RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-01-05_09:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.61 28.9065 0.964602 2 to 25 15.81 22.7871 0.843688 3 to 26 15.69 13.0955 0.270227 4 to 27 15.55 23.0786 0.853290 5 to 28 16.05 14.2229 0.348731 6 to 29 15.67 15.5981 0.447518 7 to 30 15.50 21.1414 0.779971 8 to 31 15.93 15.3913 0.432684 9 to 32 15.75 15.2432 0.422033 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.401679 Tough bday spacings test for dh-ranFile-2016-01-05_09:31: 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 4 40 68 104 92 79 44 33 19 9 8 (O-E)^2/E 2.9 0.3 0.4 0.4 0.3 0.0 1.3 0.4 1.1 0.9 3.8 Birthday Spacings: Sum(O-E)^2/E= 11.753, p= 0.698 RESULTS OF GCD FOR dh-ranFile-2016-01-05_09:31 Euclid's algorithm: p-value, steps to gcd: 0.736718 p-value, dist. of gcd's: 0.844249 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-01-05_09:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.502 0.601 0.418 0.626 0.682 0.990 0.033 0.442 Bits 8 to 15---> 0.970 0.536 0.184 0.648 0.365 0.256 0.751 0.541 Bits 16 to 23---> 0.360 0.143 0.262 0.331 0.436 0.726 0.313 0.507 Bits 24 to 31---> 0.810 0.633 0.881 0.613 0.952 0.800 0.030 0.180 KS test for the above 32 p values: 0.167 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-01-05_09:31, p-values for 5 runs: 0.8212, 0.2344, 0.6675, 0.6078, 0.7423 Rank test for binary matrices (31x31) for dh-ranFile-2016-01-05_09:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 213 211.4 0.012 0.012 r= 29 5103 5134.0 0.187 0.199 r= 30 23202 23103.0 0.424 0.623 r= 31 11482 11551.5 0.418 1.041 chi-square = 1.041 with df = 3; p-value = 0.209 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-01-05_09:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 220 211.4 0.348 0.348 r= 30 5161 5134.0 0.142 0.490 r= 31 23024 23103.0 0.270 0.761 r= 32 11595 11551.5 0.164 0.924 chi-square = 0.924 with df = 3; p-value = 0.180 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-01-05_09:31 b-rank test for bits 1 to 8, p=0.13744 b-rank test for bits 2 to 9, p=0.25650 b-rank test for bits 3 to 10, p=0.27264 b-rank test for bits 4 to 11, p=0.06022 b-rank test for bits 5 to 12, p=0.19767 b-rank test for bits 6 to 13, p=0.44743 b-rank test for bits 7 to 14, p=0.00299 b-rank test for bits 8 to 15, p=0.43085 b-rank test for bits 9 to 16, p=0.17890 b-rank test for bits 10 to 17, p=0.42388 b-rank test for bits 11 to 18, p=0.90745 b-rank test for bits 12 to 19, p=0.36243 b-rank test for bits 13 to 20, p=0.18963 b-rank test for bits 14 to 21, p=0.20705 b-rank test for bits 15 to 22, p=0.56795 b-rank test for bits 16 to 23, p=0.63206 b-rank test for bits 17 to 24, p=0.36057 b-rank test for bits 18 to 25, p=0.30916 b-rank test for bits 19 to 26, p=0.01972 b-rank test for bits 20 to 27, p=0.12319 b-rank test for bits 21 to 28, p=0.37381 b-rank test for bits 22 to 29, p=0.48712 b-rank test for bits 23 to 30, p=0.01565 b-rank test for bits 24 to 31, p=0.20641 b-rank test for bits 25 to 32, p=0.88612 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 = 0.002594 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-01-05_09:31 (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 141721 -0.44 0.329960 2 141884 -0.06 0.476404 3 142156 0.58 0.717805 4 142249 0.79 0.786292 5 141523 -0.90 0.183358 6 141983 0.17 0.568331 7 142231 0.75 0.773844 8 141955 0.11 0.542489 9 142564 1.53 0.936942 10 141832 -0.18 0.428310 11 141517 -0.92 0.179661 12 142276 0.86 0.804196 13 141192 -1.68 0.046869 14 141411 -1.16 0.122147 15 141926 0.04 0.515534 16 141598 -0.73 0.233489 17 141193 -1.67 0.047098 18 142227 0.74 0.771023 19 142205 0.69 0.755160 20 142050 0.33 0.628797 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-01-05_09:31 Bits used No. missing words z-score p-value 23 to 32 141712 -0.6804 0.248110 22 to 31 141449 -1.5873 0.056217 21 to 30 141726 -0.6322 0.263637 20 to 29 141818 -0.3149 0.376407 19 to 28 141975 0.2264 0.589574 18 to 27 141626 -0.9770 0.164285 17 to 26 142090 0.6230 0.733358 16 to 25 142497 2.0264 0.978641 15 to 24 141798 -0.3839 0.350528 14 to 23 142023 0.3920 0.652458 13 to 22 142417 1.7506 0.959991 12 to 21 141555 -1.2218 0.110886 11 to 20 142258 1.2023 0.885378 10 to 19 142561 2.2471 0.987684 9 to 18 141932 0.0782 0.531155 8 to 17 141781 -0.4425 0.329058 7 to 16 141987 0.2678 0.605584 6 to 15 141828 -0.2804 0.389567 5 to 14 141506 -1.3908 0.082144 4 to 13 141993 0.2885 0.613525 3 to 12 141811 -0.3391 0.367279 2 to 11 141993 0.2885 0.613525 1 to 10 141641 -0.9253 0.177411 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-01-05_09:31 Bits used No. missing words z-score p-value 28 to 32 141984 0.2531 0.599912 27 to 31 142221 1.0565 0.854632 26 to 30 141986 0.2599 0.602529 25 to 29 141965 0.1887 0.574841 24 to 28 142312 1.3650 0.913871 23 to 27 142238 1.1141 0.867390 22 to 26 142340 1.4599 0.927841 21 to 25 142165 0.8667 0.806941 20 to 24 142087 0.6023 0.726503 19 to 23 141473 -1.4791 0.069559 18 to 22 141146 -2.5876 0.004833 17 to 21 141768 -0.4791 0.315939 16 to 20 142149 0.8124 0.791731 15 to 19 142130 0.7480 0.772780 14 to 18 141741 -0.5706 0.284132 13 to 17 142404 1.6768 0.953214 12 to 16 142106 0.6667 0.747511 11 to 15 142178 0.9107 0.818785 10 to 14 141462 -1.5164 0.064713 9 to 13 141823 -0.2926 0.384897 8 to 12 141587 -1.0926 0.137275 7 to 11 142010 0.3413 0.633544 6 to 10 142136 0.7684 0.778867 5 to 9 142671 2.5819 0.995088 4 to 8 141465 -1.5062 0.066008 3 to 7 141671 -0.8079 0.209575 2 to 6 141819 -0.3062 0.379725 1 to 5 141771 -0.4689 0.319565 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-01-05_09:31 Bits used No. missing words z-score p-value 31 to 32 141800 -0.3225 0.373534 30 to 31 142047 0.4061 0.657668 29 to 30 142210 0.8869 0.812442 28 to 29 142014 0.3088 0.621248 27 to 28 141828 -0.2399 0.405199 26 to 27 142201 0.8604 0.805211 25 to 26 141997 0.2586 0.602033 24 to 25 141375 -1.5762 0.057490 23 to 24 142039 0.3825 0.648958 22 to 23 141929 0.0580 0.523135 21 to 22 141883 -0.0777 0.469045 20 to 21 141521 -1.1455 0.125998 19 to 20 142000 0.2675 0.605444 18 to 19 141896 -0.0393 0.484317 17 to 18 142115 0.6067 0.727974 16 to 17 141471 -1.2930 0.098004 15 to 16 141584 -0.9597 0.168609 14 to 15 141792 -0.3461 0.364632 13 to 14 141761 -0.4376 0.330856 12 to 13 142021 0.3294 0.629077 11 to 12 141378 -1.5673 0.058517 10 to 11 141568 -1.0069 0.156998 9 to 10 142293 1.1318 0.871134 8 to 9 141611 -0.8800 0.189422 7 to 8 142295 1.1377 0.872371 6 to 7 142604 2.0492 0.979777 5 to 6 141518 -1.1544 0.124175 4 to 5 141591 -0.9390 0.173859 3 to 4 141850 -0.1750 0.430534 2 to 3 141993 0.2468 0.597474 1 to 2 141882 -0.0806 0.467872 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-01-05_09:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2308.15 -2.713 0.003332 Test results for specific bytes for dh-ranFile-2016-01-05_09:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2425.97 -1.047 0.147549 2 to 9 2593.40 1.321 0.906738 3 to 10 2572.65 1.027 0.847891 4 to 11 2544.53 0.630 0.735565 5 to 12 2569.28 0.980 0.836391 6 to 13 2586.14 1.218 0.888421 7 to 14 2346.88 -2.165 0.015177 8 to 15 2427.61 -1.024 0.152975 9 to 16 2438.11 -0.875 0.190734 10 to 17 2609.10 1.543 0.938567 11 to 18 2587.39 1.236 0.891746 12 to 19 2350.63 -2.112 0.017326 13 to 20 2540.78 0.577 0.717948 14 to 21 2497.81 -0.031 0.487620 15 to 22 2460.75 -0.555 0.289436 16 to 23 2549.81 0.704 0.759398 17 to 24 2446.01 -0.763 0.222592 18 to 25 2557.88 0.819 0.793489 19 to 26 2525.75 0.364 0.642141 20 to 27 2525.31 0.358 0.639810 21 to 28 2386.49 -1.605 0.054214 22 to 29 2481.66 -0.259 0.397657 23 to 30 2606.84 1.511 0.934599 24 to 31 2408.10 -1.300 0.096865 25 to 32 2296.61 -2.876 0.002012 CDPARK for dh-ranFile-2016-01-05_09:31: 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 3527 0.1826 0.572463 3490 -1.5068 0.065925 3503 -0.9132 0.180558 3547 1.0959 0.863437 3544 0.9589 0.831196 3471 -2.3744 0.008788 3541 0.8219 0.794438 3497 -1.1872 0.117571 3501 -1.0046 0.157553 3517 -0.2740 0.392053 Square side=100, avg. no. parked=3513.80 sample std.=24.29 p-value of the KSTEST for those 10 p-values: 0.261417 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-01-05_09:31 0.6408,0.9667,0.3277,0.3625,0.4031,0.2700,0.4857,0.4579,0.3242,0.8764, The KS test for those 10 p-values: 0.468565 The 3DSPHERES test for dh-ranFile-2016-01-05_09:31 sample no r^3 equiv. uni. 1 5.645 0.171514 2 12.316 0.336709 3 9.313 0.266861 4 17.086 0.434219 5 2.028 0.065371 6 55.383 0.842150 7 23.692 0.546038 8 11.505 0.318539 9 5.013 0.153886 10 24.675 0.560666 11 109.204 0.973752 12 3.020 0.095766 13 23.903 0.549211 14 32.047 0.656384 15 33.572 0.673411 16 13.031 0.352317 17 48.101 0.798779 18 26.725 0.589693 19 41.971 0.753165 20 8.508 0.246932 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.862318 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-01-05_09:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 2.0 1.3 0.1 0.5 1.1 -0.6 1.4 0.8 0.9 -2.1 -1.6 1.0 -0.3 0.2 -0.3 -0.9 0.9 -1.2 0.5 0.3 -0.3 0.8 0.3 -0.5 2.8 -0.5 0.1 -0.3 -1.3 -0.4 -0.6 -0.7 0.0 0.1 0.5 -0.5 1.0 -0.1 -0.4 1.0 0.1 0.0 1.8 Chi-square with 42 degrees of freedom:40.239200 z-score=-0.192119, p-value=0.451531 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-01-05_09:31 Test no p-value 1 0.579484 2 0.530328 3 0.074664 4 0.315382 5 0.033721 6 0.271901 7 0.597314 8 0.570516 9 0.996332 10 0.133313 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.366016 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-01-05_09:31: (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 66603 0.06 66568 0.15 3 25000.00 24897 0.42 25064 0.16 4 6666.67 6789 2.24 6740 0.81 5 1388.89 1395 0.03 1371 0.23 6 238.10 271 4.55 222 1.09 7 34.72 39 0.53 28 1.30 8 4.96 5 0.00 6 0.22 p=0.74934 p=0.31705 Number of rngs required: 688687, p-value: 0.628 RESULTS OF CRAPS TEST for dh-ranFile-2016-01-05_09:31 No. of wins: Observed Expected 98294 98585.9 z-score=-1.305, pvalue=0.09588 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66436 66666.7 0.798 0.798 2 37629 37654.3 0.017 0.815 3 27224 26954.7 2.690 3.505 4 19132 19313.5 1.705 5.210 5 13909 13851.4 0.239 5.449 6 9813 9943.5 1.714 7.163 7 7147 7145.0 0.001 7.164 8 5238 5139.1 1.904 9.068 9 3781 3699.9 1.779 10.847 10 2626 2666.3 0.609 11.456 11 1897 1923.3 0.360 11.817 12 1419 1388.7 0.659 12.476 13 1002 1003.7 0.003 12.479 14 742 726.1 0.346 12.825 15 508 525.8 0.605 13.430 16 409 381.2 2.035 15.465 17 286 276.5 0.324 15.789 18 218 200.8 1.468 17.257 19 160 146.0 1.346 18.602 20 112 106.2 0.315 18.918 21 312 287.1 2.157 21.075 Chisq= 21.07 for 20 degrees of freedom, p= 0.60724 SUMMARY of craptest p-value for no. of wins: 0.095885 p-value for throws/game: 0.607244 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-01-05_09:31 No. of wins: Observed Expected 98728 98585.9 z-score= 0.636, pvalue=0.73753 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66830 66666.7 0.400 0.400 2 37683 37654.3 0.022 0.422 3 27049 26954.7 0.330 0.752 4 19311 19313.5 0.000 0.752 5 13842 13851.4 0.006 0.758 6 9992 9943.5 0.236 0.995 7 7077 7145.0 0.648 1.642 8 4969 5139.1 5.628 7.271 9 3680 3699.9 0.107 7.377 10 2690 2666.3 0.211 7.588 11 1951 1923.3 0.398 7.986 12 1395 1388.7 0.028 8.014 13 985 1003.7 0.349 8.363 14 695 726.1 1.335 9.699 15 489 525.8 2.580 12.279 16 408 381.2 1.891 14.170 17 269 276.5 0.206 14.376 18 179 200.8 2.373 16.749 19 135 146.0 0.827 17.575 20 89 106.2 2.790 20.366 21 282 287.1 0.091 20.457 Chisq= 20.46 for 20 degrees of freedom, p= 0.57029 SUMMARY of craptest p-value for no. of wins: 0.737527 p-value for throws/game: 0.570293 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0020,0.0026,0.0030,0.0033,0.0048,0.0088,0.0152,0.0156,0.0173,0.0197, 0.0296,0.0332,0.0337,0.0469,0.0471,0.0542,0.0562,0.0575,0.0585,0.0602, 0.0647,0.0654,0.0659,0.0660,0.0696,0.0747,0.0821,0.0958,0.0959,0.0969, 0.0980,0.1109,0.1176,0.1221,0.1232,0.1242,0.1260,0.1333,0.1373,0.1374, 0.1435,0.1475,0.1530,0.1539,0.1570,0.1576,0.1643,0.1671,0.1686,0.1715, 0.1739,0.1774,0.1789,0.1797,0.1803,0.1804,0.1806,0.1834,0.1839,0.1894, 0.1896,0.1907,0.1977,0.2064,0.2070,0.2088,0.2096,0.2226,0.2335,0.2344, 0.2469,0.2481,0.2560,0.2565,0.2614,0.2621,0.2636,0.2669,0.2700,0.2702, 0.2719,0.2726,0.2841,0.2894,0.3092,0.3125,0.3154,0.3159,0.3171,0.3185, 0.3196,0.3242,0.3277,0.3291,0.3300,0.3309,0.3312,0.3367,0.3487,0.3505, 0.3523,0.3596,0.3606,0.3624,0.3625,0.3646,0.3649,0.3660,0.3673,0.3735, 0.3738,0.3764,0.3797,0.3849,0.3896,0.3921,0.3977,0.4017,0.4031,0.4052, 0.4178,0.4220,0.4239,0.4283,0.4305,0.4309,0.4327,0.4342,0.4360,0.4423, 0.4474,0.4475,0.4515,0.4579,0.4679,0.4686,0.4690,0.4764,0.4843,0.4857, 0.4871,0.4876,0.5018,0.5067,0.5155,0.5231,0.5303,0.5312,0.5364,0.5412, 0.5425,0.5460,0.5492,0.5607,0.5680,0.5683,0.5703,0.5705,0.5725,0.5748, 0.5795,0.5896,0.5897,0.5973,0.5975,0.5999,0.6009,0.6020,0.6025,0.6054, 0.6056,0.6072,0.6078,0.6131,0.6135,0.6135,0.6212,0.6265,0.6281,0.6288, 0.6291,0.6321,0.6329,0.6335,0.6398,0.6408,0.6421,0.6477,0.6490,0.6525, 0.6564,0.6577,0.6675,0.6734,0.6817,0.6981,0.7178,0.7179,0.7265,0.7265, 0.7280,0.7334,0.7356,0.7367,0.7375,0.7423,0.7475,0.7493,0.7512,0.7532, 0.7552,0.7594,0.7710,0.7728,0.7738,0.7789,0.7800,0.7863,0.7917,0.7935, 0.7944,0.7988,0.8001,0.8042,0.8052,0.8069,0.8100,0.8124,0.8188,0.8212, 0.8312,0.8364,0.8421,0.8437,0.8442,0.8479,0.8533,0.8546,0.8623,0.8634, 0.8674,0.8711,0.8724,0.8764,0.8806,0.8854,0.8861,0.8884,0.8917,0.9067, 0.9074,0.9139,0.9278,0.9346,0.9369,0.9386,0.9524,0.9532,0.9600,0.9646, 0.9667,0.9704,0.9738,0.9786,0.9798,0.9877,0.9898,0.9951,0.9963, Overall p-value after applying KStest on 269 p-values = 0.337599 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.