RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-01-06_20:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.59 13.6941 0.311376 2 to 25 15.84 12.4433 0.227415 3 to 26 15.89 14.9143 0.398346 4 to 27 15.94 10.1833 0.104253 5 to 28 15.67 16.7257 0.526905 6 to 29 15.78 18.0795 0.616156 7 to 30 15.74 14.3743 0.359551 8 to 31 15.53 14.5925 0.375191 9 to 32 15.73 15.2751 0.424325 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.124070 Tough bday spacings test for dh-ranFile-2017-01-06_20:31: 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 16 36 72 102 87 90 45 33 13 3 3 (O-E)^2/E 5.1 0.0 0.0 0.2 1.2 1.8 1.0 0.4 0.2 2.0 0.3 Birthday Spacings: Sum(O-E)^2/E= 12.113, p= 0.722 RESULTS OF GCD FOR dh-ranFile-2017-01-06_20:31 Euclid's algorithm: p-value, steps to gcd: 0.792400 p-value, dist. of gcd's: 0.399936 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-01-06_20:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.032 0.255 0.042 0.579 0.987 0.284 0.642 0.178 Bits 8 to 15---> 0.606 0.320 0.070 0.230 0.969 0.160 0.090 0.805 Bits 16 to 23---> 0.611 0.823 0.564 0.235 0.510 0.042 0.316 0.855 Bits 24 to 31---> 0.953 0.272 0.684 0.600 0.457 0.619 0.322 0.349 KS test for the above 32 p values: 0.468 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-01-06_20:31, p-values for 5 runs: 0.5517, 0.4162, 0.5057, 0.7603, 0.7426 Rank test for binary matrices (31x31) for dh-ranFile-2017-01-06_20:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 193 211.4 1.605 1.605 r= 29 5152 5134.0 0.063 1.668 r= 30 22928 23103.0 1.326 2.994 r= 31 11727 11551.5 2.666 5.659 chi-square = 5.659 with df = 3; p-value = 0.871 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2017-01-06_20:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 201 211.4 0.513 0.513 r= 30 5164 5134.0 0.175 0.689 r= 31 23167 23103.0 0.177 0.866 r= 32 11468 11551.5 0.604 1.469 chi-square = 1.469 with df = 3; p-value = 0.311 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2017-01-06_20:31 b-rank test for bits 1 to 8, p=0.71502 b-rank test for bits 2 to 9, p=0.69228 b-rank test for bits 3 to 10, p=0.62410 b-rank test for bits 4 to 11, p=0.39982 b-rank test for bits 5 to 12, p=0.22666 b-rank test for bits 6 to 13, p=0.68219 b-rank test for bits 7 to 14, p=0.33820 b-rank test for bits 8 to 15, p=0.53179 b-rank test for bits 9 to 16, p=0.88097 b-rank test for bits 10 to 17, p=0.48556 b-rank test for bits 11 to 18, p=0.69459 b-rank test for bits 12 to 19, p=0.79178 b-rank test for bits 13 to 20, p=0.75025 b-rank test for bits 14 to 21, p=0.88943 b-rank test for bits 15 to 22, p=0.59287 b-rank test for bits 16 to 23, p=0.57204 b-rank test for bits 17 to 24, p=0.87961 b-rank test for bits 18 to 25, p=0.76383 b-rank test for bits 19 to 26, p=0.14809 b-rank test for bits 20 to 27, p=0.59099 b-rank test for bits 21 to 28, p=0.17176 b-rank test for bits 22 to 29, p=0.34269 b-rank test for bits 23 to 30, p=0.33665 b-rank test for bits 24 to 31, p=0.24543 b-rank test for bits 25 to 32, p=0.00757 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 = 0.478475 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-01-06_20:31 (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 141137 -1.80 0.035576 2 141918 0.02 0.508081 3 141594 -0.74 0.230637 4 142039 0.30 0.619043 5 141596 -0.73 0.232060 6 142231 0.75 0.773844 7 141773 -0.32 0.375042 8 142170 0.61 0.728752 9 141812 -0.23 0.410054 10 141924 0.03 0.513671 11 141702 -0.48 0.314045 12 142477 1.33 0.907635 13 141122 -1.84 0.032917 14 141766 -0.33 0.368857 15 142771 2.01 0.977956 16 141559 -0.82 0.206528 17 141619 -0.68 0.248778 18 141792 -0.27 0.391990 19 142102 0.45 0.673704 20 142466 1.30 0.903308 ---------------------------------------------------------------- OPSO test for dh-ranFile-2017-01-06_20:31 Bits used No. missing words z-score p-value 23 to 32 141977 0.2333 0.592253 22 to 31 142136 0.7816 0.782781 21 to 30 142680 2.6575 0.996064 20 to 29 141815 -0.3253 0.372486 19 to 28 142252 1.1816 0.881322 18 to 27 141466 -1.5287 0.063166 17 to 26 141936 0.0920 0.536637 16 to 25 141844 -0.2253 0.410882 15 to 24 141724 -0.6391 0.261389 14 to 23 141902 -0.0253 0.489918 13 to 22 142021 0.3851 0.649907 12 to 21 142003 0.3230 0.626652 11 to 20 141686 -0.7701 0.220619 10 to 19 141487 -1.4563 0.072653 9 to 18 141257 -2.2494 0.012243 8 to 17 141895 -0.0494 0.480295 7 to 16 142024 0.3954 0.653731 6 to 15 141691 -0.7529 0.225766 5 to 14 141934 0.0851 0.533897 4 to 13 141514 -1.3632 0.086409 3 to 12 141437 -1.6287 0.051686 2 to 11 141373 -1.8494 0.032199 1 to 10 142060 0.5196 0.698312 ----------------------------------------------------------------- OQSO test for dh-ranFile-2017-01-06_20:31 Bits used No. missing words z-score p-value 28 to 32 141698 -0.7164 0.236881 27 to 31 141984 0.2531 0.599912 26 to 30 141132 -2.6350 0.004207 25 to 29 141863 -0.1571 0.437602 24 to 28 142100 0.6463 0.740970 23 to 27 141423 -1.6486 0.049617 22 to 26 142105 0.6633 0.746427 21 to 25 141599 -1.0520 0.146408 20 to 24 141874 -0.1198 0.452336 19 to 23 142438 1.7921 0.963442 18 to 22 141822 -0.2960 0.383602 17 to 21 141515 -1.3367 0.090658 16 to 20 142104 0.6599 0.745341 15 to 19 141936 0.0904 0.536018 14 to 18 141976 0.2260 0.589399 13 to 17 142117 0.7040 0.759273 12 to 16 141356 -1.8757 0.030349 11 to 15 142033 0.4192 0.662473 10 to 14 141992 0.2802 0.610352 9 to 13 141986 0.2599 0.602529 8 to 12 141709 -0.6791 0.248542 7 to 11 142184 0.9311 0.824095 6 to 10 142195 0.9684 0.833571 5 to 9 142417 1.7209 0.957367 4 to 8 141924 0.0497 0.519831 3 to 7 142197 0.9752 0.835258 2 to 6 141339 -1.9333 0.026598 1 to 5 142197 0.9752 0.835258 ----------------------------------------------------------------- DNA test for dh-ranFile-2017-01-06_20:31 Bits used No. missing words z-score p-value 31 to 32 141574 -0.9892 0.161289 30 to 31 141941 0.0934 0.537216 29 to 30 142267 1.0551 0.854304 28 to 29 141717 -0.5673 0.285240 27 to 28 141983 0.2173 0.586019 26 to 27 142929 3.0079 0.998685 25 to 26 142146 0.6981 0.757456 24 to 25 142308 1.1760 0.880206 23 to 24 141743 -0.4906 0.311837 22 to 23 141928 0.0551 0.521960 21 to 22 141799 -0.3255 0.372418 20 to 21 142442 1.5713 0.941943 19 to 20 141153 -2.2311 0.012839 18 to 19 141929 0.0580 0.523135 17 to 18 141640 -0.7945 0.213457 16 to 17 142052 0.4209 0.663070 15 to 16 142362 1.3353 0.909113 14 to 15 141650 -0.7650 0.222140 13 to 14 141606 -0.8948 0.185453 12 to 13 141116 -2.3402 0.009637 11 to 12 141973 0.1878 0.574490 10 to 11 142101 0.5654 0.714099 9 to 10 141274 -1.8741 0.030456 8 to 9 142398 1.4415 0.925279 7 to 8 142011 0.2999 0.617878 6 to 7 141992 0.2439 0.596332 5 to 6 141362 -1.6145 0.053205 4 to 5 141720 -0.5585 0.288253 3 to 4 142087 0.5241 0.699896 2 to 3 142206 0.8751 0.809249 1 to 2 141770 -0.4110 0.340535 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2017-01-06_20:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2595.03 1.344 0.910516 Test results for specific bytes for dh-ranFile-2017-01-06_20:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2638.47 1.958 0.974900 2 to 9 2553.56 0.757 0.775611 3 to 10 2524.98 0.353 0.638072 4 to 11 2430.86 -0.978 0.164096 5 to 12 2419.88 -1.133 0.128603 6 to 13 2506.74 0.095 0.537977 7 to 14 2470.48 -0.417 0.338180 8 to 15 2439.12 -0.861 0.194613 9 to 16 2404.22 -1.355 0.087786 10 to 17 2467.13 -0.465 0.321027 11 to 18 2502.92 0.041 0.516472 12 to 19 2480.84 -0.271 0.393214 13 to 20 2533.74 0.477 0.683381 14 to 21 2544.47 0.629 0.735316 15 to 22 2557.37 0.811 0.791419 16 to 23 2465.19 -0.492 0.311234 17 to 24 2548.88 0.691 0.755307 18 to 25 2558.84 0.832 0.797346 19 to 26 2383.66 -1.645 0.049955 20 to 27 2414.39 -1.211 0.113011 21 to 28 2546.92 0.664 0.746517 22 to 29 2603.84 1.469 0.929017 23 to 30 2594.88 1.342 0.910166 24 to 31 2486.26 -0.194 0.422964 25 to 32 2585.41 1.208 0.886450 CDPARK for dh-ranFile-2017-01-06_20:31: 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 3515 -0.3653 0.357445 3549 1.1872 0.882429 3523 0.0000 0.500000 3514 -0.4110 0.340551 3508 -0.6849 0.246694 3538 0.6849 0.753306 3515 -0.3653 0.357445 3500 -1.0502 0.146807 3522 -0.0457 0.481790 3522 -0.0457 0.481790 Square side=100, avg. no. parked=3520.60 sample std.=13.45 p-value of the KSTEST for those 10 p-values: 0.474119 Results for the MINIMUM DISTANCE test for dh-ranFile-2017-01-06_20:31 0.5484,0.4635,0.2662,0.3697,0.3538,0.2651,0.5844,0.5916,0.2618,0.6713, The KS test for those 10 p-values: 0.182453 The 3DSPHERES test for dh-ranFile-2017-01-06_20:31 sample no r^3 equiv. uni. 1 61.205 0.869991 2 1.743 0.056435 3 80.576 0.931837 4 15.681 0.407083 5 50.935 0.816919 6 6.322 0.190014 7 23.496 0.543055 8 33.536 0.673026 9 5.867 0.177626 10 1.633 0.052981 11 39.427 0.731324 12 34.261 0.680834 13 67.423 0.894329 14 4.161 0.129501 15 5.056 0.155107 16 114.536 0.978025 17 3.978 0.124175 18 29.146 0.621492 19 7.262 0.215004 20 67.844 0.895802 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.551049 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-01-06_20:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 0.1 2.0 -0.5 0.6 -1.0 0.7 0.3 0.2 -2.0 -0.1 -0.8 0.4 -0.8 2.0 -1.2 -1.0 0.1 1.7 1.2 -0.6 1.3 -0.3 -1.3 -1.3 0.4 0.4 0.3 0.0 0.9 -0.9 0.1 -1.1 0.3 0.1 -0.3 1.2 -1.3 0.5 -0.1 0.1 -1.0 -0.1 Chi-square with 42 degrees of freedom:36.650201 z-score=-0.583711, p-value=0.295670 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2017-01-06_20:31 Test no p-value 1 0.249688 2 0.647484 3 0.064755 4 0.267439 5 0.335463 6 0.327626 7 0.769114 8 0.211030 9 0.153033 10 0.113724 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.055457 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-01-06_20:31: (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 66740 0.08 66848 0.49 3 25000.00 25050 0.10 24744 2.62 4 6666.67 6590 0.88 6713 0.32 5 1388.89 1324 3.03 1380 0.06 6 238.10 257 1.50 273 5.12 7 34.72 29 0.94 39 0.53 8 4.96 9 3.29 2 1.77 p=0.86792 p=0.90863 Number of rngs required: 687563, p-value: 0.165 RESULTS OF CRAPS TEST for dh-ranFile-2017-01-06_20:31 No. of wins: Observed Expected 98610 98585.9 z-score= 0.108, pvalue=0.54299 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66690 66666.7 0.008 0.008 2 37349 37654.3 2.476 2.484 3 27245 26954.7 3.126 5.610 4 19252 19313.5 0.196 5.805 5 13761 13851.4 0.590 6.396 6 10092 9943.5 2.216 8.612 7 7151 7145.0 0.005 8.617 8 5136 5139.1 0.002 8.619 9 3671 3699.9 0.225 8.844 10 2654 2666.3 0.057 8.901 11 1954 1923.3 0.489 9.390 12 1380 1388.7 0.055 9.445 13 975 1003.7 0.822 10.266 14 736 726.1 0.134 10.400 15 567 525.8 3.222 13.623 16 378 381.2 0.026 13.649 17 284 276.5 0.201 13.850 18 198 200.8 0.040 13.890 19 145 146.0 0.007 13.896 20 96 106.2 0.982 14.879 21 286 287.1 0.004 14.883 Chisq= 14.88 for 20 degrees of freedom, p= 0.21695 SUMMARY of craptest p-value for no. of wins: 0.542992 p-value for throws/game: 0.216952 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2017-01-06_20:31 No. of wins: Observed Expected 98711 98585.9 z-score= 0.560, pvalue=0.71216 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66736 66666.7 0.072 0.072 2 37528 37654.3 0.424 0.496 3 27018 26954.7 0.148 0.644 4 19123 19313.5 1.878 2.523 5 13887 13851.4 0.091 2.614 6 9902 9943.5 0.174 2.788 7 7264 7145.0 1.981 4.769 8 5261 5139.1 2.893 7.662 9 3644 3699.9 0.844 8.505 10 2670 2666.3 0.005 8.510 11 1866 1923.3 1.709 10.219 12 1430 1388.7 1.226 11.445 13 1014 1003.7 0.105 11.550 14 757 726.1 1.311 12.862 15 506 525.8 0.748 13.610 16 390 381.2 0.205 13.815 17 292 276.5 0.864 14.680 18 209 200.8 0.332 15.012 19 132 146.0 1.340 16.352 20 97 106.2 0.800 17.151 21 274 287.1 0.599 17.750 Chisq= 17.75 for 20 degrees of freedom, p= 0.39614 SUMMARY of craptest p-value for no. of wins: 0.712160 p-value for throws/game: 0.396141 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0042,0.0076,0.0096,0.0122,0.0128,0.0266,0.0303,0.0305,0.0321,0.0322, 0.0329,0.0356,0.0422,0.0424,0.0496,0.0500,0.0517,0.0530,0.0532,0.0555, 0.0564,0.0632,0.0648,0.0702,0.0727,0.0864,0.0878,0.0896,0.0907,0.1043, 0.1130,0.1137,0.1241,0.1242,0.1286,0.1295,0.1464,0.1468,0.1481,0.1530, 0.1551,0.1599,0.1613,0.1641,0.1653,0.1718,0.1776,0.1777,0.1825,0.1855, 0.1900,0.1946,0.2065,0.2110,0.2135,0.2150,0.2170,0.2206,0.2221,0.2258, 0.2267,0.2274,0.2301,0.2306,0.2321,0.2348,0.2369,0.2454,0.2467,0.2485, 0.2488,0.2497,0.2555,0.2614,0.2618,0.2651,0.2662,0.2674,0.2720,0.2840, 0.2852,0.2883,0.2957,0.3107,0.3112,0.3114,0.3118,0.3140,0.3155,0.3197, 0.3210,0.3223,0.3276,0.3355,0.3366,0.3382,0.3382,0.3405,0.3406,0.3427, 0.3486,0.3538,0.3574,0.3574,0.3596,0.3689,0.3697,0.3724,0.3725,0.3750, 0.3752,0.3836,0.3920,0.3932,0.3961,0.3983,0.3998,0.3999,0.4071,0.4101, 0.4109,0.4162,0.4230,0.4243,0.4376,0.4523,0.4566,0.4635,0.4678,0.4741, 0.4785,0.4803,0.4818,0.4818,0.4856,0.4899,0.5000,0.5057,0.5081,0.5104, 0.5137,0.5165,0.5198,0.5220,0.5231,0.5269,0.5318,0.5339,0.5360,0.5366, 0.5372,0.5380,0.5430,0.5431,0.5484,0.5510,0.5517,0.5641,0.5720,0.5745, 0.5785,0.5844,0.5860,0.5894,0.5910,0.5916,0.5923,0.5929,0.5963,0.5998, 0.5999,0.6025,0.6063,0.6104,0.6111,0.6162,0.6179,0.6185,0.6190,0.6215, 0.6241,0.6267,0.6381,0.6423,0.6475,0.6499,0.6537,0.6625,0.6631,0.6713, 0.6730,0.6737,0.6808,0.6822,0.6834,0.6839,0.6923,0.6946,0.6983,0.6999, 0.7122,0.7141,0.7150,0.7225,0.7288,0.7313,0.7353,0.7410,0.7426,0.7453, 0.7464,0.7465,0.7503,0.7533,0.7553,0.7575,0.7593,0.7603,0.7638,0.7691, 0.7738,0.7756,0.7828,0.7914,0.7918,0.7924,0.7973,0.8046,0.8092,0.8169, 0.8229,0.8241,0.8336,0.8353,0.8353,0.8543,0.8546,0.8679,0.8700,0.8706, 0.8796,0.8802,0.8810,0.8813,0.8824,0.8865,0.8894,0.8943,0.8958,0.9033, 0.9076,0.9086,0.9091,0.9102,0.9105,0.9253,0.9290,0.9318,0.9419,0.9531, 0.9574,0.9634,0.9694,0.9749,0.9780,0.9780,0.9875,0.9961,0.9987, Overall p-value after applying KStest on 269 p-values = 0.358654 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.