 0.293 r= 31 23073 23103.0 0.039 0.332 r= 32 11602 11551.5 0.221 0.553 chi-square = 0.553 with df = 3; p-value = 0.093 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-03-29_04:31 b-rank test for bits 1 to 8, p=0.20087 b-rank test for bits 2 to 9, p=0.54361 b-rank test for bits 3 to 10, p=0.81679 b-rank test for bits 4 to 11, p=0.53217 b-rank test for bits 5 to 12, p=0.78333 b-rank test for bits 6 to 13, p=0.77881 b-rank test for bits 7 to 14, p=0.85201 b-rank test for bits 8 to 15, p=0.34241 b-rank test for bits 9 to 16, p=0.23133 b-rank test for bits 10 to 17, p=0.64782 b-rank test for bits 11 to 18, p=0.92183 b-rank test for bits 12 to 19, p=0.45842 b-rank test for bits 13 to 20, p=0.58860 b-rank test for bits 14 to 21, p=0.50257 b-rank test for bits 15 to 22, p=0.87244 b-rank test for bits 16 to 23, p=0.79731 b-rank test for bits 17 to 24, p=0.30740 b-rank test for bits 18 to 25, p=0.79798 b-rank test for bits 19 to 26, p=0.45569 b-rank test for bits 20 to 27, p=0.66440 b-rank test for bits 21 to 28, p=0.81285 b-rank test for bits 22 to 29, p=0.48331 b-rank test for bits 23 to 30, p=0.74404 b-rank test for bits 24 to 31, p=0.77348 b-rank test for bits 25 to 32, p=0.28143 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 = 0.043774 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-03-29_04:31 (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 141966 0.13 0.552669 2 141040 -2.03 0.021120 3 141408 -1.17 0.120733 4 141608 -0.70 0.240703 5 142518 1.42 0.922505 6 141754 -0.36 0.358332 7 141842 -0.16 0.437499 8 141961 0.12 0.548045 9 141869 -0.09 0.462464 10 141841 -0.16 0.436579 11 142207 0.70 0.756626 12 141375 -1.25 0.105936 13 142093 0.43 0.666088 14 141778 -0.31 0.379480 15 141549 -0.84 0.199924 16 141448 -1.08 0.140545 17 141899 -0.02 0.490372 18 142702 1.85 0.967989 19 141922 0.03 0.511808 20 141743 -0.39 0.348778 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-03-29_04:31 Bits used No. missing words z-score p-value 23 to 32 141655 -0.8770 0.190243 22 to 31 142087 0.6127 0.729948 21 to 30 141688 -0.7632 0.222670 20 to 29 141870 -0.1356 0.446061 19 to 28 141601 -1.0632 0.143844 18 to 27 142303 1.3575 0.912686 17 to 26 141798 -0.3839 0.350528 16 to 25 141894 -0.0529 0.478921 15 to 24 141408 -1.7287 0.041929 14 to 23 141876 -0.1149 0.454250 13 to 22 141750 -0.5494 0.291361 12 to 21 141677 -0.8011 0.211526 11 to 20 141991 0.2816 0.610883 10 to 19 142137 0.7851 0.783793 9 to 18 141845 -0.2218 0.412224 8 to 17 141917 0.0264 0.510550 7 to 16 141861 -0.1667 0.433821 6 to 15 141675 -0.8080 0.209535 5 to 14 141714 -0.6736 0.250298 4 to 13 141675 -0.8080 0.209535 3 to 12 141536 -1.2873 0.098987 2 to 11 141753 -0.5391 0.294920 1 to 10 142370 1.5885 0.943915 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-03-29_04:31 Bits used No. missing words z-score p-value 28 to 32 141970 0.2057 0.581472 27 to 31 142124 0.7277 0.766600 26 to 30 141704 -0.6960 0.243204 25 to 29 141794 -0.3909 0.347917 24 to 28 141527 -1.2960 0.097482 23 to 27 141687 -0.7537 0.225526 22 to 26 141521 -1.3164 0.094024 21 to 25 142402 1.6701 0.952547 20 to 24 142161 0.8531 0.803203 19 to 23 142189 0.9480 0.828444 18 to 22 142438 1.7921 0.963442 17 to 21 141730 -0.6079 0.271628 16 to 20 141887 -0.0757 0.469831 15 to 19 141792 -0.3977 0.345415 14 to 18 141915 0.0192 0.507667 13 to 17 141479 -1.4587 0.072318 12 to 16 142503 2.0124 0.977913 11 to 15 141948 0.1311 0.552146 10 to 14 142146 0.8023 0.788802 9 to 13 141938 0.0972 0.538711 8 to 12 141691 -0.7401 0.229619 7 to 11 142113 0.6904 0.755031 6 to 10 141757 -0.5164 0.302797 5 to 9 141919 0.0328 0.513075 4 to 8 142146 0.8023 0.788802 3 to 7 141910 0.0023 0.500906 2 to 6 141821 -0.2994 0.382308 1 to 5 142204 0.9989 0.841074 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-03-29_04:31 Bits used No. missing words z-score p-value 31 to 32 141645 -0.7797 0.217774 30 to 31 140767 -3.3697 0.000376 29 to 30 142349 1.2970 0.902678 28 to 29 142250 1.0049 0.842534 27 to 28 141903 -0.0187 0.492551 26 to 27 142284 1.1052 0.865468 25 to 26 141696 -0.6293 0.264579 24 to 25 142047 0.4061 0.657668 23 to 24 141888 -0.0629 0.474915 22 to 23 142116 0.6096 0.728952 21 to 22 141985 0.2232 0.588316 20 to 21 141767 -0.4199 0.337297 19 to 20 142092 0.5388 0.705005 18 to 19 142290 1.1229 0.869264 17 to 18 141393 -1.5231 0.063867 16 to 17 141867 -0.1249 0.450314 15 to 16 142005 0.2822 0.611110 14 to 15 141883 -0.0777 0.469045 13 to 14 141933 0.0698 0.527833 12 to 13 141576 -0.9833 0.162736 11 to 12 142007 0.2881 0.613370 10 to 11 142470 1.6539 0.950925 9 to 10 142271 1.0669 0.856985 8 to 9 142058 0.4386 0.669508 7 to 8 141724 -0.5467 0.292294 6 to 7 141824 -0.2517 0.400632 5 to 6 141523 -1.1396 0.127223 4 to 5 141654 -0.7532 0.225669 3 to 4 141629 -0.8269 0.204138 2 to 3 142119 0.6185 0.731876 1 to 2 142036 0.3737 0.645671 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-03-29_04:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2557.42 0.812 0.791629 Test results for specific bytes for dh-ranFile-2018-03-29_04:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2496.89 -0.044 0.482459 2 to 9 2513.81 0.195 0.577415 3 to 10 2531.98 0.452 0.674453 4 to 11 2539.01 0.552 0.709400 5 to 12 2569.01 0.976 0.835468 6 to 13 2570.83 1.002 0.841757 7 to 14 2494.57 -0.077 0.469402 8 to 15 2568.18 0.964 0.832518 9 to 16 2588.72 1.255 0.895204 10 to 17 2644.97 2.050 0.979830 11 to 18 2333.31 -2.357 0.009201 12 to 19 2574.86 1.059 0.855135 13 to 20 2468.77 -0.442 0.329381 14 to 21 2416.60 -1.179 0.119115 15 to 22 2497.06 -0.042 0.483445 16 to 23 2495.67 -0.061 0.475614 17 to 24 2532.87 0.465 0.678957 18 to 25 2471.49 -0.403 0.343381 19 to 26 2600.18 1.417 0.921733 20 to 27 2431.66 -0.966 0.166918 21 to 28 2491.35 -0.122 0.451298 22 to 29 2478.36 -0.306 0.379781 23 to 30 2468.08 -0.451 0.325853 24 to 31 2483.67 -0.231 0.408660 25 to 32 2501.83 0.026 0.510345 CDPARK for dh-ranFile-2018-03-29_04:31: 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 3516 -0.3196 0.374623 3526 0.1370 0.554479 3510 -0.5936 0.276387 3523 0.0000 0.500000 3515 -0.3653 0.357445 3505 -0.8219 0.205562 3516 -0.3196 0.374623 3521 -0.0913 0.463617 3490 -1.5068 0.065925 3502 -0.9589 0.168804 Square side=100, avg. no. parked=3512.40 sample std.=10.37 p-value of the KSTEST for those 10 p-values: 0.064916 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-03-29_04:31 0.3755,0.5722,0.0291,0.9450,0.5008,0.4482,0.4022,0.5579,0.4354,0.6250, The KS test for those 10 p-values: 0.413262 The 3DSPHERES test for dh-ranFile-2018-03-29_04:31 sample no r^3 equiv. uni. 1 32.761 0.664467 2 1.400 0.045593 3 19.224 0.473132 4 0.695 0.022894 5 33.111 0.668363 6 6.328 0.190176 7 16.613 0.425222 8 54.699 0.838508 9 6.489 0.194507 10 2.276 0.073070 11 44.343 0.771926 12 52.854 0.828263 13 70.917 0.905946 14 0.638 0.021050 15 142.636 0.991387 16 18.846 0.466448 17 14.681 0.386993 18 17.317 0.438554 19 1.931 0.062353 20 11.058 0.308305 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.359528 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-03-29_04:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 0.1 1.3 -0.3 -0.5 -0.8 -0.1 -1.2 -1.9 0.0 0.4 0.3 -0.8 0.7 -3.1 -1.5 -0.2 1.0 0.1 1.7 0.5 -0.6 0.5 -0.6 1.3 1.7 1.9 1.0 -0.3 0.4 0.5 -0.6 -0.1 0.5 -1.0 0.6 0.5 -0.1 2.5 -0.7 0.1 0.0 0.8 Chi-square with 42 degrees of freedom:46.607815 z-score=0.502754, p-value=0.711456 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-03-29_04:31 Test no p-value 1 0.553733 2 0.375576 3 0.933303 4 0.732867 5 0.274445 6 0.307945 7 0.965686 8 0.426448 9 0.005606 10 0.013972 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.417454 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-03-29_04:31: (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 66725 0.05 66508 0.38 3 25000.00 24946 0.12 25197 1.55 4 6666.67 6650 0.04 6629 0.21 5 1388.89 1408 0.26 1396 0.04 6 238.10 233 0.11 223 0.96 7 34.72 33 0.09 41 1.14 8 4.96 4 0.19 5 0.00 p=0.00940 p=0.36015 Number of rngs required: 689131, p-value: 0.800 RESULTS OF CRAPS TEST for dh-ranFile-2018-03-29_04:31 No. of wins: Observed Expected 98511 98585.9 z-score=-0.335, pvalue=0.36888 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66732 66666.7 0.064 0.064 2 37754 37654.3 0.264 0.328 3 26771 26954.7 1.252 1.580 4 19315 19313.5 0.000 1.580 5 13871 13851.4 0.028 1.608 6 10103 9943.5 2.557 4.165 7 7186 7145.0 0.235 4.400 8 5047 5139.1 1.650 6.050 9 3733 3699.9 0.297 6.346 10 2686 2666.3 0.146 6.492 11 1966 1923.3 0.947 7.439 12 1298 1388.7 5.929 13.368 13 954 1003.7 2.462 15.830 14 726 726.1 0.000 15.830 15 507 525.8 0.675 16.505 16 344 381.2 3.621 20.126 17 291 276.5 0.756 20.882 18 199 200.8 0.017 20.899 19 141 146.0 0.170 21.069 20 99 106.2 0.490 21.559 21 277 287.1 0.356 21.915 Chisq= 21.92 for 20 degrees of freedom, p= 0.65488 SUMMARY of craptest p-value for no. of wins: 0.368884 p-value for throws/game: 0.654881 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-03-29_04:31 No. of wins: Observed Expected 98400 98585.9 z-score=-0.831, pvalue=0.20291 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66562 66666.7 0.164 0.164 2 37978 37654.3 2.782 2.947 3 26818 26954.7 0.694 3.640 4 19420 19313.5 0.588 4.228 5 13806 13851.4 0.149 4.377 6 9823 9943.5 1.461 5.838 7 7048 7145.0 1.318 7.156 8 5132 5139.1 0.010 7.166 9 3647 3699.9 0.755 7.921 10 2662 2666.3 0.007 7.928 11 1918 1923.3 0.015 7.943 12 1449 1388.7 2.615 10.557 13 1056 1003.7 2.724 13.281 14 716 726.1 0.142 13.423 15 562 525.8 2.487 15.910 16 357 381.2 1.530 17.440 17 298 276.5 1.665 19.105 18 202 200.8 0.007 19.112 19 159 146.0 1.160 20.273 20 95 106.2 1.184 21.457 21 292 287.1 0.083 21.540 Chisq= 21.54 for 20 degrees of freedom, p= 0.63402 SUMMARY of craptest p-value for no. of wins: 0.202911 p-value for throws/game: 0.634015 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0004,0.0056,0.0092,0.0094,0.0140,0.0210,0.0211,0.0229,0.0291,0.0419, 0.0438,0.0456,0.0542,0.0624,0.0637,0.0639,0.0649,0.0659,0.0705,0.0723, 0.0731,0.0762,0.0826,0.0929,0.0940,0.0975,0.0990,0.1055,0.1059,0.1191, 0.1207,0.1258,0.1272,0.1405,0.1438,0.1627,0.1669,0.1688,0.1795,0.1902, 0.1902,0.1945,0.1999,0.2009,0.2029,0.2041,0.2056,0.2095,0.2095,0.2115, 0.2178,0.2227,0.2255,0.2257,0.2296,0.2313,0.2407,0.2432,0.2461,0.2503, 0.2646,0.2716,0.2744,0.2764,0.2814,0.2901,0.2914,0.2923,0.2949,0.3028, 0.3074,0.3079,0.3083,0.3259,0.3294,0.3373,0.3424,0.3428,0.3434,0.3454, 0.3479,0.3488,0.3505,0.3574,0.3583,0.3591,0.3595,0.3601,0.3641,0.3689, 0.3746,0.3746,0.3755,0.3756,0.3756,0.3795,0.3798,0.3823,0.3870,0.3873, 0.3917,0.3950,0.4006,0.4010,0.4022,0.4087,0.4122,0.4133,0.4175,0.4175, 0.4252,0.4264,0.4302,0.4338,0.4354,0.4366,0.4375,0.4386,0.4397,0.4461, 0.4482,0.4503,0.4513,0.4542,0.4557,0.4584,0.4625,0.4636,0.4664,0.4690, 0.4694,0.4698,0.4731,0.4749,0.4756,0.4772,0.4789,0.4825,0.4833,0.4834, 0.4904,0.4926,0.5000,0.5008,0.5009,0.5026,0.5067,0.5077,0.5103,0.5106, 0.5118,0.5131,0.5278,0.5322,0.5387,0.5436,0.5454,0.5480,0.5521,0.5527, 0.5537,0.5544,0.5545,0.5577,0.5579,0.5610,0.5620,0.5722,0.5774,0.5815, 0.5883,0.5886,0.6009,0.6093,0.6109,0.6111,0.6134,0.6237,0.6250,0.6300, 0.6340,0.6368,0.6457,0.6478,0.6549,0.6577,0.6602,0.6632,0.6644,0.6645, 0.6661,0.6680,0.6684,0.6695,0.6701,0.6745,0.6790,0.7017,0.7050,0.7094, 0.7115,0.7290,0.7290,0.7299,0.7319,0.7319,0.7329,0.7395,0.7431,0.7440, 0.7473,0.7479,0.7550,0.7566,0.7651,0.7666,0.7719,0.7735,0.7788,0.7808, 0.7833,0.7838,0.7888,0.7888,0.7916,0.7973,0.7980,0.8000,0.8032,0.8129, 0.8168,0.8283,0.8284,0.8325,0.8334,0.8355,0.8385,0.8411,0.8411,0.8418, 0.8425,0.8445,0.8520,0.8551,0.8553,0.8570,0.8638,0.8655,0.8693,0.8724, 0.8952,0.9027,0.9059,0.9127,0.9217,0.9218,0.9225,0.9333,0.9439,0.9450, 0.9509,0.9525,0.9634,0.9657,0.9680,0.9728,0.9779,0.9798,0.9914, Overall p-value after applying KStest on 269 p-values = 0.114583 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.