RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-09-19_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 24.4036 0.891123 2 to 25 15.79 16.0569 0.480195 3 to 26 16.05 28.5412 0.961001 4 to 27 15.86 16.1192 0.484599 5 to 28 15.80 11.6280 0.177877 6 to 29 15.55 27.6192 0.950411 7 to 30 15.68 24.2344 0.886796 8 to 31 15.56 20.8283 0.765937 9 to 32 15.73 9.7554 0.086447 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.164567 Tough bday spacings test for dh-ranFile-2016-09-19_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 13 39 82 109 85 70 51 28 10 9 4 (O-E)^2/E 1.6 0.2 1.0 1.3 1.6 0.8 0.0 0.1 1.6 0.9 0.0 Birthday Spacings: Sum(O-E)^2/E= 9.206, p= 0.487 RESULTS OF GCD FOR dh-ranFile-2016-09-19_22:31 Euclid's algorithm: p-value, steps to gcd: 0.969652 p-value, dist. of gcd's: 0.565896 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-09-19_22:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.896 0.445 0.534 0.485 0.712 0.848 0.560 0.740 Bits 8 to 15---> 0.113 0.755 0.667 0.233 0.568 0.587 0.971 0.373 Bits 16 to 23---> 0.556 0.705 0.625 0.929 0.525 0.879 0.214 0.707 Bits 24 to 31---> 0.107 0.948 0.220 0.958 0.698 0.365 0.724 0.351 KS test for the above 32 p values: 0.914 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-09-19_22:31, p-values for 5 runs: 0.4114, 0.4150, 0.7400, 0.2792, 0.3647 Rank test for binary matrices (31x31) for dh-ranFile-2016-09-19_22:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 199 211.4 0.729 0.729 r= 29 5105 5134.0 0.164 0.893 r= 30 23100 23103.0 0.000 0.894 r= 31 11596 11551.5 0.171 1.065 chi-square = 1.065 with df = 3; p-value = 0.214 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-09-19_22:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 198 211.4 0.852 0.852 r= 30 5162 5134.0 0.153 1.004 r= 31 23030 23103.0 0.231 1.235 r= 32 11610 11551.5 0.296 1.531 chi-square = 1.531 with df = 3; p-value = 0.325 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-09-19_22:31 b-rank test for bits 1 to 8, p=0.63369 b-rank test for bits 2 to 9, p=0.16503 b-rank test for bits 3 to 10, p=0.63155 b-rank test for bits 4 to 11, p=0.05194 b-rank test for bits 5 to 12, p=0.44502 b-rank test for bits 6 to 13, p=0.35583 b-rank test for bits 7 to 14, p=0.31481 b-rank test for bits 8 to 15, p=0.05357 b-rank test for bits 9 to 16, p=0.02686 b-rank test for bits 10 to 17, p=0.71814 b-rank test for bits 11 to 18, p=0.02297 b-rank test for bits 12 to 19, p=0.97495 b-rank test for bits 13 to 20, p=0.99155 b-rank test for bits 14 to 21, p=0.62572 b-rank test for bits 15 to 22, p=0.82105 b-rank test for bits 16 to 23, p=0.69990 b-rank test for bits 17 to 24, p=0.27166 b-rank test for bits 18 to 25, p=0.56031 b-rank test for bits 19 to 26, p=0.38672 b-rank test for bits 20 to 27, p=0.68609 b-rank test for bits 21 to 28, p=0.24239 b-rank test for bits 22 to 29, p=0.69886 b-rank test for bits 23 to 30, p=0.03544 b-rank test for bits 24 to 31, p=0.06776 b-rank test for bits 25 to 32, p=0.34629 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 = 0.221161 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-09-19_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 141139 -1.80 0.035943 2 142838 2.17 0.984989 3 142433 1.22 0.889435 4 141246 -1.55 0.060590 5 141263 -1.51 0.065507 6 141761 -0.35 0.364459 7 141131 -1.82 0.034492 8 141808 -0.24 0.406425 9 141885 -0.06 0.477334 10 141949 0.09 0.536924 11 141864 -0.11 0.457826 12 142374 1.09 0.861189 13 142431 1.22 0.888550 14 142140 0.54 0.705039 15 141958 0.11 0.545268 16 142436 1.23 0.890752 17 143065 2.70 0.996535 18 141882 -0.06 0.474543 19 141780 -0.30 0.381260 20 141924 0.03 0.513671 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-09-19_22:31 Bits used No. missing words z-score p-value 23 to 32 141828 -0.2804 0.389567 22 to 31 141961 0.1782 0.570706 21 to 30 141857 -0.1804 0.428400 20 to 29 141874 -0.1218 0.451518 19 to 28 141712 -0.6804 0.248110 18 to 27 142282 1.2851 0.900616 17 to 26 141887 -0.0770 0.469312 16 to 25 141514 -1.3632 0.086409 15 to 24 141896 -0.0460 0.481669 14 to 23 141686 -0.7701 0.220619 13 to 22 141196 -2.4598 0.006952 12 to 21 141396 -1.7701 0.038355 11 to 20 141462 -1.5425 0.061474 10 to 19 141760 -0.5149 0.303301 9 to 18 142052 0.4920 0.688628 8 to 17 141792 -0.4046 0.342891 7 to 16 142327 1.4402 0.925100 6 to 15 141646 -0.9080 0.181930 5 to 14 141544 -1.2598 0.103878 4 to 13 141783 -0.4356 0.331556 3 to 12 141796 -0.3908 0.347975 2 to 11 142427 1.7851 0.962875 1 to 10 142169 0.8954 0.814717 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-09-19_22:31 Bits used No. missing words z-score p-value 28 to 32 141813 -0.3265 0.372007 27 to 31 141718 -0.6486 0.258306 26 to 30 141571 -1.1469 0.125715 25 to 29 141928 0.0633 0.525232 24 to 28 142118 0.7074 0.760327 23 to 27 142036 0.4294 0.666180 22 to 26 141672 -0.8045 0.210552 21 to 25 141969 0.2023 0.580148 20 to 24 141595 -1.0655 0.143319 19 to 23 142212 1.0260 0.847554 18 to 22 141909 -0.0011 0.499554 17 to 21 141875 -0.1164 0.453679 16 to 20 142245 1.1379 0.872411 15 to 19 142030 0.4091 0.658749 14 to 18 141664 -0.8316 0.202810 13 to 17 141632 -0.9401 0.173583 12 to 16 141750 -0.5401 0.294564 11 to 15 142071 0.5480 0.708166 10 to 14 141813 -0.3265 0.372007 9 to 13 141687 -0.7537 0.225526 8 to 12 141975 0.2226 0.588081 7 to 11 141870 -0.1333 0.446969 6 to 10 141783 -0.4282 0.334239 5 to 9 142053 0.4870 0.686877 4 to 8 142484 1.9480 0.974295 3 to 7 142065 0.5277 0.701145 2 to 6 142325 1.4091 0.920590 1 to 5 142408 1.6904 0.954525 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-09-19_22:31 Bits used No. missing words z-score p-value 31 to 32 141813 -0.2842 0.388144 30 to 31 141653 -0.7561 0.224784 29 to 30 142098 0.5565 0.711082 28 to 29 142469 1.6509 0.950625 27 to 28 142163 0.7483 0.772857 26 to 27 141468 -1.3019 0.096482 25 to 26 141191 -2.1190 0.017047 24 to 25 141805 -0.3078 0.379133 23 to 24 142180 0.7984 0.787691 22 to 23 142012 0.3029 0.619002 21 to 22 141432 -1.4081 0.079558 20 to 21 141583 -0.9626 0.167868 19 to 20 142224 0.9282 0.823356 18 to 19 142106 0.5801 0.719092 17 to 18 141967 0.1701 0.567541 16 to 17 141613 -0.8741 0.191024 15 to 16 141835 -0.2193 0.413223 14 to 15 142346 1.2881 0.901147 13 to 14 141991 0.2409 0.595189 12 to 13 141595 -0.9272 0.176904 11 to 12 142100 0.5624 0.713095 10 to 11 141627 -0.8328 0.202470 9 to 10 141714 -0.5762 0.282242 8 to 9 141763 -0.4317 0.332997 7 to 8 141993 0.2468 0.597474 6 to 7 141818 -0.2694 0.393807 5 to 6 141905 -0.0128 0.494905 4 to 5 141787 -0.3609 0.359104 3 to 4 141752 -0.4641 0.321288 2 to 3 142158 0.7335 0.768385 1 to 2 141781 -0.3786 0.352509 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-09-19_22:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2510.66 0.151 0.559925 Test results for specific bytes for dh-ranFile-2016-09-19_22:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2477.81 -0.314 0.376811 2 to 9 2510.89 0.154 0.561223 3 to 10 2562.36 0.882 0.811096 4 to 11 2672.20 2.435 0.992560 5 to 12 2462.06 -0.537 0.295803 6 to 13 2392.67 -1.518 0.064521 7 to 14 2572.57 1.026 0.847610 8 to 15 2433.50 -0.940 0.173493 9 to 16 2504.79 0.068 0.527017 10 to 17 2478.43 -0.305 0.380166 11 to 18 2536.47 0.516 0.697006 12 to 19 2491.23 -0.124 0.450672 13 to 20 2531.54 0.446 0.672214 14 to 21 2542.00 0.594 0.723739 15 to 22 2632.00 1.867 0.969037 16 to 23 2633.70 1.891 0.970677 17 to 24 2474.49 -0.361 0.359160 18 to 25 2535.17 0.497 0.690524 19 to 26 2482.76 -0.244 0.403666 20 to 27 2380.80 -1.686 0.045925 21 to 28 2382.23 -1.665 0.047907 22 to 29 2556.92 0.805 0.789594 23 to 30 2461.03 -0.551 0.290771 24 to 31 2574.64 1.056 0.854432 25 to 32 2503.04 0.043 0.517164 CDPARK for dh-ranFile-2016-09-19_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 3570 2.1461 0.984068 3534 0.5023 0.692266 3505 -0.8219 0.205562 3544 0.9589 0.831196 3504 -0.8676 0.192812 3481 -1.9178 0.027568 3527 0.1826 0.572463 3535 0.5479 0.708135 3553 1.3699 0.914635 3510 -0.5936 0.276387 Square side=100, avg. no. parked=3526.30 sample std.=25.18 p-value of the KSTEST for those 10 p-values: 0.807346 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-09-19_22:31 0.1910,0.5428,0.0535,0.5126,0.0599,0.8692,0.0035,0.8686,0.9860,0.0356, The KS test for those 10 p-values: 0.070833 The 3DSPHERES test for dh-ranFile-2016-09-19_22:31 sample no r^3 equiv. uni. 1 9.162 0.263174 2 69.200 0.900408 3 33.862 0.676562 4 10.922 0.305148 5 23.657 0.545506 6 4.368 0.135498 7 15.329 0.400083 8 11.541 0.319346 9 24.359 0.556016 10 40.163 0.737828 11 24.245 0.554319 12 56.208 0.846431 13 15.711 0.407672 14 5.949 0.179867 15 1.197 0.039107 16 11.832 0.325923 17 9.212 0.264398 18 9.823 0.279238 19 27.543 0.600720 20 14.274 0.378618 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.288237 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-09-19_22:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 0.5 -0.1 -0.1 -0.5 -1.9 -0.1 -1.9 1.1 0.0 -1.2 0.4 -0.5 0.8 -0.3 1.3 -0.3 0.6 0.6 -1.5 -1.8 0.8 1.3 1.2 0.0 1.0 -0.3 -0.5 -0.7 -1.3 0.2 -0.6 0.6 1.3 -1.9 -1.0 -0.7 0.5 -1.2 -0.1 0.1 0.0 -1.1 Chi-square with 42 degrees of freedom:39.497611 z-score=-0.273033, p-value=0.418604 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-09-19_22:31 Test no p-value 1 0.040561 2 0.020481 3 0.597827 4 0.126079 5 0.143351 6 0.906349 7 0.121190 8 0.243038 9 0.477935 10 0.013733 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.006288 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-09-19_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 66548 0.21 66914 0.92 3 25000.00 25012 0.01 24899 0.41 4 6666.67 6749 1.02 6581 1.10 5 1388.89 1420 0.70 1322 3.22 6 238.10 223 0.96 234 0.07 7 34.72 42 1.53 43 1.97 8 4.96 5 0.00 6 0.22 p=0.37921 p=0.75531 Number of rngs required: 688108, p-value: 0.367 RESULTS OF CRAPS TEST for dh-ranFile-2016-09-19_22:31 No. of wins: Observed Expected 98941 98585.9 z-score= 1.588, pvalue=0.94390 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66983 66666.7 1.501 1.501 2 37709 37654.3 0.079 1.580 3 26870 26954.7 0.266 1.847 4 19172 19313.5 1.036 2.883 5 13851 13851.4 0.000 2.883 6 10036 9943.5 0.860 3.743 7 7089 7145.0 0.439 4.182 8 5001 5139.1 3.710 7.892 9 3699 3699.9 0.000 7.892 10 2638 2666.3 0.300 8.192 11 1870 1923.3 1.479 9.671 12 1357 1388.7 0.725 10.396 13 1048 1003.7 1.954 12.350 14 746 726.1 0.543 12.893 15 531 525.8 0.051 12.944 16 385 381.2 0.039 12.983 17 296 276.5 1.369 14.352 18 197 200.8 0.073 14.425 19 144 146.0 0.027 14.452 20 102 106.2 0.167 14.620 21 276 287.1 0.430 15.050 Chisq= 15.05 for 20 degrees of freedom, p= 0.22645 SUMMARY of craptest p-value for no. of wins: 0.943902 p-value for throws/game: 0.226447 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-09-19_22:31 No. of wins: Observed Expected 98651 98585.9 z-score= 0.291, pvalue=0.61461 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66629 66666.7 0.021 0.021 2 37817 37654.3 0.703 0.724 3 27065 26954.7 0.451 1.175 4 19191 19313.5 0.777 1.952 5 13751 13851.4 0.728 2.680 6 10035 9943.5 0.841 3.521 7 7023 7145.0 2.084 5.605 8 5148 5139.1 0.016 5.620 9 3733 3699.9 0.297 5.917 10 2597 2666.3 1.801 7.718 11 1922 1923.3 0.001 7.719 12 1385 1388.7 0.010 7.729 13 988 1003.7 0.246 7.975 14 744 726.1 0.439 8.415 15 528 525.8 0.009 8.423 16 398 381.2 0.745 9.168 17 288 276.5 0.475 9.643 18 213 200.8 0.737 10.381 19 144 146.0 0.027 10.408 20 103 106.2 0.097 10.505 21 298 287.1 0.413 10.918 Chisq= 10.92 for 20 degrees of freedom, p= 0.05167 SUMMARY of craptest p-value for no. of wins: 0.614608 p-value for throws/game: 0.051673 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0035,0.0063,0.0070,0.0137,0.0170,0.0205,0.0230,0.0269,0.0276,0.0345, 0.0354,0.0356,0.0359,0.0384,0.0391,0.0406,0.0459,0.0479,0.0517,0.0519, 0.0535,0.0536,0.0599,0.0606,0.0615,0.0645,0.0655,0.0678,0.0708,0.0796, 0.0864,0.0864,0.0965,0.1039,0.1067,0.1128,0.1212,0.1257,0.1261,0.1355, 0.1433,0.1434,0.1646,0.1650,0.1679,0.1735,0.1736,0.1769,0.1779,0.1799, 0.1819,0.1910,0.1910,0.1928,0.2025,0.2028,0.2056,0.2106,0.2138,0.2145, 0.2199,0.2206,0.2212,0.2248,0.2255,0.2264,0.2334,0.2424,0.2430,0.2481, 0.2583,0.2632,0.2644,0.2717,0.2764,0.2792,0.2792,0.2822,0.2882,0.2908, 0.2946,0.2958,0.3033,0.3051,0.3148,0.3193,0.3213,0.3249,0.3259,0.3316, 0.3330,0.3342,0.3429,0.3463,0.3480,0.3514,0.3525,0.3558,0.3591,0.3592, 0.3645,0.3647,0.3648,0.3671,0.3720,0.3720,0.3725,0.3768,0.3786,0.3791, 0.3792,0.3802,0.3813,0.3867,0.3881,0.3896,0.3938,0.4001,0.4037,0.4064, 0.4077,0.4114,0.4132,0.4150,0.4186,0.4284,0.4448,0.4450,0.4470,0.4507, 0.4515,0.4537,0.4578,0.4693,0.4745,0.4773,0.4779,0.4802,0.4817,0.4846, 0.4853,0.4874,0.4949,0.4996,0.5126,0.5137,0.5172,0.5249,0.5252,0.5270, 0.5337,0.5369,0.5428,0.5453,0.5455,0.5543,0.5556,0.5560,0.5599,0.5601, 0.5603,0.5612,0.5659,0.5675,0.5682,0.5707,0.5725,0.5801,0.5868,0.5881, 0.5952,0.5975,0.5978,0.6007,0.6146,0.6190,0.6247,0.6257,0.6315,0.6337, 0.6587,0.6662,0.6674,0.6722,0.6766,0.6861,0.6869,0.6886,0.6905,0.6923, 0.6970,0.6976,0.6989,0.6999,0.7011,0.7050,0.7050,0.7074,0.7081,0.7082, 0.7111,0.7116,0.7131,0.7181,0.7191,0.7237,0.7245,0.7378,0.7400,0.7401, 0.7549,0.7553,0.7603,0.7659,0.7684,0.7729,0.7877,0.7896,0.8073,0.8111, 0.8147,0.8211,0.8234,0.8312,0.8464,0.8476,0.8476,0.8485,0.8544,0.8612, 0.8686,0.8692,0.8724,0.8794,0.8868,0.8886,0.8894,0.8908,0.8911,0.8957, 0.9004,0.9006,0.9011,0.9063,0.9143,0.9146,0.9206,0.9251,0.9294,0.9439, 0.9479,0.9504,0.9506,0.9545,0.9577,0.9610,0.9629,0.9690,0.9697,0.9707, 0.9710,0.9743,0.9749,0.9841,0.9850,0.9860,0.9915,0.9926,0.9965, Overall p-value after applying KStest on 269 p-values = 0.484616 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.