RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-04-06_07:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.55 17.8277 0.600215 2 to 25 15.66 27.3064 0.946275 3 to 26 15.82 13.8163 0.319937 4 to 27 15.54 16.1084 0.483838 5 to 28 15.97 16.9407 0.541611 6 to 29 15.73 24.6426 0.896999 7 to 30 15.54 16.8947 0.538475 8 to 31 15.84 12.0578 0.203373 9 to 32 15.60 16.5349 0.513721 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.518506 Tough bday spacings test for dh-ranFile-2018-04-06_07:31: 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 40 70 94 103 80 42 30 19 6 6 (O-E)^2/E 0.1 0.3 0.1 0.1 0.3 0.0 2.0 0.0 1.1 0.1 0.9 Birthday Spacings: Sum(O-E)^2/E= 5.078, p= 0.114 RESULTS OF GCD FOR dh-ranFile-2018-04-06_07:31 Euclid's algorithm: p-value, steps to gcd: 0.959333 p-value, dist. of gcd's: 0.206593 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-04-06_07:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.894 0.983 0.948 0.782 0.115 0.538 0.553 0.000 Bits 8 to 15---> 0.719 0.099 0.489 0.207 0.191 0.275 0.954 0.650 Bits 16 to 23---> 0.663 0.394 0.387 0.740 0.433 0.777 0.720 0.469 Bits 24 to 31---> 0.188 0.875 0.948 0.615 0.201 0.453 0.240 0.399 KS test for the above 32 p values: 0.245 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-04-06_07:31, p-values for 5 runs: 0.8678, 0.6583, 0.8128, 0.7361, 0.1236 Rank test for binary matrices (31x31) for dh-ranFile-2018-04-06_07:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 207 211.4 0.092 0.092 r= 29 5169 5134.0 0.238 0.331 r= 30 23033 23103.0 0.212 0.543 r= 31 11591 11551.5 0.135 0.678 chi-square = 0.678 with df = 3; p-value = 0.122 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-04-06_07:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 224 211.4 0.749 0.749 r= 30 5079 5134.0 0.589 1.338 r= 31 23100 23103.0 0.000 1.339 r= 32 11597 11551.5 0.179 1.518 chi-square = 1.518 with df = 3; p-value = 0.322 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-04-06_07:31 b-rank test for bits 1 to 8, p=0.47873 b-rank test for bits 2 to 9, p=0.29692 b-rank test for bits 3 to 10, p=0.25401 b-rank test for bits 4 to 11, p=0.81004 b-rank test for bits 5 to 12, p=0.60918 b-rank test for bits 6 to 13, p=0.41205 b-rank test for bits 7 to 14, p=0.74220 b-rank test for bits 8 to 15, p=0.17674 b-rank test for bits 9 to 16, p=0.20418 b-rank test for bits 10 to 17, p=0.29827 b-rank test for bits 11 to 18, p=0.48060 b-rank test for bits 12 to 19, p=0.67379 b-rank test for bits 13 to 20, p=0.90456 b-rank test for bits 14 to 21, p=0.94818 b-rank test for bits 15 to 22, p=0.91099 b-rank test for bits 16 to 23, p=0.65947 b-rank test for bits 17 to 24, p=0.64669 b-rank test for bits 18 to 25, p=0.48227 b-rank test for bits 19 to 26, p=0.74943 b-rank test for bits 20 to 27, p=0.80553 b-rank test for bits 21 to 28, p=0.90359 b-rank test for bits 22 to 29, p=0.09044 b-rank test for bits 23 to 30, p=0.91155 b-rank test for bits 24 to 31, p=0.55498 b-rank test for bits 25 to 32, p=0.82726 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 = 0.163521 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-04-06_07:31 (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 140828 -2.53 0.005761 2 141994 0.20 0.578410 3 141075 -1.95 0.025626 4 142063 0.36 0.640218 5 141659 -0.58 0.279313 6 141949 0.09 0.536924 7 141598 -0.73 0.233489 8 141997 0.20 0.581150 9 141286 -1.46 0.072644 10 142063 0.36 0.640218 11 142293 0.90 0.814987 12 141631 -0.65 0.257748 13 142043 0.31 0.622599 14 141279 -1.47 0.070411 15 141226 -1.60 0.055181 16 142037 0.30 0.617261 17 141738 -0.40 0.344466 18 141507 -0.94 0.173603 19 142887 2.28 0.988822 20 142587 1.58 0.943328 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-04-06_07:31 Bits used No. missing words z-score p-value 23 to 32 141810 -0.3425 0.365981 22 to 31 141992 0.2851 0.612204 21 to 30 141731 -0.6149 0.269300 20 to 29 141635 -0.9460 0.172083 19 to 28 141748 -0.5563 0.288999 18 to 27 141687 -0.7667 0.221643 17 to 26 142243 1.1506 0.875049 16 to 25 142035 0.4333 0.667618 15 to 24 141847 -0.2149 0.414911 14 to 23 141884 -0.0873 0.465199 13 to 22 142333 1.4609 0.927983 12 to 21 141671 -0.8218 0.205588 11 to 20 141975 0.2264 0.589574 10 to 19 142016 0.3678 0.643499 9 to 18 141898 -0.0391 0.484418 8 to 17 141857 -0.1804 0.428400 7 to 16 141879 -0.1046 0.458352 6 to 15 142352 1.5264 0.936551 5 to 14 141731 -0.6149 0.269300 4 to 13 141792 -0.4046 0.342891 3 to 12 142014 0.3609 0.640925 2 to 11 141472 -1.5080 0.065773 1 to 10 141463 -1.5391 0.061894 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-04-06_07:31 Bits used No. missing words z-score p-value 28 to 32 142117 0.7040 0.759273 27 to 31 142576 2.2599 0.988086 26 to 30 141775 -0.4554 0.324427 25 to 29 142022 0.3819 0.648744 24 to 28 141811 -0.3333 0.369446 23 to 27 142170 0.8836 0.811551 22 to 26 141985 0.2565 0.601221 21 to 25 141749 -0.5435 0.293396 20 to 24 141967 0.1955 0.577496 19 to 23 141778 -0.4452 0.328093 18 to 22 142127 0.7379 0.769702 17 to 21 141710 -0.6757 0.249617 16 to 20 142104 0.6599 0.745341 15 to 19 142153 0.8260 0.795598 14 to 18 142182 0.9243 0.822336 13 to 17 141965 0.1887 0.574841 12 to 16 142038 0.4362 0.668643 11 to 15 141979 0.2362 0.593349 10 to 14 141718 -0.6486 0.258306 9 to 13 141924 0.0497 0.519831 8 to 12 141441 -1.5876 0.056193 7 to 11 141648 -0.8859 0.187845 6 to 10 142075 0.5616 0.712803 5 to 9 142114 0.6938 0.756095 4 to 8 141901 -0.0282 0.488737 3 to 7 142490 1.9684 0.975487 2 to 6 141592 -1.0757 0.141032 1 to 5 142349 1.4904 0.931941 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-04-06_07:31 Bits used No. missing words z-score p-value 31 to 32 142005 0.2822 0.611110 30 to 31 142379 1.3855 0.917044 29 to 30 141831 -0.2311 0.408633 28 to 29 142694 2.3147 0.989684 27 to 28 141836 -0.2163 0.414372 26 to 27 141758 -0.4464 0.327654 25 to 26 142780 2.5683 0.994891 24 to 25 142103 0.5713 0.716101 23 to 24 141633 -0.8151 0.207498 22 to 23 142470 1.6539 0.950925 21 to 22 141631 -0.8210 0.205814 20 to 21 141717 -0.5673 0.285240 19 to 20 141599 -0.9154 0.179984 18 to 19 141708 -0.5939 0.276292 17 to 18 141754 -0.4582 0.323404 16 to 17 142214 0.8987 0.815602 15 to 16 141928 0.0551 0.521960 14 to 15 140874 -3.0541 0.001129 13 to 14 141626 -0.8358 0.201639 12 to 13 142341 1.2734 0.898555 11 to 12 142347 1.2911 0.901659 10 to 11 141379 -1.5644 0.058862 9 to 10 141832 -0.2281 0.409780 8 to 9 141802 -0.3166 0.375771 7 to 8 141768 -0.4169 0.338375 6 to 7 142321 1.2144 0.887696 5 to 6 141967 0.1701 0.567541 4 to 5 141986 0.2262 0.589464 3 to 4 141999 0.2645 0.604308 2 to 3 141864 -0.1337 0.446813 1 to 2 142030 0.3560 0.639064 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-04-06_07:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2457.06 -0.607 0.271860 Test results for specific bytes for dh-ranFile-2018-04-06_07:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2438.34 -0.872 0.191608 2 to 9 2463.77 -0.512 0.304175 3 to 10 2505.80 0.082 0.532693 4 to 11 2469.42 -0.432 0.332702 5 to 12 2541.92 0.593 0.723340 6 to 13 2492.34 -0.108 0.456890 7 to 14 2457.84 -0.596 0.275518 8 to 15 2492.46 -0.107 0.457567 9 to 16 2495.15 -0.069 0.472677 10 to 17 2411.84 -1.247 0.106229 11 to 18 2493.69 -0.089 0.464469 12 to 19 2452.63 -0.670 0.251434 13 to 20 2397.93 -1.444 0.074437 14 to 21 2460.49 -0.559 0.288180 15 to 22 2573.63 1.041 0.851132 16 to 23 2488.02 -0.169 0.432749 17 to 24 2498.61 -0.020 0.492166 18 to 25 2488.46 -0.163 0.435167 19 to 26 2514.96 0.212 0.583765 20 to 27 2434.58 -0.925 0.177440 21 to 28 2535.43 0.501 0.691833 22 to 29 2536.85 0.521 0.698874 23 to 30 2438.91 -0.864 0.193802 24 to 31 2526.31 0.372 0.645081 25 to 32 2571.70 1.014 0.844704 CDPARK for dh-ranFile-2018-04-06_07:31: 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 3518 -0.2283 0.409702 3545 1.0046 0.842447 3510 -0.5936 0.276387 3543 0.9132 0.819442 3497 -1.1872 0.117571 3496 -1.2329 0.108811 3511 -0.5479 0.291865 3480 -1.9635 0.024796 3544 0.9589 0.831196 3520 -0.1370 0.445521 Square side=100, avg. no. parked=3516.40 sample std.=21.19 p-value of the KSTEST for those 10 p-values: 0.496881 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-04-06_07:31 0.1183,0.6840,0.1929,0.2389,0.0366,0.7148,0.0659,0.8272,0.0880,0.8036, The KS test for those 10 p-values: 0.133402 The 3DSPHERES test for dh-ranFile-2018-04-06_07:31 sample no r^3 equiv. uni. 1 29.073 0.620574 2 38.076 0.718945 3 19.119 0.471276 4 30.346 0.636340 5 36.591 0.704679 6 8.013 0.234410 7 3.694 0.115866 8 50.019 0.811245 9 69.960 0.902898 10 10.954 0.305891 11 52.126 0.824043 12 27.711 0.602958 13 50.512 0.814322 14 68.911 0.899445 15 5.184 0.158698 16 23.474 0.542726 17 81.263 0.933381 18 26.520 0.586873 19 73.282 0.913076 20 28.312 0.610828 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.081699 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-04-06_07:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 1.3 -0.3 0.6 -0.7 -0.2 -0.3 1.1 1.1 2.0 0.5 -0.7 -1.1 0.3 0.5 0.7 1.2 -1.5 -1.3 0.4 -1.0 0.3 -0.7 -1.3 2.0 0.1 -0.0 0.0 0.1 -0.2 0.7 0.7 -1.3 -0.7 3.0 0.8 1.1 0.5 -0.1 0.1 2.6 -0.6 0.0 -0.1 Chi-square with 42 degrees of freedom:46.550088 z-score=0.496455, p-value=0.709447 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-04-06_07:31 Test no p-value 1 0.814776 2 0.141023 3 0.402743 4 0.051351 5 0.450427 6 0.114998 7 0.827923 8 0.599134 9 0.147452 10 0.551244 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.511171 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-04-06_07:31: (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 66475 0.55 66869 0.61 3 25000.00 25225 2.02 24796 1.66 4 6666.67 6681 0.03 6727 0.55 5 1388.89 1360 0.60 1321 3.32 6 238.10 216 2.05 240 0.02 7 34.72 35 0.00 44 2.48 8 4.96 7 0.84 2 1.77 p=0.58787 p=0.89141 Number of rngs required: 689208, p-value: 0.824 RESULTS OF CRAPS TEST for dh-ranFile-2018-04-06_07:31 No. of wins: Observed Expected 98530 98585.9 z-score=-0.250, pvalue=0.40136 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66986 66666.7 1.530 1.530 2 37346 37654.3 2.525 4.054 3 26856 26954.7 0.362 4.416 4 19128 19313.5 1.781 6.197 5 14060 13851.4 3.141 9.338 6 10031 9943.5 0.769 10.107 7 6948 7145.0 5.433 15.540 8 5185 5139.1 0.410 15.950 9 3807 3699.9 3.102 19.053 10 2666 2666.3 0.000 19.053 11 1970 1923.3 1.133 20.185 12 1376 1388.7 0.117 20.302 13 949 1003.7 2.983 23.285 14 741 726.1 0.304 23.589 15 549 525.8 1.020 24.609 16 375 381.2 0.099 24.708 17 280 276.5 0.043 24.752 18 190 200.8 0.584 25.336 19 137 146.0 0.553 25.889 20 123 106.2 2.652 28.541 21 297 287.1 0.340 28.882 Chisq= 28.88 for 20 degrees of freedom, p= 0.90988 SUMMARY of craptest p-value for no. of wins: 0.401359 p-value for throws/game: 0.909881 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-04-06_07:31 No. of wins: Observed Expected 98952 98585.9 z-score= 1.638, pvalue=0.94925 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66786 66666.7 0.214 0.214 2 37691 37654.3 0.036 0.249 3 26841 26954.7 0.480 0.729 4 19183 19313.5 0.881 1.610 5 13756 13851.4 0.657 2.268 6 10152 9943.5 4.370 6.638 7 7119 7145.0 0.095 6.733 8 5231 5139.1 1.644 8.377 9 3688 3699.9 0.038 8.415 10 2574 2666.3 3.195 11.610 11 1945 1923.3 0.244 11.854 12 1421 1388.7 0.749 12.604 13 986 1003.7 0.313 12.916 14 737 726.1 0.162 13.079 15 487 525.8 2.868 15.947 16 384 381.2 0.021 15.968 17 265 276.5 0.482 16.450 18 188 200.8 0.820 17.269 19 144 146.0 0.027 17.296 20 128 106.2 4.468 21.765 21 294 287.1 0.165 21.930 Chisq= 21.93 for 20 degrees of freedom, p= 0.65566 SUMMARY of craptest p-value for no. of wins: 0.949247 p-value for throws/game: 0.655661 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0001,0.0011,0.0058,0.0248,0.0256,0.0366,0.0514,0.0552,0.0562,0.0589, 0.0619,0.0658,0.0659,0.0704,0.0726,0.0744,0.0817,0.0880,0.0904,0.0994, 0.1062,0.1088,0.1141,0.1150,0.1151,0.1159,0.1176,0.1183,0.1217,0.1236, 0.1334,0.1410,0.1410,0.1475,0.1587,0.1635,0.1721,0.1736,0.1767,0.1774, 0.1800,0.1877,0.1878,0.1915,0.1916,0.1929,0.1938,0.2010,0.2016,0.2034, 0.2042,0.2056,0.2058,0.2066,0.2068,0.2075,0.2216,0.2335,0.2344,0.2389, 0.2401,0.2450,0.2496,0.2514,0.2540,0.2577,0.2583,0.2693,0.2693,0.2719, 0.2749,0.2755,0.2763,0.2764,0.2793,0.2852,0.2882,0.2890,0.2919,0.2934, 0.2969,0.2983,0.3042,0.3059,0.3199,0.3218,0.3234,0.3244,0.3277,0.3281, 0.3327,0.3384,0.3429,0.3445,0.3660,0.3694,0.3758,0.3871,0.3938,0.3986, 0.4014,0.4027,0.4086,0.4097,0.4098,0.4121,0.4144,0.4149,0.4284,0.4326, 0.4327,0.4352,0.4455,0.4468,0.4504,0.4534,0.4569,0.4576,0.4584,0.4645, 0.4652,0.4690,0.4713,0.4727,0.4787,0.4806,0.4823,0.4838,0.4844,0.4887, 0.4888,0.4922,0.4969,0.5112,0.5137,0.5185,0.5198,0.5220,0.5327,0.5369, 0.5381,0.5385,0.5416,0.5427,0.5512,0.5527,0.5550,0.5675,0.5748,0.5775, 0.5784,0.5812,0.5838,0.5869,0.5879,0.5895,0.5896,0.5933,0.5991,0.6002, 0.6012,0.6030,0.6043,0.6092,0.6108,0.6111,0.6122,0.6153,0.6173,0.6206, 0.6226,0.6363,0.6391,0.6402,0.6402,0.6409,0.6435,0.6451,0.6467,0.6487, 0.6497,0.6557,0.6583,0.6595,0.6630,0.6676,0.6686,0.6738,0.6840,0.6918, 0.6989,0.7047,0.7094,0.7128,0.7148,0.7161,0.7188,0.7189,0.7200,0.7233, 0.7361,0.7399,0.7422,0.7453,0.7494,0.7561,0.7593,0.7697,0.7770,0.7824, 0.7956,0.8036,0.8055,0.8100,0.8112,0.8116,0.8128,0.8143,0.8148,0.8150, 0.8156,0.8194,0.8223,0.8240,0.8243,0.8272,0.8273,0.8279,0.8312,0.8424, 0.8447,0.8511,0.8678,0.8748,0.8750,0.8877,0.8914,0.8935,0.8970,0.8986, 0.8994,0.9017,0.9029,0.9036,0.9046,0.9099,0.9110,0.9115,0.9131,0.9170, 0.9280,0.9319,0.9334,0.9366,0.9433,0.9463,0.9477,0.9478,0.9482,0.9492, 0.9509,0.9539,0.9593,0.9755,0.9834,0.9881,0.9888,0.9897,0.9949, Overall p-value after applying KStest on 269 p-values = 0.672852 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.