RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-14_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 15.81 13.2295 0.279308 2 to 25 16.03 16.7796 0.530609 3 to 26 15.73 13.4373 0.293541 4 to 27 15.77 17.5878 0.584723 5 to 28 15.98 15.0350 0.407041 6 to 29 15.62 21.0676 0.776718 7 to 30 15.78 20.4577 0.748512 8 to 31 15.92 7.2230 0.019527 9 to 32 15.80 16.1926 0.489772 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.680622 Tough bday spacings test for dh-ranFile-2018-06-14_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 35 75 82 108 77 64 23 13 3 9 (O-E)^2/E 0.4 0.1 0.0 2.5 1.1 0.0 2.7 1.5 0.2 2.0 6.0 Birthday Spacings: Sum(O-E)^2/E= 16.569, p= 0.916 RESULTS OF GCD FOR dh-ranFile-2018-06-14_20:31 Euclid's algorithm: p-value, steps to gcd: 0.429104 p-value, dist. of gcd's: 0.270182 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-14_20:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.160 0.138 0.552 0.394 0.001 0.260 0.328 0.117 Bits 8 to 15---> 0.668 0.409 0.118 0.502 0.633 0.598 0.079 0.588 Bits 16 to 23---> 0.673 0.131 0.586 0.769 0.724 0.918 0.504 0.812 Bits 24 to 31---> 0.071 0.378 0.374 0.090 0.484 0.656 0.822 0.871 KS test for the above 32 p values: 0.621 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-14_20:31, p-values for 5 runs: 0.5432, 0.3221, 0.0017, 0.5904, 0.6135 Rank test for binary matrices (31x31) for dh-ranFile-2018-06-14_20:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 200 211.4 0.617 0.617 r= 29 5101 5134.0 0.212 0.829 r= 30 23030 23103.0 0.231 1.060 r= 31 11669 11551.5 1.195 2.255 chi-square = 2.255 with df = 3; p-value = 0.479 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-06-14_20:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 204 211.4 0.260 0.260 r= 30 5123 5134.0 0.024 0.284 r= 31 23177 23103.0 0.237 0.521 r= 32 11496 11551.5 0.267 0.787 chi-square = 0.787 with df = 3; p-value = 0.148 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-06-14_20:31 b-rank test for bits 1 to 8, p=0.15295 b-rank test for bits 2 to 9, p=0.23367 b-rank test for bits 3 to 10, p=0.52025 b-rank test for bits 4 to 11, p=0.99023 b-rank test for bits 5 to 12, p=0.60942 b-rank test for bits 6 to 13, p=0.73037 b-rank test for bits 7 to 14, p=0.91142 b-rank test for bits 8 to 15, p=0.16711 b-rank test for bits 9 to 16, p=0.65919 b-rank test for bits 10 to 17, p=0.19330 b-rank test for bits 11 to 18, p=0.80748 b-rank test for bits 12 to 19, p=0.44149 b-rank test for bits 13 to 20, p=0.54329 b-rank test for bits 14 to 21, p=0.86306 b-rank test for bits 15 to 22, p=0.04649 b-rank test for bits 16 to 23, p=0.59142 b-rank test for bits 17 to 24, p=0.82171 b-rank test for bits 18 to 25, p=0.86377 b-rank test for bits 19 to 26, p=0.99018 b-rank test for bits 20 to 27, p=0.45459 b-rank test for bits 21 to 28, p=0.97339 b-rank test for bits 22 to 29, p=0.80761 b-rank test for bits 23 to 30, p=0.71081 b-rank test for bits 24 to 31, p=0.75980 b-rank test for bits 25 to 32, p=0.39712 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 = 0.085384 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-14_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 141843 -0.15 0.438420 2 142329 0.98 0.836590 3 141658 -0.59 0.278528 4 142330 0.98 0.837165 5 141924 0.03 0.513671 6 142325 0.97 0.834274 7 142067 0.37 0.643708 8 141987 0.18 0.572001 9 141752 -0.37 0.356588 10 142058 0.35 0.635840 11 141425 -1.13 0.128899 12 141601 -0.72 0.235640 13 142193 0.66 0.746264 14 142291 0.89 0.813737 15 141669 -0.56 0.287222 16 142479 1.33 0.908406 17 141783 -0.30 0.383935 18 141946 0.09 0.534139 19 141374 -1.25 0.105509 20 142831 2.15 0.984358 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-06-14_20:31 Bits used No. missing words z-score p-value 23 to 32 142030 0.4161 0.661333 22 to 31 142478 1.9609 0.975056 21 to 30 141875 -0.1184 0.452884 20 to 29 141856 -0.1839 0.427047 19 to 28 141439 -1.6218 0.052420 18 to 27 142449 1.8609 0.968623 17 to 26 142244 1.1540 0.875757 16 to 25 142471 1.9368 0.973615 15 to 24 142023 0.3920 0.652458 14 to 23 141714 -0.6736 0.250298 13 to 22 141962 0.1816 0.572060 12 to 21 141990 0.2782 0.609560 11 to 20 141472 -1.5080 0.065773 10 to 19 141544 -1.2598 0.103878 9 to 18 141378 -1.8322 0.033463 8 to 17 141695 -0.7391 0.229933 7 to 16 141513 -1.3667 0.085867 6 to 15 142104 0.6713 0.748978 5 to 14 141886 -0.0804 0.467940 4 to 13 141867 -0.1460 0.441974 3 to 12 141908 -0.0046 0.498170 2 to 11 142119 0.7230 0.765160 1 to 10 142248 1.1678 0.878562 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-06-14_20:31 Bits used No. missing words z-score p-value 28 to 32 141971 0.2091 0.582796 27 to 31 141816 -0.3164 0.375860 26 to 30 142108 0.6735 0.749672 25 to 29 142118 0.7074 0.760327 24 to 28 141267 -2.1774 0.014726 23 to 27 142256 1.1752 0.880033 22 to 26 142403 1.6735 0.952881 21 to 25 141777 -0.4486 0.326869 20 to 24 142268 1.2158 0.887975 19 to 23 142016 0.3616 0.641172 18 to 22 141581 -1.1130 0.132858 17 to 21 141989 0.2701 0.606446 16 to 20 141025 -2.9977 0.001360 15 to 19 141889 -0.0689 0.472529 14 to 18 141741 -0.5706 0.284132 13 to 17 142424 1.7446 0.959477 12 to 16 142268 1.2158 0.887975 11 to 15 142267 1.2124 0.887328 10 to 14 141917 0.0260 0.510371 9 to 13 141689 -0.7469 0.227568 8 to 12 141797 -0.3808 0.351683 7 to 11 141510 -1.3537 0.087922 6 to 10 141885 -0.0825 0.467135 5 to 9 142008 0.3345 0.630989 4 to 8 141914 0.0158 0.506315 3 to 7 141825 -0.2859 0.387491 2 to 6 141851 -0.1977 0.421629 1 to 5 141594 -1.0689 0.142554 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-06-14_20:31 Bits used No. missing words z-score p-value 31 to 32 141778 -0.3874 0.349229 30 to 31 142512 1.7778 0.962281 29 to 30 142063 0.4533 0.674835 28 to 29 142184 0.8102 0.791098 27 to 28 142179 0.7955 0.786835 26 to 27 141798 -0.3284 0.371302 25 to 26 141952 0.1259 0.550083 24 to 25 141695 -0.6322 0.263614 23 to 24 141956 0.1377 0.554749 22 to 23 141784 -0.3697 0.355801 21 to 22 141834 -0.2222 0.412074 20 to 21 141651 -0.7620 0.223019 19 to 20 141677 -0.6853 0.246565 18 to 19 142069 0.4710 0.681181 17 to 18 141690 -0.6470 0.258819 16 to 17 141754 -0.4582 0.323404 15 to 16 141984 0.2203 0.587168 14 to 15 142430 1.5359 0.937719 13 to 14 141929 0.0580 0.523135 12 to 13 142189 0.8250 0.795310 11 to 12 142033 0.3648 0.642373 10 to 11 141517 -1.1573 0.123572 9 to 10 141549 -1.0629 0.143909 8 to 9 141772 -0.4051 0.342701 7 to 8 141860 -0.1455 0.442152 6 to 7 141638 -0.8004 0.211744 5 to 6 142449 1.5919 0.944302 4 to 5 141597 -0.9213 0.178440 3 to 4 141809 -0.2960 0.383631 2 to 3 141871 -0.1131 0.454988 1 to 2 141779 -0.3845 0.350321 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-14_20:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2515.18 0.215 0.584987 Test results for specific bytes for dh-ranFile-2018-06-14_20:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2525.45 0.360 0.640521 2 to 9 2488.97 -0.156 0.438017 3 to 10 2541.76 0.591 0.722591 4 to 11 2601.56 1.436 0.924548 5 to 12 2502.68 0.038 0.515112 6 to 13 2587.87 1.243 0.893007 7 to 14 2600.39 1.420 0.922161 8 to 15 2479.86 -0.285 0.387874 9 to 16 2589.36 1.264 0.896842 10 to 17 2373.64 -1.787 0.036966 11 to 18 2447.35 -0.745 0.228261 12 to 19 2619.16 1.685 0.954018 13 to 20 2463.63 -0.514 0.303520 14 to 21 2518.82 0.266 0.604931 15 to 22 2514.31 0.202 0.580184 16 to 23 2493.07 -0.098 0.460977 17 to 24 2455.47 -0.630 0.264432 18 to 25 2471.66 -0.401 0.344289 19 to 26 2491.27 -0.123 0.450886 20 to 27 2527.57 0.390 0.651675 21 to 28 2557.58 0.814 0.792269 22 to 29 2522.72 0.321 0.625993 23 to 30 2557.38 0.812 0.791467 24 to 31 2352.89 -2.080 0.018744 25 to 32 2625.45 1.774 0.961982 CDPARK for dh-ranFile-2018-06-14_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 3540 0.7763 0.781201 3495 -1.2785 0.100530 3507 -0.7306 0.232514 3501 -1.0046 0.157553 3502 -0.9589 0.168804 3490 -1.5068 0.065925 3484 -1.7808 0.037471 3543 0.9132 0.819442 3550 1.2329 0.891189 3506 -0.7763 0.218799 Square side=100, avg. no. parked=3511.80 sample std.=22.42 p-value of the KSTEST for those 10 p-values: 0.058763 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-14_20:31 0.8323,0.0744,0.3119,0.2560,0.1343,0.8525,0.5398,0.8289,0.8077,0.5966, The KS test for those 10 p-values: 0.836121 The 3DSPHERES test for dh-ranFile-2018-06-14_20:31 sample no r^3 equiv. uni. 1 5.519 0.168034 2 38.747 0.725161 3 161.237 0.995367 4 7.094 0.210590 5 51.833 0.822319 6 39.672 0.733505 7 2.688 0.085701 8 35.143 0.690081 9 16.913 0.430930 10 36.279 0.701592 11 19.195 0.472624 12 0.705 0.023240 13 3.251 0.102711 14 55.070 0.840494 15 18.348 0.457522 16 32.375 0.660117 17 112.297 0.976322 18 28.607 0.614634 19 85.837 0.942803 20 0.109 0.003612 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.465984 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-14_20:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.5 1.1 -0.4 0.1 0.9 1.2 -0.0 -1.5 0.0 0.2 -1.0 -0.7 -0.8 -0.3 -0.5 1.2 -0.1 -0.4 0.8 1.9 0.0 0.1 -0.6 -0.8 1.0 -1.2 1.0 1.5 -0.2 -0.6 -0.8 -0.2 -1.1 0.9 -1.2 -0.5 -1.0 0.1 1.0 1.6 0.0 -0.1 Chi-square with 42 degrees of freedom:30.711881 z-score=-1.231635, p-value=0.098742 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-06-14_20:31 Test no p-value 1 0.509168 2 0.049219 3 0.040465 4 0.025595 5 0.017279 6 0.869993 7 0.822032 8 0.122389 9 0.996872 10 0.018477 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.002885 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-14_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 66675 0.00 66510 0.37 3 25000.00 25086 0.30 25044 0.08 4 6666.67 6574 1.29 6722 0.46 5 1388.89 1372 0.21 1469 4.62 6 238.10 247 0.33 223 0.96 7 34.72 41 1.14 27 1.72 8 4.96 4 0.19 4 0.19 p=0.24875 p=0.78876 Number of rngs required: 688357, p-value: 0.479 RESULTS OF CRAPS TEST for dh-ranFile-2018-06-14_20:31 No. of wins: Observed Expected 98850 98585.9 z-score= 1.181, pvalue=0.88128 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67008 66666.7 1.748 1.748 2 37466 37654.3 0.942 2.689 3 26712 26954.7 2.186 4.875 4 19354 19313.5 0.085 4.960 5 14124 13851.4 5.364 10.324 6 9860 9943.5 0.702 11.026 7 7036 7145.0 1.664 12.690 8 5103 5139.1 0.253 12.943 9 3733 3699.9 0.297 13.240 10 2663 2666.3 0.004 13.244 11 1892 1923.3 0.510 13.754 12 1344 1388.7 1.441 15.196 13 1037 1003.7 1.104 16.300 14 722 726.1 0.024 16.323 15 563 525.8 2.627 18.950 16 371 381.2 0.270 19.220 17 281 276.5 0.072 19.292 18 213 200.8 0.737 20.030 19 155 146.0 0.557 20.586 20 106 106.2 0.000 20.587 21 257 287.1 3.159 23.745 Chisq= 23.75 for 20 degrees of freedom, p= 0.74630 SUMMARY of craptest p-value for no. of wins: 0.881277 p-value for throws/game: 0.746302 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-14_20:31 No. of wins: Observed Expected 98482 98585.9 z-score=-0.465, pvalue=0.32114 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66527 66666.7 0.293 0.293 2 37709 37654.3 0.079 0.372 3 27009 26954.7 0.109 0.481 4 19270 19313.5 0.098 0.579 5 14055 13851.4 2.992 3.571 6 9743 9943.5 4.045 7.616 7 7165 7145.0 0.056 7.672 8 5065 5139.1 1.068 8.739 9 3771 3699.9 1.368 10.107 10 2683 2666.3 0.105 10.212 11 1904 1923.3 0.194 10.406 12 1354 1388.7 0.869 11.275 13 1054 1003.7 2.519 13.794 14 724 726.1 0.006 13.800 15 527 525.8 0.003 13.803 16 396 381.2 0.579 14.381 17 290 276.5 0.655 15.037 18 200 200.8 0.003 15.040 19 170 146.0 3.951 18.991 20 100 106.2 0.364 19.355 21 284 287.1 0.034 19.388 Chisq= 19.39 for 20 degrees of freedom, p= 0.50327 SUMMARY of craptest p-value for no. of wins: 0.321139 p-value for throws/game: 0.503270 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0008,0.0014,0.0017,0.0029,0.0036,0.0147,0.0173,0.0185,0.0187,0.0195, 0.0232,0.0256,0.0335,0.0370,0.0375,0.0405,0.0465,0.0492,0.0524,0.0588, 0.0658,0.0659,0.0710,0.0744,0.0787,0.0854,0.0857,0.0859,0.0879,0.0901, 0.0987,0.1005,0.1027,0.1039,0.1055,0.1173,0.1180,0.1224,0.1236,0.1289, 0.1314,0.1329,0.1343,0.1379,0.1426,0.1439,0.1475,0.1529,0.1576,0.1597, 0.1671,0.1680,0.1688,0.1784,0.1933,0.2106,0.2117,0.2188,0.2230,0.2276, 0.2283,0.2299,0.2325,0.2337,0.2356,0.2466,0.2488,0.2503,0.2560,0.2588, 0.2601,0.2636,0.2644,0.2702,0.2785,0.2793,0.2841,0.2872,0.2935,0.3035, 0.3119,0.3211,0.3221,0.3234,0.3269,0.3277,0.3427,0.3443,0.3492,0.3503, 0.3517,0.3558,0.3566,0.3713,0.3741,0.3759,0.3778,0.3836,0.3839,0.3875, 0.3879,0.3945,0.3971,0.4070,0.4091,0.4121,0.4216,0.4270,0.4291,0.4309, 0.4380,0.4384,0.4415,0.4420,0.4422,0.4509,0.4529,0.4546,0.4550,0.4575, 0.4610,0.4660,0.4671,0.4679,0.4725,0.4726,0.4787,0.4789,0.4838,0.4898, 0.4982,0.5024,0.5033,0.5039,0.5063,0.5092,0.5104,0.5137,0.5151,0.5203, 0.5231,0.5306,0.5341,0.5398,0.5432,0.5433,0.5501,0.5520,0.5547,0.5720, 0.5721,0.5802,0.5828,0.5847,0.5850,0.5861,0.5872,0.5884,0.5904,0.5914, 0.5966,0.5981,0.6049,0.6064,0.6094,0.6096,0.6135,0.6146,0.6214,0.6260, 0.6310,0.6326,0.6358,0.6405,0.6412,0.6424,0.6437,0.6517,0.6525,0.6565, 0.6592,0.6601,0.6613,0.6676,0.6732,0.6748,0.6806,0.6812,0.6901,0.7016, 0.7108,0.7226,0.7237,0.7252,0.7304,0.7335,0.7463,0.7463,0.7485,0.7490, 0.7497,0.7598,0.7603,0.7652,0.7686,0.7767,0.7812,0.7868,0.7888,0.7911, 0.7915,0.7923,0.7953,0.8075,0.8076,0.8077,0.8117,0.8137,0.8194,0.8217, 0.8219,0.8220,0.8223,0.8289,0.8323,0.8343,0.8361,0.8366,0.8372,0.8405, 0.8525,0.8631,0.8638,0.8700,0.8711,0.8758,0.8786,0.8800,0.8813,0.8873, 0.8880,0.8880,0.8912,0.8930,0.8968,0.9084,0.9114,0.9155,0.9177,0.9222, 0.9245,0.9377,0.9428,0.9443,0.9529,0.9540,0.9595,0.9620,0.9623,0.9686, 0.9734,0.9736,0.9751,0.9763,0.9844,0.9902,0.9902,0.9954,0.9969, Overall p-value after applying KStest on 269 p-values = 0.849521 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.