RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-02-15_09:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.97 23.6611 0.871061 2 to 25 15.78 19.0729 0.675638 3 to 26 15.84 14.6226 0.377357 4 to 27 15.42 30.8074 0.978923 5 to 28 15.75 12.4243 0.226210 6 to 29 15.93 16.9996 0.545607 7 to 30 15.84 11.6175 0.177277 8 to 31 15.62 19.1702 0.681149 9 to 32 15.75 8.8253 0.054416 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.993874 Tough bday spacings test for dh-ranFile-2017-02-15_09:31: 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 36 84 100 77 79 57 30 15 8 2 (O-E)^2/E 0.9 0.0 1.6 0.1 4.4 0.0 0.5 0.0 0.0 0.3 1.0 Birthday Spacings: Sum(O-E)^2/E= 8.714, p= 0.441 RESULTS OF GCD FOR dh-ranFile-2017-02-15_09:31 Euclid's algorithm: p-value, steps to gcd: 0.005873 p-value, dist. of gcd's: 0.098022 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-02-15_09:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.522 0.785 0.257 0.723 0.298 0.982 0.599 0.445 Bits 8 to 15---> 0.069 0.093 0.205 0.279 0.688 0.747 0.960 0.044 Bits 16 to 23---> 0.453 0.898 0.525 0.393 0.147 0.381 0.534 0.248 Bits 24 to 31---> 0.327 0.225 0.703 0.413 0.020 0.736 0.144 0.290 KS test for the above 32 p values: 0.551 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-02-15_09:31, p-values for 5 runs: 0.0441, 0.0398, 0.4612, 0.8285, 0.3864 Rank test for binary matrices (31x31) for dh-ranFile-2017-02-15_09:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 239 211.4 3.598 3.598 r= 29 5099 5134.0 0.239 3.837 r= 30 23220 23103.0 0.592 4.429 r= 31 11442 11551.5 1.038 5.468 chi-square = 5.468 with df = 3; p-value = 0.859 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2017-02-15_09:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 231 211.4 1.814 1.814 r= 30 5167 5134.0 0.212 2.026 r= 31 23062 23103.0 0.073 2.099 r= 32 11540 11551.5 0.011 2.110 chi-square = 2.110 with df = 3; p-value = 0.450 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2017-02-15_09:31 b-rank test for bits 1 to 8, p=0.05522 b-rank test for bits 2 to 9, p=0.46130 b-rank test for bits 3 to 10, p=0.88289 b-rank test for bits 4 to 11, p=0.05554 b-rank test for bits 5 to 12, p=0.47698 b-rank test for bits 6 to 13, p=0.45833 b-rank test for bits 7 to 14, p=0.98712 b-rank test for bits 8 to 15, p=0.58763 b-rank test for bits 9 to 16, p=0.41882 b-rank test for bits 10 to 17, p=0.52961 b-rank test for bits 11 to 18, p=0.86743 b-rank test for bits 12 to 19, p=0.68851 b-rank test for bits 13 to 20, p=0.52932 b-rank test for bits 14 to 21, p=0.89869 b-rank test for bits 15 to 22, p=0.05698 b-rank test for bits 16 to 23, p=0.34629 b-rank test for bits 17 to 24, p=0.13217 b-rank test for bits 18 to 25, p=0.66036 b-rank test for bits 19 to 26, p=0.01503 b-rank test for bits 20 to 27, p=0.32263 b-rank test for bits 21 to 28, p=0.71582 b-rank test for bits 22 to 29, p=0.78645 b-rank test for bits 23 to 30, p=0.35401 b-rank test for bits 24 to 31, p=0.07123 b-rank test for bits 25 to 32, p=0.26494 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 = 0.726629 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-02-15_09:31 (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 142463 1.29 0.902102 2 142392 1.13 0.870284 3 141017 -2.08 0.018540 4 142070 0.38 0.646317 5 141264 -1.51 0.065805 6 141600 -0.72 0.234922 7 142013 0.24 0.595695 8 142757 1.98 0.976178 9 142011 0.24 0.593884 10 141366 -1.27 0.102138 11 141009 -2.10 0.017708 12 141744 -0.39 0.349643 13 141645 -0.62 0.268422 14 141916 0.02 0.506217 15 142191 0.66 0.744765 16 141966 0.13 0.552669 17 141695 -0.50 0.308266 18 141903 -0.01 0.494100 19 141875 -0.08 0.468035 20 140867 -2.44 0.007439 ---------------------------------------------------------------- OPSO test for dh-ranFile-2017-02-15_09:31 Bits used No. missing words z-score p-value 23 to 32 142233 1.1161 0.867811 22 to 31 142226 1.0920 0.862576 21 to 30 141359 -1.8977 0.028868 20 to 29 141952 0.1471 0.558488 19 to 28 142165 0.8816 0.811009 18 to 27 142034 0.4299 0.666365 17 to 26 141974 0.2230 0.588232 16 to 25 142199 0.9989 0.841069 15 to 24 141840 -0.2391 0.405526 14 to 23 141313 -2.0563 0.019876 13 to 22 141504 -1.3977 0.081103 12 to 21 142291 1.3161 0.905930 11 to 20 142196 0.9885 0.838550 10 to 19 141840 -0.2391 0.405526 9 to 18 140956 -3.2873 0.000506 8 to 17 141912 0.0092 0.503673 7 to 16 141852 -0.1977 0.421644 6 to 15 142387 1.6471 0.950235 5 to 14 142064 0.5333 0.703103 4 to 13 141354 -1.9149 0.027751 3 to 12 142104 0.6713 0.748978 2 to 11 142253 1.1851 0.882005 1 to 10 142098 0.6506 0.742343 ----------------------------------------------------------------- OQSO test for dh-ranFile-2017-02-15_09:31 Bits used No. missing words z-score p-value 28 to 32 142220 1.0531 0.853857 27 to 31 141618 -0.9876 0.161684 26 to 30 141890 -0.0655 0.473878 25 to 29 142168 0.8768 0.809715 24 to 28 141812 -0.3299 0.370726 23 to 27 141667 -0.8215 0.205693 22 to 26 142086 0.5989 0.725374 21 to 25 142242 1.1277 0.870276 20 to 24 142222 1.0599 0.855405 19 to 23 142148 0.8091 0.790757 18 to 22 141515 -1.3367 0.090658 17 to 21 141679 -0.7808 0.217466 16 to 20 142344 1.4735 0.929686 15 to 19 141874 -0.1198 0.452336 14 to 18 142019 0.3718 0.644965 13 to 17 141797 -0.3808 0.351683 12 to 16 141749 -0.5435 0.293396 11 to 15 141922 0.0429 0.517129 10 to 14 142090 0.6124 0.729877 9 to 13 142495 1.9853 0.976446 8 to 12 141877 -0.1096 0.456366 7 to 11 141980 0.2396 0.594664 6 to 10 141804 -0.3571 0.360527 5 to 9 141407 -1.7028 0.044301 4 to 8 141528 -1.2926 0.098067 3 to 7 141434 -1.6113 0.053558 2 to 6 141691 -0.7401 0.229619 1 to 5 141732 -0.6011 0.273881 ----------------------------------------------------------------- DNA test for dh-ranFile-2017-02-15_09:31 Bits used No. missing words z-score p-value 31 to 32 141947 0.1111 0.544240 30 to 31 141650 -0.7650 0.222140 29 to 30 141268 -1.8918 0.029257 28 to 29 142017 0.3176 0.624610 27 to 28 141708 -0.5939 0.276292 26 to 27 141679 -0.6794 0.248430 25 to 26 141968 0.1731 0.568701 24 to 25 141952 0.1259 0.550083 23 to 24 142047 0.4061 0.657668 22 to 23 142200 0.8574 0.804397 21 to 22 142402 1.4533 0.926930 20 to 21 142343 1.2793 0.899598 19 to 20 142132 0.6568 0.744359 18 to 19 141564 -1.0187 0.154179 17 to 18 142018 0.3206 0.625728 16 to 17 141985 0.2232 0.588316 15 to 16 142177 0.7896 0.785116 14 to 15 141310 -1.7679 0.038536 13 to 14 142289 1.1200 0.868637 12 to 13 142406 1.4651 0.928554 11 to 12 141976 0.1967 0.577956 10 to 11 142191 0.8309 0.796981 9 to 10 142024 0.3383 0.632416 8 to 9 142507 1.7630 0.961053 7 to 8 141273 -1.8771 0.030254 6 to 7 141763 -0.4317 0.332997 5 to 6 141921 0.0344 0.513731 4 to 5 142502 1.7483 0.959793 3 to 4 142527 1.8220 0.965775 2 to 3 141219 -2.0364 0.020857 1 to 2 141823 -0.2547 0.399493 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2017-02-15_09:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2453.86 -0.652 0.257050 Test results for specific bytes for dh-ranFile-2017-02-15_09:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2522.41 0.317 0.624328 2 to 9 2560.72 0.859 0.804757 3 to 10 2560.12 0.850 0.802403 4 to 11 2496.49 -0.050 0.480205 5 to 12 2442.60 -0.812 0.208477 6 to 13 2462.38 -0.532 0.297335 7 to 14 2457.70 -0.598 0.274846 8 to 15 2505.16 0.073 0.529099 9 to 16 2617.21 1.658 0.951297 10 to 17 2491.70 -0.117 0.453281 11 to 18 2382.21 -1.666 0.047881 12 to 19 2561.36 0.868 0.807256 13 to 20 2621.65 1.720 0.957319 14 to 21 2324.42 -2.483 0.006513 15 to 22 2629.78 1.835 0.966778 16 to 23 2405.14 -1.342 0.089875 17 to 24 2445.93 -0.765 0.222246 18 to 25 2532.31 0.457 0.676148 19 to 26 2629.12 1.826 0.966082 20 to 27 2448.52 -0.728 0.233278 21 to 28 2438.93 -0.864 0.193874 22 to 29 2505.77 0.082 0.532539 23 to 30 2496.09 -0.055 0.477960 24 to 31 2434.83 -0.922 0.178364 25 to 32 2426.61 -1.038 0.149662 CDPARK for dh-ranFile-2017-02-15_09:31: 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 3499 -1.0959 0.136563 3520 -0.1370 0.445521 3515 -0.3653 0.357445 3490 -1.5068 0.065925 3535 0.5479 0.708135 3563 1.8265 0.966111 3536 0.5936 0.723613 3546 1.0502 0.853193 3527 0.1826 0.572463 3518 -0.2283 0.409702 Square side=100, avg. no. parked=3524.90 sample std.=20.46 p-value of the KSTEST for those 10 p-values: 0.995059 Results for the MINIMUM DISTANCE test for dh-ranFile-2017-02-15_09:31 0.8829,0.4834,0.9238,0.1154,0.5864,0.5768,0.4414,0.0315,0.5369,0.3412, The KS test for those 10 p-values: 0.908628 The 3DSPHERES test for dh-ranFile-2017-02-15_09:31 sample no r^3 equiv. uni. 1 4.273 0.132742 2 10.355 0.291906 3 21.708 0.515003 4 44.760 0.775080 5 39.554 0.732455 6 4.161 0.129517 7 19.100 0.470947 8 82.447 0.935959 9 22.220 0.523201 10 67.926 0.896087 11 84.638 0.940470 12 50.276 0.812852 13 32.888 0.665884 14 26.927 0.592445 15 38.929 0.726823 16 29.146 0.621502 17 91.867 0.953217 18 12.591 0.342748 19 19.567 0.479118 20 135.146 0.988945 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.082705 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-02-15_09:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 1.3 0.5 -1.3 -0.1 0.0 0.7 0.6 -0.4 0.1 -0.0 -1.3 1.2 -0.4 -0.9 1.0 -1.5 0.4 -3.4 0.5 1.8 1.2 -0.4 0.8 0.3 0.5 1.0 -2.4 1.5 -0.1 -1.0 0.7 1.4 0.6 0.4 0.3 2.2 1.2 0.8 0.1 0.4 -0.6 0.0 -1.1 Chi-square with 42 degrees of freedom:51.759690 z-score=1.064869, p-value=0.856232 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2017-02-15_09:31 Test no p-value 1 0.666852 2 0.776874 3 0.167596 4 0.307700 5 0.542329 6 0.260584 7 0.315000 8 0.241254 9 0.981361 10 0.000089 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.295849 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-02-15_09:31: (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 66609 0.05 66759 0.13 3 25000.00 25053 0.11 24936 0.16 4 6666.67 6720 0.43 6695 0.12 5 1388.89 1359 0.64 1360 0.60 6 238.10 213 2.65 224 0.83 7 34.72 37 0.15 21 5.42 8 4.96 8 1.86 4 0.19 p=0.56439 p=0.71918 Number of rngs required: 688453, p-value: 0.523 RESULTS OF CRAPS TEST for dh-ranFile-2017-02-15_09:31 No. of wins: Observed Expected 98551 98585.9 z-score=-0.156, pvalue=0.43805 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66625 66666.7 0.026 0.026 2 37562 37654.3 0.226 0.252 3 27232 26954.7 2.852 3.104 4 19191 19313.5 0.777 3.881 5 13812 13851.4 0.112 3.993 6 9857 9943.5 0.753 4.746 7 7152 7145.0 0.007 4.753 8 5121 5139.1 0.064 4.817 9 3763 3699.9 1.077 5.894 10 2718 2666.3 1.003 6.897 11 1909 1923.3 0.107 7.003 12 1389 1388.7 0.000 7.003 13 985 1003.7 0.349 7.352 14 757 726.1 1.311 8.664 15 540 525.8 0.382 9.045 16 369 381.2 0.387 9.433 17 262 276.5 0.764 10.197 18 207 200.8 0.190 10.387 19 156 146.0 0.687 11.074 20 101 106.2 0.256 11.330 21 292 287.1 0.083 11.413 Chisq= 11.41 for 20 degrees of freedom, p= 0.06520 SUMMARY of craptest p-value for no. of wins: 0.438053 p-value for throws/game: 0.065203 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2017-02-15_09:31 No. of wins: Observed Expected 98453 98585.9 z-score=-0.594, pvalue=0.27618 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66741 66666.7 0.083 0.083 2 37654 37654.3 0.000 0.083 3 26948 26954.7 0.002 0.085 4 19306 19313.5 0.003 0.087 5 13830 13851.4 0.033 0.121 6 10020 9943.5 0.588 0.708 7 7084 7145.0 0.521 1.230 8 5066 5139.1 1.039 2.269 9 3728 3699.9 0.214 2.483 10 2636 2666.3 0.344 2.827 11 1920 1923.3 0.006 2.833 12 1427 1388.7 1.054 3.887 13 968 1003.7 1.271 5.158 14 742 726.1 0.346 5.504 15 519 525.8 0.089 5.593 16 388 381.2 0.123 5.716 17 300 276.5 1.990 7.706 18 192 200.8 0.388 8.094 19 130 146.0 1.750 9.845 20 106 106.2 0.000 9.845 21 295 287.1 0.217 10.062 Chisq= 10.06 for 20 degrees of freedom, p= 0.03296 SUMMARY of craptest p-value for no. of wins: 0.276182 p-value for throws/game: 0.032960 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0001,0.0005,0.0059,0.0065,0.0074,0.0150,0.0177,0.0185,0.0198,0.0199, 0.0209,0.0278,0.0289,0.0293,0.0303,0.0315,0.0330,0.0385,0.0398,0.0441, 0.0441,0.0443,0.0479,0.0536,0.0544,0.0552,0.0555,0.0570,0.0652,0.0658, 0.0659,0.0694,0.0712,0.0811,0.0827,0.0899,0.0907,0.0930,0.0980,0.0981, 0.1021,0.1154,0.1295,0.1322,0.1327,0.1366,0.1442,0.1473,0.1497,0.1542, 0.1617,0.1676,0.1773,0.1784,0.1939,0.2052,0.2057,0.2085,0.2175,0.2221, 0.2222,0.2254,0.2262,0.2296,0.2333,0.2349,0.2413,0.2481,0.2484,0.2570, 0.2570,0.2606,0.2649,0.2684,0.2739,0.2748,0.2762,0.2763,0.2785,0.2896, 0.2919,0.2934,0.2958,0.2973,0.2983,0.3077,0.3083,0.3150,0.3226,0.3271, 0.3330,0.3412,0.3427,0.3463,0.3496,0.3517,0.3540,0.3574,0.3605,0.3707, 0.3774,0.3811,0.3864,0.3933,0.3995,0.4055,0.4055,0.4097,0.4132,0.4188, 0.4216,0.4381,0.4405,0.4414,0.4446,0.4455,0.4501,0.4523,0.4528,0.4533, 0.4564,0.4583,0.4612,0.4613,0.4680,0.4709,0.4739,0.4770,0.4780,0.4791, 0.4802,0.4834,0.4941,0.5037,0.5062,0.5137,0.5150,0.5171,0.5221,0.5229, 0.5232,0.5248,0.5291,0.5293,0.5296,0.5325,0.5340,0.5369,0.5423,0.5442, 0.5456,0.5501,0.5510,0.5527,0.5585,0.5644,0.5687,0.5725,0.5768,0.5780, 0.5864,0.5876,0.5882,0.5883,0.5924,0.5939,0.5947,0.5957,0.5986,0.6215, 0.6243,0.6246,0.6257,0.6324,0.6450,0.6463,0.6577,0.6604,0.6659,0.6664, 0.6669,0.6756,0.6761,0.6811,0.6877,0.6885,0.7031,0.7034,0.7081,0.7158, 0.7192,0.7226,0.7236,0.7254,0.7266,0.7268,0.7299,0.7325,0.7357,0.7423, 0.7444,0.7448,0.7473,0.7490,0.7751,0.7769,0.7851,0.7855,0.7865,0.7908, 0.7970,0.8024,0.8044,0.8048,0.8073,0.8097,0.8110,0.8129,0.8285,0.8386, 0.8411,0.8532,0.8539,0.8554,0.8562,0.8594,0.8626,0.8674,0.8678,0.8686, 0.8703,0.8703,0.8711,0.8820,0.8829,0.8829,0.8961,0.8978,0.8987,0.8996, 0.9021,0.9059,0.9086,0.9238,0.9269,0.9286,0.9297,0.9360,0.9405,0.9502, 0.9513,0.9532,0.9573,0.9598,0.9601,0.9611,0.9658,0.9661,0.9661,0.9668, 0.9762,0.9764,0.9789,0.9814,0.9818,0.9871,0.9889,0.9939,0.9951, Overall p-value after applying KStest on 269 p-values = 0.340789 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.