RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-09_14:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.70 22.6439 0.838795 2 to 25 15.72 16.8996 0.538814 3 to 26 15.79 21.2908 0.786448 4 to 27 15.86 14.4670 0.366190 5 to 28 15.55 15.4281 0.435321 6 to 29 15.69 12.6526 0.240886 7 to 30 16.37 16.5783 0.516728 8 to 31 15.53 23.6398 0.870444 9 to 32 15.54 29.1810 0.967107 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.371639 Tough bday spacings test for dh-ranFile-2018-07-09_14:31: 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 9 34 73 96 108 80 55 26 13 5 1 (O-E)^2/E 0.0 0.2 0.0 0.0 1.1 0.0 0.2 0.5 0.2 0.4 2.3 Birthday Spacings: Sum(O-E)^2/E= 4.940, p= 0.105 RESULTS OF GCD FOR dh-ranFile-2018-07-09_14:31 Euclid's algorithm: p-value, steps to gcd: 0.429005 p-value, dist. of gcd's: 0.602634 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-09_14:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.139 0.866 0.335 0.394 0.421 0.341 0.049 0.478 Bits 8 to 15---> 0.453 0.396 0.811 0.893 0.449 0.796 0.766 0.331 Bits 16 to 23---> 0.652 0.949 0.943 0.043 0.913 0.669 0.888 0.560 Bits 24 to 31---> 0.266 0.907 0.250 0.383 0.534 0.677 0.595 0.192 KS test for the above 32 p values: 0.415 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-09_14:31, p-values for 5 runs: 0.9893, 0.3809, 0.9867, 0.8171, 0.0000 Rank test for binary matrices (31x31) for dh-ranFile-2018-07-09_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 208 211.4 0.055 0.055 r= 29 5198 5134.0 0.798 0.853 r= 30 23030 23103.0 0.231 1.084 r= 31 11564 11551.5 0.013 1.097 chi-square = 1.097 with df = 3; p-value = 0.222 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-07-09_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 189 211.4 2.377 2.377 r= 30 5212 5134.0 1.185 3.562 r= 31 23177 23103.0 0.237 3.799 r= 32 11422 11551.5 1.452 5.251 chi-square = 5.251 with df = 3; p-value = 0.846 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-07-09_14:31 b-rank test for bits 1 to 8, p=0.43108 b-rank test for bits 2 to 9, p=0.94291 b-rank test for bits 3 to 10, p=0.90077 b-rank test for bits 4 to 11, p=0.60932 b-rank test for bits 5 to 12, p=0.71059 b-rank test for bits 6 to 13, p=0.24507 b-rank test for bits 7 to 14, p=0.56982 b-rank test for bits 8 to 15, p=0.18152 b-rank test for bits 9 to 16, p=0.02692 b-rank test for bits 10 to 17, p=0.09270 b-rank test for bits 11 to 18, p=0.72587 b-rank test for bits 12 to 19, p=0.55101 b-rank test for bits 13 to 20, p=0.18355 b-rank test for bits 14 to 21, p=0.29076 b-rank test for bits 15 to 22, p=0.76553 b-rank test for bits 16 to 23, p=0.95356 b-rank test for bits 17 to 24, p=0.37615 b-rank test for bits 18 to 25, p=0.31412 b-rank test for bits 19 to 26, p=0.04043 b-rank test for bits 20 to 27, p=0.32404 b-rank test for bits 21 to 28, p=0.37006 b-rank test for bits 22 to 29, p=0.95791 b-rank test for bits 23 to 30, p=0.79220 b-rank test for bits 24 to 31, p=0.31758 b-rank test for bits 25 to 32, p=0.18961 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 = 0.878236 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-09_14:31 (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 142328 0.98 0.836013 2 141961 0.12 0.548045 3 142291 0.89 0.813737 4 142015 0.25 0.597504 5 141551 -0.84 0.201235 6 141963 0.13 0.549895 7 141238 -1.57 0.058379 8 142092 0.43 0.665237 9 141461 -1.05 0.147435 10 142497 1.37 0.915133 11 141792 -0.27 0.391990 12 141392 -1.21 0.113386 13 142326 0.97 0.834855 14 142458 1.28 0.900068 15 142968 2.47 0.993311 16 142139 0.54 0.704232 17 141517 -0.92 0.179661 18 141738 -0.40 0.344466 19 141938 0.07 0.526704 20 142066 0.37 0.642837 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-07-09_14:31 Bits used No. missing words z-score p-value 23 to 32 142156 0.8506 0.802500 22 to 31 142387 1.6471 0.950235 21 to 30 142106 0.6782 0.751169 20 to 29 142191 0.9713 0.834295 19 to 28 142017 0.3713 0.644784 18 to 27 141309 -2.0701 0.019221 17 to 26 141785 -0.4287 0.334062 16 to 25 141745 -0.5667 0.285474 15 to 24 141740 -0.5839 0.279645 14 to 23 141943 0.1161 0.546215 13 to 22 142012 0.3540 0.638344 12 to 21 141616 -1.0115 0.155893 11 to 20 141751 -0.5460 0.292545 10 to 19 141668 -0.8322 0.202656 9 to 18 141987 0.2678 0.605584 8 to 17 142188 0.9609 0.831707 7 to 16 141444 -1.6046 0.054292 6 to 15 142517 2.0954 0.981933 5 to 14 142109 0.6885 0.754436 4 to 13 141449 -1.5873 0.056217 3 to 12 141760 -0.5149 0.303301 2 to 11 142033 0.4264 0.665109 1 to 10 141668 -0.8322 0.202656 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-07-09_14:31 Bits used No. missing words z-score p-value 28 to 32 142759 2.8802 0.998013 27 to 31 142010 0.3413 0.633544 26 to 30 141976 0.2260 0.589399 25 to 29 142039 0.4396 0.669872 24 to 28 141998 0.3006 0.618131 23 to 27 141847 -0.2113 0.416331 22 to 26 142216 1.0396 0.850728 21 to 25 141773 -0.4621 0.321992 20 to 24 141336 -1.9435 0.025978 19 to 23 141743 -0.5638 0.286435 18 to 22 141661 -0.8418 0.199951 17 to 21 142452 1.8396 0.967084 16 to 20 141735 -0.5909 0.277277 15 to 19 141428 -1.6316 0.051379 14 to 18 142083 0.5887 0.721973 13 to 17 141251 -2.2316 0.012820 12 to 16 142085 0.5955 0.724243 11 to 15 141855 -0.1842 0.426940 10 to 14 142251 1.1582 0.876610 9 to 13 142217 1.0429 0.851514 8 to 12 142122 0.7209 0.764519 7 to 11 142098 0.6396 0.738770 6 to 10 142009 0.3379 0.632267 5 to 9 141729 -0.6113 0.270504 4 to 8 141938 0.0972 0.538711 3 to 7 142082 0.5853 0.720834 2 to 6 141958 0.1650 0.565521 1 to 5 141962 0.1785 0.570852 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-07-09_14:31 Bits used No. missing words z-score p-value 31 to 32 141774 -0.3992 0.344872 30 to 31 141420 -1.4435 0.074447 29 to 30 141753 -0.4612 0.322345 28 to 29 142035 0.3707 0.644573 27 to 28 142177 0.7896 0.785116 26 to 27 141918 0.0256 0.510202 25 to 26 141295 -1.8122 0.034979 24 to 25 142050 0.4150 0.660913 23 to 24 142338 1.2645 0.896977 22 to 23 141652 -0.7591 0.223901 21 to 22 142267 1.0551 0.854304 20 to 21 142045 0.4002 0.655498 19 to 20 142500 1.7424 0.959280 18 to 19 141845 -0.1898 0.424747 17 to 18 142718 2.3855 0.991471 16 to 17 141819 -0.2665 0.394942 15 to 16 141658 -0.7414 0.229230 14 to 15 142284 1.1052 0.865468 13 to 14 141082 -2.4405 0.007333 12 to 13 142668 2.2380 0.987388 11 to 12 141849 -0.1780 0.429375 10 to 11 141611 -0.8800 0.189422 9 to 10 141858 -0.1514 0.439824 8 to 9 141366 -1.6027 0.054496 7 to 8 141765 -0.4258 0.335144 6 to 7 141819 -0.2665 0.394942 5 to 6 141570 -1.0010 0.158420 4 to 5 141735 -0.5142 0.303539 3 to 4 141607 -0.8918 0.186242 2 to 3 142591 2.0108 0.977828 1 to 2 142096 0.5506 0.709063 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-09_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2592.47 1.308 0.904512 Test results for specific bytes for dh-ranFile-2018-07-09_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2495.90 -0.058 0.476871 2 to 9 2492.63 -0.104 0.458499 3 to 10 2475.07 -0.353 0.362224 4 to 11 2546.48 0.657 0.744516 5 to 12 2519.03 0.269 0.606091 6 to 13 2530.35 0.429 0.666140 7 to 14 2564.35 0.910 0.818615 8 to 15 2604.04 1.471 0.929408 9 to 16 2633.95 1.894 0.970911 10 to 17 2473.89 -0.369 0.355951 11 to 18 2601.53 1.436 0.924486 12 to 19 2572.71 1.028 0.848100 13 to 20 2489.12 -0.154 0.438862 14 to 21 2636.73 1.934 0.973418 15 to 22 2571.27 1.008 0.843256 16 to 23 2512.21 0.173 0.568538 17 to 24 2578.98 1.117 0.867999 18 to 25 2608.86 1.540 0.938165 19 to 26 2562.39 0.882 0.811197 20 to 27 2500.50 0.007 0.502842 21 to 28 2520.79 0.294 0.615642 22 to 29 2527.28 0.386 0.650160 23 to 30 2574.88 1.059 0.855188 24 to 31 2594.60 1.338 0.909529 25 to 32 2621.04 1.712 0.956527 CDPARK for dh-ranFile-2018-07-09_14:31: 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 3523 0.0000 0.500000 3463 -2.7397 0.003075 3533 0.4566 0.676028 3500 -1.0502 0.146807 3537 0.6393 0.738676 3525 0.0913 0.536383 3480 -1.9635 0.024796 3479 -2.0091 0.022262 3524 0.0457 0.518210 3512 -0.5023 0.307734 Square side=100, avg. no. parked=3507.60 sample std.=24.42 p-value of the KSTEST for those 10 p-values: 0.052697 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-09_14:31 0.2523,0.4405,0.1513,0.1931,0.0947,0.8699,0.8656,0.2846,0.1886,0.4333, The KS test for those 10 p-values: 0.198834 The 3DSPHERES test for dh-ranFile-2018-07-09_14:31 sample no r^3 equiv. uni. 1 26.920 0.592348 2 17.450 0.441031 3 18.147 0.453877 4 44.599 0.773866 5 13.593 0.364352 6 16.046 0.414250 7 27.952 0.606134 8 120.307 0.981871 9 32.543 0.662018 10 42.934 0.760959 11 2.808 0.089339 12 4.951 0.152146 13 26.314 0.584021 14 21.199 0.506698 15 17.857 0.448575 16 88.706 0.948018 17 33.001 0.667139 18 28.801 0.617125 19 18.980 0.468818 20 16.792 0.428644 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.221800 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-09_14:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -1.2 -0.6 1.2 1.4 0.1 -0.9 -0.3 2.0 -0.1 -0.5 2.2 -0.1 -0.2 1.8 -1.5 0.3 1.6 -2.0 0.4 -1.0 -0.9 -0.4 -0.1 -0.7 1.0 -2.0 1.0 1.2 -0.7 -0.2 1.0 0.3 -1.2 -0.1 0.6 -1.2 1.1 0.9 0.4 -1.3 0.0 0.8 Chi-square with 42 degrees of freedom:46.658437 z-score=0.508277, p-value=0.713211 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-07-09_14:31 Test no p-value 1 0.214621 2 0.519014 3 0.344222 4 0.422205 5 0.974390 6 0.222877 7 0.717770 8 0.889391 9 0.182025 10 0.036282 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.847254 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-09_14:31: (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 66673 0.00 66398 1.08 3 25000.00 25045 0.08 25077 0.24 4 6666.67 6641 0.10 6759 1.28 5 1388.89 1358 0.69 1481 6.11 6 238.10 244 0.15 246 0.26 7 34.72 34 0.01 32 0.21 8 4.96 4 0.19 6 0.22 p=0.02384 p=0.84774 Number of rngs required: 689460, p-value: 0.890 RESULTS OF CRAPS TEST for dh-ranFile-2018-07-09_14:31 No. of wins: Observed Expected 98567 98585.9 z-score=-0.084, pvalue=0.46639 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66453 66666.7 0.685 0.685 2 37756 37654.3 0.275 0.959 3 26894 26954.7 0.137 1.096 4 19411 19313.5 0.493 1.589 5 13961 13851.4 0.867 2.456 6 9869 9943.5 0.559 3.015 7 7141 7145.0 0.002 3.017 8 5140 5139.1 0.000 3.017 9 3666 3699.9 0.310 3.327 10 2648 2666.3 0.126 3.452 11 1890 1923.3 0.578 4.030 12 1438 1388.7 1.747 5.777 13 1028 1003.7 0.588 6.365 14 768 726.1 2.413 8.778 15 542 525.8 0.497 9.275 16 385 381.2 0.039 9.314 17 277 276.5 0.001 9.314 18 187 200.8 0.952 10.267 19 137 146.0 0.553 10.820 20 111 106.2 0.216 11.035 21 298 287.1 0.413 11.448 Chisq= 11.45 for 20 degrees of freedom, p= 0.06623 SUMMARY of craptest p-value for no. of wins: 0.466390 p-value for throws/game: 0.066235 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-09_14:31 No. of wins: Observed Expected 98429 98585.9 z-score=-0.702, pvalue=0.24148 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66924 66666.7 0.993 0.993 2 37292 37654.3 3.486 4.480 3 26849 26954.7 0.415 4.894 4 19194 19313.5 0.739 5.633 5 13891 13851.4 0.113 5.746 6 10030 9943.5 0.752 6.498 7 7198 7145.0 0.393 6.891 8 5118 5139.1 0.086 6.977 9 3783 3699.9 1.868 8.845 10 2700 2666.3 0.426 9.271 11 1940 1923.3 0.144 9.416 12 1431 1388.7 1.286 10.702 13 995 1003.7 0.076 10.778 14 726 726.1 0.000 10.778 15 525 525.8 0.001 10.779 16 391 381.2 0.255 11.033 17 270 276.5 0.155 11.188 18 203 200.8 0.023 11.211 19 142 146.0 0.109 11.320 20 124 106.2 2.978 14.298 21 274 287.1 0.599 14.897 Chisq= 14.90 for 20 degrees of freedom, p= 0.21774 SUMMARY of craptest p-value for no. of wins: 0.241476 p-value for throws/game: 0.217735 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0000,0.0031,0.0073,0.0128,0.0192,0.0223,0.0238,0.0248,0.0260,0.0269, 0.0350,0.0363,0.0404,0.0426,0.0492,0.0514,0.0527,0.0543,0.0545,0.0562, 0.0584,0.0662,0.0744,0.0893,0.0927,0.0947,0.1048,0.1134,0.1390,0.1468, 0.1474,0.1513,0.1521,0.1559,0.1584,0.1797,0.1815,0.1820,0.1835,0.1862, 0.1886,0.1894,0.1896,0.1917,0.1931,0.1988,0.2000,0.2012,0.2027,0.2027, 0.2146,0.2177,0.2218,0.2223,0.2229,0.2239,0.2292,0.2409,0.2415,0.2451, 0.2498,0.2523,0.2665,0.2705,0.2773,0.2796,0.2846,0.2855,0.2864,0.2908, 0.2925,0.3033,0.3035,0.3077,0.3141,0.3176,0.3220,0.3223,0.3240,0.3307, 0.3341,0.3346,0.3351,0.3409,0.3442,0.3445,0.3449,0.3560,0.3622,0.3644, 0.3662,0.3701,0.3716,0.3762,0.3809,0.3831,0.3920,0.3940,0.3949,0.3949, 0.3959,0.4142,0.4154,0.4163,0.4206,0.4222,0.4247,0.4269,0.4286,0.4290, 0.4294,0.4311,0.4333,0.4353,0.4389,0.4398,0.4405,0.4410,0.4486,0.4490, 0.4532,0.4539,0.4585,0.4664,0.4688,0.4769,0.4782,0.5000,0.5028,0.5067, 0.5102,0.5167,0.5182,0.5190,0.5267,0.5341,0.5364,0.5387,0.5388,0.5462, 0.5480,0.5499,0.5510,0.5596,0.5655,0.5685,0.5698,0.5709,0.5840,0.5894, 0.5923,0.5950,0.5975,0.6026,0.6056,0.6061,0.6061,0.6093,0.6156,0.6171, 0.6181,0.6323,0.6335,0.6383,0.6428,0.6446,0.6448,0.6502,0.6524,0.6555, 0.6609,0.6620,0.6651,0.6652,0.6661,0.6671,0.6689,0.6699,0.6760,0.6765, 0.7042,0.7091,0.7106,0.7132,0.7178,0.7208,0.7220,0.7242,0.7259,0.7387, 0.7388,0.7445,0.7512,0.7544,0.7610,0.7645,0.7655,0.7659,0.7739,0.7851, 0.7864,0.7922,0.7955,0.8025,0.8109,0.8112,0.8137,0.8171,0.8186,0.8317, 0.8343,0.8349,0.8360,0.8388,0.8433,0.8457,0.8473,0.8477,0.8481,0.8507, 0.8515,0.8543,0.8552,0.8655,0.8656,0.8660,0.8680,0.8699,0.8704,0.8766, 0.8782,0.8875,0.8894,0.8905,0.8927,0.8970,0.9001,0.9008,0.9045,0.9070, 0.9095,0.9133,0.9151,0.9245,0.9294,0.9382,0.9429,0.9429,0.9480,0.9490, 0.9502,0.9536,0.9565,0.9579,0.9593,0.9671,0.9671,0.9709,0.9734,0.9744, 0.9778,0.9819,0.9819,0.9867,0.9874,0.9893,0.9915,0.9933,0.9980, Overall p-value after applying KStest on 269 p-values = 0.236189 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.