RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-10-19_02:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.88 37.9129 0.997474 2 to 25 15.75 15.5830 0.446435 3 to 26 15.72 22.9895 0.850406 4 to 27 15.77 21.6495 0.801423 5 to 28 15.56 22.9145 0.847944 6 to 29 15.63 20.6906 0.759564 7 to 30 15.39 21.8432 0.809175 8 to 31 15.79 19.3037 0.688620 9 to 32 15.94 21.0543 0.776131 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.003760 Tough bday spacings test for dh-ranFile-2015-10-19_02:31: 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 12 38 80 83 92 77 67 35 10 3 3 (O-E)^2/E 0.9 0.1 0.6 2.2 0.3 0.0 4.3 0.9 1.6 2.0 0.3 Birthday Spacings: Sum(O-E)^2/E= 13.148, p= 0.784 RESULTS OF GCD FOR dh-ranFile-2015-10-19_02:31 Euclid's algorithm: p-value, steps to gcd: 0.771852 p-value, dist. of gcd's: 0.202044 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-10-19_02:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.211 0.060 0.650 0.532 0.874 0.300 0.574 0.057 Bits 8 to 15---> 0.061 0.241 0.652 0.093 0.180 0.025 0.551 0.872 Bits 16 to 23---> 0.038 0.234 0.586 0.360 0.317 0.572 0.963 0.165 Bits 24 to 31---> 0.021 0.461 0.614 0.089 0.869 0.452 0.081 0.717 KS test for the above 32 p values: 0.967 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-10-19_02:31, p-values for 5 runs: 0.7346, 0.8241, 0.6995, 0.4812, 0.1036 Rank test for binary matrices (31x31) for dh-ranFile-2015-10-19_02:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 217 211.4 0.147 0.147 r= 29 5149 5134.0 0.044 0.191 r= 30 22992 23103.0 0.534 0.725 r= 31 11642 11551.5 0.709 1.434 chi-square = 1.434 with df = 3; p-value = 0.302 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-10-19_02:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 207 211.4 0.092 0.092 r= 30 5140 5134.0 0.007 0.099 r= 31 23044 23103.0 0.151 0.250 r= 32 11609 11551.5 0.286 0.536 chi-square = 0.536 with df = 3; p-value = 0.089 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-10-19_02:31 b-rank test for bits 1 to 8, p=0.81524 b-rank test for bits 2 to 9, p=0.32948 b-rank test for bits 3 to 10, p=0.53969 b-rank test for bits 4 to 11, p=0.12735 b-rank test for bits 5 to 12, p=0.24096 b-rank test for bits 6 to 13, p=0.15911 b-rank test for bits 7 to 14, p=0.25223 b-rank test for bits 8 to 15, p=0.25359 b-rank test for bits 9 to 16, p=0.12556 b-rank test for bits 10 to 17, p=0.28836 b-rank test for bits 11 to 18, p=0.62287 b-rank test for bits 12 to 19, p=0.87449 b-rank test for bits 13 to 20, p=0.84455 b-rank test for bits 14 to 21, p=0.77812 b-rank test for bits 15 to 22, p=0.27966 b-rank test for bits 16 to 23, p=0.05732 b-rank test for bits 17 to 24, p=0.97976 b-rank test for bits 18 to 25, p=0.98468 b-rank test for bits 19 to 26, p=0.78957 b-rank test for bits 20 to 27, p=0.50821 b-rank test for bits 21 to 28, p=0.59954 b-rank test for bits 22 to 29, p=0.50173 b-rank test for bits 23 to 30, p=0.40941 b-rank test for bits 24 to 31, p=0.49734 b-rank test for bits 25 to 32, p=0.11690 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 = 0.848258 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-10-19_02:31 (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 141602 -0.72 0.236360 2 142075 0.39 0.650651 3 142757 1.98 0.976178 4 141962 0.12 0.548971 5 141476 -1.01 0.155661 6 141647 -0.61 0.269964 7 142077 0.39 0.652379 8 141433 -1.11 0.132871 9 142025 0.27 0.606519 10 142661 1.76 0.960476 11 141503 -0.95 0.171216 12 142500 1.38 0.916217 13 142005 0.22 0.588438 14 141640 -0.63 0.264584 15 142401 1.15 0.874673 16 141477 -1.01 0.156220 17 142031 0.28 0.611900 18 142168 0.60 0.727201 19 141782 -0.30 0.383042 20 142440 1.24 0.892491 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-10-19_02:31 Bits used No. missing words z-score p-value 23 to 32 141880 -0.1011 0.459721 22 to 31 141971 0.2127 0.584202 21 to 30 141771 -0.4770 0.316681 20 to 29 142342 1.4920 0.932146 19 to 28 141652 -0.8873 0.187447 18 to 27 141726 -0.6322 0.263637 17 to 26 142047 0.4747 0.682508 16 to 25 142399 1.6885 0.954344 15 to 24 142506 2.0575 0.980180 14 to 23 141565 -1.1873 0.117546 13 to 22 142172 0.9058 0.817468 12 to 21 141664 -0.8460 0.198786 11 to 20 141515 -1.3598 0.086953 10 to 19 141768 -0.4873 0.313007 9 to 18 142284 1.2920 0.901815 8 to 17 141858 -0.1770 0.429754 7 to 16 142206 1.0230 0.846846 6 to 15 142311 1.3851 0.916984 5 to 14 142170 0.8989 0.815637 4 to 13 142462 1.9058 0.971659 3 to 12 142073 0.5644 0.713752 2 to 11 141995 0.2954 0.616161 1 to 10 141699 -0.7253 0.234141 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-10-19_02:31 Bits used No. missing words z-score p-value 28 to 32 141362 -1.8554 0.031773 27 to 31 141794 -0.3909 0.347917 26 to 30 141557 -1.1943 0.116173 25 to 29 142054 0.4904 0.688077 24 to 28 141475 -1.4723 0.070469 23 to 27 141449 -1.5604 0.059328 22 to 26 141384 -1.7808 0.037474 21 to 25 141802 -0.3638 0.357992 20 to 24 141665 -0.8282 0.203768 19 to 23 142057 0.5006 0.691665 18 to 22 142092 0.6192 0.732114 17 to 21 142080 0.5785 0.718551 16 to 20 141808 -0.3435 0.365614 15 to 19 142115 0.6972 0.757157 14 to 18 142199 0.9819 0.836933 13 to 17 142228 1.0802 0.859982 12 to 16 142272 1.2294 0.890537 11 to 15 142412 1.7040 0.955806 10 to 14 141966 0.1921 0.576169 9 to 13 141706 -0.6893 0.245332 8 to 12 142031 0.4124 0.659992 7 to 11 141212 -2.3638 0.009044 6 to 10 142341 1.4633 0.928306 5 to 9 142014 0.3548 0.638635 4 to 8 142049 0.4735 0.682057 3 to 7 141781 -0.4350 0.331775 2 to 6 142154 0.8294 0.796558 1 to 5 141837 -0.2452 0.403156 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-10-19_02:31 Bits used No. missing words z-score p-value 31 to 32 141860 -0.1455 0.442152 30 to 31 142313 1.1908 0.883127 29 to 30 141867 -0.1249 0.450314 28 to 29 141656 -0.7473 0.227445 27 to 28 141705 -0.6027 0.273340 26 to 27 142058 0.4386 0.669508 25 to 26 141765 -0.4258 0.335144 24 to 25 141554 -1.0482 0.147280 23 to 24 141802 -0.3166 0.375771 22 to 23 141765 -0.4258 0.335144 21 to 22 142378 1.3825 0.916592 20 to 21 141554 -1.0482 0.147280 19 to 20 141171 -2.1780 0.014704 18 to 19 141352 -1.6440 0.050084 17 to 18 142335 1.2557 0.895381 16 to 17 141942 0.0964 0.538387 15 to 16 141810 -0.2930 0.384758 14 to 15 141379 -1.5644 0.058862 13 to 14 141972 0.1849 0.573333 12 to 13 141830 -0.2340 0.407488 11 to 12 142299 1.1495 0.874819 10 to 11 142150 0.7099 0.761130 9 to 10 142069 0.4710 0.681181 8 to 9 141556 -1.0423 0.148643 7 to 8 142188 0.8220 0.794472 6 to 7 141739 -0.5024 0.307676 5 to 6 141476 -1.2783 0.100579 4 to 5 141850 -0.1750 0.430534 3 to 4 141993 0.2468 0.597474 2 to 3 141985 0.2232 0.588316 1 to 2 141209 -2.0659 0.019420 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-10-19_02:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2444.93 -0.779 0.218034 Test results for specific bytes for dh-ranFile-2015-10-19_02:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2508.52 0.120 0.547933 2 to 9 2386.84 -1.600 0.054758 3 to 10 2481.72 -0.258 0.398012 4 to 11 2484.42 -0.220 0.412788 5 to 12 2579.36 1.122 0.869135 6 to 13 2517.07 0.241 0.595386 7 to 14 2566.44 0.940 0.826283 8 to 15 2442.47 -0.814 0.207925 9 to 16 2600.29 1.418 0.921949 10 to 17 2534.70 0.491 0.688182 11 to 18 2370.06 -1.838 0.033061 12 to 19 2548.25 0.682 0.752514 13 to 20 2427.28 -1.028 0.151866 14 to 21 2325.24 -2.471 0.006728 15 to 22 2521.07 0.298 0.617141 16 to 23 2431.75 -0.965 0.167215 17 to 24 2574.15 1.049 0.852817 18 to 25 2502.77 0.039 0.515619 19 to 26 2315.58 -2.608 0.004553 20 to 27 2383.76 -1.644 0.050094 21 to 28 2362.44 -1.945 0.025863 22 to 29 2445.94 -0.765 0.222280 23 to 30 2470.21 -0.421 0.336752 24 to 31 2478.75 -0.300 0.381908 25 to 32 2624.65 1.763 0.961036 CDPARK for dh-ranFile-2015-10-19_02:31: 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 3509 -0.6393 0.261324 3503 -0.9132 0.180558 3522 -0.0457 0.481790 3530 0.3196 0.625377 3550 1.2329 0.891189 3518 -0.2283 0.409702 3495 -1.2785 0.100530 3527 0.1826 0.572463 3535 0.5479 0.708135 3544 0.9589 0.831196 Square side=100, avg. no. parked=3523.30 sample std.=16.69 p-value of the KSTEST for those 10 p-values: 0.991312 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-10-19_02:31 0.0420,0.1095,0.0312,0.2808,0.3236,0.8959,0.2274,0.3682,0.9731,0.2749, The KS test for those 10 p-values: 0.087310 The 3DSPHERES test for dh-ranFile-2015-10-19_02:31 sample no r^3 equiv. uni. 1 25.236 0.568809 2 17.424 0.440540 3 55.286 0.841639 4 0.586 0.019349 5 61.604 0.871711 6 12.857 0.348551 7 45.869 0.783243 8 13.514 0.362680 9 36.258 0.701385 10 39.114 0.728500 11 28.740 0.616346 12 8.925 0.257319 13 19.684 0.481152 14 4.702 0.145075 15 13.669 0.365955 16 5.650 0.171648 17 1.333 0.043461 18 86.794 0.944598 19 63.372 0.879054 20 9.531 0.272178 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.998124 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-10-19_02:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -1.2 -0.6 0.3 -0.9 0.3 -0.6 -0.1 -0.2 -1.0 -1.5 -0.5 -0.4 0.2 0.4 2.0 -0.6 0.9 -0.8 0.5 0.2 -0.6 -0.4 0.3 -1.4 -1.7 1.9 0.5 2.0 0.9 0.0 -0.1 -0.2 2.8 0.6 -0.3 -0.2 -0.7 -0.4 0.4 0.9 1.0 -0.1 Chi-square with 42 degrees of freedom:38.106614 z-score=-0.424803, p-value=0.357447 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-10-19_02:31 Test no p-value 1 0.391099 2 0.065979 3 0.239311 4 0.912049 5 0.798477 6 0.210246 7 0.888345 8 0.872152 9 0.692327 10 0.054516 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.648126 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-10-19_02:31: (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 66755 0.12 66546 0.22 3 25000.00 24930 0.20 25144 0.83 4 6666.67 6658 0.01 6605 0.57 5 1388.89 1378 0.09 1399 0.07 6 238.10 250 0.60 255 1.20 7 34.72 26 2.19 45 3.04 8 4.96 2 1.77 5 0.00 p=0.45123 p=0.56963 Number of rngs required: 687552, p-value: 0.162 RESULTS OF CRAPS TEST for dh-ranFile-2015-10-19_02:31 No. of wins: Observed Expected 98381 98585.9 z-score=-0.916, pvalue=0.17977 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66560 66666.7 0.171 0.171 2 37594 37654.3 0.097 0.267 3 26962 26954.7 0.002 0.269 4 19463 19313.5 1.158 1.427 5 13966 13851.4 0.948 2.375 6 9956 9943.5 0.016 2.391 7 7175 7145.0 0.126 2.516 8 4956 5139.1 6.522 9.038 9 3735 3699.9 0.334 9.372 10 2767 2666.3 3.803 13.175 11 1865 1923.3 1.769 14.944 12 1361 1388.7 0.554 15.498 13 1015 1003.7 0.127 15.625 14 720 726.1 0.052 15.677 15 527 525.8 0.003 15.679 16 376 381.2 0.070 15.749 17 278 276.5 0.008 15.757 18 192 200.8 0.388 16.145 19 140 146.0 0.245 16.390 20 105 106.2 0.014 16.404 21 287 287.1 0.000 16.404 Chisq= 16.40 for 20 degrees of freedom, p= 0.30875 SUMMARY of craptest p-value for no. of wins: 0.179769 p-value for throws/game: 0.308751 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-10-19_02:31 No. of wins: Observed Expected 98630 98585.9 z-score= 0.197, pvalue=0.57825 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66398 66666.7 1.083 1.083 2 37898 37654.3 1.577 2.660 3 26807 26954.7 0.810 3.469 4 19454 19313.5 1.023 4.492 5 13943 13851.4 0.605 5.098 6 9975 9943.5 0.100 5.197 7 7053 7145.0 1.185 6.382 8 5158 5139.1 0.070 6.452 9 3710 3699.9 0.028 6.480 10 2647 2666.3 0.140 6.619 11 1905 1923.3 0.175 6.794 12 1367 1388.7 0.340 7.134 13 1074 1003.7 4.922 12.056 14 698 726.1 1.091 13.147 15 535 525.8 0.160 13.306 16 390 381.2 0.205 13.512 17 278 276.5 0.008 13.520 18 191 200.8 0.481 14.001 19 133 146.0 1.155 15.156 20 112 106.2 0.315 15.471 21 274 287.1 0.599 16.070 Chisq= 16.07 for 20 degrees of freedom, p= 0.28770 SUMMARY of craptest p-value for no. of wins: 0.578253 p-value for throws/game: 0.287704 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0038,0.0046,0.0067,0.0090,0.0147,0.0193,0.0194,0.0206,0.0251,0.0259, 0.0312,0.0318,0.0331,0.0375,0.0378,0.0420,0.0435,0.0501,0.0501,0.0545, 0.0548,0.0569,0.0573,0.0589,0.0593,0.0603,0.0609,0.0660,0.0705,0.0809, 0.0870,0.0873,0.0890,0.0891,0.0926,0.1005,0.1006,0.1036,0.1095,0.1162, 0.1169,0.1175,0.1256,0.1273,0.1329,0.1451,0.1473,0.1473,0.1486,0.1519, 0.1557,0.1562,0.1591,0.1621,0.1654,0.1672,0.1712,0.1716,0.1798,0.1799, 0.1806,0.1874,0.1988,0.2020,0.2038,0.2079,0.2102,0.2111,0.2180,0.2223, 0.2274,0.2274,0.2337,0.2341,0.2364,0.2393,0.2410,0.2414,0.2453,0.2522, 0.2536,0.2573,0.2613,0.2636,0.2646,0.2700,0.2722,0.2733,0.2749,0.2797, 0.2808,0.2877,0.2884,0.3002,0.3023,0.3077,0.3088,0.3130,0.3167,0.3171, 0.3236,0.3295,0.3318,0.3351,0.3351,0.3368,0.3479,0.3486,0.3574,0.3580, 0.3604,0.3627,0.3656,0.3660,0.3682,0.3758,0.3819,0.3830,0.3848,0.3911, 0.3980,0.4032,0.4075,0.4094,0.4097,0.4128,0.4298,0.4305,0.4405,0.4422, 0.4464,0.4503,0.4512,0.4523,0.4597,0.4615,0.4812,0.4812,0.4818,0.4973, 0.5017,0.5082,0.5156,0.5320,0.5384,0.5397,0.5479,0.5490,0.5509,0.5688, 0.5696,0.5724,0.5725,0.5733,0.5738,0.5762,0.5783,0.5842,0.5860,0.5883, 0.5884,0.5954,0.5975,0.5995,0.6065,0.6119,0.6141,0.6162,0.6163,0.6171, 0.6229,0.6254,0.6386,0.6481,0.6505,0.6507,0.6516,0.6524,0.6600,0.6695, 0.6812,0.6821,0.6825,0.6881,0.6882,0.6886,0.6917,0.6923,0.6995,0.7014, 0.7081,0.7138,0.7166,0.7186,0.7272,0.7285,0.7321,0.7346,0.7525,0.7572, 0.7596,0.7611,0.7719,0.7761,0.7781,0.7832,0.7845,0.7896,0.7945,0.7966, 0.7985,0.8014,0.8092,0.8152,0.8156,0.8175,0.8241,0.8263,0.8312,0.8369, 0.8416,0.8446,0.8468,0.8479,0.8483,0.8504,0.8528,0.8600,0.8691,0.8691, 0.8717,0.8719,0.8722,0.8738,0.8745,0.8747,0.8748,0.8791,0.8831,0.8883, 0.8905,0.8912,0.8925,0.8954,0.8959,0.9018,0.9120,0.9162,0.9166,0.9170, 0.9219,0.9283,0.9321,0.9446,0.9543,0.9558,0.9605,0.9610,0.9631,0.9667, 0.9717,0.9731,0.9762,0.9798,0.9802,0.9847,0.9913,0.9975,0.9981, Overall p-value after applying KStest on 269 p-values = 0.207647 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.