RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-09-05_02:31 (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 9.5805 0.079725 2 to 25 15.73 19.0073 0.671887 3 to 26 15.63 17.0533 0.549241 4 to 27 15.70 22.3752 0.829284 5 to 28 15.74 19.7598 0.713303 6 to 29 15.84 21.8720 0.810307 7 to 30 15.53 23.8342 0.875990 8 to 31 15.87 12.9808 0.262530 9 to 32 15.69 23.8474 0.876359 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.221438 Tough bday spacings test for dh-ranFile-2015-09-05_02:31: 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 11 36 73 92 86 81 57 27 25 5 7 (O-E)^2/E 0.4 0.0 0.0 0.3 1.4 0.1 0.5 0.3 6.9 0.4 2.1 Birthday Spacings: Sum(O-E)^2/E= 12.319, p= 0.736 RESULTS OF GCD FOR dh-ranFile-2015-09-05_02:31 Euclid's algorithm: p-value, steps to gcd: 0.261418 p-value, dist. of gcd's: 0.501066 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-09-05_02:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.610 0.824 0.714 0.534 0.906 0.451 0.034 0.848 Bits 8 to 15---> 0.144 0.902 0.616 0.251 0.369 0.248 0.567 0.344 Bits 16 to 23---> 0.502 0.465 0.776 0.309 0.898 0.939 0.664 0.377 Bits 24 to 31---> 0.211 0.786 0.891 0.671 0.710 0.486 0.264 0.678 KS test for the above 32 p values: 0.723 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-09-05_02:31, p-values for 5 runs: 0.6647, 0.0647, 0.7216, 0.9438, 0.3073 Rank test for binary matrices (31x31) for dh-ranFile-2015-09-05_02:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 212 211.4 0.002 0.002 r= 29 5106 5134.0 0.153 0.154 r= 30 23027 23103.0 0.250 0.405 r= 31 11655 11551.5 0.927 1.332 chi-square = 1.332 with df = 3; p-value = 0.278 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-09-05_02:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 207 211.4 0.092 0.092 r= 30 5043 5134.0 1.613 1.706 r= 31 23222 23103.0 0.612 2.318 r= 32 11528 11551.5 0.048 2.366 chi-square = 2.366 with df = 3; p-value = 0.500 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-09-05_02:31 b-rank test for bits 1 to 8, p=0.99986 b-rank test for bits 2 to 9, p=0.98215 b-rank test for bits 3 to 10, p=0.97827 b-rank test for bits 4 to 11, p=0.10459 b-rank test for bits 5 to 12, p=0.54997 b-rank test for bits 6 to 13, p=0.88427 b-rank test for bits 7 to 14, p=0.93070 b-rank test for bits 8 to 15, p=0.31335 b-rank test for bits 9 to 16, p=0.03214 b-rank test for bits 10 to 17, p=0.34858 b-rank test for bits 11 to 18, p=0.54188 b-rank test for bits 12 to 19, p=0.19106 b-rank test for bits 13 to 20, p=0.68053 b-rank test for bits 14 to 21, p=0.22989 b-rank test for bits 15 to 22, p=0.31928 b-rank test for bits 16 to 23, p=0.90470 b-rank test for bits 17 to 24, p=0.78636 b-rank test for bits 18 to 25, p=0.06685 b-rank test for bits 19 to 26, p=0.99358 b-rank test for bits 20 to 27, p=0.00251 b-rank test for bits 21 to 28, p=0.87445 b-rank test for bits 22 to 29, p=0.71589 b-rank test for bits 23 to 30, p=0.76145 b-rank test for bits 24 to 31, p=0.14810 b-rank test for bits 25 to 32, p=0.56468 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 = 0.083763 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-09-05_02:31 (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 141608 -0.70 0.240703 2 141833 -0.18 0.429228 3 141745 -0.38 0.350508 4 142414 1.18 0.880828 5 141815 -0.22 0.412781 6 141551 -0.84 0.201235 7 141950 0.10 0.537852 8 141431 -1.12 0.131870 9 141460 -1.05 0.146897 10 141609 -0.70 0.241431 11 141912 0.01 0.502489 12 142548 1.49 0.932179 13 141506 -0.94 0.173004 14 142626 1.67 0.952980 15 142685 1.81 0.965031 16 141887 -0.05 0.479196 17 141793 -0.27 0.392888 18 142180 0.63 0.736439 19 142218 0.72 0.764604 20 141670 -0.56 0.288019 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-09-05_02:31 Bits used No. missing words z-score p-value 23 to 32 141884 -0.0873 0.465199 22 to 31 142400 1.6920 0.954674 21 to 30 141822 -0.3011 0.381655 20 to 29 142500 2.0368 0.979165 19 to 28 142459 1.8954 0.970981 18 to 27 141983 0.2540 0.600266 17 to 26 141806 -0.3563 0.360804 16 to 25 141259 -2.2425 0.012464 15 to 24 141291 -2.1322 0.016496 14 to 23 141734 -0.6046 0.272727 13 to 22 141904 -0.0184 0.492668 12 to 21 141708 -0.6942 0.243765 11 to 20 141795 -0.3942 0.346701 10 to 19 141957 0.1644 0.565284 9 to 18 141826 -0.2873 0.386924 8 to 17 141869 -0.1391 0.444698 7 to 16 141388 -1.7977 0.036113 6 to 15 141702 -0.7149 0.237326 5 to 14 141624 -0.9839 0.162583 4 to 13 141952 0.1471 0.558488 3 to 12 141487 -1.4563 0.072653 2 to 11 142330 1.4506 0.926552 1 to 10 142447 1.8540 0.968133 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-09-05_02:31 Bits used No. missing words z-score p-value 28 to 32 141527 -1.2960 0.097482 27 to 31 141951 0.1413 0.556166 26 to 30 141971 0.2091 0.582796 25 to 29 141365 -1.8452 0.032505 24 to 28 141853 -0.1909 0.424283 23 to 27 141989 0.2701 0.606446 22 to 26 141931 0.0735 0.529279 21 to 25 142257 1.1785 0.880710 20 to 24 142166 0.8701 0.807868 19 to 23 142614 2.3887 0.991546 18 to 22 141341 -1.9265 0.027018 17 to 21 141773 -0.4621 0.321992 16 to 20 142128 0.7413 0.770730 15 to 19 141106 -2.7232 0.003233 14 to 18 141769 -0.4757 0.317146 13 to 17 142025 0.3921 0.652509 12 to 16 142013 0.3514 0.637365 11 to 15 141767 -0.4825 0.314734 10 to 14 141614 -1.0011 0.158385 9 to 13 141871 -0.1299 0.448310 8 to 12 142178 0.9107 0.818785 7 to 11 141718 -0.6486 0.258306 6 to 10 141498 -1.3943 0.081608 5 to 9 142024 0.3887 0.651255 4 to 8 142383 1.6057 0.945826 3 to 7 141408 -1.6994 0.044620 2 to 6 142119 0.7107 0.761379 1 to 5 141813 -0.3265 0.372007 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-09-05_02:31 Bits used No. missing words z-score p-value 31 to 32 141607 -0.8918 0.186242 30 to 31 142418 1.5005 0.933258 29 to 30 142421 1.5094 0.934395 28 to 29 141696 -0.6293 0.264579 27 to 28 141774 -0.3992 0.344872 26 to 27 141752 -0.4641 0.321288 25 to 26 141392 -1.5260 0.063499 24 to 25 141480 -1.2665 0.102674 23 to 24 141848 -0.1809 0.428217 22 to 23 141538 -1.0954 0.136678 21 to 22 142103 0.5713 0.716101 20 to 21 142888 2.8869 0.998055 19 to 20 141887 -0.0659 0.473741 18 to 19 142180 0.7984 0.787691 17 to 18 141812 -0.2871 0.387014 16 to 17 141667 -0.7148 0.237355 15 to 16 141599 -0.9154 0.179984 14 to 15 141375 -1.5762 0.057490 13 to 14 142308 1.1760 0.880206 12 to 13 141790 -0.3520 0.362417 11 to 12 141989 0.2350 0.592901 10 to 11 141855 -0.1603 0.436336 9 to 10 141877 -0.0954 0.462011 8 to 9 142623 2.1052 0.982364 7 to 8 141997 0.2586 0.602033 6 to 7 142239 0.9725 0.834594 5 to 6 141893 -0.0482 0.480790 4 to 5 142388 1.4120 0.921026 3 to 4 142063 0.4533 0.674835 2 to 3 142019 0.3235 0.626846 1 to 2 142426 1.5241 0.936258 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-09-05_02:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2509.97 0.141 0.556048 Test results for specific bytes for dh-ranFile-2015-09-05_02:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2641.18 1.997 0.977068 2 to 9 2628.18 1.813 0.965060 3 to 10 2479.04 -0.296 0.383474 4 to 11 2388.95 -1.571 0.058147 5 to 12 2547.84 0.677 0.750639 6 to 13 2553.10 0.751 0.773660 7 to 14 2433.34 -0.943 0.172897 8 to 15 2432.11 -0.960 0.168491 9 to 16 2511.84 0.167 0.566492 10 to 17 2495.23 -0.067 0.473135 11 to 18 2359.98 -1.980 0.023840 12 to 19 2516.89 0.239 0.594414 13 to 20 2547.13 0.667 0.747480 14 to 21 2589.80 1.270 0.897941 15 to 22 2484.08 -0.225 0.410936 16 to 23 2507.72 0.109 0.543462 17 to 24 2411.44 -1.252 0.105219 18 to 25 2408.39 -1.296 0.097558 19 to 26 2519.06 0.270 0.606258 20 to 27 2438.49 -0.870 0.192195 21 to 28 2445.06 -0.777 0.218568 22 to 29 2518.93 0.268 0.605547 23 to 30 2451.83 -0.681 0.247886 24 to 31 2557.30 0.810 0.791115 25 to 32 2548.70 0.689 0.754522 CDPARK for dh-ranFile-2015-09-05_02:31: 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 3568 2.0548 0.980051 3540 0.7763 0.781201 3509 -0.6393 0.261324 3542 0.8676 0.807188 3587 2.9224 0.998263 3510 -0.5936 0.276387 3485 -1.7352 0.041356 3533 0.4566 0.676028 3501 -1.0046 0.157553 Square side=100, avg. no. parked=3527.60 sample std.=30.72 p-value of the KSTEST for those 10 p-values: 0.311512 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-09-05_02:31 0.9506,0.7718,0.5549,0.7309,0.6397,0.6287,0.6242,0.9582,0.8481,0.4598, The KS test for those 10 p-values: 0.023905 The 3DSPHERES test for dh-ranFile-2015-09-05_02:31 sample no r^3 equiv. uni. 1 9.496 0.271330 2 8.108 0.236830 3 25.514 0.572785 4 3.697 0.115928 5 28.954 0.619067 6 3.905 0.122053 7 7.916 0.231924 8 18.501 0.460279 9 5.288 0.161599 10 26.167 0.581987 11 4.158 0.129418 12 69.829 0.902474 13 89.808 0.949894 14 10.539 0.296226 15 34.196 0.680137 16 24.305 0.555219 17 2.755 0.087738 18 32.840 0.665343 19 65.793 0.888429 20 60.870 0.868534 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.772973 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-09-05_02:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 2.6 0.3 0.3 0.0 0.7 0.6 -1.5 -0.2 -0.4 0.7 0.4 -1.5 0.3 -0.4 0.1 1.0 -0.0 0.2 -0.8 0.0 1.8 -0.0 -0.3 0.5 -0.3 0.2 -0.8 -0.6 0.1 -0.6 -0.9 -0.4 -0.3 -0.4 0.4 -1.9 -0.4 0.5 -1.3 0.9 -1.0 -1.1 Chi-square with 42 degrees of freedom:29.483004 z-score=-1.365716, p-value=0.072626 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-09-05_02:31 Test no p-value 1 0.230888 2 0.142227 3 0.608026 4 0.823152 5 0.632860 6 0.177809 7 0.363386 8 0.006238 9 0.400411 10 0.624653 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.423788 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-09-05_02:31: (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 66669 0.00 66834 0.42 3 25000.00 24998 0.00 24869 0.69 4 6666.67 6716 0.37 6605 0.57 5 1388.89 1367 0.35 1411 0.35 6 238.10 212 2.86 243 0.10 7 34.72 34 0.01 35 0.00 8 4.96 3 0.77 2 1.77 p=0.37188 p=0.30961 Number of rngs required: 688367, p-value: 0.483 RESULTS OF CRAPS TEST for dh-ranFile-2015-09-05_02:31 No. of wins: Observed Expected 98401 98585.9 z-score=-0.827, pvalue=0.20418 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66775 66666.7 0.176 0.176 2 37851 37654.3 1.027 1.203 3 26986 26954.7 0.036 1.240 4 19230 19313.5 0.361 1.600 5 13838 13851.4 0.013 1.613 6 9777 9943.5 2.789 4.403 7 7294 7145.0 3.106 7.509 8 5145 5139.1 0.007 7.516 9 3677 3699.9 0.141 7.657 10 2540 2666.3 5.982 13.639 11 1904 1923.3 0.194 13.834 12 1391 1388.7 0.004 13.837 13 974 1003.7 0.880 14.717 14 706 726.1 0.559 15.276 15 488 525.8 2.722 17.998 16 392 381.2 0.309 18.307 17 298 276.5 1.665 19.972 18 177 200.8 2.828 22.800 19 160 146.0 1.346 24.146 20 107 106.2 0.006 24.151 21 290 287.1 0.029 24.180 Chisq= 24.18 for 20 degrees of freedom, p= 0.76540 SUMMARY of craptest p-value for no. of wins: 0.204177 p-value for throws/game: 0.765399 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-09-05_02:31 No. of wins: Observed Expected 98452 98585.9 z-score=-0.599, pvalue=0.27469 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66632 66666.7 0.018 0.018 2 37611 37654.3 0.050 0.068 3 27022 26954.7 0.168 0.236 4 19437 19313.5 0.790 1.026 5 13911 13851.4 0.256 1.282 6 9916 9943.5 0.076 1.359 7 7148 7145.0 0.001 1.360 8 5165 5139.1 0.131 1.491 9 3679 3699.9 0.118 1.608 10 2604 2666.3 1.456 3.064 11 1887 1923.3 0.686 3.750 12 1348 1388.7 1.195 4.945 13 998 1003.7 0.033 4.978 14 747 726.1 0.599 5.577 15 503 525.8 0.992 6.569 16 379 381.2 0.012 6.581 17 267 276.5 0.329 6.910 18 213 200.8 0.737 7.647 19 148 146.0 0.028 7.675 20 112 106.2 0.315 7.990 21 273 287.1 0.694 8.684 Chisq= 8.68 for 20 degrees of freedom, p= 0.01371 SUMMARY of craptest p-value for no. of wins: 0.274689 p-value for throws/game: 0.013714 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0025,0.0032,0.0062,0.0125,0.0137,0.0165,0.0238,0.0239,0.0270,0.0321, 0.0325,0.0338,0.0361,0.0414,0.0446,0.0575,0.0581,0.0635,0.0647,0.0668, 0.0726,0.0727,0.0797,0.0816,0.0838,0.0877,0.0975,0.0976,0.1027,0.1046, 0.1052,0.1159,0.1221,0.1294,0.1319,0.1367,0.1422,0.1444,0.1469,0.1481, 0.1576,0.1576,0.1584,0.1616,0.1626,0.1685,0.1729,0.1730,0.1778,0.1800, 0.1862,0.1911,0.1922,0.2012,0.2042,0.2105,0.2186,0.2214,0.2299,0.2309, 0.2319,0.2368,0.2373,0.2374,0.2407,0.2414,0.2438,0.2479,0.2479,0.2507, 0.2583,0.2613,0.2614,0.2625,0.2636,0.2646,0.2713,0.2727,0.2747,0.2764, 0.2784,0.2880,0.2962,0.3073,0.3086,0.3096,0.3115,0.3133,0.3147,0.3171, 0.3193,0.3213,0.3220,0.3440,0.3449,0.3467,0.3486,0.3505,0.3608,0.3624, 0.3634,0.3689,0.3719,0.3720,0.3772,0.3817,0.3835,0.3869,0.3870,0.3929, 0.4004,0.4109,0.4128,0.4238,0.4243,0.4282,0.4292,0.4363,0.4447,0.4483, 0.4510,0.4598,0.4603,0.4620,0.4652,0.4655,0.4731,0.4737,0.4792,0.4808, 0.4835,0.4860,0.4927,0.5000,0.5011,0.5024,0.5025,0.5293,0.5340,0.5379, 0.5419,0.5435,0.5492,0.5500,0.5549,0.5552,0.5560,0.5562,0.5585,0.5647, 0.5653,0.5665,0.5669,0.5728,0.5820,0.5828,0.5929,0.5944,0.6003,0.6020, 0.6055,0.6063,0.6064,0.6080,0.6102,0.6161,0.6191,0.6242,0.6247,0.6268, 0.6287,0.6329,0.6374,0.6397,0.6513,0.6525,0.6645,0.6647,0.6653,0.6713, 0.6719,0.6748,0.6760,0.6776,0.6801,0.6805,0.7097,0.7133,0.7139,0.7159, 0.7161,0.7216,0.7228,0.7309,0.7357,0.7364,0.7475,0.7506,0.7545,0.7614, 0.7615,0.7646,0.7654,0.7707,0.7718,0.7730,0.7737,0.7759,0.7812,0.7862, 0.7864,0.7877,0.7911,0.8072,0.8079,0.8103,0.8188,0.8232,0.8238,0.8293, 0.8346,0.8479,0.8481,0.8685,0.8745,0.8760,0.8764,0.8802,0.8807,0.8808, 0.8843,0.8884,0.8915,0.8979,0.8980,0.9018,0.9025,0.9047,0.9063,0.9210, 0.9266,0.9307,0.9322,0.9333,0.9344,0.9363,0.9386,0.9438,0.9458,0.9499, 0.9506,0.9530,0.9547,0.9582,0.9650,0.9651,0.9681,0.9710,0.9771,0.9783, 0.9792,0.9801,0.9822,0.9824,0.9915,0.9936,0.9981,0.9983,0.9999, Overall p-value after applying KStest on 269 p-values = 0.762258 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.