RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-01-21_01:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.84 25.1945 0.909559 2 to 25 15.88 16.6912 0.524532 3 to 26 15.81 23.4884 0.865984 4 to 27 15.92 13.2455 0.280398 5 to 28 15.87 10.4882 0.118097 6 to 29 16.01 10.9769 0.142238 7 to 30 15.75 31.2884 0.981582 8 to 31 15.77 17.4317 0.574489 9 to 32 15.97 22.2694 0.825420 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.529521 Tough bday spacings test for dh-ranFile-2017-01-21_01:31: 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 40 60 98 97 84 47 41 8 7 7 (O-E)^2/E 0.4 0.3 2.4 0.0 0.0 0.4 0.5 4.2 3.2 0.0 2.1 Birthday Spacings: Sum(O-E)^2/E= 13.584, p= 0.807 RESULTS OF GCD FOR dh-ranFile-2017-01-21_01:31 Euclid's algorithm: p-value, steps to gcd: 0.156680 p-value, dist. of gcd's: 0.594736 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-01-21_01:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.583 0.933 0.017 0.194 0.467 0.570 0.256 0.527 Bits 8 to 15---> 0.172 0.584 0.191 0.305 0.103 0.525 0.604 0.849 Bits 16 to 23---> 0.514 0.568 0.705 0.822 0.632 0.491 0.983 0.192 Bits 24 to 31---> 0.509 0.589 0.125 0.840 0.251 0.610 0.536 0.974 KS test for the above 32 p values: 0.472 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-01-21_01:31, p-values for 5 runs: 0.2763, 0.7807, 0.1843, 0.2600, 0.2971 Rank test for binary matrices (31x31) for dh-ranFile-2017-01-21_01:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 237 211.4 3.095 3.095 r= 29 5060 5134.0 1.067 4.162 r= 30 22909 23103.0 1.630 5.792 r= 31 11794 11551.5 5.090 10.882 chi-square = 10.882 with df = 3; p-value = 0.988 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2017-01-21_01:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 215 211.4 0.061 0.061 r= 30 5086 5134.0 0.449 0.510 r= 31 23146 23103.0 0.080 0.590 r= 32 11553 11551.5 0.000 0.590 chi-square = 0.590 with df = 3; p-value = 0.101 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2017-01-21_01:31 b-rank test for bits 1 to 8, p=0.69874 b-rank test for bits 2 to 9, p=0.50645 b-rank test for bits 3 to 10, p=0.70951 b-rank test for bits 4 to 11, p=0.46542 b-rank test for bits 5 to 12, p=0.85465 b-rank test for bits 6 to 13, p=0.30407 b-rank test for bits 7 to 14, p=0.02895 b-rank test for bits 8 to 15, p=0.14350 b-rank test for bits 9 to 16, p=0.33024 b-rank test for bits 10 to 17, p=0.00600 b-rank test for bits 11 to 18, p=0.58352 b-rank test for bits 12 to 19, p=0.86968 b-rank test for bits 13 to 20, p=0.25940 b-rank test for bits 14 to 21, p=0.01202 b-rank test for bits 15 to 22, p=0.40553 b-rank test for bits 16 to 23, p=0.61263 b-rank test for bits 17 to 24, p=0.52542 b-rank test for bits 18 to 25, p=0.69155 b-rank test for bits 19 to 26, p=0.04229 b-rank test for bits 20 to 27, p=0.29817 b-rank test for bits 21 to 28, p=0.45882 b-rank test for bits 22 to 29, p=0.78809 b-rank test for bits 23 to 30, p=0.38659 b-rank test for bits 24 to 31, p=0.59128 b-rank test for bits 25 to 32, p=0.52189 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 = 0.261816 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-01-21_01:31 (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 142316 0.95 0.828985 2 141743 -0.39 0.348778 3 142173 0.62 0.731070 4 142251 0.80 0.787650 5 142191 0.66 0.744765 6 142370 1.08 0.859111 7 141430 -1.12 0.131372 8 142036 0.30 0.616369 9 142285 0.88 0.809956 10 142667 1.77 0.961658 11 142004 0.22 0.587528 12 141125 -1.83 0.033435 13 142149 0.56 0.712252 14 141815 -0.22 0.412781 15 141378 -1.24 0.107224 16 142025 0.27 0.606519 17 141576 -0.78 0.218046 18 142155 0.57 0.717015 19 141784 -0.29 0.384827 20 142554 1.51 0.933997 ---------------------------------------------------------------- OPSO test for dh-ranFile-2017-01-21_01:31 Bits used No. missing words z-score p-value 23 to 32 141973 0.2196 0.586890 22 to 31 142152 0.8368 0.798646 21 to 30 141580 -1.1356 0.128058 20 to 29 141826 -0.2873 0.386924 19 to 28 141499 -1.4149 0.078544 18 to 27 141848 -0.2115 0.416255 17 to 26 141192 -2.4736 0.006689 16 to 25 141772 -0.4736 0.317910 15 to 24 141656 -0.8736 0.191181 14 to 23 141909 -0.0011 0.499546 13 to 22 141916 0.0230 0.509175 12 to 21 141751 -0.5460 0.292545 11 to 20 142110 0.6920 0.755521 10 to 19 141633 -0.9529 0.170330 9 to 18 141614 -1.0184 0.154249 8 to 17 141953 0.1506 0.559849 7 to 16 141993 0.2885 0.613525 6 to 15 141740 -0.5839 0.279645 5 to 14 141751 -0.5460 0.292545 4 to 13 141910 0.0023 0.500922 3 to 12 141823 -0.2977 0.382970 2 to 11 142026 0.4023 0.656272 1 to 10 142852 3.2506 0.999424 ----------------------------------------------------------------- OQSO test for dh-ranFile-2017-01-21_01:31 Bits used No. missing words z-score p-value 28 to 32 141919 0.0328 0.513075 27 to 31 142084 0.5921 0.723109 26 to 30 142187 0.9413 0.826713 25 to 29 141856 -0.1808 0.428270 24 to 28 142265 1.2057 0.886026 23 to 27 142753 2.8599 0.997881 22 to 26 141595 -1.0655 0.143319 21 to 25 142013 0.3514 0.637365 20 to 24 141740 -0.5740 0.282984 19 to 23 141609 -1.0181 0.154323 18 to 22 142224 1.0667 0.856941 17 to 21 142094 0.6260 0.734343 16 to 20 141735 -0.5909 0.277277 15 to 19 141881 -0.0960 0.461747 14 to 18 141936 0.0904 0.536018 13 to 17 142199 0.9819 0.836933 12 to 16 141838 -0.2418 0.404469 11 to 15 142027 0.3989 0.655010 10 to 14 141795 -0.3876 0.349171 9 to 13 142317 1.3819 0.916504 8 to 12 142084 0.5921 0.723109 7 to 11 142015 0.3582 0.639905 6 to 10 142010 0.3413 0.633544 5 to 9 142287 1.2802 0.899769 4 to 8 141403 -1.7164 0.043047 3 to 7 141668 -0.8181 0.206659 2 to 6 141823 -0.2926 0.384897 1 to 5 141611 -1.0113 0.155939 ----------------------------------------------------------------- DNA test for dh-ranFile-2017-01-21_01:31 Bits used No. missing words z-score p-value 31 to 32 142339 1.2675 0.897505 30 to 31 142701 2.3353 0.990236 29 to 30 141657 -0.7443 0.228337 28 to 29 141564 -1.0187 0.154179 27 to 28 141611 -0.8800 0.189422 26 to 27 141947 0.1111 0.544240 25 to 26 141238 -1.9803 0.023834 24 to 25 142236 0.9636 0.832384 23 to 24 141471 -1.2930 0.098004 22 to 23 141903 -0.0187 0.492551 21 to 22 142358 1.3235 0.907167 20 to 21 141707 -0.5968 0.275306 19 to 20 141475 -1.2812 0.100060 18 to 19 141471 -1.2930 0.098004 17 to 18 141887 -0.0659 0.473741 16 to 17 142046 0.4032 0.656583 15 to 16 142091 0.5359 0.703986 14 to 15 142148 0.7040 0.759297 13 to 14 142125 0.6362 0.737675 12 to 13 141924 0.0433 0.517259 11 to 12 141349 -1.6529 0.049177 10 to 11 141930 0.0610 0.524310 9 to 10 141021 -2.6204 0.004391 8 to 9 141553 -1.0511 0.146602 7 to 8 142270 1.0639 0.856318 6 to 7 141602 -0.9066 0.182315 5 to 6 141995 0.2527 0.599755 4 to 5 142187 0.8191 0.793631 3 to 4 141934 0.0728 0.529007 2 to 3 142060 0.4445 0.671643 1 to 2 141622 -0.8476 0.198336 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2017-01-21_01:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2446.36 -0.759 0.224060 Test results for specific bytes for dh-ranFile-2017-01-21_01:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2430.51 -0.983 0.162853 2 to 9 2528.35 0.401 0.655762 3 to 10 2511.34 0.160 0.563694 4 to 11 2447.63 -0.741 0.229467 5 to 12 2413.95 -1.217 0.111813 6 to 13 2370.62 -1.830 0.033644 7 to 14 2584.95 1.201 0.885210 8 to 15 2387.38 -1.593 0.055623 9 to 16 2429.74 -0.994 0.160186 10 to 17 2547.26 0.668 0.748048 11 to 18 2542.40 0.600 0.725609 12 to 19 2448.29 -0.731 0.232296 13 to 20 2533.23 0.470 0.680784 14 to 21 2456.87 -0.610 0.270951 15 to 22 2523.38 0.331 0.629552 16 to 23 2401.15 -1.398 0.081062 17 to 24 2449.86 -0.709 0.239115 18 to 25 2389.02 -1.569 0.058266 19 to 26 2527.42 0.388 0.650900 20 to 27 2435.84 -0.907 0.182122 21 to 28 2563.15 0.893 0.814108 22 to 29 2400.53 -1.407 0.079763 23 to 30 2398.13 -1.441 0.074848 24 to 31 2382.09 -1.667 0.047712 25 to 32 2472.09 -0.395 0.346545 CDPARK for dh-ranFile-2017-01-21_01:31: 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 3530 0.3196 0.625377 3516 -0.3196 0.374623 3530 0.3196 0.625377 3556 1.5068 0.934075 3526 0.1370 0.554479 3542 0.8676 0.807188 3536 0.5936 0.723613 3543 0.9132 0.819442 3516 -0.3196 0.374623 3511 -0.5479 0.291865 Square side=100, avg. no. parked=3530.60 sample std.=13.38 p-value of the KSTEST for those 10 p-values: 0.286710 Results for the MINIMUM DISTANCE test for dh-ranFile-2017-01-21_01:31 0.1928,0.5636,0.8288,0.3531,0.5471,0.9497,0.4014,0.0745,0.8789,0.2183, The KS test for those 10 p-values: 0.992382 The 3DSPHERES test for dh-ranFile-2017-01-21_01:31 sample no r^3 equiv. uni. 1 15.655 0.406570 2 16.595 0.424881 3 53.783 0.833500 4 15.533 0.404152 5 9.047 0.260350 6 120.814 0.982174 7 19.319 0.474793 8 2.605 0.083162 9 6.932 0.206324 10 34.486 0.683218 11 37.292 0.711498 12 72.306 0.910204 13 33.296 0.670398 14 18.827 0.466116 15 25.995 0.579583 16 43.058 0.761947 17 16.016 0.413670 18 14.449 0.382225 19 47.637 0.795645 20 76.986 0.923174 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.402355 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-01-21_01:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 1.8 -1.3 -0.3 0.0 -1.1 0.6 1.5 -0.6 0.0 -2.5 1.0 -0.0 0.3 -0.1 0.2 -0.2 -0.5 -1.1 0.4 1.5 0.6 1.2 0.8 0.2 -1.0 -2.2 0.5 -0.8 -0.5 0.6 0.3 1.0 -0.9 -0.1 1.0 -0.7 -0.1 0.5 0.4 0.1 -1.0 -0.1 Chi-square with 42 degrees of freedom:36.938148 z-score=-0.552293, p-value=0.307620 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2017-01-21_01:31 Test no p-value 1 0.253765 2 0.878713 3 0.043307 4 0.407898 5 0.152589 6 0.072141 7 0.191343 8 0.142949 9 0.906821 10 0.849868 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.166226 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-01-21_01:31: (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 66776 0.18 66468 0.59 3 25000.00 25018 0.01 25099 0.39 4 6666.67 6506 3.87 6746 0.94 5 1388.89 1428 1.10 1380 0.06 6 238.10 225 0.72 256 1.35 7 34.72 38 0.31 45 3.04 8 4.96 8 1.86 5 0.00 p=0.76620 p=0.61753 Number of rngs required: 688329, p-value: 0.466 RESULTS OF CRAPS TEST for dh-ranFile-2017-01-21_01:31 No. of wins: Observed Expected 98766 98585.9 z-score= 0.806, pvalue=0.78979 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66783 66666.7 0.203 0.203 2 37535 37654.3 0.378 0.581 3 26851 26954.7 0.399 0.980 4 19450 19313.5 0.965 1.946 5 13784 13851.4 0.328 2.274 6 10026 9943.5 0.684 2.958 7 7230 7145.0 1.011 3.968 8 5024 5139.1 2.577 6.545 9 3645 3699.9 0.814 7.358 10 2585 2666.3 2.479 9.837 11 1951 1923.3 0.398 10.235 12 1422 1388.7 0.797 11.032 13 1001 1003.7 0.007 11.039 14 726 726.1 0.000 11.039 15 542 525.8 0.497 11.536 16 377 381.2 0.045 11.581 17 304 276.5 2.727 14.308 18 206 200.8 0.133 14.441 19 147 146.0 0.007 14.448 20 111 106.2 0.216 14.664 21 300 287.1 0.578 15.242 Chisq= 15.24 for 20 degrees of freedom, p= 0.23761 SUMMARY of craptest p-value for no. of wins: 0.789791 p-value for throws/game: 0.237612 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2017-01-21_01:31 No. of wins: Observed Expected 98720 98585.9 z-score= 0.600, pvalue=0.72573 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66553 66666.7 0.194 0.194 2 37821 37654.3 0.738 0.932 3 26953 26954.7 0.000 0.932 4 19153 19313.5 1.333 2.265 5 14016 13851.4 1.956 4.220 6 10038 9943.5 0.897 5.118 7 7046 7145.0 1.372 6.490 8 5142 5139.1 0.002 6.492 9 3593 3699.9 3.087 9.578 10 2680 2666.3 0.070 9.649 11 1976 1923.3 1.442 11.091 12 1356 1388.7 0.772 11.863 13 1017 1003.7 0.176 12.039 14 732 726.1 0.047 12.086 15 530 525.8 0.033 12.119 16 389 381.2 0.162 12.281 17 267 276.5 0.329 12.610 18 196 200.8 0.116 12.726 19 126 146.0 2.736 15.462 20 123 106.2 2.652 18.114 21 293 287.1 0.121 18.235 Chisq= 18.23 for 20 degrees of freedom, p= 0.42806 SUMMARY of craptest p-value for no. of wins: 0.725733 p-value for throws/game: 0.428064 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0044,0.0060,0.0067,0.0120,0.0166,0.0238,0.0290,0.0334,0.0336,0.0423, 0.0430,0.0433,0.0477,0.0492,0.0556,0.0583,0.0721,0.0745,0.0748,0.0785, 0.0798,0.0811,0.0832,0.0980,0.0980,0.1001,0.1012,0.1033,0.1072,0.1118, 0.1181,0.1249,0.1281,0.1314,0.1422,0.1429,0.1433,0.1435,0.1466,0.1526, 0.1542,0.1542,0.1543,0.1559,0.1567,0.1602,0.1629,0.1662,0.1703,0.1725, 0.1821,0.1823,0.1843,0.1894,0.1912,0.1913,0.1914,0.1918,0.1928,0.1936, 0.1983,0.2063,0.2067,0.2180,0.2183,0.2241,0.2283,0.2295,0.2323,0.2376, 0.2391,0.2506,0.2538,0.2562,0.2594,0.2600,0.2604,0.2618,0.2710,0.2753, 0.2763,0.2773,0.2796,0.2804,0.2830,0.2867,0.2919,0.2925,0.2925,0.2971, 0.2982,0.3041,0.3054,0.3076,0.3179,0.3302,0.3465,0.3488,0.3492,0.3531, 0.3746,0.3746,0.3822,0.3830,0.3848,0.3849,0.3866,0.3869,0.4014,0.4024, 0.4042,0.4045,0.4055,0.4066,0.4079,0.4128,0.4137,0.4163,0.4249,0.4281, 0.4283,0.4588,0.4617,0.4654,0.4661,0.4661,0.4667,0.4720,0.4737,0.4748, 0.4915,0.4926,0.4995,0.5009,0.5065,0.5089,0.5092,0.5131,0.5144,0.5173, 0.5219,0.5243,0.5245,0.5251,0.5254,0.5267,0.5290,0.5295,0.5359,0.5360, 0.5442,0.5471,0.5545,0.5598,0.5636,0.5637,0.5675,0.5697,0.5745,0.5796, 0.5825,0.5835,0.5841,0.5869,0.5875,0.5885,0.5913,0.5947,0.5998,0.6044, 0.6065,0.6105,0.6126,0.6135,0.6164,0.6175,0.6254,0.6254,0.6296,0.6323, 0.6335,0.6374,0.6399,0.6509,0.6550,0.6558,0.6563,0.6566,0.6704,0.6716, 0.6808,0.6832,0.6915,0.6987,0.7040,0.7053,0.7095,0.7115,0.7123,0.7170, 0.7231,0.7231,0.7236,0.7256,0.7257,0.7311,0.7343,0.7377,0.7448,0.7480, 0.7555,0.7593,0.7619,0.7662,0.7807,0.7877,0.7881,0.7898,0.7936,0.7956, 0.7986,0.8072,0.8072,0.8100,0.8141,0.8194,0.8224,0.8254,0.8267,0.8288, 0.8290,0.8324,0.8335,0.8369,0.8395,0.8494,0.8499,0.8547,0.8563,0.8569, 0.8591,0.8660,0.8697,0.8787,0.8789,0.8852,0.8860,0.8975,0.8998,0.9068, 0.9072,0.9096,0.9102,0.9165,0.9232,0.9329,0.9340,0.9341,0.9497,0.9617, 0.9736,0.9816,0.9822,0.9834,0.9876,0.9902,0.9924,0.9979,0.9994, Overall p-value after applying KStest on 269 p-values = 0.554847 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.