RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-05-05_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 15.83 15.2374 0.421614 2 to 25 15.82 23.3816 0.862766 3 to 26 15.60 20.3872 0.745097 4 to 27 15.82 22.2694 0.825419 5 to 28 15.70 16.6654 0.522749 6 to 29 15.86 15.3876 0.432412 7 to 30 15.80 19.5390 0.701513 8 to 31 16.00 30.1092 0.974432 9 to 32 15.67 19.7585 0.713232 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.075462 Tough bday spacings test for dh-ranFile-2016-05-05_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 10 47 71 93 95 74 56 32 15 4 3 (O-E)^2/E 0.1 2.9 0.1 0.2 0.1 0.2 0.3 0.2 0.0 1.0 0.3 Birthday Spacings: Sum(O-E)^2/E= 5.374, p= 0.135 RESULTS OF GCD FOR dh-ranFile-2016-05-05_14:31 Euclid's algorithm: p-value, steps to gcd: 0.547834 p-value, dist. of gcd's: 0.773208 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-05-05_14:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.306 0.310 0.374 0.252 0.665 0.793 0.956 0.686 Bits 8 to 15---> 0.588 0.023 0.849 0.629 0.709 0.706 0.220 0.465 Bits 16 to 23---> 0.082 0.930 0.232 0.174 0.939 0.794 0.562 0.441 Bits 24 to 31---> 0.291 0.020 0.256 0.166 0.017 0.981 0.040 0.124 KS test for the above 32 p values: 0.511 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-05-05_14:31, p-values for 5 runs: 0.9713, 0.2294, 0.7305, 0.0645, 0.8227 Rank test for binary matrices (31x31) for dh-ranFile-2016-05-05_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 237 211.4 3.095 3.095 r= 29 5236 5134.0 2.026 5.122 r= 30 23010 23103.0 0.375 5.496 r= 31 11517 11551.5 0.103 5.599 chi-square = 5.599 with df = 3; p-value = 0.867 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-05-05_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 217 211.4 0.147 0.147 r= 30 5189 5134.0 0.589 0.736 r= 31 23139 23103.0 0.056 0.792 r= 32 11455 11551.5 0.807 1.599 chi-square = 1.599 with df = 3; p-value = 0.340 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-05-05_14:31 b-rank test for bits 1 to 8, p=0.67824 b-rank test for bits 2 to 9, p=0.91624 b-rank test for bits 3 to 10, p=0.87245 b-rank test for bits 4 to 11, p=0.73100 b-rank test for bits 5 to 12, p=0.38730 b-rank test for bits 6 to 13, p=0.52099 b-rank test for bits 7 to 14, p=0.76085 b-rank test for bits 8 to 15, p=0.07203 b-rank test for bits 9 to 16, p=0.91952 b-rank test for bits 10 to 17, p=0.52923 b-rank test for bits 11 to 18, p=0.65186 b-rank test for bits 12 to 19, p=0.81312 b-rank test for bits 13 to 20, p=0.22148 b-rank test for bits 14 to 21, p=0.66369 b-rank test for bits 15 to 22, p=0.95555 b-rank test for bits 16 to 23, p=0.16555 b-rank test for bits 17 to 24, p=0.41805 b-rank test for bits 18 to 25, p=0.23046 b-rank test for bits 19 to 26, p=0.11847 b-rank test for bits 20 to 27, p=0.57581 b-rank test for bits 21 to 28, p=0.47804 b-rank test for bits 22 to 29, p=0.83355 b-rank test for bits 23 to 30, p=0.73229 b-rank test for bits 24 to 31, p=0.68002 b-rank test for bits 25 to 32, p=0.27907 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 = 0.399763 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-05-05_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 142494 1.37 0.914039 2 141482 -1.00 0.159034 3 141445 -1.08 0.138987 4 141588 -0.75 0.226395 5 141845 -0.15 0.440263 6 142102 0.45 0.673704 7 141502 -0.95 0.170623 8 141315 -1.39 0.082474 9 141667 -0.57 0.285632 10 142303 0.92 0.821159 11 142287 0.88 0.811222 12 141696 -0.50 0.309089 13 141327 -1.36 0.086823 14 141535 -0.87 0.190895 15 141817 -0.22 0.414601 16 141007 -2.11 0.017505 17 141369 -1.26 0.103393 18 141838 -0.17 0.433819 19 141887 -0.05 0.479196 20 142468 1.31 0.904105 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-05-05_14:31 Bits used No. missing words z-score p-value 23 to 32 141994 0.2920 0.614844 22 to 31 142234 1.1196 0.868548 21 to 30 142579 2.3092 0.989534 20 to 29 142079 0.5851 0.720749 19 to 28 142209 1.0333 0.849279 18 to 27 141687 -0.7667 0.221643 17 to 26 142022 0.3885 0.651183 16 to 25 142119 0.7230 0.765160 15 to 24 141830 -0.2736 0.392215 14 to 23 141804 -0.3632 0.358225 13 to 22 141549 -1.2425 0.107023 12 to 21 141581 -1.1322 0.128781 11 to 20 141822 -0.3011 0.381655 10 to 19 141949 0.1368 0.554403 9 to 18 141942 0.1127 0.544848 8 to 17 141750 -0.5494 0.291361 7 to 16 142100 0.6575 0.744565 6 to 15 142004 0.3264 0.627957 5 to 14 141654 -0.8804 0.189308 4 to 13 141414 -1.7080 0.043815 3 to 12 141755 -0.5322 0.297303 2 to 11 141939 0.1023 0.540745 1 to 10 141849 -0.2080 0.417601 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-05-05_14:31 Bits used No. missing words z-score p-value 28 to 32 141811 -0.3333 0.369446 27 to 31 141915 0.0192 0.507667 26 to 30 141862 -0.1604 0.436267 25 to 29 141903 -0.0215 0.491440 24 to 28 142113 0.6904 0.755031 23 to 27 142075 0.5616 0.712803 22 to 26 142219 1.0497 0.853079 21 to 25 142150 0.8158 0.792702 20 to 24 141852 -0.1943 0.422955 19 to 23 141071 -2.8418 0.002243 18 to 22 142020 0.3752 0.646227 17 to 21 141961 0.1752 0.569520 16 to 20 141856 -0.1808 0.428270 15 to 19 141410 -1.6926 0.045262 14 to 18 141696 -0.7232 0.234793 13 to 17 141552 -1.2113 0.112893 12 to 16 141771 -0.4689 0.319565 11 to 15 141678 -0.7842 0.216470 10 to 14 142217 1.0429 0.851514 9 to 13 141553 -1.2079 0.113543 8 to 12 141596 -1.0621 0.144087 7 to 11 141935 0.0870 0.534671 6 to 10 141934 0.0836 0.533324 5 to 9 142371 1.5650 0.941207 4 to 8 142091 0.6158 0.730997 3 to 7 142015 0.3582 0.639905 2 to 6 142155 0.8328 0.797516 1 to 5 141845 -0.2181 0.413688 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-05-05_14:31 Bits used No. missing words z-score p-value 31 to 32 141991 0.2409 0.595189 30 to 31 142102 0.5683 0.715101 29 to 30 141892 -0.0511 0.479615 28 to 29 141855 -0.1603 0.436336 27 to 28 141947 0.1111 0.544240 26 to 27 142159 0.7365 0.769284 25 to 26 141575 -0.9862 0.162012 24 to 25 141758 -0.4464 0.327654 23 to 24 141623 -0.8446 0.199158 22 to 23 141709 -0.5909 0.277279 21 to 22 142197 0.8486 0.801944 20 to 21 141715 -0.5732 0.283240 19 to 20 141877 -0.0954 0.462011 18 to 19 141687 -0.6558 0.255963 17 to 18 141580 -0.9715 0.165656 16 to 17 142441 1.5683 0.941600 15 to 16 142262 1.0403 0.850905 14 to 15 142127 0.6421 0.739594 13 to 14 142740 2.4504 0.992864 12 to 13 142431 1.5388 0.938080 11 to 12 142044 0.3973 0.654411 10 to 11 142270 1.0639 0.856318 9 to 10 141864 -0.1337 0.446813 8 to 9 142332 1.2468 0.893767 7 to 8 141440 -1.3845 0.083110 6 to 7 141872 -0.1101 0.456158 5 to 6 142157 0.7306 0.767485 4 to 5 141926 0.0492 0.519610 3 to 4 141650 -0.7650 0.222140 2 to 3 141709 -0.5909 0.277279 1 to 2 141658 -0.7414 0.229230 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-05-05_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2553.80 0.761 0.776642 Test results for specific bytes for dh-ranFile-2016-05-05_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2541.60 0.588 0.721832 2 to 9 2530.30 0.428 0.665849 3 to 10 2462.33 -0.533 0.297124 4 to 11 2555.61 0.786 0.784204 5 to 12 2612.86 1.596 0.944767 6 to 13 2425.79 -1.049 0.146988 7 to 14 2641.34 1.999 0.977185 8 to 15 2545.53 0.644 0.740158 9 to 16 2599.39 1.406 0.920070 10 to 17 2654.84 2.190 0.985727 11 to 18 2590.07 1.274 0.898636 12 to 19 2524.69 0.349 0.636507 13 to 20 2437.50 -0.884 0.188380 14 to 21 2511.78 0.167 0.566136 15 to 22 2431.61 -0.967 0.166721 16 to 23 2482.26 -0.251 0.400955 17 to 24 2534.56 0.489 0.687495 18 to 25 2479.91 -0.284 0.388157 19 to 26 2535.39 0.501 0.691656 20 to 27 2498.07 -0.027 0.489087 21 to 28 2478.82 -0.299 0.382285 22 to 29 2497.64 -0.033 0.486701 23 to 30 2442.81 -0.809 0.209321 24 to 31 2420.02 -1.131 0.129022 25 to 32 2559.30 0.839 0.799145 CDPARK for dh-ranFile-2016-05-05_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 3552 1.3242 0.907282 3518 -0.2283 0.409702 3498 -1.1416 0.126820 3509 -0.6393 0.261324 3500 -1.0502 0.146807 3524 0.0457 0.518210 3526 0.1370 0.554479 3538 0.6849 0.753306 3533 0.4566 0.676028 3577 2.4658 0.993164 Square side=100, avg. no. parked=3527.50 sample std.=22.94 p-value of the KSTEST for those 10 p-values: 0.914626 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-05-05_14:31 0.3916,0.4914,0.5777,0.2431,0.4905,0.1327,0.0555,0.3132,0.3343,0.2019, The KS test for those 10 p-values: 0.065026 The 3DSPHERES test for dh-ranFile-2016-05-05_14:31 sample no r^3 equiv. uni. 1 18.076 0.452570 2 37.112 0.709769 3 13.857 0.369908 4 11.979 0.329201 5 24.392 0.556511 6 7.542 0.222300 7 30.183 0.634361 8 4.471 0.138456 9 28.928 0.618737 10 25.902 0.578279 11 16.872 0.430161 12 60.790 0.868184 13 45.785 0.782630 14 17.733 0.446291 15 30.099 0.633335 16 80.025 0.930574 17 1.732 0.056104 18 152.201 0.993739 19 1.159 0.037890 20 23.230 0.538985 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.882671 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-05-05_14:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 1.3 0.6 0.3 2.1 -0.2 1.5 1.4 1.0 -0.2 -0.8 0.2 0.2 0.4 -1.1 0.7 -0.2 -0.8 0.7 -1.1 -0.6 -1.9 0.2 1.7 0.2 0.4 -1.0 0.4 0.9 1.0 0.5 0.6 0.6 0.8 0.8 1.3 0.0 -1.0 -0.4 -0.1 -1.3 0.0 -1.1 Chi-square with 42 degrees of freedom:35.502616 z-score=-0.708923, p-value=0.249717 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-05-05_14:31 Test no p-value 1 0.081892 2 0.173649 3 0.516983 4 0.986918 5 0.266694 6 0.320630 7 0.533999 8 0.754074 9 0.299311 10 0.090298 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.408038 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-05-05_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 66657 0.00 66651 0.00 3 25000.00 25026 0.03 25095 0.36 4 6666.67 6687 0.06 6666 0.00 5 1388.89 1391 0.00 1294 6.48 6 238.10 201 5.78 248 0.41 7 34.72 34 0.01 40 0.80 8 4.96 3 0.77 5 0.00 p=0.64681 p=0.76648 Number of rngs required: 688320, p-value: 0.462 RESULTS OF CRAPS TEST for dh-ranFile-2016-05-05_14:31 No. of wins: Observed Expected 98776 98585.9 z-score= 0.850, pvalue=0.80246 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66492 66666.7 0.458 0.458 2 37582 37654.3 0.139 0.597 3 27096 26954.7 0.740 1.337 4 19354 19313.5 0.085 1.422 5 13859 13851.4 0.004 1.426 6 10009 9943.5 0.431 1.857 7 7179 7145.0 0.162 2.019 8 5159 5139.1 0.077 2.096 9 3672 3699.9 0.210 2.306 10 2715 2666.3 0.890 3.195 11 1910 1923.3 0.092 3.288 12 1352 1388.7 0.972 4.260 13 1040 1003.7 1.312 5.571 14 711 726.1 0.316 5.887 15 526 525.8 0.000 5.887 16 384 381.2 0.021 5.908 17 267 276.5 0.329 6.238 18 172 200.8 4.139 10.376 19 123 146.0 3.619 13.995 20 119 106.2 1.539 15.534 21 279 287.1 0.229 15.763 Chisq= 15.76 for 20 degrees of freedom, p= 0.26879 SUMMARY of craptest p-value for no. of wins: 0.802455 p-value for throws/game: 0.268791 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-05-05_14:31 No. of wins: Observed Expected 98268 98585.9 z-score=-1.422, pvalue=0.07756 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66774 66666.7 0.173 0.173 2 37713 37654.3 0.091 0.264 3 26540 26954.7 6.381 6.645 4 19308 19313.5 0.002 6.647 5 13883 13851.4 0.072 6.719 6 9994 9943.5 0.256 6.975 7 7313 7145.0 3.949 10.924 8 5100 5139.1 0.297 11.221 9 3657 3699.9 0.497 11.718 10 2718 2666.3 1.003 12.720 11 1901 1923.3 0.259 12.979 12 1448 1388.7 2.529 15.508 13 959 1003.7 1.992 17.500 14 770 726.1 2.649 20.149 15 532 525.8 0.072 20.222 16 384 381.2 0.021 20.243 17 276 276.5 0.001 20.244 18 209 200.8 0.332 20.576 19 162 146.0 1.757 22.333 20 100 106.2 0.364 22.697 21 259 287.1 2.753 25.450 Chisq= 25.45 for 20 degrees of freedom, p= 0.81524 SUMMARY of craptest p-value for no. of wins: 0.077564 p-value for throws/game: 0.815244 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0022,0.0173,0.0175,0.0200,0.0233,0.0379,0.0398,0.0438,0.0453,0.0555, 0.0561,0.0645,0.0650,0.0720,0.0755,0.0776,0.0819,0.0823,0.0825,0.0831, 0.0868,0.0903,0.1034,0.1070,0.1129,0.1135,0.1185,0.1238,0.1268,0.1288, 0.1290,0.1327,0.1352,0.1385,0.1390,0.1441,0.1468,0.1470,0.1590,0.1620, 0.1655,0.1657,0.1658,0.1667,0.1706,0.1736,0.1740,0.1884,0.1893,0.1909, 0.1992,0.2019,0.2093,0.2165,0.2199,0.2215,0.2216,0.2221,0.2223,0.2264, 0.2292,0.2294,0.2305,0.2320,0.2348,0.2431,0.2497,0.2517,0.2560,0.2564, 0.2613,0.2667,0.2688,0.2773,0.2773,0.2791,0.2832,0.2856,0.2914,0.2915, 0.2971,0.2973,0.2993,0.3061,0.3091,0.3096,0.3132,0.3196,0.3206,0.3277, 0.3292,0.3343,0.3404,0.3582,0.3694,0.3699,0.3735,0.3817,0.3823,0.3873, 0.3882,0.3916,0.3922,0.3998,0.4010,0.4080,0.4097,0.4137,0.4146,0.4176, 0.4181,0.4216,0.4230,0.4283,0.4302,0.4324,0.4338,0.4363,0.4363,0.4403, 0.4407,0.4463,0.4468,0.4526,0.4562,0.4620,0.4620,0.4646,0.4780,0.4792, 0.4796,0.4867,0.4891,0.4905,0.4914,0.4914,0.5077,0.5108,0.5170,0.5182, 0.5196,0.5210,0.5227,0.5292,0.5333,0.5340,0.5347,0.5390,0.5407,0.5442, 0.5448,0.5478,0.5544,0.5545,0.5565,0.5621,0.5661,0.5695,0.5758,0.5777, 0.5783,0.5876,0.5952,0.6148,0.6187,0.6280,0.6289,0.6333,0.6344,0.6365, 0.6399,0.6462,0.6468,0.6512,0.6519,0.6544,0.6637,0.6653,0.6658,0.6737, 0.6760,0.6782,0.6800,0.6862,0.6875,0.6917,0.7015,0.7059,0.7090,0.7098, 0.7128,0.7132,0.7151,0.7207,0.7218,0.7305,0.7310,0.7310,0.7323,0.7396, 0.7402,0.7446,0.7451,0.7533,0.7541,0.7550,0.7609,0.7652,0.7665,0.7675, 0.7693,0.7732,0.7766,0.7826,0.7842,0.7927,0.7931,0.7939,0.7975,0.7991, 0.8019,0.8025,0.8112,0.8131,0.8152,0.8212,0.8227,0.8254,0.8335,0.8487, 0.8493,0.8509,0.8515,0.8531,0.8563,0.8628,0.8672,0.8682,0.8685,0.8725, 0.8827,0.8938,0.8986,0.9041,0.9073,0.9140,0.9146,0.9162,0.9195,0.9201, 0.9299,0.9306,0.9381,0.9391,0.9412,0.9416,0.9448,0.9555,0.9555,0.9713, 0.9744,0.9772,0.9809,0.9857,0.9869,0.9895,0.9929,0.9932,0.9937, Overall p-value after applying KStest on 269 p-values = 0.936373 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.