RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-07-31_06:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.71 15.5153 0.441585 2 to 25 15.70 20.8836 0.768458 3 to 26 15.98 21.1036 0.778311 4 to 27 15.44 37.8506 0.997423 5 to 28 15.51 22.1930 0.822588 6 to 29 15.63 20.3825 0.744865 7 to 30 15.58 14.8358 0.392695 8 to 31 15.85 12.5888 0.236751 9 to 32 16.14 29.0206 0.965664 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.062904 Tough bday spacings test for dh-ranFile-2016-07-31_06:31: 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 31 77 93 107 93 46 29 12 4 4 (O-E)^2/E 2.9 0.9 0.2 0.2 0.9 2.8 0.7 0.0 0.6 1.0 0.0 Birthday Spacings: Sum(O-E)^2/E= 10.226, p= 0.579 RESULTS OF GCD FOR dh-ranFile-2016-07-31_06:31 Euclid's algorithm: p-value, steps to gcd: 0.853832 p-value, dist. of gcd's: 0.361510 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-07-31_06:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.945 0.211 0.538 0.460 0.209 0.094 0.597 0.982 Bits 8 to 15---> 0.042 0.090 0.674 0.524 0.428 0.687 0.746 0.753 Bits 16 to 23---> 0.164 0.578 0.401 0.288 0.713 0.424 0.506 0.582 Bits 24 to 31---> 0.174 0.518 0.970 0.097 0.844 0.717 0.649 0.521 KS test for the above 32 p values: 0.244 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-07-31_06:31, p-values for 5 runs: 0.9569, 0.1992, 0.7902, 0.3585, 0.8973 Rank test for binary matrices (31x31) for dh-ranFile-2016-07-31_06:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 233 211.4 2.203 2.203 r= 29 5053 5134.0 1.278 3.481 r= 30 23218 23103.0 0.572 4.053 r= 31 11496 11551.5 0.267 4.320 chi-square = 4.320 with df = 3; p-value = 0.771 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-07-31_06:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 194 211.4 1.435 1.435 r= 30 5159 5134.0 0.122 1.557 r= 31 23139 23103.0 0.056 1.613 r= 32 11508 11551.5 0.164 1.777 chi-square = 1.777 with df = 3; p-value = 0.380 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-07-31_06:31 b-rank test for bits 1 to 8, p=0.25793 b-rank test for bits 2 to 9, p=0.44663 b-rank test for bits 3 to 10, p=0.18760 b-rank test for bits 4 to 11, p=0.66550 b-rank test for bits 5 to 12, p=0.34485 b-rank test for bits 6 to 13, p=0.25561 b-rank test for bits 7 to 14, p=0.11555 b-rank test for bits 8 to 15, p=0.95888 b-rank test for bits 9 to 16, p=0.70637 b-rank test for bits 10 to 17, p=0.38699 b-rank test for bits 11 to 18, p=0.66258 b-rank test for bits 12 to 19, p=0.01205 b-rank test for bits 13 to 20, p=0.05230 b-rank test for bits 14 to 21, p=0.00079 b-rank test for bits 15 to 22, p=0.45129 b-rank test for bits 16 to 23, p=0.63694 b-rank test for bits 17 to 24, p=0.22854 b-rank test for bits 18 to 25, p=0.07179 b-rank test for bits 19 to 26, p=0.17283 b-rank test for bits 20 to 27, p=0.31873 b-rank test for bits 21 to 28, p=0.26235 b-rank test for bits 22 to 29, p=0.54395 b-rank test for bits 23 to 30, p=0.61593 b-rank test for bits 24 to 31, p=0.81723 b-rank test for bits 25 to 32, p=0.45354 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 = 0.067734 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-07-31_06:31 (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 141948 0.09 0.535996 2 142324 0.97 0.833691 3 142421 1.20 0.884052 4 141681 -0.53 0.296850 5 141796 -0.26 0.395586 6 141901 -0.02 0.492236 7 141559 -0.82 0.206528 8 142031 0.28 0.611900 9 141265 -1.51 0.066105 10 142398 1.14 0.873222 11 142079 0.40 0.654104 12 141818 -0.21 0.415512 13 142236 0.76 0.777342 14 142666 1.77 0.961463 15 142103 0.45 0.674546 16 142163 0.59 0.723305 17 142229 0.75 0.772436 18 141729 -0.42 0.336756 19 142052 0.33 0.630562 20 142202 0.68 0.752952 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-07-31_06:31 Bits used No. missing words z-score p-value 23 to 32 141699 -0.7253 0.234141 22 to 31 141947 0.1299 0.551676 21 to 30 141956 0.1609 0.563926 20 to 29 141956 0.1609 0.563926 19 to 28 142171 0.9023 0.816554 18 to 27 141718 -0.6598 0.254704 17 to 26 141439 -1.6218 0.052420 16 to 25 141797 -0.3873 0.349251 15 to 24 141949 0.1368 0.554403 14 to 23 141784 -0.4322 0.332808 13 to 22 141850 -0.2046 0.418948 12 to 21 141470 -1.5149 0.064895 11 to 20 142132 0.7678 0.778705 10 to 19 141795 -0.3942 0.346701 9 to 18 141654 -0.8804 0.189308 8 to 17 141759 -0.5184 0.302097 7 to 16 141737 -0.5942 0.276175 6 to 15 141839 -0.2425 0.404190 5 to 14 141924 0.0506 0.520172 4 to 13 141782 -0.4391 0.330306 3 to 12 141576 -1.1494 0.125193 2 to 11 142295 1.3299 0.908224 1 to 10 141847 -0.2149 0.414911 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-07-31_06:31 Bits used No. missing words z-score p-value 28 to 32 142082 0.5853 0.720834 27 to 31 141933 0.0802 0.531976 26 to 30 142139 0.7785 0.781875 25 to 29 141925 0.0531 0.521181 24 to 28 141837 -0.2452 0.403156 23 to 27 142053 0.4870 0.686877 22 to 26 141645 -0.8960 0.185117 21 to 25 142094 0.6260 0.734343 20 to 24 142498 1.9955 0.977005 19 to 23 142222 1.0599 0.855405 18 to 22 141667 -0.8215 0.205693 17 to 21 141885 -0.0825 0.467135 16 to 20 141415 -1.6757 0.046899 15 to 19 141555 -1.2011 0.114853 14 to 18 141709 -0.6791 0.248542 13 to 17 141677 -0.7876 0.215477 12 to 16 141658 -0.8520 0.197116 11 to 15 141654 -0.8655 0.193375 10 to 14 141634 -0.9333 0.175327 9 to 13 141913 0.0124 0.504963 8 to 12 142165 0.8667 0.806941 7 to 11 142154 0.8294 0.796558 6 to 10 142119 0.7107 0.761379 5 to 9 142028 0.4023 0.656258 4 to 8 142186 0.9379 0.825843 3 to 7 142042 0.4497 0.673547 2 to 6 141654 -0.8655 0.193375 1 to 5 142020 0.3752 0.646227 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-07-31_06:31 Bits used No. missing words z-score p-value 31 to 32 142516 1.7896 0.963240 30 to 31 141795 -0.3373 0.367962 29 to 30 142208 0.8810 0.810850 28 to 29 142231 0.9489 0.828659 27 to 28 141749 -0.4729 0.318125 26 to 27 141955 0.1347 0.553583 25 to 26 141963 0.1583 0.562897 24 to 25 142785 2.5831 0.995104 23 to 24 141655 -0.7502 0.226556 22 to 23 141943 0.0993 0.539559 21 to 22 141521 -1.1455 0.125998 20 to 21 142250 1.0049 0.842534 19 to 20 142038 0.3796 0.647863 18 to 19 142213 0.8958 0.814815 17 to 18 142101 0.5654 0.714099 16 to 17 141701 -0.6145 0.269428 15 to 16 142181 0.8014 0.788546 14 to 15 142071 0.4769 0.683284 13 to 14 142099 0.5595 0.712089 12 to 13 142050 0.4150 0.660913 11 to 12 141792 -0.3461 0.364632 10 to 11 141564 -1.0187 0.154179 9 to 10 142208 0.8810 0.810850 8 to 9 141005 -2.6676 0.003819 7 to 8 142084 0.5153 0.696811 6 to 7 142014 0.3088 0.621248 5 to 6 141024 -2.6116 0.004506 4 to 5 141769 -0.4140 0.339454 3 to 4 141955 0.1347 0.553583 2 to 3 141104 -2.3756 0.008760 1 to 2 141489 -1.2399 0.107504 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-07-31_06:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2623.10 1.741 0.959150 Test results for specific bytes for dh-ranFile-2016-07-31_06:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2558.81 0.832 0.797222 2 to 9 2487.09 -0.183 0.427591 3 to 10 2436.68 -0.895 0.185283 4 to 11 2440.58 -0.840 0.200346 5 to 12 2408.80 -1.290 0.098568 6 to 13 2537.16 0.526 0.700407 7 to 14 2493.51 -0.092 0.463457 8 to 15 2518.28 0.259 0.601996 9 to 16 2479.94 -0.284 0.388346 10 to 17 2653.72 2.174 0.985146 11 to 18 2520.73 0.293 0.615328 12 to 19 2506.53 0.092 0.536812 13 to 20 2548.54 0.686 0.753783 14 to 21 2403.17 -1.369 0.085449 15 to 22 2533.23 0.470 0.680781 16 to 23 2542.07 0.595 0.724059 17 to 24 2587.28 1.234 0.891461 18 to 25 2503.77 0.053 0.521253 19 to 26 2591.78 1.298 0.902856 20 to 27 2637.69 1.947 0.974249 21 to 28 2483.90 -0.228 0.409953 22 to 29 2464.11 -0.508 0.305900 23 to 30 2469.63 -0.429 0.333780 24 to 31 2571.85 1.016 0.845215 25 to 32 2516.91 0.239 0.594527 CDPARK for dh-ranFile-2016-07-31_06:31: 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 3545 1.0046 0.842447 3533 0.4566 0.676028 3526 0.1370 0.554479 3537 0.6393 0.738676 3461 -2.8311 0.002320 3499 -1.0959 0.136563 3534 0.5023 0.692266 3537 0.6393 0.738676 3576 2.4201 0.992242 3516 -0.3196 0.374623 Square side=100, avg. no. parked=3526.40 sample std.=28.75 p-value of the KSTEST for those 10 p-values: 0.368239 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-07-31_06:31 0.9073,0.2602,0.6313,0.5696,0.7537,0.0893,0.2876,0.9856,0.9532,0.1480, The KS test for those 10 p-values: 0.579362 The 3DSPHERES test for dh-ranFile-2016-07-31_06:31 sample no r^3 equiv. uni. 1 19.793 0.483023 2 1.076 0.035232 3 53.228 0.830391 4 24.801 0.562515 5 23.430 0.542055 6 32.076 0.656722 7 10.645 0.298704 8 34.808 0.686601 9 4.114 0.128141 10 119.385 0.981305 11 24.623 0.559911 12 78.752 0.927565 13 20.392 0.493252 14 3.073 0.097371 15 36.317 0.701977 16 3.442 0.108392 17 9.848 0.279839 18 53.428 0.831517 19 62.206 0.874259 20 22.096 0.521227 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.903089 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-07-31_06:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.1 -2.0 -1.6 0.8 1.6 0.1 0.3 -0.7 1.7 0.7 1.2 1.4 -0.4 1.2 -0.8 -1.2 0.4 0.4 -0.6 -1.2 -1.2 -0.4 0.0 -0.7 -0.2 -1.0 1.0 1.4 0.4 -0.6 0.4 2.0 1.0 0.1 -1.2 -0.7 -1.3 -2.0 1.0 3.1 2.0 3.7 Chi-square with 42 degrees of freedom:71.008544 z-score=3.165092, p-value=0.996597 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-07-31_06:31 Test no p-value 1 0.695764 2 0.006402 3 0.307743 4 0.023922 5 0.008746 6 0.310290 7 0.781999 8 0.740359 9 0.247335 10 0.401702 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.048934 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-07-31_06:31: (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 66676 0.00 66651 0.00 3 25000.00 25069 0.19 24953 0.09 4 6666.67 6641 0.10 6676 0.01 5 1388.89 1328 2.67 1472 4.97 6 238.10 247 0.33 217 1.87 7 34.72 33 0.09 28 1.30 8 4.96 5 0.00 2 1.77 p=0.23996 p=0.87596 Number of rngs required: 688286, p-value: 0.446 RESULTS OF CRAPS TEST for dh-ranFile-2016-07-31_06:31 No. of wins: Observed Expected 98042 98585.9 z-score=-2.432, pvalue=0.00750 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66828 66666.7 0.390 0.390 2 37771 37654.3 0.362 0.752 3 26776 26954.7 1.185 1.937 4 19284 19313.5 0.045 1.982 5 13749 13851.4 0.757 2.739 6 9973 9943.5 0.087 2.827 7 7079 7145.0 0.610 3.437 8 5045 5139.1 1.722 5.159 9 3701 3699.9 0.000 5.159 10 2663 2666.3 0.004 5.163 11 2007 1923.3 3.640 8.803 12 1376 1388.7 0.117 8.920 13 1033 1003.7 0.854 9.774 14 739 726.1 0.228 10.002 15 521 525.8 0.044 10.047 16 408 381.2 1.891 11.938 17 283 276.5 0.151 12.089 18 189 200.8 0.697 12.786 19 145 146.0 0.007 12.792 20 124 106.2 2.978 15.770 21 306 287.1 1.242 17.013 Chisq= 17.01 for 20 degrees of freedom, p= 0.34785 SUMMARY of craptest p-value for no. of wins: 0.007498 p-value for throws/game: 0.347847 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-07-31_06:31 No. of wins: Observed Expected 98796 98585.9 z-score= 0.940, pvalue=0.82636 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66685 66666.7 0.005 0.005 2 37984 37654.3 2.886 2.892 3 26912 26954.7 0.068 2.959 4 19277 19313.5 0.069 3.028 5 13759 13851.4 0.617 3.645 6 9860 9943.5 0.702 4.347 7 7079 7145.0 0.610 4.957 8 5153 5139.1 0.038 4.995 9 3667 3699.9 0.292 5.286 10 2758 2666.3 3.154 8.440 11 1850 1923.3 2.796 11.236 12 1332 1388.7 2.318 13.554 13 1029 1003.7 0.637 14.191 14 709 726.1 0.405 14.596 15 535 525.8 0.160 14.756 16 393 381.2 0.368 15.124 17 275 276.5 0.009 15.133 18 212 200.8 0.621 15.754 19 160 146.0 1.346 17.100 20 100 106.2 0.364 17.463 21 271 287.1 0.904 18.368 Chisq= 18.37 for 20 degrees of freedom, p= 0.43679 SUMMARY of craptest p-value for no. of wins: 0.826359 p-value for throws/game: 0.436794 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0008,0.0023,0.0038,0.0045,0.0064,0.0075,0.0087,0.0088,0.0120,0.0239, 0.0352,0.0418,0.0469,0.0489,0.0523,0.0524,0.0629,0.0649,0.0661,0.0677, 0.0718,0.0854,0.0893,0.0899,0.0944,0.0967,0.0974,0.0986,0.1075,0.1084, 0.1149,0.1156,0.1252,0.1260,0.1281,0.1366,0.1480,0.1542,0.1640,0.1728, 0.1738,0.1753,0.1851,0.1853,0.1876,0.1893,0.1934,0.1934,0.1971,0.1992, 0.2003,0.2057,0.2065,0.2091,0.2105,0.2155,0.2266,0.2285,0.2341,0.2368, 0.2400,0.2436,0.2473,0.2485,0.2547,0.2556,0.2579,0.2602,0.2623,0.2694, 0.2762,0.2798,0.2876,0.2882,0.2969,0.2987,0.3021,0.3059,0.3077,0.3103, 0.3181,0.3187,0.3303,0.3328,0.3338,0.3368,0.3395,0.3448,0.3467,0.3478, 0.3493,0.3585,0.3615,0.3646,0.3680,0.3682,0.3746,0.3800,0.3870,0.3883, 0.3927,0.3956,0.4006,0.4017,0.4032,0.4042,0.4100,0.4149,0.4155,0.4189, 0.4242,0.4276,0.4282,0.4368,0.4416,0.4465,0.4466,0.4513,0.4535,0.4601, 0.4635,0.4671,0.4830,0.4922,0.4933,0.5050,0.5062,0.5179,0.5202,0.5209, 0.5212,0.5212,0.5213,0.5241,0.5320,0.5360,0.5368,0.5384,0.5396,0.5421, 0.5440,0.5517,0.5536,0.5536,0.5544,0.5545,0.5599,0.5625,0.5629,0.5639, 0.5639,0.5696,0.5782,0.5791,0.5794,0.5822,0.5945,0.5974,0.6020,0.6119, 0.6153,0.6159,0.6212,0.6306,0.6313,0.6369,0.6462,0.6479,0.6491,0.6541, 0.6563,0.6567,0.6609,0.6626,0.6655,0.6735,0.6744,0.6745,0.6760,0.6808, 0.6833,0.6866,0.6869,0.6870,0.6923,0.6958,0.6968,0.7004,0.7020,0.7064, 0.7121,0.7130,0.7141,0.7166,0.7208,0.7233,0.7241,0.7343,0.7387,0.7387, 0.7404,0.7449,0.7463,0.7530,0.7531,0.7537,0.7538,0.7614,0.7685,0.7711, 0.7724,0.7773,0.7783,0.7787,0.7819,0.7820,0.7885,0.7902,0.7966,0.7972, 0.8069,0.8108,0.8108,0.8148,0.8166,0.8172,0.8226,0.8258,0.8264,0.8287, 0.8304,0.8315,0.8337,0.8424,0.8425,0.8436,0.8452,0.8538,0.8554,0.8732, 0.8743,0.8760,0.8841,0.8915,0.8973,0.9029,0.9031,0.9073,0.9082,0.9276, 0.9447,0.9532,0.9569,0.9589,0.9591,0.9615,0.9632,0.9657,0.9699,0.9742, 0.9770,0.9813,0.9816,0.9851,0.9856,0.9922,0.9951,0.9966,0.9974, Overall p-value after applying KStest on 269 p-values = 0.670715 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.