RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-07-03_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 15.94 21.5837 0.798738 2 to 25 15.77 29.8732 0.972726 3 to 26 15.52 21.0942 0.777897 4 to 27 15.51 19.6168 0.705703 5 to 28 15.66 19.0044 0.671718 6 to 29 15.45 32.9271 0.988486 7 to 30 15.29 32.7099 0.987735 8 to 31 15.84 16.1818 0.489013 9 to 32 15.66 14.4456 0.364654 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.006619 Tough bday spacings test for dh-ranFile-2015-07-03_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 10 28 57 98 114 82 52 35 12 8 4 (O-E)^2/E 0.1 2.0 3.6 0.0 2.7 0.2 0.0 0.9 0.6 0.3 0.0 Birthday Spacings: Sum(O-E)^2/E= 10.406, p= 0.594 RESULTS OF GCD FOR dh-ranFile-2015-07-03_13:31 Euclid's algorithm: p-value, steps to gcd: 0.688971 p-value, dist. of gcd's: 0.538918 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-07-03_13:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.552 0.024 0.508 0.743 0.413 0.750 0.922 0.554 Bits 8 to 15---> 0.383 0.107 0.473 0.147 0.898 0.498 0.604 0.099 Bits 16 to 23---> 0.968 0.936 0.287 0.861 0.212 0.422 0.525 0.716 Bits 24 to 31---> 0.875 0.977 0.109 0.888 0.973 0.045 0.417 0.593 KS test for the above 32 p values: 0.540 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-07-03_13:31, p-values for 5 runs: 0.7608, 0.6183, 0.2537, 0.7512, 0.2151 Rank test for binary matrices (31x31) for dh-ranFile-2015-07-03_13:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 215 211.4 0.061 0.061 r= 29 5221 5134.0 1.474 1.535 r= 30 22925 23103.0 1.372 2.907 r= 31 11639 11551.5 0.662 3.569 chi-square = 3.569 with df = 3; p-value = 0.688 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-07-03_13:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 202 211.4 0.420 0.420 r= 30 5061 5134.0 1.038 1.458 r= 31 23067 23103.0 0.056 1.514 r= 32 11670 11551.5 1.215 2.729 chi-square = 2.729 with df = 3; p-value = 0.565 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-07-03_13:31 b-rank test for bits 1 to 8, p=0.12455 b-rank test for bits 2 to 9, p=0.25972 b-rank test for bits 3 to 10, p=0.01286 b-rank test for bits 4 to 11, p=0.45595 b-rank test for bits 5 to 12, p=0.37556 b-rank test for bits 6 to 13, p=0.80257 b-rank test for bits 7 to 14, p=0.56838 b-rank test for bits 8 to 15, p=0.46885 b-rank test for bits 9 to 16, p=0.43186 b-rank test for bits 10 to 17, p=0.40445 b-rank test for bits 11 to 18, p=0.26745 b-rank test for bits 12 to 19, p=0.04245 b-rank test for bits 13 to 20, p=0.69322 b-rank test for bits 14 to 21, p=0.58542 b-rank test for bits 15 to 22, p=0.36331 b-rank test for bits 16 to 23, p=0.23568 b-rank test for bits 17 to 24, p=0.13020 b-rank test for bits 18 to 25, p=0.96762 b-rank test for bits 19 to 26, p=0.99034 b-rank test for bits 20 to 27, p=0.90563 b-rank test for bits 21 to 28, p=0.23613 b-rank test for bits 22 to 29, p=0.94032 b-rank test for bits 23 to 30, p=0.55949 b-rank test for bits 24 to 31, p=0.35662 b-rank test for bits 25 to 32, p=0.70815 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 = 0.830816 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-07-03_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 141825 -0.20 0.421901 2 141646 -0.62 0.269193 3 142183 0.64 0.738724 4 141583 -0.76 0.222895 5 142174 0.62 0.731840 6 141958 0.11 0.545268 7 142108 0.46 0.678741 8 142149 0.56 0.712252 9 141978 0.16 0.563734 10 141835 -0.17 0.431063 11 141889 -0.05 0.481057 12 142460 1.29 0.900885 13 141768 -0.33 0.370621 14 141596 -0.73 0.232060 15 141579 -0.77 0.220117 16 141642 -0.62 0.266116 17 142503 1.39 0.917291 18 141602 -0.72 0.236360 19 141525 -0.90 0.184602 20 141524 -0.90 0.183979 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-07-03_13:31 Bits used No. missing words z-score p-value 23 to 32 141451 -1.5804 0.057002 22 to 31 141682 -0.7839 0.216550 21 to 30 142127 0.7506 0.773549 20 to 29 142375 1.6058 0.945837 19 to 28 141608 -1.0391 0.149386 18 to 27 142101 0.6609 0.745672 17 to 26 141694 -0.7425 0.228887 16 to 25 141741 -0.5804 0.280806 15 to 24 141807 -0.3529 0.362096 14 to 23 141459 -1.5529 0.060228 13 to 22 141434 -1.6391 0.050599 12 to 21 141444 -1.6046 0.054292 11 to 20 142093 0.6333 0.736746 10 to 19 141866 -0.1494 0.440614 9 to 18 141363 -1.8839 0.029789 8 to 17 141091 -2.8218 0.002388 7 to 16 141746 -0.5632 0.286647 6 to 15 142265 1.2264 0.889985 5 to 14 141914 0.0161 0.506424 4 to 13 141745 -0.5667 0.285474 3 to 12 141626 -0.9770 0.164285 2 to 11 141368 -1.8667 0.030975 1 to 10 141861 -0.1667 0.433821 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-07-03_13:31 Bits used No. missing words z-score p-value 28 to 32 141920 0.0362 0.514426 27 to 31 142319 1.3887 0.917540 26 to 30 142197 0.9752 0.835258 25 to 29 142221 1.0565 0.854632 24 to 28 142129 0.7446 0.771757 23 to 27 141599 -1.0520 0.146408 22 to 26 141915 0.0192 0.507667 21 to 25 141807 -0.3469 0.364340 20 to 24 141682 -0.7706 0.220469 19 to 23 142082 0.5853 0.720834 18 to 22 142292 1.2972 0.902717 17 to 21 142295 1.3074 0.904454 16 to 20 141717 -0.6520 0.257212 15 to 19 142148 0.8091 0.790757 14 to 18 141528 -1.2926 0.098067 13 to 17 141727 -0.6181 0.268265 12 to 16 141453 -1.5469 0.060946 11 to 15 142340 1.4599 0.927841 10 to 14 142203 0.9955 0.840251 9 to 13 142272 1.2294 0.890537 8 to 12 141825 -0.2859 0.387491 7 to 11 141846 -0.2147 0.415009 6 to 10 141604 -1.0350 0.150331 5 to 9 142138 0.7752 0.780875 4 to 8 142069 0.5413 0.705834 3 to 7 141294 -2.0859 0.018495 2 to 6 142396 1.6497 0.950501 1 to 5 142230 1.0870 0.861485 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-07-03_13:31 Bits used No. missing words z-score p-value 31 to 32 142274 1.0757 0.858974 30 to 31 141756 -0.4523 0.325526 29 to 30 141498 -1.2134 0.112496 28 to 29 142419 1.5035 0.933639 27 to 28 142304 1.1642 0.877832 26 to 27 141833 -0.2252 0.410927 25 to 26 141925 0.0462 0.518434 24 to 25 141950 0.1200 0.547747 23 to 24 141244 -1.9626 0.024845 22 to 23 141913 0.0108 0.504319 21 to 22 141755 -0.4553 0.324464 20 to 21 142242 0.9813 0.836784 19 to 20 141710 -0.5880 0.278268 18 to 19 141608 -0.8889 0.187034 17 to 18 142361 1.3324 0.908629 16 to 17 142348 1.2940 0.902169 15 to 16 141714 -0.5762 0.282242 14 to 15 141929 0.0580 0.523135 13 to 14 141863 -0.1367 0.445647 12 to 13 141696 -0.6293 0.264579 11 to 12 141597 -0.9213 0.178440 10 to 11 141658 -0.7414 0.229230 9 to 10 142355 1.3147 0.905688 8 to 9 142463 1.6332 0.948791 7 to 8 141260 -1.9154 0.027719 6 to 7 142411 1.4799 0.930544 5 to 6 142316 1.1996 0.884856 4 to 5 142063 0.4533 0.674835 3 to 4 142019 0.3235 0.626846 2 to 3 141384 -1.5496 0.060613 1 to 2 141667 -0.7148 0.237355 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-07-03_13:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2618.06 1.670 0.952504 Test results for specific bytes for dh-ranFile-2015-07-03_13:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2515.54 0.220 0.586999 2 to 9 2527.58 0.390 0.651725 3 to 10 2577.95 1.102 0.864867 4 to 11 2356.44 -2.030 0.021168 5 to 12 2485.30 -0.208 0.417651 6 to 13 2460.08 -0.565 0.286192 7 to 14 2606.31 1.503 0.933642 8 to 15 2522.33 0.316 0.623894 9 to 16 2485.67 -0.203 0.419691 10 to 17 2564.87 0.917 0.820538 11 to 18 2510.77 0.152 0.560513 12 to 19 2515.36 0.217 0.585976 13 to 20 2519.15 0.271 0.606728 14 to 21 2490.94 -0.128 0.449045 15 to 22 2461.50 -0.544 0.293063 16 to 23 2467.09 -0.465 0.320839 17 to 24 2447.58 -0.741 0.229254 18 to 25 2610.13 1.557 0.940323 19 to 26 2448.60 -0.727 0.233658 20 to 27 2476.68 -0.330 0.370761 21 to 28 2428.57 -1.010 0.156214 22 to 29 2471.06 -0.409 0.341169 23 to 30 2403.72 -1.362 0.086657 24 to 31 2362.30 -1.947 0.025749 25 to 32 2574.94 1.060 0.855380 CDPARK for dh-ranFile-2015-07-03_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 3557 1.5525 0.939730 3533 0.4566 0.676028 3494 -1.3242 0.092718 3525 0.0913 0.536383 3550 1.2329 0.891189 3483 -1.8265 0.033889 3500 -1.0502 0.146807 3527 0.1826 0.572463 3518 -0.2283 0.409702 3510 -0.5936 0.276387 Square side=100, avg. no. parked=3519.70 sample std.=22.49 p-value of the KSTEST for those 10 p-values: 0.943999 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-07-03_13:31 0.2735,0.9894,0.6302,0.8295,0.8418,0.1202,0.8386,0.0632,0.5785,0.6319, The KS test for those 10 p-values: 0.495722 The 3DSPHERES test for dh-ranFile-2015-07-03_13:31 sample no r^3 equiv. uni. 1 28.714 0.616006 2 28.155 0.608787 3 1.476 0.048012 4 24.705 0.561110 5 6.659 0.199059 6 31.924 0.654970 7 53.886 0.834073 8 18.062 0.452320 9 19.078 0.470566 10 31.511 0.650185 11 49.598 0.808579 12 4.157 0.129388 13 17.715 0.445943 14 21.744 0.515580 15 23.758 0.547030 16 68.536 0.898177 17 21.157 0.506014 18 10.029 0.284167 19 15.786 0.409147 20 29.190 0.622053 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.317440 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-07-03_13:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.5 -0.1 -0.7 -1.2 0.8 -0.1 -0.7 0.7 0.0 -0.1 -1.1 0.6 0.3 0.7 -0.1 0.1 0.4 -0.4 1.1 -0.9 -0.7 -0.7 -0.3 0.1 0.7 1.2 -0.8 0.8 -1.4 -1.0 0.8 -1.5 1.0 0.8 1.9 0.3 -0.7 0.1 0.4 -0.6 0.0 0.8 Chi-square with 42 degrees of freedom:25.503811 z-score=-1.799882, p-value=0.020916 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-07-03_13:31 Test no p-value 1 0.817503 2 0.038009 3 0.470298 4 0.016978 5 0.169605 6 0.851980 7 0.295232 8 0.626667 9 0.157642 10 0.222564 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.200735 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-07-03_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 66852 0.52 66534 0.26 3 25000.00 24941 0.14 25161 1.04 4 6666.67 6520 3.23 6677 0.02 5 1388.89 1414 0.45 1365 0.41 6 238.10 234 0.07 223 0.96 7 34.72 34 0.01 37 0.15 8 4.96 4 0.19 2 1.77 p=0.40481 p=0.40409 Number of rngs required: 687491, p-value: 0.145 RESULTS OF CRAPS TEST for dh-ranFile-2015-07-03_13:31 No. of wins: Observed Expected 98799 98585.9 z-score= 0.953, pvalue=0.82978 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66485 66666.7 0.495 0.495 2 37738 37654.3 0.186 0.681 3 27103 26954.7 0.816 1.497 4 19269 19313.5 0.102 1.599 5 13899 13851.4 0.163 1.762 6 9920 9943.5 0.056 1.818 7 7153 7145.0 0.009 1.827 8 5106 5139.1 0.213 2.040 9 3709 3699.9 0.023 2.062 10 2706 2666.3 0.591 2.654 11 1867 1923.3 1.650 4.303 12 1350 1388.7 1.081 5.384 13 1076 1003.7 5.206 10.590 14 724 726.1 0.006 10.596 15 482 525.8 3.654 14.250 16 394 381.2 0.433 14.684 17 269 276.5 0.206 14.889 18 210 200.8 0.419 15.308 19 166 146.0 2.744 18.052 20 118 106.2 1.308 19.360 21 256 287.1 3.372 22.731 Chisq= 22.73 for 20 degrees of freedom, p= 0.69783 SUMMARY of craptest p-value for no. of wins: 0.829779 p-value for throws/game: 0.697829 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-07-03_13:31 No. of wins: Observed Expected 98555 98585.9 z-score=-0.138, pvalue=0.44511 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66471 66666.7 0.574 0.574 2 37626 37654.3 0.021 0.596 3 26865 26954.7 0.299 0.894 4 19461 19313.5 1.127 2.021 5 13988 13851.4 1.347 3.368 6 10000 9943.5 0.321 3.689 7 7126 7145.0 0.051 3.739 8 5105 5139.1 0.226 3.965 9 3606 3699.9 2.381 6.347 10 2684 2666.3 0.118 6.464 11 1986 1923.3 2.042 8.506 12 1412 1388.7 0.390 8.896 13 1061 1003.7 3.269 12.165 14 694 726.1 1.423 13.588 15 547 525.8 0.852 14.440 16 377 381.2 0.045 14.485 17 246 276.5 3.373 17.857 18 217 200.8 1.302 19.159 19 143 146.0 0.061 19.220 20 86 106.2 3.847 23.068 21 299 287.1 0.492 23.560 Chisq= 23.56 for 20 degrees of freedom, p= 0.73785 SUMMARY of craptest p-value for no. of wins: 0.445113 p-value for throws/game: 0.737853 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0024,0.0066,0.0129,0.0170,0.0185,0.0209,0.0212,0.0239,0.0248,0.0257, 0.0277,0.0298,0.0310,0.0339,0.0380,0.0424,0.0453,0.0480,0.0506,0.0543, 0.0570,0.0602,0.0606,0.0609,0.0632,0.0867,0.0927,0.0981,0.0989,0.1067, 0.1086,0.1125,0.1202,0.1246,0.1294,0.1302,0.1451,0.1464,0.1466,0.1468, 0.1494,0.1503,0.1562,0.1576,0.1643,0.1696,0.1784,0.1840,0.1846,0.1870, 0.1991,0.2007,0.2120,0.2151,0.2166,0.2201,0.2205,0.2226,0.2229,0.2289, 0.2292,0.2293,0.2321,0.2337,0.2357,0.2361,0.2364,0.2374,0.2537,0.2572, 0.2597,0.2646,0.2661,0.2674,0.2683,0.2692,0.2735,0.2764,0.2783,0.2808, 0.2822,0.2842,0.2855,0.2862,0.2866,0.2870,0.2931,0.2952,0.3174,0.3208, 0.3245,0.3255,0.3412,0.3566,0.3621,0.3633,0.3643,0.3647,0.3706,0.3708, 0.3756,0.3825,0.3875,0.4041,0.4045,0.4048,0.4091,0.4097,0.4109,0.4126, 0.4150,0.4173,0.4177,0.4197,0.4217,0.4219,0.4311,0.4319,0.4338,0.4406, 0.4451,0.4456,0.4459,0.4490,0.4523,0.4560,0.4688,0.4703,0.4706,0.4728, 0.4811,0.4890,0.4957,0.4977,0.5043,0.5060,0.5064,0.5077,0.5083,0.5144, 0.5156,0.5184,0.5231,0.5252,0.5364,0.5389,0.5399,0.5453,0.5470,0.5477, 0.5521,0.5544,0.5595,0.5605,0.5611,0.5637,0.5647,0.5684,0.5725,0.5785, 0.5854,0.5860,0.5870,0.5928,0.5944,0.6040,0.6067,0.6088,0.6160,0.6183, 0.6221,0.6239,0.6267,0.6268,0.6302,0.6319,0.6502,0.6517,0.6550,0.6717, 0.6748,0.6760,0.6787,0.6881,0.6890,0.6932,0.6978,0.7057,0.7058,0.7081, 0.7123,0.7160,0.7208,0.7318,0.7367,0.7379,0.7387,0.7429,0.7457,0.7500, 0.7512,0.7608,0.7718,0.7735,0.7779,0.7809,0.7908,0.7987,0.8026,0.8086, 0.8175,0.8205,0.8295,0.8298,0.8308,0.8341,0.8353,0.8368,0.8386,0.8403, 0.8418,0.8520,0.8546,0.8554,0.8590,0.8605,0.8615,0.8649,0.8749,0.8778, 0.8849,0.8878,0.8900,0.8905,0.8912,0.8981,0.8982,0.9009,0.9022,0.9027, 0.9045,0.9056,0.9057,0.9086,0.9173,0.9175,0.9218,0.9278,0.9305,0.9336, 0.9336,0.9360,0.9397,0.9403,0.9403,0.9440,0.9458,0.9488,0.9505,0.9525, 0.9676,0.9684,0.9727,0.9731,0.9766,0.9877,0.9885,0.9894,0.9903, Overall p-value after applying KStest on 269 p-values = 0.824564 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.