RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-03-22_16:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.80 11.8056 0.188239 2 to 25 15.41 27.5910 0.950050 3 to 26 15.85 18.1681 0.621690 4 to 27 15.96 15.4380 0.436034 5 to 28 15.91 27.2219 0.945107 6 to 29 15.72 27.0495 0.942655 7 to 30 15.91 19.0079 0.671921 8 to 31 15.82 11.8970 0.193666 9 to 32 15.59 25.7893 0.921614 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.082160 Tough bday spacings test for dh-ranFile-2018-03-22_16:31: 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 34 77 91 96 83 58 29 8 8 1 (O-E)^2/E 3.7 0.2 0.2 0.5 0.0 0.3 0.7 0.0 3.2 0.3 2.3 Birthday Spacings: Sum(O-E)^2/E= 11.369, p= 0.671 RESULTS OF GCD FOR dh-ranFile-2018-03-22_16:31 Euclid's algorithm: p-value, steps to gcd: 0.300949 p-value, dist. of gcd's: 0.084023 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-03-22_16:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.992 0.494 0.752 0.149 0.116 0.060 0.515 0.488 Bits 8 to 15---> 0.591 0.881 0.105 0.868 0.573 0.557 0.219 0.853 Bits 16 to 23---> 0.147 0.283 0.483 0.881 0.853 0.165 0.950 0.834 Bits 24 to 31---> 0.083 0.580 0.364 0.568 0.901 0.465 0.714 0.143 KS test for the above 32 p values: 0.258 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-03-22_16:31, p-values for 5 runs: 0.3684, 0.0149, 0.0813, 0.7636, 0.3158 Rank test for binary matrices (31x31) for dh-ranFile-2018-03-22_16:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 218 211.4 0.205 0.205 r= 29 5047 5134.0 1.475 1.680 r= 30 22982 23103.0 0.634 2.314 r= 31 11753 11551.5 3.514 5.828 chi-square = 5.828 with df = 3; p-value = 0.880 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-03-22_16:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 213 211.4 0.012 0.012 r= 30 5083 5134.0 0.507 0.519 r= 31 22974 23103.0 0.721 1.239 r= 32 11730 11551.5 2.758 3.997 chi-square = 3.997 with df = 3; p-value = 0.738 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-03-22_16:31 b-rank test for bits 1 to 8, p=0.94883 b-rank test for bits 2 to 9, p=0.68531 b-rank test for bits 3 to 10, p=0.83621 b-rank test for bits 4 to 11, p=0.85076 b-rank test for bits 5 to 12, p=0.35955 b-rank test for bits 6 to 13, p=0.25840 b-rank test for bits 7 to 14, p=0.50224 b-rank test for bits 8 to 15, p=0.73069 b-rank test for bits 9 to 16, p=0.33669 b-rank test for bits 10 to 17, p=0.81266 b-rank test for bits 11 to 18, p=0.42163 b-rank test for bits 12 to 19, p=0.78163 b-rank test for bits 13 to 20, p=0.68901 b-rank test for bits 14 to 21, p=0.15057 b-rank test for bits 15 to 22, p=0.06236 b-rank test for bits 16 to 23, p=0.52517 b-rank test for bits 17 to 24, p=0.59878 b-rank test for bits 18 to 25, p=0.13203 b-rank test for bits 19 to 26, p=0.04518 b-rank test for bits 20 to 27, p=0.90711 b-rank test for bits 21 to 28, p=0.68541 b-rank test for bits 22 to 29, p=0.93327 b-rank test for bits 23 to 30, p=0.54443 b-rank test for bits 24 to 31, p=0.80914 b-rank test for bits 25 to 32, p=0.98097 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 = 0.266009 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-03-22_16:31 (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 141886 -0.05 0.478265 2 142024 0.27 0.605620 3 141405 -1.18 0.119330 4 141713 -0.46 0.323219 5 141599 -0.73 0.234205 6 142335 0.99 0.840024 7 142534 1.46 0.927788 8 141751 -0.37 0.355717 9 142713 1.88 0.969791 10 141958 0.11 0.545268 11 141963 0.13 0.549895 12 141428 -1.12 0.130379 13 141878 -0.07 0.470823 14 142424 1.20 0.885415 15 141912 0.01 0.502489 16 142808 2.10 0.982122 17 141702 -0.48 0.314045 18 143312 3.28 0.999476 19 141797 -0.26 0.396486 20 142491 1.36 0.912933 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-03-22_16:31 Bits used No. missing words z-score p-value 23 to 32 141966 0.1954 0.577466 22 to 31 142033 0.4264 0.665109 21 to 30 141653 -0.8839 0.188376 20 to 29 142209 1.0333 0.849279 19 to 28 142207 1.0264 0.847660 18 to 27 141697 -0.7322 0.232032 17 to 26 141806 -0.3563 0.360804 16 to 25 142267 1.2333 0.891276 15 to 24 141869 -0.1391 0.444698 14 to 23 142250 1.1747 0.879947 13 to 22 141340 -1.9632 0.024811 12 to 21 141508 -1.3839 0.083195 11 to 20 141534 -1.2942 0.097791 10 to 19 142041 0.4540 0.675098 9 to 18 141529 -1.3115 0.094847 8 to 17 141983 0.2540 0.600266 7 to 16 141969 0.2058 0.581510 6 to 15 141887 -0.0770 0.469312 5 to 14 141736 -0.5977 0.275024 4 to 13 141408 -1.7287 0.041929 3 to 12 142137 0.7851 0.783793 2 to 11 141969 0.2058 0.581510 1 to 10 141886 -0.0804 0.467940 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-03-22_16:31 Bits used No. missing words z-score p-value 28 to 32 142222 1.0599 0.855405 27 to 31 142511 2.0396 0.979303 26 to 30 141952 0.1446 0.557504 25 to 29 142134 0.7616 0.776849 24 to 28 142128 0.7413 0.770730 23 to 27 141940 0.1040 0.541402 22 to 26 142435 1.7819 0.962620 21 to 25 142130 0.7480 0.772780 20 to 24 141841 -0.2316 0.408414 19 to 23 142042 0.4497 0.673547 18 to 22 142181 0.9209 0.821453 17 to 21 142326 1.4124 0.921090 16 to 20 142001 0.3107 0.622003 15 to 19 142107 0.6701 0.748593 14 to 18 141922 0.0429 0.517129 13 to 17 141998 0.3006 0.618131 12 to 16 141434 -1.6113 0.053558 11 to 15 141413 -1.6825 0.046238 10 to 14 141178 -2.4791 0.006586 9 to 13 141801 -0.3672 0.356727 8 to 12 142390 1.6294 0.948385 7 to 11 141699 -0.7130 0.237928 6 to 10 142204 0.9989 0.841074 5 to 9 141638 -0.9198 0.178848 4 to 8 141339 -1.9333 0.026598 3 to 7 141675 -0.7943 0.213499 2 to 6 142188 0.9446 0.827580 1 to 5 141720 -0.6418 0.260503 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-03-22_16:31 Bits used No. missing words z-score p-value 31 to 32 140990 -2.7119 0.003345 30 to 31 142123 0.6303 0.735749 29 to 30 142198 0.8515 0.802764 28 to 29 141440 -1.3845 0.083110 27 to 28 141655 -0.7502 0.226556 26 to 27 141671 -0.7030 0.241016 25 to 26 141679 -0.6794 0.248430 24 to 25 141674 -0.6942 0.243782 23 to 24 141695 -0.6322 0.263614 22 to 23 142068 0.4681 0.680127 21 to 22 142506 1.7601 0.960804 20 to 21 141930 0.0610 0.524310 19 to 20 141314 -1.7561 0.039533 18 to 19 141872 -0.1101 0.456158 17 to 18 142090 0.5329 0.702966 16 to 17 142218 0.9105 0.818729 15 to 16 141503 -1.1986 0.115339 14 to 15 141587 -0.9508 0.170846 13 to 14 142249 1.0020 0.841823 12 to 13 141465 -1.3107 0.094978 11 to 12 141557 -1.0393 0.149328 10 to 11 142080 0.5035 0.692677 9 to 10 141123 -2.3196 0.010182 8 to 9 142265 1.0492 0.852951 7 to 8 141624 -0.8417 0.199983 6 to 7 141359 -1.6234 0.052253 5 to 6 141575 -0.9862 0.162012 4 to 5 141952 0.1259 0.550083 3 to 4 142453 1.6037 0.945615 2 to 3 141901 -0.0246 0.490198 1 to 2 141848 -0.1809 0.428217 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-03-22_16:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2365.11 -1.908 0.028220 Test results for specific bytes for dh-ranFile-2018-03-22_16:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2447.82 -0.738 0.230258 2 to 9 2398.16 -1.440 0.074898 3 to 10 2503.77 0.053 0.521271 4 to 11 2434.72 -0.923 0.177952 5 to 12 2491.03 -0.127 0.449510 6 to 13 2417.29 -1.170 0.121075 7 to 14 2374.26 -1.778 0.037686 8 to 15 2526.86 0.380 0.647960 9 to 16 2448.95 -0.722 0.235158 10 to 17 2515.49 0.219 0.586699 11 to 18 2517.20 0.243 0.596066 12 to 19 2487.12 -0.182 0.427709 13 to 20 2373.99 -1.782 0.037375 14 to 21 2472.27 -0.392 0.347464 15 to 22 2520.27 0.287 0.612810 16 to 23 2542.43 0.600 0.725783 17 to 24 2579.95 1.131 0.870905 18 to 25 2452.73 -0.668 0.251928 19 to 26 2618.56 1.677 0.953197 20 to 27 2416.65 -1.179 0.119262 21 to 28 2559.49 0.841 0.799913 22 to 29 2633.76 1.892 0.970731 23 to 30 2630.79 1.850 0.967815 24 to 31 2480.82 -0.271 0.393075 25 to 32 2448.14 -0.733 0.231649 CDPARK for dh-ranFile-2018-03-22_16:31: 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 3525 0.0913 0.536383 3512 -0.5023 0.307734 3521 -0.0913 0.463617 3561 1.7352 0.958644 3506 -0.7763 0.218799 3519 -0.1826 0.427537 3533 0.4566 0.676028 3512 -0.5023 0.307734 3546 1.0502 0.853193 3509 -0.6393 0.261324 Square side=100, avg. no. parked=3524.40 sample std.=16.75 p-value of the KSTEST for those 10 p-values: 0.736417 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-03-22_16:31 0.0905,0.4177,0.0682,0.8939,0.5060,0.3551,0.1404,0.6140,0.0921,0.2872, The KS test for those 10 p-values: 0.141942 The 3DSPHERES test for dh-ranFile-2018-03-22_16:31 sample no r^3 equiv. uni. 1 10.104 0.285945 2 9.655 0.275188 3 33.996 0.677999 4 23.757 0.547020 5 48.658 0.802483 6 1.139 0.037250 7 1.181 0.038617 8 12.485 0.340423 9 8.705 0.251867 10 109.050 0.973616 11 48.211 0.799518 12 1.769 0.057277 13 34.201 0.680190 14 9.796 0.278589 15 3.827 0.119771 16 5.801 0.175811 17 49.084 0.805266 18 36.186 0.700664 19 50.581 0.814745 20 65.337 0.886722 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.693261 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-03-22_16:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -0.7 -0.4 -2.2 -0.5 1.1 -1.5 -0.3 0.5 1.2 -1.1 0.3 -3.0 0.6 -0.3 0.4 1.1 -0.5 -0.4 0.0 0.3 -0.1 -0.6 0.2 1.1 -0.7 1.4 -0.1 0.2 -0.1 2.4 0.6 1.0 0.2 -1.3 1.0 0.7 1.1 -0.8 1.0 1.6 0.0 1.8 Chi-square with 42 degrees of freedom:46.359887 z-score=0.475703, p-value=0.702771 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-03-22_16:31 Test no p-value 1 0.034776 2 0.001380 3 0.899065 4 0.780281 5 0.552029 6 0.661077 7 0.395439 8 0.049775 9 0.792875 10 0.428306 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.314362 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-03-22_16:31: (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 66975 1.43 67060 2.32 3 25000.00 24803 1.55 24652 4.84 4 6666.67 6532 2.72 6635 0.15 5 1388.89 1420 0.70 1380 0.06 6 238.10 233 0.11 236 0.02 7 34.72 31 0.40 30 0.64 8 4.96 5 0.00 6 0.22 p=0.67014 p=0.77967 Number of rngs required: 687384, p-value: 0.118 RESULTS OF CRAPS TEST for dh-ranFile-2018-03-22_16:31 No. of wins: Observed Expected 98749 98585.9 z-score= 0.730, pvalue=0.76720 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66316 66666.7 1.845 1.845 2 37765 37654.3 0.325 2.170 3 27013 26954.7 0.126 2.296 4 19362 19313.5 0.122 2.418 5 13892 13851.4 0.119 2.537 6 9840 9943.5 1.078 3.615 7 7190 7145.0 0.283 3.898 8 5188 5139.1 0.466 4.364 9 3776 3699.9 1.567 5.930 10 2683 2666.3 0.105 6.035 11 1968 1923.3 1.038 7.073 12 1362 1388.7 0.515 7.588 13 1028 1003.7 0.588 8.175 14 688 726.1 2.003 10.178 15 519 525.8 0.089 10.267 16 408 381.2 1.891 12.159 17 291 276.5 0.756 12.915 18 164 200.8 6.754 19.669 19 128 146.0 2.216 21.885 20 108 106.2 0.030 21.915 21 311 287.1 1.987 23.902 Chisq= 23.90 for 20 degrees of freedom, p= 0.75329 SUMMARY of craptest p-value for no. of wins: 0.767202 p-value for throws/game: 0.753287 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-03-22_16:31 No. of wins: Observed Expected 98579 98585.9 z-score=-0.031, pvalue=0.48776 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66512 66666.7 0.359 0.359 2 37614 37654.3 0.043 0.402 3 26948 26954.7 0.002 0.404 4 19255 19313.5 0.177 0.581 5 13998 13851.4 1.551 2.132 6 10014 9943.5 0.499 2.631 7 7184 7145.0 0.213 2.844 8 5158 5139.1 0.070 2.913 9 3716 3699.9 0.070 2.984 10 2659 2666.3 0.020 3.004 11 1952 1923.3 0.427 3.431 12 1382 1388.7 0.033 3.464 13 975 1003.7 0.822 4.285 14 695 726.1 1.335 5.621 15 514 525.8 0.266 5.887 16 420 381.2 3.960 9.847 17 290 276.5 0.655 10.502 18 194 200.8 0.232 10.734 19 114 146.0 7.008 17.742 20 111 106.2 0.216 17.958 21 295 287.1 0.217 18.174 Chisq= 18.17 for 20 degrees of freedom, p= 0.42406 SUMMARY of craptest p-value for no. of wins: 0.487764 p-value for throws/game: 0.424065 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0014,0.0033,0.0066,0.0102,0.0149,0.0248,0.0266,0.0282,0.0348,0.0372, 0.0374,0.0377,0.0386,0.0395,0.0419,0.0452,0.0462,0.0498,0.0523,0.0536, 0.0573,0.0604,0.0624,0.0682,0.0749,0.0813,0.0822,0.0831,0.0832,0.0835, 0.0840,0.0905,0.0921,0.0948,0.0950,0.0978,0.1047,0.1153,0.1155,0.1182, 0.1193,0.1193,0.1198,0.1211,0.1304,0.1320,0.1404,0.1419,0.1428,0.1467, 0.1487,0.1493,0.1506,0.1620,0.1647,0.1708,0.1758,0.1780,0.1788,0.1882, 0.1884,0.1937,0.2000,0.2135,0.2186,0.2188,0.2266,0.2303,0.2316,0.2320, 0.2342,0.2352,0.2379,0.2410,0.2438,0.2484,0.2519,0.2519,0.2583,0.2584, 0.2605,0.2613,0.2636,0.2660,0.2750,0.2752,0.2786,0.2826,0.2859,0.2872, 0.3009,0.3077,0.3077,0.3140,0.3144,0.3158,0.3232,0.3367,0.3404,0.3475, 0.3551,0.3557,0.3567,0.3596,0.3608,0.3638,0.3684,0.3931,0.3954,0.3965, 0.4084,0.4177,0.4216,0.4241,0.4275,0.4277,0.4282,0.4283,0.4360,0.4447, 0.4495,0.4562,0.4636,0.4645,0.4679,0.4693,0.4708,0.4783,0.4832,0.4878, 0.4881,0.4902,0.4936,0.5022,0.5025,0.5060,0.5149,0.5171,0.5213,0.5243, 0.5252,0.5364,0.5414,0.5444,0.5453,0.5470,0.5499,0.5501,0.5520,0.5567, 0.5575,0.5678,0.5726,0.5775,0.5805,0.5815,0.5815,0.5867,0.5911,0.5961, 0.5988,0.6003,0.6056,0.6128,0.6140,0.6181,0.6217,0.6220,0.6480,0.6611, 0.6651,0.6701,0.6705,0.6719,0.6735,0.6751,0.6760,0.6780,0.6801,0.6802, 0.6853,0.6854,0.6890,0.6927,0.6933,0.7007,0.7028,0.7030,0.7137,0.7258, 0.7307,0.7357,0.7364,0.7382,0.7486,0.7525,0.7533,0.7636,0.7672,0.7707, 0.7728,0.7768,0.7797,0.7803,0.7816,0.7838,0.7929,0.7995,0.7999,0.8025, 0.8028,0.8053,0.8091,0.8127,0.8147,0.8187,0.8215,0.8276,0.8338,0.8362, 0.8400,0.8411,0.8418,0.8477,0.8493,0.8508,0.8525,0.8526,0.8530,0.8532, 0.8554,0.8676,0.8709,0.8797,0.8799,0.8810,0.8813,0.8854,0.8867,0.8913, 0.8939,0.8991,0.9008,0.9071,0.9129,0.9211,0.9216,0.9278,0.9333,0.9427, 0.9451,0.9456,0.9484,0.9488,0.9497,0.9501,0.9532,0.9586,0.9608,0.9626, 0.9678,0.9698,0.9707,0.9736,0.9793,0.9810,0.9821,0.9920,0.9995, Overall p-value after applying KStest on 269 p-values = 0.459977 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.