RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-10-25_08:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.80 10.6607 0.126349 2 to 25 15.79 17.2706 0.563817 3 to 26 15.98 14.0080 0.333463 4 to 27 15.83 11.3155 0.160298 5 to 28 15.64 24.4539 0.892383 6 to 29 15.87 15.2582 0.423113 7 to 30 15.50 23.5284 0.867175 8 to 31 16.00 22.2931 0.826291 9 to 32 16.04 9.9569 0.094594 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.886369 Tough bday spacings test for dh-ranFile-2015-10-25_08:31: 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 8 29 70 99 91 84 60 36 12 7 4 (O-E)^2/E 0.1 1.6 0.1 0.0 0.5 0.4 1.2 1.3 0.6 0.0 0.0 Birthday Spacings: Sum(O-E)^2/E= 5.880, p= 0.175 RESULTS OF GCD FOR dh-ranFile-2015-10-25_08:31 Euclid's algorithm: p-value, steps to gcd: 0.351959 p-value, dist. of gcd's: 0.222674 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-10-25_08:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.645 0.569 0.140 0.734 0.261 0.075 0.042 0.835 Bits 8 to 15---> 0.174 0.772 0.868 0.757 0.482 0.712 0.968 0.105 Bits 16 to 23---> 0.084 0.649 0.028 0.190 0.450 0.031 0.798 0.215 Bits 24 to 31---> 0.369 0.760 0.146 0.923 0.962 0.094 0.405 0.297 KS test for the above 32 p values: 0.659 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-10-25_08:31, p-values for 5 runs: 0.1885, 0.8110, 0.2117, 0.7869, 0.8126 Rank test for binary matrices (31x31) for dh-ranFile-2015-10-25_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 200 211.4 0.617 0.617 r= 29 5013 5134.0 2.852 3.469 r= 30 23284 23103.0 1.417 4.886 r= 31 11503 11551.5 0.204 5.090 chi-square = 5.090 with df = 3; p-value = 0.835 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-10-25_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 216 211.4 0.099 0.099 r= 30 4997 5134.0 3.656 3.756 r= 31 23225 23103.0 0.644 4.399 r= 32 11562 11551.5 0.010 4.409 chi-square = 4.409 with df = 3; p-value = 0.779 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-10-25_08:31 b-rank test for bits 1 to 8, p=0.44246 b-rank test for bits 2 to 9, p=0.39264 b-rank test for bits 3 to 10, p=0.95893 b-rank test for bits 4 to 11, p=0.69699 b-rank test for bits 5 to 12, p=0.86521 b-rank test for bits 6 to 13, p=0.20112 b-rank test for bits 7 to 14, p=0.76388 b-rank test for bits 8 to 15, p=0.25294 b-rank test for bits 9 to 16, p=0.36890 b-rank test for bits 10 to 17, p=0.49608 b-rank test for bits 11 to 18, p=0.48644 b-rank test for bits 12 to 19, p=0.15957 b-rank test for bits 13 to 20, p=0.09457 b-rank test for bits 14 to 21, p=0.00227 b-rank test for bits 15 to 22, p=0.94730 b-rank test for bits 16 to 23, p=0.43141 b-rank test for bits 17 to 24, p=0.30232 b-rank test for bits 18 to 25, p=0.94893 b-rank test for bits 19 to 26, p=0.93424 b-rank test for bits 20 to 27, p=0.39714 b-rank test for bits 21 to 28, p=0.02271 b-rank test for bits 22 to 29, p=0.91371 b-rank test for bits 23 to 30, p=0.14866 b-rank test for bits 24 to 31, p=0.29667 b-rank test for bits 25 to 32, p=0.34227 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 = 0.485513 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-10-25_08:31 (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 141089 -1.92 0.027641 2 141478 -1.01 0.156780 3 141916 0.02 0.506217 4 141644 -0.62 0.267652 5 141982 0.17 0.567412 6 142550 1.50 0.932789 7 142105 0.46 0.676227 8 141560 -0.82 0.207195 9 142576 1.56 0.940341 10 141784 -0.29 0.384827 11 141260 -1.52 0.064617 12 142070 0.38 0.646317 13 141762 -0.34 0.365337 14 142211 0.70 0.759544 15 141668 -0.56 0.286426 16 142236 0.76 0.777342 17 141474 -1.02 0.154547 18 141931 0.05 0.520190 19 142256 0.81 0.791023 20 142056 0.34 0.634083 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-10-25_08:31 Bits used No. missing words z-score p-value 23 to 32 141587 -1.1115 0.133180 22 to 31 141611 -1.0287 0.151805 21 to 30 141686 -0.7701 0.220619 20 to 29 142077 0.5782 0.718426 19 to 28 141674 -0.8115 0.208544 18 to 27 142239 1.1368 0.872188 17 to 26 141843 -0.2287 0.409542 16 to 25 142346 1.5058 0.933935 15 to 24 141733 -0.6080 0.271582 14 to 23 141922 0.0437 0.517424 13 to 22 141579 -1.1391 0.127337 12 to 21 141037 -3.0080 0.001315 11 to 20 142207 1.0264 0.847660 10 to 19 141876 -0.1149 0.454250 9 to 18 141579 -1.1391 0.127337 8 to 17 141569 -1.1736 0.120287 7 to 16 141664 -0.8460 0.198786 6 to 15 141889 -0.0701 0.472056 5 to 14 142053 0.4954 0.689846 4 to 13 141584 -1.1218 0.130968 3 to 12 141593 -1.0908 0.137682 2 to 11 141598 -1.0736 0.141512 1 to 10 141730 -0.6184 0.268163 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-10-25_08:31 Bits used No. missing words z-score p-value 28 to 32 141605 -1.0316 0.151123 27 to 31 142103 0.6565 0.744252 26 to 30 142167 0.8735 0.808793 25 to 29 141894 -0.0520 0.479278 24 to 28 141810 -0.3367 0.368167 23 to 27 141817 -0.3130 0.377147 22 to 26 141369 -1.8316 0.033504 21 to 25 142266 1.2091 0.886678 20 to 24 141781 -0.4350 0.331775 19 to 23 142235 1.1040 0.865196 18 to 22 141516 -1.3333 0.091213 17 to 21 142044 0.4565 0.675988 16 to 20 141861 -0.1638 0.434932 15 to 19 142398 1.6565 0.951191 14 to 18 141598 -1.0554 0.145631 13 to 17 142514 2.0497 0.979805 12 to 16 141604 -1.0350 0.150331 11 to 15 141863 -0.1571 0.437602 10 to 14 141720 -0.6418 0.260503 9 to 13 141899 -0.0350 0.486033 8 to 12 141941 0.1074 0.542747 7 to 11 141458 -1.5299 0.063017 6 to 10 142466 1.8870 0.970421 5 to 9 142055 0.4938 0.689275 4 to 8 141869 -0.1367 0.445629 3 to 7 141718 -0.6486 0.258306 2 to 6 142027 0.3989 0.655010 1 to 5 142091 0.6158 0.730997 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-10-25_08:31 Bits used No. missing words z-score p-value 31 to 32 141339 -1.6824 0.046247 30 to 31 141853 -0.1662 0.434014 29 to 30 141865 -0.1308 0.447980 28 to 29 142023 0.3353 0.631304 27 to 28 142119 0.6185 0.731876 26 to 27 141790 -0.3520 0.362417 25 to 26 141558 -1.0364 0.150014 24 to 25 142434 1.5477 0.939153 23 to 24 142452 1.6008 0.945289 22 to 23 142159 0.7365 0.769284 21 to 22 141770 -0.4110 0.340535 20 to 21 141843 -0.1957 0.422437 19 to 20 142267 1.0551 0.854304 18 to 19 141954 0.1318 0.552417 17 to 18 142145 0.6952 0.756532 16 to 17 142217 0.9076 0.817950 15 to 16 142383 1.3973 0.918832 14 to 15 141710 -0.5880 0.278268 13 to 14 141949 0.1170 0.546578 12 to 13 142188 0.8220 0.794472 11 to 12 141935 0.0757 0.530180 10 to 11 142023 0.3353 0.631304 9 to 10 141434 -1.4022 0.080435 8 to 9 141421 -1.4405 0.074863 7 to 8 141538 -1.0954 0.136678 6 to 7 142034 0.3678 0.643473 5 to 6 142362 1.3353 0.909113 4 to 5 142107 0.5831 0.720086 3 to 4 142461 1.6273 0.948168 2 to 3 141972 0.1849 0.573333 1 to 2 141397 -1.5113 0.065356 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-10-25_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2474.89 -0.355 0.361245 Test results for specific bytes for dh-ranFile-2015-10-25_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2538.48 0.544 0.706856 2 to 9 2577.63 1.098 0.863878 3 to 10 2561.96 0.876 0.809539 4 to 11 2472.82 -0.384 0.350340 5 to 12 2663.96 2.319 0.989796 6 to 13 2492.50 -0.106 0.457776 7 to 14 2512.10 0.171 0.567948 8 to 15 2582.62 1.168 0.878671 9 to 16 2620.35 1.702 0.955627 10 to 17 2628.77 1.821 0.965698 11 to 18 2498.13 -0.027 0.489429 12 to 19 2426.91 -1.034 0.150665 13 to 20 2554.20 0.766 0.778304 14 to 21 2659.37 2.254 0.987898 15 to 22 2494.96 -0.071 0.471583 16 to 23 2541.58 0.588 0.721736 17 to 24 2371.69 -1.815 0.034797 18 to 25 2502.57 0.036 0.514495 19 to 26 2576.65 1.084 0.860815 20 to 27 2583.30 1.178 0.880622 21 to 28 2533.75 0.477 0.683442 22 to 29 2466.58 -0.473 0.318231 23 to 30 2458.70 -0.584 0.279570 24 to 31 2489.54 -0.148 0.441214 25 to 32 2505.29 0.075 0.529820 CDPARK for dh-ranFile-2015-10-25_08:31: 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 3488 -1.5982 0.055002 3505 -0.8219 0.205562 3541 0.8219 0.794438 3524 0.0457 0.518210 3548 1.1416 0.873180 3496 -1.2329 0.108811 3518 -0.2283 0.409702 3554 1.4155 0.921543 3533 0.4566 0.676028 3549 1.1872 0.882429 Square side=100, avg. no. parked=3525.60 sample std.=22.19 p-value of the KSTEST for those 10 p-values: 0.796075 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-10-25_08:31 0.3602,0.7346,0.4483,0.2008,0.0630,0.0221,0.8292,0.8998,0.2300,0.3881, The KS test for those 10 p-values: 0.620804 The 3DSPHERES test for dh-ranFile-2015-10-25_08:31 sample no r^3 equiv. uni. 1 20.680 0.498082 2 73.498 0.913700 3 83.486 0.938140 4 12.224 0.334661 5 25.532 0.573041 6 91.498 0.952638 7 30.786 0.641634 8 36.458 0.703372 9 0.500 0.016526 10 3.275 0.103412 11 11.805 0.325313 12 3.697 0.115952 13 25.070 0.566409 14 61.304 0.870421 15 6.479 0.194249 16 11.418 0.316552 17 19.110 0.471130 18 17.698 0.445630 19 23.944 0.549835 20 23.542 0.543761 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.926980 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-10-25_08:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.5 -0.6 0.2 -1.0 2.4 -0.1 0.5 -0.4 -2.1 -1.6 1.1 1.1 0.3 0.1 0.4 0.5 0.0 0.5 -1.2 -0.7 -0.1 2.5 -1.0 0.5 -0.9 -0.1 -0.5 0.2 -0.6 -1.4 -0.9 0.6 0.1 -0.9 -0.3 0.5 -0.1 -0.4 0.4 0.9 0.0 -0.1 Chi-square with 42 degrees of freedom:34.091978 z-score=-0.862836, p-value=0.197713 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-10-25_08:31 Test no p-value 1 0.823848 2 0.327938 3 0.381494 4 0.123053 5 0.438942 6 0.085181 7 0.125893 8 0.342950 9 0.000284 10 0.182994 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.017257 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-10-25_08:31: (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 66631 0.02 66688 0.01 3 25000.00 24926 0.22 24926 0.22 4 6666.67 6729 0.58 6743 0.87 5 1388.89 1441 1.96 1360 0.60 6 238.10 234 0.07 239 0.00 7 34.72 32 0.21 38 0.31 8 4.96 6 0.22 5 0.00 p=0.22671 p=0.08163 Number of rngs required: 687857, p-value: 0.264 RESULTS OF CRAPS TEST for dh-ranFile-2015-10-25_08:31 No. of wins: Observed Expected 98938 98585.9 z-score= 1.575, pvalue=0.94237 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66873 66666.7 0.639 0.639 2 37840 37654.3 0.916 1.554 3 26780 26954.7 1.133 2.687 4 19246 19313.5 0.236 2.923 5 13727 13851.4 1.118 4.040 6 9898 9943.5 0.209 4.249 7 7233 7145.0 1.083 5.332 8 5143 5139.1 0.003 5.335 9 3684 3699.9 0.068 5.403 10 2663 2666.3 0.004 5.407 11 1948 1923.3 0.316 5.724 12 1390 1388.7 0.001 5.725 13 988 1003.7 0.246 5.971 14 702 726.1 0.803 6.773 15 501 525.8 1.173 7.946 16 368 381.2 0.454 8.400 17 275 276.5 0.009 8.409 18 201 200.8 0.000 8.409 19 165 146.0 2.477 10.886 20 116 106.2 0.901 11.787 21 259 287.1 2.753 14.540 Chisq= 14.54 for 20 degrees of freedom, p= 0.19790 SUMMARY of craptest p-value for no. of wins: 0.942370 p-value for throws/game: 0.197902 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-10-25_08:31 No. of wins: Observed Expected 99025 98585.9 z-score= 1.964, pvalue=0.97524 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66564 66666.7 0.158 0.158 2 37586 37654.3 0.124 0.282 3 26944 26954.7 0.004 0.286 4 19332 19313.5 0.018 0.304 5 13923 13851.4 0.370 0.674 6 9893 9943.5 0.257 0.931 7 7135 7145.0 0.014 0.945 8 5241 5139.1 2.022 2.967 9 3686 3699.9 0.052 3.019 10 2593 2666.3 2.015 5.034 11 2012 1923.3 4.088 9.122 12 1328 1388.7 2.657 11.778 13 1023 1003.7 0.371 12.149 14 750 726.1 0.784 12.933 15 508 525.8 0.605 13.538 16 393 381.2 0.368 13.906 17 299 276.5 1.824 15.730 18 231 200.8 4.532 20.263 19 149 146.0 0.062 20.325 20 104 106.2 0.046 20.371 21 306 287.1 1.242 21.613 Chisq= 21.61 for 20 degrees of freedom, p= 0.63815 SUMMARY of craptest p-value for no. of wins: 0.975241 p-value for throws/game: 0.638151 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0003,0.0013,0.0023,0.0165,0.0173,0.0221,0.0227,0.0276,0.0276,0.0309, 0.0335,0.0348,0.0424,0.0462,0.0550,0.0630,0.0630,0.0646,0.0654,0.0748, 0.0749,0.0804,0.0816,0.0840,0.0852,0.0912,0.0941,0.0946,0.0946,0.1034, 0.1046,0.1088,0.1160,0.1203,0.1231,0.1259,0.1263,0.1273,0.1273,0.1310, 0.1332,0.1367,0.1377,0.1404,0.1415,0.1456,0.1457,0.1487,0.1500,0.1503, 0.1507,0.1511,0.1518,0.1545,0.1568,0.1596,0.1603,0.1743,0.1747,0.1830, 0.1885,0.1901,0.1942,0.1977,0.1979,0.1988,0.2008,0.2011,0.2056,0.2072, 0.2085,0.2117,0.2155,0.2206,0.2227,0.2267,0.2300,0.2529,0.2583,0.2605, 0.2608,0.2644,0.2677,0.2682,0.2716,0.2783,0.2796,0.2864,0.2967,0.2967, 0.3023,0.3166,0.3182,0.3253,0.3279,0.3318,0.3335,0.3347,0.3405,0.3423, 0.3430,0.3503,0.3520,0.3602,0.3612,0.3624,0.3653,0.3682,0.3687,0.3689, 0.3771,0.3815,0.3848,0.3881,0.3926,0.3971,0.4053,0.4095,0.4097,0.4224, 0.4231,0.4314,0.4340,0.4349,0.4376,0.4389,0.4412,0.4425,0.4456,0.4456, 0.4480,0.4483,0.4504,0.4542,0.4578,0.4711,0.4716,0.4721,0.4793,0.4825, 0.4855,0.4860,0.4864,0.4894,0.4961,0.4981,0.5062,0.5145,0.5174,0.5182, 0.5202,0.5298,0.5302,0.5427,0.5438,0.5466,0.5498,0.5524,0.5638,0.5664, 0.5674,0.5679,0.5691,0.5730,0.5733,0.6208,0.6313,0.6313,0.6341,0.6382, 0.6416,0.6435,0.6449,0.6463,0.6495,0.6550,0.6587,0.6760,0.6760,0.6762, 0.6834,0.6893,0.6898,0.6970,0.7034,0.7069,0.7122,0.7184,0.7201,0.7217, 0.7310,0.7319,0.7343,0.7346,0.7443,0.7565,0.7570,0.7595,0.7602,0.7639, 0.7693,0.7724,0.7773,0.7783,0.7794,0.7869,0.7910,0.7944,0.7945,0.7961, 0.7977,0.8088,0.8095,0.8110,0.8126,0.8180,0.8238,0.8263,0.8292,0.8346, 0.8347,0.8477,0.8543,0.8608,0.8639,0.8652,0.8652,0.8672,0.8676,0.8704, 0.8722,0.8732,0.8787,0.8806,0.8824,0.8864,0.8867,0.8924,0.8998,0.9091, 0.9137,0.9137,0.9188,0.9215,0.9233,0.9270,0.9328,0.9339,0.9342,0.9381, 0.9392,0.9403,0.9424,0.9453,0.9473,0.9482,0.9489,0.9512,0.9526,0.9556, 0.9589,0.9617,0.9657,0.9682,0.9704,0.9752,0.9798,0.9879,0.9898, Overall p-value after applying KStest on 269 p-values = 0.302846 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.