RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-12_05:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.55 14.5261 0.370427 2 to 25 15.49 31.1741 0.980980 3 to 26 15.95 18.7092 0.654520 4 to 27 15.88 7.7421 0.028246 5 to 28 15.85 12.0540 0.203146 6 to 29 15.85 12.9341 0.259415 7 to 30 16.21 12.3471 0.221319 8 to 31 16.30 26.1537 0.928294 9 to 32 16.13 17.9360 0.607109 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.798165 Tough bday spacings test for dh-ranFile-2018-07-12_05:31: 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 12 37 77 101 90 72 48 31 16 10 6 (O-E)^2/E 0.9 0.0 0.2 0.1 0.6 0.5 0.3 0.1 0.1 1.7 0.9 Birthday Spacings: Sum(O-E)^2/E= 5.385, p= 0.136 RESULTS OF GCD FOR dh-ranFile-2018-07-12_05:31 Euclid's algorithm: p-value, steps to gcd: 0.198376 p-value, dist. of gcd's: 0.415692 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-12_05:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.258 0.982 0.867 0.838 0.158 0.777 0.220 0.816 Bits 8 to 15---> 0.914 0.955 0.133 0.152 0.349 0.163 0.906 0.728 Bits 16 to 23---> 0.888 0.248 0.474 0.500 0.515 0.783 0.011 0.935 Bits 24 to 31---> 0.802 0.176 0.546 0.850 0.309 0.495 0.861 0.771 KS test for the above 32 p values: 0.876 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-12_05:31, p-values for 5 runs: 0.4434, 0.9084, 0.5066, 0.5354, 0.3979 Rank test for binary matrices (31x31) for dh-ranFile-2018-07-12_05:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 203 211.4 0.335 0.335 r= 29 5208 5134.0 1.066 1.401 r= 30 23135 23103.0 0.044 1.446 r= 31 11454 11551.5 0.823 2.269 chi-square = 2.269 with df = 3; p-value = 0.482 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-07-12_05:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 217 211.4 0.147 0.147 r= 30 5102 5134.0 0.200 0.347 r= 31 23136 23103.0 0.047 0.394 r= 32 11545 11551.5 0.004 0.398 chi-square = 0.398 with df = 3; p-value = 0.059 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-07-12_05:31 b-rank test for bits 1 to 8, p=0.92114 b-rank test for bits 2 to 9, p=0.45773 b-rank test for bits 3 to 10, p=0.06885 b-rank test for bits 4 to 11, p=0.43680 b-rank test for bits 5 to 12, p=0.93743 b-rank test for bits 6 to 13, p=0.58492 b-rank test for bits 7 to 14, p=0.88971 b-rank test for bits 8 to 15, p=0.41625 b-rank test for bits 9 to 16, p=0.46540 b-rank test for bits 10 to 17, p=0.24066 b-rank test for bits 11 to 18, p=0.66563 b-rank test for bits 12 to 19, p=0.58564 b-rank test for bits 13 to 20, p=0.82151 b-rank test for bits 14 to 21, p=0.54535 b-rank test for bits 15 to 22, p=0.87963 b-rank test for bits 16 to 23, p=0.08316 b-rank test for bits 17 to 24, p=0.30301 b-rank test for bits 18 to 25, p=0.88750 b-rank test for bits 19 to 26, p=0.47875 b-rank test for bits 20 to 27, p=0.05953 b-rank test for bits 21 to 28, p=0.72933 b-rank test for bits 22 to 29, p=0.41146 b-rank test for bits 23 to 30, p=0.75153 b-rank test for bits 24 to 31, p=0.38889 b-rank test for bits 25 to 32, p=0.88496 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 = 0.443624 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-12_05:31 (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 141789 -0.28 0.389300 2 142369 1.07 0.858588 3 142273 0.85 0.802253 4 141354 -1.30 0.097230 5 141642 -0.62 0.266116 6 142159 0.58 0.720168 7 141927 0.04 0.516466 8 141041 -2.03 0.021239 9 141619 -0.68 0.248778 10 141704 -0.48 0.315705 11 141968 0.14 0.554516 12 142396 1.14 0.872247 13 141826 -0.19 0.422815 14 142198 0.67 0.749991 15 141384 -1.23 0.109835 16 142213 0.71 0.760996 17 141809 -0.23 0.407331 18 141965 0.13 0.551745 19 141186 -1.69 0.045512 20 143032 2.62 0.995643 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-07-12_05:31 Bits used No. missing words z-score p-value 23 to 32 142229 1.1023 0.864837 22 to 31 142267 1.2333 0.891276 21 to 30 142014 0.3609 0.640925 20 to 29 142067 0.5437 0.706673 19 to 28 142127 0.7506 0.773549 18 to 27 142097 0.6471 0.741229 17 to 26 141861 -0.1667 0.433821 16 to 25 142230 1.1058 0.865585 15 to 24 142158 0.8575 0.804411 14 to 23 141937 0.0954 0.538007 13 to 22 142397 1.6816 0.953679 12 to 21 141716 -0.6667 0.252496 11 to 20 142251 1.1782 0.880636 10 to 19 142039 0.4471 0.672612 9 to 18 142001 0.3161 0.624038 8 to 17 142303 1.3575 0.912686 7 to 16 142021 0.3851 0.649907 6 to 15 142427 1.7851 0.962875 5 to 14 141702 -0.7149 0.237326 4 to 13 142175 0.9161 0.820194 3 to 12 141876 -0.1149 0.454250 2 to 11 141863 -0.1598 0.436536 1 to 10 141995 0.2954 0.616161 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-07-12_05:31 Bits used No. missing words z-score p-value 28 to 32 141954 0.1514 0.560179 27 to 31 141515 -1.3367 0.090658 26 to 30 142145 0.7989 0.787820 25 to 29 141627 -0.9571 0.169271 24 to 28 141831 -0.2655 0.395302 23 to 27 142338 1.4531 0.926905 22 to 26 141700 -0.7096 0.238978 21 to 25 141542 -1.2452 0.106532 20 to 24 141725 -0.6248 0.266036 19 to 23 142146 0.8023 0.788802 18 to 22 142015 0.3582 0.639905 17 to 21 142306 1.3446 0.910630 16 to 20 142110 0.6802 0.751823 15 to 19 142110 0.6802 0.751823 14 to 18 141658 -0.8520 0.197116 13 to 17 142425 1.7480 0.959771 12 to 16 142072 0.5514 0.709328 11 to 15 142171 0.8870 0.812465 10 to 14 141209 -2.3740 0.008798 9 to 13 141694 -0.7299 0.232716 8 to 12 141506 -1.3672 0.085778 7 to 11 141865 -0.1503 0.440275 6 to 10 141631 -0.9435 0.172715 5 to 9 141669 -0.8147 0.207628 4 to 8 142315 1.3752 0.915458 3 to 7 142537 2.1277 0.983319 2 to 6 142343 1.4701 0.929228 1 to 5 141785 -0.4215 0.336711 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-07-12_05:31 Bits used No. missing words z-score p-value 31 to 32 141797 -0.3314 0.370187 30 to 31 141694 -0.6352 0.262652 29 to 30 141631 -0.8210 0.205814 28 to 29 142166 0.7571 0.775517 27 to 28 141758 -0.4464 0.327654 26 to 27 141406 -1.4847 0.068805 25 to 26 142056 0.4327 0.667367 24 to 25 141336 -1.6912 0.045396 23 to 24 141703 -0.6086 0.271381 22 to 23 141656 -0.7473 0.227445 21 to 22 141923 0.0403 0.516083 20 to 21 142128 0.6450 0.740551 19 to 20 141970 0.1790 0.571018 18 to 19 142232 0.9518 0.829408 17 to 18 142486 1.7011 0.955537 16 to 17 141896 -0.0393 0.484317 15 to 16 141902 -0.0216 0.491375 14 to 15 141601 -0.9095 0.181536 13 to 14 142558 1.9135 0.972157 12 to 13 141341 -1.6765 0.046821 11 to 12 141569 -1.0039 0.157708 10 to 11 141710 -0.5880 0.278268 9 to 10 142371 1.3619 0.913379 8 to 9 142433 1.5447 0.938797 7 to 8 141831 -0.2311 0.408633 6 to 7 142039 0.3825 0.648958 5 to 6 142186 0.8161 0.792789 4 to 5 141852 -0.1691 0.432853 3 to 4 141928 0.0551 0.521960 2 to 3 142403 1.4563 0.927339 1 to 2 142712 2.3678 0.991052 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-12_05:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2535.24 0.498 0.690874 Test results for specific bytes for dh-ranFile-2018-07-12_05:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2483.76 -0.230 0.409162 2 to 9 2541.09 0.581 0.719425 3 to 10 2438.19 -0.874 0.191028 4 to 11 2482.64 -0.246 0.403012 5 to 12 2447.31 -0.745 0.228074 6 to 13 2402.26 -1.382 0.083448 7 to 14 2482.07 -0.254 0.399903 8 to 15 2418.63 -1.151 0.124933 9 to 16 2462.87 -0.525 0.299746 10 to 17 2578.13 1.105 0.865397 11 to 18 2452.94 -0.665 0.252877 12 to 19 2530.14 0.426 0.665041 13 to 20 2578.67 1.113 0.867060 14 to 21 2440.59 -0.840 0.200388 15 to 22 2449.33 -0.717 0.236835 16 to 23 2570.11 0.992 0.839292 17 to 24 2617.18 1.657 0.951256 18 to 25 2577.34 1.094 0.862963 19 to 26 2605.76 1.496 0.932629 20 to 27 2557.10 0.808 0.790322 21 to 28 2599.71 1.410 0.920756 22 to 29 2456.02 -0.622 0.266969 23 to 30 2481.83 -0.257 0.398625 24 to 31 2463.06 -0.522 0.300685 25 to 32 2452.01 -0.679 0.248660 CDPARK for dh-ranFile-2018-07-12_05:31: 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 3527 0.1826 0.572463 3507 -0.7306 0.232514 3523 0.0000 0.500000 3537 0.6393 0.738676 3533 0.4566 0.676028 3508 -0.6849 0.246694 3548 1.1416 0.873180 3554 1.4155 0.921543 3494 -1.3242 0.092718 3516 -0.3196 0.374623 Square side=100, avg. no. parked=3524.70 sample std.=18.00 p-value of the KSTEST for those 10 p-values: 0.994889 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-12_05:31 0.0077,0.5201,0.5454,0.1814,0.5747,0.1920,0.6044,0.6563,0.5320,0.6776, The KS test for those 10 p-values: 0.301174 The 3DSPHERES test for dh-ranFile-2018-07-12_05:31 sample no r^3 equiv. uni. 1 13.419 0.360647 2 17.221 0.436746 3 3.947 0.123273 4 32.582 0.662456 5 30.333 0.636186 6 42.657 0.758741 7 20.260 0.491006 8 273.655 0.999891 9 26.779 0.590420 10 82.369 0.935793 11 5.559 0.169159 12 9.890 0.280827 13 1.574 0.051125 14 1.424 0.046367 15 63.979 0.881477 16 16.442 0.421938 17 25.062 0.566296 18 18.424 0.458897 19 26.566 0.587505 20 9.642 0.274857 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.762713 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-12_05:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -1.2 0.6 -0.8 0.0 -1.4 -0.0 0.1 -1.6 2.4 -1.1 -1.4 -0.3 -0.1 0.7 -1.2 -1.0 0.6 0.9 0.7 -0.2 1.3 -2.2 -0.4 1.2 -0.3 0.2 1.8 -1.3 1.8 0.3 1.8 0.1 1.4 0.9 2.0 2.4 0.2 -0.8 -0.7 -0.6 -1.0 0.8 Chi-square with 42 degrees of freedom:56.695756 z-score=1.603438, p-value=0.935512 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-07-12_05:31 Test no p-value 1 0.288338 2 0.004178 3 0.161400 4 0.284239 5 0.435368 6 0.520494 7 0.066922 8 0.926410 9 0.498358 10 0.356893 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.152614 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-12_05:31: (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 66463 0.62 66631 0.02 3 25000.00 25237 2.25 24956 0.08 4 6666.67 6581 1.10 6783 2.03 5 1388.89 1432 1.34 1363 0.48 6 238.10 240 0.02 232 0.16 7 34.72 39 0.53 29 0.94 8 4.96 7 0.84 5 0.00 p=0.64952 p=0.28384 Number of rngs required: 689983, p-value: 0.968 RESULTS OF CRAPS TEST for dh-ranFile-2018-07-12_05:31 No. of wins: Observed Expected 98724 98585.9 z-score= 0.618, pvalue=0.73166 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66566 66666.7 0.152 0.152 2 37402 37654.3 1.691 1.843 3 26826 26954.7 0.615 2.458 4 19561 19313.5 3.173 5.630 5 13993 13851.4 1.447 7.077 6 10054 9943.5 1.227 8.304 7 7296 7145.0 3.190 11.494 8 5150 5139.1 0.023 11.518 9 3529 3699.9 7.891 19.409 10 2607 2666.3 1.319 20.727 11 1926 1923.3 0.004 20.731 12 1403 1388.7 0.146 20.877 13 1038 1003.7 1.171 22.048 14 679 726.1 3.060 25.109 15 531 525.8 0.051 25.160 16 365 381.2 0.684 25.844 17 273 276.5 0.045 25.889 18 224 200.8 2.673 28.562 19 156 146.0 0.687 29.250 20 116 106.2 0.901 30.151 21 305 287.1 1.114 31.265 Chisq= 31.27 for 20 degrees of freedom, p= 0.94821 SUMMARY of craptest p-value for no. of wins: 0.731663 p-value for throws/game: 0.948214 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-12_05:31 No. of wins: Observed Expected 98257 98585.9 z-score=-1.471, pvalue=0.07067 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66273 66666.7 2.325 2.325 2 37981 37654.3 2.834 5.159 3 27155 26954.7 1.488 6.647 4 19434 19313.5 0.752 7.399 5 13610 13851.4 4.208 11.607 6 9938 9943.5 0.003 11.610 7 7174 7145.0 0.117 11.727 8 5202 5139.1 0.771 12.498 9 3653 3699.9 0.594 13.092 10 2687 2666.3 0.161 13.252 11 1845 1923.3 3.190 16.442 12 1390 1388.7 0.001 16.443 13 991 1003.7 0.161 16.605 14 737 726.1 0.162 16.767 15 494 525.8 1.927 18.694 16 417 381.2 3.372 22.066 17 271 276.5 0.111 22.177 18 194 200.8 0.232 22.409 19 146 146.0 0.000 22.409 20 114 106.2 0.571 22.980 21 294 287.1 0.165 23.145 Chisq= 23.15 for 20 degrees of freedom, p= 0.71828 SUMMARY of craptest p-value for no. of wins: 0.070666 p-value for throws/game: 0.718277 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0042,0.0077,0.0088,0.0109,0.0212,0.0282,0.0454,0.0455,0.0464,0.0468, 0.0511,0.0593,0.0595,0.0669,0.0688,0.0689,0.0707,0.0832,0.0834,0.0858, 0.0907,0.0927,0.0972,0.1065,0.1098,0.1233,0.1249,0.1333,0.1360,0.1520, 0.1526,0.1577,0.1582,0.1614,0.1629,0.1692,0.1693,0.1727,0.1761,0.1814, 0.1815,0.1910,0.1920,0.1971,0.1984,0.2004,0.2031,0.2058,0.2076,0.2200, 0.2213,0.2274,0.2281,0.2325,0.2327,0.2368,0.2373,0.2390,0.2407,0.2467, 0.2476,0.2487,0.2488,0.2525,0.2529,0.2576,0.2594,0.2627,0.2660,0.2661, 0.2670,0.2714,0.2749,0.2783,0.2808,0.2838,0.2842,0.2883,0.2997,0.3007, 0.3012,0.3030,0.3091,0.3157,0.3277,0.3367,0.3488,0.3569,0.3606,0.3702, 0.3704,0.3746,0.3889,0.3893,0.3953,0.3979,0.3986,0.3999,0.4030,0.4073, 0.4086,0.4092,0.4115,0.4157,0.4162,0.4219,0.4228,0.4329,0.4338,0.4354, 0.4365,0.4367,0.4368,0.4403,0.4434,0.4436,0.4542,0.4577,0.4589,0.4654, 0.4745,0.4788,0.4815,0.4843,0.4910,0.4914,0.4951,0.4984,0.5000,0.5000, 0.5066,0.5145,0.5161,0.5165,0.5201,0.5205,0.5220,0.5320,0.5354,0.5380, 0.5453,0.5454,0.5464,0.5517,0.5545,0.5602,0.5663,0.5710,0.5725,0.5747, 0.5849,0.5856,0.5875,0.5904,0.6044,0.6071,0.6162,0.6240,0.6362,0.6399, 0.6409,0.6490,0.6495,0.6499,0.6545,0.6563,0.6625,0.6650,0.6656,0.6674, 0.6726,0.6760,0.6776,0.6909,0.7067,0.7093,0.7183,0.7194,0.7202,0.7278, 0.7293,0.7317,0.7387,0.7406,0.7412,0.7500,0.7515,0.7518,0.7518,0.7587, 0.7610,0.7627,0.7714,0.7735,0.7755,0.7768,0.7832,0.7878,0.7888,0.7903, 0.7928,0.7982,0.8016,0.8023,0.8044,0.8125,0.8158,0.8202,0.8215,0.8294, 0.8377,0.8393,0.8495,0.8586,0.8612,0.8630,0.8648,0.8654,0.8656,0.8666, 0.8671,0.8722,0.8732,0.8759,0.8796,0.8806,0.8815,0.8850,0.8875,0.8877, 0.8897,0.8913,0.9058,0.9084,0.9106,0.9127,0.9134,0.9143,0.9155,0.9208, 0.9211,0.9215,0.9264,0.9269,0.9273,0.9283,0.9292,0.9326,0.9347,0.9355, 0.9358,0.9374,0.9388,0.9482,0.9513,0.9537,0.9546,0.9555,0.9598,0.9629, 0.9685,0.9722,0.9810,0.9818,0.9833,0.9911,0.9949,0.9956,0.9999, Overall p-value after applying KStest on 269 p-values = 0.106551 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.