RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-07-04_14:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.75 18.3432 0.632494 2 to 25 15.86 13.0005 0.263849 3 to 26 15.77 14.1175 0.341229 4 to 27 15.98 14.8249 0.391908 5 to 28 15.91 15.2441 0.422097 6 to 29 15.63 17.6770 0.590516 7 to 30 16.12 19.9244 0.721887 8 to 31 15.71 23.5030 0.866421 9 to 32 15.80 12.4587 0.228399 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.670522 Tough bday spacings test for dh-ranFile-2016-07-04_14:31: 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 4 37 70 91 107 82 59 25 16 7 2 (O-E)^2/E 2.9 0.0 0.1 0.5 0.9 0.2 0.9 0.8 0.1 0.0 1.0 Birthday Spacings: Sum(O-E)^2/E= 7.424, p= 0.315 RESULTS OF GCD FOR dh-ranFile-2016-07-04_14:31 Euclid's algorithm: p-value, steps to gcd: 0.574354 p-value, dist. of gcd's: 0.701540 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-07-04_14:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.371 0.545 0.208 0.578 0.370 0.503 0.522 0.856 Bits 8 to 15---> 0.420 0.126 0.894 0.007 0.407 0.966 0.735 0.739 Bits 16 to 23---> 0.872 0.611 0.055 0.257 0.151 0.097 0.366 0.086 Bits 24 to 31---> 0.999 0.272 0.788 0.293 0.818 0.825 0.210 0.051 KS test for the above 32 p values: 0.179 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-07-04_14:31, p-values for 5 runs: 0.7618, 0.1031, 0.8084, 0.4602, 0.5293 Rank test for binary matrices (31x31) for dh-ranFile-2016-07-04_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 211 211.4 0.001 0.001 r= 29 5324 5134.0 7.031 7.032 r= 30 22862 23103.0 2.515 9.547 r= 31 11603 11551.5 0.229 9.776 chi-square = 9.776 with df = 3; p-value = 0.979 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-07-04_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 212 211.4 0.002 0.002 r= 30 5221 5134.0 1.474 1.476 r= 31 23077 23103.0 0.029 1.505 r= 32 11490 11551.5 0.328 1.833 chi-square = 1.833 with df = 3; p-value = 0.392 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-07-04_14:31 b-rank test for bits 1 to 8, p=0.00191 b-rank test for bits 2 to 9, p=0.65389 b-rank test for bits 3 to 10, p=0.20083 b-rank test for bits 4 to 11, p=0.39238 b-rank test for bits 5 to 12, p=0.16730 b-rank test for bits 6 to 13, p=0.74310 b-rank test for bits 7 to 14, p=0.02136 b-rank test for bits 8 to 15, p=0.04844 b-rank test for bits 9 to 16, p=0.31626 b-rank test for bits 10 to 17, p=0.21348 b-rank test for bits 11 to 18, p=0.31030 b-rank test for bits 12 to 19, p=0.69357 b-rank test for bits 13 to 20, p=0.42984 b-rank test for bits 14 to 21, p=0.15446 b-rank test for bits 15 to 22, p=0.46378 b-rank test for bits 16 to 23, p=0.61918 b-rank test for bits 17 to 24, p=0.71133 b-rank test for bits 18 to 25, p=0.76663 b-rank test for bits 19 to 26, p=0.22614 b-rank test for bits 20 to 27, p=0.91930 b-rank test for bits 21 to 28, p=0.11348 b-rank test for bits 22 to 29, p=0.83188 b-rank test for bits 23 to 30, p=0.56605 b-rank test for bits 24 to 31, p=0.00899 b-rank test for bits 25 to 32, p=0.30226 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 = 0.086673 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-07-04_14:31 (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 141947 0.09 0.535067 2 142078 0.39 0.653242 3 141860 -0.12 0.454121 4 142286 0.88 0.810589 5 142448 1.26 0.895908 6 141800 -0.26 0.399190 7 142212 0.71 0.760271 8 142095 0.43 0.667786 9 141518 -0.91 0.180274 10 141699 -0.49 0.311563 11 141450 -1.07 0.141591 12 141390 -1.21 0.112491 13 141757 -0.36 0.360954 14 142368 1.07 0.858063 15 141032 -2.05 0.020190 16 142036 0.30 0.616369 17 142297 0.91 0.817471 18 142457 1.28 0.899658 19 140752 -2.70 0.003425 20 141330 -1.35 0.087936 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-07-04_14:31 Bits used No. missing words z-score p-value 23 to 32 142146 0.8161 0.792780 22 to 31 142458 1.8920 0.970752 21 to 30 141961 0.1782 0.570706 20 to 29 142153 0.8402 0.799614 19 to 28 142043 0.4609 0.677576 18 to 27 142476 1.9540 0.974651 17 to 26 141786 -0.4253 0.335318 16 to 25 141919 0.0333 0.513300 15 to 24 142255 1.1920 0.883363 14 to 23 142001 0.3161 0.624038 13 to 22 141412 -1.7149 0.043179 12 to 21 141897 -0.0425 0.483043 11 to 20 141920 0.0368 0.514675 10 to 19 141757 -0.5253 0.299696 9 to 18 142288 1.3058 0.904183 8 to 17 142087 0.6127 0.729948 7 to 16 141783 -0.4356 0.331556 6 to 15 141790 -0.4115 0.340359 5 to 14 141747 -0.5598 0.287822 4 to 13 141415 -1.7046 0.044136 3 to 12 141452 -1.5770 0.057398 2 to 11 141681 -0.7873 0.215540 1 to 10 142151 0.8333 0.797675 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-07-04_14:31 Bits used No. missing words z-score p-value 28 to 32 142431 1.7684 0.961501 27 to 31 142283 1.2667 0.897365 26 to 30 142021 0.3785 0.647486 25 to 29 142095 0.6294 0.735453 24 to 28 141425 -1.6418 0.050316 23 to 27 142307 1.3480 0.911176 22 to 26 142510 2.0362 0.979133 21 to 25 141680 -0.7774 0.218464 20 to 24 141600 -1.0486 0.147187 19 to 23 141799 -0.3740 0.354202 18 to 22 141661 -0.8418 0.199951 17 to 21 141663 -0.8350 0.201854 16 to 20 142023 0.3853 0.650001 15 to 19 141862 -0.1604 0.436267 14 to 18 141758 -0.5130 0.303982 13 to 17 142293 1.3006 0.903298 12 to 16 142113 0.6904 0.755031 11 to 15 141491 -1.4181 0.078086 10 to 14 142250 1.1548 0.875917 9 to 13 141592 -1.0757 0.141032 8 to 12 141892 -0.0587 0.476577 7 to 11 141974 0.2192 0.586761 6 to 10 141999 0.3040 0.619423 5 to 9 141953 0.1480 0.558842 4 to 8 141978 0.2328 0.592034 3 to 7 142166 0.8701 0.807868 2 to 6 142246 1.1413 0.873118 1 to 5 141879 -0.1028 0.459056 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-07-04_14:31 Bits used No. missing words z-score p-value 31 to 32 141779 -0.3845 0.350321 30 to 31 142204 0.8692 0.807640 29 to 30 141866 -0.1278 0.449147 28 to 29 140861 -3.0924 0.000993 27 to 28 141420 -1.4435 0.074447 26 to 27 141561 -1.0275 0.152087 25 to 26 141719 -0.5614 0.287247 24 to 25 141833 -0.2252 0.410927 23 to 24 142223 0.9253 0.822590 22 to 23 142137 0.6716 0.749079 21 to 22 142296 1.1406 0.872986 20 to 21 142186 0.8161 0.792789 19 to 20 141932 0.0669 0.526659 18 to 19 142456 1.6126 0.946584 17 to 18 142150 0.7099 0.761130 16 to 17 142008 0.2911 0.614498 15 to 16 142336 1.2586 0.895915 14 to 15 141573 -0.9921 0.160569 13 to 14 142077 0.4946 0.689559 12 to 13 141787 -0.3609 0.359104 11 to 12 141919 0.0285 0.511378 10 to 11 142004 0.2793 0.609978 9 to 10 142601 2.0403 0.979341 8 to 9 142218 0.9105 0.818729 7 to 8 141974 0.1908 0.575646 6 to 7 141780 -0.3815 0.351415 5 to 6 142196 0.8456 0.801122 4 to 5 141789 -0.3550 0.361311 3 to 4 141850 -0.1750 0.430534 2 to 3 142078 0.4976 0.690600 1 to 2 141813 -0.2842 0.388144 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-07-04_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2587.26 1.234 0.891414 Test results for specific bytes for dh-ranFile-2016-07-04_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2453.41 -0.659 0.254977 2 to 9 2545.77 0.647 0.741255 3 to 10 2416.34 -1.183 0.118382 4 to 11 2567.01 0.948 0.828353 5 to 12 2529.01 0.410 0.659214 6 to 13 2462.24 -0.534 0.296670 7 to 14 2440.90 -0.836 0.201646 8 to 15 2492.95 -0.100 0.460281 9 to 16 2294.92 -2.900 0.001864 10 to 17 2531.32 0.443 0.671102 11 to 18 2462.81 -0.526 0.299471 12 to 19 2651.65 2.145 0.984007 13 to 20 2367.33 -1.876 0.030315 14 to 21 2503.97 0.056 0.522405 15 to 22 2423.79 -1.078 0.140569 16 to 23 2623.92 1.753 0.960157 17 to 24 2487.89 -0.171 0.432015 18 to 25 2397.76 -1.446 0.074096 19 to 26 2418.45 -1.153 0.124402 20 to 27 2545.12 0.638 0.738275 21 to 28 2446.82 -0.752 0.225984 22 to 29 2364.45 -1.917 0.027617 23 to 30 2650.31 2.126 0.983234 24 to 31 2419.32 -1.141 0.126938 25 to 32 2460.98 -0.552 0.290521 CDPARK for dh-ranFile-2016-07-04_14:31: 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 3527 0.1826 0.572463 3533 0.4566 0.676028 3592 3.1507 0.999186 3517 -0.2740 0.392053 3518 -0.2283 0.409702 3508 -0.6849 0.246694 3517 -0.2740 0.392053 3534 0.5023 0.692266 3517 -0.2740 0.392053 3487 -1.6438 0.050105 Square side=100, avg. no. parked=3525.00 sample std.=25.71 p-value of the KSTEST for those 10 p-values: 0.463858 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-07-04_14:31 0.7361,0.4225,0.3996,0.4610,0.0526,0.9907,0.5068,0.3671,0.3594,0.4843, The KS test for those 10 p-values: 0.398422 The 3DSPHERES test for dh-ranFile-2016-07-04_14:31 sample no r^3 equiv. uni. 1 4.114 0.128144 2 83.926 0.939039 3 10.206 0.288362 4 22.948 0.534639 5 29.439 0.625180 6 0.256 0.008498 7 38.490 0.722792 8 15.509 0.403669 9 56.296 0.846881 10 17.849 0.448416 11 7.266 0.215095 12 38.345 0.721450 13 5.760 0.174697 14 35.839 0.697181 15 0.008 0.000261 16 45.107 0.777664 17 99.714 0.963984 18 7.291 0.215747 19 1.796 0.058100 20 4.824 0.148535 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.368108 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-07-04_14:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.5 -0.1 -0.3 -0.3 0.5 0.3 0.7 -0.1 -0.7 0.9 -0.2 0.5 0.2 -1.2 -0.1 -0.4 1.3 0.4 2.2 -0.6 -0.0 -2.3 1.0 0.6 -1.0 -0.8 -0.6 -0.7 -0.7 -0.4 -0.7 -0.6 -1.2 -0.6 0.4 1.2 -2.3 0.9 -0.7 0.1 -1.0 -0.1 Chi-square with 42 degrees of freedom:32.773116 z-score=-1.006736, p-value=0.154482 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-07-04_14:31 Test no p-value 1 0.465100 2 0.597361 3 0.111769 4 0.066827 5 0.480845 6 0.082187 7 0.069093 8 0.188877 9 0.142361 10 0.013077 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.001932 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-07-04_14:31: (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 66797 0.25 66711 0.03 3 25000.00 24865 0.73 24861 0.77 4 6666.67 6646 0.06 6700 0.17 5 1388.89 1384 0.02 1420 0.70 6 238.10 263 2.61 265 3.04 7 34.72 40 0.80 37 0.15 8 4.96 4 0.19 5 0.00 p=0.41175 p=0.43760 Number of rngs required: 687805, p-value: 0.245 RESULTS OF CRAPS TEST for dh-ranFile-2016-07-04_14:31 No. of wins: Observed Expected 98871 98585.9 z-score= 1.275, pvalue=0.89890 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66404 66666.7 1.035 1.035 2 37670 37654.3 0.007 1.041 3 27058 26954.7 0.396 1.437 4 19516 19313.5 2.124 3.561 5 13936 13851.4 0.516 4.078 6 9940 9943.5 0.001 4.079 7 7080 7145.0 0.592 4.671 8 5176 5139.1 0.265 4.936 9 3721 3699.9 0.121 5.057 10 2715 2666.3 0.890 5.946 11 1852 1923.3 2.645 8.592 12 1423 1388.7 0.845 9.437 13 972 1003.7 1.002 10.439 14 723 726.1 0.014 10.452 15 476 525.8 4.723 15.176 16 362 381.2 0.962 16.138 17 281 276.5 0.072 16.210 18 181 200.8 1.958 18.168 19 139 146.0 0.334 18.502 20 97 106.2 0.800 19.301 21 278 287.1 0.289 19.591 Chisq= 19.59 for 20 degrees of freedom, p= 0.51622 SUMMARY of craptest p-value for no. of wins: 0.898902 p-value for throws/game: 0.516224 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-07-04_14:31 No. of wins: Observed Expected 98352 98585.9 z-score=-1.046, pvalue=0.14779 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66594 66666.7 0.079 0.079 2 37692 37654.3 0.038 0.117 3 26889 26954.7 0.160 0.277 4 19203 19313.5 0.632 0.909 5 13896 13851.4 0.143 1.052 6 10092 9943.5 2.216 3.269 7 7230 7145.0 1.011 4.280 8 5121 5139.1 0.064 4.343 9 3726 3699.9 0.185 4.528 10 2634 2666.3 0.391 4.919 11 1917 1923.3 0.021 4.940 12 1395 1388.7 0.028 4.968 13 1052 1003.7 2.323 7.291 14 699 726.1 1.014 8.305 15 518 525.8 0.117 8.422 16 348 381.2 2.883 11.305 17 277 276.5 0.001 11.306 18 193 200.8 0.305 11.611 19 135 146.0 0.827 12.438 20 101 106.2 0.256 12.694 21 288 287.1 0.003 12.697 Chisq= 12.70 for 20 degrees of freedom, p= 0.10998 SUMMARY of craptest p-value for no. of wins: 0.147792 p-value for throws/game: 0.109980 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0003,0.0010,0.0019,0.0019,0.0019,0.0034,0.0067,0.0085,0.0090,0.0131, 0.0202,0.0214,0.0276,0.0303,0.0432,0.0441,0.0484,0.0501,0.0503,0.0512, 0.0526,0.0553,0.0574,0.0581,0.0668,0.0691,0.0741,0.0744,0.0781,0.0822, 0.0861,0.0867,0.0879,0.0973,0.1031,0.1100,0.1118,0.1125,0.1135,0.1184, 0.1244,0.1259,0.1269,0.1281,0.1406,0.1410,0.1416,0.1424,0.1472,0.1478, 0.1485,0.1513,0.1521,0.1545,0.1545,0.1606,0.1673,0.1747,0.1795,0.1803, 0.1889,0.2000,0.2008,0.2016,0.2019,0.2076,0.2096,0.2135,0.2151,0.2155, 0.2157,0.2185,0.2260,0.2261,0.2284,0.2450,0.2467,0.2550,0.2570,0.2638, 0.2723,0.2872,0.2878,0.2884,0.2905,0.2928,0.2967,0.2995,0.2997,0.3023, 0.3040,0.3103,0.3116,0.3151,0.3163,0.3316,0.3353,0.3404,0.3412,0.3503, 0.3514,0.3542,0.3591,0.3594,0.3610,0.3613,0.3658,0.3671,0.3681,0.3697, 0.3711,0.3881,0.3919,0.3921,0.3921,0.3921,0.3921,0.3924,0.3984,0.3992, 0.3996,0.4037,0.4070,0.4097,0.4109,0.4118,0.4200,0.4221,0.4225,0.4298, 0.4305,0.4320,0.4363,0.4376,0.4484,0.4491,0.4541,0.4591,0.4602,0.4603, 0.4610,0.4638,0.4639,0.4651,0.4766,0.4808,0.4830,0.4843,0.5033,0.5068, 0.5114,0.5133,0.5147,0.5162,0.5215,0.5224,0.5267,0.5293,0.5346,0.5351, 0.5455,0.5588,0.5660,0.5707,0.5725,0.5744,0.5756,0.5780,0.5868,0.5905, 0.5920,0.5974,0.6100,0.6111,0.6145,0.6164,0.6192,0.6194,0.6240,0.6252, 0.6325,0.6475,0.6500,0.6532,0.6539,0.6592,0.6678,0.6705,0.6711,0.6760, 0.6776,0.6896,0.6906,0.6923,0.6936,0.6972,0.7015,0.7113,0.7215,0.7219, 0.7228,0.7299,0.7346,0.7355,0.7361,0.7383,0.7387,0.7413,0.7431,0.7491, 0.7550,0.7603,0.7611,0.7618,0.7666,0.7777,0.7882,0.7928,0.7928,0.7977, 0.7996,0.8011,0.8076,0.8079,0.8084,0.8106,0.8175,0.8181,0.8187,0.8226, 0.8250,0.8284,0.8319,0.8469,0.8562,0.8581,0.8664,0.8720,0.8730,0.8731, 0.8759,0.8834,0.8914,0.8944,0.8959,0.8959,0.8974,0.8989,0.8997,0.9033, 0.9042,0.9112,0.9193,0.9390,0.9466,0.9602,0.9615,0.9640,0.9658,0.9708, 0.9747,0.9791,0.9793,0.9794,0.9832,0.9840,0.9907,0.9987,0.9992, Overall p-value after applying KStest on 269 p-values = 0.094385 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.