RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-03-29_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 16.21 17.7276 0.593780 2 to 25 15.89 4.7987 0.001716 3 to 26 15.88 21.6340 0.800793 4 to 27 15.77 26.8142 0.939150 5 to 28 15.48 19.0955 0.676923 6 to 29 15.65 20.3911 0.745286 7 to 30 15.82 18.3419 0.632413 8 to 31 15.34 20.7550 0.762561 9 to 32 15.92 11.5160 0.171484 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.247898 Tough bday spacings test for dh-ranFile-2018-03-29_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 15 32 99 103 79 76 54 17 17 6 2 (O-E)^2/E 3.7 0.6 9.0 0.3 3.6 0.1 0.1 5.5 0.3 0.1 1.0 Birthday Spacings: Sum(O-E)^2/E= 24.231, p= 0.993 RESULTS OF GCD FOR dh-ranFile-2018-03-29_14:31 Euclid's algorithm: p-value, steps to gcd: 0.565063 p-value, dist. of gcd's: 0.188078 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-03-29_14:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.775 0.648 0.672 0.317 0.306 0.111 0.226 0.169 Bits 8 to 15---> 0.583 0.911 0.959 0.863 0.119 0.509 0.354 0.573 Bits 16 to 23---> 0.226 0.658 0.568 0.375 0.874 0.471 0.070 0.648 Bits 24 to 31---> 0.479 0.135 0.330 0.642 0.816 0.163 0.369 0.026 KS test for the above 32 p values: 0.202 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-03-29_14:31, p-values for 5 runs: 0.9968, 0.4475, 0.6229, 0.3266, 0.1528 Rank test for binary matrices (31x31) for dh-ranFile-2018-03-29_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 210 211.4 0.010 0.010 r= 29 5190 5134.0 0.611 0.620 r= 30 22877 23103.0 2.212 2.832 r= 31 11723 11551.5 2.545 5.377 chi-square = 5.377 with df = 3; p-value = 0.854 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-03-29_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 208 211.4 0.055 0.055 r= 30 5150 5134.0 0.050 0.105 r= 31 22988 23103.0 0.573 0.678 r= 32 11654 11551.5 0.909 1.587 chi-square = 1.587 with df = 3; p-value = 0.338 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-03-29_14:31 b-rank test for bits 1 to 8, p=0.86295 b-rank test for bits 2 to 9, p=0.93775 b-rank test for bits 3 to 10, p=0.14459 b-rank test for bits 4 to 11, p=0.54520 b-rank test for bits 5 to 12, p=0.20974 b-rank test for bits 6 to 13, p=0.13754 b-rank test for bits 7 to 14, p=0.95637 b-rank test for bits 8 to 15, p=0.69230 b-rank test for bits 9 to 16, p=0.84346 b-rank test for bits 10 to 17, p=0.64862 b-rank test for bits 11 to 18, p=0.95893 b-rank test for bits 12 to 19, p=0.24752 b-rank test for bits 13 to 20, p=0.28719 b-rank test for bits 14 to 21, p=0.34036 b-rank test for bits 15 to 22, p=0.84972 b-rank test for bits 16 to 23, p=0.29185 b-rank test for bits 17 to 24, p=0.89995 b-rank test for bits 18 to 25, p=0.58121 b-rank test for bits 19 to 26, p=0.74466 b-rank test for bits 20 to 27, p=0.57883 b-rank test for bits 21 to 28, p=0.62866 b-rank test for bits 22 to 29, p=0.18029 b-rank test for bits 23 to 30, p=0.89677 b-rank test for bits 24 to 31, p=0.53311 b-rank test for bits 25 to 32, p=0.44927 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 = 0.267903 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-03-29_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 142345 1.02 0.845642 2 141706 -0.48 0.317369 3 141714 -0.46 0.324059 4 141991 0.19 0.575666 5 142329 0.98 0.836590 6 141847 -0.15 0.442106 7 141784 -0.29 0.384827 8 142233 0.76 0.775247 9 141282 -1.47 0.071362 10 142209 0.70 0.758087 11 142309 0.93 0.824799 12 142020 0.26 0.602018 13 141907 -0.01 0.497828 14 142102 0.45 0.673704 15 141706 -0.48 0.317369 16 141959 0.12 0.546194 17 141827 -0.19 0.423730 18 141847 -0.15 0.442106 19 141809 -0.23 0.407331 20 141510 -0.93 0.175406 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-03-29_14:31 Bits used No. missing words z-score p-value 23 to 32 141712 -0.6804 0.248110 22 to 31 141957 0.1644 0.565284 21 to 30 141932 0.0782 0.531155 20 to 29 141993 0.2885 0.613525 19 to 28 142110 0.6920 0.755521 18 to 27 142007 0.3368 0.631864 17 to 26 141862 -0.1632 0.435178 16 to 25 141764 -0.5011 0.308137 15 to 24 141895 -0.0494 0.480295 14 to 23 142097 0.6471 0.741229 13 to 22 141540 -1.2736 0.101411 12 to 21 142025 0.3989 0.655003 11 to 20 142169 0.8954 0.814717 10 to 19 141921 0.0402 0.516050 9 to 18 141918 0.0299 0.511925 8 to 17 141922 0.0437 0.517424 7 to 16 142026 0.4023 0.656272 6 to 15 141717 -0.6632 0.253599 5 to 14 142168 0.8920 0.813794 4 to 13 141890 -0.0667 0.473428 3 to 12 142118 0.7196 0.764100 2 to 11 142006 0.3333 0.630563 1 to 10 141776 -0.4598 0.322845 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-03-29_14:31 Bits used No. missing words z-score p-value 28 to 32 141889 -0.0689 0.472529 27 to 31 142150 0.8158 0.792702 26 to 30 142028 0.4023 0.656258 25 to 29 141820 -0.3028 0.381016 24 to 28 141889 -0.0689 0.472529 23 to 27 142284 1.2701 0.897970 22 to 26 141317 -2.0079 0.022327 21 to 25 141586 -1.0960 0.136532 20 to 24 141843 -0.2248 0.411049 19 to 23 142290 1.2904 0.901545 18 to 22 141279 -2.1367 0.016311 17 to 21 141973 0.2158 0.585440 16 to 20 142417 1.7209 0.957367 15 to 19 141724 -0.6282 0.264924 14 to 18 142211 1.0226 0.846754 13 to 17 142173 0.8938 0.814285 12 to 16 141479 -1.4587 0.072318 11 to 15 141558 -1.1909 0.116837 10 to 14 141251 -2.2316 0.012820 9 to 13 142047 0.4667 0.679635 8 to 12 142314 1.3718 0.914931 7 to 11 141819 -0.3062 0.379725 6 to 10 141651 -0.8757 0.190598 5 to 9 142408 1.6904 0.954525 4 to 8 142171 0.8870 0.812465 3 to 7 142378 1.5887 0.943937 2 to 6 141781 -0.4350 0.331775 1 to 5 142168 0.8768 0.809715 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-03-29_14:31 Bits used No. missing words z-score p-value 31 to 32 142290 1.1229 0.869264 30 to 31 142512 1.7778 0.962281 29 to 30 141864 -0.1337 0.446813 28 to 29 141757 -0.4494 0.326589 27 to 28 141736 -0.5113 0.304571 26 to 27 142464 1.6362 0.949101 25 to 26 142435 1.5506 0.939507 24 to 25 142201 0.8604 0.805211 23 to 24 142026 0.3442 0.634637 22 to 23 142281 1.0964 0.863542 21 to 22 141809 -0.2960 0.383631 20 to 21 141895 -0.0423 0.483141 19 to 20 141232 -1.9980 0.022857 18 to 19 142120 0.6214 0.732847 17 to 18 142185 0.8132 0.791944 16 to 17 141635 -0.8092 0.209191 15 to 16 142219 0.9135 0.819505 14 to 15 142105 0.5772 0.718097 13 to 14 141476 -1.2783 0.100579 12 to 13 142356 1.3176 0.906183 11 to 12 141944 0.1023 0.540729 10 to 11 142089 0.5300 0.701944 9 to 10 141941 0.0934 0.537216 8 to 9 141654 -0.7532 0.225669 7 to 8 142106 0.5801 0.719092 6 to 7 142086 0.5212 0.698869 5 to 6 142176 0.7866 0.784253 4 to 5 142023 0.3353 0.631304 3 to 4 142173 0.7778 0.781653 2 to 3 141300 -1.7974 0.036133 1 to 2 142235 0.9607 0.831643 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-03-29_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2596.08 1.359 0.912899 Test results for specific bytes for dh-ranFile-2018-03-29_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2509.34 0.132 0.552563 2 to 9 2486.39 -0.192 0.423684 3 to 10 2387.40 -1.592 0.055647 4 to 11 2567.57 0.956 0.830364 5 to 12 2418.60 -1.151 0.124842 6 to 13 2539.93 0.565 0.713854 7 to 14 2375.87 -1.755 0.039592 8 to 15 2478.40 -0.305 0.380023 9 to 16 2547.37 0.670 0.748554 10 to 17 2531.08 0.440 0.669865 11 to 18 2548.37 0.684 0.753011 12 to 19 2521.32 0.301 0.618482 13 to 20 2553.08 0.751 0.773559 14 to 21 2494.20 -0.082 0.467315 15 to 22 2474.85 -0.356 0.361018 16 to 23 2422.56 -1.095 0.136728 17 to 24 2523.32 0.330 0.629200 18 to 25 2548.33 0.683 0.752845 19 to 26 2561.00 0.863 0.805834 20 to 27 2411.93 -1.245 0.106479 21 to 28 2515.66 0.221 0.587632 22 to 29 2396.73 -1.460 0.072080 23 to 30 2545.45 0.643 0.739816 24 to 31 2532.49 0.460 0.677070 25 to 32 2409.75 -1.276 0.100929 CDPARK for dh-ranFile-2018-03-29_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 3529 0.2740 0.607947 3567 2.0091 0.977738 3556 1.5068 0.934075 3530 0.3196 0.625377 3541 0.8219 0.794438 3527 0.1826 0.572463 3526 0.1370 0.554479 3488 -1.5982 0.055002 3524 0.0457 0.518210 3500 -1.0502 0.146807 Square side=100, avg. no. parked=3528.80 sample std.=22.09 p-value of the KSTEST for those 10 p-values: 0.521164 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-03-29_14:31 0.0200,0.9585,0.9191,0.3043,0.2050,0.9280,0.2974,0.6170,0.0293,0.3905, The KS test for those 10 p-values: 0.394776 The 3DSPHERES test for dh-ranFile-2018-03-29_14:31 sample no r^3 equiv. uni. 1 1.766 0.057169 2 14.744 0.388276 3 6.425 0.192792 4 6.399 0.192087 5 23.334 0.540586 6 31.655 0.651866 7 11.436 0.316960 8 12.121 0.332378 9 61.345 0.870600 10 87.381 0.945672 11 20.681 0.498113 12 22.847 0.533065 13 7.602 0.223832 14 14.407 0.381358 15 29.809 0.629765 16 74.033 0.915225 17 35.852 0.697317 18 55.854 0.844609 19 78.631 0.927272 20 53.584 0.832393 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.734895 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-03-29_14:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 0.1 -0.6 -0.3 -0.6 0.4 0.4 0.1 1.8 -0.2 1.2 -0.4 -1.1 -0.4 0.1 0.6 0.5 -0.4 -0.3 0.3 0.5 0.3 -1.0 -0.3 -0.0 -0.7 1.5 -1.3 0.3 -1.9 -0.1 1.7 -0.2 -0.4 -0.4 1.0 -0.9 -0.4 -0.8 0.4 0.9 -1.0 -0.1 Chi-square with 42 degrees of freedom:26.129475 z-score=-1.731616, p-value=0.026175 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-03-29_14:31 Test no p-value 1 0.092575 2 0.277208 3 0.005986 4 0.491534 5 0.179519 6 0.242410 7 0.518246 8 0.681743 9 0.525526 10 0.110483 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.060881 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-03-29_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 66690 0.01 66575 0.13 3 25000.00 24933 0.18 24978 0.02 4 6666.67 6738 0.76 6828 3.90 5 1388.89 1358 0.69 1358 0.69 6 238.10 239 0.00 225 0.72 7 34.72 33 0.09 29 0.94 8 4.96 8 1.86 6 0.22 p=0.26801 p=0.64230 Number of rngs required: 687517, p-value: 0.152 RESULTS OF CRAPS TEST for dh-ranFile-2018-03-29_14:31 No. of wins: Observed Expected 98590 98585.9 z-score= 0.019, pvalue=0.50739 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66596 66666.7 0.075 0.075 2 37500 37654.3 0.632 0.707 3 27055 26954.7 0.373 1.080 4 19343 19313.5 0.045 1.126 5 13838 13851.4 0.013 1.139 6 9868 9943.5 0.574 1.712 7 7234 7145.0 1.108 2.820 8 5105 5139.1 0.226 3.046 9 3749 3699.9 0.653 3.699 10 2671 2666.3 0.008 3.707 11 1977 1923.3 1.498 5.205 12 1389 1388.7 0.000 5.205 13 1017 1003.7 0.176 5.381 14 718 726.1 0.091 5.472 15 505 525.8 0.826 6.298 16 374 381.2 0.134 6.432 17 279 276.5 0.022 6.454 18 213 200.8 0.737 7.191 19 156 146.0 0.687 7.878 20 109 106.2 0.073 7.951 21 304 287.1 0.993 8.944 Chisq= 8.94 for 20 degrees of freedom, p= 0.01646 SUMMARY of craptest p-value for no. of wins: 0.507389 p-value for throws/game: 0.016458 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-03-29_14:31 No. of wins: Observed Expected 98927 98585.9 z-score= 1.526, pvalue=0.93647 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66895 66666.7 0.782 0.782 2 37524 37654.3 0.451 1.233 3 26971 26954.7 0.010 1.243 4 19249 19313.5 0.215 1.458 5 13761 13851.4 0.590 2.048 6 10054 9943.5 1.227 3.275 7 7072 7145.0 0.746 4.022 8 5096 5139.1 0.361 4.383 9 3784 3699.9 1.913 6.296 10 2793 2666.3 6.021 12.317 11 1884 1923.3 0.804 13.121 12 1325 1388.7 2.926 16.047 13 959 1003.7 1.992 18.039 14 726 726.1 0.000 18.039 15 541 525.8 0.437 18.476 16 346 381.2 3.242 21.718 17 286 276.5 0.324 22.041 18 190 200.8 0.584 22.625 19 139 146.0 0.334 22.959 20 106 106.2 0.000 22.960 21 299 287.1 0.492 23.452 Chisq= 23.45 for 20 degrees of freedom, p= 0.73285 SUMMARY of craptest p-value for no. of wins: 0.936468 p-value for throws/game: 0.732848 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0017,0.0060,0.0128,0.0163,0.0165,0.0200,0.0223,0.0229,0.0262,0.0265, 0.0293,0.0361,0.0396,0.0550,0.0556,0.0572,0.0609,0.0704,0.0714,0.0721, 0.0723,0.0926,0.1006,0.1009,0.1014,0.1065,0.1105,0.1109,0.1168,0.1192, 0.1248,0.1349,0.1365,0.1367,0.1375,0.1446,0.1468,0.1522,0.1528,0.1630, 0.1686,0.1715,0.1754,0.1795,0.1803,0.1881,0.1906,0.1921,0.1928,0.2015, 0.2050,0.2092,0.2097,0.2238,0.2256,0.2257,0.2262,0.2424,0.2475,0.2479, 0.2481,0.2536,0.2649,0.2679,0.2680,0.2772,0.2872,0.2919,0.2974,0.3043, 0.3046,0.3063,0.3081,0.3165,0.3170,0.3174,0.3174,0.3228,0.3241,0.3266, 0.3266,0.3303,0.3318,0.3324,0.3377,0.3404,0.3537,0.3610,0.3685,0.3747, 0.3797,0.3800,0.3810,0.3814,0.3836,0.3848,0.3883,0.3905,0.3948,0.4073, 0.4110,0.4237,0.4237,0.4352,0.4421,0.4421,0.4468,0.4475,0.4493,0.4673, 0.4714,0.4725,0.4725,0.4734,0.4790,0.4803,0.4831,0.4915,0.4978,0.4981, 0.5074,0.5095,0.5119,0.5160,0.5174,0.5182,0.5182,0.5212,0.5255,0.5312, 0.5331,0.5331,0.5372,0.5406,0.5407,0.5452,0.5462,0.5526,0.5545,0.5651, 0.5653,0.5684,0.5725,0.5729,0.5757,0.5788,0.5812,0.5834,0.5854,0.5876, 0.5938,0.6020,0.6079,0.6135,0.6170,0.6185,0.6229,0.6254,0.6287,0.6292, 0.6298,0.6306,0.6313,0.6319,0.6324,0.6346,0.6422,0.6423,0.6477,0.6481, 0.6486,0.6519,0.6550,0.6563,0.6563,0.6576,0.6699,0.6720,0.6737,0.6769, 0.6771,0.6796,0.6817,0.6923,0.6973,0.6989,0.7019,0.7139,0.7181,0.7191, 0.7328,0.7328,0.7349,0.7398,0.7412,0.7447,0.7453,0.7486,0.7528,0.7530, 0.7555,0.7581,0.7626,0.7641,0.7736,0.7748,0.7752,0.7817,0.7843,0.7919, 0.7927,0.7944,0.8008,0.8052,0.8058,0.8097,0.8125,0.8138,0.8143,0.8147, 0.8156,0.8195,0.8248,0.8304,0.8316,0.8324,0.8366,0.8435,0.8446,0.8456, 0.8468,0.8497,0.8538,0.8630,0.8631,0.8635,0.8693,0.8706,0.8738,0.8968, 0.8980,0.8999,0.9015,0.9062,0.9107,0.9129,0.9149,0.9152,0.9191,0.9273, 0.9280,0.9341,0.9365,0.9378,0.9392,0.9395,0.9439,0.9457,0.9491,0.9545, 0.9564,0.9574,0.9585,0.9589,0.9590,0.9623,0.9777,0.9930,0.9968, Overall p-value after applying KStest on 269 p-values = 0.345845 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.