RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-07-02_01:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.66 16.3993 0.504278 2 to 25 15.75 14.3226 0.355848 3 to 26 15.70 22.0651 0.817770 4 to 27 15.51 16.7508 0.528633 5 to 28 15.78 24.7765 0.900176 6 to 29 15.88 13.0539 0.267428 7 to 30 15.86 15.8682 0.466807 8 to 31 15.72 20.2491 0.738314 9 to 32 15.62 13.5997 0.304793 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.650082 Tough bday spacings test for dh-ranFile-2015-07-02_01:31: 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 38 73 89 108 71 51 34 19 2 4 (O-E)^2/E 0.4 0.1 0.0 0.8 1.1 0.7 0.0 0.6 1.1 3.2 0.0 Birthday Spacings: Sum(O-E)^2/E= 7.921, p= 0.363 RESULTS OF GCD FOR dh-ranFile-2015-07-02_01:31 Euclid's algorithm: p-value, steps to gcd: 0.733301 p-value, dist. of gcd's: 0.856283 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-07-02_01:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.879 0.205 0.054 0.242 0.485 0.730 0.074 0.613 Bits 8 to 15---> 0.237 0.334 0.713 0.353 0.449 0.204 0.762 0.258 Bits 16 to 23---> 0.368 0.661 0.772 0.589 0.498 0.257 0.609 0.271 Bits 24 to 31---> 0.975 0.840 0.647 0.883 0.683 0.052 0.064 0.524 KS test for the above 32 p values: 0.172 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-07-02_01:31, p-values for 5 runs: 0.5801, 0.6756, 0.4650, 0.6533, 0.0079 Rank test for binary matrices (31x31) for dh-ranFile-2015-07-02_01:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 235 211.4 2.630 2.630 r= 29 5063 5134.0 0.982 3.613 r= 30 23099 23103.0 0.001 3.613 r= 31 11603 11551.5 0.229 3.843 chi-square = 3.843 with df = 3; p-value = 0.721 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-07-02_01:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 208 211.4 0.055 0.055 r= 30 5175 5134.0 0.327 0.383 r= 31 23088 23103.0 0.010 0.392 r= 32 11529 11551.5 0.044 0.436 chi-square = 0.436 with df = 3; p-value = 0.067 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-07-02_01:31 b-rank test for bits 1 to 8, p=0.05194 b-rank test for bits 2 to 9, p=0.61852 b-rank test for bits 3 to 10, p=0.91269 b-rank test for bits 4 to 11, p=0.66873 b-rank test for bits 5 to 12, p=0.79653 b-rank test for bits 6 to 13, p=0.23689 b-rank test for bits 7 to 14, p=0.88114 b-rank test for bits 8 to 15, p=0.54801 b-rank test for bits 9 to 16, p=0.77277 b-rank test for bits 10 to 17, p=0.24435 b-rank test for bits 11 to 18, p=0.42762 b-rank test for bits 12 to 19, p=0.58783 b-rank test for bits 13 to 20, p=0.57352 b-rank test for bits 14 to 21, p=0.12526 b-rank test for bits 15 to 22, p=0.32449 b-rank test for bits 16 to 23, p=0.10715 b-rank test for bits 17 to 24, p=0.87803 b-rank test for bits 18 to 25, p=0.33451 b-rank test for bits 19 to 26, p=0.60339 b-rank test for bits 20 to 27, p=0.67593 b-rank test for bits 21 to 28, p=0.11981 b-rank test for bits 22 to 29, p=0.21777 b-rank test for bits 23 to 30, p=0.04509 b-rank test for bits 24 to 31, p=0.22978 b-rank test for bits 25 to 32, p=0.73451 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 = 0.818831 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-07-02_01:31 (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 142516 1.42 0.921825 2 141187 -1.69 0.045736 3 142166 0.60 0.725646 4 141999 0.21 0.582975 5 141496 -0.97 0.167091 6 142239 0.77 0.779426 7 142119 0.49 0.687892 8 141787 -0.29 0.387509 9 141458 -1.05 0.145825 10 141682 -0.53 0.297659 11 141996 0.20 0.580237 12 141964 0.13 0.550820 13 141719 -0.44 0.328270 14 142626 1.67 0.952980 15 141512 -0.93 0.176615 16 142053 0.34 0.631443 17 141851 -0.14 0.445798 18 142324 0.97 0.833691 19 141947 0.09 0.535067 20 142888 2.29 0.988891 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-07-02_01:31 Bits used No. missing words z-score p-value 23 to 32 141804 -0.3632 0.358225 22 to 31 142612 2.4230 0.992304 21 to 30 141968 0.2023 0.580163 20 to 29 141879 -0.1046 0.458352 19 to 28 141832 -0.2667 0.394867 18 to 27 141835 -0.2563 0.398856 17 to 26 142376 1.6092 0.946214 16 to 25 141712 -0.6804 0.248110 15 to 24 141508 -1.3839 0.083195 14 to 23 141676 -0.8046 0.210529 13 to 22 141716 -0.6667 0.252496 12 to 21 141818 -0.3149 0.376407 11 to 20 141900 -0.0322 0.487167 10 to 19 141288 -2.1425 0.016076 9 to 18 141190 -2.4804 0.006561 8 to 17 141951 0.1437 0.557127 7 to 16 141703 -0.7115 0.238393 6 to 15 142139 0.7920 0.785810 5 to 14 142553 2.2196 0.986775 4 to 13 142441 1.8333 0.966624 3 to 12 142042 0.4575 0.676338 2 to 11 141337 -1.9736 0.024216 1 to 10 141783 -0.4356 0.331556 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-07-02_01:31 Bits used No. missing words z-score p-value 28 to 32 142013 0.3514 0.637365 27 to 31 141586 -1.0960 0.136532 26 to 30 142430 1.7650 0.961217 25 to 29 142159 0.8463 0.801318 24 to 28 142222 1.0599 0.855405 23 to 27 141402 -1.7198 0.042738 22 to 26 141699 -0.7130 0.237928 21 to 25 141322 -1.9909 0.023243 20 to 24 142129 0.7446 0.771757 19 to 23 142207 1.0091 0.843525 18 to 22 141491 -1.4181 0.078086 17 to 21 141608 -1.0215 0.153519 16 to 20 141795 -0.3876 0.349171 15 to 19 142047 0.4667 0.679635 14 to 18 142097 0.6362 0.737667 13 to 17 142443 1.8091 0.964778 12 to 16 141743 -0.5638 0.286435 11 to 15 142034 0.4226 0.663710 10 to 14 141899 -0.0350 0.486033 9 to 13 142002 0.3141 0.623291 8 to 12 141924 0.0497 0.519831 7 to 11 141852 -0.1943 0.422955 6 to 10 142066 0.5311 0.702320 5 to 9 142046 0.4633 0.678421 4 to 8 141723 -0.6316 0.263815 3 to 7 141490 -1.4215 0.077592 2 to 6 142444 1.8124 0.965041 1 to 5 141860 -0.1672 0.433598 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-07-02_01:31 Bits used No. missing words z-score p-value 31 to 32 142170 0.7689 0.779035 30 to 31 141765 -0.4258 0.335144 29 to 30 141690 -0.6470 0.258819 28 to 29 141569 -1.0039 0.157708 27 to 28 142099 0.5595 0.712089 26 to 27 141558 -1.0364 0.150014 25 to 26 142495 1.7276 0.957974 24 to 25 141928 0.0551 0.521960 23 to 24 141137 -2.2783 0.011356 22 to 23 141707 -0.5968 0.275306 21 to 22 141447 -1.3638 0.086314 20 to 21 141764 -0.4287 0.334070 19 to 20 141842 -0.1986 0.421283 18 to 19 141544 -1.0777 0.140591 17 to 18 141692 -0.6411 0.260732 16 to 17 142273 1.0728 0.858314 15 to 16 141749 -0.4729 0.318125 14 to 15 141944 0.1023 0.540729 13 to 14 141520 -1.1485 0.125388 12 to 13 141570 -1.0010 0.158420 11 to 12 142146 0.6981 0.757456 10 to 11 142089 0.5300 0.701944 9 to 10 141557 -1.0393 0.149328 8 to 9 141940 0.0905 0.536044 7 to 8 141870 -0.1160 0.453819 6 to 7 142677 2.2645 0.988229 5 to 6 142495 1.7276 0.957974 4 to 5 142327 1.2321 0.891038 3 to 4 142002 0.2734 0.607713 2 to 3 141852 -0.1691 0.432853 1 to 2 141796 -0.3343 0.369074 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-07-02_01:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2614.07 1.613 0.946646 Test results for specific bytes for dh-ranFile-2015-07-02_01:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2382.00 -1.669 0.047583 2 to 9 2407.62 -1.306 0.095698 3 to 10 2421.89 -1.105 0.134642 4 to 11 2508.43 0.119 0.547449 5 to 12 2441.66 -0.825 0.204671 6 to 13 2540.23 0.569 0.715291 7 to 14 2549.59 0.701 0.758446 8 to 15 2470.44 -0.418 0.337963 9 to 16 2464.40 -0.503 0.307320 10 to 17 2506.49 0.092 0.536567 11 to 18 2517.11 0.242 0.595579 12 to 19 2442.19 -0.818 0.206794 13 to 20 2501.89 0.027 0.510677 14 to 21 2513.16 0.186 0.573800 15 to 22 2537.98 0.537 0.704416 16 to 23 2441.90 -0.822 0.205648 17 to 24 2466.94 -0.467 0.320076 18 to 25 2523.38 0.331 0.629535 19 to 26 2478.00 -0.311 0.377857 20 to 27 2476.31 -0.335 0.368816 21 to 28 2594.11 1.331 0.908394 22 to 29 2459.46 -0.573 0.283206 23 to 30 2277.98 -3.140 0.000845 24 to 31 2508.85 0.125 0.549782 25 to 32 2475.93 -0.340 0.366792 CDPARK for dh-ranFile-2015-07-02_01:31: 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 3525 0.0913 0.536383 3496 -1.2329 0.108811 3539 0.7306 0.767486 3538 0.6849 0.753306 3545 1.0046 0.842447 3501 -1.0046 0.157553 3522 -0.0457 0.481790 3499 -1.0959 0.136563 3513 -0.4566 0.323972 3510 -0.5936 0.276387 Square side=100, avg. no. parked=3518.80 sample std.=16.89 p-value of the KSTEST for those 10 p-values: 0.746660 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-07-02_01:31 0.0019,0.0517,0.4477,0.5722,0.3548,0.4613,0.6676,0.2762,0.4078,0.4002, The KS test for those 10 p-values: 0.105888 The 3DSPHERES test for dh-ranFile-2015-07-02_01:31 sample no r^3 equiv. uni. 1 6.454 0.193569 2 122.976 0.983414 3 22.818 0.532612 4 26.313 0.584012 5 18.343 0.457419 6 3.146 0.099557 7 21.411 0.510174 8 0.385 0.012752 9 61.791 0.872510 10 14.761 0.388608 11 55.309 0.841757 12 32.797 0.664874 13 20.405 0.493472 14 15.403 0.401555 15 51.584 0.820838 16 141.253 0.990981 17 14.005 0.373016 18 15.357 0.400639 19 7.353 0.217379 20 49.680 0.809097 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.745413 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-07-02_01:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 1.8 0.8 1.2 0.0 0.6 0.5 -1.1 -0.2 -1.2 -1.3 0.7 -0.3 0.4 1.2 0.6 -0.9 0.2 -1.2 1.1 -0.2 0.1 0.6 -0.8 -0.5 1.4 0.7 -0.7 -1.4 -0.2 0.9 -0.9 -0.6 -1.8 1.7 -1.2 0.7 0.5 1.7 1.5 4.6 0.0 -1.1 Chi-square with 42 degrees of freedom:63.164918 z-score=2.309282, p-value=0.981079 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-07-02_01:31 Test no p-value 1 0.795968 2 0.221287 3 0.016208 4 0.778624 5 0.127245 6 0.319047 7 0.589580 8 0.549255 9 0.254907 10 0.186590 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.344605 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-07-02_01:31: (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 66874 0.64 66637 0.01 3 25000.00 24886 0.52 25032 0.04 4 6666.67 6527 2.93 6623 0.29 5 1388.89 1427 1.05 1423 0.84 6 238.10 243 0.10 251 0.70 7 34.72 36 0.05 30 0.64 8 4.96 6 0.22 3 0.77 p=0.51888 p=0.22880 Number of rngs required: 688352, p-value: 0.477 RESULTS OF CRAPS TEST for dh-ranFile-2015-07-02_01:31 No. of wins: Observed Expected 98689 98585.9 z-score= 0.461, pvalue=0.67771 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67159 66666.7 3.636 3.636 2 37557 37654.3 0.252 3.887 3 27060 26954.7 0.411 4.299 4 19198 19313.5 0.690 4.989 5 13737 13851.4 0.945 5.934 6 9718 9943.5 5.116 11.050 7 7157 7145.0 0.020 11.070 8 5144 5139.1 0.005 11.075 9 3709 3699.9 0.023 11.097 10 2709 2666.3 0.684 11.781 11 1833 1923.3 4.242 16.023 12 1356 1388.7 0.772 16.795 13 1025 1003.7 0.451 17.247 14 739 726.1 0.228 17.474 15 564 525.8 2.770 20.244 16 362 381.2 0.962 21.206 17 254 276.5 1.837 23.044 18 188 200.8 0.820 23.863 19 145 146.0 0.007 23.870 20 104 106.2 0.046 23.916 21 282 287.1 0.091 24.007 Chisq= 24.01 for 20 degrees of freedom, p= 0.75792 SUMMARY of craptest p-value for no. of wins: 0.677711 p-value for throws/game: 0.757917 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-07-02_01:31 No. of wins: Observed Expected 98541 98585.9 z-score=-0.201, pvalue=0.42049 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66898 66666.7 0.803 0.803 2 37711 37654.3 0.085 0.888 3 27337 26954.7 5.421 6.309 4 19306 19313.5 0.003 6.312 5 13771 13851.4 0.467 6.779 6 9799 9943.5 2.101 8.880 7 7037 7145.0 1.633 10.513 8 5110 5139.1 0.164 10.678 9 3544 3699.9 6.566 17.244 10 2624 2666.3 0.671 17.915 11 1887 1923.3 0.686 18.601 12 1404 1388.7 0.168 18.769 13 1006 1003.7 0.005 18.774 14 720 726.1 0.052 18.826 15 468 525.8 6.361 25.187 16 395 381.2 0.503 25.691 17 270 276.5 0.155 25.845 18 203 200.8 0.023 25.869 19 152 146.0 0.248 26.117 20 96 106.2 0.982 27.099 21 262 287.1 2.197 29.296 Chisq= 29.30 for 20 degrees of freedom, p= 0.91790 SUMMARY of craptest p-value for no. of wins: 0.420492 p-value for throws/game: 0.917903 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0008,0.0019,0.0066,0.0079,0.0114,0.0128,0.0161,0.0162,0.0232,0.0242, 0.0427,0.0451,0.0457,0.0476,0.0517,0.0519,0.0523,0.0545,0.0642,0.0673, 0.0742,0.0776,0.0781,0.0832,0.0863,0.0957,0.0996,0.1059,0.1071,0.1088, 0.1198,0.1253,0.1254,0.1272,0.1346,0.1365,0.1366,0.1406,0.1458,0.1493, 0.1500,0.1535,0.1576,0.1577,0.1584,0.1671,0.1720,0.1766,0.1866,0.1936, 0.2037,0.2046,0.2047,0.2056,0.2068,0.2105,0.2174,0.2178,0.2213,0.2288, 0.2298,0.2369,0.2372,0.2379,0.2384,0.2416,0.2444,0.2481,0.2525,0.2549, 0.2567,0.2583,0.2588,0.2607,0.2638,0.2674,0.2706,0.2753,0.2762,0.2764, 0.2832,0.2864,0.2977,0.3048,0.3073,0.3181,0.3190,0.3201,0.3240,0.3245, 0.3283,0.3316,0.3339,0.3341,0.3345,0.3351,0.3380,0.3446,0.3492,0.3533, 0.3548,0.3558,0.3582,0.3634,0.3668,0.3683,0.3688,0.3691,0.3730,0.3764, 0.3779,0.3875,0.3886,0.3949,0.3989,0.4002,0.4006,0.4016,0.4078,0.4205, 0.4213,0.4230,0.4276,0.4329,0.4336,0.4458,0.4477,0.4489,0.4538,0.4574, 0.4584,0.4613,0.4650,0.4668,0.4766,0.4818,0.4846,0.4860,0.4872,0.4935, 0.4984,0.5043,0.5102,0.5107,0.5189,0.5198,0.5220,0.5239,0.5286,0.5326, 0.5351,0.5360,0.5364,0.5366,0.5407,0.5474,0.5480,0.5493,0.5498,0.5508, 0.5571,0.5722,0.5735,0.5738,0.5801,0.5802,0.5802,0.5830,0.5840,0.5878, 0.5893,0.5896,0.5956,0.6034,0.6077,0.6095,0.6133,0.6185,0.6233,0.6295, 0.6314,0.6374,0.6466,0.6501,0.6533,0.6607,0.6637,0.6649,0.6676,0.6687, 0.6756,0.6759,0.6763,0.6777,0.6784,0.6796,0.6829,0.6879,0.7019,0.7023, 0.7044,0.7121,0.7134,0.7153,0.7210,0.7256,0.7304,0.7333,0.7345,0.7377, 0.7383,0.7454,0.7467,0.7533,0.7575,0.7579,0.7584,0.7616,0.7675,0.7718, 0.7720,0.7728,0.7786,0.7790,0.7794,0.7858,0.7960,0.7965,0.8013,0.8091, 0.8178,0.8188,0.8208,0.8337,0.8402,0.8418,0.8424,0.8435,0.8554,0.8563, 0.8583,0.8725,0.8780,0.8794,0.8811,0.8831,0.8910,0.9002,0.9084,0.9127, 0.9179,0.9218,0.9462,0.9466,0.9530,0.9580,0.9580,0.9612,0.9648,0.9650, 0.9666,0.9752,0.9811,0.9834,0.9868,0.9882,0.9889,0.9910,0.9923, Overall p-value after applying KStest on 269 p-values = 0.327880 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.