RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-01-20_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 16.11 25.0831 0.907135 2 to 25 16.01 11.5759 0.174892 3 to 26 15.91 16.1149 0.484298 4 to 27 15.85 11.6641 0.179964 5 to 28 16.21 20.1171 0.731717 6 to 29 16.14 6.6015 0.011854 7 to 30 16.04 24.5304 0.894274 8 to 31 15.85 16.5619 0.515593 9 to 32 15.97 12.2892 0.217681 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.779149 Tough bday spacings test for dh-ranFile-2017-01-20_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 13 41 76 92 93 84 43 38 10 5 5 (O-E)^2/E 1.6 0.5 0.1 0.3 0.2 0.4 1.6 2.3 1.6 0.4 0.2 Birthday Spacings: Sum(O-E)^2/E= 9.305, p= 0.497 RESULTS OF GCD FOR dh-ranFile-2017-01-20_04:31 Euclid's algorithm: p-value, steps to gcd: 0.007656 p-value, dist. of gcd's: 0.170609 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-01-20_04:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.201 0.415 0.228 0.058 0.592 0.619 0.589 0.253 Bits 8 to 15---> 0.314 0.279 0.793 0.786 0.727 0.268 0.838 0.050 Bits 16 to 23---> 0.722 0.813 0.240 0.531 0.547 0.273 0.955 0.643 Bits 24 to 31---> 0.038 0.291 0.081 0.121 0.188 0.361 0.954 0.168 KS test for the above 32 p values: 0.688 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-01-20_04:31, p-values for 5 runs: 0.9432, 0.0334, 0.2638, 0.6623, 0.8758 Rank test for binary matrices (31x31) for dh-ranFile-2017-01-20_04:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 224 211.4 0.749 0.749 r= 29 5103 5134.0 0.187 0.936 r= 30 23245 23103.0 0.872 1.808 r= 31 11428 11551.5 1.321 3.129 chi-square = 3.129 with df = 3; p-value = 0.628 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2017-01-20_04:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 211 211.4 0.001 0.001 r= 30 5178 5134.0 0.377 0.378 r= 31 22922 23103.0 1.419 1.797 r= 32 11689 11551.5 1.636 3.433 chi-square = 3.433 with df = 3; p-value = 0.670 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2017-01-20_04:31 b-rank test for bits 1 to 8, p=0.95523 b-rank test for bits 2 to 9, p=0.55813 b-rank test for bits 3 to 10, p=0.32651 b-rank test for bits 4 to 11, p=0.21463 b-rank test for bits 5 to 12, p=0.39379 b-rank test for bits 6 to 13, p=0.52550 b-rank test for bits 7 to 14, p=0.71130 b-rank test for bits 8 to 15, p=0.20541 b-rank test for bits 9 to 16, p=0.11973 b-rank test for bits 10 to 17, p=0.10109 b-rank test for bits 11 to 18, p=0.26034 b-rank test for bits 12 to 19, p=0.65974 b-rank test for bits 13 to 20, p=0.58937 b-rank test for bits 14 to 21, p=0.51058 b-rank test for bits 15 to 22, p=0.32604 b-rank test for bits 16 to 23, p=0.86762 b-rank test for bits 17 to 24, p=0.69412 b-rank test for bits 18 to 25, p=0.71928 b-rank test for bits 19 to 26, p=0.81095 b-rank test for bits 20 to 27, p=0.58110 b-rank test for bits 21 to 28, p=0.11725 b-rank test for bits 22 to 29, p=0.22674 b-rank test for bits 23 to 30, p=0.58406 b-rank test for bits 24 to 31, p=0.21536 b-rank test for bits 25 to 32, p=0.20646 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 = 0.467440 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-01-20_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 142296 0.90 0.816852 2 141964 0.13 0.550820 3 142262 0.82 0.795029 4 142109 0.47 0.679578 5 142108 0.46 0.678741 6 141822 -0.20 0.419160 7 141119 -1.85 0.032405 8 142420 1.19 0.883596 9 141865 -0.10 0.458753 10 142728 1.91 0.972112 11 142111 0.47 0.681248 12 142045 0.32 0.624373 13 141631 -0.65 0.257748 14 142291 0.89 0.813737 15 141602 -0.72 0.236360 16 141434 -1.11 0.133374 17 142011 0.24 0.593884 18 142651 1.73 0.958441 19 142625 1.67 0.952750 20 141630 -0.65 0.256994 ---------------------------------------------------------------- OPSO test for dh-ranFile-2017-01-20_04:31 Bits used No. missing words z-score p-value 23 to 32 142258 1.2023 0.885378 22 to 31 142350 1.5196 0.935688 21 to 30 141935 0.0885 0.535267 20 to 29 141792 -0.4046 0.342891 19 to 28 141772 -0.4736 0.317910 18 to 27 141834 -0.2598 0.397525 17 to 26 142093 0.6333 0.736746 16 to 25 141818 -0.3149 0.376407 15 to 24 141803 -0.3667 0.356938 14 to 23 142215 1.0540 0.854066 13 to 22 141871 -0.1322 0.447424 12 to 21 141980 0.2437 0.596264 11 to 20 141777 -0.4563 0.324083 10 to 19 141476 -1.4942 0.067556 9 to 18 141771 -0.4770 0.316681 8 to 17 142003 0.3230 0.626652 7 to 16 142097 0.6471 0.741229 6 to 15 142475 1.9506 0.974447 5 to 14 142007 0.3368 0.631864 4 to 13 142161 0.8678 0.807256 3 to 12 142175 0.9161 0.820194 2 to 11 142003 0.3230 0.626652 1 to 10 142163 0.8747 0.809138 ----------------------------------------------------------------- OQSO test for dh-ranFile-2017-01-20_04:31 Bits used No. missing words z-score p-value 28 to 32 141902 -0.0248 0.490088 27 to 31 141764 -0.4926 0.311132 26 to 30 141531 -1.2825 0.099838 25 to 29 141621 -0.9774 0.164188 24 to 28 141682 -0.7706 0.220469 23 to 27 142413 1.7074 0.956122 22 to 26 141294 -2.0859 0.018495 21 to 25 141379 -1.7977 0.036110 20 to 24 141984 0.2531 0.599912 19 to 23 142064 0.5243 0.699967 18 to 22 141985 0.2565 0.601221 17 to 21 141259 -2.2045 0.013744 16 to 20 141730 -0.6079 0.271628 15 to 19 141792 -0.3977 0.345415 14 to 18 142254 1.1684 0.878672 13 to 17 141882 -0.0926 0.463093 12 to 16 142283 1.2667 0.897365 11 to 15 142229 1.0836 0.860735 10 to 14 142065 0.5277 0.701145 9 to 13 141837 -0.2452 0.403156 8 to 12 142291 1.2938 0.902132 7 to 11 142143 0.7921 0.785849 6 to 10 141590 -1.0825 0.139521 5 to 9 141905 -0.0147 0.494145 4 to 8 142089 0.6091 0.728755 3 to 7 141278 -2.1401 0.016173 2 to 6 141580 -1.1164 0.132131 1 to 5 141819 -0.3062 0.379725 ----------------------------------------------------------------- DNA test for dh-ranFile-2017-01-20_04:31 Bits used No. missing words z-score p-value 31 to 32 142090 0.5329 0.702966 30 to 31 141786 -0.3638 0.358002 29 to 30 141513 -1.1691 0.121179 28 to 29 141931 0.0639 0.525484 27 to 28 142042 0.3914 0.652233 26 to 27 142029 0.3530 0.637959 25 to 26 141383 -1.5526 0.060260 24 to 25 141769 -0.4140 0.339454 23 to 24 142092 0.5388 0.705005 22 to 23 141793 -0.3432 0.365740 21 to 22 142014 0.3088 0.621248 20 to 21 141838 -0.2104 0.416673 19 to 20 142287 1.1141 0.867376 18 to 19 142068 0.4681 0.680127 17 to 18 142107 0.5831 0.720086 16 to 17 141878 -0.0924 0.463183 15 to 16 141739 -0.5024 0.307676 14 to 15 142028 0.3501 0.636853 13 to 14 142081 0.5064 0.693713 12 to 13 142106 0.5801 0.719092 11 to 12 141369 -1.5939 0.055480 10 to 11 141780 -0.3815 0.351415 9 to 10 142330 1.2409 0.892681 8 to 9 141637 -0.8033 0.210891 7 to 8 142414 1.4887 0.931717 6 to 7 142003 0.2763 0.608846 5 to 6 141790 -0.3520 0.362417 4 to 5 141653 -0.7561 0.224784 3 to 4 141296 -1.8092 0.035207 2 to 3 142013 0.3058 0.620126 1 to 2 142004 0.2793 0.609978 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2017-01-20_04:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2517.31 0.245 0.596712 Test results for specific bytes for dh-ranFile-2017-01-20_04:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2477.67 -0.316 0.376092 2 to 9 2564.65 0.914 0.819726 3 to 10 2458.90 -0.581 0.280561 4 to 11 2395.70 -1.475 0.070110 5 to 12 2614.62 1.621 0.947493 6 to 13 2484.17 -0.224 0.411450 7 to 14 2578.56 1.111 0.866720 8 to 15 2470.45 -0.418 0.337994 9 to 16 2562.09 0.878 0.810068 10 to 17 2500.60 0.009 0.503403 11 to 18 2550.37 0.712 0.761873 12 to 19 2470.40 -0.419 0.337762 13 to 20 2431.93 -0.963 0.167870 14 to 21 2450.52 -0.700 0.242028 15 to 22 2578.96 1.117 0.867934 16 to 23 2584.72 1.198 0.884566 17 to 24 2444.47 -0.785 0.216151 18 to 25 2518.10 0.256 0.600993 19 to 26 2446.86 -0.751 0.226189 20 to 27 2514.39 0.203 0.580609 21 to 28 2509.81 0.139 0.555173 22 to 29 2515.03 0.213 0.584143 23 to 30 2448.30 -0.731 0.232364 24 to 31 2522.26 0.315 0.623563 25 to 32 2534.29 0.485 0.686137 CDPARK for dh-ranFile-2017-01-20_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 3528 0.2283 0.590298 3527 0.1826 0.572463 3556 1.5068 0.934075 3522 -0.0457 0.481790 3522 -0.0457 0.481790 3477 -2.1005 0.017844 3497 -1.1872 0.117571 3492 -1.4155 0.078457 3549 1.1872 0.882429 3546 1.0502 0.853193 Square side=100, avg. no. parked=3521.60 sample std.=24.64 p-value of the KSTEST for those 10 p-values: 0.761726 Results for the MINIMUM DISTANCE test for dh-ranFile-2017-01-20_04:31 0.2677,0.9099,0.9865,0.8429,0.4828,0.4626,0.6257,0.9409,0.3854,0.7133, The KS test for those 10 p-values: 0.119740 The 3DSPHERES test for dh-ranFile-2017-01-20_04:31 sample no r^3 equiv. uni. 1 28.941 0.618904 2 36.769 0.706433 3 7.329 0.216745 4 196.657 0.998577 5 41.440 0.748760 6 8.766 0.253393 7 1.474 0.047958 8 84.310 0.939814 9 18.471 0.459746 10 27.590 0.601355 11 5.399 0.164703 12 60.512 0.866954 13 46.884 0.790450 14 2.636 0.084108 15 56.246 0.846627 16 88.229 0.947186 17 34.151 0.679660 18 15.290 0.399311 19 33.848 0.676401 20 6.935 0.206405 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.491298 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-01-20_04:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -1.6 0.6 0.8 -0.9 -0.4 1.0 0.8 0.4 0.2 -1.1 1.0 -1.7 -1.8 1.6 -0.7 1.1 -0.3 -0.1 2.0 -0.2 0.0 0.2 0.7 -1.6 0.5 -0.8 -0.8 -1.1 0.9 -0.2 2.0 -1.1 0.3 -0.9 -0.1 1.7 -1.3 -0.4 0.4 -1.3 0.0 -0.1 Chi-square with 42 degrees of freedom:42.679639 z-score=0.074155, p-value=0.558230 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2017-01-20_04:31 Test no p-value 1 0.923929 2 0.953914 3 0.252258 4 0.421174 5 0.037505 6 0.155207 7 0.467141 8 0.009826 9 0.754199 10 0.125697 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.285221 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-01-20_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 66753 0.11 66732 0.06 3 25000.00 24862 0.76 25035 0.05 4 6666.67 6688 0.07 6649 0.05 5 1388.89 1440 1.88 1327 2.76 6 238.10 208 3.80 209 3.56 7 34.72 46 3.66 39 0.53 8 4.96 2 1.77 8 1.86 p=0.93931 p=0.81863 Number of rngs required: 687377, p-value: 0.117 RESULTS OF CRAPS TEST for dh-ranFile-2017-01-20_04:31 No. of wins: Observed Expected 98752 98585.9 z-score= 0.743, pvalue=0.77128 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66596 66666.7 0.075 0.075 2 37849 37654.3 1.007 1.081 3 27129 26954.7 1.127 2.208 4 19160 19313.5 1.219 3.427 5 13669 13851.4 2.402 5.830 6 10020 9943.5 0.588 6.418 7 7084 7145.0 0.521 6.939 8 5177 5139.1 0.280 7.219 9 3738 3699.9 0.393 7.612 10 2680 2666.3 0.070 7.682 11 1915 1923.3 0.036 7.718 12 1363 1388.7 0.477 8.196 13 1007 1003.7 0.011 8.206 14 749 726.1 0.720 8.926 15 498 525.8 1.474 10.400 16 403 381.2 1.253 11.652 17 262 276.5 0.764 12.416 18 181 200.8 1.958 14.374 19 135 146.0 0.827 15.201 20 109 106.2 0.073 15.274 21 276 287.1 0.430 15.704 Chisq= 15.70 for 20 degrees of freedom, p= 0.26520 SUMMARY of craptest p-value for no. of wins: 0.771284 p-value for throws/game: 0.265202 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2017-01-20_04:31 No. of wins: Observed Expected 98714 98585.9 z-score= 0.573, pvalue=0.71672 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66842 66666.7 0.461 0.461 2 37335 37654.3 2.708 3.169 3 26862 26954.7 0.319 3.488 4 19504 19313.5 1.880 5.368 5 13806 13851.4 0.149 5.517 6 9939 9943.5 0.002 5.519 7 7092 7145.0 0.394 5.912 8 5282 5139.1 3.975 9.888 9 3680 3699.9 0.107 9.994 10 2618 2666.3 0.875 10.869 11 1898 1923.3 0.334 11.203 12 1381 1388.7 0.043 11.246 13 970 1003.7 1.132 12.378 14 757 726.1 1.311 13.690 15 528 525.8 0.009 13.699 16 393 381.2 0.368 14.067 17 323 276.5 7.806 21.873 18 226 200.8 3.155 25.027 19 150 146.0 0.110 25.138 20 108 106.2 0.030 25.168 21 306 287.1 1.242 26.410 Chisq= 26.41 for 20 degrees of freedom, p= 0.84731 SUMMARY of craptest p-value for no. of wins: 0.716719 p-value for throws/game: 0.847306 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0077,0.0098,0.0119,0.0137,0.0162,0.0178,0.0185,0.0324,0.0334,0.0352, 0.0361,0.0375,0.0383,0.0480,0.0499,0.0555,0.0576,0.0603,0.0676,0.0701, 0.0785,0.0808,0.0841,0.0998,0.1011,0.1166,0.1172,0.1176,0.1197,0.1197, 0.1212,0.1212,0.1257,0.1321,0.1334,0.1395,0.1552,0.1642,0.1647,0.1679, 0.1682,0.1706,0.1749,0.1800,0.1882,0.2010,0.2054,0.2064,0.2065,0.2109, 0.2146,0.2154,0.2162,0.2167,0.2177,0.2205,0.2248,0.2262,0.2267,0.2285, 0.2324,0.2364,0.2396,0.2420,0.2523,0.2528,0.2534,0.2570,0.2577,0.2603, 0.2638,0.2652,0.2677,0.2683,0.2716,0.2734,0.2787,0.2806,0.2852,0.2910, 0.3077,0.3111,0.3137,0.3167,0.3179,0.3241,0.3260,0.3265,0.3378,0.3380, 0.3395,0.3429,0.3454,0.3514,0.3569,0.3580,0.3610,0.3624,0.3657,0.3761, 0.3764,0.3797,0.3854,0.3938,0.3975,0.3993,0.4032,0.4115,0.4147,0.4167, 0.4192,0.4212,0.4474,0.4588,0.4597,0.4626,0.4631,0.4632,0.4671,0.4674, 0.4818,0.4818,0.4828,0.4843,0.4901,0.4913,0.4941,0.4966,0.5034,0.5106, 0.5156,0.5255,0.5255,0.5306,0.5353,0.5474,0.5508,0.5552,0.5581,0.5582, 0.5725,0.5806,0.5811,0.5841,0.5841,0.5889,0.5894,0.5903,0.5923,0.5939, 0.5963,0.5967,0.5999,0.6010,0.6012,0.6014,0.6088,0.6100,0.6189,0.6192, 0.6201,0.6212,0.6236,0.6244,0.6257,0.6267,0.6267,0.6279,0.6319,0.6369, 0.6380,0.6425,0.6522,0.6597,0.6623,0.6704,0.6764,0.6787,0.6796,0.6797, 0.6801,0.6812,0.6861,0.6885,0.6937,0.6941,0.7000,0.7011,0.7030,0.7050, 0.7064,0.7113,0.7133,0.7167,0.7191,0.7193,0.7201,0.7219,0.7265,0.7288, 0.7317,0.7367,0.7412,0.7488,0.7542,0.7617,0.7619,0.7713,0.7791,0.7857, 0.7858,0.7904,0.7928,0.7950,0.8073,0.8091,0.8101,0.8110,0.8131,0.8137, 0.8169,0.8186,0.8197,0.8202,0.8383,0.8429,0.8466,0.8473,0.8532,0.8541, 0.8607,0.8667,0.8670,0.8674,0.8676,0.8679,0.8758,0.8787,0.8824,0.8836, 0.8846,0.8854,0.8927,0.8943,0.8974,0.9021,0.9071,0.9099,0.9239,0.9317, 0.9341,0.9357,0.9393,0.9398,0.9409,0.9432,0.9472,0.9475,0.9528,0.9537, 0.9539,0.9545,0.9552,0.9561,0.9584,0.9721,0.9744,0.9865,0.9986, Overall p-value after applying KStest on 269 p-values = 0.736405 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.