RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-24_08:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 16.00 6.2005 0.008266 2 to 25 15.77 16.2478 0.493659 3 to 26 16.11 18.2367 0.625941 4 to 27 15.72 16.6615 0.522483 5 to 28 15.85 13.8744 0.324029 6 to 29 15.65 13.9481 0.329225 7 to 30 15.57 20.9707 0.772398 8 to 31 15.73 16.2788 0.495833 9 to 32 15.99 18.1494 0.620525 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.417341 Tough bday spacings test for dh-ranFile-2018-06-24_08:31: 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 7 25 76 102 105 72 54 32 14 11 2 (O-E)^2/E 0.5 3.7 0.1 0.2 0.5 0.5 0.1 0.2 0.1 2.9 1.0 Birthday Spacings: Sum(O-E)^2/E= 9.771, p= 0.539 RESULTS OF GCD FOR dh-ranFile-2018-06-24_08:31 Euclid's algorithm: p-value, steps to gcd: 0.760222 p-value, dist. of gcd's: 0.003748 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-24_08:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.366 0.794 0.868 0.625 0.608 0.595 0.336 0.639 Bits 8 to 15---> 0.611 0.025 0.031 0.622 0.063 0.814 0.984 0.445 Bits 16 to 23---> 0.959 0.289 0.918 0.200 0.759 0.114 0.514 0.134 Bits 24 to 31---> 0.530 0.326 0.363 0.698 0.713 0.374 0.857 0.563 KS test for the above 32 p values: 0.091 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-24_08:31, p-values for 5 runs: 0.4325, 0.1788, 0.5230, 0.4112, 0.2080 Rank test for binary matrices (31x31) for dh-ranFile-2018-06-24_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 215 211.4 0.061 0.061 r= 29 5147 5134.0 0.033 0.094 r= 30 23034 23103.0 0.206 0.300 r= 31 11604 11551.5 0.238 0.538 chi-square = 0.538 with df = 3; p-value = 0.090 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-06-24_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 191 211.4 1.972 1.972 r= 30 5185 5134.0 0.506 2.478 r= 31 22910 23103.0 1.613 4.091 r= 32 11714 11551.5 2.285 6.377 chi-square = 6.377 with df = 3; p-value = 0.905 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-06-24_08:31 b-rank test for bits 1 to 8, p=0.46682 b-rank test for bits 2 to 9, p=0.51799 b-rank test for bits 3 to 10, p=0.17277 b-rank test for bits 4 to 11, p=0.34062 b-rank test for bits 5 to 12, p=0.62285 b-rank test for bits 6 to 13, p=0.13246 b-rank test for bits 7 to 14, p=0.32893 b-rank test for bits 8 to 15, p=0.66637 b-rank test for bits 9 to 16, p=0.50332 b-rank test for bits 10 to 17, p=0.30036 b-rank test for bits 11 to 18, p=0.96374 b-rank test for bits 12 to 19, p=0.78777 b-rank test for bits 13 to 20, p=0.05675 b-rank test for bits 14 to 21, p=0.27504 b-rank test for bits 15 to 22, p=0.63058 b-rank test for bits 16 to 23, p=0.29547 b-rank test for bits 17 to 24, p=0.85561 b-rank test for bits 18 to 25, p=0.17015 b-rank test for bits 19 to 26, p=0.23382 b-rank test for bits 20 to 27, p=0.19543 b-rank test for bits 21 to 28, p=0.71928 b-rank test for bits 22 to 29, p=0.38389 b-rank test for bits 23 to 30, p=0.78467 b-rank test for bits 24 to 31, p=0.92879 b-rank test for bits 25 to 32, p=0.26671 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 = 0.648279 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-24_08:31 (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 143345 3.35 0.999602 2 141953 0.10 0.540635 3 142202 0.68 0.752952 4 142206 0.69 0.755894 5 141778 -0.31 0.379480 6 142011 0.24 0.593884 7 141890 -0.05 0.481989 8 141746 -0.38 0.351375 9 142137 0.53 0.702616 10 141986 0.18 0.571084 11 141429 -1.12 0.130875 12 142164 0.60 0.724086 13 141723 -0.44 0.331654 14 141411 -1.16 0.122147 15 142061 0.35 0.638469 16 142035 0.29 0.615476 17 142329 0.98 0.836590 18 141873 -0.08 0.466177 19 141824 -0.20 0.420987 20 142683 1.81 0.964669 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-06-24_08:31 Bits used No. missing words z-score p-value 23 to 32 141743 -0.5736 0.283136 22 to 31 141920 0.0368 0.514675 21 to 30 141519 -1.3460 0.089157 20 to 29 142197 0.9920 0.839393 19 to 28 141876 -0.1149 0.454250 18 to 27 141939 0.1023 0.540745 17 to 26 141912 0.0092 0.503673 16 to 25 141736 -0.5977 0.275024 15 to 24 141919 0.0333 0.513300 14 to 23 141485 -1.4632 0.071705 13 to 22 141395 -1.7736 0.038069 12 to 21 141598 -1.0736 0.141512 11 to 20 142051 0.4885 0.687408 10 to 19 141629 -0.9667 0.166858 9 to 18 141778 -0.4529 0.325324 8 to 17 142348 1.5127 0.934816 7 to 16 142121 0.7299 0.767273 6 to 15 141942 0.1127 0.544848 5 to 14 141879 -0.1046 0.458352 4 to 13 141880 -0.1011 0.459721 3 to 12 141928 0.0644 0.525666 2 to 11 142068 0.5471 0.707858 1 to 10 141677 -0.8011 0.211526 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-06-24_08:31 Bits used No. missing words z-score p-value 28 to 32 141467 -1.4994 0.066882 27 to 31 141685 -0.7604 0.223496 26 to 30 141692 -0.7367 0.230649 25 to 29 142335 1.4429 0.925483 24 to 28 142548 2.1650 0.984806 23 to 27 142506 2.0226 0.978443 22 to 26 141698 -0.7164 0.236881 21 to 25 141652 -0.8723 0.191521 20 to 24 141929 0.0667 0.526581 19 to 23 142320 1.3921 0.918054 18 to 22 142021 0.3785 0.647486 17 to 21 141903 -0.0215 0.491440 16 to 20 142158 0.8429 0.800372 15 to 19 141631 -0.9435 0.172715 14 to 18 141896 -0.0452 0.481979 13 to 17 142078 0.5718 0.716259 12 to 16 141545 -1.2350 0.108412 11 to 15 141440 -1.5909 0.055811 10 to 14 141797 -0.3808 0.351683 9 to 13 142088 0.6057 0.727630 8 to 12 142165 0.8667 0.806941 7 to 11 142089 0.6091 0.728755 6 to 10 141851 -0.1977 0.421629 5 to 9 142258 1.1819 0.881384 4 to 8 142206 1.0057 0.842711 3 to 7 142001 0.3107 0.622003 2 to 6 142295 1.3074 0.904454 1 to 5 141626 -0.9604 0.168417 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-06-24_08:31 Bits used No. missing words z-score p-value 31 to 32 141823 -0.2547 0.399493 30 to 31 142099 0.5595 0.712089 29 to 30 141288 -1.8328 0.033414 28 to 29 141705 -0.6027 0.273340 27 to 28 141818 -0.2694 0.393807 26 to 27 142226 0.9341 0.824882 25 to 26 141395 -1.5172 0.064608 24 to 25 141894 -0.0452 0.481966 23 to 24 141572 -0.9951 0.159850 22 to 23 142192 0.8338 0.797813 21 to 22 141783 -0.3727 0.354703 20 to 21 142178 0.7925 0.785976 19 to 20 141516 -1.1603 0.122970 18 to 19 141397 -1.5113 0.065356 17 to 18 141746 -0.4818 0.314974 16 to 17 141941 0.0934 0.537216 15 to 16 142024 0.3383 0.632416 14 to 15 141871 -0.1131 0.454988 13 to 14 142562 1.9253 0.972903 12 to 13 141815 -0.2783 0.390407 11 to 12 141875 -0.1013 0.459669 10 to 11 141932 0.0669 0.526659 9 to 10 141649 -0.7679 0.221263 8 to 9 141226 -2.0157 0.021914 7 to 8 141947 0.1111 0.544240 6 to 7 141871 -0.1131 0.454988 5 to 6 141992 0.2439 0.596332 4 to 5 142285 1.1082 0.866106 3 to 4 141753 -0.4612 0.322345 2 to 3 142056 0.4327 0.667367 1 to 2 141954 0.1318 0.552417 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-24_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2566.40 0.939 0.826135 Test results for specific bytes for dh-ranFile-2018-06-24_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2575.82 1.072 0.858191 2 to 9 2677.49 2.510 0.993964 3 to 10 2458.35 -0.589 0.277937 4 to 11 2551.68 0.731 0.767586 5 to 12 2538.74 0.548 0.708117 6 to 13 2468.76 -0.442 0.329314 7 to 14 2521.33 0.302 0.618553 8 to 15 2495.51 -0.064 0.474674 9 to 16 2551.36 0.726 0.766169 10 to 17 2396.78 -1.460 0.072177 11 to 18 2511.58 0.164 0.565028 12 to 19 2661.70 2.287 0.988896 13 to 20 2565.19 0.922 0.821722 14 to 21 2512.52 0.177 0.570253 15 to 22 2549.03 0.693 0.755980 16 to 23 2537.38 0.529 0.701485 17 to 24 2549.66 0.702 0.758747 18 to 25 2552.32 0.740 0.770309 19 to 26 2464.76 -0.498 0.309132 20 to 27 2402.58 -1.378 0.084142 21 to 28 2580.36 1.136 0.872120 22 to 29 2518.56 0.262 0.603515 23 to 30 2418.93 -1.147 0.125782 24 to 31 2462.84 -0.526 0.299598 25 to 32 2480.37 -0.278 0.390637 CDPARK for dh-ranFile-2018-06-24_08:31: 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 3522 -0.0457 0.481790 3524 0.0457 0.518210 3536 0.5936 0.723613 3527 0.1826 0.572463 3518 -0.2283 0.409702 3545 1.0046 0.842447 3511 -0.5479 0.291865 3523 0.0000 0.500000 3493 -1.3699 0.085365 3514 -0.4110 0.340551 Square side=100, avg. no. parked=3521.30 sample std.=13.39 p-value of the KSTEST for those 10 p-values: 0.571406 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-24_08:31 0.4630,0.2338,0.8541,0.1689,0.9486,0.3393,0.6619,0.8920,0.1384,0.6977, The KS test for those 10 p-values: 0.921907 The 3DSPHERES test for dh-ranFile-2018-06-24_08:31 sample no r^3 equiv. uni. 1 41.263 0.747267 2 8.743 0.252819 3 33.583 0.673532 4 1.072 0.035097 5 4.144 0.129018 6 7.509 0.221422 7 162.395 0.995543 8 15.005 0.393577 9 7.539 0.222214 10 4.518 0.139795 11 88.144 0.947036 12 30.430 0.637351 13 18.856 0.466622 14 8.606 0.249379 15 22.250 0.523684 16 17.698 0.445638 17 36.572 0.704493 18 77.853 0.925361 19 52.265 0.824860 20 60.884 0.868595 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.955242 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-24_08:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -0.7 -0.8 0.0 -0.5 1.6 -0.5 0.4 0.0 0.7 0.1 -2.4 1.1 1.7 -0.5 -0.7 -0.7 -1.8 -0.3 0.5 2.8 0.1 0.2 0.5 1.1 -1.3 -0.6 -0.6 -0.9 -0.7 0.3 -2.5 -0.1 0.2 1.3 0.8 2.1 -0.4 1.3 -1.3 0.1 0.0 0.8 Chi-square with 42 degrees of freedom:50.404038 z-score=0.916956, p-value=0.824785 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-06-24_08:31 Test no p-value 1 0.281716 2 0.388945 3 0.146258 4 0.765593 5 0.001462 6 0.444401 7 0.820510 8 0.984818 9 0.109173 10 0.018844 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.156480 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-24_08:31: (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 66524 0.31 66679 0.00 3 25000.00 25059 0.14 25030 0.04 4 6666.67 6740 0.81 6703 0.20 5 1388.89 1343 1.52 1346 1.32 6 238.10 289 10.88 204 4.88 7 34.72 39 0.53 35 0.00 8 4.96 5 0.00 2 1.77 p=0.97230 p=0.77701 Number of rngs required: 689247, p-value: 0.836 RESULTS OF CRAPS TEST for dh-ranFile-2018-06-24_08:31 No. of wins: Observed Expected 98391 98585.9 z-score=-0.872, pvalue=0.19173 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66784 66666.7 0.207 0.207 2 37547 37654.3 0.306 0.512 3 26809 26954.7 0.788 1.300 4 19409 19313.5 0.473 1.773 5 13843 13851.4 0.005 1.778 6 9849 9943.5 0.899 2.677 7 7264 7145.0 1.981 4.658 8 5172 5139.1 0.211 4.869 9 3698 3699.9 0.001 4.870 10 2642 2666.3 0.221 5.091 11 1946 1923.3 0.267 5.359 12 1355 1388.7 0.820 6.178 13 1077 1003.7 5.351 11.529 14 713 726.1 0.238 11.767 15 500 525.8 1.269 13.036 16 384 381.2 0.021 13.058 17 281 276.5 0.072 13.130 18 207 200.8 0.190 13.319 19 162 146.0 1.757 15.076 20 102 106.2 0.167 15.243 21 256 287.1 3.372 18.615 Chisq= 18.62 for 20 degrees of freedom, p= 0.45305 SUMMARY of craptest p-value for no. of wins: 0.191735 p-value for throws/game: 0.453051 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-24_08:31 No. of wins: Observed Expected 98582 98585.9 z-score=-0.017, pvalue=0.49312 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66747 66666.7 0.097 0.097 2 37896 37654.3 1.551 1.648 3 26903 26954.7 0.099 1.747 4 19212 19313.5 0.533 2.280 5 13857 13851.4 0.002 2.283 6 9959 9943.5 0.024 2.307 7 7144 7145.0 0.000 2.307 8 5177 5139.1 0.280 2.587 9 3660 3699.9 0.430 3.016 10 2695 2666.3 0.309 3.325 11 1869 1923.3 1.535 4.860 12 1330 1388.7 2.485 7.344 13 911 1003.7 8.564 15.909 14 700 726.1 0.941 16.850 15 493 525.8 2.050 18.900 16 418 381.2 3.563 22.463 17 316 276.5 5.631 28.093 18 205 200.8 0.087 28.180 19 129 146.0 1.976 30.156 20 104 106.2 0.046 30.202 21 275 287.1 0.511 30.713 Chisq= 30.71 for 20 degrees of freedom, p= 0.94091 SUMMARY of craptest p-value for no. of wins: 0.493115 p-value for throws/game: 0.940911 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0015,0.0037,0.0083,0.0188,0.0219,0.0248,0.0308,0.0334,0.0351,0.0381, 0.0558,0.0568,0.0629,0.0646,0.0654,0.0669,0.0717,0.0722,0.0841,0.0854, 0.0892,0.0896,0.0911,0.1084,0.1092,0.1141,0.1221,0.1230,0.1258,0.1290, 0.1309,0.1325,0.1341,0.1384,0.1398,0.1415,0.1463,0.1565,0.1599,0.1669, 0.1684,0.1689,0.1701,0.1727,0.1728,0.1788,0.1915,0.1917,0.1954,0.1999, 0.2080,0.2115,0.2213,0.2214,0.2222,0.2235,0.2306,0.2338,0.2338,0.2369, 0.2494,0.2528,0.2667,0.2733,0.2750,0.2750,0.2779,0.2817,0.2831,0.2889, 0.2919,0.2955,0.2996,0.3004,0.3091,0.3150,0.3223,0.3240,0.3253,0.3256, 0.3289,0.3292,0.3293,0.3317,0.3359,0.3393,0.3406,0.3406,0.3514,0.3517, 0.3547,0.3631,0.3661,0.3735,0.3795,0.3839,0.3889,0.3904,0.3906,0.3936, 0.3938,0.3995,0.4097,0.4112,0.4173,0.4210,0.4216,0.4325,0.4444,0.4448, 0.4456,0.4531,0.4542,0.4550,0.4550,0.4584,0.4597,0.4597,0.4630,0.4662, 0.4666,0.4668,0.4747,0.4818,0.4820,0.4820,0.4820,0.4914,0.4931,0.4937, 0.4958,0.5000,0.5033,0.5037,0.5133,0.5136,0.5147,0.5180,0.5182,0.5225, 0.5230,0.5237,0.5257,0.5266,0.5267,0.5303,0.5372,0.5392,0.5406,0.5407, 0.5442,0.5448,0.5524,0.5630,0.5650,0.5703,0.5711,0.5714,0.5725,0.5939, 0.5947,0.5963,0.6035,0.6078,0.6109,0.6155,0.6186,0.6205,0.6217,0.6220, 0.6228,0.6251,0.6259,0.6306,0.6324,0.6374,0.6385,0.6393,0.6475,0.6483, 0.6619,0.6664,0.6674,0.6735,0.6874,0.6977,0.6980,0.7015,0.7026,0.7045, 0.7079,0.7081,0.7121,0.7134,0.7163,0.7193,0.7236,0.7241,0.7276,0.7288, 0.7473,0.7530,0.7559,0.7560,0.7587,0.7587,0.7602,0.7656,0.7662,0.7673, 0.7676,0.7703,0.7724,0.7770,0.7847,0.7860,0.7878,0.7942,0.7978,0.8004, 0.8069,0.8137,0.8205,0.8217,0.8248,0.8249,0.8249,0.8261,0.8359,0.8366, 0.8394,0.8424,0.8427,0.8541,0.8556,0.8571,0.8582,0.8661,0.8679,0.8686, 0.8721,0.8814,0.8920,0.9045,0.9053,0.9175,0.9181,0.9219,0.9254,0.9255, 0.9288,0.9348,0.9409,0.9470,0.9486,0.9552,0.9592,0.9637,0.9647,0.9723, 0.9729,0.9784,0.9842,0.9848,0.9848,0.9889,0.9940,0.9955,0.9996, Overall p-value after applying KStest on 269 p-values = 0.764507 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.