RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-10-01_22:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.64 17.4512 0.575778 2 to 25 15.49 22.0075 0.815570 3 to 26 15.84 20.7066 0.760311 4 to 27 15.93 8.8630 0.055538 5 to 28 15.93 9.2970 0.069519 6 to 29 16.13 8.3053 0.040423 7 to 30 15.74 13.3870 0.290084 8 to 31 15.38 21.7965 0.807329 9 to 32 15.88 26.6803 0.937074 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.431414 Tough bday spacings test for dh-ranFile-2015-10-01_22:31: 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 6 43 81 96 90 82 46 25 20 6 5 (O-E)^2/E 1.1 1.1 0.8 0.0 0.6 0.2 0.7 0.8 1.8 0.1 0.2 Birthday Spacings: Sum(O-E)^2/E= 7.344, p= 0.307 RESULTS OF GCD FOR dh-ranFile-2015-10-01_22:31 Euclid's algorithm: p-value, steps to gcd: 0.597892 p-value, dist. of gcd's: 0.214296 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-10-01_22:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.624 0.641 0.578 0.120 0.309 0.505 0.963 0.603 Bits 8 to 15---> 0.501 0.631 0.160 0.472 0.115 0.892 0.973 0.667 Bits 16 to 23---> 0.095 0.163 0.761 0.405 0.249 0.407 0.774 0.485 Bits 24 to 31---> 0.432 0.643 0.775 0.587 0.439 0.484 0.290 0.081 KS test for the above 32 p values: 0.481 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-10-01_22:31, p-values for 5 runs: 0.1745, 0.6521, 0.4327, 0.2996, 0.2165 Rank test for binary matrices (31x31) for dh-ranFile-2015-10-01_22:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 201 211.4 0.513 0.513 r= 29 5102 5134.0 0.200 0.713 r= 30 23204 23103.0 0.441 1.154 r= 31 11493 11551.5 0.297 1.451 chi-square = 1.451 with df = 3; p-value = 0.306 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-10-01_22:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 243 211.4 4.718 4.718 r= 30 5209 5134.0 1.095 5.813 r= 31 23154 23103.0 0.112 5.925 r= 32 11394 11551.5 2.148 8.074 chi-square = 8.074 with df = 3; p-value = 0.955 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-10-01_22:31 b-rank test for bits 1 to 8, p=0.13740 b-rank test for bits 2 to 9, p=0.63907 b-rank test for bits 3 to 10, p=0.60821 b-rank test for bits 4 to 11, p=0.17277 b-rank test for bits 5 to 12, p=0.39566 b-rank test for bits 6 to 13, p=0.24350 b-rank test for bits 7 to 14, p=0.56246 b-rank test for bits 8 to 15, p=0.80510 b-rank test for bits 9 to 16, p=0.86822 b-rank test for bits 10 to 17, p=0.01380 b-rank test for bits 11 to 18, p=0.22503 b-rank test for bits 12 to 19, p=0.87977 b-rank test for bits 13 to 20, p=0.65410 b-rank test for bits 14 to 21, p=0.24448 b-rank test for bits 15 to 22, p=0.56143 b-rank test for bits 16 to 23, p=0.43483 b-rank test for bits 17 to 24, p=0.87396 b-rank test for bits 18 to 25, p=0.89512 b-rank test for bits 19 to 26, p=0.23927 b-rank test for bits 20 to 27, p=0.01940 b-rank test for bits 21 to 28, p=0.16897 b-rank test for bits 22 to 29, p=0.55885 b-rank test for bits 23 to 30, p=0.94719 b-rank test for bits 24 to 31, p=0.08414 b-rank test for bits 25 to 32, p=0.21627 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 = 0.611465 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-10-01_22:31 (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 142269 0.84 0.799644 2 141719 -0.44 0.328270 3 141723 -0.44 0.331654 4 142398 1.14 0.873222 5 141709 -0.47 0.319871 6 142779 2.03 0.978920 7 142143 0.55 0.707453 8 141890 -0.05 0.481989 9 141885 -0.06 0.477334 10 142232 0.75 0.774546 11 141715 -0.45 0.324899 12 142080 0.40 0.654966 13 141847 -0.15 0.442106 14 141770 -0.33 0.372387 15 142246 0.79 0.784246 16 142088 0.42 0.661827 17 142511 1.41 0.920104 18 141045 -2.02 0.021720 19 141954 0.10 0.541562 20 142231 0.75 0.773844 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-10-01_22:31 Bits used No. missing words z-score p-value 23 to 32 142263 1.2196 0.888683 22 to 31 141468 -1.5218 0.064026 21 to 30 141716 -0.6667 0.252496 20 to 29 141590 -1.1011 0.135418 19 to 28 141437 -1.6287 0.051686 18 to 27 141842 -0.2322 0.408202 17 to 26 142233 1.1161 0.867811 16 to 25 142339 1.4816 0.930779 15 to 24 141742 -0.5770 0.281970 14 to 23 141624 -0.9839 0.162583 13 to 22 141821 -0.3046 0.380341 12 to 21 142137 0.7851 0.783793 11 to 20 142016 0.3678 0.643499 10 to 19 141668 -0.8322 0.202656 9 to 18 141654 -0.8804 0.189308 8 to 17 141762 -0.5080 0.305715 7 to 16 141854 -0.1908 0.424344 6 to 15 142111 0.6954 0.756602 5 to 14 141889 -0.0701 0.472056 4 to 13 141530 -1.3080 0.095431 3 to 12 142072 0.5609 0.712578 2 to 11 142071 0.5575 0.711401 1 to 10 142169 0.8954 0.814717 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-10-01_22:31 Bits used No. missing words z-score p-value 28 to 32 141832 -0.2621 0.396609 27 to 31 141765 -0.4893 0.312331 26 to 30 142087 0.6023 0.726503 25 to 29 141806 -0.3503 0.363068 24 to 28 141915 0.0192 0.507667 23 to 27 141920 0.0362 0.514426 22 to 26 142076 0.5650 0.713957 21 to 25 141687 -0.7537 0.225526 20 to 24 142060 0.5107 0.695236 19 to 23 142150 0.8158 0.792702 18 to 22 141457 -1.5333 0.062598 17 to 21 142101 0.6497 0.742066 16 to 20 141595 -1.0655 0.143319 15 to 19 141959 0.1684 0.566855 14 to 18 141903 -0.0215 0.491440 13 to 17 142345 1.4768 0.930142 12 to 16 141438 -1.5977 0.055052 11 to 15 142051 0.4802 0.684471 10 to 14 142240 1.1209 0.868838 9 to 13 141653 -0.8689 0.192447 8 to 12 141709 -0.6791 0.248542 7 to 11 142110 0.6802 0.751823 6 to 10 142076 0.5650 0.713957 5 to 9 142398 1.6565 0.951191 4 to 8 142278 1.2497 0.894301 3 to 7 141791 -0.4011 0.344166 2 to 6 141833 -0.2587 0.397916 1 to 5 141842 -0.2282 0.409731 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-10-01_22:31 Bits used No. missing words z-score p-value 31 to 32 142117 0.6126 0.729928 30 to 31 141660 -0.7355 0.231022 29 to 30 141556 -1.0423 0.148643 28 to 29 142110 0.5919 0.723057 27 to 28 141232 -1.9980 0.022857 26 to 27 142075 0.4887 0.687474 25 to 26 142406 1.4651 0.928554 24 to 25 141715 -0.5732 0.283240 23 to 24 141805 -0.3078 0.379133 22 to 23 141712 -0.5821 0.280252 21 to 22 141950 0.1200 0.547747 20 to 21 141507 -1.1868 0.117650 19 to 20 141922 0.0374 0.514907 18 to 19 141463 -1.3166 0.093985 17 to 18 141496 -1.2193 0.111372 16 to 17 141942 0.0964 0.538387 15 to 16 142015 0.3117 0.622370 14 to 15 141747 -0.4788 0.316023 13 to 14 141376 -1.5732 0.057831 12 to 13 141313 -1.7591 0.039282 11 to 12 141922 0.0374 0.514907 10 to 11 141577 -0.9803 0.163463 9 to 10 141431 -1.4110 0.079122 8 to 9 141739 -0.5024 0.307676 7 to 8 141286 -1.8387 0.032977 6 to 7 141677 -0.6853 0.246565 5 to 6 142560 1.9194 0.972532 4 to 5 142189 0.8250 0.795310 3 to 4 142073 0.4828 0.685382 2 to 3 142282 1.0993 0.864186 1 to 2 141234 -1.9921 0.023179 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-10-01_22:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2474.33 -0.363 0.358283 Test results for specific bytes for dh-ranFile-2015-10-01_22:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2372.17 -1.808 0.035320 2 to 9 2468.34 -0.448 0.327169 3 to 10 2442.16 -0.818 0.206677 4 to 11 2645.97 2.064 0.980510 5 to 12 2530.40 0.430 0.666391 6 to 13 2512.32 0.174 0.569166 7 to 14 2571.28 1.008 0.843276 8 to 15 2614.04 1.613 0.946602 9 to 16 2487.58 -0.176 0.430312 10 to 17 2490.50 -0.134 0.446564 11 to 18 2439.53 -0.855 0.196231 12 to 19 2515.99 0.226 0.589446 13 to 20 2486.35 -0.193 0.423467 14 to 21 2372.97 -1.796 0.036214 15 to 22 2652.08 2.151 0.984252 16 to 23 2575.15 1.063 0.856063 17 to 24 2407.43 -1.309 0.095250 18 to 25 2608.29 1.531 0.937164 19 to 26 2461.61 -0.543 0.293591 20 to 27 2585.94 1.215 0.887876 21 to 28 2368.68 -1.857 0.031644 22 to 29 2444.01 -0.792 0.214252 23 to 30 2388.99 -1.570 0.058220 24 to 31 2457.19 -0.605 0.272467 25 to 32 2477.68 -0.316 0.376135 CDPARK for dh-ranFile-2015-10-01_22:31: 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 3512 -0.5023 0.307734 3522 -0.0457 0.481790 3511 -0.5479 0.291865 3527 0.1826 0.572463 3505 -0.8219 0.205562 3516 -0.3196 0.374623 3501 -1.0046 0.157553 3527 0.1826 0.572463 3533 0.4566 0.676028 3555 1.4612 0.928018 Square side=100, avg. no. parked=3520.90 sample std.=14.95 p-value of the KSTEST for those 10 p-values: 0.649782 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-10-01_22:31 0.9874,0.0471,0.8958,0.9448,0.7196,0.6588,0.0357,0.4741,0.0426,0.8639, The KS test for those 10 p-values: 0.125543 The 3DSPHERES test for dh-ranFile-2015-10-01_22:31 sample no r^3 equiv. uni. 1 45.706 0.782062 2 14.463 0.382518 3 15.537 0.404228 4 4.721 0.145623 5 17.948 0.450233 6 8.733 0.252563 7 48.694 0.802721 8 78.722 0.927494 9 28.368 0.611551 10 15.547 0.404428 11 28.642 0.615091 12 14.250 0.378116 13 24.049 0.551407 14 50.704 0.815505 15 27.843 0.604699 16 5.595 0.170138 17 90.780 0.951491 18 6.102 0.184044 19 60.106 0.865142 20 48.684 0.802653 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.546022 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-10-01_22:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 1.3 -0.7 -0.1 -0.1 0.3 1.0 -1.5 -0.6 0.5 -1.4 -1.7 -1.9 -0.0 -0.7 0.7 -1.6 0.4 0.5 1.2 1.9 -0.4 0.6 -0.2 -0.6 0.8 0.6 -0.2 0.2 0.4 1.3 -0.6 1.2 0.2 0.5 0.2 -0.7 -1.4 0.8 1.3 0.4 0.1 0.0 0.8 Chi-square with 42 degrees of freedom:35.623454 z-score=-0.695738, p-value=0.254416 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-10-01_22:31 Test no p-value 1 0.001190 2 0.211234 3 0.019554 4 0.923451 5 0.509630 6 0.350584 7 0.175585 8 0.073219 9 0.257360 10 0.372572 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.018293 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-10-01_22:31: (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 66436 0.80 66673 0.00 3 25000.00 25264 2.79 24922 0.24 4 6666.67 6572 1.34 6735 0.70 5 1388.89 1429 1.16 1390 0.00 6 238.10 249 0.50 233 0.11 7 34.72 45 3.04 40 0.80 8 4.96 4 0.19 6 0.22 p=0.86746 p=0.08735 Number of rngs required: 691361, p-value: 1.000 RESULTS OF CRAPS TEST for dh-ranFile-2015-10-01_22:31 No. of wins: Observed Expected 98780 98585.9 z-score= 0.868, pvalue=0.80739 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66845 66666.7 0.477 0.477 2 37871 37654.3 1.247 1.724 3 26872 26954.7 0.254 1.978 4 19187 19313.5 0.828 2.806 5 13882 13851.4 0.068 2.873 6 9910 9943.5 0.113 2.987 7 7303 7145.0 3.493 6.479 8 5022 5139.1 2.667 9.146 9 3729 3699.9 0.229 9.376 10 2689 2666.3 0.193 9.569 11 1860 1923.3 2.085 11.654 12 1398 1388.7 0.062 11.716 13 978 1003.7 0.659 12.375 14 715 726.1 0.171 12.546 15 489 525.8 2.580 15.126 16 343 381.2 3.819 18.945 17 253 276.5 2.004 20.949 18 185 200.8 1.248 22.196 19 125 146.0 3.016 25.213 20 96 106.2 0.982 26.195 21 248 287.1 5.329 31.524 Chisq= 31.52 for 20 degrees of freedom, p= 0.95135 SUMMARY of craptest p-value for no. of wins: 0.807389 p-value for throws/game: 0.951354 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-10-01_22:31 No. of wins: Observed Expected 98485 98585.9 z-score=-0.451, pvalue=0.32596 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66243 66666.7 2.692 2.692 2 37841 37654.3 0.925 3.618 3 26782 26954.7 1.107 4.725 4 19399 19313.5 0.379 5.104 5 13946 13851.4 0.646 5.749 6 10100 9943.5 2.462 8.211 7 7075 7145.0 0.686 8.898 8 5218 5139.1 1.212 10.110 9 3750 3699.9 0.679 10.789 10 2692 2666.3 0.248 11.037 11 1889 1923.3 0.613 11.650 12 1364 1388.7 0.441 12.090 13 1007 1003.7 0.011 12.101 14 737 726.1 0.162 12.263 15 531 525.8 0.051 12.314 16 383 381.2 0.009 12.323 17 284 276.5 0.201 12.524 18 209 200.8 0.332 12.857 19 141 146.0 0.170 13.027 20 117 106.2 1.095 14.122 21 292 287.1 0.083 14.205 Chisq= 14.21 for 20 degrees of freedom, p= 0.18006 SUMMARY of craptest p-value for no. of wins: 0.325959 p-value for throws/game: 0.180059 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0012,0.0138,0.0183,0.0194,0.0196,0.0217,0.0229,0.0232,0.0316,0.0330, 0.0353,0.0357,0.0362,0.0393,0.0404,0.0426,0.0471,0.0517,0.0551,0.0555, 0.0578,0.0582,0.0626,0.0640,0.0695,0.0732,0.0791,0.0815,0.0841,0.0874, 0.0940,0.0946,0.0953,0.0954,0.1114,0.1153,0.1177,0.1199,0.1255,0.1354, 0.1374,0.1433,0.1456,0.1486,0.1576,0.1599,0.1626,0.1629,0.1635,0.1690, 0.1701,0.1728,0.1745,0.1756,0.1801,0.1840,0.1893,0.1924,0.1962,0.2027, 0.2056,0.2067,0.2112,0.2143,0.2143,0.2163,0.2165,0.2250,0.2255,0.2310, 0.2393,0.2435,0.2445,0.2466,0.2485,0.2494,0.2525,0.2526,0.2544,0.2574, 0.2725,0.2803,0.2820,0.2832,0.2901,0.2902,0.2919,0.2936,0.2996,0.3057, 0.3063,0.3074,0.3077,0.3077,0.3092,0.3123,0.3160,0.3199,0.3249,0.3260, 0.3272,0.3283,0.3317,0.3442,0.3506,0.3583,0.3631,0.3724,0.3726,0.3746, 0.3761,0.3781,0.3791,0.3803,0.3825,0.3957,0.3966,0.3979,0.4042,0.4044, 0.4051,0.4072,0.4082,0.4097,0.4235,0.4243,0.4303,0.4314,0.4320,0.4327, 0.4348,0.4386,0.4421,0.4466,0.4502,0.4721,0.4722,0.4741,0.4773,0.4813, 0.4818,0.4820,0.4840,0.4855,0.4914,0.5008,0.5051,0.5077,0.5096,0.5144, 0.5149,0.5149,0.5384,0.5416,0.5460,0.5477,0.5514,0.5588,0.5614,0.5625, 0.5669,0.5692,0.5725,0.5725,0.5758,0.5779,0.5873,0.5894,0.5979,0.6027, 0.6047,0.6082,0.6115,0.6116,0.6151,0.6224,0.6245,0.6313,0.6391,0.6410, 0.6432,0.6435,0.6498,0.6521,0.6541,0.6550,0.6588,0.6618,0.6664,0.6669, 0.6760,0.6845,0.6854,0.6875,0.6952,0.7075,0.7114,0.7126,0.7140,0.7140, 0.7196,0.7231,0.7265,0.7299,0.7421,0.7518,0.7566,0.7603,0.7611,0.7738, 0.7745,0.7745,0.7750,0.7821,0.7838,0.7842,0.7927,0.7953,0.7996,0.8027, 0.8027,0.8051,0.8073,0.8074,0.8147,0.8155,0.8156,0.8433,0.8561,0.8639, 0.8642,0.8651,0.8675,0.8678,0.8682,0.8688,0.8732,0.8740,0.8798,0.8879, 0.8887,0.8917,0.8943,0.8951,0.8958,0.9201,0.9235,0.9275,0.9280,0.9286, 0.9301,0.9308,0.9371,0.9372,0.9448,0.9466,0.9472,0.9512,0.9514,0.9515, 0.9555,0.9633,0.9725,0.9726,0.9789,0.9805,0.9843,0.9874,0.9998, Overall p-value after applying KStest on 269 p-values = 0.331596 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.