RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-09-13_00:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.73 23.3115 0.860618 2 to 25 15.68 15.4696 0.438306 3 to 26 15.68 14.1695 0.344932 4 to 27 15.38 26.1879 0.928895 5 to 28 15.94 13.4894 0.297145 6 to 29 15.87 19.2156 0.683704 7 to 30 15.95 20.4087 0.746139 8 to 31 15.75 20.5817 0.754439 9 to 32 15.99 14.1440 0.343120 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.420701 Tough bday spacings test for dh-ranFile-2016-09-13_00:31: 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 25 84 103 91 76 52 33 15 7 2 (O-E)^2/E 0.9 3.7 1.6 0.3 0.5 0.1 0.0 0.4 0.0 0.0 1.0 Birthday Spacings: Sum(O-E)^2/E= 8.378, p= 0.408 RESULTS OF GCD FOR dh-ranFile-2016-09-13_00:31 Euclid's algorithm: p-value, steps to gcd: 0.197241 p-value, dist. of gcd's: 0.928439 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-09-13_00:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.342 0.519 0.465 0.756 0.162 0.010 0.714 0.581 Bits 8 to 15---> 0.171 0.398 0.959 0.403 0.585 0.999 0.923 0.015 Bits 16 to 23---> 0.370 0.915 0.982 0.445 0.611 0.785 0.289 0.160 Bits 24 to 31---> 0.641 0.489 0.089 0.677 0.386 0.069 0.996 0.847 KS test for the above 32 p values: 0.462 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-09-13_00:31, p-values for 5 runs: 0.4172, 0.2818, 0.3510, 0.0831, 0.3577 Rank test for binary matrices (31x31) for dh-ranFile-2016-09-13_00:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 227 211.4 1.148 1.148 r= 29 5146 5134.0 0.028 1.176 r= 30 23268 23103.0 1.178 2.354 r= 31 11359 11551.5 3.209 5.563 chi-square = 5.563 with df = 3; p-value = 0.865 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-09-13_00:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 222 211.4 0.530 0.530 r= 30 5153 5134.0 0.070 0.600 r= 31 23154 23103.0 0.112 0.712 r= 32 11471 11551.5 0.561 1.274 chi-square = 1.274 with df = 3; p-value = 0.265 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-09-13_00:31 b-rank test for bits 1 to 8, p=0.14886 b-rank test for bits 2 to 9, p=0.35942 b-rank test for bits 3 to 10, p=0.18225 b-rank test for bits 4 to 11, p=0.25924 b-rank test for bits 5 to 12, p=0.72272 b-rank test for bits 6 to 13, p=0.66770 b-rank test for bits 7 to 14, p=0.07374 b-rank test for bits 8 to 15, p=0.11845 b-rank test for bits 9 to 16, p=0.51646 b-rank test for bits 10 to 17, p=0.40236 b-rank test for bits 11 to 18, p=0.87016 b-rank test for bits 12 to 19, p=0.88644 b-rank test for bits 13 to 20, p=0.11049 b-rank test for bits 14 to 21, p=0.12249 b-rank test for bits 15 to 22, p=0.39040 b-rank test for bits 16 to 23, p=0.56205 b-rank test for bits 17 to 24, p=0.67760 b-rank test for bits 18 to 25, p=0.70940 b-rank test for bits 19 to 26, p=0.40242 b-rank test for bits 20 to 27, p=0.49333 b-rank test for bits 21 to 28, p=0.02888 b-rank test for bits 22 to 29, p=0.25911 b-rank test for bits 23 to 30, p=0.48455 b-rank test for bits 24 to 31, p=0.22641 b-rank test for bits 25 to 32, p=0.65314 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 = 0.204232 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-09-13_00:31 (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 142115 0.48 0.684577 2 141814 -0.22 0.411871 3 141532 -0.88 0.188993 4 142762 1.99 0.976827 5 141943 0.08 0.531352 6 141777 -0.31 0.378591 7 141855 -0.13 0.449494 8 141666 -0.57 0.284838 9 142194 0.67 0.747012 10 141989 0.19 0.573834 11 142858 2.22 0.986672 12 142331 0.99 0.837740 13 142188 0.65 0.742508 14 141859 -0.12 0.453195 15 140905 -2.35 0.009474 16 141602 -0.72 0.236360 17 141033 -2.05 0.020305 18 142223 0.73 0.768182 19 142412 1.17 0.879895 20 142547 1.49 0.931873 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-09-13_00:31 Bits used No. missing words z-score p-value 23 to 32 141571 -1.1667 0.121675 22 to 31 141913 0.0127 0.505049 21 to 30 142292 1.3196 0.906508 20 to 29 142326 1.4368 0.924612 19 to 28 142315 1.3989 0.919073 18 to 27 142299 1.3437 0.910476 17 to 26 141954 0.1540 0.561209 16 to 25 142295 1.3299 0.908224 15 to 24 141649 -0.8977 0.184676 14 to 23 141711 -0.6839 0.247020 13 to 22 142034 0.4299 0.666365 12 to 21 141918 0.0299 0.511925 11 to 20 142322 1.4230 0.922632 10 to 19 142480 1.9678 0.975456 9 to 18 142099 0.6540 0.743455 8 to 17 142312 1.3885 0.917510 7 to 16 141844 -0.2253 0.410882 6 to 15 142162 0.8713 0.808198 5 to 14 142028 0.4092 0.658806 4 to 13 142087 0.6127 0.729948 3 to 12 142022 0.3885 0.651183 2 to 11 142080 0.5885 0.721907 1 to 10 141944 0.1196 0.547581 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-09-13_00:31 Bits used No. missing words z-score p-value 28 to 32 141622 -0.9740 0.165028 27 to 31 141658 -0.8520 0.197116 26 to 30 142199 0.9819 0.836933 25 to 29 141805 -0.3537 0.361797 24 to 28 142169 0.8802 0.810635 23 to 27 141590 -1.0825 0.139521 22 to 26 142234 1.1006 0.864459 21 to 25 141695 -0.7265 0.233753 20 to 24 141698 -0.7164 0.236881 19 to 23 142226 1.0735 0.858467 18 to 22 141914 0.0158 0.506315 17 to 21 142077 0.5684 0.715109 16 to 20 142348 1.4870 0.931495 15 to 19 142340 1.4599 0.927841 14 to 18 142167 0.8735 0.808793 13 to 17 141603 -1.0384 0.149540 12 to 16 141568 -1.1571 0.123626 11 to 15 141681 -0.7740 0.219465 10 to 14 142286 1.2768 0.899172 9 to 13 141558 -1.1909 0.116837 8 to 12 142162 0.8565 0.804142 7 to 11 141936 0.0904 0.536018 6 to 10 141640 -0.9130 0.180626 5 to 9 141844 -0.2215 0.412368 4 to 8 141920 0.0362 0.514426 3 to 7 141828 -0.2757 0.391391 2 to 6 142307 1.3480 0.911176 1 to 5 142443 1.8091 0.964778 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-09-13_00:31 Bits used No. missing words z-score p-value 31 to 32 141815 -0.2783 0.390407 30 to 31 141843 -0.1957 0.422437 29 to 30 141783 -0.3727 0.354703 28 to 29 141402 -1.4965 0.067255 27 to 28 142245 0.9902 0.838956 26 to 27 141901 -0.0246 0.490198 25 to 26 141071 -2.4729 0.006700 24 to 25 141621 -0.8505 0.197515 23 to 24 141605 -0.8977 0.184665 22 to 23 141640 -0.7945 0.213457 21 to 22 142194 0.8397 0.799471 20 to 21 141675 -0.6912 0.244708 19 to 20 141540 -1.0895 0.137974 18 to 19 142402 1.4533 0.926930 17 to 18 141734 -0.5172 0.302509 16 to 17 142236 0.9636 0.832384 15 to 16 141729 -0.5319 0.297381 14 to 15 141442 -1.3786 0.084016 13 to 14 141440 -1.3845 0.083110 12 to 13 141919 0.0285 0.511378 11 to 12 140994 -2.7001 0.003466 10 to 11 141465 -1.3107 0.094978 9 to 10 141613 -0.8741 0.191024 8 to 9 142309 1.1790 0.880794 7 to 8 142343 1.2793 0.899598 6 to 7 142259 1.0315 0.848841 5 to 6 142251 1.0079 0.843243 4 to 5 142238 0.9695 0.833859 3 to 4 141809 -0.2960 0.383631 2 to 3 141795 -0.3373 0.367962 1 to 2 142001 0.2704 0.606579 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-09-13_00:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2527.15 0.384 0.649486 Test results for specific bytes for dh-ranFile-2016-09-13_00:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2491.57 -0.119 0.452570 2 to 9 2527.33 0.387 0.650460 3 to 10 2520.49 0.290 0.613999 4 to 11 2576.86 1.087 0.861474 5 to 12 2388.85 -1.572 0.057987 6 to 13 2484.12 -0.225 0.411132 7 to 14 2421.61 -1.109 0.133789 8 to 15 2482.91 -0.242 0.404506 9 to 16 2486.89 -0.185 0.426451 10 to 17 2535.06 0.496 0.689968 11 to 18 2611.24 1.573 0.942165 12 to 19 2535.11 0.497 0.690256 13 to 20 2450.36 -0.702 0.241335 14 to 21 2559.68 0.844 0.800661 15 to 22 2443.18 -0.804 0.210833 16 to 23 2514.89 0.211 0.583381 17 to 24 2508.18 0.116 0.546060 18 to 25 2494.42 -0.079 0.468534 19 to 26 2469.57 -0.430 0.333476 20 to 27 2485.63 -0.203 0.419488 21 to 28 2412.94 -1.231 0.109114 22 to 29 2403.54 -1.364 0.086252 23 to 30 2486.93 -0.185 0.426693 24 to 31 2568.85 0.974 0.834908 25 to 32 2623.75 1.750 0.959945 CDPARK for dh-ranFile-2016-09-13_00:31: 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 3498 -1.1416 0.126820 3531 0.3653 0.642555 3531 0.3653 0.642555 3493 -1.3699 0.085365 3510 -0.5936 0.276387 3517 -0.2740 0.392053 3544 0.9589 0.831196 3503 -0.9132 0.180558 3544 0.9589 0.831196 3493 -1.3699 0.085365 Square side=100, avg. no. parked=3516.40 sample std.=18.99 p-value of the KSTEST for those 10 p-values: 0.453093 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-09-13_00:31 0.4612,0.4962,0.2796,0.7476,0.8555,0.8858,0.7897,0.2990,0.3265,0.2380, The KS test for those 10 p-values: 0.679598 The 3DSPHERES test for dh-ranFile-2016-09-13_00:31 sample no r^3 equiv. uni. 1 23.534 0.543641 2 4.801 0.147879 3 9.510 0.271672 4 44.310 0.771677 5 9.369 0.268241 6 24.717 0.561281 7 46.739 0.789437 8 9.603 0.273928 9 8.486 0.246368 10 69.520 0.901463 11 8.778 0.253681 12 13.923 0.371309 13 4.545 0.140593 14 53.122 0.829792 15 19.819 0.483481 16 40.497 0.740736 17 19.359 0.475492 18 5.076 0.155659 19 58.966 0.859918 20 2.656 0.084713 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.600921 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-09-13_00:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.5 0.1 -0.8 1.9 0.5 1.1 -1.1 -0.3 1.1 1.0 0.2 -0.3 0.3 0.4 -0.4 -0.6 -0.4 0.9 0.1 0.1 0.6 -0.6 0.7 -0.1 0.7 -2.0 -0.0 -2.2 -2.0 -1.9 1.0 0.5 0.7 0.3 0.8 1.0 -0.7 1.7 -1.3 -0.6 -1.0 -1.1 Chi-square with 42 degrees of freedom:40.822744 z-score=-0.128449, p-value=0.477401 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-09-13_00:31 Test no p-value 1 0.007870 2 0.001054 3 0.328339 4 0.537193 5 0.526651 6 0.620548 7 0.229521 8 0.768085 9 0.001274 10 0.937073 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.023091 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-09-13_00:31: (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 66470 0.58 66795 0.25 3 25000.00 25208 1.73 24958 0.07 4 6666.67 6649 0.05 6567 1.49 5 1388.89 1403 0.14 1366 0.38 6 238.10 225 0.72 276 6.03 7 34.72 41 1.14 29 0.94 8 4.96 3 0.77 8 1.86 p=0.47295 p=0.91239 Number of rngs required: 688322, p-value: 0.463 RESULTS OF CRAPS TEST for dh-ranFile-2016-09-13_00:31 No. of wins: Observed Expected 98469 98585.9 z-score=-0.523, pvalue=0.30061 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66394 66666.7 1.115 1.115 2 37629 37654.3 0.017 1.132 3 26839 26954.7 0.497 1.629 4 19335 19313.5 0.024 1.653 5 13943 13851.4 0.605 2.259 6 10069 9943.5 1.583 3.842 7 7127 7145.0 0.045 3.887 8 5288 5139.1 4.316 8.203 9 3659 3699.9 0.451 8.654 10 2665 2666.3 0.001 8.655 11 1953 1923.3 0.458 9.113 12 1418 1388.7 0.616 9.729 13 1078 1003.7 5.498 15.227 14 728 726.1 0.005 15.232 15 534 525.8 0.127 15.358 16 381 381.2 0.000 15.358 17 270 276.5 0.155 15.513 18 176 200.8 3.070 18.583 19 125 146.0 3.016 21.599 20 108 106.2 0.030 21.629 21 281 287.1 0.130 21.760 Chisq= 21.76 for 20 degrees of freedom, p= 0.64630 SUMMARY of craptest p-value for no. of wins: 0.300606 p-value for throws/game: 0.646300 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-09-13_00:31 No. of wins: Observed Expected 98135 98585.9 z-score=-2.017, pvalue=0.02187 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66639 66666.7 0.011 0.011 2 37690 37654.3 0.034 0.045 3 26903 26954.7 0.099 0.145 4 19459 19313.5 1.097 1.241 5 13890 13851.4 0.107 1.349 6 9857 9943.5 0.753 2.102 7 7161 7145.0 0.036 2.138 8 5147 5139.1 0.012 2.150 9 3688 3699.9 0.038 2.188 10 2667 2666.3 0.000 2.188 11 1859 1923.3 2.152 4.340 12 1392 1388.7 0.008 4.347 13 1028 1003.7 0.588 4.935 14 693 726.1 1.513 6.447 15 556 525.8 1.730 8.178 16 382 381.2 0.002 8.180 17 263 276.5 0.663 8.843 18 197 200.8 0.073 8.916 19 144 146.0 0.027 8.943 20 102 106.2 0.167 9.110 21 283 287.1 0.059 9.169 Chisq= 9.17 for 20 degrees of freedom, p= 0.01913 SUMMARY of craptest p-value for no. of wins: 0.021874 p-value for throws/game: 0.019132 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0011,0.0013,0.0035,0.0067,0.0079,0.0095,0.0101,0.0149,0.0191,0.0203, 0.0219,0.0231,0.0289,0.0580,0.0673,0.0694,0.0737,0.0831,0.0831,0.0840, 0.0847,0.0854,0.0854,0.0863,0.0889,0.0950,0.1091,0.1105,0.1168,0.1185, 0.1217,0.1225,0.1236,0.1268,0.1338,0.1380,0.1395,0.1406,0.1479,0.1489, 0.1495,0.1557,0.1600,0.1623,0.1650,0.1712,0.1806,0.1806,0.1822,0.1847, 0.1847,0.1890,0.1910,0.1971,0.1972,0.1975,0.2042,0.2108,0.2135,0.2195, 0.2264,0.2295,0.2338,0.2364,0.2369,0.2380,0.2413,0.2447,0.2464,0.2470, 0.2537,0.2591,0.2592,0.2646,0.2682,0.2717,0.2739,0.2764,0.2796,0.2818, 0.2848,0.2893,0.2971,0.2974,0.2990,0.3006,0.3025,0.3265,0.3283,0.3335, 0.3417,0.3431,0.3449,0.3510,0.3547,0.3577,0.3594,0.3618,0.3680,0.3704, 0.3713,0.3786,0.3836,0.3864,0.3904,0.3904,0.3914,0.3921,0.3979,0.4024, 0.4024,0.4034,0.4045,0.4081,0.4109,0.4111,0.4119,0.4124,0.4172,0.4195, 0.4207,0.4224,0.4265,0.4267,0.4383,0.4452,0.4495,0.4526,0.4531,0.4532, 0.4612,0.4625,0.4629,0.4653,0.4685,0.4729,0.4755,0.4774,0.4835,0.4845, 0.4893,0.4902,0.4933,0.4962,0.5050,0.5063,0.5114,0.5119,0.5144,0.5165, 0.5188,0.5267,0.5314,0.5360,0.5372,0.5436,0.5461,0.5476,0.5612,0.5613, 0.5621,0.5738,0.5812,0.5834,0.5852,0.6009,0.6066,0.6113,0.6140,0.6205, 0.6410,0.6426,0.6426,0.6463,0.6495,0.6505,0.6512,0.6531,0.6588,0.6664, 0.6677,0.6768,0.6776,0.6796,0.6837,0.6846,0.6900,0.6903,0.7094,0.7138, 0.7151,0.7219,0.7227,0.7299,0.7407,0.7425,0.7435,0.7461,0.7470,0.7476, 0.7544,0.7565,0.7681,0.7682,0.7717,0.7854,0.7894,0.7897,0.7995,0.8007, 0.8041,0.8082,0.8088,0.8106,0.8298,0.8312,0.8312,0.8324,0.8339,0.8349, 0.8369,0.8377,0.8390,0.8432,0.8472,0.8488,0.8555,0.8585,0.8599,0.8606, 0.8615,0.8645,0.8651,0.8702,0.8799,0.8808,0.8858,0.8864,0.8992,0.8996, 0.9015,0.9065,0.9082,0.9105,0.9112,0.9124,0.9146,0.9175,0.9191,0.9226, 0.9226,0.9246,0.9269,0.9278,0.9284,0.9289,0.9315,0.9319,0.9371,0.9422, 0.9590,0.9599,0.9648,0.9755,0.9768,0.9818,0.9867,0.9960,0.9987, Overall p-value after applying KStest on 269 p-values = 0.726281 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.