RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-07-02_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 15.24 30.1028 0.974387 2 to 25 15.51 22.3907 0.829845 3 to 26 15.54 15.5449 0.443706 4 to 27 15.92 9.5363 0.078078 5 to 28 16.07 16.4531 0.508030 6 to 29 15.91 12.3459 0.221249 7 to 30 15.87 26.3498 0.931681 8 to 31 15.82 23.3656 0.862277 9 to 32 15.45 21.3452 0.788770 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.256179 Tough bday spacings test for dh-ranFile-2015-07-02_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 7 39 68 97 86 97 45 40 10 10 1 (O-E)^2/E 0.5 0.2 0.4 0.0 1.4 4.5 1.0 3.5 1.6 1.7 2.3 Birthday Spacings: Sum(O-E)^2/E= 17.119, p= 0.928 RESULTS OF GCD FOR dh-ranFile-2015-07-02_14:31 Euclid's algorithm: p-value, steps to gcd: 0.821994 p-value, dist. of gcd's: 0.973430 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-07-02_14:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.938 0.029 0.836 0.453 0.821 0.623 0.314 0.460 Bits 8 to 15---> 0.284 0.837 0.620 0.124 0.133 0.562 0.614 0.736 Bits 16 to 23---> 0.399 0.951 0.164 0.239 0.820 0.487 0.468 0.388 Bits 24 to 31---> 0.346 0.308 0.210 0.760 0.325 0.818 0.099 0.256 KS test for the above 32 p values: 0.176 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-07-02_14:31, p-values for 5 runs: 0.8761, 0.8889, 0.8237, 0.7045, 0.4057 Rank test for binary matrices (31x31) for dh-ranFile-2015-07-02_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 199 211.4 0.729 0.729 r= 29 5196 5134.0 0.748 1.478 r= 30 23054 23103.0 0.104 1.582 r= 31 11551 11551.5 0.000 1.582 chi-square = 1.582 with df = 3; p-value = 0.337 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-07-02_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 213 211.4 0.012 0.012 r= 30 5167 5134.0 0.212 0.224 r= 31 23124 23103.0 0.019 0.243 r= 32 11496 11551.5 0.267 0.510 chi-square = 0.510 with df = 3; p-value = 0.083 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-07-02_14:31 b-rank test for bits 1 to 8, p=0.48616 b-rank test for bits 2 to 9, p=0.14329 b-rank test for bits 3 to 10, p=0.07994 b-rank test for bits 4 to 11, p=0.18069 b-rank test for bits 5 to 12, p=0.43025 b-rank test for bits 6 to 13, p=0.60692 b-rank test for bits 7 to 14, p=0.78562 b-rank test for bits 8 to 15, p=0.10579 b-rank test for bits 9 to 16, p=0.21875 b-rank test for bits 10 to 17, p=0.18996 b-rank test for bits 11 to 18, p=0.18803 b-rank test for bits 12 to 19, p=0.78400 b-rank test for bits 13 to 20, p=0.79803 b-rank test for bits 14 to 21, p=0.51698 b-rank test for bits 15 to 22, p=0.13615 b-rank test for bits 16 to 23, p=0.49869 b-rank test for bits 17 to 24, p=0.45842 b-rank test for bits 18 to 25, p=0.22470 b-rank test for bits 19 to 26, p=0.48526 b-rank test for bits 20 to 27, p=0.20859 b-rank test for bits 21 to 28, p=0.48122 b-rank test for bits 22 to 29, p=0.15269 b-rank test for bits 23 to 30, p=0.01754 b-rank test for bits 24 to 31, p=0.02430 b-rank test for bits 25 to 32, p=0.92786 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 = 0.024263 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-07-02_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 142102 0.45 0.673704 2 141727 -0.43 0.335052 3 141779 -0.30 0.380370 4 142407 1.16 0.877541 5 142041 0.31 0.620822 6 141619 -0.68 0.248778 7 142044 0.31 0.623486 8 141709 -0.47 0.319871 9 142370 1.08 0.859111 10 141662 -0.58 0.281675 11 141636 -0.64 0.261535 12 141910 0.00 0.500625 13 142228 0.74 0.771730 14 142015 0.25 0.597504 15 141023 -2.07 0.019186 16 141343 -1.32 0.092884 17 141725 -0.43 0.333351 18 142013 0.24 0.595695 19 141569 -0.80 0.213259 20 141198 -1.66 0.048258 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-07-02_14:31 Bits used No. missing words z-score p-value 23 to 32 142335 1.4678 0.928924 22 to 31 141746 -0.5632 0.286647 21 to 30 141796 -0.3908 0.347975 20 to 29 142001 0.3161 0.624038 19 to 28 141943 0.1161 0.546215 18 to 27 142271 1.2471 0.893827 17 to 26 141855 -0.1873 0.425695 16 to 25 141682 -0.7839 0.216550 15 to 24 141644 -0.9149 0.180114 14 to 23 141513 -1.3667 0.085867 13 to 22 142517 2.0954 0.981933 12 to 21 142094 0.6368 0.737870 11 to 20 141647 -0.9046 0.182842 10 to 19 141535 -1.2908 0.098388 9 to 18 142072 0.5609 0.712578 8 to 17 141733 -0.6080 0.271582 7 to 16 141551 -1.2356 0.108300 6 to 15 141897 -0.0425 0.483043 5 to 14 142247 1.1644 0.877865 4 to 13 141848 -0.2115 0.416255 3 to 12 142274 1.2575 0.895711 2 to 11 142326 1.4368 0.924612 1 to 10 141479 -1.4839 0.068918 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-07-02_14:31 Bits used No. missing words z-score p-value 28 to 32 142070 0.5446 0.707001 27 to 31 142339 1.4565 0.927374 26 to 30 141997 0.2972 0.616838 25 to 29 142211 1.0226 0.846754 24 to 28 142248 1.1480 0.874523 23 to 27 141792 -0.3977 0.345415 22 to 26 142029 0.4057 0.657504 21 to 25 141874 -0.1198 0.452336 20 to 24 142059 0.5074 0.694048 19 to 23 141961 0.1752 0.569520 18 to 22 142185 0.9345 0.824970 17 to 21 142073 0.5548 0.710489 16 to 20 141665 -0.8282 0.203768 15 to 19 141784 -0.4248 0.335474 14 to 18 141688 -0.7503 0.226546 13 to 17 142065 0.5277 0.701145 12 to 16 141299 -2.0689 0.019277 11 to 15 141943 0.1141 0.545435 10 to 14 141849 -0.2045 0.418978 9 to 13 141916 0.0226 0.509019 8 to 12 141855 -0.1842 0.426940 7 to 11 141982 0.2463 0.597290 6 to 10 141873 -0.1232 0.450993 5 to 9 141551 -1.2147 0.112244 4 to 8 141992 0.2802 0.610352 3 to 7 141922 0.0429 0.517129 2 to 6 142024 0.3887 0.651255 1 to 5 141805 -0.3537 0.361797 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-07-02_14:31 Bits used No. missing words z-score p-value 31 to 32 141626 -0.8358 0.201639 30 to 31 142329 1.2380 0.892135 29 to 30 141613 -0.8741 0.191024 28 to 29 141720 -0.5585 0.288253 27 to 28 141742 -0.4936 0.310795 26 to 27 142196 0.8456 0.801122 25 to 26 141672 -0.7001 0.241936 24 to 25 141583 -0.9626 0.167868 23 to 24 142219 0.9135 0.819505 22 to 23 142088 0.5271 0.700921 21 to 22 141661 -0.7325 0.231921 20 to 21 142404 1.4592 0.927745 19 to 20 141839 -0.2075 0.417824 18 to 19 142376 1.3766 0.915683 17 to 18 141786 -0.3638 0.358002 16 to 17 141666 -0.7178 0.236444 15 to 16 142371 1.3619 0.913379 14 to 15 142072 0.4799 0.684334 13 to 14 141573 -0.9921 0.160569 12 to 13 141565 -1.0157 0.154881 11 to 12 141860 -0.1455 0.442152 10 to 11 141990 0.2380 0.594046 9 to 10 141990 0.2380 0.594046 8 to 9 141999 0.2645 0.604308 7 to 8 141964 0.1613 0.564059 6 to 7 141413 -1.4641 0.071583 5 to 6 142298 1.1465 0.874210 4 to 5 141596 -0.9243 0.177671 3 to 4 142753 2.4887 0.993589 2 to 3 142397 1.4386 0.924862 1 to 2 141994 0.2498 0.598615 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-07-02_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2528.98 0.410 0.659040 Test results for specific bytes for dh-ranFile-2015-07-02_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2410.12 -1.271 0.101847 2 to 9 2517.09 0.242 0.595509 3 to 10 2473.16 -0.380 0.352153 4 to 11 2359.23 -1.991 0.023253 5 to 12 2554.42 0.770 0.779216 6 to 13 2451.49 -0.686 0.246336 7 to 14 2555.18 0.780 0.782432 8 to 15 2429.43 -0.998 0.159123 9 to 16 2486.91 -0.185 0.426584 10 to 17 2455.76 -0.626 0.265771 11 to 18 2543.24 0.611 0.729554 12 to 19 2518.10 0.256 0.601021 13 to 20 2514.84 0.210 0.583089 14 to 21 2520.71 0.293 0.615169 15 to 22 2519.57 0.277 0.609044 16 to 23 2512.25 0.173 0.568760 17 to 24 2504.20 0.059 0.523707 18 to 25 2431.04 -0.975 0.164728 19 to 26 2457.01 -0.608 0.271591 20 to 27 2563.71 0.901 0.816220 21 to 28 2497.76 -0.032 0.487361 22 to 29 2424.71 -1.065 0.143482 23 to 30 2587.11 1.232 0.891016 24 to 31 2425.22 -1.058 0.145134 25 to 32 2568.24 0.965 0.832753 CDPARK for dh-ranFile-2015-07-02_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 3548 1.1416 0.873180 3518 -0.2283 0.409702 3531 0.3653 0.642555 3518 -0.2283 0.409702 3531 0.3653 0.642555 3458 -2.9680 0.001499 3521 -0.0913 0.463617 3502 -0.9589 0.168804 3516 -0.3196 0.374623 3551 1.2785 0.899470 Square side=100, avg. no. parked=3519.40 sample std.=24.85 p-value of the KSTEST for those 10 p-values: 0.697125 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-07-02_14:31 0.6773,0.7668,0.5789,0.6467,0.7205,0.5315,0.8446,0.5650,0.4388,0.3551, The KS test for those 10 p-values: 0.121108 The 3DSPHERES test for dh-ranFile-2015-07-02_14:31 sample no r^3 equiv. uni. 1 38.250 0.720565 2 47.709 0.796136 3 11.663 0.322106 4 8.229 0.239906 5 26.177 0.582117 6 54.382 0.836791 7 24.341 0.555748 8 3.396 0.107034 9 6.221 0.187269 10 9.046 0.260316 11 6.514 0.195166 12 12.904 0.349576 13 107.482 0.972200 14 62.881 0.877057 15 6.866 0.204572 16 6.590 0.197207 17 27.800 0.604132 18 10.139 0.286787 19 60.324 0.866118 20 13.078 0.353337 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.607395 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-07-02_14:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 -1.2 -1.3 0.5 -0.2 2.0 0.4 -0.1 -0.2 1.4 2.5 -0.5 0.1 -1.2 -1.2 0.7 -0.4 1.2 -1.9 -0.6 -0.2 0.2 0.2 0.6 0.4 1.2 -0.7 0.1 0.8 -0.4 0.8 -1.0 -0.2 -1.0 -0.1 -1.2 -0.7 -0.7 -1.6 -1.3 0.9 -1.0 2.7 Chi-square with 42 degrees of freedom:47.991085 z-score=0.653681, p-value=0.757083 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-07-02_14:31 Test no p-value 1 0.720216 2 0.686569 3 0.121231 4 0.182660 5 0.575441 6 0.131833 7 0.218991 8 0.530956 9 0.190794 10 0.359510 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.200585 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-07-02_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 66627 0.02 66758 0.13 3 25000.00 25087 0.30 24861 0.77 4 6666.67 6634 0.16 6731 0.62 5 1388.89 1392 0.01 1379 0.07 6 238.10 224 0.83 234 0.07 7 34.72 29 0.94 34 0.01 8 4.96 6 0.22 2 1.77 p=0.13022 p=0.24819 Number of rngs required: 687707, p-value: 0.211 RESULTS OF CRAPS TEST for dh-ranFile-2015-07-02_14:31 No. of wins: Observed Expected 98278 98585.9 z-score=-1.377, pvalue=0.08427 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66789 66666.7 0.224 0.224 2 37644 37654.3 0.003 0.227 3 27011 26954.7 0.117 0.345 4 19323 19313.5 0.005 0.349 5 13708 13851.4 1.485 1.834 6 9915 9943.5 0.082 1.916 7 7019 7145.0 2.223 4.139 8 5216 5139.1 1.152 5.291 9 3788 3699.9 2.099 7.390 10 2705 2666.3 0.562 7.952 11 1901 1923.3 0.259 8.211 12 1364 1388.7 0.441 8.652 13 1013 1003.7 0.086 8.738 14 727 726.1 0.001 8.739 15 518 525.8 0.117 8.856 16 365 381.2 0.684 9.540 17 256 276.5 1.526 11.066 18 211 200.8 0.515 11.581 19 155 146.0 0.557 12.137 20 117 106.2 1.095 13.232 21 255 287.1 3.592 16.824 Chisq= 16.82 for 20 degrees of freedom, p= 0.33566 SUMMARY of craptest p-value for no. of wins: 0.084268 p-value for throws/game: 0.335660 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-07-02_14:31 No. of wins: Observed Expected 98168 98585.9 z-score=-1.869, pvalue=0.03082 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66575 66666.7 0.126 0.126 2 37586 37654.3 0.124 0.250 3 26958 26954.7 0.000 0.250 4 19432 19313.5 0.728 0.978 5 13782 13851.4 0.348 1.326 6 9930 9943.5 0.018 1.344 7 7181 7145.0 0.181 1.525 8 5113 5139.1 0.132 1.658 9 3694 3699.9 0.009 1.667 10 2715 2666.3 0.890 2.557 11 1918 1923.3 0.015 2.571 12 1363 1388.7 0.477 3.048 13 1045 1003.7 1.698 4.747 14 756 726.1 1.228 5.974 15 519 525.8 0.089 6.063 16 397 381.2 0.659 6.722 17 284 276.5 0.201 6.924 18 192 200.8 0.388 7.312 19 156 146.0 0.687 7.999 20 105 106.2 0.014 8.013 21 299 287.1 0.492 8.505 Chisq= 8.50 for 20 degrees of freedom, p= 0.01204 SUMMARY of craptest p-value for no. of wins: 0.030818 p-value for throws/game: 0.012036 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0015,0.0120,0.0175,0.0192,0.0193,0.0233,0.0243,0.0243,0.0289,0.0308, 0.0483,0.0689,0.0716,0.0781,0.0799,0.0832,0.0843,0.0859,0.0929,0.0984, 0.0986,0.1018,0.1058,0.1070,0.1083,0.1122,0.1211,0.1212,0.1243,0.1302, 0.1318,0.1328,0.1361,0.1433,0.1435,0.1451,0.1527,0.1549,0.1591,0.1606, 0.1641,0.1647,0.1679,0.1688,0.1762,0.1777,0.1801,0.1807,0.1827,0.1828, 0.1873,0.1880,0.1900,0.1908,0.1910,0.1952,0.1972,0.2006,0.2016,0.2038, 0.2046,0.2086,0.2101,0.2106,0.2133,0.2166,0.2187,0.2190,0.2212,0.2247, 0.2265,0.2319,0.2364,0.2391,0.2399,0.2419,0.2463,0.2482,0.2488,0.2562, 0.2563,0.2603,0.2615,0.2658,0.2716,0.2716,0.2817,0.2837,0.2866,0.2868, 0.2883,0.3077,0.3108,0.3138,0.3199,0.3221,0.3253,0.3334,0.3351,0.3355, 0.3357,0.3365,0.3454,0.3464,0.3480,0.3496,0.3522,0.3533,0.3551,0.3580, 0.3595,0.3618,0.3746,0.3804,0.3880,0.3991,0.4057,0.4097,0.4097,0.4163, 0.4178,0.4190,0.4257,0.4266,0.4269,0.4302,0.4388,0.4422,0.4437,0.4510, 0.4523,0.4526,0.4584,0.4598,0.4636,0.4681,0.4812,0.4830,0.4853,0.4862, 0.4871,0.4874,0.4987,0.5006,0.5080,0.5090,0.5170,0.5171,0.5237,0.5310, 0.5315,0.5454,0.5462,0.5557,0.5618,0.5641,0.5650,0.5688,0.5695,0.5754, 0.5789,0.5821,0.5831,0.5940,0.5940,0.5955,0.5957,0.5973,0.5975,0.5986, 0.6010,0.6041,0.6043,0.6069,0.6074,0.6090,0.6104,0.6137,0.6152,0.6168, 0.6199,0.6208,0.6227,0.6235,0.6240,0.6426,0.6426,0.6467,0.6513,0.6575, 0.6590,0.6737,0.6773,0.6843,0.6866,0.6940,0.6971,0.7009,0.7011,0.7045, 0.7070,0.7105,0.7126,0.7202,0.7205,0.7206,0.7296,0.7363,0.7379,0.7571, 0.7596,0.7668,0.7717,0.7792,0.7824,0.7840,0.7856,0.7888,0.7961,0.7980, 0.8011,0.8162,0.8179,0.8195,0.8202,0.8210,0.8220,0.8237,0.8250,0.8298, 0.8328,0.8362,0.8368,0.8373,0.8446,0.8468,0.8591,0.8623,0.8661,0.8732, 0.8742,0.8745,0.8761,0.8771,0.8775,0.8779,0.8889,0.8910,0.8921,0.8938, 0.8957,0.8995,0.9134,0.9157,0.9246,0.9249,0.9274,0.9277,0.9279,0.9282, 0.9289,0.9317,0.9379,0.9505,0.9722,0.9734,0.9744,0.9819,0.9936, Overall p-value after applying KStest on 269 p-values = 0.162965 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.