RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-10-17_23:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.78 14.8197 0.391532 2 to 25 15.60 28.7615 0.963210 3 to 26 15.82 11.0260 0.144790 4 to 27 15.80 8.5527 0.046741 5 to 28 15.66 23.2860 0.859829 6 to 29 15.83 16.7697 0.529926 7 to 30 15.84 19.5442 0.701795 8 to 31 15.65 11.3515 0.162280 9 to 32 15.75 12.1163 0.206958 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.812311 Tough bday spacings test for dh-ranFile-2016-10-17_23:31: 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 8 41 68 93 102 82 60 28 10 4 4 (O-E)^2/E 0.1 0.5 0.4 0.2 0.2 0.2 1.2 0.1 1.6 1.0 0.0 Birthday Spacings: Sum(O-E)^2/E= 5.593, p= 0.152 RESULTS OF GCD FOR dh-ranFile-2016-10-17_23:31 Euclid's algorithm: p-value, steps to gcd: 0.905930 p-value, dist. of gcd's: 0.583820 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-10-17_23:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.878 0.567 0.222 0.890 0.943 0.522 0.090 0.931 Bits 8 to 15---> 0.451 0.539 0.560 0.591 0.386 0.682 0.219 0.178 Bits 16 to 23---> 0.644 0.257 0.302 0.467 0.347 0.818 0.248 0.781 Bits 24 to 31---> 0.143 0.917 0.433 0.692 0.749 0.042 0.419 0.405 KS test for the above 32 p values: 0.119 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-10-17_23:31, p-values for 5 runs: 0.8393, 0.9521, 0.8656, 0.4531, 0.2619 Rank test for binary matrices (31x31) for dh-ranFile-2016-10-17_23:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 223 211.4 0.634 0.634 r= 29 5185 5134.0 0.506 1.141 r= 30 23002 23103.0 0.442 1.583 r= 31 11590 11551.5 0.128 1.711 chi-square = 1.711 with df = 3; p-value = 0.366 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-10-17_23:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 226 211.4 1.006 1.006 r= 30 5118 5134.0 0.050 1.056 r= 31 23062 23103.0 0.073 1.129 r= 32 11594 11551.5 0.156 1.285 chi-square = 1.285 with df = 3; p-value = 0.267 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-10-17_23:31 b-rank test for bits 1 to 8, p=0.30760 b-rank test for bits 2 to 9, p=0.02652 b-rank test for bits 3 to 10, p=0.23667 b-rank test for bits 4 to 11, p=0.15621 b-rank test for bits 5 to 12, p=0.32921 b-rank test for bits 6 to 13, p=0.95911 b-rank test for bits 7 to 14, p=0.50307 b-rank test for bits 8 to 15, p=0.13898 b-rank test for bits 9 to 16, p=0.31349 b-rank test for bits 10 to 17, p=0.88706 b-rank test for bits 11 to 18, p=0.93114 b-rank test for bits 12 to 19, p=0.98140 b-rank test for bits 13 to 20, p=0.93102 b-rank test for bits 14 to 21, p=0.43539 b-rank test for bits 15 to 22, p=0.73157 b-rank test for bits 16 to 23, p=0.95909 b-rank test for bits 17 to 24, p=0.66207 b-rank test for bits 18 to 25, p=0.74785 b-rank test for bits 19 to 26, p=0.98848 b-rank test for bits 20 to 27, p=0.46613 b-rank test for bits 21 to 28, p=0.92363 b-rank test for bits 22 to 29, p=0.63660 b-rank test for bits 23 to 30, p=0.57174 b-rank test for bits 24 to 31, p=0.30676 b-rank test for bits 25 to 32, p=0.07246 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 = 0.162202 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-10-17_23:31 (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 142427 1.21 0.886766 2 141664 -0.57 0.283254 3 141559 -0.82 0.206528 4 141110 -1.87 0.030909 5 141903 -0.01 0.494100 6 141762 -0.34 0.365337 7 142820 2.13 0.983320 8 142635 1.70 0.955009 9 141538 -0.87 0.192808 10 142027 0.27 0.608315 11 141804 -0.25 0.402803 12 141767 -0.33 0.369738 13 141767 -0.33 0.369738 14 141343 -1.32 0.092884 15 142175 0.62 0.732610 16 142124 0.50 0.692013 17 141781 -0.30 0.382151 18 141264 -1.51 0.065805 19 142299 0.91 0.818706 20 140981 -2.17 0.015042 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-10-17_23:31 Bits used No. missing words z-score p-value 23 to 32 142440 1.8299 0.966367 22 to 31 142351 1.5230 0.936121 21 to 30 141672 -0.8184 0.206570 20 to 29 142139 0.7920 0.785810 19 to 28 141940 0.1058 0.542113 18 to 27 142218 1.0644 0.856422 17 to 26 142103 0.6678 0.747878 16 to 25 142012 0.3540 0.638344 15 to 24 142071 0.5575 0.711401 14 to 23 142180 0.9333 0.824679 13 to 22 142238 1.1333 0.871465 12 to 21 142339 1.4816 0.930779 11 to 20 141654 -0.8804 0.189308 10 to 19 141403 -1.7460 0.040408 9 to 18 142873 3.3230 0.999555 8 to 17 141534 -1.2942 0.097791 7 to 16 141958 0.1678 0.566641 6 to 15 142249 1.1713 0.879256 5 to 14 141495 -1.4287 0.076542 4 to 13 141777 -0.4563 0.324083 3 to 12 141787 -0.4218 0.336575 2 to 11 141271 -2.2011 0.013863 1 to 10 142117 0.7161 0.763036 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-10-17_23:31 Bits used No. missing words z-score p-value 28 to 32 141131 -2.6384 0.004165 27 to 31 141820 -0.3028 0.381016 26 to 30 141195 -2.4215 0.007729 25 to 29 141708 -0.6825 0.247470 24 to 28 141958 0.1650 0.565521 23 to 27 141998 0.3006 0.618131 22 to 26 141662 -0.8384 0.200901 21 to 25 141920 0.0362 0.514426 20 to 24 141998 0.3006 0.618131 19 to 23 142064 0.5243 0.699967 18 to 22 141341 -1.9265 0.027018 17 to 21 142388 1.6226 0.947664 16 to 20 141786 -0.4181 0.337949 15 to 19 141950 0.1379 0.554826 14 to 18 141970 0.2057 0.581472 13 to 17 141808 -0.3435 0.365614 12 to 16 141771 -0.4689 0.319565 11 to 15 142061 0.5141 0.696421 10 to 14 142502 2.0091 0.977734 9 to 13 141608 -1.0215 0.153519 8 to 12 142185 0.9345 0.824970 7 to 11 142138 0.7752 0.780875 6 to 10 141512 -1.3469 0.089009 5 to 9 142098 0.6396 0.738770 4 to 8 142312 1.3650 0.913871 3 to 7 141894 -0.0520 0.479278 2 to 6 141512 -1.3469 0.089009 1 to 5 142186 0.9379 0.825843 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-10-17_23:31 Bits used No. missing words z-score p-value 31 to 32 142264 1.0462 0.852271 30 to 31 141704 -0.6057 0.272359 29 to 30 141883 -0.0777 0.469045 28 to 29 142152 0.7158 0.762955 27 to 28 142190 0.8279 0.796146 26 to 27 142108 0.5860 0.721078 25 to 26 142253 1.0138 0.844655 24 to 25 141997 0.2586 0.602033 23 to 24 142099 0.5595 0.712089 22 to 23 141660 -0.7355 0.231022 21 to 22 142519 1.7984 0.963946 20 to 21 141567 -1.0098 0.156290 19 to 20 142251 1.0079 0.843243 18 to 19 141566 -1.0128 0.155584 17 to 18 142436 1.5536 0.939860 16 to 17 142028 0.3501 0.636853 15 to 16 142217 0.9076 0.817950 14 to 15 142193 0.8368 0.798643 13 to 14 141911 0.0049 0.501965 12 to 13 141871 -0.1131 0.454988 11 to 12 141888 -0.0629 0.474915 10 to 11 141697 -0.6263 0.265545 9 to 10 141573 -0.9921 0.160569 8 to 9 142426 1.5241 0.936258 7 to 8 141351 -1.6470 0.049780 6 to 7 142782 2.5742 0.994977 5 to 6 141870 -0.1160 0.453819 4 to 5 141647 -0.7738 0.219514 3 to 4 141691 -0.6440 0.259774 2 to 3 141815 -0.2783 0.390407 1 to 2 141542 -1.0836 0.139278 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-10-17_23:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2488.13 -0.168 0.433363 Test results for specific bytes for dh-ranFile-2016-10-17_23:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2513.88 0.196 0.577790 2 to 9 2533.61 0.475 0.682720 3 to 10 2566.31 0.938 0.825820 4 to 11 2530.86 0.436 0.668716 5 to 12 2473.53 -0.374 0.354060 6 to 13 2500.35 0.005 0.501966 7 to 14 2330.83 -2.392 0.008368 8 to 15 2422.28 -1.099 0.135849 9 to 16 2541.30 0.584 0.720415 10 to 17 2620.68 1.707 0.956058 11 to 18 2429.26 -1.000 0.158562 12 to 19 2599.55 1.408 0.920407 13 to 20 2601.98 1.442 0.925380 14 to 21 2550.41 0.713 0.762035 15 to 22 2523.87 0.338 0.632142 16 to 23 2483.58 -0.232 0.408176 17 to 24 2527.80 0.393 0.652890 18 to 25 2601.56 1.436 0.924530 19 to 26 2310.49 -2.680 0.003680 20 to 27 2550.88 0.720 0.764093 21 to 28 2473.35 -0.377 0.353154 22 to 29 2507.59 0.107 0.542743 23 to 30 2422.84 -1.091 0.137589 24 to 31 2425.77 -1.050 0.146911 25 to 32 2527.54 0.390 0.651548 CDPARK for dh-ranFile-2016-10-17_23:31: 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 3528 0.2283 0.590298 3541 0.8219 0.794438 3527 0.1826 0.572463 3503 -0.9132 0.180558 3561 1.7352 0.958644 3508 -0.6849 0.246694 3504 -0.8676 0.192812 3496 -1.2329 0.108811 3495 -1.2785 0.100530 3556 1.5068 0.934075 Square side=100, avg. no. parked=3521.90 sample std.=23.21 p-value of the KSTEST for those 10 p-values: 0.644418 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-10-17_23:31 0.1133,0.0599,0.6689,0.6941,0.1800,0.4052,0.9448,0.9753,0.2581,0.2065, The KS test for those 10 p-values: 0.606361 The 3DSPHERES test for dh-ranFile-2016-10-17_23:31 sample no r^3 equiv. uni. 1 63.278 0.878675 2 18.922 0.467802 3 6.054 0.182744 4 4.204 0.130756 5 40.548 0.741174 6 4.066 0.126744 7 22.911 0.534061 8 9.280 0.266058 9 24.785 0.562276 10 17.260 0.437479 11 4.575 0.141429 12 28.269 0.610273 13 60.587 0.867287 14 37.254 0.711141 15 2.073 0.066768 16 14.364 0.380478 17 11.454 0.317362 18 90.804 0.951530 19 59.759 0.863572 20 19.871 0.484365 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.978016 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-10-17_23:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 -0.7 -0.1 -0.5 -0.5 -3.0 0.3 -0.4 0.1 1.2 0.2 1.1 -0.3 0.2 -0.9 -0.1 -0.4 -0.6 0.5 -0.2 1.4 -0.1 0.7 -0.5 -1.3 0.1 0.5 1.7 -0.6 -0.3 -2.2 1.6 -1.3 0.1 1.2 0.2 0.3 -0.7 -0.8 -1.8 0.1 0.0 0.8 Chi-square with 42 degrees of freedom:39.202299 z-score=-0.305254, p-value=0.405523 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-10-17_23:31 Test no p-value 1 0.003738 2 0.066834 3 0.220211 4 0.299468 5 0.758036 6 0.037567 7 0.049196 8 0.148440 9 0.074123 10 0.389460 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000630 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-10-17_23:31: (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 66635 0.02 66969 1.37 3 25000.00 24961 0.06 24729 2.94 4 6666.67 6738 0.76 6610 0.48 5 1388.89 1387 0.00 1408 0.26 6 238.10 237 0.01 250 0.60 7 34.72 37 0.15 31 0.40 8 4.96 4 0.19 2 1.77 p=0.02225 p=0.74792 Number of rngs required: 688217, p-value: 0.415 RESULTS OF CRAPS TEST for dh-ranFile-2016-10-17_23:31 No. of wins: Observed Expected 98444 98585.9 z-score=-0.634, pvalue=0.26289 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66696 66666.7 0.013 0.013 2 37582 37654.3 0.139 0.152 3 27007 26954.7 0.101 0.253 4 19331 19313.5 0.016 0.269 5 13850 13851.4 0.000 0.269 6 9964 9943.5 0.042 0.311 7 7164 7145.0 0.050 0.362 8 5136 5139.1 0.002 0.364 9 3685 3699.9 0.060 0.423 10 2660 2666.3 0.015 0.438 11 1885 1923.3 0.764 1.202 12 1397 1388.7 0.049 1.251 13 991 1003.7 0.161 1.412 14 722 726.1 0.024 1.436 15 536 525.8 0.196 1.632 16 355 381.2 1.794 3.426 17 263 276.5 0.663 4.089 18 216 200.8 1.146 5.235 19 156 146.0 0.687 5.922 20 130 106.2 5.326 11.249 21 274 287.1 0.599 11.848 Chisq= 11.85 for 20 degrees of freedom, p= 0.07878 SUMMARY of craptest p-value for no. of wins: 0.262886 p-value for throws/game: 0.078775 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-10-17_23:31 No. of wins: Observed Expected 98591 98585.9 z-score= 0.023, pvalue=0.50917 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66609 66666.7 0.050 0.050 2 37892 37654.3 1.500 1.550 3 26809 26954.7 0.788 2.338 4 19438 19313.5 0.803 3.141 5 13616 13851.4 4.001 7.142 6 10053 9943.5 1.205 8.347 7 7070 7145.0 0.788 9.135 8 5123 5139.1 0.050 9.185 9 3763 3699.9 1.077 10.263 10 2613 2666.3 1.065 11.328 11 1905 1923.3 0.175 11.503 12 1402 1388.7 0.127 11.629 13 996 1003.7 0.059 11.689 14 768 726.1 2.413 14.102 15 535 525.8 0.160 14.261 16 380 381.2 0.003 14.265 17 269 276.5 0.206 14.470 18 201 200.8 0.000 14.471 19 141 146.0 0.170 14.641 20 108 106.2 0.030 14.671 21 309 287.1 1.668 16.339 Chisq= 16.34 for 20 degrees of freedom, p= 0.30462 SUMMARY of craptest p-value for no. of wins: 0.509173 p-value for throws/game: 0.304616 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0006,0.0037,0.0037,0.0042,0.0077,0.0084,0.0139,0.0150,0.0222,0.0265, 0.0270,0.0309,0.0376,0.0404,0.0422,0.0467,0.0492,0.0498,0.0599,0.0658, 0.0668,0.0668,0.0725,0.0741,0.0765,0.0788,0.0890,0.0890,0.0902,0.0929, 0.0978,0.1005,0.1088,0.1133,0.1187,0.1267,0.1308,0.1358,0.1376,0.1390, 0.1393,0.1414,0.1433,0.1448,0.1469,0.1484,0.1518,0.1535,0.1556,0.1562, 0.1563,0.1586,0.1606,0.1622,0.1623,0.1785,0.1800,0.1806,0.1827,0.1893, 0.1928,0.1928,0.2009,0.2065,0.2065,0.2066,0.2070,0.2191,0.2195,0.2202, 0.2221,0.2310,0.2367,0.2467,0.2475,0.2483,0.2570,0.2581,0.2598,0.2619, 0.2629,0.2655,0.2661,0.2673,0.2724,0.2833,0.2995,0.3017,0.3046,0.3068, 0.3076,0.3135,0.3174,0.3196,0.3241,0.3292,0.3366,0.3379,0.3470,0.3532, 0.3541,0.3653,0.3655,0.3656,0.3697,0.3697,0.3805,0.3810,0.3822,0.3858, 0.3895,0.3904,0.3915,0.4028,0.4051,0.4052,0.4055,0.4082,0.4153,0.4188, 0.4332,0.4334,0.4354,0.4375,0.4507,0.4531,0.4538,0.4550,0.4661,0.4671, 0.4678,0.4690,0.4749,0.4793,0.4844,0.4941,0.5020,0.5020,0.5031,0.5092, 0.5144,0.5216,0.5299,0.5341,0.5393,0.5421,0.5427,0.5548,0.5601,0.5623, 0.5655,0.5666,0.5669,0.5717,0.5725,0.5778,0.5815,0.5838,0.5903,0.5912, 0.6020,0.6064,0.6083,0.6103,0.6181,0.6181,0.6321,0.6366,0.6369,0.6383, 0.6439,0.6444,0.6515,0.6529,0.6621,0.6687,0.6689,0.6817,0.6827,0.6919, 0.6920,0.6941,0.6964,0.7000,0.7018,0.7111,0.7114,0.7121,0.7204,0.7211, 0.7316,0.7326,0.7388,0.7412,0.7478,0.7479,0.7479,0.7486,0.7580,0.7620, 0.7630,0.7630,0.7641,0.7809,0.7813,0.7858,0.7944,0.7961,0.7986,0.8123, 0.8180,0.8180,0.8187,0.8247,0.8250,0.8258,0.8258,0.8393,0.8432,0.8447, 0.8523,0.8564,0.8598,0.8636,0.8656,0.8673,0.8715,0.8779,0.8787,0.8793, 0.8868,0.8871,0.8897,0.9059,0.9139,0.9171,0.9204,0.9236,0.9245,0.9254, 0.9308,0.9310,0.9311,0.9311,0.9341,0.9361,0.9363,0.9399,0.9432,0.9448, 0.9477,0.9515,0.9521,0.9550,0.9561,0.9586,0.9591,0.9591,0.9632,0.9639, 0.9664,0.9753,0.9777,0.9780,0.9814,0.9833,0.9885,0.9950,0.9996, Overall p-value after applying KStest on 269 p-values = 0.359039 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.