RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-06-11_04:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.99 26.2627 0.930195 2 to 25 15.67 13.8368 0.321382 3 to 26 15.53 15.2166 0.420113 4 to 27 15.86 14.6077 0.376286 5 to 28 15.81 17.1392 0.555027 6 to 29 15.59 24.9021 0.903078 7 to 30 15.98 6.4464 0.010351 8 to 31 16.00 10.2087 0.105367 9 to 32 15.68 11.8121 0.188619 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.591044 Tough bday spacings test for dh-ranFile-2016-06-11_04:31: 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 6 40 77 79 114 75 51 32 18 4 4 (O-E)^2/E 1.1 0.3 0.2 3.6 2.7 0.1 0.0 0.2 0.7 1.0 0.0 Birthday Spacings: Sum(O-E)^2/E= 9.892, p= 0.550 RESULTS OF GCD FOR dh-ranFile-2016-06-11_04:31 Euclid's algorithm: p-value, steps to gcd: 0.939010 p-value, dist. of gcd's: 0.863425 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-06-11_04:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.605 0.418 0.940 0.567 0.920 0.786 0.313 0.165 Bits 8 to 15---> 0.538 0.940 0.522 0.131 0.728 0.076 0.257 0.657 Bits 16 to 23---> 0.800 0.058 0.116 0.477 0.330 0.653 0.641 0.103 Bits 24 to 31---> 0.591 0.936 0.976 0.103 0.741 0.236 0.238 0.595 KS test for the above 32 p values: 0.072 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-06-11_04:31, p-values for 5 runs: 0.6163, 0.0794, 0.0494, 0.0374, 0.1370 Rank test for binary matrices (31x31) for dh-ranFile-2016-06-11_04:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 209 211.4 0.028 0.028 r= 29 5017 5134.0 2.667 2.694 r= 30 23192 23103.0 0.342 3.037 r= 31 11582 11551.5 0.080 3.117 chi-square = 3.117 with df = 3; p-value = 0.626 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-06-11_04:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 235 211.4 2.630 2.630 r= 30 5201 5134.0 0.874 3.504 r= 31 23046 23103.0 0.141 3.645 r= 32 11518 11551.5 0.097 3.743 chi-square = 3.743 with df = 3; p-value = 0.709 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-06-11_04:31 b-rank test for bits 1 to 8, p=0.39419 b-rank test for bits 2 to 9, p=0.92006 b-rank test for bits 3 to 10, p=0.22266 b-rank test for bits 4 to 11, p=0.69738 b-rank test for bits 5 to 12, p=0.96731 b-rank test for bits 6 to 13, p=0.83649 b-rank test for bits 7 to 14, p=0.49786 b-rank test for bits 8 to 15, p=0.37863 b-rank test for bits 9 to 16, p=0.57814 b-rank test for bits 10 to 17, p=0.51395 b-rank test for bits 11 to 18, p=0.03158 b-rank test for bits 12 to 19, p=0.44801 b-rank test for bits 13 to 20, p=0.50303 b-rank test for bits 14 to 21, p=0.74625 b-rank test for bits 15 to 22, p=0.96270 b-rank test for bits 16 to 23, p=0.84513 b-rank test for bits 17 to 24, p=0.40399 b-rank test for bits 18 to 25, p=0.71067 b-rank test for bits 19 to 26, p=0.20996 b-rank test for bits 20 to 27, p=0.46205 b-rank test for bits 21 to 28, p=0.06280 b-rank test for bits 22 to 29, p=0.43763 b-rank test for bits 23 to 30, p=0.82975 b-rank test for bits 24 to 31, p=0.73562 b-rank test for bits 25 to 32, p=0.38891 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 = 0.496459 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-06-11_04:31 (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 142342 1.01 0.843971 2 141976 0.16 0.561893 3 142192 0.66 0.745516 4 141859 -0.12 0.453195 5 141955 0.11 0.542489 6 141694 -0.50 0.307444 7 141290 -1.45 0.073944 8 141263 -1.51 0.065507 9 142512 1.41 0.920450 10 141458 -1.05 0.145825 11 141969 0.14 0.555439 12 141875 -0.08 0.468035 13 141244 -1.55 0.060031 14 142172 0.61 0.730298 15 141950 0.10 0.537852 16 141661 -0.58 0.280886 17 142050 0.33 0.628797 18 142323 0.97 0.833108 19 141973 0.15 0.559129 20 142498 1.38 0.915496 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-06-11_04:31 Bits used No. missing words z-score p-value 23 to 32 141973 0.2196 0.586890 22 to 31 141919 0.0333 0.513300 21 to 30 141486 -1.4598 0.072178 20 to 29 141604 -1.0529 0.146202 19 to 28 141533 -1.2977 0.097197 18 to 27 142088 0.6161 0.731087 17 to 26 141794 -0.3977 0.345430 16 to 25 141556 -1.2184 0.111540 15 to 24 141613 -1.0218 0.153431 14 to 23 141809 -0.3460 0.364684 13 to 22 141782 -0.4391 0.330306 12 to 21 141764 -0.5011 0.308137 11 to 20 141957 0.1644 0.565284 10 to 19 142041 0.4540 0.675098 9 to 18 141095 -2.8080 0.002492 8 to 17 141801 -0.3736 0.354369 7 to 16 141695 -0.7391 0.229933 6 to 15 141722 -0.6460 0.259151 5 to 14 141775 -0.4632 0.321608 4 to 13 142002 0.3196 0.625346 3 to 12 141795 -0.3942 0.346701 2 to 11 141987 0.2678 0.605584 1 to 10 142012 0.3540 0.638344 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-06-11_04:31 Bits used No. missing words z-score p-value 28 to 32 141861 -0.1638 0.434932 27 to 31 142174 0.8972 0.815190 26 to 30 141850 -0.2011 0.420303 25 to 29 142037 0.4328 0.667413 24 to 28 142007 0.3311 0.629710 23 to 27 141947 0.1277 0.550805 22 to 26 142222 1.0599 0.855405 21 to 25 142214 1.0328 0.849147 20 to 24 141631 -0.9435 0.172715 19 to 23 142098 0.6396 0.738770 18 to 22 141925 0.0531 0.521181 17 to 21 141849 -0.2045 0.418978 16 to 20 141702 -0.7028 0.241086 15 to 19 142126 0.7345 0.768670 14 to 18 142074 0.5582 0.711647 13 to 17 141747 -0.5503 0.291067 12 to 16 142022 0.3819 0.648744 11 to 15 141641 -0.9096 0.181519 10 to 14 141408 -1.6994 0.044620 9 to 13 142353 1.5040 0.933705 8 to 12 141858 -0.1740 0.430933 7 to 11 142310 1.3582 0.912800 6 to 10 142592 2.3141 0.989670 5 to 9 141717 -0.6520 0.257212 4 to 8 141665 -0.8282 0.203768 3 to 7 142150 0.8158 0.792702 2 to 6 141439 -1.5943 0.055430 1 to 5 141793 -0.3943 0.346665 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-06-11_04:31 Bits used No. missing words z-score p-value 31 to 32 141794 -0.3402 0.366851 30 to 31 142153 0.7188 0.763865 29 to 30 141369 -1.5939 0.055480 28 to 29 141991 0.2409 0.595189 27 to 28 141894 -0.0452 0.481966 26 to 27 141514 -1.1662 0.121774 25 to 26 141937 0.0816 0.532527 24 to 25 142277 1.0846 0.860944 23 to 24 141801 -0.3196 0.374652 22 to 23 141946 0.1082 0.543070 21 to 22 141683 -0.6676 0.252182 20 to 21 141561 -1.0275 0.152087 19 to 20 141968 0.1731 0.568701 18 to 19 141056 -2.5172 0.005915 17 to 18 142457 1.6155 0.946904 16 to 17 141410 -1.4729 0.070382 15 to 16 142010 0.2970 0.616752 14 to 15 142357 1.3206 0.906676 13 to 14 141655 -0.7502 0.226556 12 to 13 142134 0.6627 0.746253 11 to 12 141983 0.2173 0.586019 10 to 11 141877 -0.0954 0.462011 9 to 10 141664 -0.7237 0.234629 8 to 9 141785 -0.3668 0.356901 7 to 8 141899 -0.0305 0.487845 6 to 7 141580 -0.9715 0.165656 5 to 6 141657 -0.7443 0.228337 4 to 5 142173 0.7778 0.781653 3 to 4 142210 0.8869 0.812442 2 to 3 141322 -1.7325 0.041589 1 to 2 141857 -0.1544 0.438661 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-06-11_04:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2585.51 1.209 0.886722 Test results for specific bytes for dh-ranFile-2016-06-11_04:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2596.12 1.359 0.912973 2 to 9 2437.82 -0.879 0.189586 3 to 10 2321.27 -2.528 0.005743 4 to 11 2489.57 -0.147 0.441379 5 to 12 2481.86 -0.257 0.398767 6 to 13 2501.12 0.016 0.506317 7 to 14 2771.19 3.835 0.999937 8 to 15 2424.17 -1.072 0.141776 9 to 16 2506.71 0.095 0.537777 10 to 17 2565.14 0.921 0.821542 11 to 18 2474.56 -0.360 0.359522 12 to 19 2502.63 0.037 0.514812 13 to 20 2464.52 -0.502 0.307896 14 to 21 2410.83 -1.261 0.103656 15 to 22 2525.77 0.364 0.642228 16 to 23 2555.67 0.787 0.784442 17 to 24 2491.52 -0.120 0.452281 18 to 25 2403.29 -1.368 0.085696 19 to 26 2462.75 -0.527 0.299174 20 to 27 2492.19 -0.110 0.456044 21 to 28 2557.93 0.819 0.793698 22 to 29 2387.09 -1.597 0.055163 23 to 30 2426.34 -1.042 0.148781 24 to 31 2410.09 -1.272 0.101769 25 to 32 2525.79 0.365 0.642344 CDPARK for dh-ranFile-2016-06-11_04:31: 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 3542 0.8676 0.807188 3495 -1.2785 0.100530 3515 -0.3653 0.357445 3527 0.1826 0.572463 3492 -1.4155 0.078457 3510 -0.5936 0.276387 3554 1.4155 0.921543 3510 -0.5936 0.276387 3502 -0.9589 0.168804 3553 1.3699 0.914635 Square side=100, avg. no. parked=3520.00 sample std.=21.76 p-value of the KSTEST for those 10 p-values: 0.673323 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-06-11_04:31 0.0886,0.1762,0.6313,0.9269,0.9846,0.7064,0.8851,0.2800,0.8580,0.6420, The KS test for those 10 p-values: 0.259037 The 3DSPHERES test for dh-ranFile-2016-06-11_04:31 sample no r^3 equiv. uni. 1 8.070 0.235854 2 125.083 0.984539 3 35.532 0.694067 4 0.639 0.021067 5 9.801 0.278691 6 58.746 0.858887 7 19.419 0.476536 8 45.586 0.781188 9 9.725 0.276879 10 35.322 0.691924 11 12.429 0.339198 12 20.536 0.495670 13 2.934 0.093171 14 6.567 0.196600 15 9.757 0.277636 16 32.421 0.660645 17 27.206 0.596206 18 8.454 0.245580 19 0.534 0.017628 20 21.896 0.518026 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.526055 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-06-11_04:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 0.1 1.3 -0.3 -1.1 0.2 0.8 1.2 -0.6 -0.3 -1.2 -1.3 -1.0 0.7 1.7 -0.4 1.4 -0.8 -0.1 -0.7 -0.4 0.4 1.1 0.6 0.1 0.1 0.9 -0.2 -0.9 -2.2 -0.2 -0.9 0.2 0.5 -0.1 -0.5 1.0 -0.4 0.5 0.4 -0.6 -1.0 -0.1 Chi-square with 42 degrees of freedom:30.979016 z-score=-1.202488, p-value=0.105121 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-06-11_04:31 Test no p-value 1 0.073062 2 0.126903 3 0.002376 4 0.313240 5 0.188099 6 0.264881 7 0.358611 8 0.183183 9 0.646424 10 0.048183 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.002569 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-06-11_04:31: (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 66537 0.25 66641 0.01 3 25000.00 25116 0.54 24902 0.38 4 6666.67 6724 0.49 6725 0.51 5 1388.89 1321 3.32 1449 2.60 6 238.10 271 4.55 240 0.02 7 34.72 25 2.72 36 0.05 8 4.96 5 0.00 6 0.22 p=0.93509 p=0.29444 Number of rngs required: 687909, p-value: 0.284 RESULTS OF CRAPS TEST for dh-ranFile-2016-06-11_04:31 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 66910 66666.7 0.888 0.888 2 37508 37654.3 0.569 1.457 3 26703 26954.7 2.351 3.808 4 19554 19313.5 2.996 6.803 5 13829 13851.4 0.036 6.840 6 9812 9943.5 1.740 8.580 7 7092 7145.0 0.394 8.973 8 5118 5139.1 0.086 9.060 9 3757 3699.9 0.882 9.942 10 2726 2666.3 1.337 11.279 11 1956 1923.3 0.555 11.834 12 1394 1388.7 0.020 11.854 13 993 1003.7 0.114 11.968 14 705 726.1 0.615 12.584 15 540 525.8 0.382 12.965 16 385 381.2 0.039 13.004 17 261 276.5 0.873 13.877 18 215 200.8 1.000 14.877 19 148 146.0 0.028 14.905 20 107 106.2 0.006 14.911 21 287 287.1 0.000 14.911 Chisq= 14.91 for 20 degrees of freedom, p= 0.21851 SUMMARY of craptest p-value for no. of wins: 0.147792 p-value for throws/game: 0.218515 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-06-11_04:31 No. of wins: Observed Expected 98600 98585.9 z-score= 0.063, pvalue=0.52522 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66664 66666.7 0.000 0.000 2 37693 37654.3 0.040 0.040 3 27009 26954.7 0.109 0.149 4 19379 19313.5 0.222 0.371 5 13842 13851.4 0.006 0.378 6 9954 9943.5 0.011 0.389 7 7098 7145.0 0.310 0.698 8 5172 5139.1 0.211 0.909 9 3743 3699.9 0.503 1.412 10 2639 2666.3 0.279 1.692 11 1877 1923.3 1.116 2.808 12 1343 1388.7 1.507 4.314 13 994 1003.7 0.094 4.408 14 694 726.1 1.423 5.831 15 502 525.8 1.080 6.911 16 402 381.2 1.140 8.052 17 278 276.5 0.008 8.060 18 193 200.8 0.305 8.365 19 144 146.0 0.027 8.392 20 99 106.2 0.490 8.882 21 281 287.1 0.130 9.012 Chisq= 9.01 for 20 degrees of freedom, p= 0.01723 SUMMARY of craptest p-value for no. of wins: 0.525216 p-value for throws/game: 0.017234 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0024,0.0025,0.0026,0.0057,0.0059,0.0104,0.0172,0.0176,0.0211,0.0316, 0.0374,0.0416,0.0446,0.0482,0.0494,0.0552,0.0554,0.0555,0.0583,0.0600, 0.0628,0.0655,0.0704,0.0722,0.0723,0.0731,0.0739,0.0759,0.0785,0.0794, 0.0857,0.0886,0.0932,0.0972,0.1005,0.1018,0.1032,0.1035,0.1037,0.1051, 0.1054,0.1115,0.1157,0.1218,0.1269,0.1311,0.1370,0.1418,0.1458,0.1462, 0.1478,0.1488,0.1521,0.1534,0.1654,0.1657,0.1688,0.1727,0.1762,0.1815, 0.1832,0.1881,0.1886,0.1896,0.1966,0.2038,0.2100,0.2185,0.2227,0.2266, 0.2283,0.2299,0.2346,0.2359,0.2360,0.2379,0.2411,0.2456,0.2522,0.2565, 0.2572,0.2590,0.2592,0.2649,0.2764,0.2764,0.2769,0.2776,0.2787,0.2800, 0.2809,0.2845,0.2911,0.2944,0.2992,0.3074,0.3079,0.3081,0.3132,0.3132, 0.3214,0.3216,0.3303,0.3304,0.3392,0.3454,0.3467,0.3467,0.3544,0.3569, 0.3574,0.3586,0.3595,0.3647,0.3669,0.3747,0.3763,0.3786,0.3889,0.3942, 0.3988,0.4040,0.4182,0.4190,0.4201,0.4203,0.4309,0.4349,0.4376,0.4387, 0.4414,0.4480,0.4523,0.4532,0.4560,0.4620,0.4621,0.4680,0.4765,0.4769, 0.4820,0.4878,0.4957,0.4965,0.4979,0.5030,0.5063,0.5133,0.5140,0.5148, 0.5180,0.5212,0.5220,0.5252,0.5261,0.5325,0.5378,0.5379,0.5383,0.5425, 0.5431,0.5500,0.5508,0.5550,0.5554,0.5591,0.5619,0.5653,0.5670,0.5687, 0.5725,0.5781,0.5860,0.5869,0.5908,0.5910,0.5951,0.5952,0.5962,0.6051, 0.6056,0.6163,0.6168,0.6253,0.6261,0.6288,0.6297,0.6313,0.6383,0.6406, 0.6420,0.6422,0.6423,0.6464,0.6487,0.6528,0.6571,0.6606,0.6674,0.6733, 0.6751,0.6919,0.6941,0.6974,0.7064,0.7094,0.7107,0.7116,0.7284,0.7303, 0.7311,0.7356,0.7388,0.7411,0.7455,0.7463,0.7463,0.7639,0.7687,0.7812, 0.7817,0.7844,0.7856,0.7927,0.7937,0.7997,0.8072,0.8124,0.8152,0.8215, 0.8297,0.8331,0.8365,0.8440,0.8451,0.8491,0.8554,0.8580,0.8589,0.8609, 0.8634,0.8851,0.8867,0.9031,0.9067,0.9128,0.9130,0.9146,0.9155,0.9201, 0.9204,0.9205,0.9215,0.9269,0.9302,0.9337,0.9351,0.9359,0.9390,0.9397, 0.9404,0.9469,0.9627,0.9673,0.9755,0.9845,0.9846,0.9897,0.9999, Overall p-value after applying KStest on 269 p-values = 0.039414 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.