RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-02-01_05:31 (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 13.8542 0.322604 2 to 25 15.60 14.5472 0.371938 3 to 26 15.57 17.0997 0.552370 4 to 27 15.37 24.6557 0.897315 5 to 28 15.48 22.7652 0.842947 6 to 29 15.60 18.2410 0.626206 7 to 30 15.82 23.1806 0.856536 8 to 31 15.74 22.4062 0.830402 9 to 32 15.79 16.2830 0.496129 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.179446 Tough bday spacings test for dh-ranFile-2016-02-01_05:31: 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 42 69 92 97 78 50 34 17 5 6 (O-E)^2/E 0.1 0.8 0.2 0.3 0.0 0.0 0.1 0.6 0.3 0.4 0.9 Birthday Spacings: Sum(O-E)^2/E= 3.748, p= 0.042 RESULTS OF GCD FOR dh-ranFile-2016-02-01_05:31 Euclid's algorithm: p-value, steps to gcd: 0.637854 p-value, dist. of gcd's: 0.398881 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-02-01_05:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.145 0.929 0.522 0.900 0.468 0.318 0.294 0.314 Bits 8 to 15---> 0.870 0.492 0.792 0.881 0.200 0.013 0.616 0.929 Bits 16 to 23---> 0.606 0.699 0.859 0.109 0.259 0.306 0.966 0.492 Bits 24 to 31---> 0.014 0.244 0.344 0.091 0.550 0.982 0.315 0.726 KS test for the above 32 p values: 0.122 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-02-01_05:31, p-values for 5 runs: 0.2314, 0.3013, 0.3465, 0.4684, 0.2084 Rank test for binary matrices (31x31) for dh-ranFile-2016-02-01_05:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 203 211.4 0.335 0.335 r= 29 5130 5134.0 0.003 0.338 r= 30 23132 23103.0 0.036 0.375 r= 31 11535 11551.5 0.024 0.398 chi-square = 0.398 with df = 3; p-value = 0.059 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-02-01_05:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 246 211.4 5.657 5.657 r= 30 5002 5134.0 3.394 9.051 r= 31 23190 23103.0 0.327 9.378 r= 32 11562 11551.5 0.010 9.388 chi-square = 9.388 with df = 3; p-value = 0.975 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-02-01_05:31 b-rank test for bits 1 to 8, p=0.40785 b-rank test for bits 2 to 9, p=0.42570 b-rank test for bits 3 to 10, p=0.80899 b-rank test for bits 4 to 11, p=0.45522 b-rank test for bits 5 to 12, p=0.33745 b-rank test for bits 6 to 13, p=0.15582 b-rank test for bits 7 to 14, p=0.30779 b-rank test for bits 8 to 15, p=0.83651 b-rank test for bits 9 to 16, p=0.69078 b-rank test for bits 10 to 17, p=0.13203 b-rank test for bits 11 to 18, p=0.63143 b-rank test for bits 12 to 19, p=0.64992 b-rank test for bits 13 to 20, p=0.15255 b-rank test for bits 14 to 21, p=0.10353 b-rank test for bits 15 to 22, p=0.71069 b-rank test for bits 16 to 23, p=0.84149 b-rank test for bits 17 to 24, p=0.10035 b-rank test for bits 18 to 25, p=0.64189 b-rank test for bits 19 to 26, p=0.14883 b-rank test for bits 20 to 27, p=0.11944 b-rank test for bits 21 to 28, p=0.64053 b-rank test for bits 22 to 29, p=0.06260 b-rank test for bits 23 to 30, p=0.24860 b-rank test for bits 24 to 31, p=0.87618 b-rank test for bits 25 to 32, p=0.77029 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 = 0.421616 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-02-01_05:31 (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 141276 -1.48 0.069471 2 141435 -1.11 0.133877 3 141779 -0.30 0.380370 4 142096 0.44 0.668634 5 141851 -0.14 0.445798 6 142980 2.50 0.993818 7 141482 -1.00 0.159034 8 141668 -0.56 0.286426 9 141850 -0.14 0.444875 10 142175 0.62 0.732610 11 141637 -0.64 0.262295 12 142777 2.03 0.978682 13 142381 1.10 0.864776 14 141874 -0.08 0.467106 15 141533 -0.88 0.189626 16 142366 1.07 0.857011 17 141778 -0.31 0.379480 18 141812 -0.23 0.410054 19 142689 1.82 0.965747 20 140921 -2.31 0.010467 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-02-01_05:31 Bits used No. missing words z-score p-value 23 to 32 141490 -1.4460 0.074093 22 to 31 141779 -0.4494 0.326567 21 to 30 141867 -0.1460 0.441974 20 to 29 141646 -0.9080 0.181930 19 to 28 141576 -1.1494 0.125193 18 to 27 141611 -1.0287 0.151805 17 to 26 142094 0.6368 0.737870 16 to 25 142038 0.4437 0.671367 15 to 24 142286 1.2989 0.903004 14 to 23 141988 0.2713 0.606911 13 to 22 141982 0.2506 0.598933 12 to 21 142263 1.2196 0.888683 11 to 20 142175 0.9161 0.820194 10 to 19 141886 -0.0804 0.467940 9 to 18 141771 -0.4770 0.316681 8 to 17 141839 -0.2425 0.404190 7 to 16 141679 -0.7942 0.213528 6 to 15 141582 -1.1287 0.129507 5 to 14 142181 0.9368 0.825568 4 to 13 142163 0.8747 0.809138 3 to 12 141903 -0.0218 0.491293 2 to 11 141576 -1.1494 0.125193 1 to 10 142428 1.7885 0.963154 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-02-01_05:31 Bits used No. missing words z-score p-value 28 to 32 141004 -3.0689 0.001074 27 to 31 141335 -1.9469 0.025774 26 to 30 142090 0.6124 0.729877 25 to 29 141602 -1.0418 0.148753 24 to 28 141617 -0.9909 0.160855 23 to 27 142337 1.4497 0.926433 22 to 26 142085 0.5955 0.724243 21 to 25 141322 -1.9909 0.023243 20 to 24 141650 -0.8791 0.189678 19 to 23 141986 0.2599 0.602529 18 to 22 142216 1.0396 0.850728 17 to 21 142095 0.6294 0.735453 16 to 20 142475 1.9175 0.972414 15 to 19 142003 0.3175 0.624578 14 to 18 142220 1.0531 0.853857 13 to 17 141709 -0.6791 0.248542 12 to 16 142216 1.0396 0.850728 11 to 15 141480 -1.4554 0.072785 10 to 14 141898 -0.0384 0.484682 9 to 13 141651 -0.8757 0.190598 8 to 12 141914 0.0158 0.506315 7 to 11 141362 -1.8554 0.031773 6 to 10 141969 0.2023 0.580148 5 to 9 142315 1.3752 0.915458 4 to 8 141945 0.1209 0.548121 3 to 7 142407 1.6870 0.954200 2 to 6 141497 -1.3977 0.081097 1 to 5 141851 -0.1977 0.421629 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-02-01_05:31 Bits used No. missing words z-score p-value 31 to 32 142010 0.2970 0.616752 30 to 31 142168 0.7630 0.777280 29 to 30 141407 -1.4818 0.069197 28 to 29 141739 -0.5024 0.307676 27 to 28 142143 0.6893 0.754680 26 to 27 141971 0.1819 0.572176 25 to 26 141776 -0.3933 0.347048 24 to 25 141911 0.0049 0.501965 23 to 24 141770 -0.4110 0.340535 22 to 23 142043 0.3943 0.653323 21 to 22 141609 -0.8859 0.187828 20 to 21 141874 -0.1042 0.458498 19 to 20 142056 0.4327 0.667367 18 to 19 141682 -0.6706 0.251241 17 to 18 142299 1.1495 0.874819 16 to 17 141777 -0.3904 0.348137 15 to 16 142247 0.9961 0.840394 14 to 15 142090 0.5329 0.702966 13 to 14 142024 0.3383 0.632416 12 to 13 142521 1.8043 0.964411 11 to 12 141607 -0.8918 0.186242 10 to 11 142096 0.5506 0.709063 9 to 10 141788 -0.3579 0.360207 8 to 9 142130 0.6509 0.742459 7 to 8 142073 0.4828 0.685382 6 to 7 142067 0.4651 0.679071 5 to 6 141618 -0.8594 0.195065 4 to 5 142027 0.3471 0.635745 3 to 4 141184 -2.1396 0.016193 2 to 3 141565 -1.0157 0.154881 1 to 2 141750 -0.4700 0.319178 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-02-01_05:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2446.51 -0.757 0.224674 Test results for specific bytes for dh-ranFile-2016-02-01_05:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2523.91 0.338 0.632382 2 to 9 2556.03 0.792 0.785926 3 to 10 2439.37 -0.857 0.195605 4 to 11 2545.97 0.650 0.742193 5 to 12 2597.43 1.378 0.915880 6 to 13 2502.24 0.032 0.512631 7 to 14 2495.14 -0.069 0.472575 8 to 15 2589.62 1.267 0.897490 9 to 16 2424.81 -1.063 0.143822 10 to 17 2450.99 -0.693 0.244132 11 to 18 2510.43 0.148 0.558635 12 to 19 2457.58 -0.600 0.274263 13 to 20 2495.00 -0.071 0.471835 14 to 21 2471.20 -0.407 0.341905 15 to 22 2476.72 -0.329 0.370998 16 to 23 2424.22 -1.072 0.141944 17 to 24 2509.77 0.138 0.554966 18 to 25 2354.43 -2.059 0.019763 19 to 26 2488.34 -0.165 0.434496 20 to 27 2530.28 0.428 0.665771 21 to 28 2430.05 -0.989 0.161257 22 to 29 2573.11 1.034 0.849417 23 to 30 2412.53 -1.237 0.108032 24 to 31 2636.34 1.928 0.973080 25 to 32 2532.16 0.455 0.675364 CDPARK for dh-ranFile-2016-02-01_05:31: 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 3544 0.9589 0.831196 3530 0.3196 0.625377 3514 -0.4110 0.340551 3522 -0.0457 0.481790 3487 -1.6438 0.050105 3532 0.4110 0.659449 3556 1.5068 0.934075 3535 0.5479 0.708135 3518 -0.2283 0.409702 3532 0.4110 0.659449 Square side=100, avg. no. parked=3527.00 sample std.=17.69 p-value of the KSTEST for those 10 p-values: 0.612065 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-02-01_05:31 0.8701,0.0225,0.3070,0.9764,0.0842,0.8553,0.1296,0.4528,0.8307,0.0300, The KS test for those 10 p-values: 0.219306 The 3DSPHERES test for dh-ranFile-2016-02-01_05:31 sample no r^3 equiv. uni. 1 14.698 0.387341 2 6.527 0.195516 3 42.191 0.754965 4 57.900 0.854853 5 6.917 0.205907 6 17.732 0.446260 7 12.154 0.333101 8 24.495 0.558019 9 32.313 0.659419 10 45.473 0.780357 11 3.716 0.116511 12 25.981 0.579377 13 50.778 0.815960 14 61.212 0.870025 15 18.889 0.467213 16 50.529 0.814426 17 27.686 0.602622 18 20.401 0.493405 19 2.202 0.070768 20 20.951 0.502601 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.646877 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-02-01_05:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 1.3 -0.3 0.8 4.4 -1.2 2.2 -1.1 -0.4 -0.7 0.0 -0.9 -0.1 0.2 0.9 -0.8 -0.1 -1.8 2.3 -1.1 0.5 -0.1 -0.1 0.9 -0.8 -0.1 0.1 2.1 -0.8 0.4 -0.6 2.0 -0.7 -1.1 -1.5 -0.1 0.6 -0.9 1.5 -1.6 0.4 0.1 0.0 -1.1 Chi-square with 42 degrees of freedom:64.885514 z-score=2.497014, p-value=0.986750 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-02-01_05:31 Test no p-value 1 0.229107 2 0.649005 3 0.866709 4 0.009479 5 0.781594 6 0.000509 7 0.411715 8 0.997117 9 0.227315 10 0.544986 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.234756 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-02-01_05:31: (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 66483 0.51 66690 0.01 3 25000.00 25176 1.24 25053 0.11 4 6666.67 6679 0.02 6618 0.36 5 1388.89 1387 0.00 1377 0.10 6 238.10 233 0.11 224 0.83 7 34.72 38 0.31 29 0.94 8 4.96 3 0.77 8 1.86 p=0.18663 p=0.35275 Number of rngs required: 688262, p-value: 0.436 RESULTS OF CRAPS TEST for dh-ranFile-2016-02-01_05:31 No. of wins: Observed Expected 98579 98585.9 z-score=-0.031, pvalue=0.48776 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66918 66666.7 0.948 0.948 2 37814 37654.3 0.677 1.625 3 26754 26954.7 1.495 3.120 4 19211 19313.5 0.544 3.663 5 13750 13851.4 0.743 4.406 6 10010 9943.5 0.444 4.850 7 7122 7145.0 0.074 4.924 8 5123 5139.1 0.050 4.974 9 3634 3699.9 1.173 6.147 10 2683 2666.3 0.105 6.251 11 1928 1923.3 0.011 6.263 12 1386 1388.7 0.005 6.268 13 1019 1003.7 0.233 6.501 14 704 726.1 0.675 7.176 15 562 525.8 2.487 9.663 16 389 381.2 0.162 9.825 17 255 276.5 1.678 11.503 18 184 200.8 1.410 12.913 19 146 146.0 0.000 12.913 20 124 106.2 2.978 15.891 21 284 287.1 0.034 15.925 Chisq= 15.92 for 20 degrees of freedom, p= 0.27871 SUMMARY of craptest p-value for no. of wins: 0.487764 p-value for throws/game: 0.278713 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-02-01_05:31 No. of wins: Observed Expected 98833 98585.9 z-score= 1.105, pvalue=0.86550 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66654 66666.7 0.002 0.002 2 37583 37654.3 0.135 0.137 3 27218 26954.7 2.571 2.709 4 19350 19313.5 0.069 2.778 5 13728 13851.4 1.100 3.878 6 10030 9943.5 0.752 4.629 7 7069 7145.0 0.809 5.438 8 5136 5139.1 0.002 5.440 9 3676 3699.9 0.154 5.594 10 2709 2666.3 0.684 6.278 11 1948 1923.3 0.316 6.594 12 1315 1388.7 3.916 10.510 13 1045 1003.7 1.698 12.208 14 740 726.1 0.265 12.473 15 493 525.8 2.050 14.523 16 363 381.2 0.864 15.387 17 240 276.5 4.828 20.215 18 192 200.8 0.388 20.604 19 135 146.0 0.827 21.430 20 82 106.2 5.521 26.951 21 294 287.1 0.165 27.116 Chisq= 27.12 for 20 degrees of freedom, p= 0.86797 SUMMARY of craptest p-value for no. of wins: 0.865498 p-value for throws/game: 0.867967 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0005,0.0011,0.0095,0.0105,0.0133,0.0137,0.0162,0.0198,0.0225,0.0232, 0.0258,0.0300,0.0318,0.0420,0.0501,0.0594,0.0626,0.0692,0.0695,0.0708, 0.0728,0.0741,0.0811,0.0842,0.0910,0.1004,0.1035,0.1080,0.1085,0.1165, 0.1194,0.1217,0.1252,0.1252,0.1295,0.1296,0.1320,0.1339,0.1419,0.1438, 0.1454,0.1488,0.1488,0.1518,0.1525,0.1549,0.1558,0.1590,0.1609,0.1613, 0.1794,0.1819,0.1862,0.1866,0.1878,0.1896,0.1897,0.1906,0.1951,0.1955, 0.1956,0.1997,0.2059,0.2084,0.2135,0.2193,0.2247,0.2273,0.2291,0.2314, 0.2348,0.2438,0.2441,0.2485,0.2486,0.2512,0.2585,0.2623,0.2743,0.2787, 0.2864,0.2939,0.3013,0.3055,0.3070,0.3077,0.3078,0.3137,0.3148,0.3167, 0.3176,0.3192,0.3226,0.3266,0.3331,0.3375,0.3405,0.3406,0.3419,0.3440, 0.3465,0.3470,0.3481,0.3527,0.3602,0.3710,0.3719,0.3795,0.3804,0.3873, 0.3989,0.4042,0.4078,0.4097,0.4101,0.4117,0.4216,0.4216,0.4257,0.4345, 0.4356,0.4420,0.4449,0.4458,0.4463,0.4528,0.4552,0.4585,0.4671,0.4672, 0.4679,0.4682,0.4684,0.4718,0.4726,0.4818,0.4847,0.4878,0.4913,0.4917, 0.4917,0.4934,0.4961,0.5020,0.5026,0.5063,0.5126,0.5225,0.5450,0.5481, 0.5497,0.5524,0.5550,0.5580,0.5586,0.5722,0.5794,0.5801,0.5989,0.6025, 0.6026,0.6063,0.6069,0.6121,0.6162,0.6168,0.6246,0.6254,0.6262,0.6314, 0.6324,0.6324,0.6357,0.6379,0.6405,0.6419,0.6469,0.6490,0.6499,0.6533, 0.6594,0.6594,0.6594,0.6658,0.6674,0.6686,0.6714,0.6754,0.6791,0.6854, 0.6908,0.6993,0.7030,0.7081,0.7091,0.7107,0.7242,0.7265,0.7299,0.7326, 0.7355,0.7379,0.7422,0.7425,0.7547,0.7550,0.7703,0.7773,0.7804,0.7816, 0.7859,0.7915,0.8090,0.8091,0.8144,0.8160,0.8202,0.8256,0.8304,0.8307, 0.8312,0.8365,0.8404,0.8415,0.8429,0.8494,0.8507,0.8507,0.8539,0.8549, 0.8553,0.8565,0.8570,0.8586,0.8648,0.8655,0.8667,0.8680,0.8700,0.8701, 0.8702,0.8748,0.8762,0.8806,0.8887,0.8973,0.8975,0.8996,0.9030,0.9155, 0.9159,0.9264,0.9293,0.9295,0.9341,0.9542,0.9632,0.9644,0.9657,0.9657, 0.9724,0.9731,0.9754,0.9764,0.9787,0.9819,0.9867,0.9938,0.9971, Overall p-value after applying KStest on 269 p-values = 0.821643 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.