RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-08-08_21:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.69 19.5372 0.701418 2 to 25 15.88 20.4169 0.746538 3 to 26 15.72 17.5884 0.584757 4 to 27 15.65 21.2043 0.782713 5 to 28 15.82 21.9721 0.814207 6 to 29 15.79 23.7676 0.874112 7 to 30 15.58 15.6405 0.450551 8 to 31 15.59 19.1794 0.681670 9 to 32 15.80 20.6931 0.759682 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.022127 Tough bday spacings test for dh-ranFile-2015-08-08_21:31: 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 9 38 82 84 100 87 44 24 19 9 4 (O-E)^2/E 0.0 0.1 1.0 1.9 0.1 1.0 1.3 1.1 1.1 0.9 0.0 Birthday Spacings: Sum(O-E)^2/E= 8.446, p= 0.415 RESULTS OF GCD FOR dh-ranFile-2015-08-08_21:31 Euclid's algorithm: p-value, steps to gcd: 0.754594 p-value, dist. of gcd's: 0.314503 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-08-08_21:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.456 0.481 0.945 0.763 0.520 0.516 0.179 0.492 Bits 8 to 15---> 0.676 0.625 0.166 0.198 0.535 0.649 0.440 0.677 Bits 16 to 23---> 0.313 0.231 0.330 0.810 0.325 0.570 0.722 0.091 Bits 24 to 31---> 0.596 0.842 0.221 0.765 0.308 0.218 0.386 0.671 KS test for the above 32 p values: 0.732 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-08-08_21:31, p-values for 5 runs: 0.4380, 0.5322, 0.0797, 0.6302, 0.1444 Rank test for binary matrices (31x31) for dh-ranFile-2015-08-08_21:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 212 211.4 0.002 0.002 r= 29 5214 5134.0 1.246 1.248 r= 30 23149 23103.0 0.091 1.339 r= 31 11425 11551.5 1.386 2.725 chi-square = 2.725 with df = 3; p-value = 0.564 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-08-08_21:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 197 211.4 0.983 0.983 r= 30 5229 5134.0 1.757 2.741 r= 31 23031 23103.0 0.225 2.965 r= 32 11543 11551.5 0.006 2.972 chi-square = 2.972 with df = 3; p-value = 0.604 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-08-08_21:31 b-rank test for bits 1 to 8, p=0.44277 b-rank test for bits 2 to 9, p=0.43725 b-rank test for bits 3 to 10, p=0.80623 b-rank test for bits 4 to 11, p=0.42883 b-rank test for bits 5 to 12, p=0.13469 b-rank test for bits 6 to 13, p=0.82598 b-rank test for bits 7 to 14, p=0.88575 b-rank test for bits 8 to 15, p=0.59022 b-rank test for bits 9 to 16, p=0.48920 b-rank test for bits 10 to 17, p=0.18844 b-rank test for bits 11 to 18, p=0.80011 b-rank test for bits 12 to 19, p=0.61848 b-rank test for bits 13 to 20, p=0.28459 b-rank test for bits 14 to 21, p=0.71284 b-rank test for bits 15 to 22, p=0.38143 b-rank test for bits 16 to 23, p=0.97030 b-rank test for bits 17 to 24, p=0.08379 b-rank test for bits 18 to 25, p=0.48677 b-rank test for bits 19 to 26, p=0.03829 b-rank test for bits 20 to 27, p=0.66331 b-rank test for bits 21 to 28, p=0.26836 b-rank test for bits 22 to 29, p=0.13966 b-rank test for bits 23 to 30, p=0.03937 b-rank test for bits 24 to 31, p=0.23418 b-rank test for bits 25 to 32, p=0.83357 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 = 0.958594 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-08-08_21:31 (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 142398 1.14 0.873222 2 141702 -0.48 0.314045 3 141894 -0.04 0.485714 4 142068 0.37 0.644579 5 141577 -0.78 0.218735 6 142160 0.59 0.720954 7 141235 -1.58 0.057566 8 141463 -1.04 0.148514 9 142340 1.01 0.842850 10 141626 -0.66 0.253990 11 142330 0.98 0.837165 12 141967 0.13 0.553593 13 141626 -0.66 0.253990 14 141797 -0.26 0.396486 15 141683 -0.53 0.298469 16 141181 -1.70 0.044405 17 141816 -0.22 0.413691 18 141523 -0.90 0.183358 19 141012 -2.10 0.018016 20 141412 -1.16 0.122621 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-08-08_21:31 Bits used No. missing words z-score p-value 23 to 32 141599 -1.0701 0.142286 22 to 31 141230 -2.3425 0.009577 21 to 30 141596 -1.0804 0.139971 20 to 29 141523 -1.3322 0.091402 19 to 28 141659 -0.8632 0.194012 18 to 27 141134 -2.6736 0.003753 17 to 26 142046 0.4713 0.681278 16 to 25 141951 0.1437 0.557127 15 to 24 141997 0.3023 0.618792 14 to 23 142005 0.3299 0.629261 13 to 22 142370 1.5885 0.943915 12 to 21 141596 -1.0804 0.139971 11 to 20 142035 0.4333 0.667618 10 to 19 142344 1.4989 0.933045 9 to 18 141949 0.1368 0.554403 8 to 17 142083 0.5989 0.725368 7 to 16 141668 -0.8322 0.202656 6 to 15 142063 0.5299 0.701908 5 to 14 141852 -0.1977 0.421644 4 to 13 141995 0.2954 0.616161 3 to 12 141754 -0.5356 0.296110 2 to 11 142008 0.3402 0.633163 1 to 10 142287 1.3023 0.903595 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-08-08_21:31 Bits used No. missing words z-score p-value 28 to 32 142304 1.3379 0.909530 27 to 31 141815 -0.3198 0.374574 26 to 30 141912 0.0091 0.503611 25 to 29 141736 -0.5876 0.278414 24 to 28 141395 -1.7435 0.040624 23 to 27 142279 1.2531 0.894919 22 to 26 142232 1.0938 0.862978 21 to 25 141930 0.0701 0.527930 20 to 24 141361 -1.8587 0.031532 19 to 23 141971 0.2091 0.582796 18 to 22 141638 -0.9198 0.178848 17 to 21 141860 -0.1672 0.433598 16 to 20 142046 0.4633 0.678421 15 to 19 142404 1.6768 0.953214 14 to 18 141698 -0.7164 0.236881 13 to 17 141517 -1.3299 0.091770 12 to 16 142183 0.9277 0.823217 11 to 15 141890 -0.0655 0.473878 10 to 14 141803 -0.3604 0.359259 9 to 13 141975 0.2226 0.588081 8 to 12 141137 -2.6181 0.004421 7 to 11 141805 -0.3537 0.361797 6 to 10 142378 1.5887 0.943937 5 to 9 141587 -1.0926 0.137275 4 to 8 141658 -0.8520 0.197116 3 to 7 141801 -0.3672 0.356727 2 to 6 141957 0.1616 0.564187 1 to 5 142024 0.3887 0.651255 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-08-08_21:31 Bits used No. missing words z-score p-value 31 to 32 141910 0.0020 0.500789 30 to 31 141532 -1.1131 0.132840 29 to 30 141711 -0.5850 0.279259 28 to 29 142182 0.8043 0.789399 27 to 28 141933 0.0698 0.527833 26 to 27 141507 -1.1868 0.117650 25 to 26 142652 2.1908 0.985766 24 to 25 141615 -0.8682 0.192634 23 to 24 142572 1.9548 0.974695 22 to 23 141493 -1.2281 0.109702 21 to 22 141669 -0.7089 0.239182 20 to 21 141664 -0.7237 0.234629 19 to 20 141384 -1.5496 0.060613 18 to 19 142553 1.8987 0.971200 17 to 18 141812 -0.2871 0.387014 16 to 17 141581 -0.9685 0.166391 15 to 16 141794 -0.3402 0.366851 14 to 15 141937 0.0816 0.532527 13 to 14 142383 1.3973 0.918832 12 to 13 142236 0.9636 0.832384 11 to 12 141686 -0.6588 0.255015 10 to 11 142266 1.0521 0.853629 9 to 10 142299 1.1495 0.874819 8 to 9 141484 -1.2547 0.104801 7 to 8 141724 -0.5467 0.292294 6 to 7 141412 -1.4671 0.071181 5 to 6 142013 0.3058 0.620126 4 to 5 141969 0.1760 0.569860 3 to 4 142268 1.0580 0.854978 2 to 3 141957 0.1406 0.555915 1 to 2 142586 1.9961 0.977037 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-08-08_21:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2445.86 -0.766 0.221957 Test results for specific bytes for dh-ranFile-2015-08-08_21:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2375.06 -1.767 0.038618 2 to 9 2513.60 0.192 0.576243 3 to 10 2417.57 -1.166 0.121850 4 to 11 2577.18 1.092 0.862474 5 to 12 2514.83 0.210 0.583082 6 to 13 2651.60 2.144 0.983983 7 to 14 2524.62 0.348 0.636142 8 to 15 2513.31 0.188 0.574641 9 to 16 2494.52 -0.077 0.469122 10 to 17 2465.94 -0.482 0.315016 11 to 18 2392.45 -1.521 0.064128 12 to 19 2480.51 -0.276 0.391433 13 to 20 2472.41 -0.390 0.348210 14 to 21 2466.26 -0.477 0.316640 15 to 22 2557.59 0.814 0.792318 16 to 23 2501.46 0.021 0.508250 17 to 24 2549.60 0.701 0.758485 18 to 25 2635.64 1.918 0.972459 19 to 26 2497.01 -0.042 0.483134 20 to 27 2446.26 -0.760 0.223628 21 to 28 2416.77 -1.177 0.119599 22 to 29 2389.33 -1.565 0.058772 23 to 30 2644.06 2.037 0.979189 24 to 31 2433.13 -0.946 0.172163 25 to 32 2503.81 0.054 0.521494 CDPARK for dh-ranFile-2015-08-08_21:31: 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 3572 2.2374 0.987371 3449 -3.3790 0.000364 3539 0.7306 0.767486 3567 2.0091 0.977738 3536 0.5936 0.723613 3558 1.5982 0.944998 3481 -1.9178 0.027568 3520 -0.1370 0.445521 3484 -1.7808 0.037471 3488 -1.5982 0.055002 Square side=100, avg. no. parked=3519.40 sample std.=39.82 p-value of the KSTEST for those 10 p-values: 0.022937 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-08-08_21:31 0.1975,0.6792,0.2317,0.6990,0.1869,0.4813,0.3090,0.9890,0.9193,0.9333, The KS test for those 10 p-values: 0.501900 The 3DSPHERES test for dh-ranFile-2015-08-08_21:31 sample no r^3 equiv. uni. 1 79.182 0.928595 2 10.401 0.292982 3 16.498 0.423021 4 7.019 0.208603 5 2.067 0.066575 6 98.693 0.962737 7 69.464 0.901278 8 7.145 0.211934 9 30.593 0.639321 10 6.203 0.186804 11 28.360 0.611449 12 5.926 0.179242 13 27.497 0.600110 14 17.668 0.445090 15 9.620 0.274329 16 14.562 0.384558 17 9.883 0.280661 18 26.950 0.592751 19 3.636 0.114151 20 30.729 0.640948 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.504441 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-08-08_21:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 0.5 1.1 0.2 1.1 -2.2 1.7 -1.4 1.0 0.0 1.0 -1.5 1.4 -1.0 -0.1 0.6 0.5 -0.7 -0.7 -0.5 -1.0 -0.7 1.4 1.5 -0.5 -0.6 0.7 0.6 1.1 0.2 0.8 0.0 -0.1 -0.9 0.8 -0.8 1.4 -0.1 -1.2 -0.1 0.1 0.0 2.7 Chi-square with 42 degrees of freedom:43.439304 z-score=0.157041, p-value=0.590137 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-08-08_21:31 Test no p-value 1 0.868409 2 0.013465 3 0.999606 4 0.473762 5 0.317315 6 0.136458 7 0.004245 8 0.543490 9 0.881769 10 0.375127 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.204721 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-08-08_21:31: (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 66550 0.20 66604 0.06 3 25000.00 25123 0.61 25133 0.71 4 6666.67 6716 0.37 6636 0.14 5 1388.89 1371 0.23 1302 5.44 6 238.10 204 4.88 279 7.03 7 34.72 30 0.64 39 0.53 8 4.96 5 0.00 6 0.22 p=0.67256 p=0.97164 Number of rngs required: 688108, p-value: 0.367 RESULTS OF CRAPS TEST for dh-ranFile-2015-08-08_21:31 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 66719 66666.7 0.041 0.041 2 37613 37654.3 0.045 0.086 3 26936 26954.7 0.013 0.099 4 19339 19313.5 0.034 0.133 5 13783 13851.4 0.338 0.471 6 10014 9943.5 0.499 0.970 7 7009 7145.0 2.590 3.560 8 5130 5139.1 0.016 3.576 9 3778 3699.9 1.650 5.226 10 2700 2666.3 0.426 5.652 11 1922 1923.3 0.001 5.653 12 1411 1388.7 0.357 6.010 13 963 1003.7 1.652 7.661 14 688 726.1 2.003 9.665 15 550 525.8 1.110 10.775 16 387 381.2 0.090 10.865 17 296 276.5 1.369 12.234 18 209 200.8 0.332 12.567 19 153 146.0 0.337 12.904 20 110 106.2 0.135 13.039 21 290 287.1 0.029 13.068 Chisq= 13.07 for 20 degrees of freedom, p= 0.12555 SUMMARY of craptest p-value for no. of wins: 0.712160 p-value for throws/game: 0.125546 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-08-08_21:31 No. of wins: Observed Expected 98654 98585.9 z-score= 0.305, pvalue=0.61973 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66466 66666.7 0.604 0.604 2 37691 37654.3 0.036 0.640 3 26889 26954.7 0.160 0.800 4 19341 19313.5 0.039 0.839 5 13999 13851.4 1.572 2.412 6 9989 9943.5 0.208 2.619 7 7104 7145.0 0.236 2.855 8 5243 5139.1 2.102 4.957 9 3696 3699.9 0.004 4.961 10 2652 2666.3 0.077 5.038 11 1896 1923.3 0.388 5.426 12 1457 1388.7 3.355 8.781 13 957 1003.7 2.174 10.955 14 717 726.1 0.115 11.070 15 542 525.8 0.497 11.567 16 377 381.2 0.045 11.612 17 273 276.5 0.045 11.658 18 196 200.8 0.116 11.774 19 119 146.0 4.988 16.762 20 103 106.2 0.097 16.859 21 293 287.1 0.121 16.980 Chisq= 16.98 for 20 degrees of freedom, p= 0.34571 SUMMARY of craptest p-value for no. of wins: 0.619729 p-value for throws/game: 0.345707 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0004,0.0038,0.0042,0.0044,0.0096,0.0135,0.0180,0.0221,0.0229,0.0276, 0.0315,0.0375,0.0383,0.0386,0.0394,0.0406,0.0444,0.0550,0.0576,0.0588, 0.0606,0.0641,0.0666,0.0712,0.0797,0.0838,0.0912,0.0914,0.0918,0.1048, 0.1097,0.1142,0.1177,0.1196,0.1219,0.1226,0.1255,0.1328,0.1347,0.1365, 0.1373,0.1397,0.1400,0.1400,0.1423,0.1444,0.1485,0.1660,0.1664,0.1722, 0.1786,0.1788,0.1792,0.1834,0.1868,0.1869,0.1884,0.1926,0.1940,0.1971, 0.1975,0.1978,0.2027,0.2047,0.2086,0.2119,0.2177,0.2187,0.2208,0.2220, 0.2236,0.2314,0.2317,0.2342,0.2346,0.2369,0.2392,0.2540,0.2540,0.2550, 0.2684,0.2743,0.2784,0.2793,0.2807,0.2846,0.2923,0.2930,0.2961,0.2985, 0.3083,0.3090,0.3130,0.3140,0.3145,0.3150,0.3166,0.3173,0.3245,0.3296, 0.3457,0.3482,0.3567,0.3593,0.3618,0.3669,0.3671,0.3746,0.3751,0.3814, 0.3846,0.3860,0.3870,0.3914,0.3965,0.4137,0.4146,0.4216,0.4230,0.4288, 0.4336,0.4373,0.4380,0.4398,0.4428,0.4451,0.4455,0.4506,0.4561,0.4691, 0.4738,0.4739,0.4811,0.4813,0.4831,0.4857,0.4868,0.4892,0.4918,0.5008, 0.5019,0.5036,0.5044,0.5082,0.5160,0.5200,0.5215,0.5278,0.5279,0.5322, 0.5325,0.5355,0.5435,0.5536,0.5544,0.5559,0.5571,0.5640,0.5642,0.5699, 0.5702,0.5746,0.5762,0.5828,0.5831,0.5848,0.5881,0.5901,0.5902,0.5928, 0.5963,0.6001,0.6040,0.6114,0.6162,0.6185,0.6188,0.6197,0.6201,0.6250, 0.6293,0.6302,0.6332,0.6361,0.6393,0.6409,0.6446,0.6491,0.6513,0.6633, 0.6676,0.6711,0.6726,0.6762,0.6774,0.6784,0.6792,0.6813,0.6817,0.6990, 0.7014,0.7019,0.7122,0.7128,0.7210,0.7217,0.7236,0.7254,0.7317,0.7465, 0.7546,0.7585,0.7597,0.7627,0.7655,0.7675,0.7827,0.7894,0.7923,0.8001, 0.8062,0.8096,0.8142,0.8232,0.8260,0.8324,0.8336,0.8372,0.8417,0.8428, 0.8536,0.8550,0.8625,0.8630,0.8684,0.8732,0.8741,0.8748,0.8818,0.8858, 0.8949,0.9013,0.9036,0.9095,0.9188,0.9193,0.9286,0.9330,0.9333,0.9439, 0.9439,0.9450,0.9453,0.9532,0.9586,0.9627,0.9703,0.9712,0.9716,0.9725, 0.9747,0.9770,0.9777,0.9792,0.9840,0.9858,0.9874,0.9890,0.9996, Overall p-value after applying KStest on 269 p-values = 0.345831 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.