RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-08-12_19:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.71 20.5903 0.754847 2 to 25 15.60 24.5944 0.895837 3 to 26 16.12 19.6997 0.710125 4 to 27 16.10 17.9933 0.610737 5 to 28 15.81 15.8295 0.464047 6 to 29 15.69 22.7460 0.842295 7 to 30 15.81 15.5548 0.444414 8 to 31 15.61 20.3308 0.742341 9 to 32 15.85 7.3325 0.021180 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.295482 Tough bday spacings test for dh-ranFile-2016-08-12_19:31: 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 9 38 63 80 105 89 60 24 22 5 5 (O-E)^2/E 0.0 0.1 1.4 3.2 0.5 1.5 1.2 1.1 3.4 0.4 0.2 Birthday Spacings: Sum(O-E)^2/E= 13.075, p= 0.780 RESULTS OF GCD FOR dh-ranFile-2016-08-12_19:31 Euclid's algorithm: p-value, steps to gcd: 0.843592 p-value, dist. of gcd's: 0.411373 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-08-12_19:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.050 0.869 0.266 0.906 0.651 0.483 0.675 0.753 Bits 8 to 15---> 0.710 0.282 0.732 0.696 0.714 0.291 0.563 0.637 Bits 16 to 23---> 0.495 0.661 0.820 0.051 0.779 0.356 0.230 0.222 Bits 24 to 31---> 0.244 0.014 0.660 0.826 0.800 0.904 0.650 0.452 KS test for the above 32 p values: 0.731 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-08-12_19:31, p-values for 5 runs: 0.8025, 0.0912, 0.3274, 0.9686, 0.8367 Rank test for binary matrices (31x31) for dh-ranFile-2016-08-12_19:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 218 211.4 0.205 0.205 r= 29 5111 5134.0 0.103 0.308 r= 30 23113 23103.0 0.004 0.312 r= 31 11558 11551.5 0.004 0.316 chi-square = 0.316 with df = 3; p-value = 0.043 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-08-12_19:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 185 211.4 3.301 3.301 r= 30 5205 5134.0 0.982 4.283 r= 31 23051 23103.0 0.117 4.400 r= 32 11559 11551.5 0.005 4.405 chi-square = 4.405 with df = 3; p-value = 0.779 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-08-12_19:31 b-rank test for bits 1 to 8, p=0.68235 b-rank test for bits 2 to 9, p=0.31695 b-rank test for bits 3 to 10, p=0.43681 b-rank test for bits 4 to 11, p=0.46478 b-rank test for bits 5 to 12, p=0.20981 b-rank test for bits 6 to 13, p=0.04103 b-rank test for bits 7 to 14, p=0.43886 b-rank test for bits 8 to 15, p=0.92522 b-rank test for bits 9 to 16, p=0.84554 b-rank test for bits 10 to 17, p=0.27637 b-rank test for bits 11 to 18, p=0.61883 b-rank test for bits 12 to 19, p=0.18018 b-rank test for bits 13 to 20, p=0.16949 b-rank test for bits 14 to 21, p=0.97849 b-rank test for bits 15 to 22, p=0.27557 b-rank test for bits 16 to 23, p=0.32246 b-rank test for bits 17 to 24, p=0.50013 b-rank test for bits 18 to 25, p=0.49627 b-rank test for bits 19 to 26, p=0.03325 b-rank test for bits 20 to 27, p=0.48086 b-rank test for bits 21 to 28, p=0.96933 b-rank test for bits 22 to 29, p=0.70015 b-rank test for bits 23 to 30, p=0.39337 b-rank test for bits 24 to 31, p=0.03727 b-rank test for bits 25 to 32, p=0.01683 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 = 0.310398 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-08-12_19:31 (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 142567 1.54 0.937806 2 141813 -0.23 0.410962 3 141935 0.06 0.523913 4 142170 0.61 0.728752 5 142441 1.24 0.892922 6 142189 0.65 0.743262 7 142230 0.75 0.773140 8 142313 0.94 0.827199 9 142374 1.09 0.861189 10 142509 1.40 0.919408 11 141397 -1.20 0.115647 12 141564 -0.81 0.209878 13 141884 -0.06 0.476404 14 141457 -1.06 0.145291 15 141735 -0.41 0.341889 16 141531 -0.88 0.188362 17 140954 -2.23 0.012805 18 142428 1.21 0.887214 19 142335 0.99 0.840024 20 142114 0.48 0.683746 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-08-12_19:31 Bits used No. missing words z-score p-value 23 to 32 141745 -0.5667 0.285474 22 to 31 141900 -0.0322 0.487167 21 to 30 141697 -0.7322 0.232032 20 to 29 142153 0.8402 0.799614 19 to 28 142061 0.5230 0.699513 18 to 27 142099 0.6540 0.743455 17 to 26 142164 0.8782 0.810075 16 to 25 142435 1.8127 0.965058 15 to 24 141836 -0.2529 0.400187 14 to 23 142131 0.7644 0.777679 13 to 22 141867 -0.1460 0.441974 12 to 21 141785 -0.4287 0.334062 11 to 20 142173 0.9092 0.818380 10 to 19 142047 0.4747 0.682508 9 to 18 141799 -0.3804 0.351806 8 to 17 142106 0.6782 0.751169 7 to 16 141488 -1.4529 0.073131 6 to 15 142074 0.5678 0.714924 5 to 14 141832 -0.2667 0.394867 4 to 13 141934 0.0851 0.533897 3 to 12 142209 1.0333 0.849279 2 to 11 142171 0.9023 0.816554 1 to 10 142342 1.4920 0.932146 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-08-12_19:31 Bits used No. missing words z-score p-value 28 to 32 142285 1.2735 0.898572 27 to 31 141691 -0.7401 0.229619 26 to 30 141846 -0.2147 0.415009 25 to 29 141743 -0.5638 0.286435 24 to 28 142101 0.6497 0.742066 23 to 27 141890 -0.0655 0.473878 22 to 26 142085 0.5955 0.724243 21 to 25 141874 -0.1198 0.452336 20 to 24 141943 0.1141 0.545435 19 to 23 141748 -0.5469 0.292230 18 to 22 142173 0.8938 0.814285 17 to 21 141409 -1.6960 0.044940 16 to 20 142408 1.6904 0.954525 15 to 19 141988 0.2667 0.605141 14 to 18 141824 -0.2893 0.386193 13 to 17 142000 0.3074 0.620714 12 to 16 142007 0.3311 0.629710 11 to 15 142079 0.5752 0.717406 10 to 14 142134 0.7616 0.776849 9 to 13 141829 -0.2723 0.392694 8 to 12 142099 0.6429 0.739872 7 to 11 141748 -0.5469 0.292230 6 to 10 142071 0.5480 0.708166 5 to 9 141677 -0.7876 0.215477 4 to 8 142047 0.4667 0.679635 3 to 7 141932 0.0768 0.530628 2 to 6 142335 1.4429 0.925483 1 to 5 141577 -1.1265 0.129968 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-08-12_19:31 Bits used No. missing words z-score p-value 31 to 32 142237 0.9666 0.833123 30 to 31 141498 -1.2134 0.112496 29 to 30 141534 -1.1072 0.134111 28 to 29 141310 -1.7679 0.038536 27 to 28 142029 0.3530 0.637959 26 to 27 141548 -1.0659 0.143241 25 to 26 141805 -0.3078 0.379133 24 to 25 141932 0.0669 0.526659 23 to 24 142252 1.0108 0.843950 22 to 23 142255 1.0197 0.846059 21 to 22 142006 0.2852 0.612240 20 to 21 142011 0.2999 0.617878 19 to 20 141331 -1.7060 0.044005 18 to 19 141752 -0.4641 0.321288 17 to 18 141748 -0.4759 0.317073 16 to 17 141706 -0.5998 0.274322 15 to 16 141930 0.0610 0.524310 14 to 15 142285 1.1082 0.866106 13 to 14 141778 -0.3874 0.349229 12 to 13 141924 0.0433 0.517259 11 to 12 141996 0.2557 0.600895 10 to 11 141563 -1.0216 0.153480 9 to 10 142169 0.7660 0.778158 8 to 9 141946 0.1082 0.543070 7 to 8 142037 0.3766 0.646767 6 to 7 141962 0.1554 0.561735 5 to 6 141373 -1.5821 0.056814 4 to 5 141812 -0.2871 0.387014 3 to 4 142045 0.4002 0.655498 2 to 3 141900 -0.0275 0.489022 1 to 2 141979 0.2055 0.581416 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-08-12_19:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2536.05 0.510 0.694895 Test results for specific bytes for dh-ranFile-2016-08-12_19:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2547.58 0.673 0.749485 2 to 9 2593.15 1.317 0.906133 3 to 10 2519.04 0.269 0.606116 4 to 11 2552.93 0.749 0.772928 5 to 12 2584.74 1.198 0.884632 6 to 13 2445.05 -0.777 0.218532 7 to 14 2506.06 0.086 0.534154 8 to 15 2476.66 -0.330 0.370660 9 to 16 2533.40 0.472 0.681666 10 to 17 2577.49 1.096 0.863444 11 to 18 2517.64 0.249 0.598507 12 to 19 2546.20 0.653 0.743246 13 to 20 2634.30 1.899 0.971238 14 to 21 2576.20 1.078 0.859397 15 to 22 2488.52 -0.162 0.435488 16 to 23 2473.37 -0.377 0.353256 17 to 24 2485.39 -0.207 0.418173 18 to 25 2494.06 -0.084 0.466550 19 to 26 2468.38 -0.447 0.327352 20 to 27 2494.52 -0.077 0.469126 21 to 28 2576.60 1.083 0.860665 22 to 29 2566.27 0.937 0.825659 23 to 30 2546.12 0.652 0.742875 24 to 31 2507.40 0.105 0.541670 25 to 32 2540.01 0.566 0.714247 CDPARK for dh-ranFile-2016-08-12_19:31: 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 3508 -0.6849 0.246694 3504 -0.8676 0.192812 3497 -1.1872 0.117571 3529 0.2740 0.607947 3535 0.5479 0.708135 3479 -2.0091 0.022262 3481 -1.9178 0.027568 3491 -1.4612 0.071982 3527 0.1826 0.572463 3533 0.4566 0.676028 Square side=100, avg. no. parked=3508.40 sample std.=20.37 p-value of the KSTEST for those 10 p-values: 0.051646 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-08-12_19:31 0.5521,0.3999,0.8997,0.6065,0.1221,0.7984,0.0232,0.7467,0.9286,0.5829, The KS test for those 10 p-values: 0.698152 The 3DSPHERES test for dh-ranFile-2016-08-12_19:31 sample no r^3 equiv. uni. 1 25.803 0.576882 2 94.697 0.957428 3 8.991 0.258950 4 11.035 0.307757 5 1.984 0.063988 6 5.137 0.157384 7 3.759 0.117763 8 73.340 0.913244 9 12.767 0.346595 10 48.777 0.803266 11 26.251 0.583157 12 17.984 0.450895 13 18.392 0.458315 14 43.334 0.764132 15 13.753 0.367735 16 37.027 0.708942 17 16.847 0.429682 18 22.143 0.521986 19 33.985 0.677883 20 21.107 0.505186 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.862013 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-08-12_19:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 1.3 2.2 -0.4 0.9 0.2 0.9 1.3 0.4 -0.2 -0.3 -0.7 -2.4 1.1 -0.2 0.6 -0.9 0.5 1.3 -1.6 0.9 0.9 0.2 -1.0 0.3 -0.0 -0.3 -0.2 1.3 -0.6 -2.3 0.3 1.6 0.6 -2.1 -0.1 0.1 -0.2 -0.1 -0.4 2.1 0.1 0.0 -1.1 Chi-square with 42 degrees of freedom:46.028307 z-score=0.439524, p-value=0.690923 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-08-12_19:31 Test no p-value 1 0.454546 2 0.647279 3 0.577884 4 0.000925 5 0.273556 6 0.955267 7 0.581289 8 0.681075 9 0.158585 10 0.384091 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.637518 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-08-12_19:31: (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 66541 0.24 66645 0.01 3 25000.00 25105 0.44 24971 0.03 4 6666.67 6605 0.57 6751 1.07 5 1388.89 1443 2.11 1379 0.07 6 238.10 250 0.60 213 2.65 7 34.72 48 5.08 38 0.31 8 4.96 7 0.84 2 1.77 p=0.86977 p=0.56542 Number of rngs required: 688474, p-value: 0.533 RESULTS OF CRAPS TEST for dh-ranFile-2016-08-12_19:31 No. of wins: Observed Expected 98578 98585.9 z-score=-0.035, pvalue=0.48598 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66719 66666.7 0.041 0.041 2 37615 37654.3 0.041 0.082 3 26842 26954.7 0.471 0.554 4 19300 19313.5 0.009 0.563 5 13918 13851.4 0.320 0.883 6 9915 9943.5 0.082 0.965 7 7093 7145.0 0.379 1.344 8 5157 5139.1 0.063 1.406 9 3782 3699.9 1.823 3.230 10 2606 2666.3 1.364 4.593 11 1912 1923.3 0.067 4.660 12 1408 1388.7 0.267 4.927 13 1073 1003.7 4.783 9.710 14 723 726.1 0.014 9.723 15 537 525.8 0.237 9.960 16 368 381.2 0.454 10.414 17 284 276.5 0.201 10.615 18 176 200.8 3.070 13.685 19 149 146.0 0.062 13.748 20 106 106.2 0.000 13.748 21 317 287.1 3.111 16.859 Chisq= 16.86 for 20 degrees of freedom, p= 0.33788 SUMMARY of craptest p-value for no. of wins: 0.485981 p-value for throws/game: 0.337880 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-08-12_19:31 No. of wins: Observed Expected 98852 98585.9 z-score= 1.190, pvalue=0.88304 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66485 66666.7 0.495 0.495 2 37742 37654.3 0.204 0.699 3 27044 26954.7 0.296 0.995 4 19271 19313.5 0.093 1.088 5 13902 13851.4 0.185 1.273 6 9972 9943.5 0.081 1.354 7 7065 7145.0 0.896 2.251 8 5145 5139.1 0.007 2.257 9 3651 3699.9 0.645 2.903 10 2786 2666.3 5.374 8.277 11 1974 1923.3 1.335 9.612 12 1362 1388.7 0.515 10.127 13 969 1003.7 1.201 11.327 14 714 726.1 0.203 11.530 15 556 525.8 1.730 13.261 16 382 381.2 0.002 13.263 17 261 276.5 0.873 14.136 18 217 200.8 1.302 15.438 19 127 146.0 2.469 17.907 20 87 106.2 3.476 21.383 21 288 287.1 0.003 21.385 Chisq= 21.39 for 20 degrees of freedom, p= 0.62524 SUMMARY of craptest p-value for no. of wins: 0.883044 p-value for throws/game: 0.625236 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0009,0.0128,0.0135,0.0168,0.0212,0.0223,0.0232,0.0276,0.0332,0.0373, 0.0385,0.0410,0.0430,0.0440,0.0449,0.0500,0.0509,0.0516,0.0568,0.0640, 0.0720,0.0731,0.0912,0.1125,0.1156,0.1176,0.1178,0.1221,0.1300,0.1341, 0.1432,0.1453,0.1535,0.1574,0.1586,0.1695,0.1802,0.1884,0.1928,0.2098, 0.2099,0.2155,0.2185,0.2219,0.2296,0.2304,0.2320,0.2439,0.2467,0.2589, 0.2655,0.2736,0.2743,0.2756,0.2764,0.2822,0.2855,0.2864,0.2910,0.2922, 0.2922,0.2955,0.3078,0.3104,0.3169,0.3171,0.3213,0.3225,0.3274,0.3274, 0.3341,0.3379,0.3419,0.3466,0.3492,0.3518,0.3533,0.3565,0.3677,0.3707, 0.3791,0.3841,0.3862,0.3870,0.3927,0.3934,0.3949,0.3999,0.4002,0.4110, 0.4114,0.4150,0.4182,0.4297,0.4355,0.4368,0.4389,0.4420,0.4444,0.4509, 0.4516,0.4523,0.4545,0.4583,0.4640,0.4648,0.4666,0.4691,0.4739,0.4764, 0.4809,0.4829,0.4860,0.4872,0.4890,0.4954,0.4963,0.5001,0.5052,0.5173, 0.5220,0.5239,0.5243,0.5267,0.5306,0.5325,0.5339,0.5342,0.5417,0.5431, 0.5454,0.5521,0.5617,0.5630,0.5654,0.5725,0.5769,0.5779,0.5813,0.5814, 0.5829,0.5832,0.5985,0.6009,0.6051,0.6061,0.6065,0.6079,0.6107,0.6122, 0.6179,0.6188,0.6207,0.6252,0.6297,0.6367,0.6375,0.6380,0.6468,0.6473, 0.6500,0.6512,0.6555,0.6603,0.6608,0.6751,0.6760,0.6779,0.6796,0.6811, 0.6817,0.6823,0.6825,0.6837,0.6909,0.6949,0.6961,0.6982,0.6995,0.7002, 0.7081,0.7082,0.7089,0.7096,0.7101,0.7135,0.7142,0.7149,0.7174,0.7242, 0.7288,0.7309,0.7316,0.7399,0.7421,0.7423,0.7429,0.7432,0.7433,0.7435, 0.7467,0.7495,0.7512,0.7529,0.7548,0.7641,0.7729,0.7731,0.7768,0.7777, 0.7782,0.7791,0.7795,0.7805,0.7984,0.7996,0.7996,0.8025,0.8033,0.8101, 0.8143,0.8166,0.8184,0.8197,0.8257,0.8260,0.8272,0.8331,0.8367,0.8400, 0.8423,0.8436,0.8440,0.8455,0.8461,0.8493,0.8594,0.8607,0.8612,0.8620, 0.8634,0.8661,0.8690,0.8698,0.8830,0.8846,0.8872,0.8929,0.8958,0.8986, 0.8997,0.9044,0.9060,0.9061,0.9132,0.9194,0.9252,0.9255,0.9286,0.9321, 0.9378,0.9545,0.9553,0.9574,0.9651,0.9686,0.9693,0.9712,0.9785, Overall p-value after applying KStest on 269 p-values = 0.015408 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.