RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-02-07_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 15.91 13.3460 0.287264 2 to 25 15.85 24.0858 0.882877 3 to 26 15.48 19.8935 0.720289 4 to 27 15.65 30.9829 0.979932 5 to 28 15.55 18.4291 0.637733 6 to 29 16.03 10.4568 0.116629 7 to 30 15.45 24.1470 0.884505 8 to 31 15.82 8.4731 0.044643 9 to 32 15.51 19.4979 0.699286 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.448361 Tough bday spacings test for dh-ranFile-2017-02-07_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 9 38 67 100 107 70 60 24 17 5 3 (O-E)^2/E 0.0 0.1 0.5 0.1 0.9 0.8 1.2 1.1 0.3 0.4 0.3 Birthday Spacings: Sum(O-E)^2/E= 5.674, p= 0.158 RESULTS OF GCD FOR dh-ranFile-2017-02-07_08:31 Euclid's algorithm: p-value, steps to gcd: 0.340657 p-value, dist. of gcd's: 0.243156 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-02-07_08:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.804 0.424 0.383 0.972 0.631 0.259 0.431 0.552 Bits 8 to 15---> 0.059 0.129 0.780 0.386 0.226 0.947 0.256 0.469 Bits 16 to 23---> 0.126 0.133 0.584 0.233 0.531 0.566 0.295 0.684 Bits 24 to 31---> 0.341 0.428 0.298 0.105 0.319 0.401 0.119 0.059 KS test for the above 32 p values: 0.937 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-02-07_08:31, p-values for 5 runs: 0.0660, 0.0631, 0.3136, 0.3866, 0.3520 Rank test for binary matrices (31x31) for dh-ranFile-2017-02-07_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 194 211.4 1.435 1.435 r= 29 5200 5134.0 0.848 2.283 r= 30 22960 23103.0 0.886 3.169 r= 31 11646 11551.5 0.773 3.942 chi-square = 3.942 with df = 3; p-value = 0.732 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2017-02-07_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 229 211.4 1.462 1.462 r= 30 5078 5134.0 0.611 2.073 r= 31 23141 23103.0 0.062 2.136 r= 32 11552 11551.5 0.000 2.136 chi-square = 2.136 with df = 3; p-value = 0.455 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2017-02-07_08:31 b-rank test for bits 1 to 8, p=0.58201 b-rank test for bits 2 to 9, p=0.53412 b-rank test for bits 3 to 10, p=0.87568 b-rank test for bits 4 to 11, p=0.63771 b-rank test for bits 5 to 12, p=0.68180 b-rank test for bits 6 to 13, p=0.60158 b-rank test for bits 7 to 14, p=0.85600 b-rank test for bits 8 to 15, p=0.93425 b-rank test for bits 9 to 16, p=0.69029 b-rank test for bits 10 to 17, p=0.82096 b-rank test for bits 11 to 18, p=0.89019 b-rank test for bits 12 to 19, p=0.41753 b-rank test for bits 13 to 20, p=0.02402 b-rank test for bits 14 to 21, p=0.52840 b-rank test for bits 15 to 22, p=0.20705 b-rank test for bits 16 to 23, p=0.20852 b-rank test for bits 17 to 24, p=0.93423 b-rank test for bits 18 to 25, p=0.49323 b-rank test for bits 19 to 26, p=0.37679 b-rank test for bits 20 to 27, p=0.66856 b-rank test for bits 21 to 28, p=0.66970 b-rank test for bits 22 to 29, p=0.08781 b-rank test for bits 23 to 30, p=0.63410 b-rank test for bits 24 to 31, p=0.27530 b-rank test for bits 25 to 32, p=0.40953 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 = 0.375158 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-02-07_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 141714 -0.46 0.324059 2 141493 -0.97 0.165343 3 141905 -0.01 0.495964 4 142108 0.46 0.678741 5 142331 0.99 0.837740 6 141688 -0.52 0.302534 7 141996 0.20 0.580237 8 141287 -1.45 0.072967 9 142332 0.99 0.838313 10 141640 -0.63 0.264584 11 141725 -0.43 0.333351 12 142260 0.82 0.793699 13 141525 -0.90 0.184602 14 142779 2.03 0.978920 15 141485 -0.99 0.160739 16 142335 0.99 0.840024 17 141379 -1.24 0.107656 18 142224 0.74 0.768894 19 141374 -1.25 0.105509 20 141463 -1.04 0.148514 ---------------------------------------------------------------- OPSO test for dh-ranFile-2017-02-07_08:31 Bits used No. missing words z-score p-value 23 to 32 142084 0.6023 0.726516 22 to 31 142286 1.2989 0.903004 21 to 30 141456 -1.5632 0.059002 20 to 29 141734 -0.6046 0.272727 19 to 28 141328 -2.0046 0.022504 18 to 27 142518 2.0989 0.982085 17 to 26 142190 0.9678 0.833435 16 to 25 141641 -0.9253 0.177411 15 to 24 141698 -0.7287 0.233085 14 to 23 141535 -1.2908 0.098388 13 to 22 142331 1.4540 0.927032 12 to 21 142132 0.7678 0.778705 11 to 20 142246 1.1609 0.877165 10 to 19 142244 1.1540 0.875757 9 to 18 142289 1.3092 0.904768 8 to 17 142196 0.9885 0.838550 7 to 16 142061 0.5230 0.699513 6 to 15 141719 -0.6563 0.255812 5 to 14 141912 0.0092 0.503673 4 to 13 142023 0.3920 0.652458 3 to 12 141724 -0.6391 0.261389 2 to 11 142053 0.4954 0.689846 1 to 10 141613 -1.0218 0.153431 ----------------------------------------------------------------- OQSO test for dh-ranFile-2017-02-07_08:31 Bits used No. missing words z-score p-value 28 to 32 141655 -0.8621 0.194306 27 to 31 141853 -0.1909 0.424283 26 to 30 141306 -2.0452 0.020418 25 to 29 142029 0.4057 0.657504 24 to 28 142096 0.6328 0.736561 23 to 27 142097 0.6362 0.737667 22 to 26 142037 0.4328 0.667413 21 to 25 142271 1.2260 0.889901 20 to 24 142010 0.3413 0.633544 19 to 23 141249 -2.2384 0.012597 18 to 22 141846 -0.2147 0.415009 17 to 21 142045 0.4599 0.677205 16 to 20 142306 1.3446 0.910630 15 to 19 141920 0.0362 0.514426 14 to 18 141640 -0.9130 0.180626 13 to 17 141784 -0.4248 0.335474 12 to 16 141966 0.1921 0.576169 11 to 15 141879 -0.1028 0.459056 10 to 14 141922 0.0429 0.517129 9 to 13 141926 0.0565 0.522532 8 to 12 141870 -0.1333 0.446969 7 to 11 142022 0.3819 0.648744 6 to 10 141875 -0.1164 0.453679 5 to 9 142407 1.6870 0.954200 4 to 8 142119 0.7107 0.761379 3 to 7 142077 0.5684 0.715109 2 to 6 141816 -0.3164 0.375860 1 to 5 141527 -1.2960 0.097482 ----------------------------------------------------------------- DNA test for dh-ranFile-2017-02-07_08:31 Bits used No. missing words z-score p-value 31 to 32 141984 0.2203 0.587168 30 to 31 141485 -1.2517 0.105338 29 to 30 141283 -1.8476 0.032331 28 to 29 141809 -0.2960 0.383631 27 to 28 141738 -0.5054 0.306640 26 to 27 141796 -0.3343 0.369074 25 to 26 142387 1.4091 0.920591 24 to 25 142483 1.6922 0.954700 23 to 24 142009 0.2940 0.615626 22 to 23 142262 1.0403 0.850905 21 to 22 141569 -1.0039 0.157708 20 to 21 142054 0.4268 0.665221 19 to 20 142036 0.3737 0.645671 18 to 19 142293 1.1318 0.871134 17 to 18 141937 0.0816 0.532527 16 to 17 141805 -0.3078 0.379133 15 to 16 141999 0.2645 0.604308 14 to 15 141763 -0.4317 0.332997 13 to 14 141902 -0.0216 0.491375 12 to 13 142562 1.9253 0.972903 11 to 12 142364 1.3412 0.910074 10 to 11 142162 0.7453 0.771967 9 to 10 142017 0.3176 0.624610 8 to 9 142093 0.5418 0.706022 7 to 8 142003 0.2763 0.608846 6 to 7 141909 -0.0010 0.499612 5 to 6 141948 0.1141 0.545409 4 to 5 141183 -2.1426 0.016074 3 to 4 142021 0.3294 0.629077 2 to 3 141595 -0.9272 0.176904 1 to 2 141898 -0.0334 0.486669 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2017-02-07_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2524.59 0.348 0.635993 Test results for specific bytes for dh-ranFile-2017-02-07_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2519.32 0.273 0.607678 2 to 9 2385.43 -1.620 0.052593 3 to 10 2463.15 -0.521 0.301132 4 to 11 2394.13 -1.497 0.067168 5 to 12 2535.20 0.498 0.690686 6 to 13 2481.16 -0.266 0.394933 7 to 14 2482.60 -0.246 0.402816 8 to 15 2415.78 -1.191 0.116830 9 to 16 2545.35 0.641 0.739339 10 to 17 2449.85 -0.709 0.239105 11 to 18 2506.21 0.088 0.534964 12 to 19 2501.63 0.023 0.509212 13 to 20 2511.05 0.156 0.562113 14 to 21 2471.85 -0.398 0.345280 15 to 22 2549.49 0.700 0.758012 16 to 23 2307.56 -2.722 0.003249 17 to 24 2523.48 0.332 0.630054 18 to 25 2528.13 0.398 0.654601 19 to 26 2433.94 -0.934 0.175094 20 to 27 2419.96 -1.132 0.128829 21 to 28 2378.98 -1.711 0.043499 22 to 29 2566.06 0.934 0.824915 23 to 30 2585.09 1.203 0.885593 24 to 31 2556.07 0.793 0.786084 25 to 32 2495.99 -0.057 0.477393 CDPARK for dh-ranFile-2017-02-07_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 3536 0.5936 0.723613 3528 0.2283 0.590298 3552 1.3242 0.907282 3552 1.3242 0.907282 3517 -0.2740 0.392053 3580 2.6027 0.995376 3510 -0.5936 0.276387 3492 -1.4155 0.078457 3517 -0.2740 0.392053 3495 -1.2785 0.100530 Square side=100, avg. no. parked=3527.90 sample std.=26.21 p-value of the KSTEST for those 10 p-values: 0.682718 Results for the MINIMUM DISTANCE test for dh-ranFile-2017-02-07_08:31 0.3579,0.8504,0.1346,0.0596,0.4802,0.4109,0.4075,0.2869,0.3687,0.8849, The KS test for those 10 p-values: 0.493134 The 3DSPHERES test for dh-ranFile-2017-02-07_08:31 sample no r^3 equiv. uni. 1 32.024 0.656119 2 2.809 0.089382 3 78.345 0.926576 4 23.437 0.542153 5 22.652 0.530017 6 20.915 0.502003 7 4.155 0.129346 8 9.535 0.272282 9 48.917 0.804180 10 25.184 0.568065 11 3.007 0.095363 12 5.092 0.156110 13 14.772 0.388842 14 0.086 0.002863 15 38.217 0.720260 16 5.918 0.179018 17 5.515 0.167918 18 8.832 0.255029 19 1.888 0.060996 20 4.621 0.142760 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.039700 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-02-07_08:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -1.2 -0.6 0.9 -0.4 -0.1 0.0 0.4 0.3 1.2 0.1 0.6 0.3 -0.5 -0.8 -0.0 -0.9 0.5 -0.2 0.8 -0.8 -1.2 1.1 -1.0 1.0 1.1 -0.5 -0.2 0.3 1.0 -1.4 0.4 -0.1 -0.2 0.6 0.2 0.0 -1.7 0.9 1.5 1.6 -1.0 -1.1 Chi-square with 42 degrees of freedom:28.601015 z-score=-1.461949, p-value=0.057065 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2017-02-07_08:31 Test no p-value 1 0.185820 2 0.113983 3 0.118624 4 0.963023 5 0.344510 6 0.336086 7 0.417721 8 0.017652 9 0.561612 10 0.100468 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.053941 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-02-07_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 66775 0.18 66639 0.01 3 25000.00 24764 2.23 25065 0.17 4 6666.67 6773 1.70 6628 0.22 5 1388.89 1395 0.03 1413 0.42 6 238.10 250 0.60 231 0.21 7 34.72 33 0.09 18 8.05 8 4.96 9 3.29 5 0.00 p=0.76897 p=0.83125 Number of rngs required: 688098, p-value: 0.363 RESULTS OF CRAPS TEST for dh-ranFile-2017-02-07_08:31 No. of wins: Observed Expected 98411 98585.9 z-score=-0.782, pvalue=0.21709 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66669 66666.7 0.000 0.000 2 37824 37654.3 0.765 0.765 3 26933 26954.7 0.018 0.782 4 19344 19313.5 0.048 0.831 5 13682 13851.4 2.072 2.903 6 9804 9943.5 1.958 4.861 7 7177 7145.0 0.143 5.004 8 5242 5139.1 2.061 7.066 9 3668 3699.9 0.274 7.340 10 2633 2666.3 0.416 7.756 11 1868 1923.3 1.592 9.348 12 1447 1388.7 2.444 11.792 13 1033 1003.7 0.854 12.646 14 711 726.1 0.316 12.962 15 546 525.8 0.773 13.735 16 373 381.2 0.174 13.909 17 284 276.5 0.201 14.111 18 212 200.8 0.621 14.732 19 152 146.0 0.248 14.980 20 108 106.2 0.030 15.010 21 290 287.1 0.029 15.039 Chisq= 15.04 for 20 degrees of freedom, p= 0.22581 SUMMARY of craptest p-value for no. of wins: 0.217087 p-value for throws/game: 0.225809 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2017-02-07_08:31 No. of wins: Observed Expected 98850 98585.9 z-score= 1.181, pvalue=0.88128 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66617 66666.7 0.037 0.037 2 37831 37654.3 0.829 0.866 3 27160 26954.7 1.563 2.429 4 18982 19313.5 5.689 8.118 5 13906 13851.4 0.215 8.333 6 9994 9943.5 0.256 8.589 7 7097 7145.0 0.323 8.912 8 5123 5139.1 0.050 8.962 9 3650 3699.9 0.672 9.634 10 2659 2666.3 0.020 9.654 11 1945 1923.3 0.244 9.898 12 1363 1388.7 0.477 10.375 13 996 1003.7 0.059 10.435 14 723 726.1 0.014 10.448 15 520 525.8 0.065 10.513 16 377 381.2 0.045 10.558 17 289 276.5 0.561 11.120 18 199 200.8 0.017 11.136 19 148 146.0 0.028 11.164 20 101 106.2 0.256 11.420 21 320 287.1 3.767 15.187 Chisq= 15.19 for 20 degrees of freedom, p= 0.23439 SUMMARY of craptest p-value for no. of wins: 0.881277 p-value for throws/game: 0.234386 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0029,0.0032,0.0126,0.0161,0.0177,0.0204,0.0225,0.0240,0.0323,0.0397, 0.0435,0.0446,0.0526,0.0539,0.0571,0.0586,0.0588,0.0590,0.0596,0.0610, 0.0631,0.0660,0.0672,0.0730,0.0785,0.0878,0.0894,0.0954,0.0975,0.0984, 0.1005,0.1005,0.1053,0.1053,0.1055,0.1077,0.1140,0.1166,0.1168,0.1186, 0.1190,0.1262,0.1288,0.1293,0.1293,0.1330,0.1346,0.1428,0.1485,0.1534, 0.1561,0.1577,0.1581,0.1607,0.1653,0.1679,0.1751,0.1769,0.1774,0.1790, 0.1806,0.1846,0.1858,0.1943,0.2070,0.2085,0.2171,0.2258,0.2263,0.2329, 0.2331,0.2344,0.2391,0.2432,0.2550,0.2558,0.2561,0.2593,0.2614,0.2646, 0.2723,0.2727,0.2753,0.2764,0.2869,0.2873,0.2953,0.2983,0.3011,0.3025, 0.3066,0.3136,0.3194,0.3241,0.3330,0.3334,0.3355,0.3361,0.3407,0.3413, 0.3445,0.3453,0.3520,0.3579,0.3627,0.3687,0.3691,0.3752,0.3759,0.3768, 0.3791,0.3833,0.3836,0.3857,0.3866,0.3888,0.3921,0.3921,0.3949,0.4012, 0.4028,0.4075,0.4095,0.4109,0.4150,0.4175,0.4177,0.4238,0.4243,0.4283, 0.4305,0.4470,0.4484,0.4537,0.4553,0.4591,0.4694,0.4774,0.4802,0.4867, 0.4914,0.4931,0.4932,0.4960,0.4996,0.5020,0.5037,0.5092,0.5144,0.5171, 0.5225,0.5284,0.5300,0.5308,0.5325,0.5341,0.5350,0.5422,0.5454,0.5517, 0.5616,0.5621,0.5659,0.5681,0.5762,0.5802,0.5820,0.5836,0.5872,0.5903, 0.6016,0.6043,0.6077,0.6088,0.6156,0.6246,0.6291,0.6301,0.6312,0.6335, 0.6341,0.6360,0.6377,0.6377,0.6457,0.6487,0.6525,0.6546,0.6561,0.6575, 0.6652,0.6674,0.6686,0.6697,0.6772,0.6787,0.6818,0.6827,0.6837,0.6898, 0.6903,0.6907,0.6993,0.6995,0.7060,0.7151,0.7203,0.7203,0.7236,0.7265, 0.7322,0.7366,0.7377,0.7393,0.7580,0.7614,0.7689,0.7690,0.7720,0.7787, 0.7796,0.7861,0.7937,0.8035,0.8042,0.8210,0.8249,0.8312,0.8334,0.8377, 0.8383,0.8386,0.8400,0.8504,0.8509,0.8560,0.8711,0.8757,0.8758,0.8772, 0.8813,0.8829,0.8845,0.8849,0.8856,0.8899,0.8902,0.9030,0.9048,0.9073, 0.9073,0.9101,0.9106,0.9206,0.9266,0.9270,0.9342,0.9343,0.9373,0.9467, 0.9542,0.9547,0.9630,0.9722,0.9729,0.9789,0.9799,0.9821,0.9954, Overall p-value after applying KStest on 269 p-values = 0.148165 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.