RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-07-30_06:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.64 20.4181 0.746598 2 to 25 15.33 28.6304 0.961910 3 to 26 15.60 20.7421 0.761959 4 to 27 15.79 22.6986 0.840677 5 to 28 15.91 23.7426 0.873400 6 to 29 16.00 7.6355 0.026267 7 to 30 15.89 29.5850 0.970502 8 to 31 15.72 13.9278 0.327794 9 to 32 15.83 14.6085 0.376344 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.102450 Tough bday spacings test for dh-ranFile-2016-07-30_06:31: 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 14 47 68 86 95 72 55 34 16 6 7 (O-E)^2/E 2.6 2.9 0.4 1.4 0.1 0.5 0.2 0.6 0.1 0.1 2.1 Birthday Spacings: Sum(O-E)^2/E= 10.848, p= 0.631 RESULTS OF GCD FOR dh-ranFile-2016-07-30_06:31 Euclid's algorithm: p-value, steps to gcd: 0.401504 p-value, dist. of gcd's: 0.185521 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-07-30_06:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.738 0.427 0.522 0.247 0.677 0.611 0.826 0.848 Bits 8 to 15---> 0.949 0.292 0.694 0.962 0.228 0.114 0.684 0.243 Bits 16 to 23---> 0.357 0.883 0.716 0.874 0.109 0.497 0.269 0.126 Bits 24 to 31---> 0.631 0.961 0.919 0.806 0.426 0.734 0.717 0.698 KS test for the above 32 p values: 0.870 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-07-30_06:31, p-values for 5 runs: 0.4414, 0.5794, 0.6154, 0.8477, 0.6044 Rank test for binary matrices (31x31) for dh-ranFile-2016-07-30_06:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 220 211.4 0.348 0.348 r= 29 5095 5134.0 0.296 0.645 r= 30 23276 23103.0 1.295 1.940 r= 31 11409 11551.5 1.758 3.698 chi-square = 3.698 with df = 3; p-value = 0.704 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-07-30_06:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 241 211.4 4.139 4.139 r= 30 5160 5134.0 0.132 4.271 r= 31 23009 23103.0 0.383 4.654 r= 32 11590 11551.5 0.128 4.782 chi-square = 4.782 with df = 3; p-value = 0.812 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-07-30_06:31 b-rank test for bits 1 to 8, p=0.71653 b-rank test for bits 2 to 9, p=0.62079 b-rank test for bits 3 to 10, p=0.59427 b-rank test for bits 4 to 11, p=0.13372 b-rank test for bits 5 to 12, p=0.53263 b-rank test for bits 6 to 13, p=0.13149 b-rank test for bits 7 to 14, p=0.52912 b-rank test for bits 8 to 15, p=0.67946 b-rank test for bits 9 to 16, p=0.79347 b-rank test for bits 10 to 17, p=0.88872 b-rank test for bits 11 to 18, p=0.65950 b-rank test for bits 12 to 19, p=0.78523 b-rank test for bits 13 to 20, p=0.40333 b-rank test for bits 14 to 21, p=0.39909 b-rank test for bits 15 to 22, p=0.69905 b-rank test for bits 16 to 23, p=0.23351 b-rank test for bits 17 to 24, p=0.86353 b-rank test for bits 18 to 25, p=0.81903 b-rank test for bits 19 to 26, p=0.44317 b-rank test for bits 20 to 27, p=0.82779 b-rank test for bits 21 to 28, p=0.18214 b-rank test for bits 22 to 29, p=0.17951 b-rank test for bits 23 to 30, p=0.88478 b-rank test for bits 24 to 31, p=0.75163 b-rank test for bits 25 to 32, p=0.52675 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 = 0.195646 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-07-30_06:31 (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 141751 -0.37 0.355717 2 141622 -0.67 0.251005 3 142804 2.09 0.981707 4 141880 -0.07 0.472683 5 142231 0.75 0.773844 6 141500 -0.96 0.169441 7 142665 1.77 0.961267 8 142387 1.12 0.867800 9 140771 -2.66 0.003911 10 142730 1.92 0.972410 11 141967 0.13 0.553593 12 141530 -0.89 0.187732 13 142136 0.53 0.701806 14 141301 -1.42 0.077610 15 142352 1.03 0.849496 16 141333 -1.35 0.089060 17 142216 0.72 0.763164 18 141631 -0.65 0.257748 19 141517 -0.92 0.179661 20 141824 -0.20 0.420987 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-07-30_06:31 Bits used No. missing words z-score p-value 23 to 32 142032 0.4230 0.663852 22 to 31 141455 -1.5667 0.058598 21 to 30 141854 -0.1908 0.424344 20 to 29 141773 -0.4701 0.319141 19 to 28 141780 -0.4460 0.327811 18 to 27 141719 -0.6563 0.255812 17 to 26 141681 -0.7873 0.215540 16 to 25 142119 0.7230 0.765160 15 to 24 141588 -1.1080 0.133923 14 to 23 142249 1.1713 0.879256 13 to 22 142459 1.8954 0.970981 12 to 21 141742 -0.5770 0.281970 11 to 20 142464 1.9127 0.972104 10 to 19 141937 0.0954 0.538007 9 to 18 141941 0.1092 0.543481 8 to 17 141694 -0.7425 0.228887 7 to 16 141448 -1.5908 0.055828 6 to 15 141816 -0.3218 0.373792 5 to 14 141784 -0.4322 0.332808 4 to 13 142407 1.7161 0.956928 3 to 12 142448 1.8575 0.968379 2 to 11 142393 1.6678 0.952325 1 to 10 141647 -0.9046 0.182842 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-07-30_06:31 Bits used No. missing words z-score p-value 28 to 32 141764 -0.4926 0.311132 27 to 31 141993 0.2836 0.611652 26 to 30 141913 0.0124 0.504963 25 to 29 141554 -1.2045 0.114197 24 to 28 141554 -1.2045 0.114197 23 to 27 141986 0.2599 0.602529 22 to 26 141350 -1.8960 0.028978 21 to 25 141878 -0.1062 0.457711 20 to 24 141648 -0.8859 0.187845 19 to 23 141934 0.0836 0.533324 18 to 22 142006 0.3277 0.628429 17 to 21 141833 -0.2587 0.397916 16 to 20 141539 -1.2554 0.104675 15 to 19 141882 -0.0926 0.463093 14 to 18 141935 0.0870 0.534671 13 to 17 141998 0.3006 0.618131 12 to 16 141775 -0.4554 0.324427 11 to 15 141866 -0.1469 0.441613 10 to 14 142207 1.0091 0.843525 9 to 13 141950 0.1379 0.554826 8 to 12 141924 0.0497 0.519831 7 to 11 141655 -0.8621 0.194306 6 to 10 141998 0.3006 0.618131 5 to 9 142272 1.2294 0.890537 4 to 8 141859 -0.1706 0.432265 3 to 7 141801 -0.3672 0.356727 2 to 6 142139 0.7785 0.781875 1 to 5 142116 0.7006 0.758216 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-07-30_06:31 Bits used No. missing words z-score p-value 31 to 32 141895 -0.0423 0.483141 30 to 31 141989 0.2350 0.592901 29 to 30 141781 -0.3786 0.352509 28 to 29 141709 -0.5909 0.277279 27 to 28 142254 1.0167 0.845358 26 to 27 141984 0.2203 0.587168 25 to 26 141685 -0.6617 0.254069 24 to 25 141498 -1.2134 0.112496 23 to 24 141488 -1.2429 0.106959 22 to 23 141766 -0.4228 0.336220 21 to 22 142253 1.0138 0.844655 20 to 21 141877 -0.0954 0.462011 19 to 20 141751 -0.4671 0.320232 18 to 19 142067 0.4651 0.679071 17 to 18 141153 -2.2311 0.012839 16 to 17 142561 1.9223 0.972718 15 to 16 141865 -0.1308 0.447980 14 to 15 141235 -1.9892 0.023341 13 to 14 142397 1.4386 0.924862 12 to 13 141866 -0.1278 0.449147 11 to 12 141872 -0.1101 0.456158 10 to 11 141983 0.2173 0.586019 9 to 10 142399 1.4445 0.925694 8 to 9 141536 -1.1013 0.135390 7 to 8 141640 -0.7945 0.213457 6 to 7 141900 -0.0275 0.489022 5 to 6 141973 0.1878 0.574490 4 to 5 141986 0.2262 0.589464 3 to 4 141882 -0.0806 0.467872 2 to 3 141932 0.0669 0.526659 1 to 2 142026 0.3442 0.634637 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-07-30_06:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2572.27 1.022 0.846608 Test results for specific bytes for dh-ranFile-2016-07-30_06:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2580.90 1.144 0.873713 2 to 9 2399.90 -1.416 0.078440 3 to 10 2434.27 -0.930 0.176296 4 to 11 2541.99 0.594 0.723671 5 to 12 2503.71 0.052 0.520900 6 to 13 2436.34 -0.900 0.183993 7 to 14 2525.33 0.358 0.639898 8 to 15 2556.46 0.798 0.787685 9 to 16 2501.27 0.018 0.507182 10 to 17 2420.14 -1.129 0.129358 11 to 18 2424.75 -1.064 0.143625 12 to 19 2326.60 -2.452 0.007098 13 to 20 2504.69 0.066 0.526449 14 to 21 2519.82 0.280 0.610352 15 to 22 2495.14 -0.069 0.472585 16 to 23 2610.26 1.559 0.940543 17 to 24 2452.98 -0.665 0.253021 18 to 25 2414.01 -1.216 0.111970 19 to 26 2581.68 1.155 0.875979 20 to 27 2479.86 -0.285 0.387868 21 to 28 2624.62 1.762 0.960996 22 to 29 2464.80 -0.498 0.309302 23 to 30 2511.97 0.169 0.567223 24 to 31 2448.50 -0.728 0.233202 25 to 32 2475.60 -0.345 0.365031 CDPARK for dh-ranFile-2016-07-30_06:31: 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 3532 0.4110 0.659449 3515 -0.3653 0.357445 3508 -0.6849 0.246694 3511 -0.5479 0.291865 3509 -0.6393 0.261324 3549 1.1872 0.882429 3508 -0.6849 0.246694 3520 -0.1370 0.445521 3506 -0.7763 0.218799 3548 1.1416 0.873180 Square side=100, avg. no. parked=3520.60 sample std.=15.74 p-value of the KSTEST for those 10 p-values: 0.397923 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-07-30_06:31 0.2063,0.3218,0.4305,0.7721,0.2223,0.5263,0.8018,0.9895,0.5316,0.5376, The KS test for those 10 p-values: 0.711818 The 3DSPHERES test for dh-ranFile-2016-07-30_06:31 sample no r^3 equiv. uni. 1 7.819 0.229436 2 26.716 0.589569 3 23.394 0.541507 4 9.719 0.276718 5 3.254 0.102795 6 60.266 0.865861 7 61.417 0.870910 8 1.571 0.051021 9 0.903 0.029661 10 72.183 0.909834 11 17.238 0.437068 12 3.339 0.105327 13 49.061 0.805119 14 21.306 0.508461 15 36.266 0.701462 16 36.570 0.704473 17 3.712 0.116388 18 28.822 0.617389 19 4.424 0.137108 20 30.908 0.643090 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.681964 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-07-30_06:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 2.0 -0.3 1.1 0.5 -2.4 -1.2 -1.1 0.7 2.0 0.7 -0.2 0.5 -1.1 0.6 -0.1 -1.4 0.9 0.0 -0.2 1.2 -0.9 0.2 0.7 -0.8 2.0 -0.3 -0.3 -0.3 -1.0 -1.7 0.3 0.7 -2.3 -0.6 -0.1 2.0 -1.4 -1.7 -1.2 0.4 0.1 0.0 0.8 Chi-square with 42 degrees of freedom:52.404129 z-score=1.135183, p-value=0.869591 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-07-30_06:31 Test no p-value 1 0.347684 2 0.520024 3 0.743748 4 0.006456 5 0.244992 6 0.045982 7 0.611121 8 0.133812 9 0.380865 10 0.767678 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.291228 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-07-30_06:31: (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 66712 0.03 66791 0.23 3 25000.00 24935 0.17 24877 0.61 4 6666.67 6660 0.01 6680 0.03 5 1388.89 1392 0.01 1363 0.48 6 238.10 261 2.20 245 0.20 7 34.72 32 0.21 35 0.00 8 4.96 7 0.84 8 1.86 p=0.25191 p=0.24436 Number of rngs required: 688102, p-value: 0.364 RESULTS OF CRAPS TEST for dh-ranFile-2016-07-30_06:31 No. of wins: Observed Expected 98899 98585.9 z-score= 1.401, pvalue=0.91933 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66819 66666.7 0.348 0.348 2 37788 37654.3 0.475 0.823 3 27007 26954.7 0.101 0.924 4 19032 19313.5 4.102 5.026 5 13922 13851.4 0.360 5.386 6 9911 9943.5 0.107 5.492 7 7089 7145.0 0.439 5.931 8 5103 5139.1 0.253 6.185 9 3728 3699.9 0.214 6.398 10 2693 2666.3 0.267 6.666 11 1915 1923.3 0.036 6.702 12 1433 1388.7 1.411 8.113 13 957 1003.7 2.174 10.287 14 707 726.1 0.505 10.791 15 514 525.8 0.266 11.058 16 400 381.2 0.932 11.990 17 288 276.5 0.475 12.465 18 189 200.8 0.697 13.162 19 135 146.0 0.827 13.988 20 98 106.2 0.635 14.624 21 272 287.1 0.796 15.419 Chisq= 15.42 for 20 degrees of freedom, p= 0.24806 SUMMARY of craptest p-value for no. of wins: 0.919326 p-value for throws/game: 0.248060 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-07-30_06:31 No. of wins: Observed Expected 98467 98585.9 z-score=-0.532, pvalue=0.29750 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66875 66666.7 0.651 0.651 2 37630 37654.3 0.016 0.667 3 26933 26954.7 0.018 0.684 4 19177 19313.5 0.964 1.648 5 13798 13851.4 0.206 1.854 6 10049 9943.5 1.118 2.973 7 7214 7145.0 0.666 3.639 8 5015 5139.1 2.995 6.634 9 3713 3699.9 0.047 6.681 10 2654 2666.3 0.057 6.738 11 1867 1923.3 1.650 8.387 12 1362 1388.7 0.515 8.902 13 953 1003.7 2.562 11.465 14 747 726.1 0.599 12.064 15 534 525.8 0.127 12.191 16 425 381.2 5.045 17.235 17 298 276.5 1.665 18.901 18 199 200.8 0.017 18.917 19 149 146.0 0.062 18.980 20 122 106.2 2.346 21.325 21 286 287.1 0.004 21.330 Chisq= 21.33 for 20 degrees of freedom, p= 0.62205 SUMMARY of craptest p-value for no. of wins: 0.297500 p-value for throws/game: 0.622046 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0039,0.0065,0.0071,0.0128,0.0233,0.0263,0.0290,0.0297,0.0460,0.0510, 0.0558,0.0586,0.0776,0.0784,0.0891,0.1024,0.1028,0.1047,0.1053,0.1070, 0.1087,0.1120,0.1125,0.1142,0.1142,0.1144,0.1164,0.1262,0.1294,0.1315, 0.1337,0.1338,0.1339,0.1354,0.1371,0.1436,0.1694,0.1763,0.1795,0.1797, 0.1821,0.1828,0.1840,0.1855,0.1877,0.1878,0.1943,0.1956,0.2063,0.2135, 0.2155,0.2188,0.2223,0.2278,0.2289,0.2294,0.2332,0.2335,0.2429,0.2444, 0.2450,0.2466,0.2467,0.2467,0.2481,0.2510,0.2519,0.2530,0.2541,0.2558, 0.2577,0.2613,0.2694,0.2767,0.2773,0.2820,0.2912,0.2917,0.2919,0.2975, 0.3093,0.3111,0.3191,0.3202,0.3218,0.3244,0.3278,0.3278,0.3328,0.3362, 0.3477,0.3525,0.3557,0.3566,0.3567,0.3574,0.3645,0.3650,0.3738,0.3763, 0.3809,0.3879,0.3979,0.3979,0.3991,0.4015,0.4033,0.4210,0.4243,0.4261, 0.4270,0.4305,0.4323,0.4371,0.4414,0.4416,0.4432,0.4455,0.4480,0.4491, 0.4562,0.4577,0.4620,0.4631,0.4679,0.4726,0.4727,0.4831,0.4890,0.4969, 0.5050,0.5072,0.5085,0.5198,0.5200,0.5209,0.5217,0.5263,0.5264,0.5267, 0.5267,0.5291,0.5316,0.5326,0.5333,0.5347,0.5376,0.5380,0.5415,0.5435, 0.5536,0.5548,0.5672,0.5745,0.5794,0.5860,0.5872,0.5895,0.5896,0.5929, 0.5943,0.6025,0.6044,0.6104,0.6108,0.6111,0.6117,0.6154,0.6174,0.6181, 0.6181,0.6208,0.6220,0.6284,0.6305,0.6309,0.6346,0.6399,0.6431,0.6594, 0.6595,0.6639,0.6768,0.6791,0.6795,0.6820,0.6839,0.6939,0.6980,0.6991, 0.7015,0.7018,0.7040,0.7045,0.7118,0.7159,0.7165,0.7174,0.7237,0.7335, 0.7385,0.7437,0.7466,0.7516,0.7582,0.7620,0.7632,0.7652,0.7677,0.7721, 0.7738,0.7819,0.7852,0.7877,0.7935,0.8018,0.8051,0.8065,0.8115,0.8190, 0.8256,0.8278,0.8407,0.8435,0.8447,0.8454,0.8466,0.8477,0.8484,0.8495, 0.8635,0.8659,0.8678,0.8695,0.8696,0.8709,0.8732,0.8734,0.8737,0.8739, 0.8760,0.8793,0.8824,0.8827,0.8848,0.8887,0.8905,0.9098,0.9189,0.9193, 0.9249,0.9257,0.9405,0.9494,0.9523,0.9569,0.9610,0.9613,0.9614,0.9617, 0.9619,0.9684,0.9705,0.9710,0.9721,0.9724,0.9727,0.9817,0.9895, Overall p-value after applying KStest on 269 p-values = 0.688062 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.