RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-07-10_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 15.55 28.7219 0.962821 2 to 25 15.88 8.6399 0.049115 3 to 26 15.65 15.3418 0.429124 4 to 27 15.76 17.6404 0.588139 5 to 28 15.87 23.5604 0.868119 6 to 29 15.88 21.8437 0.809194 7 to 30 15.97 18.2080 0.624167 8 to 31 15.69 16.2979 0.497180 9 to 32 16.02 11.0370 0.145367 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.915999 Tough bday spacings test for dh-ranFile-2015-07-10_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 6 34 90 99 101 66 54 24 12 9 5 (O-E)^2/E 1.1 0.2 3.8 0.0 0.1 1.9 0.1 1.1 0.6 0.9 0.2 Birthday Spacings: Sum(O-E)^2/E= 9.941, p= 0.554 RESULTS OF GCD FOR dh-ranFile-2015-07-10_08:31 Euclid's algorithm: p-value, steps to gcd: 0.739995 p-value, dist. of gcd's: 0.188994 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-07-10_08:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.118 0.346 0.774 0.307 0.445 0.301 0.220 0.053 Bits 8 to 15---> 0.201 0.812 0.066 0.634 0.751 0.254 0.985 0.912 Bits 16 to 23---> 0.926 0.476 0.636 0.614 0.404 0.981 0.955 0.521 Bits 24 to 31---> 0.366 0.567 0.315 0.578 0.158 0.937 0.658 0.126 KS test for the above 32 p values: 0.097 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-07-10_08:31, p-values for 5 runs: 0.2263, 0.4069, 0.4949, 0.3495, 0.9334 Rank test for binary matrices (31x31) for dh-ranFile-2015-07-10_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 217 211.4 0.147 0.147 r= 29 5132 5134.0 0.001 0.148 r= 30 23153 23103.0 0.108 0.256 r= 31 11498 11551.5 0.248 0.504 chi-square = 0.504 with df = 3; p-value = 0.082 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-07-10_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 173 211.4 6.981 6.981 r= 30 5085 5134.0 0.468 7.449 r= 31 23065 23103.0 0.063 7.512 r= 32 11677 11551.5 1.363 8.875 chi-square = 8.875 with df = 3; p-value = 0.969 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-07-10_08:31 b-rank test for bits 1 to 8, p=0.48168 b-rank test for bits 2 to 9, p=0.52261 b-rank test for bits 3 to 10, p=0.71200 b-rank test for bits 4 to 11, p=0.77843 b-rank test for bits 5 to 12, p=0.19331 b-rank test for bits 6 to 13, p=0.24085 b-rank test for bits 7 to 14, p=0.01960 b-rank test for bits 8 to 15, p=0.33102 b-rank test for bits 9 to 16, p=0.06825 b-rank test for bits 10 to 17, p=0.59675 b-rank test for bits 11 to 18, p=0.52656 b-rank test for bits 12 to 19, p=0.64995 b-rank test for bits 13 to 20, p=0.66543 b-rank test for bits 14 to 21, p=0.68021 b-rank test for bits 15 to 22, p=0.87805 b-rank test for bits 16 to 23, p=0.84016 b-rank test for bits 17 to 24, p=0.72239 b-rank test for bits 18 to 25, p=0.13986 b-rank test for bits 19 to 26, p=0.01383 b-rank test for bits 20 to 27, p=0.02969 b-rank test for bits 21 to 28, p=0.50582 b-rank test for bits 22 to 29, p=0.68391 b-rank test for bits 23 to 30, p=0.06019 b-rank test for bits 24 to 31, p=0.45627 b-rank test for bits 25 to 32, p=0.41809 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 = 0.298605 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-07-10_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 140907 -2.34 0.009593 2 142298 0.91 0.818089 3 141296 -1.43 0.075927 4 142350 1.03 0.848402 5 142737 1.93 0.973432 6 141806 -0.24 0.404613 7 141267 -1.50 0.066707 8 142204 0.69 0.754425 9 140960 -2.22 0.013275 10 141883 -0.06 0.475473 11 142626 1.67 0.952980 12 141623 -0.67 0.251749 13 141806 -0.24 0.404613 14 141430 -1.12 0.131372 15 142078 0.39 0.653242 16 141590 -0.75 0.227804 17 141539 -0.87 0.193449 18 141858 -0.12 0.452269 19 142410 1.17 0.878957 20 141149 -1.78 0.037828 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-07-10_08:31 Bits used No. missing words z-score p-value 23 to 32 141754 -0.5356 0.296110 22 to 31 141674 -0.8115 0.208544 21 to 30 142275 1.2609 0.896333 20 to 29 141776 -0.4598 0.322845 19 to 28 141978 0.2368 0.593591 18 to 27 141917 0.0264 0.510550 17 to 26 141269 -2.2080 0.013621 16 to 25 141982 0.2506 0.598933 15 to 24 142150 0.8299 0.796701 14 to 23 141703 -0.7115 0.238393 13 to 22 141925 0.0540 0.521546 12 to 21 142210 1.0368 0.850084 11 to 20 142027 0.4058 0.657540 10 to 19 142309 1.3782 0.915925 9 to 18 141251 -2.2701 0.011601 8 to 17 141508 -1.3839 0.083195 7 to 16 141809 -0.3460 0.364684 6 to 15 141911 0.0058 0.502297 5 to 14 141841 -0.2356 0.406864 4 to 13 141659 -0.8632 0.194012 3 to 12 142217 1.0609 0.855639 2 to 11 141597 -1.0770 0.140740 1 to 10 141354 -1.9149 0.027751 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-07-10_08:31 Bits used No. missing words z-score p-value 28 to 32 142080 0.5785 0.718551 27 to 31 142128 0.7413 0.770730 26 to 30 141552 -1.2113 0.112893 25 to 29 142333 1.4362 0.924523 24 to 28 141833 -0.2587 0.397916 23 to 27 141879 -0.1028 0.459056 22 to 26 141617 -0.9909 0.160855 21 to 25 141886 -0.0791 0.468483 20 to 24 141170 -2.5062 0.006102 19 to 23 141700 -0.7096 0.238978 18 to 22 141924 0.0497 0.519831 17 to 21 142327 1.4158 0.921587 16 to 20 141884 -0.0859 0.465787 15 to 19 142161 0.8531 0.803203 14 to 18 141878 -0.1062 0.457711 13 to 17 142363 1.5379 0.937959 12 to 16 142092 0.6192 0.732114 11 to 15 142118 0.7074 0.760327 10 to 14 141703 -0.6994 0.242144 9 to 13 141975 0.2226 0.588081 8 to 12 141409 -1.6960 0.044940 7 to 11 141534 -1.2723 0.101632 6 to 10 142138 0.7752 0.780875 5 to 9 141897 -0.0418 0.483330 4 to 8 142273 1.2328 0.891171 3 to 7 141929 0.0667 0.526581 2 to 6 141615 -0.9977 0.159205 1 to 5 141997 0.2972 0.616838 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-07-10_08:31 Bits used No. missing words z-score p-value 31 to 32 141645 -0.7797 0.217774 30 to 31 141801 -0.3196 0.374652 29 to 30 141720 -0.5585 0.288253 28 to 29 141900 -0.0275 0.489022 27 to 28 142380 1.3884 0.917493 26 to 27 141811 -0.2901 0.385886 25 to 26 141961 0.1524 0.560572 24 to 25 141904 -0.0157 0.493728 23 to 24 141805 -0.3078 0.379133 22 to 23 142053 0.4238 0.664146 21 to 22 141943 0.0993 0.539559 20 to 21 142002 0.2734 0.607713 19 to 20 142410 1.4769 0.930149 18 to 19 142482 1.6893 0.954418 17 to 18 141467 -1.3048 0.095979 16 to 17 142016 0.3147 0.623490 15 to 16 142089 0.5300 0.701944 14 to 15 142043 0.3943 0.653323 13 to 14 141594 -0.9302 0.176140 12 to 13 142038 0.3796 0.647863 11 to 12 142004 0.2793 0.609978 10 to 11 141374 -1.5791 0.057151 9 to 10 142132 0.6568 0.744359 8 to 9 142061 0.4474 0.672708 7 to 8 141990 0.2380 0.594046 6 to 7 141661 -0.7325 0.231921 5 to 6 142506 1.7601 0.960804 4 to 5 142141 0.6834 0.752821 3 to 4 141672 -0.7001 0.241936 2 to 3 142000 0.2675 0.605444 1 to 2 142117 0.6126 0.729928 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-07-10_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2514.35 0.203 0.580394 Test results for specific bytes for dh-ranFile-2015-07-10_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2581.71 1.156 0.876060 2 to 9 2477.97 -0.312 0.377702 3 to 10 2488.98 -0.156 0.438088 4 to 11 2494.49 -0.078 0.468944 5 to 12 2518.60 0.263 0.603759 6 to 13 2414.41 -1.210 0.113063 7 to 14 2544.38 0.628 0.734888 8 to 15 2475.61 -0.345 0.365059 9 to 16 2334.84 -2.336 0.009753 10 to 17 2565.37 0.925 0.822396 11 to 18 2590.86 1.285 0.900608 12 to 19 2369.65 -1.843 0.032636 13 to 20 2594.68 1.339 0.909719 14 to 21 2524.28 0.343 0.634334 15 to 22 2479.37 -0.292 0.385233 16 to 23 2429.97 -0.990 0.160990 17 to 24 2468.24 -0.449 0.326657 18 to 25 2508.15 0.115 0.545873 19 to 26 2499.95 -0.001 0.499690 20 to 27 2456.65 -0.613 0.269922 21 to 28 2486.86 -0.186 0.426310 22 to 29 2493.40 -0.093 0.462826 23 to 30 2458.74 -0.584 0.279767 24 to 31 2513.50 0.191 0.575695 25 to 32 2567.35 0.952 0.829553 CDPARK for dh-ranFile-2015-07-10_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 3490 -1.5068 0.065925 3536 0.5936 0.723613 3538 0.6849 0.753306 3518 -0.2283 0.409702 3489 -1.5525 0.060270 3515 -0.3653 0.357445 3535 0.5479 0.708135 3507 -0.7306 0.232514 3524 0.0457 0.518210 3505 -0.8219 0.205562 Square side=100, avg. no. parked=3515.70 sample std.=17.09 p-value of the KSTEST for those 10 p-values: 0.471251 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-07-10_08:31 0.2184,0.1205,0.6634,0.2178,0.2110,0.7828,0.3269,0.7236,0.0677,0.9082, The KS test for those 10 p-values: 0.540580 The 3DSPHERES test for dh-ranFile-2015-07-10_08:31 sample no r^3 equiv. uni. 1 18.481 0.459924 2 65.200 0.886202 3 55.328 0.841858 4 30.525 0.638502 5 15.226 0.398028 6 10.830 0.303014 7 31.701 0.652400 8 18.917 0.467702 9 57.920 0.854947 10 2.835 0.090158 11 24.040 0.551268 12 16.983 0.432259 13 25.815 0.577052 14 108.318 0.972964 15 32.123 0.657252 16 8.486 0.246373 17 23.009 0.535583 18 26.376 0.584886 19 70.284 0.903941 20 28.379 0.611696 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.191431 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-07-10_08:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -1.2 -0.4 0.2 1.1 -0.1 0.7 0.8 -0.4 0.6 0.9 -0.2 -0.2 -0.4 0.9 -0.3 -0.3 -1.4 0.8 0.6 0.4 -0.9 0.2 -0.3 -1.3 0.6 -0.2 -0.2 0.3 0.1 1.0 -2.2 1.1 0.7 1.6 -0.1 -0.5 -0.7 -0.8 0.4 0.9 -1.0 -0.1 Chi-square with 42 degrees of freedom:25.677948 z-score=-1.780882, p-value=0.022290 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-07-10_08:31 Test no p-value 1 0.107217 2 0.986378 3 0.069232 4 0.114435 5 0.312470 6 0.479500 7 0.007233 8 0.010040 9 0.179996 10 0.803248 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.011873 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-07-10_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 66395 1.11 66601 0.06 3 25000.00 25247 2.44 25016 0.01 4 6666.67 6685 0.05 6653 0.03 5 1388.89 1412 0.38 1438 1.74 6 238.10 224 0.83 256 1.35 7 34.72 33 0.09 32 0.21 8 4.96 3 0.77 3 0.77 p=0.53962 p=0.34679 Number of rngs required: 687776, p-value: 0.235 RESULTS OF CRAPS TEST for dh-ranFile-2015-07-10_08:31 No. of wins: Observed Expected 98398 98585.9 z-score=-0.840, pvalue=0.20039 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66303 66666.7 1.984 1.984 2 37860 37654.3 1.123 3.107 3 26938 26954.7 0.010 3.118 4 19154 19313.5 1.317 4.434 5 13860 13851.4 0.005 4.440 6 10062 9943.5 1.411 5.851 7 7249 7145.0 1.513 7.364 8 5250 5139.1 2.394 9.758 9 3682 3699.9 0.086 9.844 10 2700 2666.3 0.426 10.270 11 1937 1923.3 0.097 10.368 12 1345 1388.7 1.378 11.745 13 1003 1003.7 0.001 11.746 14 754 726.1 1.069 12.815 15 502 525.8 1.080 13.895 16 362 381.2 0.962 14.857 17 300 276.5 1.990 16.848 18 196 200.8 0.116 16.964 19 136 146.0 0.683 17.647 20 107 106.2 0.006 17.652 21 300 287.1 0.578 18.231 Chisq= 18.23 for 20 degrees of freedom, p= 0.42779 SUMMARY of craptest p-value for no. of wins: 0.200394 p-value for throws/game: 0.427793 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-07-10_08:31 No. of wins: Observed Expected 97978 98585.9 z-score=-2.719, pvalue=0.00328 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66474 66666.7 0.557 0.557 2 37304 37654.3 3.259 3.816 3 27274 26954.7 3.782 7.598 4 19284 19313.5 0.045 7.643 5 14158 13851.4 6.786 14.428 6 9939 9943.5 0.002 14.430 7 7180 7145.0 0.171 14.602 8 5123 5139.1 0.050 14.652 9 3778 3699.9 1.650 16.302 10 2649 2666.3 0.112 16.414 11 1888 1923.3 0.649 17.063 12 1343 1388.7 1.507 18.570 13 984 1003.7 0.387 18.957 14 744 726.1 0.439 19.396 15 532 525.8 0.072 19.468 16 340 381.2 4.443 23.911 17 267 276.5 0.329 24.240 18 213 200.8 0.737 24.978 19 142 146.0 0.109 25.086 20 113 106.2 0.433 25.520 21 271 287.1 0.904 26.424 Chisq= 26.42 for 20 degrees of freedom, p= 0.84775 SUMMARY of craptest p-value for no. of wins: 0.003277 p-value for throws/game: 0.847746 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0033,0.0061,0.0072,0.0096,0.0098,0.0100,0.0116,0.0119,0.0133,0.0136, 0.0138,0.0196,0.0223,0.0278,0.0297,0.0326,0.0378,0.0449,0.0491,0.0534, 0.0572,0.0602,0.0603,0.0659,0.0660,0.0667,0.0677,0.0682,0.0692,0.0759, 0.0820,0.0832,0.0902,0.0960,0.0974,0.1016,0.1072,0.1129,0.1131,0.1144, 0.1183,0.1205,0.1261,0.1314,0.1399,0.1407,0.1454,0.1578,0.1592,0.1609, 0.1610,0.1761,0.1800,0.1890,0.1914,0.1933,0.1934,0.1940,0.2004,0.2010, 0.2056,0.2085,0.2110,0.2178,0.2178,0.2184,0.2201,0.2263,0.2278,0.2319, 0.2325,0.2345,0.2384,0.2390,0.2408,0.2419,0.2421,0.2464,0.2517,0.2542, 0.2699,0.2798,0.2883,0.2961,0.2986,0.3008,0.3030,0.3069,0.3125,0.3153, 0.3228,0.3267,0.3269,0.3310,0.3456,0.3468,0.3495,0.3574,0.3647,0.3651, 0.3657,0.3747,0.3777,0.3791,0.3852,0.3859,0.3979,0.3980,0.4043,0.4046, 0.4046,0.4069,0.4069,0.4097,0.4181,0.4263,0.4278,0.4291,0.4323,0.4381, 0.4452,0.4523,0.4563,0.4577,0.4591,0.4599,0.4628,0.4658,0.4677,0.4685, 0.4689,0.4713,0.4755,0.4758,0.4795,0.4817,0.4833,0.4890,0.4937,0.4949, 0.4972,0.4997,0.5023,0.5058,0.5106,0.5182,0.5198,0.5207,0.5215,0.5226, 0.5266,0.5266,0.5356,0.5396,0.5396,0.5406,0.5459,0.5513,0.5543,0.5606, 0.5669,0.5757,0.5771,0.5780,0.5804,0.5849,0.5881,0.5881,0.5936,0.5940, 0.5967,0.5989,0.6038,0.6054,0.6077,0.6100,0.6117,0.6139,0.6168,0.6235, 0.6242,0.6343,0.6343,0.6357,0.6385,0.6479,0.6499,0.6524,0.6532,0.6533, 0.6573,0.6575,0.6581,0.6634,0.6641,0.6654,0.6727,0.6802,0.6839,0.7019, 0.7081,0.7120,0.7186,0.7224,0.7236,0.7236,0.7299,0.7321,0.7349,0.7400, 0.7444,0.7508,0.7528,0.7533,0.7544,0.7603,0.7707,0.7743,0.7784,0.7809, 0.7828,0.7967,0.8032,0.8032,0.8092,0.8125,0.8181,0.8224,0.8296,0.8402, 0.8419,0.8477,0.8484,0.8501,0.8549,0.8556,0.8681,0.8761,0.8781,0.8790, 0.8862,0.8912,0.8963,0.9006,0.9039,0.9082,0.9097,0.9121,0.9159,0.9160, 0.9175,0.9216,0.9245,0.9259,0.9301,0.9334,0.9366,0.9380,0.9530,0.9544, 0.9548,0.9608,0.9628,0.9690,0.9730,0.9734,0.9810,0.9851,0.9864, Overall p-value after applying KStest on 269 p-values = 0.196055 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.