RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-04-03_10:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.98 10.1324 0.102035 2 to 25 15.68 16.9206 0.540239 3 to 26 16.14 19.3218 0.689621 4 to 27 16.03 24.5453 0.894639 5 to 28 15.73 13.1270 0.272354 6 to 29 15.73 21.7949 0.807262 7 to 30 15.67 22.8294 0.845113 8 to 31 15.67 9.9157 0.092892 9 to 32 15.72 15.9277 0.471036 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.954039 Tough bday spacings test for dh-ranFile-2018-04-03_10:31: 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 6 40 77 101 89 71 57 34 17 6 2 (O-E)^2/E 1.1 0.3 0.2 0.1 0.8 0.7 0.5 0.6 0.3 0.1 1.0 Birthday Spacings: Sum(O-E)^2/E= 5.597, p= 0.152 RESULTS OF GCD FOR dh-ranFile-2018-04-03_10:31 Euclid's algorithm: p-value, steps to gcd: 0.884147 p-value, dist. of gcd's: 0.144501 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-04-03_10:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.796 0.813 0.109 0.725 0.741 0.468 0.121 0.335 Bits 8 to 15---> 0.746 0.478 0.994 0.190 0.953 0.782 0.649 0.940 Bits 16 to 23---> 0.019 0.327 0.186 0.389 0.208 1.000 0.393 0.667 Bits 24 to 31---> 0.022 0.510 0.219 0.044 0.141 0.530 0.354 0.798 KS test for the above 32 p values: 0.294 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-04-03_10:31, p-values for 5 runs: 0.2404, 0.4273, 0.0609, 0.1435, 0.1879 Rank test for binary matrices (31x31) for dh-ranFile-2018-04-03_10:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 203 211.4 0.335 0.335 r= 29 5125 5134.0 0.016 0.351 r= 30 22954 23103.0 0.962 1.313 r= 31 11718 11551.5 2.399 3.712 chi-square = 3.712 with df = 3; p-value = 0.706 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-04-03_10:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 204 211.4 0.260 0.260 r= 30 5133 5134.0 0.000 0.260 r= 31 23244 23103.0 0.860 1.120 r= 32 11419 11551.5 1.520 2.641 chi-square = 2.641 with df = 3; p-value = 0.550 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-04-03_10:31 b-rank test for bits 1 to 8, p=0.38642 b-rank test for bits 2 to 9, p=0.95447 b-rank test for bits 3 to 10, p=0.17238 b-rank test for bits 4 to 11, p=0.66160 b-rank test for bits 5 to 12, p=0.62169 b-rank test for bits 6 to 13, p=0.42331 b-rank test for bits 7 to 14, p=0.91297 b-rank test for bits 8 to 15, p=0.48067 b-rank test for bits 9 to 16, p=0.75484 b-rank test for bits 10 to 17, p=0.36051 b-rank test for bits 11 to 18, p=0.80748 b-rank test for bits 12 to 19, p=0.77083 b-rank test for bits 13 to 20, p=0.28017 b-rank test for bits 14 to 21, p=0.99402 b-rank test for bits 15 to 22, p=0.70157 b-rank test for bits 16 to 23, p=0.76624 b-rank test for bits 17 to 24, p=0.91989 b-rank test for bits 18 to 25, p=0.68019 b-rank test for bits 19 to 26, p=0.47648 b-rank test for bits 20 to 27, p=0.00949 b-rank test for bits 21 to 28, p=0.13190 b-rank test for bits 22 to 29, p=0.52999 b-rank test for bits 23 to 30, p=0.03157 b-rank test for bits 24 to 31, p=0.10823 b-rank test for bits 25 to 32, p=0.00861 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 = 0.718787 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-04-03_10:31 (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 142295 0.90 0.816232 2 142049 0.33 0.627913 3 140838 -2.50 0.006155 4 141591 -0.74 0.228510 5 142061 0.35 0.638469 6 141362 -1.28 0.100482 7 142061 0.35 0.638469 8 141461 -1.05 0.147435 9 141865 -0.10 0.458753 10 142149 0.56 0.712252 11 141931 0.05 0.520190 12 141801 -0.25 0.400093 13 141852 -0.13 0.446722 14 142444 1.25 0.894209 15 141961 0.12 0.548045 16 142127 0.51 0.694475 17 141277 -1.48 0.069783 18 141656 -0.59 0.276961 19 140972 -2.19 0.014261 20 141496 -0.97 0.167091 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-04-03_10:31 Bits used No. missing words z-score p-value 23 to 32 141659 -0.8632 0.194012 22 to 31 141785 -0.4287 0.334062 21 to 30 141816 -0.3218 0.373792 20 to 29 141389 -1.7942 0.036387 19 to 28 142291 1.3161 0.905930 18 to 27 141708 -0.6942 0.243765 17 to 26 142055 0.5023 0.692275 16 to 25 141880 -0.1011 0.459721 15 to 24 142000 0.3127 0.622729 14 to 23 141978 0.2368 0.593591 13 to 22 142462 1.9058 0.971659 12 to 21 141805 -0.3598 0.359514 11 to 20 142101 0.6609 0.745672 10 to 19 141912 0.0092 0.503673 9 to 18 141861 -0.1667 0.433821 8 to 17 142185 0.9506 0.829093 7 to 16 142148 0.8230 0.794746 6 to 15 141856 -0.1839 0.427047 5 to 14 141966 0.1954 0.577466 4 to 13 141788 -0.4184 0.337835 3 to 12 141989 0.2747 0.608236 2 to 11 142218 1.0644 0.856422 1 to 10 142470 1.9333 0.973403 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-04-03_10:31 Bits used No. missing words z-score p-value 28 to 32 141960 0.1718 0.568188 27 to 31 141957 0.1616 0.564187 26 to 30 141807 -0.3469 0.364340 25 to 29 141907 -0.0079 0.496849 24 to 28 141814 -0.3232 0.373290 23 to 27 141999 0.3040 0.619423 22 to 26 142322 1.3989 0.919076 21 to 25 142014 0.3548 0.638635 20 to 24 141789 -0.4079 0.341674 19 to 23 142139 0.7785 0.781875 18 to 22 142117 0.7040 0.759273 17 to 21 141897 -0.0418 0.483330 16 to 20 141935 0.0870 0.534671 15 to 19 141942 0.1107 0.544091 14 to 18 141758 -0.5130 0.303982 13 to 17 141960 0.1718 0.568188 12 to 16 142185 0.9345 0.824970 11 to 15 141954 0.1514 0.560179 10 to 14 142058 0.5040 0.692857 9 to 13 142064 0.5243 0.699967 8 to 12 142003 0.3175 0.624578 7 to 11 142300 1.3243 0.907299 6 to 10 141486 -1.4350 0.075641 5 to 9 142149 0.8124 0.791731 4 to 8 142021 0.3785 0.647486 3 to 7 141970 0.2057 0.581472 2 to 6 141634 -0.9333 0.175327 1 to 5 141806 -0.3503 0.363068 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-04-03_10:31 Bits used No. missing words z-score p-value 31 to 32 141377 -1.5703 0.058173 30 to 31 142295 1.1377 0.872371 29 to 30 141444 -1.3727 0.084930 28 to 29 142017 0.3176 0.624610 27 to 28 142053 0.4238 0.664146 26 to 27 142152 0.7158 0.762955 25 to 26 142097 0.5536 0.710073 24 to 25 141858 -0.1514 0.439824 23 to 24 142235 0.9607 0.831643 22 to 23 142014 0.3088 0.621248 21 to 22 142516 1.7896 0.963240 20 to 21 141976 0.1967 0.577956 19 to 20 142107 0.5831 0.720086 18 to 19 141654 -0.7532 0.225669 17 to 18 142281 1.0964 0.863542 16 to 17 142071 0.4769 0.683284 15 to 16 141872 -0.1101 0.456158 14 to 15 141382 -1.5555 0.059908 13 to 14 142409 1.4740 0.929753 12 to 13 142062 0.4504 0.673772 11 to 12 141363 -1.6116 0.053525 10 to 11 142108 0.5860 0.721078 9 to 10 142577 1.9695 0.975554 8 to 9 141512 -1.1721 0.120586 7 to 8 141763 -0.4317 0.332997 6 to 7 142282 1.0993 0.864186 5 to 6 142529 1.8279 0.966220 4 to 5 141946 0.1082 0.543070 3 to 4 141339 -1.6824 0.046247 2 to 3 141403 -1.4936 0.067640 1 to 2 141833 -0.2252 0.410927 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-04-03_10:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2474.94 -0.354 0.361500 Test results for specific bytes for dh-ranFile-2018-04-03_10:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2400.41 -1.408 0.079504 2 to 9 2433.41 -0.942 0.173177 3 to 10 2526.28 0.372 0.644917 4 to 11 2550.54 0.715 0.762623 5 to 12 2568.61 0.970 0.834054 6 to 13 2456.46 -0.616 0.269007 7 to 14 2547.33 0.669 0.748351 8 to 15 2507.73 0.109 0.543520 9 to 16 2467.82 -0.455 0.324521 10 to 17 2474.20 -0.365 0.357625 11 to 18 2465.42 -0.489 0.312408 12 to 19 2543.09 0.609 0.728883 13 to 20 2441.74 -0.824 0.204978 14 to 21 2469.43 -0.432 0.332746 15 to 22 2439.94 -0.849 0.197832 16 to 23 2519.36 0.274 0.607888 17 to 24 2393.41 -1.507 0.065848 18 to 25 2566.49 0.940 0.826481 19 to 26 2427.28 -1.028 0.151869 20 to 27 2468.52 -0.445 0.328087 21 to 28 2507.10 0.100 0.539972 22 to 29 2574.28 1.050 0.853246 23 to 30 2503.74 0.053 0.521070 24 to 31 2619.07 1.684 0.953906 25 to 32 2480.39 -0.277 0.390771 CDPARK for dh-ranFile-2018-04-03_10:31: 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 3550 1.2329 0.891189 3525 0.0913 0.536383 3489 -1.5525 0.060270 3546 1.0502 0.853193 3531 0.3653 0.642555 3493 -1.3699 0.085365 3539 0.7306 0.767486 3558 1.5982 0.944998 3500 -1.0502 0.146807 3525 0.0913 0.536383 Square side=100, avg. no. parked=3525.60 sample std.=23.08 p-value of the KSTEST for those 10 p-values: 0.684733 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-04-03_10:31 0.5090,0.8536,0.7832,0.4456,0.6750,0.8960,0.5948,0.4955,0.6075,0.2315, The KS test for those 10 p-values: 0.257356 The 3DSPHERES test for dh-ranFile-2018-04-03_10:31 sample no r^3 equiv. uni. 1 29.137 0.621379 2 30.011 0.632260 3 14.871 0.390865 4 18.989 0.468978 5 10.433 0.293725 6 6.281 0.188900 7 19.188 0.472495 8 15.446 0.402429 9 37.224 0.710847 10 58.941 0.859801 11 5.299 0.161909 12 6.037 0.182288 13 12.118 0.332319 14 36.082 0.699626 15 45.169 0.778123 16 73.506 0.913723 17 5.373 0.163971 18 36.589 0.704660 19 39.607 0.732930 20 73.317 0.913178 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.663176 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-04-03_10:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 -0.7 -0.6 0.8 0.8 -1.7 -1.3 0.0 -0.8 0.0 0.8 0.7 -0.1 -0.9 -1.0 1.0 1.4 1.4 0.5 -0.2 -1.0 0.7 -1.5 -0.3 0.6 -0.2 -1.3 0.7 -1.3 -1.1 -1.1 0.2 0.2 -0.5 0.1 0.4 0.5 0.8 1.3 0.4 0.1 -1.0 -0.1 Chi-square with 42 degrees of freedom:31.359296 z-score=-1.160996, p-value=0.114639 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-04-03_10:31 Test no p-value 1 0.290908 2 0.029234 3 0.348761 4 0.078914 5 0.121228 6 0.145819 7 0.712506 8 0.042304 9 0.487063 10 0.113610 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.004286 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-04-03_10:31: (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 67000 1.67 66613 0.04 3 25000.00 24707 3.43 25104 0.43 4 6666.67 6634 0.16 6661 0.00 5 1388.89 1376 0.12 1373 0.18 6 238.10 245 0.20 211 3.08 7 34.72 33 0.09 33 0.09 8 4.96 4 0.19 4 0.19 p=0.55998 p=0.32561 Number of rngs required: 688807, p-value: 0.679 RESULTS OF CRAPS TEST for dh-ranFile-2018-04-03_10:31 No. of wins: Observed Expected 98592 98585.9 z-score= 0.027, pvalue=0.51096 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66840 66666.7 0.451 0.451 2 37494 37654.3 0.683 1.133 3 26909 26954.7 0.078 1.211 4 19424 19313.5 0.633 1.844 5 13928 13851.4 0.423 2.267 6 9904 9943.5 0.157 2.424 7 7189 7145.0 0.271 2.695 8 5064 5139.1 1.097 3.791 9 3719 3699.9 0.099 3.890 10 2699 2666.3 0.401 4.292 11 1887 1923.3 0.686 4.978 12 1349 1388.7 1.137 6.115 13 1002 1003.7 0.003 6.118 14 749 726.1 0.720 6.837 15 513 525.8 0.313 7.151 16 340 381.2 4.443 11.594 17 242 276.5 4.314 15.908 18 185 200.8 1.248 17.155 19 150 146.0 0.110 17.266 20 110 106.2 0.135 17.401 21 303 287.1 0.879 18.280 Chisq= 18.28 for 20 degrees of freedom, p= 0.43100 SUMMARY of craptest p-value for no. of wins: 0.510957 p-value for throws/game: 0.431005 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-04-03_10:31 No. of wins: Observed Expected 98528 98585.9 z-score=-0.259, pvalue=0.39790 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66701 66666.7 0.018 0.018 2 37647 37654.3 0.001 0.019 3 26939 26954.7 0.009 0.028 4 19294 19313.5 0.020 0.048 5 13661 13851.4 2.618 2.666 6 10025 9943.5 0.667 3.333 7 7307 7145.0 3.672 7.005 8 5189 5139.1 0.485 7.490 9 3654 3699.9 0.569 8.058 10 2674 2666.3 0.022 8.081 11 1924 1923.3 0.000 8.081 12 1445 1388.7 2.279 10.360 13 982 1003.7 0.470 10.830 14 717 726.1 0.115 10.945 15 506 525.8 0.748 11.693 16 385 381.2 0.039 11.732 17 273 276.5 0.045 11.777 18 182 200.8 1.765 13.543 19 134 146.0 0.984 14.527 20 101 106.2 0.256 14.783 21 260 287.1 2.561 17.343 Chisq= 17.34 for 20 degrees of freedom, p= 0.36942 SUMMARY of craptest p-value for no. of wins: 0.397904 p-value for throws/game: 0.369422 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0043,0.0062,0.0086,0.0095,0.0143,0.0189,0.0218,0.0292,0.0316,0.0364, 0.0423,0.0445,0.0462,0.0535,0.0582,0.0599,0.0603,0.0609,0.0658,0.0676, 0.0698,0.0756,0.0789,0.0795,0.0849,0.0854,0.0929,0.1005,0.1020,0.1082, 0.1093,0.1136,0.1146,0.1206,0.1210,0.1212,0.1319,0.1415,0.1435,0.1445, 0.1458,0.1468,0.1474,0.1519,0.1521,0.1619,0.1640,0.1671,0.1724,0.1732, 0.1753,0.1823,0.1860,0.1879,0.1889,0.1902,0.1940,0.1978,0.2050,0.2083, 0.2189,0.2257,0.2285,0.2315,0.2404,0.2438,0.2574,0.2690,0.2724,0.2770, 0.2802,0.2909,0.2937,0.2943,0.3040,0.3124,0.3245,0.3256,0.3274,0.3281, 0.3323,0.3327,0.3330,0.3341,0.3352,0.3378,0.3417,0.3488,0.3541,0.3576, 0.3595,0.3605,0.3615,0.3631,0.3643,0.3694,0.3733,0.3738,0.3864,0.3893, 0.3908,0.3909,0.3926,0.3979,0.4001,0.4024,0.4109,0.4233,0.4270,0.4273, 0.4310,0.4338,0.4398,0.4456,0.4467,0.4562,0.4588,0.4597,0.4677,0.4690, 0.4710,0.4725,0.4765,0.4775,0.4807,0.4833,0.4871,0.4955,0.4968,0.5037, 0.5090,0.5097,0.5110,0.5202,0.5211,0.5295,0.5300,0.5347,0.5364,0.5364, 0.5400,0.5402,0.5431,0.5435,0.5441,0.5480,0.5496,0.5600,0.5602,0.5642, 0.5682,0.5682,0.5775,0.5780,0.5815,0.5936,0.5948,0.6075,0.6079,0.6082, 0.6194,0.6212,0.6214,0.6217,0.6227,0.6246,0.6246,0.6279,0.6323,0.6385, 0.6385,0.6386,0.6426,0.6449,0.6475,0.6491,0.6616,0.6632,0.6641,0.6671, 0.6738,0.6750,0.6792,0.6802,0.6833,0.6847,0.6896,0.6923,0.6929,0.6945, 0.6996,0.7000,0.7016,0.7047,0.7057,0.7101,0.7108,0.7123,0.7125,0.7188, 0.7201,0.7211,0.7255,0.7289,0.7329,0.7409,0.7457,0.7459,0.7484,0.7548, 0.7593,0.7626,0.7630,0.7662,0.7675,0.7708,0.7781,0.7817,0.7819,0.7832, 0.7917,0.7947,0.7959,0.7984,0.8073,0.8075,0.8131,0.8162,0.8250,0.8265, 0.8291,0.8316,0.8341,0.8451,0.8532,0.8532,0.8536,0.8564,0.8598,0.8635, 0.8642,0.8724,0.8841,0.8912,0.8942,0.8946,0.8960,0.9059,0.9073,0.9130, 0.9132,0.9137,0.9191,0.9199,0.9298,0.9398,0.9450,0.9529,0.9539,0.9540, 0.9545,0.9632,0.9662,0.9717,0.9734,0.9756,0.9940,0.9944,0.9998, Overall p-value after applying KStest on 269 p-values = 0.717392 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.