RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-05-04_04:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.75 22.1916 0.822537 2 to 25 15.75 11.2144 0.154795 3 to 26 15.62 19.5626 0.702790 4 to 27 15.76 16.1270 0.485153 5 to 28 15.65 25.3217 0.912263 6 to 29 15.87 20.8862 0.768580 7 to 30 15.70 13.8021 0.318941 8 to 31 15.82 13.1907 0.276671 9 to 32 15.82 22.7648 0.842935 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.583351 Tough bday spacings test for dh-ranFile-2016-05-04_04:31: 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 7 39 74 113 95 79 48 27 12 4 2 (O-E)^2/E 0.5 0.2 0.0 2.4 0.1 0.0 0.3 0.3 0.6 1.0 1.0 Birthday Spacings: Sum(O-E)^2/E= 6.377, p= 0.217 RESULTS OF GCD FOR dh-ranFile-2016-05-04_04:31 Euclid's algorithm: p-value, steps to gcd: 0.753433 p-value, dist. of gcd's: 0.381622 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-05-04_04:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.746 0.293 0.715 0.927 0.323 0.618 0.961 0.299 Bits 8 to 15---> 0.024 0.097 0.048 0.494 0.406 0.646 0.528 0.447 Bits 16 to 23---> 0.636 0.183 0.808 0.410 0.022 0.591 0.527 0.706 Bits 24 to 31---> 0.763 0.670 0.293 0.546 0.766 0.394 0.141 0.095 KS test for the above 32 p values: 0.317 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-05-04_04:31, p-values for 5 runs: 0.6116, 0.7187, 0.1566, 0.6649, 0.2851 Rank test for binary matrices (31x31) for dh-ranFile-2016-05-04_04:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 207 211.4 0.092 0.092 r= 29 5171 5134.0 0.267 0.359 r= 30 23040 23103.0 0.172 0.531 r= 31 11582 11551.5 0.080 0.611 chi-square = 0.611 with df = 3; p-value = 0.106 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-05-04_04:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 198 211.4 0.852 0.852 r= 30 5125 5134.0 0.016 0.867 r= 31 23021 23103.0 0.291 1.159 r= 32 11656 11551.5 0.945 2.104 chi-square = 2.104 with df = 3; p-value = 0.449 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-05-04_04:31 b-rank test for bits 1 to 8, p=0.96172 b-rank test for bits 2 to 9, p=0.61330 b-rank test for bits 3 to 10, p=0.07771 b-rank test for bits 4 to 11, p=0.84836 b-rank test for bits 5 to 12, p=0.67785 b-rank test for bits 6 to 13, p=0.77680 b-rank test for bits 7 to 14, p=0.11245 b-rank test for bits 8 to 15, p=0.35791 b-rank test for bits 9 to 16, p=0.16822 b-rank test for bits 10 to 17, p=0.84642 b-rank test for bits 11 to 18, p=0.54128 b-rank test for bits 12 to 19, p=0.05860 b-rank test for bits 13 to 20, p=0.25602 b-rank test for bits 14 to 21, p=0.67963 b-rank test for bits 15 to 22, p=0.23360 b-rank test for bits 16 to 23, p=0.43516 b-rank test for bits 17 to 24, p=0.66905 b-rank test for bits 18 to 25, p=0.95048 b-rank test for bits 19 to 26, p=0.71573 b-rank test for bits 20 to 27, p=0.27854 b-rank test for bits 21 to 28, p=0.73949 b-rank test for bits 22 to 29, p=0.78887 b-rank test for bits 23 to 30, p=0.05318 b-rank test for bits 24 to 31, p=0.84882 b-rank test for bits 25 to 32, p=0.98513 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 = 0.550027 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-05-04_04:31 (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 141610 -0.70 0.242161 2 141989 0.19 0.573834 3 141233 -1.58 0.057029 4 142465 1.30 0.902907 5 141699 -0.49 0.311563 6 142203 0.69 0.753689 7 141653 -0.60 0.274619 8 141854 -0.13 0.448570 9 142441 1.24 0.892922 10 142408 1.17 0.878014 11 141996 0.20 0.580237 12 141713 -0.46 0.323219 13 142034 0.29 0.614583 14 141530 -0.89 0.187732 15 141638 -0.63 0.263057 16 142084 0.41 0.658403 17 141815 -0.22 0.412781 18 142633 1.69 0.954564 19 141271 -1.49 0.067925 20 141810 -0.23 0.408238 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-05-04_04:31 Bits used No. missing words z-score p-value 23 to 32 142298 1.3402 0.909917 22 to 31 141841 -0.2356 0.406864 21 to 30 141675 -0.8080 0.209535 20 to 29 142109 0.6885 0.754436 19 to 28 141875 -0.1184 0.452884 18 to 27 142195 0.9851 0.837705 17 to 26 141709 -0.6908 0.244848 16 to 25 141986 0.2644 0.604256 15 to 24 141764 -0.5011 0.308137 14 to 23 141749 -0.5529 0.290179 13 to 22 141909 -0.0011 0.499546 12 to 21 141831 -0.2701 0.393540 11 to 20 141913 0.0127 0.505049 10 to 19 141824 -0.2942 0.384287 9 to 18 141959 0.1713 0.567997 8 to 17 141438 -1.6253 0.052052 7 to 16 141957 0.1644 0.565284 6 to 15 141773 -0.4701 0.319141 5 to 14 141363 -1.8839 0.029789 4 to 13 142087 0.6127 0.729948 3 to 12 141951 0.1437 0.557127 2 to 11 141417 -1.6977 0.044783 1 to 10 141662 -0.8529 0.196868 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-05-04_04:31 Bits used No. missing words z-score p-value 28 to 32 142484 1.9480 0.974295 27 to 31 142289 1.2870 0.900956 26 to 30 142114 0.6938 0.756095 25 to 29 141864 -0.1537 0.438939 24 to 28 142580 2.2735 0.988501 23 to 27 141822 -0.2960 0.383602 22 to 26 141919 0.0328 0.513075 21 to 25 142139 0.7785 0.781875 20 to 24 142051 0.4802 0.684471 19 to 23 142410 1.6972 0.955169 18 to 22 141521 -1.3164 0.094024 17 to 21 142564 2.2192 0.986764 16 to 20 141953 0.1480 0.558842 15 to 19 141898 -0.0384 0.484682 14 to 18 141895 -0.0486 0.480629 13 to 17 142167 0.8735 0.808793 12 to 16 141480 -1.4554 0.072785 11 to 15 142369 1.5582 0.940407 10 to 14 141873 -0.1232 0.450993 9 to 13 142160 0.8497 0.802262 8 to 12 142009 0.3379 0.632267 7 to 11 141638 -0.9198 0.178848 6 to 10 141649 -0.8825 0.188760 5 to 9 142226 1.0735 0.858467 4 to 8 142223 1.0633 0.856174 3 to 7 142129 0.7446 0.771757 2 to 6 142135 0.7650 0.777859 1 to 5 142100 0.6463 0.740970 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-05-04_04:31 Bits used No. missing words z-score p-value 31 to 32 141591 -0.9390 0.173859 30 to 31 142009 0.2940 0.615626 29 to 30 141438 -1.3904 0.082211 28 to 29 141327 -1.7178 0.042918 27 to 28 142145 0.6952 0.756532 26 to 27 142318 1.2055 0.885998 25 to 26 142240 0.9754 0.835326 24 to 25 141250 -1.9449 0.025892 23 to 24 141865 -0.1308 0.447980 22 to 23 141732 -0.5231 0.300453 21 to 22 141755 -0.4553 0.324464 20 to 21 141330 -1.7089 0.043731 19 to 20 142171 0.7719 0.779910 18 to 19 141735 -0.5142 0.303539 17 to 18 142247 0.9961 0.840394 16 to 17 141908 -0.0039 0.498435 15 to 16 141957 0.1406 0.555915 14 to 15 141671 -0.7030 0.241016 13 to 14 141980 0.2085 0.582568 12 to 13 142523 1.8102 0.964870 11 to 12 142580 1.9784 0.976057 10 to 11 141259 -1.9184 0.027532 9 to 10 142297 1.1436 0.873599 8 to 9 141741 -0.4965 0.309754 7 to 8 141823 -0.2547 0.399493 6 to 7 141461 -1.3225 0.093000 5 to 6 142030 0.3560 0.639064 4 to 5 141848 -0.1809 0.428217 3 to 4 141721 -0.5555 0.289261 2 to 3 141331 -1.7060 0.044005 1 to 2 142101 0.5654 0.714099 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-05-04_04:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2469.07 -0.437 0.330882 Test results for specific bytes for dh-ranFile-2016-05-04_04:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2485.93 -0.199 0.421156 2 to 9 2418.42 -1.154 0.124314 3 to 10 2497.73 -0.032 0.487216 4 to 11 2514.90 0.211 0.583463 5 to 12 2290.94 -2.956 0.001556 6 to 13 2431.35 -0.971 0.165810 7 to 14 2506.16 0.087 0.534738 8 to 15 2521.92 0.310 0.621728 9 to 16 2526.68 0.377 0.647033 10 to 17 2434.55 -0.926 0.177325 11 to 18 2477.81 -0.314 0.376838 12 to 19 2559.08 0.836 0.798298 13 to 20 2471.52 -0.403 0.343539 14 to 21 2532.35 0.458 0.676344 15 to 22 2535.99 0.509 0.694594 16 to 23 2576.43 1.081 0.860133 17 to 24 2553.22 0.753 0.774177 18 to 25 2543.38 0.614 0.730232 19 to 26 2530.73 0.435 0.668074 20 to 27 2544.60 0.631 0.735899 21 to 28 2458.60 -0.586 0.279103 22 to 29 2550.26 0.711 0.761382 23 to 30 2587.90 1.243 0.893093 24 to 31 2513.94 0.197 0.578147 25 to 32 2406.49 -1.322 0.093005 CDPARK for dh-ranFile-2016-05-04_04:31: 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 3504 -0.8676 0.192812 3527 0.1826 0.572463 3518 -0.2283 0.409702 3514 -0.4110 0.340551 3501 -1.0046 0.157553 3514 -0.4110 0.340551 3490 -1.5068 0.065925 3543 0.9132 0.819442 3550 1.2329 0.891189 3522 -0.0457 0.481790 Square side=100, avg. no. parked=3518.30 sample std.=17.45 p-value of the KSTEST for those 10 p-values: 0.712181 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-05-04_04:31 0.9476,0.4342,0.1458,0.8570,0.4758,0.7905,0.0456,0.6806,0.7046,0.9398, The KS test for those 10 p-values: 0.409288 The 3DSPHERES test for dh-ranFile-2016-05-04_04:31 sample no r^3 equiv. uni. 1 18.270 0.456099 2 7.577 0.223184 3 27.763 0.603645 4 34.417 0.682482 5 61.706 0.872147 6 6.852 0.204182 7 5.133 0.157263 8 5.982 0.180775 9 69.629 0.901822 10 10.288 0.290319 11 30.134 0.633758 12 9.877 0.280529 13 9.563 0.272957 14 83.096 0.937330 15 68.544 0.898205 16 13.529 0.362987 17 2.916 0.092629 18 73.599 0.913992 19 67.795 0.895632 20 36.365 0.702450 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.566032 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-05-04_04:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 1.3 0.1 1.5 1.1 -0.7 -0.8 -0.3 -0.9 0.3 0.2 -0.6 0.5 0.2 1.7 -0.5 0.1 0.5 0.2 -0.0 -0.4 0.5 -0.3 0.2 1.4 -0.6 -1.0 -2.4 1.5 -0.5 -1.8 -2.1 0.6 -0.8 -1.5 0.3 0.4 -0.9 -0.1 -1.6 -0.7 -1.3 2.0 -1.1 Chi-square with 42 degrees of freedom:45.920813 z-score=0.427796, p-value=0.687026 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-05-04_04:31 Test no p-value 1 0.341128 2 0.926450 3 0.609356 4 0.233647 5 0.461397 6 0.494624 7 0.111933 8 0.332486 9 0.556032 10 0.353792 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.468235 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-05-04_04:31: (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 66718 0.04 66705 0.02 3 25000.00 24933 0.18 24900 0.40 4 6666.67 6654 0.02 6750 1.04 5 1388.89 1432 1.34 1378 0.09 6 238.10 223 0.96 231 0.21 7 34.72 33 0.09 32 0.21 8 4.96 6 0.22 3 0.77 p=0.17155 p=0.16026 Number of rngs required: 687834, p-value: 0.256 RESULTS OF CRAPS TEST for dh-ranFile-2016-05-04_04:31 No. of wins: Observed Expected 98772 98585.9 z-score= 0.833, pvalue=0.79745 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66439 66666.7 0.777 0.777 2 37573 37654.3 0.176 0.953 3 27101 26954.7 0.794 1.747 4 19243 19313.5 0.257 2.004 5 13771 13851.4 0.467 2.471 6 10058 9943.5 1.317 3.788 7 7162 7145.0 0.040 3.829 8 5166 5139.1 0.141 3.970 9 3660 3699.9 0.430 4.399 10 2741 2666.3 2.093 6.492 11 1973 1923.3 1.283 7.775 12 1439 1388.7 1.819 9.594 13 1009 1003.7 0.028 9.622 14 736 726.1 0.134 9.756 15 540 525.8 0.382 10.137 16 403 381.2 1.253 11.390 17 283 276.5 0.151 11.541 18 198 200.8 0.040 11.580 19 138 146.0 0.437 12.017 20 114 106.2 0.571 12.588 21 253 287.1 4.053 16.641 Chisq= 16.64 for 20 degrees of freedom, p= 0.32386 SUMMARY of craptest p-value for no. of wins: 0.797446 p-value for throws/game: 0.323856 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-05-04_04:31 No. of wins: Observed Expected 98631 98585.9 z-score= 0.202, pvalue=0.58000 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66764 66666.7 0.142 0.142 2 38049 37654.3 4.137 4.279 3 26730 26954.7 1.874 6.153 4 19086 19313.5 2.679 8.832 5 13979 13851.4 1.175 10.007 6 9827 9943.5 1.366 11.373 7 7054 7145.0 1.160 12.532 8 5181 5139.1 0.342 12.874 9 3710 3699.9 0.028 12.902 10 2684 2666.3 0.118 13.020 11 1938 1923.3 0.112 13.132 12 1405 1388.7 0.190 13.322 13 954 1003.7 2.462 15.784 14 716 726.1 0.142 15.926 15 545 525.8 0.698 16.624 16 383 381.2 0.009 16.633 17 278 276.5 0.008 16.641 18 221 200.8 2.026 18.667 19 124 146.0 3.311 21.978 20 94 106.2 1.405 23.382 21 278 287.1 0.289 23.672 Chisq= 23.67 for 20 degrees of freedom, p= 0.74297 SUMMARY of craptest p-value for no. of wins: 0.580002 p-value for throws/game: 0.742972 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0016,0.0222,0.0241,0.0259,0.0275,0.0298,0.0429,0.0437,0.0440,0.0448, 0.0456,0.0478,0.0521,0.0532,0.0570,0.0586,0.0659,0.0679,0.0728,0.0777, 0.0822,0.0926,0.0930,0.0930,0.0940,0.0951,0.0972,0.1062,0.1119,0.1124, 0.1243,0.1408,0.1458,0.1548,0.1566,0.1573,0.1576,0.1603,0.1658,0.1682, 0.1715,0.1739,0.1773,0.1788,0.1808,0.1832,0.1877,0.1888,0.1928,0.1969, 0.2042,0.2095,0.2173,0.2232,0.2336,0.2336,0.2410,0.2422,0.2448,0.2557, 0.2560,0.2631,0.2730,0.2746,0.2767,0.2785,0.2791,0.2805,0.2851,0.2893, 0.2902,0.2903,0.2931,0.2934,0.2986,0.3005,0.3035,0.3081,0.3098,0.3116, 0.3171,0.3189,0.3191,0.3232,0.3233,0.3239,0.3245,0.3309,0.3325,0.3406, 0.3406,0.3411,0.3435,0.3538,0.3579,0.3630,0.3768,0.3816,0.3836,0.3843, 0.3935,0.3944,0.3995,0.4061,0.4069,0.4082,0.4093,0.4097,0.4098,0.4128, 0.4212,0.4282,0.4342,0.4352,0.4389,0.4471,0.4480,0.4486,0.4488,0.4510, 0.4529,0.4561,0.4614,0.4682,0.4758,0.4806,0.4818,0.4847,0.4852,0.4872, 0.4937,0.4946,0.4984,0.4995,0.5050,0.5131,0.5268,0.5277,0.5347,0.5413, 0.5462,0.5500,0.5559,0.5560,0.5571,0.5588,0.5653,0.5660,0.5680,0.5725, 0.5738,0.5781,0.5800,0.5802,0.5826,0.5834,0.5835,0.5910,0.6036,0.6043, 0.6094,0.6116,0.6133,0.6146,0.6156,0.6185,0.6217,0.6323,0.6338,0.6357, 0.6391,0.6456,0.6470,0.6584,0.6649,0.6681,0.6691,0.6701,0.6763,0.6779, 0.6796,0.6806,0.6825,0.6845,0.6870,0.6946,0.7024,0.7028,0.7046,0.7057, 0.7122,0.7141,0.7146,0.7157,0.7187,0.7299,0.7302,0.7359,0.7395,0.7410, 0.7430,0.7456,0.7534,0.7537,0.7544,0.7561,0.7565,0.7614,0.7629,0.7657, 0.7686,0.7718,0.7742,0.7768,0.7779,0.7799,0.7819,0.7889,0.7905,0.7974, 0.7983,0.8023,0.8081,0.8088,0.8194,0.8225,0.8353,0.8377,0.8404,0.8429, 0.8464,0.8484,0.8488,0.8562,0.8570,0.8585,0.8601,0.8721,0.8736,0.8780, 0.8860,0.8912,0.8929,0.8931,0.8956,0.8982,0.9010,0.9018,0.9029,0.9099, 0.9123,0.9140,0.9265,0.9269,0.9373,0.9398,0.9404,0.9476,0.9505,0.9546, 0.9552,0.9607,0.9617,0.9649,0.9743,0.9761,0.9851,0.9868,0.9885, Overall p-value after applying KStest on 269 p-values = 0.740419 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.