RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-12-15_00:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.97 16.0699 0.481115 2 to 25 15.54 19.1479 0.679891 3 to 26 15.69 28.8300 0.963874 4 to 27 15.78 11.6014 0.176350 5 to 28 15.80 16.3260 0.499146 6 to 29 15.57 11.2143 0.154791 7 to 30 15.72 21.2269 0.783693 8 to 31 15.61 27.3383 0.946710 9 to 32 15.79 18.2112 0.624363 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.572428 Tough bday spacings test for dh-ranFile-2015-12-15_00:31: 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 41 79 101 100 64 55 27 16 5 2 (O-E)^2/E 0.1 0.5 0.4 0.1 0.1 2.6 0.2 0.3 0.1 0.4 1.0 Birthday Spacings: Sum(O-E)^2/E= 5.724, p= 0.162 RESULTS OF GCD FOR dh-ranFile-2015-12-15_00:31 Euclid's algorithm: p-value, steps to gcd: 0.775397 p-value, dist. of gcd's: 0.738831 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-12-15_00:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.719 0.156 0.295 0.302 0.984 0.853 0.263 0.861 Bits 8 to 15---> 0.079 0.786 0.420 0.234 0.426 0.772 0.355 0.499 Bits 16 to 23---> 0.931 0.593 0.244 0.779 0.112 0.591 0.560 0.734 Bits 24 to 31---> 0.126 0.323 0.477 0.386 0.596 0.640 0.414 0.599 KS test for the above 32 p values: 0.273 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-12-15_00:31, p-values for 5 runs: 0.5292, 0.1243, 0.2290, 0.4056, 0.5692 Rank test for binary matrices (31x31) for dh-ranFile-2015-12-15_00:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 202 211.4 0.420 0.420 r= 29 5032 5134.0 2.027 2.446 r= 30 22990 23103.0 0.553 3.000 r= 31 11776 11551.5 4.362 7.362 chi-square = 7.362 with df = 3; p-value = 0.939 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-12-15_00:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 206 211.4 0.139 0.139 r= 30 5097 5134.0 0.267 0.406 r= 31 23098 23103.0 0.001 0.407 r= 32 11599 11551.5 0.195 0.602 chi-square = 0.602 with df = 3; p-value = 0.104 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-12-15_00:31 b-rank test for bits 1 to 8, p=0.61955 b-rank test for bits 2 to 9, p=0.79308 b-rank test for bits 3 to 10, p=0.34787 b-rank test for bits 4 to 11, p=0.97995 b-rank test for bits 5 to 12, p=0.24707 b-rank test for bits 6 to 13, p=0.06654 b-rank test for bits 7 to 14, p=0.16238 b-rank test for bits 8 to 15, p=0.92495 b-rank test for bits 9 to 16, p=0.75545 b-rank test for bits 10 to 17, p=0.66520 b-rank test for bits 11 to 18, p=0.05608 b-rank test for bits 12 to 19, p=0.22148 b-rank test for bits 13 to 20, p=0.08690 b-rank test for bits 14 to 21, p=0.09620 b-rank test for bits 15 to 22, p=0.68131 b-rank test for bits 16 to 23, p=0.25408 b-rank test for bits 17 to 24, p=0.46105 b-rank test for bits 18 to 25, p=0.04661 b-rank test for bits 19 to 26, p=0.68574 b-rank test for bits 20 to 27, p=0.06431 b-rank test for bits 21 to 28, p=0.49841 b-rank test for bits 22 to 29, p=0.51505 b-rank test for bits 23 to 30, p=0.78991 b-rank test for bits 24 to 31, p=0.37790 b-rank test for bits 25 to 32, p=0.25079 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 = 0.292041 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-12-15_00:31 (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 141214 -1.62 0.052124 2 141563 -0.81 0.209205 3 141192 -1.68 0.046869 4 141726 -0.43 0.334201 5 142293 0.90 0.814987 6 141975 0.15 0.560972 7 140871 -2.43 0.007633 8 140944 -2.26 0.012053 9 141786 -0.29 0.386614 10 142646 1.72 0.957392 11 141631 -0.65 0.257748 12 142071 0.38 0.647186 13 141781 -0.30 0.382151 14 142251 0.80 0.787650 15 141464 -1.04 0.149056 16 141873 -0.08 0.466177 17 141960 0.12 0.547120 18 142218 0.72 0.764604 19 142281 0.87 0.807409 20 141282 -1.47 0.071362 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-12-15_00:31 Bits used No. missing words z-score p-value 23 to 32 141826 -0.2873 0.386924 22 to 31 141805 -0.3598 0.359514 21 to 30 142370 1.5885 0.943915 20 to 29 141985 0.2609 0.602927 19 to 28 141571 -1.1667 0.121675 18 to 27 142012 0.3540 0.638344 17 to 26 142055 0.5023 0.692275 16 to 25 141830 -0.2736 0.392215 15 to 24 142101 0.6609 0.745672 14 to 23 142138 0.7885 0.784803 13 to 22 142339 1.4816 0.930779 12 to 21 141326 -2.0115 0.022137 11 to 20 141700 -0.7218 0.235200 10 to 19 141704 -0.7080 0.239462 9 to 18 141997 0.3023 0.618792 8 to 17 142050 0.4851 0.686186 7 to 16 142016 0.3678 0.643499 6 to 15 141690 -0.7563 0.224732 5 to 14 142280 1.2782 0.899406 4 to 13 142241 1.1437 0.873624 3 to 12 141848 -0.2115 0.416255 2 to 11 141925 0.0540 0.521546 1 to 10 141701 -0.7184 0.236262 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-12-15_00:31 Bits used No. missing words z-score p-value 28 to 32 141483 -1.4452 0.074203 27 to 31 141652 -0.8723 0.191521 26 to 30 142407 1.6870 0.954200 25 to 29 142003 0.3175 0.624578 24 to 28 141876 -0.1130 0.455022 23 to 27 142386 1.6158 0.946935 22 to 26 141970 0.2057 0.581472 21 to 25 141767 -0.4825 0.314734 20 to 24 142090 0.6124 0.729877 19 to 23 141611 -1.0113 0.155939 18 to 22 141616 -0.9943 0.160029 17 to 21 141530 -1.2859 0.099245 16 to 20 141867 -0.1435 0.442951 15 to 19 141759 -0.5096 0.305168 14 to 18 141790 -0.4045 0.342919 13 to 17 141754 -0.5265 0.299256 12 to 16 142430 1.7650 0.961217 11 to 15 141618 -0.9876 0.161684 10 to 14 141946 0.1243 0.549463 9 to 13 142092 0.6192 0.732114 8 to 12 142103 0.6565 0.744252 7 to 11 141927 0.0599 0.523882 6 to 10 141881 -0.0960 0.461747 5 to 9 141786 -0.4181 0.337949 4 to 8 141524 -1.3062 0.095742 3 to 7 141635 -0.9299 0.176203 2 to 6 142358 1.5209 0.935859 1 to 5 142247 1.1446 0.873822 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-12-15_00:31 Bits used No. missing words z-score p-value 31 to 32 141204 -2.0806 0.018734 30 to 31 141944 0.1023 0.540729 29 to 30 141951 0.1229 0.548915 28 to 29 142139 0.6775 0.750953 27 to 28 141633 -0.8151 0.207498 26 to 27 141980 0.2085 0.582568 25 to 26 142645 2.1701 0.985001 24 to 25 141726 -0.5408 0.294324 23 to 24 141892 -0.0511 0.479615 22 to 23 142335 1.2557 0.895381 21 to 22 142001 0.2704 0.606579 20 to 21 141774 -0.3992 0.344872 19 to 20 142212 0.8928 0.814026 18 to 19 142037 0.3766 0.646767 17 to 18 142139 0.6775 0.750953 16 to 17 142082 0.5094 0.694747 15 to 16 141804 -0.3107 0.378011 14 to 15 141767 -0.4199 0.337297 13 to 14 142518 1.7955 0.963712 12 to 13 141763 -0.4317 0.332997 11 to 12 141969 0.1760 0.569860 10 to 11 141374 -1.5791 0.057151 9 to 10 141171 -2.1780 0.014704 8 to 9 141737 -0.5083 0.305605 7 to 8 141962 0.1554 0.561735 6 to 7 141202 -2.0865 0.018466 5 to 6 141540 -1.0895 0.137974 4 to 5 142327 1.2321 0.891038 3 to 4 142238 0.9695 0.833859 2 to 3 141068 -2.4818 0.006536 1 to 2 141771 -0.4081 0.341617 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-12-15_00:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2380.17 -1.695 0.045066 Test results for specific bytes for dh-ranFile-2015-12-15_00:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2443.61 -0.797 0.212598 2 to 9 2447.17 -0.747 0.227486 3 to 10 2511.20 0.158 0.562927 4 to 11 2488.29 -0.166 0.434246 5 to 12 2481.71 -0.259 0.397928 6 to 13 2518.81 0.266 0.604881 7 to 14 2570.41 0.996 0.840308 8 to 15 2537.49 0.530 0.702029 9 to 16 2434.34 -0.929 0.176564 10 to 17 2442.37 -0.815 0.207521 11 to 18 2552.78 0.746 0.772296 12 to 19 2535.94 0.508 0.694360 13 to 20 2497.93 -0.029 0.488333 14 to 21 2464.01 -0.509 0.305397 15 to 22 2581.18 1.148 0.874541 16 to 23 2583.00 1.174 0.879761 17 to 24 2675.59 2.483 0.993491 18 to 25 2395.24 -1.481 0.069239 19 to 26 2490.05 -0.141 0.444065 20 to 27 2525.40 0.359 0.640263 21 to 28 2526.90 0.380 0.648202 22 to 29 2404.93 -1.345 0.089393 23 to 30 2513.72 0.194 0.576950 24 to 31 2530.58 0.432 0.667311 25 to 32 2478.63 -0.302 0.381252 CDPARK for dh-ranFile-2015-12-15_00:31: 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 3508 -0.6849 0.246694 3526 0.1370 0.554479 3493 -1.3699 0.085365 3497 -1.1872 0.117571 3516 -0.3196 0.374623 3514 -0.4110 0.340551 3483 -1.8265 0.033889 3497 -1.1872 0.117571 3526 0.1370 0.554479 3486 -1.6895 0.045562 Square side=100, avg. no. parked=3504.60 sample std.=14.86 p-value of the KSTEST for those 10 p-values: 0.007456 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-12-15_00:31 0.4889,0.1088,0.5412,0.7545,0.9492,0.4980,0.1082,0.7709,0.4859,0.6093, The KS test for those 10 p-values: 0.743026 The 3DSPHERES test for dh-ranFile-2015-12-15_00:31 sample no r^3 equiv. uni. 1 15.506 0.403612 2 0.224 0.007447 3 7.464 0.220266 4 26.898 0.592048 5 10.423 0.293512 6 17.609 0.443991 7 9.574 0.273215 8 31.800 0.653542 9 7.748 0.227614 10 10.186 0.287894 11 33.701 0.674816 12 61.472 0.871143 13 27.265 0.597002 14 12.690 0.344912 15 7.227 0.214082 16 10.882 0.304235 17 11.087 0.308961 18 20.313 0.491918 19 7.364 0.217656 20 6.861 0.204421 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.037284 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-12-15_00:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 -1.6 1.1 0.8 -1.6 0.8 -0.8 1.2 1.8 -0.3 -1.4 -1.1 -1.5 -0.5 0.1 0.9 0.5 1.1 -0.1 -1.2 0.2 0.5 0.8 -0.2 0.0 0.7 -0.1 -0.3 -0.6 -0.5 0.2 0.0 0.1 0.4 1.5 -0.5 1.2 -1.7 -1.2 -0.1 0.1 1.0 -0.1 Chi-square with 42 degrees of freedom:34.079944 z-score=-0.864149, p-value=0.197294 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-12-15_00:31 Test no p-value 1 0.005061 2 0.034821 3 0.124512 4 0.135136 5 0.238685 6 0.928384 7 0.651532 8 0.394092 9 0.175830 10 0.375681 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.037423 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-12-15_00:31: (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 66571 0.14 66725 0.05 3 25000.00 25050 0.10 25018 0.01 4 6666.67 6726 0.53 6564 1.58 5 1388.89 1375 0.14 1443 2.11 6 238.10 238 0.00 215 2.24 7 34.72 36 0.05 30 0.64 8 4.96 3 0.77 4 0.19 p=0.05690 p=0.66228 Number of rngs required: 689519, p-value: 0.903 RESULTS OF CRAPS TEST for dh-ranFile-2015-12-15_00:31 No. of wins: Observed Expected 98748 98585.9 z-score= 0.725, pvalue=0.76583 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66696 66666.7 0.013 0.013 2 37604 37654.3 0.067 0.080 3 26759 26954.7 1.421 1.501 4 19532 19313.5 2.473 3.974 5 13870 13851.4 0.025 3.999 6 9921 9943.5 0.051 4.050 7 7212 7145.0 0.628 4.678 8 5062 5139.1 1.156 5.834 9 3689 3699.9 0.032 5.866 10 2712 2666.3 0.783 6.649 11 1884 1923.3 0.804 7.453 12 1425 1388.7 0.947 8.400 13 1007 1003.7 0.011 8.411 14 723 726.1 0.014 8.425 15 562 525.8 2.487 10.912 16 346 381.2 3.242 14.153 17 271 276.5 0.111 14.264 18 208 200.8 0.256 14.520 19 146 146.0 0.000 14.520 20 102 106.2 0.167 14.688 21 269 287.1 1.143 15.830 Chisq= 15.83 for 20 degrees of freedom, p= 0.27291 SUMMARY of craptest p-value for no. of wins: 0.765833 p-value for throws/game: 0.272915 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-12-15_00:31 No. of wins: Observed Expected 98448 98585.9 z-score=-0.617, pvalue=0.26875 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66741 66666.7 0.083 0.083 2 37738 37654.3 0.186 0.269 3 26685 26954.7 2.699 2.968 4 19287 19313.5 0.036 3.004 5 13960 13851.4 0.851 3.855 6 9957 9943.5 0.018 3.874 7 7108 7145.0 0.192 4.066 8 5234 5139.1 1.753 5.819 9 3680 3699.9 0.107 5.926 10 2634 2666.3 0.391 6.317 11 1921 1923.3 0.003 6.320 12 1391 1388.7 0.004 6.323 13 1019 1003.7 0.233 6.556 14 758 726.1 1.398 7.954 15 521 525.8 0.044 7.998 16 358 381.2 1.406 9.405 17 269 276.5 0.206 9.610 18 194 200.8 0.232 9.842 19 144 146.0 0.027 9.869 20 111 106.2 0.216 10.085 21 290 287.1 0.029 10.114 Chisq= 10.11 for 20 degrees of freedom, p= 0.03394 SUMMARY of craptest p-value for no. of wins: 0.268755 p-value for throws/game: 0.033941 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0051,0.0065,0.0074,0.0075,0.0076,0.0121,0.0147,0.0185,0.0187,0.0221, 0.0339,0.0339,0.0348,0.0373,0.0374,0.0451,0.0456,0.0466,0.0469,0.0521, 0.0561,0.0569,0.0572,0.0643,0.0665,0.0692,0.0714,0.0742,0.0791,0.0854, 0.0869,0.0894,0.0957,0.0962,0.0992,0.1040,0.1082,0.1088,0.1122,0.1176, 0.1176,0.1217,0.1243,0.1245,0.1260,0.1351,0.1380,0.1491,0.1548,0.1556, 0.1559,0.1600,0.1617,0.1621,0.1624,0.1758,0.1762,0.1764,0.1766,0.1915, 0.1973,0.2044,0.2075,0.2075,0.2092,0.2126,0.2141,0.2177,0.2203,0.2215, 0.2247,0.2275,0.2276,0.2290,0.2336,0.2352,0.2363,0.2387,0.2395,0.2437, 0.2467,0.2471,0.2508,0.2541,0.2577,0.2628,0.2688,0.2729,0.2732,0.2732, 0.2879,0.2920,0.2935,0.2943,0.2953,0.2993,0.3022,0.3042,0.3052,0.3054, 0.3056,0.3090,0.3147,0.3227,0.3330,0.3342,0.3373,0.3379,0.3406,0.3416, 0.3429,0.3449,0.3449,0.3479,0.3545,0.3595,0.3746,0.3757,0.3779,0.3780, 0.3813,0.3822,0.3864,0.3866,0.3869,0.3922,0.3941,0.3979,0.4036,0.4056, 0.4143,0.4163,0.4201,0.4256,0.4342,0.4430,0.4440,0.4441,0.4550,0.4610, 0.4617,0.4662,0.4768,0.4796,0.4811,0.4859,0.4883,0.4889,0.4919,0.4980, 0.4984,0.4989,0.4991,0.5151,0.5215,0.5239,0.5292,0.5407,0.5412,0.5471, 0.5489,0.5495,0.5545,0.5545,0.5602,0.5610,0.5617,0.5629,0.5692,0.5699, 0.5724,0.5770,0.5815,0.5826,0.5908,0.5920,0.5934,0.5962,0.5970,0.5988, 0.6029,0.6049,0.6066,0.6093,0.6188,0.6196,0.6244,0.6246,0.6383,0.6397, 0.6403,0.6435,0.6468,0.6472,0.6482,0.6515,0.6535,0.6623,0.6652,0.6673, 0.6748,0.6799,0.6813,0.6857,0.6862,0.6923,0.6944,0.6947,0.7020,0.7193, 0.7299,0.7321,0.7343,0.7388,0.7430,0.7443,0.7457,0.7510,0.7510,0.7545, 0.7555,0.7646,0.7658,0.7709,0.7717,0.7723,0.7754,0.7789,0.7837,0.7848, 0.7863,0.7877,0.7899,0.7931,0.8074,0.8140,0.8150,0.8339,0.8403,0.8527, 0.8614,0.8711,0.8736,0.8738,0.8745,0.8798,0.8910,0.8954,0.8994,0.9030, 0.9249,0.9284,0.9308,0.9310,0.9359,0.9388,0.9439,0.9467,0.9469,0.9492, 0.9542,0.9574,0.9612,0.9637,0.9639,0.9799,0.9838,0.9850,0.9935, Overall p-value after applying KStest on 269 p-values = 0.011190 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.