RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-02-17_02:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.91 21.4628 0.793731 2 to 25 15.54 16.5313 0.513470 3 to 26 15.59 24.6590 0.897393 4 to 27 15.56 35.7402 0.995033 5 to 28 15.71 20.0131 0.726438 6 to 29 15.97 24.0322 0.881436 7 to 30 15.85 10.5204 0.119618 8 to 31 15.83 12.4619 0.228601 9 to 32 15.94 14.8805 0.395912 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.320583 Tough bday spacings test for dh-ranFile-2016-02-17_02:31: 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 4 48 86 86 88 75 52 37 14 5 5 (O-E)^2/E 2.9 3.5 2.2 1.4 1.0 0.1 0.0 1.8 0.1 0.4 0.2 Birthday Spacings: Sum(O-E)^2/E= 13.550, p= 0.805 RESULTS OF GCD FOR dh-ranFile-2016-02-17_02:31 Euclid's algorithm: p-value, steps to gcd: 0.702167 p-value, dist. of gcd's: 0.160972 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-02-17_02:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.507 0.243 0.719 0.546 0.197 0.044 0.289 0.527 Bits 8 to 15---> 0.710 0.393 0.915 0.478 0.174 0.280 0.274 0.768 Bits 16 to 23---> 0.252 0.032 0.428 0.584 0.465 0.144 0.956 0.432 Bits 24 to 31---> 0.438 0.915 0.958 0.265 0.549 0.548 0.080 0.327 KS test for the above 32 p values: 0.631 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-02-17_02:31, p-values for 5 runs: 0.3976, 0.6640, 0.8932, 0.7741, 0.3780 Rank test for binary matrices (31x31) for dh-ranFile-2016-02-17_02:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 219 211.4 0.272 0.272 r= 29 5221 5134.0 1.474 1.746 r= 30 23094 23103.0 0.004 1.749 r= 31 11466 11551.5 0.633 2.383 chi-square = 2.383 with df = 3; p-value = 0.503 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-02-17_02:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 219 211.4 0.272 0.272 r= 30 5280 5134.0 4.151 4.423 r= 31 22987 23103.0 0.583 5.006 r= 32 11514 11551.5 0.122 5.128 chi-square = 5.128 with df = 3; p-value = 0.837 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-02-17_02:31 b-rank test for bits 1 to 8, p=0.33324 b-rank test for bits 2 to 9, p=0.39294 b-rank test for bits 3 to 10, p=0.31317 b-rank test for bits 4 to 11, p=0.45525 b-rank test for bits 5 to 12, p=0.39583 b-rank test for bits 6 to 13, p=0.37862 b-rank test for bits 7 to 14, p=0.77958 b-rank test for bits 8 to 15, p=0.32378 b-rank test for bits 9 to 16, p=0.75781 b-rank test for bits 10 to 17, p=0.76655 b-rank test for bits 11 to 18, p=0.13437 b-rank test for bits 12 to 19, p=0.34610 b-rank test for bits 13 to 20, p=0.89631 b-rank test for bits 14 to 21, p=0.90142 b-rank test for bits 15 to 22, p=0.66750 b-rank test for bits 16 to 23, p=0.88698 b-rank test for bits 17 to 24, p=0.95878 b-rank test for bits 18 to 25, p=0.63583 b-rank test for bits 19 to 26, p=0.51818 b-rank test for bits 20 to 27, p=0.66054 b-rank test for bits 21 to 28, p=0.47678 b-rank test for bits 22 to 29, p=0.53108 b-rank test for bits 23 to 30, p=0.01133 b-rank test for bits 24 to 31, p=0.56937 b-rank test for bits 25 to 32, p=0.16875 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 = 0.639979 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-02-17_02:31 (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 140757 -2.69 0.003547 2 142365 1.06 0.856483 3 142125 0.50 0.692835 4 141626 -0.66 0.253990 5 141891 -0.04 0.482920 6 141570 -0.79 0.213939 7 141413 -1.16 0.123096 8 143074 2.72 0.996748 9 142003 0.22 0.586619 10 141416 -1.15 0.124529 11 142226 0.74 0.770315 12 141698 -0.49 0.310737 13 142248 0.79 0.785611 14 140962 -2.21 0.013435 15 141731 -0.42 0.338464 16 141318 -1.38 0.083545 17 141065 -1.97 0.024263 18 141030 -2.05 0.019963 19 141328 -1.36 0.087193 20 142259 0.82 0.793032 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-02-17_02:31 Bits used No. missing words z-score p-value 23 to 32 142141 0.7989 0.787815 22 to 31 142528 2.1333 0.983552 21 to 30 142406 1.7127 0.956612 20 to 29 141787 -0.4218 0.336575 19 to 28 141724 -0.6391 0.261389 18 to 27 141570 -1.1701 0.120980 17 to 26 141876 -0.1149 0.454250 16 to 25 141892 -0.0598 0.476174 15 to 24 142509 2.0678 0.980672 14 to 23 142114 0.7058 0.759831 13 to 22 141954 0.1540 0.561209 12 to 21 142039 0.4471 0.672612 11 to 20 142318 1.4092 0.920613 10 to 19 141958 0.1678 0.566641 9 to 18 142605 2.3989 0.991777 8 to 17 141670 -0.8253 0.204608 7 to 16 142397 1.6816 0.953679 6 to 15 141965 0.1920 0.576115 5 to 14 142278 1.2713 0.898185 4 to 13 141736 -0.5977 0.275024 3 to 12 141959 0.1713 0.567997 2 to 11 142137 0.7851 0.783793 1 to 10 142516 2.0920 0.981779 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-02-17_02:31 Bits used No. missing words z-score p-value 28 to 32 141871 -0.1299 0.448310 27 to 31 142223 1.0633 0.856174 26 to 30 141851 -0.1977 0.421629 25 to 29 142459 1.8633 0.968789 24 to 28 141698 -0.7164 0.236881 23 to 27 141723 -0.6316 0.263815 22 to 26 141722 -0.6350 0.262709 21 to 25 142075 0.5616 0.712803 20 to 24 142089 0.6091 0.728755 19 to 23 142263 1.1989 0.884713 18 to 22 141583 -1.1062 0.134319 17 to 21 142188 0.9446 0.827580 16 to 20 141787 -0.4147 0.339189 15 to 19 141985 0.2565 0.601221 14 to 18 142067 0.5345 0.703493 13 to 17 141860 -0.1672 0.433598 12 to 16 141914 0.0158 0.506315 11 to 15 141759 -0.5096 0.305168 10 to 14 142174 0.8972 0.815190 9 to 13 142148 0.8091 0.790757 8 to 12 141761 -0.5028 0.307548 7 to 11 142264 1.2023 0.885371 6 to 10 141775 -0.4554 0.324427 5 to 9 141907 -0.0079 0.496849 4 to 8 142087 0.6023 0.726503 3 to 7 141906 -0.0113 0.495497 2 to 6 142243 1.1311 0.870990 1 to 5 141866 -0.1469 0.441613 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-02-17_02:31 Bits used No. missing words z-score p-value 31 to 32 141698 -0.6234 0.266513 30 to 31 141637 -0.8033 0.210891 29 to 30 141958 0.1436 0.557080 28 to 29 142050 0.4150 0.660913 27 to 28 141449 -1.3579 0.087247 26 to 27 142240 0.9754 0.835326 25 to 26 141568 -1.0069 0.156998 24 to 25 142056 0.4327 0.667367 23 to 24 142025 0.3412 0.633527 22 to 23 142472 1.6598 0.951522 21 to 22 142162 0.7453 0.771967 20 to 21 141845 -0.1898 0.424747 19 to 20 142173 0.7778 0.781653 18 to 19 142224 0.9282 0.823356 17 to 18 141768 -0.4169 0.338375 16 to 17 142540 1.8604 0.968584 15 to 16 141850 -0.1750 0.430534 14 to 15 142141 0.6834 0.752821 13 to 14 142151 0.7129 0.762043 12 to 13 142069 0.4710 0.681181 11 to 12 141831 -0.2311 0.408633 10 to 11 141941 0.0934 0.537216 9 to 10 141958 0.1436 0.557080 8 to 9 142149 0.7070 0.760214 7 to 8 142303 1.1613 0.877234 6 to 7 142125 0.6362 0.737675 5 to 6 142172 0.7748 0.780782 4 to 5 142580 1.9784 0.976057 3 to 4 141291 -1.8240 0.034077 2 to 3 141776 -0.3933 0.347048 1 to 2 141768 -0.4169 0.338375 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-02-17_02:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2566.19 0.936 0.825390 Test results for specific bytes for dh-ranFile-2016-02-17_02:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2426.48 -1.040 0.149218 2 to 9 2364.66 -1.914 0.027813 3 to 10 2442.78 -0.809 0.209200 4 to 11 2448.42 -0.729 0.232862 5 to 12 2562.89 0.889 0.813101 6 to 13 2515.01 0.212 0.584032 7 to 14 2431.22 -0.973 0.165345 8 to 15 2505.06 0.072 0.528551 9 to 16 2560.71 0.859 0.804714 10 to 17 2504.18 0.059 0.523578 11 to 18 2474.40 -0.362 0.358639 12 to 19 2500.21 0.003 0.501165 13 to 20 2479.81 -0.286 0.387627 14 to 21 2618.74 1.679 0.953446 15 to 22 2514.43 0.204 0.580852 16 to 23 2499.08 -0.013 0.494786 17 to 24 2460.87 -0.553 0.289997 18 to 25 2487.92 -0.171 0.432173 19 to 26 2456.21 -0.619 0.267885 20 to 27 2606.66 1.508 0.934277 21 to 28 2537.18 0.526 0.700499 22 to 29 2475.26 -0.350 0.363217 23 to 30 2457.80 -0.597 0.275300 24 to 31 2457.09 -0.607 0.271965 25 to 32 2451.52 -0.686 0.246487 CDPARK for dh-ranFile-2016-02-17_02:31: 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 3522 -0.0457 0.481790 3556 1.5068 0.934075 3510 -0.5936 0.276387 3545 1.0046 0.842447 3503 -0.9132 0.180558 3532 0.4110 0.659449 3527 0.1826 0.572463 3503 -0.9132 0.180558 3486 -1.6895 0.045562 3521 -0.0913 0.463617 Square side=100, avg. no. parked=3520.50 sample std.=19.88 p-value of the KSTEST for those 10 p-values: 0.981147 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-02-17_02:31 0.4492,0.7089,0.3101,0.9587,0.9775,0.8006,0.4065,0.4458,0.9873,0.3110, The KS test for those 10 p-values: 0.097666 The 3DSPHERES test for dh-ranFile-2016-02-17_02:31 sample no r^3 equiv. uni. 1 1.407 0.045822 2 74.814 0.917406 3 2.013 0.064912 4 0.903 0.029664 5 13.008 0.351839 6 34.336 0.681622 7 56.100 0.845877 8 4.717 0.145505 9 25.209 0.568416 10 16.258 0.418387 11 5.273 0.161185 12 98.467 0.962456 13 8.226 0.239817 14 48.630 0.802296 15 8.823 0.254807 16 45.419 0.779961 17 6.910 0.205723 18 23.790 0.547520 19 53.758 0.833364 20 30.191 0.634457 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.896100 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-02-17_02:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 2.6 1.5 0.0 -0.2 -0.4 -1.3 -0.0 -0.2 1.2 1.0 -0.4 -1.7 -0.1 0.5 -0.7 0.1 -0.0 -0.4 0.0 -1.0 2.0 -0.8 0.3 0.8 0.6 -0.6 0.7 0.1 0.4 -1.2 -0.9 1.9 0.8 2.3 -1.4 0.7 0.2 0.1 -0.7 -1.3 0.0 -1.1 Chi-square with 42 degrees of freedom:44.878739 z-score=0.314096, p-value=0.647883 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-02-17_02:31 Test no p-value 1 0.104373 2 0.364049 3 0.996829 4 0.185727 5 0.435787 6 0.655385 7 0.088943 8 0.115139 9 0.004406 10 0.531025 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.081985 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-02-17_02:31: (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 66937 1.10 66647 0.01 3 25000.00 24817 1.34 24984 0.01 4 6666.67 6579 1.15 6697 0.14 5 1388.89 1359 0.64 1392 0.01 6 238.10 253 0.93 247 0.33 7 34.72 48 5.08 28 1.30 8 4.96 6 0.22 4 0.19 p=0.89352 p=0.07852 Number of rngs required: 687137, p-value: 0.070 RESULTS OF CRAPS TEST for dh-ranFile-2016-02-17_02:31 No. of wins: Observed Expected 99041 98585.9 z-score= 2.036, pvalue=0.97911 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66707 66666.7 0.024 0.024 2 37523 37654.3 0.458 0.482 3 26905 26954.7 0.092 0.574 4 19542 19313.5 2.704 3.278 5 13935 13851.4 0.504 3.783 6 9931 9943.5 0.016 3.799 7 7130 7145.0 0.032 3.830 8 5095 5139.1 0.378 4.208 9 3757 3699.9 0.882 5.090 10 2614 2666.3 1.026 6.116 11 1883 1923.3 0.846 6.962 12 1417 1388.7 0.575 7.537 13 986 1003.7 0.313 7.850 14 709 726.1 0.405 8.254 15 500 525.8 1.269 9.524 16 388 381.2 0.123 9.647 17 247 276.5 3.155 12.802 18 190 200.8 0.584 13.386 19 143 146.0 0.061 13.447 20 106 106.2 0.000 13.447 21 292 287.1 0.083 13.531 Chisq= 13.53 for 20 degrees of freedom, p= 0.14653 SUMMARY of craptest p-value for no. of wins: 0.979108 p-value for throws/game: 0.146526 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-02-17_02:31 No. of wins: Observed Expected 98733 98585.9 z-score= 0.658, pvalue=0.74476 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66749 66666.7 0.102 0.102 2 37626 37654.3 0.021 0.123 3 26678 26954.7 2.841 2.964 4 19420 19313.5 0.588 3.552 5 13748 13851.4 0.772 4.324 6 10012 9943.5 0.471 4.795 7 7192 7145.0 0.309 5.104 8 5227 5139.1 1.504 6.608 9 3764 3699.9 1.112 7.720 10 2676 2666.3 0.035 7.756 11 1968 1923.3 1.038 8.793 12 1361 1388.7 0.554 9.347 13 990 1003.7 0.187 9.535 14 716 726.1 0.142 9.676 15 513 525.8 0.313 9.990 16 353 381.2 2.079 12.069 17 297 276.5 1.514 13.582 18 218 200.8 1.468 15.050 19 137 146.0 0.553 15.603 20 104 106.2 0.046 15.650 21 251 287.1 4.543 20.192 Chisq= 20.19 for 20 degrees of freedom, p= 0.55403 SUMMARY of craptest p-value for no. of wins: 0.744764 p-value for throws/game: 0.554027 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0035,0.0044,0.0113,0.0134,0.0200,0.0243,0.0278,0.0297,0.0317,0.0341, 0.0438,0.0456,0.0458,0.0649,0.0697,0.0785,0.0805,0.0820,0.0835,0.0872, 0.0872,0.0889,0.0977,0.1044,0.1151,0.1196,0.1210,0.1231,0.1245,0.1343, 0.1344,0.1444,0.1455,0.1465,0.1492,0.1570,0.1610,0.1612,0.1653,0.1687, 0.1742,0.1806,0.1806,0.1857,0.1966,0.2046,0.2057,0.2092,0.2109,0.2139, 0.2286,0.2329,0.2369,0.2398,0.2432,0.2465,0.2523,0.2540,0.2548,0.2614, 0.2627,0.2638,0.2646,0.2665,0.2679,0.2720,0.2743,0.2750,0.2753,0.2764, 0.2800,0.2895,0.2900,0.3052,0.3075,0.3101,0.3107,0.3110,0.3132,0.3206, 0.3238,0.3244,0.3273,0.3332,0.3366,0.3384,0.3384,0.3385,0.3392,0.3461, 0.3470,0.3518,0.3586,0.3632,0.3640,0.3780,0.3786,0.3876,0.3929,0.3935, 0.3958,0.3959,0.3976,0.4065,0.4086,0.4184,0.4216,0.4247,0.4282,0.4305, 0.4316,0.4322,0.4336,0.4358,0.4382,0.4416,0.4458,0.4483,0.4492,0.4542, 0.4553,0.4636,0.4653,0.4762,0.4768,0.4778,0.4818,0.4829,0.4948,0.4955, 0.4968,0.5012,0.5031,0.5063,0.5066,0.5135,0.5182,0.5236,0.5272,0.5286, 0.5310,0.5311,0.5372,0.5460,0.5475,0.5484,0.5486,0.5540,0.5571,0.5571, 0.5612,0.5666,0.5680,0.5684,0.5694,0.5725,0.5761,0.5809,0.5840,0.5843, 0.5866,0.6012,0.6307,0.6335,0.6345,0.6358,0.6400,0.6479,0.6554,0.6594, 0.6605,0.6609,0.6640,0.6674,0.6675,0.6726,0.6812,0.6816,0.6928,0.7005, 0.7022,0.7035,0.7089,0.7100,0.7128,0.7189,0.7264,0.7265,0.7288,0.7377, 0.7448,0.7528,0.7578,0.7598,0.7602,0.7620,0.7666,0.7685,0.7703,0.7720, 0.7741,0.7796,0.7800,0.7808,0.7817,0.7838,0.7856,0.7878,0.7908,0.7930, 0.7937,0.8006,0.8023,0.8047,0.8055,0.8131,0.8152,0.8234,0.8254,0.8276, 0.8334,0.8353,0.8373,0.8424,0.8459,0.8562,0.8565,0.8710,0.8772,0.8814, 0.8847,0.8854,0.8870,0.8932,0.8935,0.8961,0.8963,0.8974,0.8982,0.9014, 0.9146,0.9152,0.9174,0.9206,0.9341,0.9343,0.9515,0.9534,0.9537,0.9559, 0.9566,0.9580,0.9587,0.9588,0.9625,0.9686,0.9688,0.9761,0.9775,0.9791, 0.9807,0.9811,0.9818,0.9836,0.9873,0.9918,0.9950,0.9967,0.9968, Overall p-value after applying KStest on 269 p-values = 0.404167 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.