RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-10-28_05:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 16.01 19.1129 0.677911 2 to 25 15.52 40.3340 0.998839 3 to 26 15.79 20.0919 0.730442 4 to 27 15.74 19.9144 0.721369 5 to 28 15.89 15.9276 0.471030 6 to 29 15.67 13.3965 0.290738 7 to 30 15.94 15.4447 0.436518 8 to 31 15.81 16.2965 0.497077 9 to 32 15.65 31.6162 0.983213 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.093824 Tough bday spacings test for dh-ranFile-2016-10-28_05:31: 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 37 67 91 95 96 54 34 10 5 5 (O-E)^2/E 1.1 0.0 0.5 0.5 0.1 4.1 0.1 0.6 1.6 0.4 0.2 Birthday Spacings: Sum(O-E)^2/E= 9.120, p= 0.479 RESULTS OF GCD FOR dh-ranFile-2016-10-28_05:31 Euclid's algorithm: p-value, steps to gcd: 0.777915 p-value, dist. of gcd's: 0.025572 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-10-28_05:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.830 0.011 0.816 0.668 0.104 0.353 0.112 0.951 Bits 8 to 15---> 0.326 0.511 0.766 0.560 0.582 0.263 0.191 0.023 Bits 16 to 23---> 0.026 0.127 0.867 0.220 0.697 0.210 0.020 0.648 Bits 24 to 31---> 0.172 0.856 0.816 0.238 0.746 0.216 0.940 0.003 KS test for the above 32 p values: 0.902 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-10-28_05:31, p-values for 5 runs: 0.1034, 0.3578, 0.2960, 0.5561, 0.9836 Rank test for binary matrices (31x31) for dh-ranFile-2016-10-28_05:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 227 211.4 1.148 1.148 r= 29 5152 5134.0 0.063 1.211 r= 30 23005 23103.0 0.416 1.628 r= 31 11616 11551.5 0.360 1.987 chi-square = 1.987 with df = 3; p-value = 0.425 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-10-28_05:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 219 211.4 0.272 0.272 r= 30 5097 5134.0 0.267 0.539 r= 31 23129 23103.0 0.029 0.568 r= 32 11555 11551.5 0.001 0.569 chi-square = 0.569 with df = 3; p-value = 0.096 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-10-28_05:31 b-rank test for bits 1 to 8, p=0.86012 b-rank test for bits 2 to 9, p=0.25367 b-rank test for bits 3 to 10, p=0.08781 b-rank test for bits 4 to 11, p=0.74708 b-rank test for bits 5 to 12, p=0.23944 b-rank test for bits 6 to 13, p=0.06609 b-rank test for bits 7 to 14, p=0.01776 b-rank test for bits 8 to 15, p=0.66661 b-rank test for bits 9 to 16, p=0.03976 b-rank test for bits 10 to 17, p=0.91402 b-rank test for bits 11 to 18, p=0.06513 b-rank test for bits 12 to 19, p=0.46087 b-rank test for bits 13 to 20, p=0.10601 b-rank test for bits 14 to 21, p=0.34049 b-rank test for bits 15 to 22, p=0.79393 b-rank test for bits 16 to 23, p=0.50672 b-rank test for bits 17 to 24, p=0.83149 b-rank test for bits 18 to 25, p=0.70352 b-rank test for bits 19 to 26, p=0.85105 b-rank test for bits 20 to 27, p=0.54806 b-rank test for bits 21 to 28, p=0.02493 b-rank test for bits 22 to 29, p=0.81233 b-rank test for bits 23 to 30, p=0.98883 b-rank test for bits 24 to 31, p=0.05684 b-rank test for bits 25 to 32, p=0.92285 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 = 0.165554 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-10-28_05:31 (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 142288 0.88 0.811852 2 141937 0.06 0.525774 3 141785 -0.29 0.385720 4 142499 1.38 0.915857 5 141971 0.14 0.557285 6 142572 1.55 0.939224 7 141683 -0.53 0.298469 8 141522 -0.90 0.182739 9 141424 -1.13 0.128408 10 141764 -0.34 0.367095 11 142044 0.31 0.623486 12 142698 1.84 0.967313 13 141573 -0.79 0.215987 14 141767 -0.33 0.369738 15 142016 0.25 0.598408 16 141900 -0.02 0.491304 17 141598 -0.73 0.233489 18 142106 0.46 0.677066 19 141865 -0.10 0.458753 20 141864 -0.11 0.457826 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-10-28_05:31 Bits used No. missing words z-score p-value 23 to 32 142076 0.5747 0.717261 22 to 31 141736 -0.5977 0.275024 21 to 30 141940 0.1058 0.542113 20 to 29 142293 1.3230 0.907082 19 to 28 141747 -0.5598 0.287822 18 to 27 142046 0.4713 0.681278 17 to 26 141548 -1.2460 0.106389 16 to 25 141834 -0.2598 0.397525 15 to 24 141791 -0.4080 0.341624 14 to 23 141828 -0.2804 0.389567 13 to 22 141684 -0.7770 0.218579 12 to 21 141785 -0.4287 0.334062 11 to 20 142296 1.3333 0.908791 10 to 19 142379 1.6196 0.947336 9 to 18 141749 -0.5529 0.290179 8 to 17 142033 0.4264 0.665109 7 to 16 142493 2.0127 0.977925 6 to 15 141554 -1.2253 0.110236 5 to 14 142143 0.8058 0.789809 4 to 13 141634 -0.9494 0.171205 3 to 12 141409 -1.7253 0.042239 2 to 11 142462 1.9058 0.971659 1 to 10 142120 0.7264 0.766218 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-10-28_05:31 Bits used No. missing words z-score p-value 28 to 32 142437 1.7887 0.963169 27 to 31 141910 0.0023 0.500906 26 to 30 141697 -0.7198 0.235836 25 to 29 141567 -1.1604 0.122935 24 to 28 141730 -0.6079 0.271628 23 to 27 142299 1.3209 0.906735 22 to 26 141747 -0.5503 0.291067 21 to 25 142013 0.3514 0.637365 20 to 24 142208 1.0124 0.844336 19 to 23 142207 1.0091 0.843525 18 to 22 141965 0.1887 0.574841 17 to 21 141366 -1.8418 0.032752 16 to 20 142228 1.0802 0.859982 15 to 19 142095 0.6294 0.735453 14 to 18 142186 0.9379 0.825843 13 to 17 142259 1.1853 0.882055 12 to 16 142105 0.6633 0.746427 11 to 15 141827 -0.2791 0.390090 10 to 14 141779 -0.4418 0.329318 9 to 13 142307 1.3480 0.911176 8 to 12 142433 1.7752 0.962064 7 to 11 142016 0.3616 0.641172 6 to 10 141869 -0.1367 0.445629 5 to 9 141564 -1.1706 0.120878 4 to 8 141729 -0.6113 0.270504 3 to 7 141659 -0.8486 0.198059 2 to 6 142151 0.8192 0.793670 1 to 5 141952 0.1446 0.557504 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-10-28_05:31 Bits used No. missing words z-score p-value 31 to 32 141405 -1.4877 0.068415 30 to 31 141968 0.1731 0.568701 29 to 30 141932 0.0669 0.526659 28 to 29 142018 0.3206 0.625728 27 to 28 141947 0.1111 0.544240 26 to 27 142128 0.6450 0.740551 25 to 26 141585 -0.9567 0.169353 24 to 25 141679 -0.6794 0.248430 23 to 24 141299 -1.8004 0.035900 22 to 23 142042 0.3914 0.652233 21 to 22 141815 -0.2783 0.390407 20 to 21 141880 -0.0865 0.465527 19 to 20 142444 1.5772 0.942625 18 to 19 141481 -1.2635 0.103203 17 to 18 141907 -0.0069 0.497258 16 to 17 141718 -0.5644 0.286243 15 to 16 142182 0.8043 0.789399 14 to 15 141956 0.1377 0.554749 13 to 14 142192 0.8338 0.797813 12 to 13 142011 0.2999 0.617878 11 to 12 142308 1.1760 0.880206 10 to 11 141421 -1.4405 0.074863 9 to 10 141582 -0.9656 0.167128 8 to 9 141932 0.0669 0.526659 7 to 8 141992 0.2439 0.596332 6 to 7 141603 -0.9036 0.183096 5 to 6 142226 0.9341 0.824882 4 to 5 141819 -0.2665 0.394942 3 to 4 142444 1.5772 0.942625 2 to 3 141407 -1.4818 0.069197 1 to 2 141723 -0.5496 0.291281 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-10-28_05:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2706.31 2.918 0.998237 Test results for specific bytes for dh-ranFile-2016-10-28_05:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2509.46 0.134 0.553228 2 to 9 2437.97 -0.877 0.190176 3 to 10 2565.17 0.922 0.821633 4 to 11 2402.99 -1.372 0.085049 5 to 12 2513.23 0.187 0.574189 6 to 13 2585.67 1.212 0.887172 7 to 14 2525.56 0.362 0.641139 8 to 15 2456.38 -0.617 0.268654 9 to 16 2600.61 1.423 0.922619 10 to 17 2529.38 0.416 0.661136 11 to 18 2506.90 0.098 0.538864 12 to 19 2445.28 -0.774 0.219487 13 to 20 2540.83 0.577 0.718171 14 to 21 2453.58 -0.656 0.255751 15 to 22 2561.16 0.865 0.806455 16 to 23 2449.64 -0.712 0.238165 17 to 24 2560.88 0.861 0.805380 18 to 25 2621.42 1.717 0.957026 19 to 26 2431.50 -0.969 0.166352 20 to 27 2419.98 -1.132 0.128887 21 to 28 2519.28 0.273 0.607436 22 to 29 2629.13 1.826 0.966083 23 to 30 2502.71 0.038 0.515306 24 to 31 2503.40 0.048 0.519168 25 to 32 2526.77 0.379 0.647503 CDPARK for dh-ranFile-2016-10-28_05:31: 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 3539 0.7306 0.767486 3538 0.6849 0.753306 3569 2.1005 0.982156 3520 -0.1370 0.445521 3510 -0.5936 0.276387 3556 1.5068 0.934075 3534 0.5023 0.692266 3519 -0.1826 0.427537 3525 0.0913 0.536383 3527 0.1826 0.572463 Square side=100, avg. no. parked=3533.70 sample std.=16.96 p-value of the KSTEST for those 10 p-values: 0.197922 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-10-28_05:31 0.6913,0.7941,0.1930,0.9223,0.6580,0.7946,0.1607,0.1731,0.8250,0.1666, The KS test for those 10 p-values: 0.497486 The 3DSPHERES test for dh-ranFile-2016-10-28_05:31 sample no r^3 equiv. uni. 1 81.943 0.934874 2 26.208 0.582556 3 79.764 0.929967 4 2.697 0.085972 5 12.962 0.350842 6 1.209 0.039496 7 10.900 0.304647 8 3.332 0.105115 9 7.615 0.224181 10 34.027 0.678336 11 25.728 0.575822 12 62.340 0.874820 13 106.659 0.971428 14 14.278 0.378701 15 19.920 0.485210 16 16.033 0.414001 17 16.345 0.420056 18 19.429 0.476717 19 17.551 0.442915 20 33.892 0.676884 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.890111 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-10-28_05:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 -1.2 0.3 0.5 1.6 -0.8 0.4 -1.5 -0.9 0.9 -0.0 0.2 -0.4 0.5 1.2 0.5 -1.2 0.2 0.3 -1.1 0.7 -0.8 0.8 1.6 0.6 -0.8 -1.2 -0.6 -0.8 0.5 -1.5 0.0 -0.9 -0.1 0.1 -0.7 -1.4 -0.1 0.9 -0.1 -0.6 0.0 -0.1 Chi-square with 42 degrees of freedom:31.111309 z-score=-1.188054, p-value=0.108374 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-10-28_05:31 Test no p-value 1 0.116256 2 0.046992 3 0.498824 4 0.610964 5 0.790566 6 0.540707 7 0.031332 8 0.426510 9 0.412049 10 0.003257 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.073063 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-10-28_05:31: (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 66510 0.37 66954 1.24 3 25000.00 25030 0.04 24807 1.49 4 6666.67 6763 1.39 6607 0.53 5 1388.89 1408 0.26 1369 0.28 6 238.10 249 0.50 219 1.53 7 34.72 34 0.01 40 0.80 8 4.96 5 0.00 3 0.77 p=0.13987 p=0.64618 Number of rngs required: 687822, p-value: 0.251 RESULTS OF CRAPS TEST for dh-ranFile-2016-10-28_05:31 No. of wins: Observed Expected 98843 98585.9 z-score= 1.150, pvalue=0.87495 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66806 66666.7 0.291 0.291 2 37639 37654.3 0.006 0.297 3 26769 26954.7 1.280 1.577 4 19214 19313.5 0.512 2.089 5 13858 13851.4 0.003 2.093 6 10073 9943.5 1.685 3.778 7 7179 7145.0 0.162 3.940 8 5094 5139.1 0.395 4.335 9 3582 3699.9 3.755 8.090 10 2638 2666.3 0.300 8.390 11 1955 1923.3 0.522 8.911 12 1448 1388.7 2.529 11.440 13 997 1003.7 0.045 11.485 14 771 726.1 2.771 14.256 15 506 525.8 0.748 15.005 16 400 381.2 0.932 15.937 17 287 276.5 0.396 16.333 18 220 200.8 1.830 18.162 19 147 146.0 0.007 18.169 20 112 106.2 0.315 18.485 21 305 287.1 1.114 19.599 Chisq= 19.60 for 20 degrees of freedom, p= 0.51673 SUMMARY of craptest p-value for no. of wins: 0.874946 p-value for throws/game: 0.516732 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-10-28_05:31 No. of wins: Observed Expected 98864 98585.9 z-score= 1.244, pvalue=0.89325 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66929 66666.7 1.032 1.032 2 37573 37654.3 0.176 1.208 3 26722 26954.7 2.009 3.217 4 19420 19313.5 0.588 3.805 5 13944 13851.4 0.619 4.424 6 9972 9943.5 0.081 4.505 7 7246 7145.0 1.427 5.932 8 5116 5139.1 0.104 6.036 9 3653 3699.9 0.594 6.629 10 2660 2666.3 0.015 6.644 11 1881 1923.3 0.932 7.576 12 1324 1388.7 3.018 10.594 13 941 1003.7 3.919 14.513 14 696 726.1 1.251 15.764 15 532 525.8 0.072 15.836 16 395 381.2 0.503 16.339 17 264 276.5 0.569 16.908 18 202 200.8 0.007 16.915 19 152 146.0 0.248 17.162 20 95 106.2 1.184 18.347 21 283 287.1 0.059 18.406 Chisq= 18.41 for 20 degrees of freedom, p= 0.43929 SUMMARY of craptest p-value for no. of wins: 0.893252 p-value for throws/game: 0.439294 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0027,0.0033,0.0112,0.0178,0.0199,0.0229,0.0249,0.0256,0.0260,0.0313, 0.0328,0.0359,0.0395,0.0398,0.0422,0.0470,0.0568,0.0651,0.0661,0.0684, 0.0692,0.0731,0.0749,0.0850,0.0860,0.0878,0.0938,0.0965,0.1032,0.1034, 0.1043,0.1051,0.1060,0.1064,0.1084,0.1102,0.1124,0.1163,0.1209,0.1229, 0.1274,0.1284,0.1289,0.1399,0.1607,0.1656,0.1664,0.1666,0.1671,0.1694, 0.1712,0.1724,0.1731,0.1827,0.1831,0.1902,0.1911,0.1930,0.1979,0.1981, 0.2097,0.2160,0.2161,0.2186,0.2195,0.2199,0.2242,0.2335,0.2358,0.2379, 0.2382,0.2394,0.2484,0.2513,0.2537,0.2558,0.2629,0.2687,0.2705,0.2716, 0.2750,0.2764,0.2862,0.2878,0.2902,0.2907,0.2911,0.2913,0.2960,0.2985, 0.3046,0.3255,0.3293,0.3341,0.3405,0.3416,0.3508,0.3527,0.3578,0.3671, 0.3697,0.3787,0.3857,0.3896,0.3901,0.3904,0.3949,0.3975,0.4120,0.4140, 0.4201,0.4250,0.4265,0.4275,0.4365,0.4393,0.4429,0.4455,0.4456,0.4578, 0.4588,0.4609,0.4655,0.4710,0.4767,0.4793,0.4852,0.4913,0.4971,0.4973, 0.4975,0.4988,0.5009,0.5067,0.5108,0.5153,0.5167,0.5192,0.5258,0.5267, 0.5267,0.5364,0.5389,0.5407,0.5421,0.5442,0.5481,0.5532,0.5547,0.5561, 0.5573,0.5575,0.5601,0.5687,0.5725,0.5742,0.5748,0.5758,0.5818,0.5826, 0.5963,0.5984,0.6074,0.6110,0.6179,0.6235,0.6257,0.6374,0.6411,0.6412, 0.6462,0.6475,0.6476,0.6522,0.6580,0.6611,0.6651,0.6666,0.6676,0.6769, 0.6771,0.6779,0.6783,0.6813,0.6913,0.6923,0.6971,0.7035,0.7173,0.7182, 0.7214,0.7304,0.7355,0.7406,0.7458,0.7464,0.7471,0.7533,0.7657,0.7662, 0.7675,0.7779,0.7894,0.7898,0.7906,0.7937,0.7939,0.7941,0.7946,0.7978, 0.8054,0.8065,0.8119,0.8123,0.8158,0.8163,0.8216,0.8249,0.8250,0.8258, 0.8297,0.8315,0.8435,0.8443,0.8510,0.8555,0.8600,0.8601,0.8672,0.8748, 0.8749,0.8802,0.8821,0.8872,0.8901,0.8933,0.9020,0.9067,0.9071,0.9088, 0.9112,0.9140,0.9159,0.9223,0.9226,0.9228,0.9300,0.9341,0.9349,0.9392, 0.9398,0.9426,0.9426,0.9473,0.9510,0.9570,0.9621,0.9632,0.9661,0.9673, 0.9714,0.9717,0.9779,0.9822,0.9832,0.9836,0.9888,0.9982,0.9988, Overall p-value after applying KStest on 269 p-values = 0.823491 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.