RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-09_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 15.68 25.6315 0.918558 2 to 25 15.60 17.7927 0.597972 3 to 26 15.57 23.5095 0.866614 4 to 27 15.86 10.4588 0.116723 5 to 28 15.84 18.6245 0.649495 6 to 29 15.90 17.6564 0.589178 7 to 30 15.97 17.7096 0.592620 8 to 31 15.79 18.0244 0.612696 9 to 32 15.96 14.2550 0.351022 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.388526 Tough bday spacings test for dh-ranFile-2018-07-09_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 13 37 65 96 105 61 54 41 14 10 4 (O-E)^2/E 1.6 0.0 0.9 0.0 0.5 3.8 0.1 4.2 0.1 1.7 0.0 Birthday Spacings: Sum(O-E)^2/E= 12.977, p= 0.775 RESULTS OF GCD FOR dh-ranFile-2018-07-09_19:31 Euclid's algorithm: p-value, steps to gcd: 0.489542 p-value, dist. of gcd's: 0.891444 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-09_19:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.282 0.357 0.132 0.043 0.890 0.466 0.464 0.371 Bits 8 to 15---> 0.795 0.619 0.398 0.842 0.875 0.055 0.178 0.060 Bits 16 to 23---> 0.687 0.558 0.286 0.660 0.791 0.204 0.569 0.239 Bits 24 to 31---> 0.898 0.237 0.284 0.014 0.228 0.877 0.954 0.789 KS test for the above 32 p values: 0.169 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-09_19:31, p-values for 5 runs: 0.9336, 0.5925, 0.9552, 0.9211, 0.5889 Rank test for binary matrices (31x31) for dh-ranFile-2018-07-09_19:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 185 211.4 3.301 3.301 r= 29 5156 5134.0 0.094 3.395 r= 30 23102 23103.0 0.000 3.395 r= 31 11557 11551.5 0.003 3.398 chi-square = 3.398 with df = 3; p-value = 0.666 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-07-09_19:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 216 211.4 0.099 0.099 r= 30 5116 5134.0 0.063 0.162 r= 31 23081 23103.0 0.021 0.184 r= 32 11587 11551.5 0.109 0.292 chi-square = 0.292 with df = 3; p-value = 0.039 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-07-09_19:31 b-rank test for bits 1 to 8, p=0.15777 b-rank test for bits 2 to 9, p=0.52096 b-rank test for bits 3 to 10, p=0.61779 b-rank test for bits 4 to 11, p=0.08674 b-rank test for bits 5 to 12, p=0.68756 b-rank test for bits 6 to 13, p=0.96388 b-rank test for bits 7 to 14, p=0.37120 b-rank test for bits 8 to 15, p=0.76337 b-rank test for bits 9 to 16, p=0.21087 b-rank test for bits 10 to 17, p=0.22141 b-rank test for bits 11 to 18, p=0.87980 b-rank test for bits 12 to 19, p=0.16230 b-rank test for bits 13 to 20, p=0.20515 b-rank test for bits 14 to 21, p=0.57326 b-rank test for bits 15 to 22, p=0.49082 b-rank test for bits 16 to 23, p=0.22141 b-rank test for bits 17 to 24, p=0.62273 b-rank test for bits 18 to 25, p=0.20389 b-rank test for bits 19 to 26, p=0.97236 b-rank test for bits 20 to 27, p=0.85774 b-rank test for bits 21 to 28, p=0.07561 b-rank test for bits 22 to 29, p=0.44766 b-rank test for bits 23 to 30, p=0.62100 b-rank test for bits 24 to 31, p=0.21214 b-rank test for bits 25 to 32, p=0.59239 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 = 0.650720 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-09_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 143346 3.36 0.999606 2 141688 -0.52 0.302534 3 142018 0.25 0.600214 4 141974 0.15 0.560051 5 141819 -0.21 0.416424 6 141443 -1.09 0.137954 7 142140 0.54 0.705039 8 142147 0.56 0.710657 9 141981 0.17 0.566493 10 141792 -0.27 0.391990 11 141971 0.14 0.557285 12 141722 -0.44 0.330807 13 142198 0.67 0.749991 14 142339 1.00 0.842287 15 142037 0.30 0.617261 16 141271 -1.49 0.067925 17 141557 -0.82 0.205197 18 142353 1.04 0.850042 19 141916 0.02 0.506217 20 142376 1.09 0.862221 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-07-09_19:31 Bits used No. missing words z-score p-value 23 to 32 141175 -2.5322 0.005668 22 to 31 141313 -2.0563 0.019876 21 to 30 142055 0.5023 0.692275 20 to 29 141855 -0.1873 0.425695 19 to 28 142014 0.3609 0.640925 18 to 27 141526 -1.3218 0.093113 17 to 26 141564 -1.1908 0.116867 16 to 25 142206 1.0230 0.846846 15 to 24 142321 1.4196 0.922131 14 to 23 141910 0.0023 0.500922 13 to 22 141593 -1.0908 0.137682 12 to 21 141377 -1.8356 0.033207 11 to 20 141751 -0.5460 0.292545 10 to 19 142301 1.3506 0.911586 9 to 18 141797 -0.3873 0.349251 8 to 17 142201 1.0058 0.842734 7 to 16 141992 0.2851 0.612204 6 to 15 142036 0.4368 0.668869 5 to 14 141947 0.1299 0.551676 4 to 13 141940 0.1058 0.542113 3 to 12 142585 2.3299 0.990094 2 to 11 142756 2.9196 0.998247 1 to 10 142275 1.2609 0.896333 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-07-09_19:31 Bits used No. missing words z-score p-value 28 to 32 141517 -1.3299 0.091770 27 to 31 141777 -0.4486 0.326869 26 to 30 141502 -1.3808 0.083673 25 to 29 142060 0.5107 0.695236 24 to 28 141793 -0.3943 0.346665 23 to 27 142047 0.4667 0.679635 22 to 26 142057 0.5006 0.691665 21 to 25 141867 -0.1435 0.442951 20 to 24 141244 -2.2554 0.012056 19 to 23 142171 0.8870 0.812465 18 to 22 141999 0.3040 0.619423 17 to 21 142366 1.5480 0.939193 16 to 20 142179 0.9141 0.819677 15 to 19 141515 -1.3367 0.090658 14 to 18 142035 0.4260 0.664946 13 to 17 141917 0.0260 0.510371 12 to 16 142222 1.0599 0.855405 11 to 15 142276 1.2429 0.893057 10 to 14 141933 0.0802 0.531976 9 to 13 142248 1.1480 0.874523 8 to 12 141899 -0.0350 0.486033 7 to 11 141734 -0.5943 0.276143 6 to 10 141843 -0.2248 0.411049 5 to 9 141606 -1.0282 0.151919 4 to 8 142191 0.9548 0.830164 3 to 7 141625 -0.9638 0.167565 2 to 6 142346 1.4802 0.930595 1 to 5 141746 -0.5537 0.289905 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-07-09_19:31 Bits used No. missing words z-score p-value 31 to 32 141654 -0.7532 0.225669 30 to 31 142142 0.6863 0.753751 29 to 30 141815 -0.2783 0.390407 28 to 29 141930 0.0610 0.524310 27 to 28 142205 0.8722 0.808446 26 to 27 141378 -1.5673 0.058517 25 to 26 141328 -1.7148 0.043188 24 to 25 141588 -0.9479 0.171596 23 to 24 142249 1.0020 0.841823 22 to 23 141945 0.1052 0.541900 21 to 22 142048 0.4091 0.658751 20 to 21 142274 1.0757 0.858974 19 to 20 142064 0.4563 0.675896 18 to 19 141909 -0.0010 0.499612 17 to 18 142232 0.9518 0.829408 16 to 17 142088 0.5271 0.700921 15 to 16 142125 0.6362 0.737675 14 to 15 142271 1.0669 0.856985 13 to 14 142689 2.2999 0.989273 12 to 13 142680 2.2734 0.988498 11 to 12 141863 -0.1367 0.445647 10 to 11 142437 1.5565 0.940211 9 to 10 142019 0.3235 0.626846 8 to 9 141439 -1.3874 0.082659 7 to 8 142188 0.8220 0.794472 6 to 7 141760 -0.4405 0.329787 5 to 6 141224 -2.0216 0.021608 4 to 5 142362 1.3353 0.909113 3 to 4 142092 0.5388 0.705005 2 to 3 141898 -0.0334 0.486669 1 to 2 142409 1.4740 0.929753 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-09_19:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2458.19 -0.591 0.277168 Test results for specific bytes for dh-ranFile-2018-07-09_19:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2482.89 -0.242 0.404404 2 to 9 2546.28 0.655 0.743624 3 to 10 2535.50 0.502 0.692175 4 to 11 2561.23 0.866 0.806737 5 to 12 2608.45 1.534 0.937447 6 to 13 2500.61 0.009 0.503459 7 to 14 2453.66 -0.655 0.256131 8 to 15 2505.04 0.071 0.528428 9 to 16 2582.60 1.168 0.878637 10 to 17 2499.58 -0.006 0.497622 11 to 18 2279.47 -3.119 0.000908 12 to 19 2470.22 -0.421 0.336839 13 to 20 2397.94 -1.443 0.074464 14 to 21 2356.06 -2.036 0.020895 15 to 22 2540.14 0.568 0.714891 16 to 23 2456.68 -0.613 0.270063 17 to 24 2372.48 -1.803 0.035659 18 to 25 2566.79 0.945 0.827573 19 to 26 2536.49 0.516 0.697090 20 to 27 2483.81 -0.229 0.409435 21 to 28 2622.29 1.729 0.958131 22 to 29 2562.90 0.890 0.813135 23 to 30 2440.91 -0.836 0.201689 24 to 31 2494.32 -0.080 0.468013 25 to 32 2529.76 0.421 0.663083 CDPARK for dh-ranFile-2018-07-09_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 3547 1.0959 0.863437 3491 -1.4612 0.071982 3513 -0.4566 0.323972 3522 -0.0457 0.481790 3520 -0.1370 0.445521 3545 1.0046 0.842447 3552 1.3242 0.907282 3516 -0.3196 0.374623 3539 0.7306 0.767486 3533 0.4566 0.676028 Square side=100, avg. no. parked=3527.80 sample std.=17.92 p-value of the KSTEST for those 10 p-values: 0.669217 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-09_19:31 0.9510,0.1527,0.1089,0.2722,0.1316,0.7552,0.6158,0.8034,0.9774,0.2682, The KS test for those 10 p-values: 0.625874 The 3DSPHERES test for dh-ranFile-2018-07-09_19:31 sample no r^3 equiv. uni. 1 76.799 0.922693 2 21.529 0.512089 3 35.968 0.698484 4 10.715 0.300347 5 0.439 0.014524 6 109.907 0.974359 7 33.153 0.668818 8 0.707 0.023289 9 61.672 0.872000 10 44.591 0.773805 11 111.861 0.975976 12 13.154 0.354980 13 21.865 0.517529 14 21.640 0.513895 15 46.250 0.785974 16 18.525 0.460710 17 58.993 0.860047 18 4.372 0.135619 19 18.907 0.467526 20 14.127 0.375569 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.496750 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-09_19:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.1 -0.1 -1.6 1.9 0.1 0.2 -0.7 -0.3 -0.7 1.1 -1.3 -0.7 -1.3 -0.8 0.3 1.3 0.5 -1.2 -0.9 2.5 -1.0 1.0 0.5 0.1 0.6 -0.3 -0.0 1.6 -1.5 0.8 0.8 0.0 0.7 0.2 0.2 1.9 -1.0 0.1 -0.1 0.1 0.0 -1.1 Chi-square with 42 degrees of freedom:38.433481 z-score=-0.389139, p-value=0.371687 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-07-09_19:31 Test no p-value 1 0.207345 2 0.076528 3 0.033279 4 0.000594 5 0.588981 6 0.969464 7 0.986269 8 0.018875 9 0.946675 10 0.582453 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.024716 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-09_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 66529 0.28 66734 0.07 3 25000.00 25083 0.28 24983 0.01 4 6666.67 6741 0.83 6592 0.84 5 1388.89 1384 0.02 1402 0.12 6 238.10 222 1.09 251 0.70 7 34.72 33 0.09 30 0.64 8 4.96 7 0.84 7 0.84 p=0.24517 p=0.21920 Number of rngs required: 687865, p-value: 0.267 RESULTS OF CRAPS TEST for dh-ranFile-2018-07-09_19:31 No. of wins: Observed Expected 98703 98585.9 z-score= 0.524, pvalue=0.69983 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66836 66666.7 0.430 0.430 2 37263 37654.3 4.067 4.497 3 27360 26954.7 6.093 10.590 4 19090 19313.5 2.586 13.176 5 13970 13851.4 1.015 14.191 6 9799 9943.5 2.101 16.292 7 7060 7145.0 1.012 17.304 8 5230 5139.1 1.609 18.913 9 3715 3699.9 0.062 18.974 10 2660 2666.3 0.015 18.989 11 1938 1923.3 0.112 19.101 12 1424 1388.7 0.895 19.996 13 971 1003.7 1.066 21.063 14 771 726.1 2.771 23.834 15 538 525.8 0.281 24.116 16 388 381.2 0.123 24.239 17 266 276.5 0.402 24.640 18 185 200.8 1.248 25.888 19 152 146.0 0.248 26.136 20 98 106.2 0.635 26.771 21 286 287.1 0.004 26.776 Chisq= 26.78 for 20 degrees of freedom, p= 0.85831 SUMMARY of craptest p-value for no. of wins: 0.699835 p-value for throws/game: 0.858305 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-09_19:31 No. of wins: Observed Expected 98714 98585.9 z-score= 0.573, pvalue=0.71672 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66483 66666.7 0.506 0.506 2 37500 37654.3 0.632 1.138 3 27122 26954.7 1.038 2.176 4 19483 19313.5 1.488 3.665 5 13917 13851.4 0.310 3.975 6 10032 9943.5 0.787 4.762 7 7152 7145.0 0.007 4.769 8 4997 5139.1 3.928 8.697 9 3698 3699.9 0.001 8.697 10 2675 2666.3 0.028 8.726 11 1999 1923.3 2.977 11.703 12 1383 1388.7 0.024 11.727 13 941 1003.7 3.919 15.645 14 704 726.1 0.675 16.320 15 524 525.8 0.006 16.327 16 397 381.2 0.659 16.986 17 275 276.5 0.009 16.995 18 210 200.8 0.419 17.413 19 139 146.0 0.334 17.747 20 106 106.2 0.000 17.748 21 263 287.1 2.025 19.773 Chisq= 19.77 for 20 degrees of freedom, p= 0.52780 SUMMARY of craptest p-value for no. of wins: 0.716719 p-value for throws/game: 0.527800 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0006,0.0009,0.0057,0.0121,0.0143,0.0145,0.0189,0.0199,0.0209,0.0216, 0.0233,0.0247,0.0332,0.0333,0.0357,0.0386,0.0432,0.0432,0.0553,0.0585, 0.0603,0.0679,0.0720,0.0745,0.0756,0.0765,0.0827,0.0837,0.0867,0.0907, 0.0918,0.0931,0.1089,0.1167,0.1169,0.1316,0.1317,0.1356,0.1377,0.1380, 0.1519,0.1527,0.1578,0.1623,0.1676,0.1687,0.1716,0.1777,0.2017,0.2039, 0.2042,0.2052,0.2052,0.2073,0.2109,0.2121,0.2192,0.2214,0.2214,0.2257, 0.2276,0.2365,0.2391,0.2452,0.2561,0.2674,0.2682,0.2701,0.2722,0.2761, 0.2772,0.2815,0.2839,0.2865,0.2899,0.2925,0.3003,0.3025,0.3240,0.3269, 0.3298,0.3308,0.3368,0.3467,0.3493,0.3510,0.3550,0.3569,0.3711,0.3712, 0.3717,0.3746,0.3756,0.3885,0.3904,0.3920,0.3980,0.4044,0.4094,0.4110, 0.4164,0.4257,0.4430,0.4455,0.4456,0.4477,0.4607,0.4640,0.4664,0.4675, 0.4680,0.4818,0.4860,0.4867,0.4895,0.4908,0.4967,0.4976,0.4996,0.5009, 0.5035,0.5062,0.5104,0.5121,0.5139,0.5175,0.5210,0.5243,0.5278,0.5284, 0.5320,0.5419,0.5421,0.5517,0.5573,0.5582,0.5601,0.5665,0.5686,0.5733, 0.5825,0.5889,0.5890,0.5892,0.5924,0.5925,0.5926,0.5980,0.6002,0.6122, 0.6127,0.6158,0.6173,0.6178,0.6190,0.6194,0.6210,0.6227,0.6259,0.6268, 0.6409,0.6495,0.6507,0.6588,0.6600,0.6631,0.6649,0.6658,0.6688,0.6689, 0.6692,0.6759,0.6760,0.6796,0.6875,0.6876,0.6917,0.6922,0.6923,0.6952, 0.6971,0.6985,0.6998,0.7009,0.7050,0.7050,0.7107,0.7149,0.7167,0.7377, 0.7436,0.7500,0.7538,0.7552,0.7634,0.7675,0.7738,0.7751,0.7860,0.7888, 0.7906,0.7945,0.7945,0.8034,0.8067,0.8084,0.8125,0.8131,0.8197,0.8276, 0.8294,0.8302,0.8418,0.8418,0.8423,0.8424,0.8427,0.8468,0.8500,0.8554, 0.8570,0.8577,0.8583,0.8590,0.8600,0.8622,0.8634,0.8666,0.8720,0.8745, 0.8754,0.8768,0.8786,0.8798,0.8899,0.8914,0.8931,0.8963,0.8977,0.9073, 0.9091,0.9116,0.9186,0.9211,0.9221,0.9227,0.9298,0.9306,0.9336,0.9374, 0.9392,0.9402,0.9467,0.9510,0.9540,0.9552,0.9581,0.9639,0.9695,0.9724, 0.9744,0.9760,0.9774,0.9863,0.9885,0.9893,0.9901,0.9982,0.9996, Overall p-value after applying KStest on 269 p-values = 0.137172 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.