RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-07-04_20:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.66 11.5505 0.173438 2 to 25 16.02 21.1333 0.779617 3 to 26 15.98 11.5466 0.173218 4 to 27 16.26 35.2913 0.994305 5 to 28 15.84 25.0781 0.907024 6 to 29 15.80 19.2074 0.683242 7 to 30 15.93 23.9323 0.878715 8 to 31 15.53 32.7236 0.987784 9 to 32 15.67 16.5464 0.514519 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.040666 Tough bday spacings test for dh-ranFile-2016-07-04_20:31: 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 11 34 73 97 101 69 56 32 16 5 6 (O-E)^2/E 0.4 0.2 0.0 0.0 0.1 1.1 0.3 0.2 0.1 0.4 0.9 Birthday Spacings: Sum(O-E)^2/E= 3.606, p= 0.037 RESULTS OF GCD FOR dh-ranFile-2016-07-04_20:31 Euclid's algorithm: p-value, steps to gcd: 0.307161 p-value, dist. of gcd's: 0.579341 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-07-04_20:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.197 0.130 0.310 0.204 0.710 0.544 0.891 0.887 Bits 8 to 15---> 0.482 0.738 0.573 0.236 0.526 0.058 0.664 0.515 Bits 16 to 23---> 0.848 0.060 0.167 0.750 0.305 0.918 0.351 0.228 Bits 24 to 31---> 0.649 0.770 0.395 0.618 0.689 0.249 0.394 0.009 KS test for the above 32 p values: 0.179 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-07-04_20:31, p-values for 5 runs: 0.0053, 0.9777, 0.2922, 0.1863, 0.0094 Rank test for binary matrices (31x31) for dh-ranFile-2016-07-04_20:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 205 211.4 0.195 0.195 r= 29 5128 5134.0 0.007 0.202 r= 30 23003 23103.0 0.433 0.635 r= 31 11664 11551.5 1.095 1.730 chi-square = 1.730 with df = 3; p-value = 0.370 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-07-04_20:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 208 211.4 0.055 0.055 r= 30 5095 5134.0 0.296 0.352 r= 31 23211 23103.0 0.504 0.856 r= 32 11486 11551.5 0.372 1.228 chi-square = 1.228 with df = 3; p-value = 0.254 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-07-04_20:31 b-rank test for bits 1 to 8, p=0.41206 b-rank test for bits 2 to 9, p=0.74159 b-rank test for bits 3 to 10, p=0.43576 b-rank test for bits 4 to 11, p=0.04005 b-rank test for bits 5 to 12, p=0.80390 b-rank test for bits 6 to 13, p=0.99781 b-rank test for bits 7 to 14, p=0.92786 b-rank test for bits 8 to 15, p=0.69246 b-rank test for bits 9 to 16, p=0.78960 b-rank test for bits 10 to 17, p=0.93270 b-rank test for bits 11 to 18, p=0.46373 b-rank test for bits 12 to 19, p=0.17479 b-rank test for bits 13 to 20, p=0.78290 b-rank test for bits 14 to 21, p=0.12554 b-rank test for bits 15 to 22, p=0.00389 b-rank test for bits 16 to 23, p=0.46930 b-rank test for bits 17 to 24, p=0.52216 b-rank test for bits 18 to 25, p=0.73231 b-rank test for bits 19 to 26, p=0.18009 b-rank test for bits 20 to 27, p=0.09620 b-rank test for bits 21 to 28, p=0.39048 b-rank test for bits 22 to 29, p=0.06184 b-rank test for bits 23 to 30, p=0.31718 b-rank test for bits 24 to 31, p=0.26220 b-rank test for bits 25 to 32, p=0.82133 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 = 0.854387 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-07-04_20:31 (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 141379 -1.24 0.107656 2 142181 0.63 0.737202 3 141274 -1.48 0.068849 4 142280 0.87 0.806769 5 142439 1.24 0.892058 6 141572 -0.79 0.215303 7 141807 -0.24 0.405518 8 142153 0.57 0.715431 9 142083 0.41 0.657545 10 142724 1.90 0.971508 11 142090 0.42 0.663534 12 142167 0.60 0.726424 13 141519 -0.91 0.180888 14 142032 0.29 0.612795 15 141828 -0.19 0.424645 16 141506 -0.94 0.173004 17 142724 1.90 0.971508 18 141342 -1.33 0.092497 19 142140 0.54 0.705039 20 142858 2.22 0.986672 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-07-04_20:31 Bits used No. missing words z-score p-value 23 to 32 142102 0.6644 0.746776 22 to 31 142025 0.3989 0.655003 21 to 30 141883 -0.0908 0.463829 20 to 29 141916 0.0230 0.509175 19 to 28 141682 -0.7839 0.216550 18 to 27 141852 -0.1977 0.421644 17 to 26 141752 -0.5425 0.293731 16 to 25 142127 0.7506 0.773549 15 to 24 141510 -1.3770 0.084256 14 to 23 142080 0.5885 0.721907 13 to 22 141560 -1.2046 0.114182 12 to 21 142007 0.3368 0.631864 11 to 20 142234 1.1196 0.868548 10 to 19 141988 0.2713 0.606911 9 to 18 142004 0.3264 0.627957 8 to 17 142229 1.1023 0.864837 7 to 16 141615 -1.0149 0.155069 6 to 15 141649 -0.8977 0.184676 5 to 14 141308 -2.0736 0.019060 4 to 13 141624 -0.9839 0.162583 3 to 12 142030 0.4161 0.661333 2 to 11 141855 -0.1873 0.425695 1 to 10 142046 0.4713 0.681278 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-07-04_20:31 Bits used No. missing words z-score p-value 28 to 32 141303 -2.0554 0.019922 27 to 31 141389 -1.7638 0.038880 26 to 30 142022 0.3819 0.648744 25 to 29 142912 3.3989 0.999662 24 to 28 142144 0.7955 0.786836 23 to 27 142004 0.3209 0.625863 22 to 26 141620 -0.9808 0.163351 21 to 25 141681 -0.7740 0.219465 20 to 24 141694 -0.7299 0.232716 19 to 23 141951 0.1413 0.556166 18 to 22 141591 -1.0791 0.140275 17 to 21 141655 -0.8621 0.194306 16 to 20 141881 -0.0960 0.461747 15 to 19 141832 -0.2621 0.396609 14 to 18 141837 -0.2452 0.403156 13 to 17 142448 1.8260 0.966075 12 to 16 141577 -1.1265 0.129968 11 to 15 142418 1.7243 0.957674 10 to 14 141558 -1.1909 0.116837 9 to 13 142205 1.0023 0.841894 8 to 12 141287 -2.1096 0.017447 7 to 11 141820 -0.3028 0.381016 6 to 10 142247 1.1446 0.873822 5 to 9 142240 1.1209 0.868838 4 to 8 141609 -1.0181 0.154323 3 to 7 142641 2.4802 0.993435 2 to 6 141536 -1.2655 0.102842 1 to 5 141199 -2.4079 0.008022 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-07-04_20:31 Bits used No. missing words z-score p-value 31 to 32 142406 1.4651 0.928554 30 to 31 141188 -2.1278 0.016676 29 to 30 141927 0.0521 0.520785 28 to 29 142370 1.3589 0.912912 27 to 28 142526 1.8191 0.965551 26 to 27 142358 1.3235 0.907167 25 to 26 142355 1.3147 0.905688 24 to 25 141931 0.0639 0.525484 23 to 24 142046 0.4032 0.656583 22 to 23 141714 -0.5762 0.282242 21 to 22 141844 -0.1927 0.423592 20 to 21 141062 -2.4995 0.006218 19 to 20 141776 -0.3933 0.347048 18 to 19 141948 0.1141 0.545409 17 to 18 141604 -0.9007 0.183880 16 to 17 141994 0.2498 0.598615 15 to 16 141991 0.2409 0.595189 14 to 15 141838 -0.2104 0.416673 13 to 14 141227 -2.0128 0.022069 12 to 13 142226 0.9341 0.824882 11 to 12 141772 -0.4051 0.342701 10 to 11 142168 0.7630 0.777280 9 to 10 141722 -0.5526 0.290270 8 to 9 142192 0.8338 0.797813 7 to 8 142130 0.6509 0.742459 6 to 7 142072 0.4799 0.684334 5 to 6 141763 -0.4317 0.332997 4 to 5 141631 -0.8210 0.205814 3 to 4 142204 0.8692 0.807640 2 to 3 142192 0.8338 0.797813 1 to 2 142153 0.7188 0.763865 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-07-04_20:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2500.59 0.008 0.503357 Test results for specific bytes for dh-ranFile-2016-07-04_20:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2433.35 -0.943 0.172962 2 to 9 2395.78 -1.474 0.070256 3 to 10 2444.32 -0.787 0.215525 4 to 11 2552.76 0.746 0.772222 5 to 12 2603.73 1.467 0.928816 6 to 13 2533.10 0.468 0.680139 7 to 14 2509.59 0.136 0.553926 8 to 15 2595.25 1.347 0.911017 9 to 16 2573.93 1.046 0.852121 10 to 17 2546.23 0.654 0.743384 11 to 18 2678.02 2.518 0.994092 12 to 19 2679.14 2.533 0.994353 13 to 20 2469.42 -0.432 0.332707 14 to 21 2501.00 0.014 0.505631 15 to 22 2433.12 -0.946 0.172131 16 to 23 2544.95 0.636 0.737517 17 to 24 2511.15 0.158 0.562638 18 to 25 2493.76 -0.088 0.464852 19 to 26 2409.59 -1.279 0.100517 20 to 27 2580.01 1.131 0.871069 21 to 28 2486.26 -0.194 0.422985 22 to 29 2430.70 -0.980 0.163545 23 to 30 2437.56 -0.883 0.188605 24 to 31 2400.21 -1.411 0.079078 25 to 32 2408.30 -1.297 0.097354 CDPARK for dh-ranFile-2016-07-04_20:31: 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 3522 -0.0457 0.481790 3522 -0.0457 0.481790 3544 0.9589 0.831196 3552 1.3242 0.907282 3518 -0.2283 0.409702 3537 0.6393 0.738676 3521 -0.0913 0.463617 3521 -0.0913 0.463617 3547 1.0959 0.863437 3496 -1.2329 0.108811 Square side=100, avg. no. parked=3528.00 sample std.=16.02 p-value of the KSTEST for those 10 p-values: 0.469599 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-07-04_20:31 0.2360,0.8546,0.9368,0.9780,0.9846,0.2969,0.8811,0.4362,0.8692,0.9109, The KS test for those 10 p-values: 0.003385 The 3DSPHERES test for dh-ranFile-2016-07-04_20:31 sample no r^3 equiv. uni. 1 8.888 0.256417 2 14.310 0.379354 3 67.670 0.895198 4 15.812 0.409673 5 11.447 0.317203 6 7.317 0.216447 7 27.897 0.605403 8 3.665 0.114994 9 24.040 0.551263 10 58.469 0.857581 11 27.343 0.598048 12 11.101 0.309278 13 25.110 0.566996 14 11.611 0.320935 15 10.826 0.302930 16 3.132 0.099129 17 14.972 0.392912 18 60.850 0.868447 19 101.161 0.965680 20 45.603 0.781309 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.739837 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-07-04_20:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.9 0.8 -1.4 0.1 0.6 -0.6 -0.9 -0.7 0.7 -1.0 1.8 -0.2 -1.3 0.5 -0.1 0.4 0.3 -1.0 0.9 1.9 -0.2 -1.1 0.1 0.6 -0.7 -0.3 -1.0 -0.6 0.8 -2.7 -0.1 1.6 1.0 -1.5 -1.0 1.4 -0.4 0.5 1.5 -0.6 2.0 -0.1 Chi-square with 42 degrees of freedom:45.498337 z-score=0.381700, p-value=0.671450 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-07-04_20:31 Test no p-value 1 0.167611 2 0.380884 3 0.642209 4 0.210299 5 0.787892 6 0.700883 7 0.235070 8 0.007195 9 0.176651 10 0.422766 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.245991 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-07-04_20:31: (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 66627 0.02 66699 0.02 3 25000.00 24971 0.03 24987 0.01 4 6666.67 6711 0.29 6647 0.06 5 1388.89 1414 0.45 1374 0.16 6 238.10 239 0.00 256 1.35 7 34.72 33 0.09 32 0.21 8 4.96 4 0.19 4 0.19 p=0.01762 p=0.07897 Number of rngs required: 688333, p-value: 0.468 RESULTS OF CRAPS TEST for dh-ranFile-2016-07-04_20:31 No. of wins: Observed Expected 98703 98585.9 z-score= 0.524, pvalue=0.69983 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66751 66666.7 0.107 0.107 2 37529 37654.3 0.417 0.524 3 26914 26954.7 0.062 0.585 4 19235 19313.5 0.319 0.904 5 13802 13851.4 0.176 1.080 6 9938 9943.5 0.003 1.083 7 7370 7145.0 7.084 8.167 8 5222 5139.1 1.338 9.505 9 3663 3699.9 0.367 9.873 10 2653 2666.3 0.066 9.939 11 1870 1923.3 1.479 11.418 12 1426 1388.7 1.000 12.417 13 981 1003.7 0.514 12.931 14 725 726.1 0.002 12.933 15 516 525.8 0.184 13.117 16 373 381.2 0.174 13.292 17 290 276.5 0.655 13.947 18 198 200.8 0.040 13.987 19 141 146.0 0.170 14.157 20 112 106.2 0.315 14.472 21 291 287.1 0.053 14.524 Chisq= 14.52 for 20 degrees of freedom, p= 0.19706 SUMMARY of craptest p-value for no. of wins: 0.699835 p-value for throws/game: 0.197058 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-07-04_20:31 No. of wins: Observed Expected 99052 98585.9 z-score= 2.085, pvalue=0.98146 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66749 66666.7 0.102 0.102 2 37299 37654.3 3.353 3.455 3 27066 26954.7 0.459 3.914 4 19275 19313.5 0.077 3.991 5 14015 13851.4 1.932 5.922 6 10022 9943.5 0.619 6.541 7 7198 7145.0 0.393 6.934 8 5195 5139.1 0.609 7.543 9 3633 3699.9 1.208 8.751 10 2665 2666.3 0.001 8.752 11 1958 1923.3 0.625 9.377 12 1353 1388.7 0.920 10.297 13 957 1003.7 2.174 12.471 14 691 726.1 1.701 14.171 15 498 525.8 1.474 15.645 16 386 381.2 0.062 15.707 17 309 276.5 3.810 19.517 18 204 200.8 0.050 19.567 19 143 146.0 0.061 19.628 20 102 106.2 0.167 19.795 21 282 287.1 0.091 19.886 Chisq= 19.89 for 20 degrees of freedom, p= 0.53494 SUMMARY of craptest p-value for no. of wins: 0.981459 p-value for throws/game: 0.534941 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0034,0.0039,0.0053,0.0062,0.0072,0.0080,0.0086,0.0094,0.0167,0.0174, 0.0176,0.0191,0.0199,0.0221,0.0366,0.0389,0.0400,0.0407,0.0584,0.0604, 0.0618,0.0688,0.0703,0.0790,0.0791,0.0843,0.0925,0.0962,0.0974,0.0991, 0.1005,0.1028,0.1077,0.1088,0.1142,0.1150,0.1168,0.1255,0.1300,0.1304, 0.1403,0.1543,0.1551,0.1626,0.1634,0.1635,0.1667,0.1676,0.1721,0.1730, 0.1730,0.1732,0.1734,0.1748,0.1767,0.1785,0.1801,0.1809,0.1839,0.1847, 0.1863,0.1886,0.1943,0.1971,0.1974,0.2042,0.2058,0.2103,0.2153,0.2155, 0.2164,0.2166,0.2195,0.2283,0.2327,0.2351,0.2360,0.2363,0.2460,0.2494, 0.2536,0.2564,0.2622,0.2822,0.2903,0.2922,0.2937,0.2969,0.3029,0.3054, 0.3072,0.3093,0.3102,0.3172,0.3172,0.3209,0.3327,0.3330,0.3427,0.3470, 0.3507,0.3698,0.3794,0.3809,0.3810,0.3905,0.3929,0.3938,0.3948,0.3966, 0.4032,0.4055,0.4097,0.4097,0.4121,0.4167,0.4216,0.4228,0.4230,0.4236, 0.4246,0.4257,0.4358,0.4362,0.4617,0.4636,0.4636,0.4637,0.4638,0.4649, 0.4679,0.4693,0.4696,0.4818,0.4818,0.4819,0.5034,0.5056,0.5092,0.5145, 0.5147,0.5208,0.5222,0.5255,0.5259,0.5349,0.5435,0.5454,0.5513,0.5539, 0.5562,0.5626,0.5670,0.5730,0.5793,0.5952,0.5980,0.5986,0.6054,0.6069, 0.6128,0.6178,0.6259,0.6280,0.6319,0.6422,0.6487,0.6495,0.6550,0.6566, 0.6575,0.6613,0.6635,0.6640,0.6714,0.6801,0.6813,0.6832,0.6843,0.6890, 0.6925,0.6998,0.7009,0.7050,0.7103,0.7154,0.7219,0.7264,0.7323,0.7372, 0.7375,0.7381,0.7387,0.7398,0.7416,0.7425,0.7434,0.7468,0.7496,0.7639, 0.7704,0.7722,0.7735,0.7773,0.7796,0.7813,0.7829,0.7868,0.7879,0.7896, 0.7978,0.7978,0.8039,0.8068,0.8076,0.8213,0.8249,0.8312,0.8419,0.8475, 0.8521,0.8544,0.8546,0.8576,0.8634,0.8648,0.8684,0.8685,0.8688,0.8692, 0.8711,0.8738,0.8787,0.8811,0.8873,0.8912,0.8921,0.8952,0.9057,0.9070, 0.9072,0.9073,0.9109,0.9110,0.9129,0.9183,0.9279,0.9286,0.9288,0.9327, 0.9368,0.9577,0.9656,0.9657,0.9661,0.9715,0.9715,0.9777,0.9780,0.9815, 0.9846,0.9867,0.9878,0.9934,0.9941,0.9943,0.9944,0.9978,0.9997, Overall p-value after applying KStest on 269 p-values = 0.301235 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.