RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-01-10_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 15.66 29.9642 0.973395 2 to 25 15.51 13.9914 0.332286 3 to 26 15.40 20.4849 0.749816 4 to 27 15.75 14.0029 0.333105 5 to 28 15.37 20.4561 0.748433 6 to 29 15.62 24.6272 0.896630 7 to 30 15.86 6.6576 0.012436 8 to 31 15.64 32.5741 0.987243 9 to 32 15.56 31.7301 0.983747 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.021820 Tough bday spacings test for dh-ranFile-2017-01-10_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 8 40 76 99 98 65 56 32 17 7 2 (O-E)^2/E 0.1 0.3 0.1 0.0 0.0 2.2 0.3 0.2 0.3 0.0 1.0 Birthday Spacings: Sum(O-E)^2/E= 4.621, p= 0.085 RESULTS OF GCD FOR dh-ranFile-2017-01-10_21:31 Euclid's algorithm: p-value, steps to gcd: 0.287422 p-value, dist. of gcd's: 0.278207 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-01-10_21:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.336 0.589 0.167 0.248 0.732 0.206 0.842 0.573 Bits 8 to 15---> 0.452 0.739 0.991 0.190 0.693 0.971 0.983 0.665 Bits 16 to 23---> 0.928 0.886 0.750 0.216 0.848 0.945 0.581 0.983 Bits 24 to 31---> 0.114 0.068 0.560 0.826 0.905 0.632 0.727 0.688 KS test for the above 32 p values: 0.985 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-01-10_21:31, p-values for 5 runs: 0.3850, 0.7031, 0.0952, 0.1654, 0.7077 Rank test for binary matrices (31x31) for dh-ranFile-2017-01-10_21:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 225 211.4 0.873 0.873 r= 29 5092 5134.0 0.344 1.216 r= 30 23019 23103.0 0.306 1.522 r= 31 11664 11551.5 1.095 2.617 chi-square = 2.617 with df = 3; p-value = 0.546 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2017-01-10_21:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 177 211.4 5.603 5.603 r= 30 5118 5134.0 0.050 5.653 r= 31 23244 23103.0 0.860 6.513 r= 32 11461 11551.5 0.709 7.222 chi-square = 7.222 with df = 3; p-value = 0.935 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2017-01-10_21:31 b-rank test for bits 1 to 8, p=0.97929 b-rank test for bits 2 to 9, p=0.99927 b-rank test for bits 3 to 10, p=0.38141 b-rank test for bits 4 to 11, p=0.54307 b-rank test for bits 5 to 12, p=0.53412 b-rank test for bits 6 to 13, p=0.61212 b-rank test for bits 7 to 14, p=0.37347 b-rank test for bits 8 to 15, p=0.84034 b-rank test for bits 9 to 16, p=0.55651 b-rank test for bits 10 to 17, p=0.75101 b-rank test for bits 11 to 18, p=0.43411 b-rank test for bits 12 to 19, p=0.69422 b-rank test for bits 13 to 20, p=0.74407 b-rank test for bits 14 to 21, p=0.84590 b-rank test for bits 15 to 22, p=0.34960 b-rank test for bits 16 to 23, p=0.60834 b-rank test for bits 17 to 24, p=0.04269 b-rank test for bits 18 to 25, p=0.08040 b-rank test for bits 19 to 26, p=0.07459 b-rank test for bits 20 to 27, p=0.72598 b-rank test for bits 21 to 28, p=0.96908 b-rank test for bits 22 to 29, p=0.31628 b-rank test for bits 23 to 30, p=0.14797 b-rank test for bits 24 to 31, p=0.74007 b-rank test for bits 25 to 32, p=0.77087 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 = 0.342893 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-01-10_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 141835 -0.17 0.431063 2 141634 -0.64 0.260017 3 141674 -0.55 0.291216 4 142329 0.98 0.836590 5 143076 2.73 0.996793 6 141740 -0.40 0.346189 7 141940 0.07 0.528563 8 141583 -0.76 0.222895 9 142969 2.48 0.993354 10 142155 0.57 0.717015 11 141491 -0.98 0.164184 12 142332 0.99 0.838313 13 141740 -0.40 0.346189 14 141425 -1.13 0.128899 15 142144 0.55 0.708255 16 141935 0.06 0.523913 17 142764 2.00 0.977082 18 141562 -0.81 0.208534 19 141995 0.20 0.579324 20 142394 1.13 0.871268 ---------------------------------------------------------------- OPSO test for dh-ranFile-2017-01-10_21:31 Bits used No. missing words z-score p-value 23 to 32 142179 0.9299 0.823788 22 to 31 142264 1.2230 0.889335 21 to 30 141837 -0.2494 0.401520 20 to 29 141722 -0.6460 0.259151 19 to 28 142471 1.9368 0.973615 18 to 27 142249 1.1713 0.879256 17 to 26 142173 0.9092 0.818380 16 to 25 141739 -0.5873 0.278486 15 to 24 141668 -0.8322 0.202656 14 to 23 141596 -1.0804 0.139971 13 to 22 142307 1.3713 0.914856 12 to 21 142752 2.9058 0.998168 11 to 20 142135 0.7782 0.781766 10 to 19 142050 0.4851 0.686186 9 to 18 142115 0.7092 0.760902 8 to 17 141906 -0.0115 0.495419 7 to 16 141741 -0.5804 0.280806 6 to 15 142169 0.8954 0.814717 5 to 14 142106 0.6782 0.751169 4 to 13 142382 1.6299 0.948438 3 to 12 142184 0.9471 0.828216 2 to 11 141959 0.1713 0.567997 1 to 10 141838 -0.2460 0.402855 ----------------------------------------------------------------- OQSO test for dh-ranFile-2017-01-10_21:31 Bits used No. missing words z-score p-value 28 to 32 142340 1.4599 0.927841 27 to 31 141840 -0.2350 0.407098 26 to 30 141851 -0.1977 0.421629 25 to 29 141974 0.2192 0.586761 24 to 28 141888 -0.0723 0.471180 23 to 27 141780 -0.4384 0.330546 22 to 26 142212 1.0260 0.847554 21 to 25 141907 -0.0079 0.496849 20 to 24 142238 1.1141 0.867390 19 to 23 141338 -1.9367 0.026390 18 to 22 142168 0.8768 0.809715 17 to 21 141596 -1.0621 0.144087 16 to 20 142005 0.3243 0.627147 15 to 19 141939 0.1006 0.540057 14 to 18 142103 0.6565 0.744252 13 to 17 142425 1.7480 0.959771 12 to 16 141982 0.2463 0.597290 11 to 15 142039 0.4396 0.669872 10 to 14 142165 0.8667 0.806941 9 to 13 142040 0.4429 0.671099 8 to 12 141691 -0.7401 0.229619 7 to 11 141852 -0.1943 0.422955 6 to 10 142344 1.4735 0.929686 5 to 9 141965 0.1887 0.574841 4 to 8 141529 -1.2893 0.098655 3 to 7 141717 -0.6520 0.257212 2 to 6 141950 0.1379 0.554826 1 to 5 142174 0.8972 0.815190 ----------------------------------------------------------------- DNA test for dh-ranFile-2017-01-10_21:31 Bits used No. missing words z-score p-value 31 to 32 142290 1.1229 0.869264 30 to 31 142229 0.9430 0.827154 29 to 30 141879 -0.0895 0.464355 28 to 29 142154 0.7217 0.764773 27 to 28 142086 0.5212 0.698869 26 to 27 142450 1.5949 0.944632 25 to 26 141694 -0.6352 0.262652 24 to 25 141771 -0.4081 0.341617 23 to 24 142797 2.6185 0.995584 22 to 23 142164 0.7512 0.773746 21 to 22 141564 -1.0187 0.154179 20 to 21 142529 1.8279 0.966220 19 to 20 142361 1.3324 0.908629 18 to 19 142312 1.1878 0.882547 17 to 18 142317 1.2026 0.885428 16 to 17 141576 -0.9833 0.162736 15 to 16 142192 0.8338 0.797813 14 to 15 142176 0.7866 0.784253 13 to 14 141634 -0.8122 0.208343 12 to 13 141936 0.0787 0.531354 11 to 12 141451 -1.3520 0.088187 10 to 11 142352 1.3058 0.904192 9 to 10 142213 0.8958 0.814815 8 to 9 142404 1.4592 0.927745 7 to 8 142333 1.2498 0.894307 6 to 7 142177 0.7896 0.785116 5 to 6 142066 0.4622 0.678014 4 to 5 141692 -0.6411 0.260732 3 to 4 141575 -0.9862 0.162012 2 to 3 141692 -0.6411 0.260732 1 to 2 141268 -1.8918 0.029257 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2017-01-10_21:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2437.62 -0.882 0.188829 Test results for specific bytes for dh-ranFile-2017-01-10_21:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2389.76 -1.559 0.059495 2 to 9 2529.56 0.418 0.662057 3 to 10 2568.19 0.964 0.832573 4 to 11 2697.11 2.787 0.997344 5 to 12 2497.99 -0.028 0.488641 6 to 13 2597.09 1.373 0.915131 7 to 14 2448.75 -0.725 0.234310 8 to 15 2594.85 1.341 0.910105 9 to 16 2671.42 2.424 0.992329 10 to 17 2660.23 2.266 0.988273 11 to 18 2546.17 0.653 0.743099 12 to 19 2557.22 0.809 0.790797 13 to 20 2556.04 0.793 0.785985 14 to 21 2430.77 -0.979 0.163781 15 to 22 2558.17 0.823 0.794626 16 to 23 2499.15 -0.012 0.495184 17 to 24 2554.23 0.767 0.778455 18 to 25 2518.27 0.258 0.601938 19 to 26 2492.03 -0.113 0.455102 20 to 27 2474.83 -0.356 0.360926 21 to 28 2474.37 -0.363 0.358488 22 to 29 2499.19 -0.012 0.495411 23 to 30 2575.80 1.072 0.858145 24 to 31 2458.07 -0.593 0.276603 25 to 32 2431.85 -0.964 0.167587 CDPARK for dh-ranFile-2017-01-10_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 3452 -3.2420 0.000593 3525 0.0913 0.536383 3510 -0.5936 0.276387 3488 -1.5982 0.055002 3516 -0.3196 0.374623 3544 0.9589 0.831196 3493 -1.3699 0.085365 3528 0.2283 0.590298 3532 0.4110 0.659449 3530 0.3196 0.625377 Square side=100, avg. no. parked=3511.80 sample std.=25.94 p-value of the KSTEST for those 10 p-values: 0.253631 Results for the MINIMUM DISTANCE test for dh-ranFile-2017-01-10_21:31 0.8976,0.8219,0.7426,0.1748,0.0893,0.4524,0.6977,0.6442,0.7049,0.0622, The KS test for those 10 p-values: 0.741414 The 3DSPHERES test for dh-ranFile-2017-01-10_21:31 sample no r^3 equiv. uni. 1 4.722 0.145645 2 6.733 0.201036 3 130.082 0.986912 4 4.822 0.148488 5 13.136 0.354587 6 10.191 0.288022 7 14.137 0.375776 8 4.243 0.131894 9 43.314 0.763969 10 1.468 0.047761 11 4.337 0.134591 12 14.988 0.393225 13 40.721 0.742660 14 22.807 0.532435 15 48.173 0.799264 16 80.040 0.930608 17 11.889 0.327193 18 60.096 0.865096 19 43.783 0.767634 20 20.963 0.502799 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.827397 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-01-10_21:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 0.1 -0.6 1.4 -0.1 -0.4 0.7 1.5 0.6 2.3 -0.1 0.6 -0.5 -0.5 -1.7 -0.6 0.6 0.4 2.8 -0.8 0.8 -1.6 0.9 -1.1 -2.2 -0.6 -0.6 -1.1 0.7 0.0 0.5 -0.1 -1.5 1.4 1.5 0.4 1.2 1.8 -0.4 0.4 -0.6 -1.0 -0.1 Chi-square with 42 degrees of freedom:51.325748 z-score=1.017523, p-value=0.846667 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2017-01-10_21:31 Test no p-value 1 0.423036 2 0.838187 3 0.205278 4 0.029466 5 0.131878 6 0.979260 7 0.845511 8 0.939364 9 0.063262 10 0.493390 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.471301 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-01-10_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 66679 0.00 66490 0.47 3 25000.00 25036 0.05 25131 0.69 4 6666.67 6603 0.61 6704 0.21 5 1388.89 1403 0.14 1393 0.01 6 238.10 240 0.02 243 0.10 7 34.72 32 0.21 30 0.64 8 4.96 6 0.22 8 1.86 p=0.02576 p=0.32085 Number of rngs required: 687825, p-value: 0.252 RESULTS OF CRAPS TEST for dh-ranFile-2017-01-10_21:31 No. of wins: Observed Expected 98244 98585.9 z-score=-1.529, pvalue=0.06313 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66730 66666.7 0.060 0.060 2 37441 37654.3 1.209 1.269 3 27136 26954.7 1.219 2.488 4 19135 19313.5 1.649 4.137 5 13866 13851.4 0.015 4.152 6 10007 9943.5 0.405 4.557 7 7101 7145.0 0.271 4.828 8 5211 5139.1 1.007 5.835 9 3723 3699.9 0.145 5.980 10 2714 2666.3 0.853 6.833 11 1939 1923.3 0.128 6.961 12 1396 1388.7 0.038 6.999 13 969 1003.7 1.201 8.199 14 743 726.1 0.391 8.591 15 474 525.8 5.110 13.701 16 391 381.2 0.255 13.955 17 241 276.5 4.567 18.523 18 203 200.8 0.023 18.546 19 155 146.0 0.557 19.103 20 107 106.2 0.006 19.109 21 318 287.1 3.323 22.431 Chisq= 22.43 for 20 degrees of freedom, p= 0.68242 SUMMARY of craptest p-value for no. of wins: 0.063133 p-value for throws/game: 0.682422 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2017-01-10_21:31 No. of wins: Observed Expected 98431 98585.9 z-score=-0.693, pvalue=0.24427 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66615 66666.7 0.040 0.040 2 37747 37654.3 0.228 0.268 3 26851 26954.7 0.399 0.667 4 19292 19313.5 0.024 0.691 5 13917 13851.4 0.310 1.002 6 9962 9943.5 0.034 1.036 7 7221 7145.0 0.808 1.844 8 5022 5139.1 2.667 4.511 9 3686 3699.9 0.052 4.563 10 2634 2666.3 0.391 4.954 11 1987 1923.3 2.108 7.062 12 1399 1388.7 0.076 7.138 13 953 1003.7 2.562 9.700 14 749 726.1 0.720 10.420 15 549 525.8 1.020 11.440 16 390 381.2 0.205 11.646 17 288 276.5 0.475 12.121 18 178 200.8 2.595 14.716 19 145 146.0 0.007 14.722 20 111 106.2 0.216 14.938 21 304 287.1 0.993 15.931 Chisq= 15.93 for 20 degrees of freedom, p= 0.27911 SUMMARY of craptest p-value for no. of wins: 0.244275 p-value for throws/game: 0.279110 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0006,0.0124,0.0218,0.0258,0.0264,0.0293,0.0295,0.0427,0.0478,0.0550, 0.0595,0.0622,0.0631,0.0633,0.0677,0.0746,0.0804,0.0850,0.0854,0.0882, 0.0893,0.0952,0.0987,0.1140,0.1289,0.1319,0.1319,0.1346,0.1400,0.1441, 0.1456,0.1480,0.1485,0.1542,0.1620,0.1627,0.1638,0.1642,0.1654,0.1669, 0.1676,0.1748,0.1888,0.1899,0.2010,0.2027,0.2053,0.2058,0.2083,0.2085, 0.2162,0.2229,0.2296,0.2343,0.2443,0.2476,0.2524,0.2536,0.2572,0.2592, 0.2600,0.2607,0.2607,0.2627,0.2764,0.2766,0.2782,0.2785,0.2791,0.2808, 0.2874,0.2880,0.2912,0.3163,0.3209,0.3272,0.3305,0.3323,0.3331,0.3365, 0.3416,0.3429,0.3462,0.3462,0.3496,0.3546,0.3585,0.3609,0.3735,0.3746, 0.3758,0.3814,0.3850,0.3932,0.4015,0.4029,0.4071,0.4216,0.4230,0.4230, 0.4311,0.4341,0.4522,0.4524,0.4551,0.4644,0.4712,0.4713,0.4886,0.4934, 0.4952,0.4954,0.4954,0.4968,0.5028,0.5239,0.5286,0.5314,0.5324,0.5341, 0.5364,0.5401,0.5431,0.5455,0.5548,0.5565,0.5604,0.5680,0.5734,0.5748, 0.5793,0.5811,0.5868,0.5890,0.5903,0.5973,0.6019,0.6083,0.6121,0.6254, 0.6271,0.6325,0.6442,0.6594,0.6621,0.6647,0.6699,0.6711,0.6780,0.6824, 0.6862,0.6881,0.6929,0.6942,0.6977,0.6989,0.7031,0.7049,0.7077,0.7083, 0.7170,0.7260,0.7272,0.7324,0.7393,0.7401,0.7414,0.7426,0.7427,0.7431, 0.7441,0.7443,0.7484,0.7498,0.7503,0.7510,0.7512,0.7609,0.7640,0.7648, 0.7676,0.7709,0.7737,0.7785,0.7818,0.7843,0.7851,0.7860,0.7908,0.7946, 0.7978,0.7993,0.8069,0.8097,0.8147,0.8148,0.8152,0.8184,0.8219,0.8238, 0.8260,0.8272,0.8274,0.8282,0.8312,0.8326,0.8366,0.8382,0.8383,0.8403, 0.8416,0.8455,0.8459,0.8467,0.8476,0.8485,0.8581,0.8651,0.8674,0.8693, 0.8713,0.8793,0.8825,0.8854,0.8860,0.8893,0.8943,0.8966,0.8976,0.9042, 0.9055,0.9086,0.9101,0.9149,0.9151,0.9277,0.9278,0.9278,0.9297,0.9306, 0.9349,0.9394,0.9446,0.9454,0.9484,0.9598,0.9662,0.9691,0.9705,0.9734, 0.9736,0.9771,0.9793,0.9793,0.9827,0.9830,0.9837,0.9853,0.9869,0.9872, 0.9883,0.9906,0.9923,0.9934,0.9956,0.9968,0.9973,0.9982,0.9993, Overall p-value after applying KStest on 269 p-values = 0.000234 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.