RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-08_20:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.90 13.3321 0.286316 2 to 25 15.60 41.0601 0.999085 3 to 26 15.54 17.5015 0.579080 4 to 27 15.52 23.0043 0.850888 5 to 28 15.69 26.5307 0.934681 6 to 29 15.76 17.4235 0.573953 7 to 30 15.85 23.4886 0.865992 8 to 31 15.83 13.8682 0.323590 9 to 32 15.95 23.3503 0.861810 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.037242 Tough bday spacings test for dh-ranFile-2018-07-08_20:31: 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 11 36 69 95 100 72 57 32 20 7 1 (O-E)^2/E 0.4 0.0 0.2 0.1 0.1 0.5 0.5 0.2 1.8 0.0 2.3 Birthday Spacings: Sum(O-E)^2/E= 5.962, p= 0.182 RESULTS OF GCD FOR dh-ranFile-2018-07-08_20:31 Euclid's algorithm: p-value, steps to gcd: 0.426836 p-value, dist. of gcd's: 0.897119 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-08_20:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.423 0.323 0.451 0.614 0.385 0.039 0.922 0.765 Bits 8 to 15---> 0.993 0.403 0.356 0.948 0.320 0.679 0.353 0.546 Bits 16 to 23---> 0.050 0.949 0.147 0.719 0.743 0.291 0.785 0.876 Bits 24 to 31---> 0.319 0.053 0.762 0.270 0.893 0.051 0.964 0.741 KS test for the above 32 p values: 0.444 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-08_20:31, p-values for 5 runs: 0.7423, 0.6247, 0.9301, 0.7563, 0.7407 Rank test for binary matrices (31x31) for dh-ranFile-2018-07-08_20:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 216 211.4 0.099 0.099 r= 29 5182 5134.0 0.449 0.548 r= 30 23028 23103.0 0.244 0.792 r= 31 11574 11551.5 0.044 0.835 chi-square = 0.835 with df = 3; p-value = 0.159 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-07-08_20:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 221 211.4 0.434 0.434 r= 30 5141 5134.0 0.010 0.444 r= 31 23101 23103.0 0.000 0.444 r= 32 11537 11551.5 0.018 0.462 chi-square = 0.462 with df = 3; p-value = 0.073 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-07-08_20:31 b-rank test for bits 1 to 8, p=0.38187 b-rank test for bits 2 to 9, p=0.49763 b-rank test for bits 3 to 10, p=0.25981 b-rank test for bits 4 to 11, p=0.18910 b-rank test for bits 5 to 12, p=0.75961 b-rank test for bits 6 to 13, p=0.77501 b-rank test for bits 7 to 14, p=0.95630 b-rank test for bits 8 to 15, p=0.97383 b-rank test for bits 9 to 16, p=0.88849 b-rank test for bits 10 to 17, p=0.99822 b-rank test for bits 11 to 18, p=0.01034 b-rank test for bits 12 to 19, p=0.81086 b-rank test for bits 13 to 20, p=0.91714 b-rank test for bits 14 to 21, p=0.02111 b-rank test for bits 15 to 22, p=0.32586 b-rank test for bits 16 to 23, p=0.70632 b-rank test for bits 17 to 24, p=0.22407 b-rank test for bits 18 to 25, p=0.44270 b-rank test for bits 19 to 26, p=0.71579 b-rank test for bits 20 to 27, p=0.04845 b-rank test for bits 21 to 28, p=0.29840 b-rank test for bits 22 to 29, p=0.35942 b-rank test for bits 23 to 30, p=0.80237 b-rank test for bits 24 to 31, p=0.50783 b-rank test for bits 25 to 32, p=0.82934 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 = 0.414578 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-08_20:31 (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 141822 -0.20 0.419160 2 142060 0.35 0.637593 3 142019 0.26 0.601117 4 141834 -0.18 0.430145 5 141468 -1.03 0.151236 6 142573 1.55 0.939505 7 142847 2.19 0.985768 8 142000 0.21 0.583886 9 141820 -0.21 0.417335 10 142213 0.71 0.760996 11 141674 -0.55 0.291216 12 141289 -1.45 0.073617 13 142602 1.62 0.947210 14 142105 0.46 0.676227 15 141574 -0.78 0.216672 16 141754 -0.36 0.358332 17 141641 -0.63 0.265350 18 141111 -1.87 0.031073 19 142039 0.30 0.619043 20 142219 0.72 0.765322 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-07-08_20:31 Bits used No. missing words z-score p-value 23 to 32 141999 0.3092 0.621418 22 to 31 141827 -0.2839 0.388245 21 to 30 141558 -1.2115 0.112855 20 to 29 141392 -1.7839 0.037220 19 to 28 141534 -1.2942 0.097791 18 to 27 141745 -0.5667 0.285474 17 to 26 142056 0.5058 0.693487 16 to 25 141708 -0.6942 0.243765 15 to 24 141872 -0.1287 0.448788 14 to 23 141598 -1.0736 0.141512 13 to 22 141653 -0.8839 0.188376 12 to 21 141514 -1.3632 0.086409 11 to 20 142022 0.3885 0.651183 10 to 19 142066 0.5402 0.705485 9 to 18 141757 -0.5253 0.299696 8 to 17 142260 1.2092 0.886708 7 to 16 141835 -0.2563 0.398856 6 to 15 142182 0.9402 0.826453 5 to 14 141952 0.1471 0.558488 4 to 13 142547 2.1989 0.986056 3 to 12 142121 0.7299 0.767273 2 to 11 141913 0.0127 0.505049 1 to 10 141038 -3.0046 0.001330 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-07-08_20:31 Bits used No. missing words z-score p-value 28 to 32 142305 1.3413 0.910081 27 to 31 142118 0.7074 0.760327 26 to 30 141690 -0.7435 0.228592 25 to 29 141943 0.1141 0.545435 24 to 28 142176 0.9040 0.816993 23 to 27 142144 0.7955 0.786836 22 to 26 141928 0.0633 0.525232 21 to 25 141451 -1.5537 0.060133 20 to 24 141812 -0.3299 0.370726 19 to 23 141629 -0.9503 0.170987 18 to 22 142184 0.9311 0.824095 17 to 21 141391 -1.7571 0.039455 16 to 20 141796 -0.3842 0.350426 15 to 19 142476 1.9209 0.972629 14 to 18 142336 1.4463 0.925959 13 to 17 141813 -0.3265 0.372007 12 to 16 141936 0.0904 0.536018 11 to 15 141587 -1.0926 0.137275 10 to 14 141775 -0.4554 0.324427 9 to 13 142348 1.4870 0.931495 8 to 12 142222 1.0599 0.855405 7 to 11 141900 -0.0316 0.487385 6 to 10 142186 0.9379 0.825843 5 to 9 141899 -0.0350 0.486033 4 to 8 142146 0.8023 0.788802 3 to 7 141817 -0.3130 0.377147 2 to 6 142238 1.1141 0.867390 1 to 5 141589 -1.0859 0.138770 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-07-08_20:31 Bits used No. missing words z-score p-value 31 to 32 142068 0.4681 0.680127 30 to 31 142844 2.7571 0.997085 29 to 30 141576 -0.9833 0.162736 28 to 29 141748 -0.4759 0.317073 27 to 28 141595 -0.9272 0.176904 26 to 27 142418 1.5005 0.933258 25 to 26 141795 -0.3373 0.367962 24 to 25 141970 0.1790 0.571018 23 to 24 141633 -0.8151 0.207498 22 to 23 142143 0.6893 0.754680 21 to 22 142401 1.4504 0.926520 20 to 21 141816 -0.2753 0.391539 19 to 20 141819 -0.2665 0.394942 18 to 19 141844 -0.1927 0.423592 17 to 18 141764 -0.4287 0.334070 16 to 17 141670 -0.7060 0.240098 15 to 16 142017 0.3176 0.624610 14 to 15 142170 0.7689 0.779035 13 to 14 141907 -0.0069 0.497258 12 to 13 141235 -1.9892 0.023341 11 to 12 141097 -2.3963 0.008282 10 to 11 141609 -0.8859 0.187828 9 to 10 142084 0.5153 0.696811 8 to 9 141849 -0.1780 0.429375 7 to 8 141890 -0.0570 0.477264 6 to 7 142116 0.6096 0.728952 5 to 6 141536 -1.1013 0.135390 4 to 5 141769 -0.4140 0.339454 3 to 4 141834 -0.2222 0.412074 2 to 3 142464 1.6362 0.949101 1 to 2 142070 0.4740 0.682233 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-08_20:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2557.72 0.816 0.792849 Test results for specific bytes for dh-ranFile-2018-07-08_20:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2517.70 0.250 0.598825 2 to 9 2484.14 -0.224 0.411246 3 to 10 2545.93 0.650 0.742009 4 to 11 2544.42 0.628 0.735041 5 to 12 2526.38 0.373 0.645446 6 to 13 2520.89 0.295 0.616158 7 to 14 2449.77 -0.710 0.238750 8 to 15 2523.53 0.333 0.630362 9 to 16 2524.79 0.351 0.637048 10 to 17 2344.73 -2.196 0.014053 11 to 18 2463.74 -0.513 0.304041 12 to 19 2494.43 -0.079 0.468627 13 to 20 2489.67 -0.146 0.441950 14 to 21 2402.65 -1.377 0.084289 15 to 22 2379.71 -1.701 0.044450 16 to 23 2462.78 -0.526 0.299317 17 to 24 2507.54 0.107 0.542483 18 to 25 2615.82 1.638 0.949280 19 to 26 2583.50 1.181 0.881169 20 to 27 2657.55 2.228 0.987064 21 to 28 2643.27 2.026 0.978623 22 to 29 2584.39 1.194 0.883665 23 to 30 2501.98 0.028 0.511177 24 to 31 2538.80 0.549 0.708390 25 to 32 2477.60 -0.317 0.375706 CDPARK for dh-ranFile-2018-07-08_20:31: 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 3476 -2.1461 0.015932 3569 2.1005 0.982156 3507 -0.7306 0.232514 3529 0.2740 0.607947 3505 -0.8219 0.205562 3532 0.4110 0.659449 3499 -1.0959 0.136563 3516 -0.3196 0.374623 3483 -1.8265 0.033889 3547 1.0959 0.863437 Square side=100, avg. no. parked=3516.30 sample std.=27.16 p-value of the KSTEST for those 10 p-values: 0.359014 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-08_20:31 0.3177,0.8173,0.7741,0.3323,0.0442,0.9288,0.1025,0.5550,0.9116,0.9664, The KS test for those 10 p-values: 0.429281 The 3DSPHERES test for dh-ranFile-2018-07-08_20:31 sample no r^3 equiv. uni. 1 34.127 0.679404 2 6.701 0.200168 3 51.840 0.822358 4 41.182 0.746586 5 14.512 0.383524 6 12.493 0.340611 7 14.792 0.389247 8 12.088 0.331646 9 1.854 0.059921 10 50.203 0.812398 11 39.927 0.735764 12 44.065 0.769803 13 54.524 0.837563 14 12.343 0.337309 15 4.511 0.139610 16 57.972 0.855202 17 95.369 0.958372 18 84.204 0.939602 19 2.908 0.092385 20 17.323 0.438665 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.663630 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-08_20:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.1 -0.6 1.5 0.4 0.4 1.2 -0.7 0.9 2.2 -0.8 -1.3 -0.4 -0.4 -0.0 0.9 -1.4 2.0 -1.2 0.5 -0.3 -1.7 1.1 0.0 1.0 -0.0 -0.3 -1.6 0.9 -0.2 0.3 0.4 2.0 0.0 1.7 -1.9 1.9 -1.3 0.9 -0.7 0.1 -1.0 -1.1 Chi-square with 42 degrees of freedom:50.059212 z-score=0.879332, p-value=0.816040 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-07-08_20:31 Test no p-value 1 0.027349 2 0.005173 3 0.049266 4 0.196728 5 0.601697 6 0.020040 7 0.071562 8 0.199754 9 0.814561 10 0.624038 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.002016 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-08_20:31: (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 66596 0.07 66709 0.03 3 25000.00 25095 0.36 24908 0.34 4 6666.67 6683 0.04 6672 0.00 5 1388.89 1343 1.52 1447 2.43 6 238.10 249 0.50 234 0.07 7 34.72 28 1.30 23 3.96 8 4.96 5 0.00 6 0.22 p=0.29528 p=0.68335 Number of rngs required: 688350, p-value: 0.476 RESULTS OF CRAPS TEST for dh-ranFile-2018-07-08_20:31 No. of wins: Observed Expected 98539 98585.9 z-score=-0.210, pvalue=0.41700 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66774 66666.7 0.173 0.173 2 37457 37654.3 1.034 1.207 3 26949 26954.7 0.001 1.208 4 19078 19313.5 2.871 4.079 5 13905 13851.4 0.207 4.286 6 9938 9943.5 0.003 4.289 7 7168 7145.0 0.074 4.363 8 5201 5139.1 0.746 5.109 9 3679 3699.9 0.118 5.227 10 2721 2666.3 1.122 6.349 11 1933 1923.3 0.049 6.398 12 1379 1388.7 0.068 6.466 13 1057 1003.7 2.829 9.295 14 759 726.1 1.487 10.782 15 548 525.8 0.934 11.716 16 395 381.2 0.503 12.219 17 305 276.5 2.929 15.148 18 202 200.8 0.007 15.155 19 150 146.0 0.110 15.266 20 104 106.2 0.046 15.312 21 298 287.1 0.413 15.725 Chisq= 15.72 for 20 degrees of freedom, p= 0.26644 SUMMARY of craptest p-value for no. of wins: 0.416998 p-value for throws/game: 0.266442 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-08_20:31 No. of wins: Observed Expected 98774 98585.9 z-score= 0.841, pvalue=0.79996 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66689 66666.7 0.007 0.007 2 37639 37654.3 0.006 0.014 3 27058 26954.7 0.396 0.409 4 19155 19313.5 1.300 1.709 5 13726 13851.4 1.136 2.845 6 10012 9943.5 0.471 3.316 7 7209 7145.0 0.573 3.889 8 5130 5139.1 0.016 3.905 9 3692 3699.9 0.017 3.922 10 2688 2666.3 0.177 4.099 11 1930 1923.3 0.023 4.122 12 1445 1388.7 2.279 6.401 13 1029 1003.7 0.637 7.038 14 729 726.1 0.011 7.049 15 508 525.8 0.605 7.654 16 356 381.2 1.660 9.314 17 270 276.5 0.155 9.468 18 203 200.8 0.023 9.492 19 159 146.0 1.160 10.652 20 86 106.2 3.847 14.500 21 287 287.1 0.000 14.500 Chisq= 14.50 for 20 degrees of freedom, p= 0.19572 SUMMARY of craptest p-value for no. of wins: 0.799960 p-value for throws/game: 0.195716 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0013,0.0020,0.0052,0.0083,0.0103,0.0141,0.0159,0.0200,0.0211,0.0233, 0.0273,0.0311,0.0339,0.0372,0.0372,0.0392,0.0395,0.0442,0.0445,0.0485, 0.0493,0.0500,0.0509,0.0528,0.0599,0.0601,0.0716,0.0729,0.0736,0.0843, 0.0864,0.0924,0.0978,0.1025,0.1129,0.1354,0.1366,0.1373,0.1388,0.1396, 0.1415,0.1465,0.1512,0.1590,0.1627,0.1710,0.1769,0.1815,0.1878,0.1884, 0.1891,0.1957,0.1967,0.1998,0.2002,0.2056,0.2075,0.2167,0.2241,0.2286, 0.2325,0.2388,0.2401,0.2438,0.2598,0.2653,0.2664,0.2704,0.2855,0.2863, 0.2909,0.2912,0.2953,0.2984,0.2993,0.2997,0.3040,0.3171,0.3177,0.3188, 0.3205,0.3231,0.3236,0.3244,0.3259,0.3316,0.3323,0.3341,0.3373,0.3395, 0.3406,0.3504,0.3534,0.3556,0.3583,0.3590,0.3594,0.3680,0.3707,0.3720, 0.3746,0.3757,0.3771,0.3819,0.3835,0.3851,0.3882,0.3892,0.3915,0.3949, 0.3989,0.4032,0.4112,0.4121,0.4146,0.4170,0.4173,0.4192,0.4232,0.4236, 0.4268,0.4293,0.4294,0.4301,0.4387,0.4420,0.4427,0.4439,0.4488,0.4512, 0.4686,0.4757,0.4773,0.4860,0.4874,0.4973,0.4976,0.5050,0.5078,0.5112, 0.5252,0.5360,0.5425,0.5454,0.5459,0.5550,0.5585,0.5710,0.5740,0.5791, 0.5839,0.5988,0.6011,0.6017,0.6079,0.6138,0.6162,0.6190,0.6214,0.6240, 0.6246,0.6247,0.6304,0.6370,0.6376,0.6454,0.6512,0.6594,0.6636,0.6762, 0.6794,0.6794,0.6801,0.6822,0.6834,0.6935,0.6968,0.7055,0.7063,0.7084, 0.7158,0.7190,0.7290,0.7350,0.7358,0.7407,0.7408,0.7420,0.7423,0.7428, 0.7466,0.7547,0.7563,0.7596,0.7603,0.7610,0.7624,0.7648,0.7653,0.7673, 0.7698,0.7741,0.7750,0.7790,0.7849,0.7868,0.7888,0.7928,0.8000,0.8024, 0.8109,0.8124,0.8146,0.8160,0.8170,0.8173,0.8224,0.8241,0.8258,0.8265, 0.8293,0.8376,0.8509,0.8552,0.8554,0.8618,0.8634,0.8660,0.8674,0.8761, 0.8812,0.8837,0.8867,0.8885,0.8928,0.8971,0.9101,0.9116,0.9171,0.9219, 0.9260,0.9265,0.9288,0.9301,0.9315,0.9333,0.9347,0.9395,0.9396,0.9472, 0.9483,0.9485,0.9491,0.9493,0.9563,0.9584,0.9641,0.9664,0.9726,0.9738, 0.9786,0.9822,0.9858,0.9861,0.9871,0.9931,0.9971,0.9982,0.9991, Overall p-value after applying KStest on 269 p-values = 0.331731 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.