RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-06-10_13:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.77 14.3245 0.355986 2 to 25 15.84 20.0734 0.729510 3 to 26 15.80 8.7334 0.051743 4 to 27 15.73 10.3209 0.110383 5 to 28 15.97 28.5198 0.960781 6 to 29 15.86 19.9062 0.720944 7 to 30 15.67 32.3610 0.986434 8 to 31 15.72 20.9174 0.769994 9 to 32 15.84 18.8447 0.662481 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.324372 Tough bday spacings test for dh-ranFile-2015-06-10_13:31: 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 43 73 99 94 75 61 26 12 6 5 (O-E)^2/E 1.1 1.1 0.0 0.0 0.1 0.1 1.5 0.5 0.6 0.1 0.2 Birthday Spacings: Sum(O-E)^2/E= 5.310, p= 0.130 RESULTS OF GCD FOR dh-ranFile-2015-06-10_13:31 Euclid's algorithm: p-value, steps to gcd: 0.149545 p-value, dist. of gcd's: 0.899107 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-06-10_13:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.148 0.299 0.581 0.704 0.492 0.121 0.398 0.803 Bits 8 to 15---> 0.252 0.495 0.283 0.711 0.775 0.156 0.806 0.670 Bits 16 to 23---> 0.057 0.569 0.912 0.411 0.917 0.569 0.896 0.971 Bits 24 to 31---> 0.862 0.084 0.569 0.476 0.885 0.222 0.047 0.500 KS test for the above 32 p values: 0.029 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-06-10_13:31, p-values for 5 runs: 0.3901, 0.0723, 0.2728, 0.6738, 0.5008 Rank test for binary matrices (31x31) for dh-ranFile-2015-06-10_13:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 235 211.4 2.630 2.630 r= 29 5170 5134.0 0.252 2.883 r= 30 22845 23103.0 2.882 5.765 r= 31 11750 11551.5 3.410 9.175 chi-square = 9.175 with df = 3; p-value = 0.973 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-06-10_13:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 205 211.4 0.195 0.195 r= 30 5011 5134.0 2.947 3.142 r= 31 23120 23103.0 0.012 3.155 r= 32 11664 11551.5 1.095 4.250 chi-square = 4.250 with df = 3; p-value = 0.764 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-06-10_13:31 b-rank test for bits 1 to 8, p=0.92612 b-rank test for bits 2 to 9, p=0.57270 b-rank test for bits 3 to 10, p=0.77685 b-rank test for bits 4 to 11, p=0.56286 b-rank test for bits 5 to 12, p=0.27557 b-rank test for bits 6 to 13, p=0.07704 b-rank test for bits 7 to 14, p=0.10676 b-rank test for bits 8 to 15, p=0.04123 b-rank test for bits 9 to 16, p=0.58321 b-rank test for bits 10 to 17, p=0.89930 b-rank test for bits 11 to 18, p=0.54685 b-rank test for bits 12 to 19, p=0.48366 b-rank test for bits 13 to 20, p=0.89718 b-rank test for bits 14 to 21, p=0.13869 b-rank test for bits 15 to 22, p=0.23188 b-rank test for bits 16 to 23, p=0.02776 b-rank test for bits 17 to 24, p=0.58652 b-rank test for bits 18 to 25, p=0.49700 b-rank test for bits 19 to 26, p=0.92963 b-rank test for bits 20 to 27, p=0.13850 b-rank test for bits 21 to 28, p=0.70898 b-rank test for bits 22 to 29, p=0.00987 b-rank test for bits 23 to 30, p=0.73520 b-rank test for bits 24 to 31, p=0.89489 b-rank test for bits 25 to 32, p=0.48147 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 = 0.602363 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-06-10_13:31 (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 142350 1.03 0.848402 2 142177 0.63 0.734145 3 141816 -0.22 0.413691 4 141627 -0.66 0.254739 5 142362 1.06 0.854890 6 141883 -0.06 0.475473 7 141183 -1.70 0.044845 8 141850 -0.14 0.444875 9 142018 0.25 0.600214 10 141898 -0.03 0.489440 11 142170 0.61 0.728752 12 142011 0.24 0.593884 13 141786 -0.29 0.386614 14 141721 -0.44 0.329960 15 141998 0.21 0.582063 16 142234 0.76 0.775947 17 142177 0.63 0.734145 18 142000 0.21 0.583886 19 141913 0.01 0.503421 20 142265 0.83 0.797015 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-06-10_13:31 Bits used No. missing words z-score p-value 23 to 32 141958 0.1678 0.566641 22 to 31 141975 0.2264 0.589574 21 to 30 142071 0.5575 0.711401 20 to 29 141637 -0.9391 0.173848 19 to 28 142039 0.4471 0.672612 18 to 27 141993 0.2885 0.613525 17 to 26 141697 -0.7322 0.232032 16 to 25 142049 0.4816 0.684962 15 to 24 141537 -1.2839 0.099589 14 to 23 141514 -1.3632 0.086409 13 to 22 142337 1.4747 0.929857 12 to 21 142351 1.5230 0.936121 11 to 20 141647 -0.9046 0.182842 10 to 19 141804 -0.3632 0.358225 9 to 18 141711 -0.6839 0.247020 8 to 17 142133 0.7713 0.779728 7 to 16 142369 1.5851 0.943525 6 to 15 142164 0.8782 0.810075 5 to 14 141751 -0.5460 0.292545 4 to 13 141779 -0.4494 0.326567 3 to 12 142151 0.8333 0.797675 2 to 11 141540 -1.2736 0.101411 1 to 10 141659 -0.8632 0.194012 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-06-10_13:31 Bits used No. missing words z-score p-value 28 to 32 142086 0.5989 0.725374 27 to 31 141718 -0.6486 0.258306 26 to 30 141923 0.0463 0.518480 25 to 29 141833 -0.2587 0.397916 24 to 28 141625 -0.9638 0.167565 23 to 27 141934 0.0836 0.533324 22 to 26 142118 0.7074 0.760327 21 to 25 141759 -0.5096 0.305168 20 to 24 141652 -0.8723 0.191521 19 to 23 141866 -0.1469 0.441613 18 to 22 141571 -1.1469 0.125715 17 to 21 141684 -0.7638 0.222484 16 to 20 142438 1.7921 0.963442 15 to 19 142017 0.3650 0.642438 14 to 18 142061 0.5141 0.696421 13 to 17 141948 0.1311 0.552146 12 to 16 141836 -0.2486 0.401844 11 to 15 142203 0.9955 0.840251 10 to 14 141751 -0.5367 0.295733 9 to 13 141803 -0.3604 0.359259 8 to 12 141958 0.1650 0.565521 7 to 11 142181 0.9209 0.821453 6 to 10 141483 -1.4452 0.074203 5 to 9 141539 -1.2554 0.104675 4 to 8 141407 -1.7028 0.044301 3 to 7 142321 1.3955 0.918566 2 to 6 141971 0.2091 0.582796 1 to 5 141921 0.0396 0.515778 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-06-10_13:31 Bits used No. missing words z-score p-value 31 to 32 142424 1.5182 0.935518 30 to 31 142182 0.8043 0.789399 29 to 30 142088 0.5271 0.700921 28 to 29 141860 -0.1455 0.442152 27 to 28 141534 -1.1072 0.134111 26 to 27 141641 -0.7915 0.214316 25 to 26 141787 -0.3609 0.359104 24 to 25 142336 1.2586 0.895915 23 to 24 141806 -0.3048 0.380256 22 to 23 142728 2.4150 0.992131 21 to 22 141904 -0.0157 0.493728 20 to 21 142015 0.3117 0.622370 19 to 20 141474 -1.2842 0.099543 18 to 19 142179 0.7955 0.786835 17 to 18 142126 0.6391 0.738636 16 to 17 142617 2.0875 0.981580 15 to 16 141465 -1.3107 0.094978 14 to 15 141143 -2.2606 0.011893 13 to 14 142023 0.3353 0.631304 12 to 13 142039 0.3825 0.648958 11 to 12 141848 -0.1809 0.428217 10 to 11 142017 0.3176 0.624610 9 to 10 142115 0.6067 0.727974 8 to 9 141826 -0.2458 0.402914 7 to 8 141766 -0.4228 0.336220 6 to 7 142132 0.6568 0.744359 5 to 6 141820 -0.2635 0.396079 4 to 5 141851 -0.1721 0.431693 3 to 4 142113 0.6008 0.726012 2 to 3 142210 0.8869 0.812442 1 to 2 141872 -0.1101 0.456158 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-06-10_13:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2370.09 -1.837 0.033092 Test results for specific bytes for dh-ranFile-2015-06-10_13:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2503.77 0.053 0.521278 2 to 9 2585.82 1.214 0.887569 3 to 10 2500.72 0.010 0.504064 4 to 11 2426.81 -1.035 0.150326 5 to 12 2413.48 -1.224 0.110544 6 to 13 2607.94 1.527 0.936566 7 to 14 2490.99 -0.127 0.449293 8 to 15 2550.83 0.719 0.763866 9 to 16 2518.12 0.256 0.601122 10 to 17 2401.26 -1.396 0.081294 11 to 18 2642.54 2.016 0.978087 12 to 19 2517.13 0.242 0.595708 13 to 20 2472.58 -0.388 0.349097 14 to 21 2432.05 -0.961 0.168297 15 to 22 2445.75 -0.767 0.221465 16 to 23 2481.28 -0.265 0.395619 17 to 24 2583.30 1.178 0.880612 18 to 25 2468.70 -0.443 0.328985 19 to 26 2472.38 -0.391 0.348041 20 to 27 2551.77 0.732 0.767976 21 to 28 2559.98 0.848 0.801836 22 to 29 2535.15 0.497 0.690462 23 to 30 2481.52 -0.261 0.396904 24 to 31 2404.02 -1.357 0.087337 25 to 32 2492.24 -0.110 0.456288 CDPARK for dh-ranFile-2015-06-10_13:31: 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 3515 -0.3653 0.357445 3562 1.7808 0.962529 3515 -0.3653 0.357445 3532 0.4110 0.659449 3524 0.0457 0.518210 3521 -0.0913 0.463617 3555 1.4612 0.928018 3523 0.0000 0.500000 3511 -0.5479 0.291865 3515 -0.3653 0.357445 Square side=100, avg. no. parked=3527.30 sample std.=16.68 p-value of the KSTEST for those 10 p-values: 0.400837 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-06-10_13:31 0.2405,0.2085,0.4052,0.4942,0.6147,0.4586,0.9706,0.6439,0.5872,0.4593, The KS test for those 10 p-values: 0.465665 The 3DSPHERES test for dh-ranFile-2015-06-10_13:31 sample no r^3 equiv. uni. 1 3.576 0.112360 2 8.092 0.236412 3 16.597 0.424917 4 7.519 0.221680 5 14.333 0.379838 6 39.166 0.728975 7 20.391 0.493228 8 70.181 0.903610 9 31.654 0.651853 10 11.319 0.314297 11 14.589 0.385107 12 19.826 0.483601 13 69.409 0.901097 14 19.596 0.479623 15 16.026 0.413855 16 0.592 0.019524 17 78.003 0.925734 18 22.822 0.532675 19 11.234 0.312349 20 9.842 0.279686 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.466862 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-06-10_13:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -0.3 -1.1 -0.5 -0.2 -0.4 0.4 1.3 -0.3 1.0 1.2 1.2 -0.0 -0.5 0.2 -2.4 -1.9 0.4 0.8 0.9 0.6 0.7 1.3 -0.6 -1.6 -1.1 0.0 -0.4 -0.8 0.6 0.9 -0.1 0.6 0.2 0.1 -0.5 0.7 -1.7 -0.4 1.0 -1.3 1.0 -0.1 Chi-square with 42 degrees of freedom:35.380376 z-score=-0.722260, p-value=0.245000 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-06-10_13:31 Test no p-value 1 0.242787 2 0.456850 3 0.641611 4 0.002237 5 0.124517 6 0.544611 7 0.686296 8 0.113420 9 0.416243 10 0.049539 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.073775 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-06-10_13:31: (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 66522 0.31 3 25000.00 24899 0.41 25019 0.01 4 6666.67 6827 3.86 6789 2.24 5 1388.89 1336 2.01 1359 0.64 6 238.10 221 1.23 272 4.83 7 34.72 36 0.05 33 0.09 8 4.96 5 0.00 5 0.00 p=0.72737 p=0.77126 Number of rngs required: 688195, p-value: 0.405 RESULTS OF CRAPS TEST for dh-ranFile-2015-06-10_13:31 No. of wins: Observed Expected 98860 98585.9 z-score= 1.226, pvalue=0.88992 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66388 66666.7 1.165 1.165 2 37726 37654.3 0.136 1.301 3 27127 26954.7 1.101 2.402 4 19354 19313.5 0.085 2.487 5 13894 13851.4 0.131 2.618 6 9829 9943.5 1.319 3.938 7 7110 7145.0 0.172 4.109 8 5191 5139.1 0.525 4.634 9 3712 3699.9 0.040 4.674 10 2746 2666.3 2.383 7.056 11 1923 1923.3 0.000 7.056 12 1406 1388.7 0.215 7.271 13 1017 1003.7 0.176 7.447 14 733 726.1 0.065 7.512 15 546 525.8 0.773 8.285 16 361 381.2 1.065 9.350 17 249 276.5 2.743 12.093 18 199 200.8 0.017 12.109 19 135 146.0 0.827 12.936 20 94 106.2 1.405 14.341 21 260 287.1 2.561 16.901 Chisq= 16.90 for 20 degrees of freedom, p= 0.34062 SUMMARY of craptest p-value for no. of wins: 0.889923 p-value for throws/game: 0.340622 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-06-10_13:31 No. of wins: Observed Expected 98815 98585.9 z-score= 1.025, pvalue=0.84728 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66416 66666.7 0.943 0.943 2 37586 37654.3 0.124 1.066 3 27053 26954.7 0.358 1.425 4 19433 19313.5 0.740 2.165 5 13930 13851.4 0.446 2.610 6 10029 9943.5 0.734 3.345 7 7078 7145.0 0.629 3.974 8 5135 5139.1 0.003 3.977 9 3707 3699.9 0.014 3.991 10 2623 2666.3 0.703 4.694 11 1942 1923.3 0.181 4.875 12 1305 1388.7 5.049 9.924 13 1047 1003.7 1.867 11.791 14 743 726.1 0.391 12.182 15 567 525.8 3.222 15.405 16 376 381.2 0.070 15.475 17 267 276.5 0.329 15.804 18 210 200.8 0.419 16.222 19 133 146.0 1.155 17.377 20 108 106.2 0.030 17.407 21 312 287.1 2.157 19.564 Chisq= 19.56 for 20 degrees of freedom, p= 0.51453 SUMMARY of craptest p-value for no. of wins: 0.847284 p-value for throws/game: 0.514531 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0022,0.0099,0.0119,0.0195,0.0278,0.0289,0.0331,0.0412,0.0443,0.0448, 0.0466,0.0495,0.0517,0.0568,0.0723,0.0738,0.0742,0.0770,0.0813,0.0838, 0.0864,0.0873,0.0950,0.0995,0.0996,0.1014,0.1047,0.1068,0.1104,0.1105, 0.1124,0.1134,0.1211,0.1245,0.1257,0.1305,0.1341,0.1385,0.1387,0.1477, 0.1495,0.1503,0.1556,0.1676,0.1683,0.1738,0.1828,0.1915,0.1940,0.2085, 0.2143,0.2215,0.2217,0.2219,0.2225,0.2319,0.2320,0.2364,0.2405,0.2428, 0.2450,0.2470,0.2520,0.2547,0.2583,0.2728,0.2756,0.2797,0.2828,0.2919, 0.2925,0.2957,0.2987,0.3052,0.3123,0.3143,0.3244,0.3266,0.3290,0.3300, 0.3362,0.3406,0.3480,0.3491,0.3560,0.3574,0.3574,0.3574,0.3582,0.3591, 0.3593,0.3798,0.3803,0.3851,0.3866,0.3901,0.3956,0.3961,0.3969,0.3979, 0.3979,0.4008,0.4018,0.4029,0.4052,0.4054,0.4115,0.4137,0.4139,0.4162, 0.4249,0.4282,0.4317,0.4416,0.4422,0.4449,0.4493,0.4562,0.4563,0.4569, 0.4586,0.4593,0.4636,0.4657,0.4669,0.4755,0.4764,0.4796,0.4815,0.4836, 0.4837,0.4894,0.4916,0.4932,0.4937,0.4942,0.4947,0.4970,0.5000,0.5000, 0.5008,0.5034,0.5041,0.5145,0.5158,0.5182,0.5185,0.5213,0.5327,0.5333, 0.5446,0.5468,0.5521,0.5629,0.5655,0.5666,0.5687,0.5690,0.5691,0.5727, 0.5810,0.5821,0.5828,0.5832,0.5839,0.5865,0.5872,0.5896,0.5939,0.5957, 0.6002,0.6011,0.6024,0.6135,0.6147,0.6224,0.6246,0.6313,0.6416,0.6424, 0.6439,0.6490,0.6519,0.6594,0.6625,0.6697,0.6726,0.6738,0.6850,0.6863, 0.6905,0.6964,0.7009,0.7039,0.7090,0.7108,0.7114,0.7209,0.7254,0.7260, 0.7274,0.7280,0.7288,0.7290,0.7295,0.7341,0.7341,0.7352,0.7386,0.7444, 0.7603,0.7639,0.7643,0.7680,0.7700,0.7713,0.7753,0.7759,0.7768,0.7797, 0.7868,0.7894,0.7970,0.7977,0.8018,0.8033,0.8058,0.8101,0.8124,0.8215, 0.8403,0.8473,0.8484,0.8549,0.8623,0.8806,0.8850,0.8876,0.8899,0.8949, 0.8959,0.8961,0.8972,0.8991,0.8993,0.9011,0.9036,0.9124,0.9171,0.9186, 0.9257,0.9261,0.9280,0.9296,0.9299,0.9355,0.9361,0.9366,0.9435,0.9608, 0.9625,0.9634,0.9706,0.9708,0.9729,0.9781,0.9816,0.9864,0.9921, Overall p-value after applying KStest on 269 p-values = 0.536336 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.