RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-15_01:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.94 9.2705 0.068608 2 to 25 15.93 16.8578 0.535961 3 to 26 15.59 24.4788 0.893002 4 to 27 15.67 12.4160 0.225679 5 to 28 15.93 12.4174 0.225773 6 to 29 15.82 15.5077 0.441036 7 to 30 16.08 18.2131 0.624481 8 to 31 15.98 12.7084 0.244526 9 to 32 15.71 10.0844 0.099967 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.315776 Tough bday spacings test for dh-ranFile-2018-06-15_01:31: 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 12 40 68 91 116 74 44 35 11 7 2 (O-E)^2/E 0.9 0.3 0.4 0.5 3.4 0.2 1.3 0.9 1.0 0.0 1.0 Birthday Spacings: Sum(O-E)^2/E= 9.945, p= 0.555 RESULTS OF GCD FOR dh-ranFile-2018-06-15_01:31 Euclid's algorithm: p-value, steps to gcd: 0.806935 p-value, dist. of gcd's: 0.111840 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-15_01:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.770 0.520 0.468 0.377 0.506 0.713 0.085 0.979 Bits 8 to 15---> 0.676 0.231 0.224 0.353 0.459 0.460 0.901 0.681 Bits 16 to 23---> 0.636 0.680 0.015 0.449 0.311 0.398 0.542 0.658 Bits 24 to 31---> 0.824 0.237 0.497 0.995 0.771 0.514 0.172 0.937 KS test for the above 32 p values: 0.502 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-15_01:31, p-values for 5 runs: 0.1999, 0.5666, 0.8584, 0.5577, 0.0235 Rank test for binary matrices (31x31) for dh-ranFile-2018-06-15_01:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 209 211.4 0.028 0.028 r= 29 5166 5134.0 0.199 0.227 r= 30 23148 23103.0 0.087 0.314 r= 31 11477 11551.5 0.481 0.795 chi-square = 0.795 with df = 3; p-value = 0.149 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-06-15_01:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 208 211.4 0.055 0.055 r= 30 5125 5134.0 0.016 0.071 r= 31 23120 23103.0 0.012 0.084 r= 32 11547 11551.5 0.002 0.085 chi-square = 0.085 with df = 3; p-value = 0.006 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-06-15_01:31 b-rank test for bits 1 to 8, p=0.96647 b-rank test for bits 2 to 9, p=0.70767 b-rank test for bits 3 to 10, p=0.25817 b-rank test for bits 4 to 11, p=0.68235 b-rank test for bits 5 to 12, p=0.06520 b-rank test for bits 6 to 13, p=0.19773 b-rank test for bits 7 to 14, p=0.96470 b-rank test for bits 8 to 15, p=0.77119 b-rank test for bits 9 to 16, p=0.55257 b-rank test for bits 10 to 17, p=0.75413 b-rank test for bits 11 to 18, p=0.48685 b-rank test for bits 12 to 19, p=0.57446 b-rank test for bits 13 to 20, p=0.91362 b-rank test for bits 14 to 21, p=0.70898 b-rank test for bits 15 to 22, p=0.98749 b-rank test for bits 16 to 23, p=0.95058 b-rank test for bits 17 to 24, p=0.51469 b-rank test for bits 18 to 25, p=0.77303 b-rank test for bits 19 to 26, p=0.75024 b-rank test for bits 20 to 27, p=0.62427 b-rank test for bits 21 to 28, p=0.20839 b-rank test for bits 22 to 29, p=0.54850 b-rank test for bits 23 to 30, p=0.98520 b-rank test for bits 24 to 31, p=0.98779 b-rank test for bits 25 to 32, p=0.74074 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 = 0.003030 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-15_01:31 (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 142165 0.60 0.724866 2 141286 -1.46 0.072644 3 141560 -0.82 0.207195 4 142160 0.59 0.720954 5 141949 0.09 0.536924 6 141903 -0.01 0.494100 7 140931 -2.29 0.011132 8 141341 -1.33 0.092110 9 141742 -0.39 0.347914 10 142155 0.57 0.717015 11 141932 0.05 0.521121 12 141526 -0.90 0.185225 13 142077 0.39 0.652379 14 142081 0.40 0.655826 15 141973 0.15 0.559129 16 141665 -0.57 0.284046 17 141990 0.19 0.574750 18 141546 -0.85 0.197968 19 142317 0.95 0.829578 20 141940 0.07 0.528563 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-06-15_01:31 Bits used No. missing words z-score p-value 23 to 32 141881 -0.0977 0.461089 22 to 31 141617 -1.0080 0.156719 21 to 30 141730 -0.6184 0.268163 20 to 29 142038 0.4437 0.671367 19 to 28 141681 -0.7873 0.215540 18 to 27 142007 0.3368 0.631864 17 to 26 141508 -1.3839 0.083195 16 to 25 141680 -0.7908 0.214532 15 to 24 141863 -0.1598 0.436536 14 to 23 142314 1.3954 0.918554 13 to 22 142034 0.4299 0.666365 12 to 21 141988 0.2713 0.606911 11 to 20 142543 2.1851 0.985558 10 to 19 141819 -0.3115 0.377717 9 to 18 141611 -1.0287 0.151805 8 to 17 141838 -0.2460 0.402855 7 to 16 141711 -0.6839 0.247020 6 to 15 141822 -0.3011 0.381655 5 to 14 141670 -0.8253 0.204608 4 to 13 141847 -0.2149 0.414911 3 to 12 141274 -2.1908 0.014233 2 to 11 141500 -1.4115 0.079051 1 to 10 141713 -0.6770 0.249203 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-06-15_01:31 Bits used No. missing words z-score p-value 28 to 32 141889 -0.0689 0.472529 27 to 31 141951 0.1413 0.556166 26 to 30 141455 -1.5401 0.061768 25 to 29 141829 -0.2723 0.392694 24 to 28 142194 0.9650 0.832723 23 to 27 141769 -0.4757 0.317146 22 to 26 141922 0.0429 0.517129 21 to 25 141539 -1.2554 0.104675 20 to 24 141585 -1.0994 0.135792 19 to 23 141885 -0.0825 0.467135 18 to 22 142424 1.7446 0.959477 17 to 21 141889 -0.0689 0.472529 16 to 20 141907 -0.0079 0.496849 15 to 19 141373 -1.8181 0.034527 14 to 18 141847 -0.2113 0.416331 13 to 17 141879 -0.1028 0.459056 12 to 16 142250 1.1548 0.875917 11 to 15 141943 0.1141 0.545435 10 to 14 141665 -0.8282 0.203768 9 to 13 142267 1.2124 0.887328 8 to 12 141863 -0.1571 0.437602 7 to 11 141521 -1.3164 0.094024 6 to 10 141502 -1.3808 0.083673 5 to 9 141999 0.3040 0.619423 4 to 8 142042 0.4497 0.673547 3 to 7 141679 -0.7808 0.217466 2 to 6 141975 0.2226 0.588081 1 to 5 141899 -0.0350 0.486033 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-06-15_01:31 Bits used No. missing words z-score p-value 31 to 32 142059 0.4415 0.670576 30 to 31 142367 1.3501 0.911501 29 to 30 141392 -1.5260 0.063499 28 to 29 141884 -0.0747 0.470219 27 to 28 142261 1.0374 0.850219 26 to 27 142092 0.5388 0.705005 25 to 26 141626 -0.8358 0.201639 24 to 25 141504 -1.1957 0.115914 23 to 24 141900 -0.0275 0.489022 22 to 23 142147 0.7011 0.758377 21 to 22 142692 2.3088 0.989522 20 to 21 142518 1.7955 0.963712 19 to 20 141834 -0.2222 0.412074 18 to 19 141396 -1.5142 0.064982 17 to 18 141975 0.1937 0.576801 16 to 17 142024 0.3383 0.632416 15 to 16 141810 -0.2930 0.384758 14 to 15 142333 1.2498 0.894307 13 to 14 142050 0.4150 0.660913 12 to 13 142185 0.8132 0.791944 11 to 12 141688 -0.6529 0.256913 10 to 11 141747 -0.4788 0.316023 9 to 10 142256 1.0226 0.846758 8 to 9 142032 0.3619 0.641271 7 to 8 141622 -0.8476 0.198336 6 to 7 141643 -0.7856 0.216041 5 to 6 141932 0.0669 0.526659 4 to 5 141998 0.2616 0.603171 3 to 4 141840 -0.2045 0.418976 2 to 3 142757 2.5005 0.993799 1 to 2 141596 -0.9243 0.177671 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-15_01:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2628.00 1.810 0.964864 Test results for specific bytes for dh-ranFile-2018-06-15_01:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2605.72 1.495 0.932563 2 to 9 2476.11 -0.338 0.367746 3 to 10 2549.21 0.696 0.756754 4 to 11 2605.32 1.489 0.931811 5 to 12 2463.07 -0.522 0.300765 6 to 13 2385.68 -1.617 0.052974 7 to 14 2548.96 0.692 0.755658 8 to 15 2511.16 0.158 0.562696 9 to 16 2578.90 1.116 0.867755 10 to 17 2645.73 2.061 0.980345 11 to 18 2513.82 0.195 0.577469 12 to 19 2613.68 1.608 0.946050 13 to 20 2499.24 -0.011 0.495699 14 to 21 2594.10 1.331 0.908367 15 to 22 2503.29 0.047 0.518568 16 to 23 2369.69 -1.843 0.032671 17 to 24 2515.09 0.213 0.584467 18 to 25 2488.62 -0.161 0.436094 19 to 26 2576.43 1.081 0.860132 20 to 27 2585.62 1.211 0.887034 21 to 28 2516.86 0.238 0.594208 22 to 29 2486.10 -0.197 0.422076 23 to 30 2640.42 1.986 0.976477 24 to 31 2397.10 -1.455 0.072808 25 to 32 2477.30 -0.321 0.374107 CDPARK for dh-ranFile-2018-06-15_01:31: 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 3501 -1.0046 0.157553 3524 0.0457 0.518210 3516 -0.3196 0.374623 3486 -1.6895 0.045562 3496 -1.2329 0.108811 3530 0.3196 0.625377 3506 -0.7763 0.218799 3560 1.6895 0.954438 3489 -1.5525 0.060270 3509 -0.6393 0.261324 Square side=100, avg. no. parked=3511.70 sample std.=21.01 p-value of the KSTEST for those 10 p-values: 0.094119 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-15_01:31 0.5980,0.9390,0.6844,0.1047,0.1054,0.4865,0.3684,0.5138,0.5868,0.9468, The KS test for those 10 p-values: 0.819626 The 3DSPHERES test for dh-ranFile-2018-06-15_01:31 sample no r^3 equiv. uni. 1 114.586 0.978062 2 22.694 0.530681 3 10.898 0.304599 4 25.497 0.572545 5 68.228 0.897128 6 38.789 0.725541 7 14.757 0.388545 8 3.718 0.116547 9 15.672 0.406911 10 50.884 0.816612 11 26.994 0.593344 12 9.794 0.278529 13 3.761 0.117826 14 39.444 0.731472 15 70.955 0.906066 16 6.228 0.187461 17 1.936 0.062509 18 5.747 0.174323 19 21.233 0.507255 20 33.802 0.675908 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.999367 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-15_01:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 2.0 0.9 0.1 -1.3 0.7 2.5 -0.4 -0.3 -0.9 0.7 0.8 0.1 -1.9 -1.1 -0.5 0.9 0.0 0.4 0.1 1.2 -1.2 1.6 0.2 -0.9 1.2 0.8 -1.2 0.4 -1.9 -1.1 -0.5 0.7 -0.1 -0.5 0.8 -0.1 -0.5 -1.3 0.1 -0.1 0.9 -1.0 -1.1 Chi-square with 42 degrees of freedom:43.126509 z-score=0.122912, p-value=0.577104 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-06-15_01:31 Test no p-value 1 0.791535 2 0.529533 3 0.154752 4 0.168732 5 0.907970 6 0.149445 7 0.633931 8 0.076787 9 0.164401 10 0.046483 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.118817 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-15_01:31: (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 66587 0.10 66579 0.12 3 25000.00 24933 0.18 25160 1.02 4 6666.67 6793 2.39 6616 0.39 5 1388.89 1401 0.11 1347 1.26 6 238.10 243 0.10 252 0.81 7 34.72 36 0.05 36 0.05 8 4.96 6 0.22 9 3.29 p=0.20899 p=0.67335 Number of rngs required: 688819, p-value: 0.684 RESULTS OF CRAPS TEST for dh-ranFile-2018-06-15_01:31 No. of wins: Observed Expected 98441 98585.9 z-score=-0.648, pvalue=0.25853 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66766 66666.7 0.148 0.148 2 37634 37654.3 0.011 0.159 3 26829 26954.7 0.586 0.745 4 19245 19313.5 0.243 0.988 5 13779 13851.4 0.379 1.367 6 10092 9943.5 2.216 3.583 7 7221 7145.0 0.808 4.391 8 5111 5139.1 0.153 4.544 9 3646 3699.9 0.784 5.329 10 2679 2666.3 0.061 5.389 11 1941 1923.3 0.162 5.552 12 1427 1388.7 1.054 6.606 13 1020 1003.7 0.264 6.870 14 736 726.1 0.134 7.004 15 534 525.8 0.127 7.130 16 365 381.2 0.684 7.815 17 254 276.5 1.837 9.652 18 186 200.8 1.095 10.747 19 149 146.0 0.062 10.809 20 101 106.2 0.256 11.065 21 285 287.1 0.016 11.081 Chisq= 11.08 for 20 degrees of freedom, p= 0.05590 SUMMARY of craptest p-value for no. of wins: 0.258527 p-value for throws/game: 0.055901 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-15_01:31 No. of wins: Observed Expected 98485 98585.9 z-score=-0.451, pvalue=0.32596 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66413 66666.7 0.965 0.965 2 37921 37654.3 1.889 2.854 3 26879 26954.7 0.213 3.067 4 19292 19313.5 0.024 3.091 5 13671 13851.4 2.350 5.441 6 9975 9943.5 0.100 5.540 7 7109 7145.0 0.182 5.722 8 5085 5139.1 0.569 6.291 9 3777 3699.9 1.608 7.899 10 2747 2666.3 2.443 10.341 11 1996 1923.3 2.746 13.087 12 1419 1388.7 0.659 13.747 13 1009 1003.7 0.028 13.774 14 731 726.1 0.033 13.807 15 550 525.8 1.110 14.917 16 381 381.2 0.000 14.917 17 296 276.5 1.369 16.287 18 215 200.8 1.000 17.287 19 149 146.0 0.062 17.349 20 98 106.2 0.635 17.984 21 287 287.1 0.000 17.984 Chisq= 17.98 for 20 degrees of freedom, p= 0.41157 SUMMARY of craptest p-value for no. of wins: 0.325959 p-value for throws/game: 0.411568 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0030,0.0065,0.0111,0.0142,0.0148,0.0235,0.0327,0.0345,0.0456,0.0465, 0.0530,0.0559,0.0603,0.0618,0.0625,0.0635,0.0650,0.0652,0.0686,0.0726, 0.0728,0.0768,0.0791,0.0832,0.0837,0.0855,0.0921,0.0940,0.0941,0.1000, 0.1047,0.1047,0.1054,0.1088,0.1118,0.1159,0.1165,0.1178,0.1188,0.1358, 0.1494,0.1494,0.1518,0.1548,0.1567,0.1576,0.1644,0.1687,0.1718,0.1743, 0.1777,0.1852,0.1875,0.1977,0.1980,0.1983,0.1999,0.2016,0.2038,0.2046, 0.2072,0.2084,0.2090,0.2145,0.2155,0.2160,0.2175,0.2188,0.2243,0.2257, 0.2258,0.2311,0.2367,0.2445,0.2470,0.2492,0.2569,0.2582,0.2585,0.2613, 0.2682,0.2785,0.2840,0.3008,0.3046,0.3113,0.3158,0.3160,0.3171,0.3260, 0.3479,0.3531,0.3677,0.3684,0.3741,0.3746,0.3772,0.3777,0.3817,0.3848, 0.3885,0.3927,0.3985,0.4029,0.4069,0.4116,0.4121,0.4149,0.4163,0.4190, 0.4221,0.4361,0.4365,0.4376,0.4410,0.4486,0.4591,0.4594,0.4598,0.4611, 0.4671,0.4679,0.4702,0.4725,0.4725,0.4860,0.4865,0.4869,0.4890,0.4941, 0.4957,0.4966,0.4968,0.5017,0.5061,0.5073,0.5138,0.5142,0.5147,0.5171, 0.5182,0.5186,0.5196,0.5211,0.5267,0.5286,0.5295,0.5307,0.5360,0.5369, 0.5418,0.5454,0.5485,0.5526,0.5547,0.5562,0.5577,0.5591,0.5627,0.5666, 0.5725,0.5745,0.5748,0.5768,0.5771,0.5775,0.5845,0.5868,0.5881,0.5933, 0.5942,0.5980,0.6032,0.6069,0.6194,0.6243,0.6245,0.6254,0.6319,0.6324, 0.6339,0.6361,0.6413,0.6524,0.6558,0.6580,0.6609,0.6664,0.6706,0.6714, 0.6734,0.6735,0.6757,0.6759,0.6800,0.6811,0.6824,0.6842,0.6844,0.7050, 0.7077,0.7090,0.7126,0.7170,0.7210,0.7249,0.7255,0.7315,0.7407,0.7502, 0.7541,0.7557,0.7568,0.7584,0.7701,0.7712,0.7713,0.7730,0.7915,0.7919, 0.8069,0.8166,0.8196,0.8240,0.8296,0.8327,0.8468,0.8502,0.8584,0.8601, 0.8678,0.8759,0.8870,0.8873,0.8930,0.8943,0.8971,0.9009,0.9061,0.9080, 0.9084,0.9115,0.9136,0.9186,0.9318,0.9326,0.9369,0.9390,0.9461,0.9468, 0.9506,0.9544,0.9595,0.9637,0.9647,0.9649,0.9665,0.9765,0.9781,0.9789, 0.9803,0.9852,0.9856,0.9875,0.9878,0.9895,0.9938,0.9949,0.9994, Overall p-value after applying KStest on 269 p-values = 0.458680 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.