RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-09-06_01:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.86 17.6439 0.588368 2 to 25 15.73 28.2602 0.958012 3 to 26 15.94 13.5853 0.303794 4 to 27 15.86 17.5809 0.584270 5 to 28 15.17 30.9232 0.979594 6 to 29 15.57 24.8063 0.900870 7 to 30 15.80 22.3622 0.828811 8 to 31 15.50 23.2388 0.858363 9 to 32 15.67 30.6068 0.977713 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.002967 Tough bday spacings test for dh-ranFile-2016-09-06_01:31: 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 37 80 96 92 82 52 28 13 10 3 (O-E)^2/E 0.5 0.0 0.6 0.0 0.3 0.2 0.0 0.1 0.2 1.7 0.3 Birthday Spacings: Sum(O-E)^2/E= 4.037, p= 0.054 RESULTS OF GCD FOR dh-ranFile-2016-09-06_01:31 Euclid's algorithm: p-value, steps to gcd: 0.415029 p-value, dist. of gcd's: 0.568356 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-09-06_01:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.328 0.068 0.586 0.273 0.295 0.480 0.350 0.428 Bits 8 to 15---> 0.710 0.887 0.640 0.327 0.407 0.976 0.190 0.481 Bits 16 to 23---> 0.238 0.927 0.781 0.701 0.897 0.547 0.600 0.318 Bits 24 to 31---> 0.277 0.657 0.858 0.968 0.599 0.056 0.800 0.346 KS test for the above 32 p values: 0.350 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-09-06_01:31, p-values for 5 runs: 0.7474, 0.2468, 0.5182, 0.9400, 0.7087 Rank test for binary matrices (31x31) for dh-ranFile-2016-09-06_01:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 205 211.4 0.195 0.195 r= 29 5052 5134.0 1.310 1.505 r= 30 23024 23103.0 0.270 1.775 r= 31 11719 11551.5 2.428 4.203 chi-square = 4.203 with df = 3; p-value = 0.760 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-09-06_01:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 204 211.4 0.260 0.260 r= 30 5153 5134.0 0.070 0.331 r= 31 23181 23103.0 0.263 0.594 r= 32 11462 11551.5 0.694 1.287 chi-square = 1.287 with df = 3; p-value = 0.268 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-09-06_01:31 b-rank test for bits 1 to 8, p=0.96924 b-rank test for bits 2 to 9, p=0.88951 b-rank test for bits 3 to 10, p=0.36749 b-rank test for bits 4 to 11, p=0.02139 b-rank test for bits 5 to 12, p=0.62351 b-rank test for bits 6 to 13, p=0.80634 b-rank test for bits 7 to 14, p=0.89424 b-rank test for bits 8 to 15, p=0.81545 b-rank test for bits 9 to 16, p=0.38123 b-rank test for bits 10 to 17, p=0.63964 b-rank test for bits 11 to 18, p=0.71190 b-rank test for bits 12 to 19, p=0.49563 b-rank test for bits 13 to 20, p=0.69317 b-rank test for bits 14 to 21, p=0.36226 b-rank test for bits 15 to 22, p=0.26916 b-rank test for bits 16 to 23, p=0.78658 b-rank test for bits 17 to 24, p=0.22061 b-rank test for bits 18 to 25, p=0.11111 b-rank test for bits 19 to 26, p=0.34687 b-rank test for bits 20 to 27, p=0.66223 b-rank test for bits 21 to 28, p=0.96711 b-rank test for bits 22 to 29, p=0.65726 b-rank test for bits 23 to 30, p=0.80458 b-rank test for bits 24 to 31, p=0.82746 b-rank test for bits 25 to 32, p=0.88210 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 = 0.090617 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-09-06_01:31 (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 141470 -1.03 0.152335 2 142457 1.28 0.899658 3 142015 0.25 0.597504 4 141482 -1.00 0.159034 5 141869 -0.09 0.462464 6 142719 1.89 0.970738 7 141701 -0.49 0.313217 8 141949 0.09 0.536924 9 141711 -0.46 0.321543 10 142512 1.41 0.920450 11 141986 0.18 0.571084 12 141561 -0.81 0.207864 13 142298 0.91 0.818089 14 142156 0.58 0.717805 15 141931 0.05 0.520190 16 142013 0.24 0.595695 17 143045 2.65 0.996016 18 142175 0.62 0.732610 19 141474 -1.02 0.154547 20 141921 0.03 0.510876 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-09-06_01:31 Bits used No. missing words z-score p-value 23 to 32 142192 0.9747 0.835151 22 to 31 142001 0.3161 0.624038 21 to 30 141999 0.3092 0.621418 20 to 29 141739 -0.5873 0.278486 19 to 28 142051 0.4885 0.687408 18 to 27 141585 -1.1184 0.131703 17 to 26 141910 0.0023 0.500922 16 to 25 141619 -1.0011 0.158380 15 to 24 141727 -0.6287 0.264765 14 to 23 141868 -0.1425 0.443336 13 to 22 142205 1.0196 0.846029 12 to 21 141560 -1.2046 0.114182 11 to 20 141826 -0.2873 0.386924 10 to 19 141778 -0.4529 0.325324 9 to 18 142312 1.3885 0.917510 8 to 17 141481 -1.4770 0.069838 7 to 16 142097 0.6471 0.741229 6 to 15 141605 -1.0494 0.146994 5 to 14 141945 0.1230 0.548947 4 to 13 141936 0.0920 0.536637 3 to 12 141702 -0.7149 0.237326 2 to 11 141296 -2.1149 0.017218 1 to 10 141270 -2.2046 0.013742 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-09-06_01:31 Bits used No. missing words z-score p-value 28 to 32 141936 0.0904 0.536018 27 to 31 142215 1.0362 0.849938 26 to 30 141812 -0.3299 0.370726 25 to 29 141893 -0.0554 0.477928 24 to 28 141595 -1.0655 0.143319 23 to 27 141548 -1.2248 0.110316 22 to 26 142141 0.7853 0.783868 21 to 25 142133 0.7582 0.775835 20 to 24 141654 -0.8655 0.193375 19 to 23 141528 -1.2926 0.098067 18 to 22 142440 1.7989 0.963981 17 to 21 142204 0.9989 0.841074 16 to 20 142151 0.8192 0.793670 15 to 19 141661 -0.8418 0.199951 14 to 18 141844 -0.2215 0.412368 13 to 17 141995 0.2904 0.614248 12 to 16 142269 1.2192 0.888620 11 to 15 141724 -0.6282 0.264924 10 to 14 142186 0.9379 0.825843 9 to 13 142617 2.3989 0.991777 8 to 12 142139 0.7785 0.781875 7 to 11 142133 0.7582 0.775835 6 to 10 142451 1.8362 0.966834 5 to 9 141814 -0.3232 0.373290 4 to 8 142108 0.6735 0.749672 3 to 7 142296 1.3107 0.905028 2 to 6 142300 1.3243 0.907299 1 to 5 142283 1.2667 0.897365 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-09-06_01:31 Bits used No. missing words z-score p-value 31 to 32 142232 0.9518 0.829408 30 to 31 141940 0.0905 0.536044 29 to 30 142052 0.4209 0.663070 28 to 29 141712 -0.5821 0.280252 27 to 28 141932 0.0669 0.526659 26 to 27 142038 0.3796 0.647863 25 to 26 141852 -0.1691 0.432853 24 to 25 141993 0.2468 0.597474 23 to 24 141921 0.0344 0.513731 22 to 23 141987 0.2291 0.590610 21 to 22 141835 -0.2193 0.413223 20 to 21 142014 0.3088 0.621248 19 to 20 141603 -0.9036 0.183096 18 to 19 142410 1.4769 0.930149 17 to 18 142040 0.3855 0.650051 16 to 17 142226 0.9341 0.824882 15 to 16 142573 1.9577 0.974869 14 to 15 142119 0.6185 0.731876 13 to 14 141502 -1.2016 0.114766 12 to 13 142174 0.7807 0.782522 11 to 12 141676 -0.6883 0.245635 10 to 11 142057 0.4356 0.668438 9 to 10 142346 1.2881 0.901147 8 to 9 142218 0.9105 0.818729 7 to 8 141872 -0.1101 0.456158 6 to 7 141858 -0.1514 0.439824 5 to 6 141314 -1.7561 0.039533 4 to 5 142049 0.4120 0.659832 3 to 4 142138 0.6745 0.750017 2 to 3 142402 1.4533 0.926930 1 to 2 141506 -1.1898 0.117070 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-09-06_01:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2477.90 -0.312 0.377341 Test results for specific bytes for dh-ranFile-2016-09-06_01:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2476.90 -0.327 0.371975 2 to 9 2620.28 1.701 0.955529 3 to 10 2598.68 1.396 0.918574 4 to 11 2564.36 0.910 0.818625 5 to 12 2581.21 1.149 0.874621 6 to 13 2674.99 2.475 0.993333 7 to 14 2616.15 1.643 0.949769 8 to 15 2477.29 -0.321 0.374024 9 to 16 2578.25 1.107 0.865785 10 to 17 2425.24 -1.057 0.145207 11 to 18 2440.14 -0.847 0.198637 12 to 19 2421.29 -1.113 0.132823 13 to 20 2583.93 1.187 0.882370 14 to 21 2384.43 -1.634 0.051093 15 to 22 2447.58 -0.741 0.229254 16 to 23 2496.44 -0.050 0.479941 17 to 24 2414.85 -1.204 0.114257 18 to 25 2440.94 -0.835 0.201801 19 to 26 2454.70 -0.641 0.260875 20 to 27 2377.47 -1.733 0.041557 21 to 28 2463.41 -0.517 0.302424 22 to 29 2568.73 0.972 0.834486 23 to 30 2446.43 -0.758 0.224353 24 to 31 2584.17 1.190 0.883044 25 to 32 2520.71 0.293 0.615180 CDPARK for dh-ranFile-2016-09-06_01:31: 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 3537 0.6393 0.738676 3532 0.4110 0.659449 3534 0.5023 0.692266 3521 -0.0913 0.463617 3537 0.6393 0.738676 3548 1.1416 0.873180 3555 1.4612 0.928018 3515 -0.3653 0.357445 3556 1.5068 0.934075 3552 1.3242 0.907282 Square side=100, avg. no. parked=3538.70 sample std.=13.33 p-value of the KSTEST for those 10 p-values: 0.017011 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-09-06_01:31 0.7567,0.2837,0.7589,0.3408,0.8255,0.6124,0.9372,0.8298,0.3267,0.7702, The KS test for those 10 p-values: 0.139752 The 3DSPHERES test for dh-ranFile-2016-09-06_01:31 sample no r^3 equiv. uni. 1 60.588 0.867293 2 7.715 0.226756 3 100.833 0.965302 4 25.885 0.578036 5 91.827 0.953154 6 8.847 0.255386 7 117.752 0.980259 8 64.962 0.885298 9 15.662 0.406714 10 14.290 0.378941 11 14.229 0.377670 12 37.358 0.712138 13 74.666 0.916996 14 70.190 0.903639 15 47.383 0.793905 16 14.464 0.382540 17 3.913 0.122291 18 34.220 0.680397 19 28.249 0.610010 20 7.085 0.210358 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.105038 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-09-06_01:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 0.9 -0.6 1.2 0.4 0.1 -0.4 -1.2 0.5 0.3 -0.4 1.2 0.6 1.4 -1.5 -0.9 0.5 -0.4 -0.9 0.1 0.4 0.3 0.2 0.1 0.1 0.7 0.2 -0.6 0.7 -0.2 -2.3 -1.3 -1.0 2.0 0.5 0.2 -0.7 0.2 1.3 -0.1 -0.6 0.0 -1.1 Chi-square with 42 degrees of freedom:32.399781 z-score=-1.047470, p-value=0.143288 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-09-06_01:31 Test no p-value 1 0.474931 2 0.131856 3 0.049759 4 0.048696 5 0.007863 6 0.363696 7 0.610114 8 0.784255 9 0.552985 10 0.573377 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.117203 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-09-06_01:31: (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 66651 0.00 66585 0.10 3 25000.00 25061 0.15 25115 0.53 4 6666.67 6621 0.31 6539 2.44 5 1388.89 1391 0.00 1474 5.22 6 238.10 237 0.01 241 0.04 7 34.72 32 0.21 37 0.15 8 4.96 6 0.22 8 1.86 p=0.01103 p=0.88887 Number of rngs required: 688568, p-value: 0.575 RESULTS OF CRAPS TEST for dh-ranFile-2016-09-06_01:31 No. of wins: Observed Expected 98110 98585.9 z-score=-2.128, pvalue=0.01666 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66544 66666.7 0.226 0.226 2 37477 37654.3 0.835 1.061 3 27021 26954.7 0.163 1.224 4 19509 19313.5 1.980 3.203 5 13880 13851.4 0.059 3.262 6 9844 9943.5 0.997 4.259 7 7090 7145.0 0.424 4.683 8 5144 5139.1 0.005 4.687 9 3772 3699.9 1.406 6.094 10 2631 2666.3 0.467 6.561 11 1945 1923.3 0.244 6.805 12 1407 1388.7 0.240 7.045 13 1038 1003.7 1.171 8.216 14 783 726.1 4.452 12.669 15 530 525.8 0.033 12.702 16 374 381.2 0.134 12.836 17 286 276.5 0.324 13.159 18 200 200.8 0.003 13.163 19 137 146.0 0.553 13.716 20 113 106.2 0.433 14.149 21 275 287.1 0.511 14.660 Chisq= 14.66 for 20 degrees of freedom, p= 0.20450 SUMMARY of craptest p-value for no. of wins: 0.016655 p-value for throws/game: 0.204497 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-09-06_01:31 No. of wins: Observed Expected 98773 98585.9 z-score= 0.837, pvalue=0.79871 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66893 66666.7 0.768 0.768 2 37698 37654.3 0.051 0.819 3 26663 26954.7 3.157 3.977 4 19209 19313.5 0.565 4.542 5 13892 13851.4 0.119 4.660 6 9903 9943.5 0.165 4.826 7 7212 7145.0 0.628 5.453 8 5139 5139.1 0.000 5.453 9 3756 3699.9 0.852 6.305 10 2721 2666.3 1.122 7.427 11 1968 1923.3 1.038 8.465 12 1343 1388.7 1.507 9.972 13 997 1003.7 0.045 10.016 14 688 726.1 2.003 12.020 15 551 525.8 1.204 13.224 16 356 381.2 1.660 14.884 17 283 276.5 0.151 15.035 18 189 200.8 0.697 15.731 19 158 146.0 0.989 16.720 20 88 106.2 3.124 19.844 21 293 287.1 0.121 19.965 Chisq= 19.96 for 20 degrees of freedom, p= 0.53987 SUMMARY of craptest p-value for no. of wins: 0.798705 p-value for throws/game: 0.539869 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0030,0.0079,0.0110,0.0137,0.0167,0.0170,0.0172,0.0214,0.0395,0.0416, 0.0487,0.0498,0.0511,0.0543,0.0559,0.0680,0.0698,0.0906,0.0981,0.1050, 0.1103,0.1111,0.1142,0.1143,0.1148,0.1171,0.1172,0.1223,0.1317,0.1319, 0.1328,0.1398,0.1433,0.1433,0.1452,0.1470,0.1523,0.1545,0.1584,0.1590, 0.1831,0.1896,0.1934,0.1986,0.2000,0.2018,0.2045,0.2079,0.2104,0.2206, 0.2244,0.2268,0.2293,0.2373,0.2378,0.2456,0.2468,0.2554,0.2609,0.2648, 0.2649,0.2679,0.2692,0.2727,0.2771,0.2785,0.2803,0.2837,0.2946,0.3024, 0.3038,0.3132,0.3180,0.3215,0.3253,0.3267,0.3270,0.3275,0.3408,0.3458, 0.3469,0.3496,0.3499,0.3574,0.3623,0.3637,0.3675,0.3707,0.3720,0.3733, 0.3740,0.3773,0.3777,0.3789,0.3812,0.3825,0.3869,0.4067,0.4069,0.4124, 0.4132,0.4150,0.4277,0.4329,0.4398,0.4433,0.4562,0.4625,0.4636,0.4749, 0.4779,0.4799,0.4799,0.4811,0.4956,0.5009,0.5109,0.5137,0.5182,0.5202, 0.5267,0.5360,0.5360,0.5366,0.5369,0.5399,0.5466,0.5489,0.5530,0.5684, 0.5711,0.5734,0.5753,0.5780,0.5843,0.5862,0.5884,0.5906,0.5957,0.5975, 0.5975,0.5988,0.5997,0.6100,0.6101,0.6124,0.6142,0.6152,0.6212,0.6214, 0.6235,0.6240,0.6396,0.6397,0.6479,0.6501,0.6573,0.6574,0.6594,0.6598, 0.6622,0.6631,0.6684,0.6804,0.6874,0.6923,0.6932,0.7008,0.7087,0.7096, 0.7119,0.7121,0.7178,0.7319,0.7326,0.7387,0.7387,0.7412,0.7474,0.7497, 0.7500,0.7567,0.7589,0.7597,0.7702,0.7758,0.7758,0.7810,0.7819,0.7825, 0.7839,0.7843,0.7866,0.7937,0.7939,0.7987,0.8000,0.8046,0.8063,0.8154, 0.8181,0.8186,0.8187,0.8249,0.8255,0.8258,0.8275,0.8288,0.8294,0.8298, 0.8345,0.8352,0.8411,0.8460,0.8499,0.8582,0.8584,0.8658,0.8673,0.8732, 0.8746,0.8821,0.8824,0.8830,0.8853,0.8873,0.8886,0.8889,0.8895,0.8942, 0.8974,0.8974,0.8997,0.9009,0.9011,0.9036,0.9050,0.9073,0.9073,0.9170, 0.9175,0.9186,0.9205,0.9269,0.9275,0.9280,0.9301,0.9341,0.9372,0.9400, 0.9498,0.9532,0.9555,0.9580,0.9640,0.9653,0.9668,0.9671,0.9682,0.9692, 0.9707,0.9749,0.9762,0.9777,0.9796,0.9803,0.9918,0.9933,0.9960, Overall p-value after applying KStest on 269 p-values = 0.009034 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.