RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-03-22_10:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.38 31.5902 0.983089 2 to 25 15.59 25.9084 0.923855 3 to 26 15.78 20.9213 0.770169 4 to 27 15.71 16.0621 0.480562 5 to 28 15.89 12.8814 0.255910 6 to 29 15.96 16.4163 0.505462 7 to 30 15.84 19.8614 0.718622 8 to 31 15.90 13.6958 0.311493 9 to 32 16.02 9.6019 0.080529 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.858966 Tough bday spacings test for dh-ranFile-2016-03-22_10:31: 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 8 33 81 96 100 78 43 34 18 7 2 (O-E)^2/E 0.1 0.4 0.8 0.0 0.1 0.0 1.6 0.6 0.7 0.0 1.0 Birthday Spacings: Sum(O-E)^2/E= 5.322, p= 0.131 RESULTS OF GCD FOR dh-ranFile-2016-03-22_10:31 Euclid's algorithm: p-value, steps to gcd: 0.013155 p-value, dist. of gcd's: 0.583711 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-03-22_10:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.249 0.626 0.494 0.575 0.642 0.165 0.301 0.953 Bits 8 to 15---> 0.746 0.898 0.675 0.178 0.585 0.074 0.247 0.647 Bits 16 to 23---> 0.184 0.571 0.958 0.927 0.574 0.038 0.442 0.614 Bits 24 to 31---> 0.834 0.827 0.199 0.596 0.796 0.085 0.663 0.821 KS test for the above 32 p values: 0.403 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-03-22_10:31, p-values for 5 runs: 0.3835, 0.2091, 0.1533, 0.8210, 0.1436 Rank test for binary matrices (31x31) for dh-ranFile-2016-03-22_10:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 238 211.4 3.342 3.342 r= 29 5182 5134.0 0.449 3.791 r= 30 22982 23103.0 0.634 4.425 r= 31 11598 11551.5 0.187 4.612 chi-square = 4.612 with df = 3; p-value = 0.797 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-03-22_10:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 218 211.4 0.205 0.205 r= 30 5143 5134.0 0.016 0.221 r= 31 23082 23103.0 0.019 0.240 r= 32 11557 11551.5 0.003 0.242 chi-square = 0.242 with df = 3; p-value = 0.030 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-03-22_10:31 b-rank test for bits 1 to 8, p=0.00301 b-rank test for bits 2 to 9, p=0.53662 b-rank test for bits 3 to 10, p=0.90605 b-rank test for bits 4 to 11, p=0.35740 b-rank test for bits 5 to 12, p=0.06609 b-rank test for bits 6 to 13, p=0.16129 b-rank test for bits 7 to 14, p=0.02124 b-rank test for bits 8 to 15, p=0.76166 b-rank test for bits 9 to 16, p=0.99078 b-rank test for bits 10 to 17, p=0.99438 b-rank test for bits 11 to 18, p=0.66036 b-rank test for bits 12 to 19, p=0.81314 b-rank test for bits 13 to 20, p=0.72071 b-rank test for bits 14 to 21, p=0.02495 b-rank test for bits 15 to 22, p=0.56044 b-rank test for bits 16 to 23, p=0.43383 b-rank test for bits 17 to 24, p=0.92678 b-rank test for bits 18 to 25, p=0.94510 b-rank test for bits 19 to 26, p=0.27140 b-rank test for bits 20 to 27, p=0.35144 b-rank test for bits 21 to 28, p=0.28958 b-rank test for bits 22 to 29, p=0.93356 b-rank test for bits 23 to 30, p=0.43517 b-rank test for bits 24 to 31, p=0.96570 b-rank test for bits 25 to 32, p=0.10443 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 = 0.165650 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-03-22_10:31 (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 142211 0.70 0.759544 2 142076 0.39 0.651516 3 142041 0.31 0.620822 4 142844 2.18 0.985512 5 141611 -0.70 0.242891 6 142006 0.23 0.589347 7 141844 -0.15 0.439341 8 141580 -0.77 0.220809 9 141755 -0.36 0.359205 10 142387 1.12 0.867800 11 142598 1.61 0.946196 12 142191 0.66 0.744765 13 142422 1.20 0.884508 14 141442 -1.09 0.137440 15 141901 -0.02 0.492236 16 142240 0.77 0.780119 17 141658 -0.59 0.278528 18 141640 -0.63 0.264584 19 142565 1.53 0.937231 20 142392 1.13 0.870284 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-03-22_10:31 Bits used No. missing words z-score p-value 23 to 32 141858 -0.1770 0.429754 22 to 31 141434 -1.6391 0.050599 21 to 30 142237 1.1299 0.870740 20 to 29 142300 1.3471 0.911032 19 to 28 141463 -1.5391 0.061894 18 to 27 141876 -0.1149 0.454250 17 to 26 141719 -0.6563 0.255812 16 to 25 141970 0.2092 0.582857 15 to 24 141543 -1.2632 0.103257 14 to 23 141754 -0.5356 0.296110 13 to 22 141736 -0.5977 0.275024 12 to 21 141939 0.1023 0.540745 11 to 20 141926 0.0575 0.522920 10 to 19 142139 0.7920 0.785810 9 to 18 141956 0.1609 0.563926 8 to 17 141813 -0.3322 0.369880 7 to 16 141958 0.1678 0.566641 6 to 15 141692 -0.7494 0.226804 5 to 14 141392 -1.7839 0.037220 4 to 13 141756 -0.5287 0.298498 3 to 12 141698 -0.7287 0.233085 2 to 11 142030 0.4161 0.661333 1 to 10 141794 -0.3977 0.345430 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-03-22_10:31 Bits used No. missing words z-score p-value 28 to 32 141709 -0.6791 0.248542 27 to 31 142362 1.5345 0.937544 26 to 30 142257 1.1785 0.880710 25 to 29 141961 0.1752 0.569520 24 to 28 142252 1.1616 0.877300 23 to 27 142012 0.3480 0.636093 22 to 26 141966 0.1921 0.576169 21 to 25 141986 0.2599 0.602529 20 to 24 141655 -0.8621 0.194306 19 to 23 142067 0.5345 0.703493 18 to 22 142308 1.3514 0.911720 17 to 21 141892 -0.0587 0.476577 16 to 20 142381 1.5989 0.945077 15 to 19 141702 -0.7028 0.241086 14 to 18 142107 0.6701 0.748593 13 to 17 142123 0.7243 0.765561 12 to 16 141482 -1.4486 0.073728 11 to 15 142031 0.4124 0.659992 10 to 14 141955 0.1548 0.561516 9 to 13 142046 0.4633 0.678421 8 to 12 141702 -0.7028 0.241086 7 to 11 142019 0.3718 0.644965 6 to 10 142478 1.9277 0.973053 5 to 9 142228 1.0802 0.859982 4 to 8 141362 -1.8554 0.031773 3 to 7 141870 -0.1333 0.446969 2 to 6 142172 0.8904 0.813376 1 to 5 141716 -0.6554 0.256119 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-03-22_10:31 Bits used No. missing words z-score p-value 31 to 32 142076 0.4917 0.688517 30 to 31 141712 -0.5821 0.280252 29 to 30 141970 0.1790 0.571018 28 to 29 142225 0.9312 0.824120 27 to 28 141832 -0.2281 0.409780 26 to 27 142284 1.1052 0.865468 25 to 26 142002 0.2734 0.607713 24 to 25 142007 0.2881 0.613370 23 to 24 141315 -1.7532 0.039785 22 to 23 142535 1.8456 0.967527 21 to 22 142478 1.6775 0.953277 20 to 21 142149 0.7070 0.760214 19 to 20 141392 -1.5260 0.063499 18 to 19 141846 -0.1868 0.425903 17 to 18 141517 -1.1573 0.123572 16 to 17 141488 -1.2429 0.106959 15 to 16 142076 0.4917 0.688517 14 to 15 141074 -2.4641 0.006868 13 to 14 142475 1.6686 0.952406 12 to 13 142990 3.1878 0.999283 11 to 12 141745 -0.4847 0.313927 10 to 11 141170 -2.1809 0.014595 9 to 10 142038 0.3796 0.647863 8 to 9 142169 0.7660 0.778158 7 to 8 142117 0.6126 0.729928 6 to 7 141484 -1.2547 0.104801 5 to 6 141547 -1.0688 0.142575 4 to 5 141816 -0.2753 0.391539 3 to 4 141394 -1.5201 0.064237 2 to 3 141935 0.0757 0.530180 1 to 2 142100 0.5624 0.713095 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-03-22_10:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2449.39 -0.716 0.237077 Test results for specific bytes for dh-ranFile-2016-03-22_10:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2583.10 1.175 0.880047 2 to 9 2541.92 0.593 0.723341 3 to 10 2459.62 -0.571 0.283968 4 to 11 2569.55 0.984 0.837327 5 to 12 2415.23 -1.199 0.115309 6 to 13 2445.07 -0.777 0.218611 7 to 14 2446.40 -0.758 0.224205 8 to 15 2557.37 0.811 0.791418 9 to 16 2631.72 1.863 0.968759 10 to 17 2466.31 -0.476 0.316864 11 to 18 2536.83 0.521 0.698750 12 to 19 2531.68 0.448 0.672949 13 to 20 2472.62 -0.387 0.349302 14 to 21 2580.96 1.145 0.873885 15 to 22 2444.48 -0.785 0.216162 16 to 23 2472.73 -0.386 0.349897 17 to 24 2549.95 0.706 0.760027 18 to 25 2598.27 1.390 0.917705 19 to 26 2551.45 0.728 0.766569 20 to 27 2509.34 0.132 0.552525 21 to 28 2373.37 -1.791 0.036657 22 to 29 2519.87 0.281 0.610642 23 to 30 2444.99 -0.778 0.218302 24 to 31 2474.72 -0.357 0.360379 25 to 32 2507.00 0.099 0.539427 CDPARK for dh-ranFile-2016-03-22_10:31: 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 3534 0.5023 0.692266 3464 -2.6941 0.003529 3556 1.5068 0.934075 3509 -0.6393 0.261324 3516 -0.3196 0.374623 3511 -0.5479 0.291865 3513 -0.4566 0.323972 3520 -0.1370 0.445521 3509 -0.6393 0.261324 3515 -0.3653 0.357445 Square side=100, avg. no. parked=3514.70 sample std.=21.82 p-value of the KSTEST for those 10 p-values: 0.204237 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-03-22_10:31 0.9350,0.8408,0.3728,0.0844,0.7045,0.9732,0.3976,0.6839,0.8978,0.7935, The KS test for those 10 p-values: 0.093851 The 3DSPHERES test for dh-ranFile-2016-03-22_10:31 sample no r^3 equiv. uni. 1 8.261 0.240702 2 44.492 0.773063 3 12.750 0.346220 4 3.076 0.097443 5 58.804 0.859160 6 91.739 0.953017 7 18.050 0.452107 8 33.674 0.674521 9 31.049 0.644761 10 3.884 0.121428 11 9.172 0.263418 12 10.374 0.292357 13 1.519 0.049382 14 2.369 0.075928 15 64.178 0.882259 16 86.932 0.944852 17 46.066 0.784661 18 43.675 0.766793 19 130.192 0.986960 20 7.220 0.213898 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.625043 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-03-22_10:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 -1.6 0.8 -0.3 0.7 -1.4 0.1 0.1 0.4 -1.1 1.1 -0.9 0.6 0.9 -0.1 -0.8 1.0 -0.8 -0.1 0.7 0.7 -0.1 -1.9 -1.2 -0.8 0.3 2.1 -1.1 -0.9 0.4 1.5 1.2 1.1 1.2 -0.5 1.7 1.0 0.2 -0.8 0.4 1.6 0.0 0.8 Chi-square with 42 degrees of freedom:40.376999 z-score=-0.177084, p-value=0.457648 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-03-22_10:31 Test no p-value 1 0.912760 2 0.753236 3 0.043565 4 0.585117 5 0.959845 6 0.127403 7 0.039688 8 0.319154 9 0.117335 10 0.025825 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.083254 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-03-22_10:31: (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 66640 0.01 66643 0.01 3 25000.00 25088 0.31 25063 0.16 4 6666.67 6666 0.00 6584 1.03 5 1388.89 1348 1.20 1404 0.16 6 238.10 221 1.23 264 2.82 7 34.72 30 0.64 36 0.05 8 4.96 6 0.22 5 0.00 p=0.27092 p=0.35343 Number of rngs required: 688299, p-value: 0.452 RESULTS OF CRAPS TEST for dh-ranFile-2016-03-22_10:31 No. of wins: Observed Expected 98790 98585.9 z-score= 0.913, pvalue=0.81939 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66926 66666.7 1.009 1.009 2 37197 37654.3 5.554 6.563 3 27084 26954.7 0.620 7.183 4 19363 19313.5 0.127 7.310 5 13920 13851.4 0.340 7.650 6 10080 9943.5 1.873 9.522 7 7139 7145.0 0.005 9.527 8 5118 5139.1 0.086 9.614 9 3720 3699.9 0.110 9.723 10 2608 2666.3 1.275 10.998 11 1903 1923.3 0.215 11.213 12 1383 1388.7 0.024 11.237 13 933 1003.7 4.982 16.219 14 704 726.1 0.675 16.894 15 538 525.8 0.281 17.175 16 360 381.2 1.174 18.349 17 300 276.5 1.990 20.339 18 218 200.8 1.468 21.807 19 157 146.0 0.831 22.638 20 87 106.2 3.476 26.115 21 262 287.1 2.197 28.311 Chisq= 28.31 for 20 degrees of freedom, p= 0.89777 SUMMARY of craptest p-value for no. of wins: 0.819389 p-value for throws/game: 0.897766 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-03-22_10:31 No. of wins: Observed Expected 98417 98585.9 z-score=-0.755, pvalue=0.22505 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66529 66666.7 0.284 0.284 2 37989 37654.3 2.975 3.259 3 26667 26954.7 3.071 6.330 4 19341 19313.5 0.039 6.370 5 13804 13851.4 0.162 6.532 6 9953 9943.5 0.009 6.541 7 7108 7145.0 0.192 6.733 8 5222 5139.1 1.338 8.071 9 3758 3699.9 0.913 8.985 10 2702 2666.3 0.478 9.463 11 1898 1923.3 0.334 9.796 12 1367 1388.7 0.340 10.137 13 993 1003.7 0.114 10.251 14 725 726.1 0.002 10.253 15 528 525.8 0.009 10.262 16 396 381.2 0.579 10.840 17 270 276.5 0.155 10.995 18 200 200.8 0.003 10.998 19 157 146.0 0.831 11.829 20 105 106.2 0.014 11.843 21 288 287.1 0.003 11.846 Chisq= 11.85 for 20 degrees of freedom, p= 0.07873 SUMMARY of craptest p-value for no. of wins: 0.225054 p-value for throws/game: 0.078727 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0030,0.0035,0.0069,0.0132,0.0146,0.0212,0.0249,0.0258,0.0295,0.0318, 0.0367,0.0372,0.0384,0.0397,0.0398,0.0436,0.0494,0.0506,0.0619,0.0635, 0.0642,0.0661,0.0737,0.0745,0.0759,0.0787,0.0805,0.0833,0.0844,0.0847, 0.0939,0.0974,0.1033,0.1044,0.1048,0.1070,0.1153,0.1173,0.1214,0.1236, 0.1274,0.1313,0.1374,0.1426,0.1436,0.1533,0.1613,0.1646,0.1657,0.1777, 0.1841,0.1943,0.1987,0.2042,0.2091,0.2139,0.2162,0.2183,0.2186,0.2208, 0.2242,0.2251,0.2268,0.2331,0.2371,0.2407,0.2411,0.2411,0.2429,0.2467, 0.2485,0.2494,0.2558,0.2559,0.2561,0.2613,0.2613,0.2634,0.2646,0.2709, 0.2714,0.2750,0.2785,0.2803,0.2840,0.2896,0.2919,0.2924,0.2961,0.2985, 0.3009,0.3115,0.3139,0.3169,0.3192,0.3240,0.3454,0.3462,0.3493,0.3499, 0.3514,0.3534,0.3574,0.3574,0.3592,0.3604,0.3699,0.3728,0.3746,0.3835, 0.3915,0.3976,0.4032,0.4098,0.4259,0.4298,0.4338,0.4352,0.4393,0.4421, 0.4455,0.4470,0.4521,0.4524,0.4542,0.4576,0.4766,0.4806,0.4922,0.4940, 0.5055,0.5229,0.5302,0.5366,0.5394,0.5407,0.5525,0.5604,0.5615,0.5639, 0.5666,0.5695,0.5708,0.5710,0.5740,0.5752,0.5762,0.5829,0.5837,0.5850, 0.5851,0.5893,0.5962,0.6025,0.6077,0.6106,0.6134,0.6141,0.6208,0.6250, 0.6261,0.6361,0.6415,0.6448,0.6450,0.6466,0.6479,0.6515,0.6600,0.6604, 0.6613,0.6632,0.6729,0.6745,0.6749,0.6784,0.6839,0.6885,0.6885,0.6923, 0.6988,0.7035,0.7045,0.7131,0.7186,0.7207,0.7233,0.7299,0.7448,0.7464, 0.7486,0.7532,0.7595,0.7600,0.7602,0.7617,0.7656,0.7666,0.7668,0.7702, 0.7731,0.7782,0.7801,0.7847,0.7858,0.7914,0.7935,0.7958,0.7975,0.8131, 0.8134,0.8194,0.8210,0.8213,0.8241,0.8270,0.8337,0.8373,0.8408,0.8590, 0.8592,0.8600,0.8655,0.8678,0.8703,0.8707,0.8739,0.8773,0.8800,0.8807, 0.8823,0.8845,0.8978,0.8978,0.8983,0.9061,0.9110,0.9117,0.9128,0.9177, 0.9239,0.9267,0.9268,0.9336,0.9341,0.9350,0.9372,0.9375,0.9449,0.9451, 0.9451,0.9462,0.9524,0.9530,0.9530,0.9533,0.9579,0.9598,0.9657,0.9675, 0.9688,0.9731,0.9732,0.9831,0.9855,0.9870,0.9908,0.9944,0.9993, Overall p-value after applying KStest on 269 p-values = 0.339806 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.