RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-08-27_17:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.95 15.0888 0.410913 2 to 25 15.58 20.5016 0.750621 3 to 26 15.89 19.2091 0.683338 4 to 27 15.96 14.9681 0.402222 5 to 28 15.63 18.6153 0.648946 6 to 29 15.70 17.6479 0.588629 7 to 30 15.97 12.7035 0.244205 8 to 31 15.61 24.0052 0.880707 9 to 32 15.74 17.2605 0.563141 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.395588 Tough bday spacings test for dh-ranFile-2015-08-27_17:31: 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 18 40 69 103 89 82 37 29 18 10 5 (O-E)^2/E 8.5 0.3 0.2 0.3 0.8 0.2 4.4 0.0 0.7 1.7 0.2 Birthday Spacings: Sum(O-E)^2/E= 17.339, p= 0.933 RESULTS OF GCD FOR dh-ranFile-2015-08-27_17:31 Euclid's algorithm: p-value, steps to gcd: 0.293542 p-value, dist. of gcd's: 0.330898 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-08-27_17:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.757 0.864 0.750 0.699 0.738 0.825 0.655 0.848 Bits 8 to 15---> 0.444 0.892 0.760 0.261 0.295 0.056 0.370 0.721 Bits 16 to 23---> 0.029 0.305 0.165 0.734 0.166 0.617 0.527 0.041 Bits 24 to 31---> 0.045 0.971 0.509 0.899 0.466 0.664 0.487 0.362 KS test for the above 32 p values: 0.313 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-08-27_17:31, p-values for 5 runs: 0.9456, 0.9487, 0.9386, 0.3244, 0.3788 Rank test for binary matrices (31x31) for dh-ranFile-2015-08-27_17:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 187 211.4 2.820 2.820 r= 29 5108 5134.0 0.132 2.952 r= 30 23190 23103.0 0.327 3.279 r= 31 11515 11551.5 0.115 3.395 chi-square = 3.395 with df = 3; p-value = 0.665 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-08-27_17:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 219 211.4 0.272 0.272 r= 30 5148 5134.0 0.038 0.310 r= 31 23080 23103.0 0.023 0.333 r= 32 11553 11551.5 0.000 0.333 chi-square = 0.333 with df = 3; p-value = 0.046 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-08-27_17:31 b-rank test for bits 1 to 8, p=0.58404 b-rank test for bits 2 to 9, p=0.90644 b-rank test for bits 3 to 10, p=0.25191 b-rank test for bits 4 to 11, p=0.53834 b-rank test for bits 5 to 12, p=0.69682 b-rank test for bits 6 to 13, p=0.96773 b-rank test for bits 7 to 14, p=0.75901 b-rank test for bits 8 to 15, p=0.42429 b-rank test for bits 9 to 16, p=0.81159 b-rank test for bits 10 to 17, p=0.84183 b-rank test for bits 11 to 18, p=0.58886 b-rank test for bits 12 to 19, p=0.13536 b-rank test for bits 13 to 20, p=0.37757 b-rank test for bits 14 to 21, p=0.35603 b-rank test for bits 15 to 22, p=0.75067 b-rank test for bits 16 to 23, p=0.61065 b-rank test for bits 17 to 24, p=0.50330 b-rank test for bits 18 to 25, p=0.06894 b-rank test for bits 19 to 26, p=0.42307 b-rank test for bits 20 to 27, p=0.00418 b-rank test for bits 21 to 28, p=0.42986 b-rank test for bits 22 to 29, p=0.36545 b-rank test for bits 23 to 30, p=0.20253 b-rank test for bits 24 to 31, p=0.75410 b-rank test for bits 25 to 32, p=0.51598 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 = 0.794839 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-08-27_17:31 (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 141614 -0.69 0.245090 2 142372 1.08 0.860153 3 142392 1.13 0.870284 4 141752 -0.37 0.356588 5 141316 -1.39 0.082830 6 141753 -0.37 0.357460 7 142205 0.69 0.755160 8 142106 0.46 0.677066 9 141387 -1.22 0.111157 10 142185 0.64 0.740241 11 141777 -0.31 0.378591 12 142294 0.90 0.815610 13 142162 0.59 0.722522 14 141325 -1.37 0.086086 15 142008 0.23 0.591163 16 142116 0.48 0.685407 17 141652 -0.60 0.273841 18 142594 1.60 0.945167 19 141676 -0.55 0.292821 20 142170 0.61 0.728752 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-08-27_17:31 Bits used No. missing words z-score p-value 23 to 32 142194 0.9816 0.836857 22 to 31 142035 0.4333 0.667618 21 to 30 141880 -0.1011 0.459721 20 to 29 141563 -1.1942 0.116192 19 to 28 141979 0.2402 0.594928 18 to 27 141708 -0.6942 0.243765 17 to 26 141552 -1.2322 0.108942 16 to 25 142086 0.6092 0.728806 15 to 24 141721 -0.6494 0.258036 14 to 23 141621 -0.9942 0.160053 13 to 22 141453 -1.5736 0.057796 12 to 21 142128 0.7540 0.774586 11 to 20 142122 0.7333 0.768326 10 to 19 141853 -0.1942 0.422994 9 to 18 141572 -1.1632 0.122373 8 to 17 141932 0.0782 0.531155 7 to 16 141569 -1.1736 0.120287 6 to 15 141034 -3.0184 0.001271 5 to 14 141705 -0.7046 0.240534 4 to 13 141618 -1.0046 0.157548 3 to 12 141898 -0.0391 0.484418 2 to 11 142319 1.4127 0.921121 1 to 10 141884 -0.0873 0.465199 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-08-27_17:31 Bits used No. missing words z-score p-value 28 to 32 141618 -0.9876 0.161684 27 to 31 142156 0.8362 0.798470 26 to 30 141587 -1.0926 0.137275 25 to 29 141903 -0.0215 0.491440 24 to 28 141591 -1.0791 0.140275 23 to 27 141894 -0.0520 0.479278 22 to 26 142363 1.5379 0.937959 21 to 25 141959 0.1684 0.566855 20 to 24 142011 0.3446 0.634819 19 to 23 142001 0.3107 0.622003 18 to 22 141601 -1.0452 0.147968 17 to 21 141687 -0.7537 0.225526 16 to 20 141953 0.1480 0.558842 15 to 19 141325 -1.9808 0.023808 14 to 18 141670 -0.8113 0.208600 13 to 17 141443 -1.5808 0.056964 12 to 16 141759 -0.5096 0.305168 11 to 15 142399 1.6599 0.951533 10 to 14 141701 -0.7062 0.240031 9 to 13 141649 -0.8825 0.188760 8 to 12 141574 -1.1367 0.127829 7 to 11 142106 0.6667 0.747511 6 to 10 142045 0.4599 0.677205 5 to 9 141744 -0.5604 0.287589 4 to 8 141363 -1.8520 0.032015 3 to 7 142337 1.4497 0.926433 2 to 6 141853 -0.1909 0.424283 1 to 5 141697 -0.7198 0.235836 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-08-27_17:31 Bits used No. missing words z-score p-value 31 to 32 141719 -0.5614 0.287247 30 to 31 141950 0.1200 0.547747 29 to 30 141698 -0.6234 0.266513 28 to 29 141828 -0.2399 0.405199 27 to 28 142573 1.9577 0.974869 26 to 27 141594 -0.9302 0.176140 25 to 26 142553 1.8987 0.971200 24 to 25 141798 -0.3284 0.371302 23 to 24 141817 -0.2724 0.392673 22 to 23 141793 -0.3432 0.365740 21 to 22 141789 -0.3550 0.361311 20 to 21 142033 0.3648 0.642373 19 to 20 141749 -0.4729 0.318125 18 to 19 142036 0.3737 0.645671 17 to 18 141871 -0.1131 0.454988 16 to 17 142094 0.5447 0.707037 15 to 16 141673 -0.6971 0.242858 14 to 15 141659 -0.7384 0.230125 13 to 14 141901 -0.0246 0.490198 12 to 13 141746 -0.4818 0.314974 11 to 12 142018 0.3206 0.625728 10 to 11 142193 0.8368 0.798643 9 to 10 141794 -0.3402 0.366851 8 to 9 142357 1.3206 0.906676 7 to 8 141217 -2.0423 0.020562 6 to 7 141213 -2.0541 0.019984 5 to 6 142488 1.7070 0.956088 4 to 5 141199 -2.0954 0.018069 3 to 4 141850 -0.1750 0.430534 2 to 3 142018 0.3206 0.625728 1 to 2 142288 1.1170 0.868007 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-08-27_17:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2528.04 0.397 0.654162 Test results for specific bytes for dh-ranFile-2015-08-27_17:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2435.36 -0.914 0.180334 2 to 9 2513.96 0.197 0.578251 3 to 10 2503.89 0.055 0.521912 4 to 11 2579.98 1.131 0.870991 5 to 12 2444.57 -0.784 0.216544 6 to 13 2439.83 -0.851 0.197408 7 to 14 2522.47 0.318 0.624666 8 to 15 2498.74 -0.018 0.492897 9 to 16 2571.06 1.005 0.842521 10 to 17 2658.03 2.235 0.987285 11 to 18 2476.70 -0.329 0.370910 12 to 19 2446.59 -0.755 0.225010 13 to 20 2443.52 -0.799 0.212211 14 to 21 2459.13 -0.578 0.281651 15 to 22 2452.43 -0.673 0.250563 16 to 23 2567.09 0.949 0.828650 17 to 24 2552.37 0.741 0.770540 18 to 25 2392.94 -1.514 0.065014 19 to 26 2548.65 0.688 0.754292 20 to 27 2467.14 -0.465 0.321093 21 to 28 2483.87 -0.228 0.409798 22 to 29 2635.01 1.909 0.971891 23 to 30 2609.40 1.547 0.939083 24 to 31 2504.17 0.059 0.523519 25 to 32 2437.30 -0.887 0.187610 CDPARK for dh-ranFile-2015-08-27_17:31: 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 3517 -0.2740 0.392053 3532 0.4110 0.659449 3518 -0.2283 0.409702 3547 1.0959 0.863437 3508 -0.6849 0.246694 3564 1.8721 0.969407 3519 -0.1826 0.427537 3535 0.5479 0.708135 3552 1.3242 0.907282 3526 0.1370 0.554479 Square side=100, avg. no. parked=3531.80 sample std.=16.91 p-value of the KSTEST for those 10 p-values: 0.345572 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-08-27_17:31 0.5921,0.6017,0.3820,0.9789,0.3243,0.9782,0.4774,0.3937,0.7136,0.2861, The KS test for those 10 p-values: 0.314774 The 3DSPHERES test for dh-ranFile-2015-08-27_17:31 sample no r^3 equiv. uni. 1 4.021 0.125452 2 63.762 0.880615 3 60.560 0.867169 4 21.798 0.516443 5 72.826 0.911746 6 40.404 0.739929 7 50.347 0.813298 8 10.815 0.302670 9 30.259 0.635289 10 7.781 0.228455 11 3.970 0.123955 12 26.680 0.589067 13 17.245 0.437196 14 4.543 0.140515 15 37.933 0.717605 16 2.084 0.067103 17 8.946 0.257854 18 24.378 0.556299 19 8.867 0.255891 20 30.171 0.634213 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.952192 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-08-27_17:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -0.3 0.1 0.6 0.3 0.1 -0.7 -0.0 -0.7 -0.9 -0.7 0.3 1.3 -1.9 0.5 0.2 -0.5 -1.3 0.1 1.3 1.3 -0.6 1.2 1.4 -0.3 -0.3 -1.7 0.1 1.2 -0.4 -0.6 -0.4 0.7 1.1 0.3 -0.1 -0.2 -0.7 -0.4 -0.1 1.6 0.0 -0.1 Chi-square with 42 degrees of freedom:28.531187 z-score=-1.469568, p-value=0.055943 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-08-27_17:31 Test no p-value 1 0.517882 2 0.089277 3 0.093791 4 0.336915 5 0.882662 6 0.145773 7 0.144297 8 0.309964 9 0.626872 10 0.418146 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.179877 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-08-27_17:31: (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 66600 0.07 66467 0.60 3 25000.00 25114 0.52 25096 0.37 4 6666.67 6692 0.10 6741 0.83 5 1388.89 1335 2.09 1420 0.70 6 238.10 222 1.09 237 0.01 7 34.72 30 0.64 34 0.01 8 4.96 6 0.22 4 0.19 p=0.42000 p=0.15432 Number of rngs required: 690504, p-value: 0.994 RESULTS OF CRAPS TEST for dh-ranFile-2015-08-27_17:31 No. of wins: Observed Expected 98809 98585.9 z-score= 0.998, pvalue=0.84086 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66808 66666.7 0.300 0.300 2 37691 37654.3 0.036 0.335 3 26893 26954.7 0.141 0.477 4 19206 19313.5 0.598 1.075 5 14043 13851.4 2.650 3.724 6 9823 9943.5 1.461 5.186 7 7103 7145.0 0.247 5.433 8 5174 5139.1 0.237 5.670 9 3667 3699.9 0.292 5.962 10 2601 2666.3 1.599 7.561 11 1968 1923.3 1.038 8.599 12 1350 1388.7 1.081 9.680 13 1032 1003.7 0.797 10.477 14 693 726.1 1.513 11.989 15 552 525.8 1.302 13.291 16 376 381.2 0.070 13.361 17 271 276.5 0.111 13.472 18 199 200.8 0.017 13.488 19 163 146.0 1.983 15.472 20 120 106.2 1.789 17.261 21 267 287.1 1.409 18.670 Chisq= 18.67 for 20 degrees of freedom, p= 0.45662 SUMMARY of craptest p-value for no. of wins: 0.840865 p-value for throws/game: 0.456620 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-08-27_17:31 No. of wins: Observed Expected 98257 98585.9 z-score=-1.471, pvalue=0.07067 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66625 66666.7 0.026 0.026 2 37707 37654.3 0.074 0.100 3 27082 26954.7 0.601 0.701 4 19375 19313.5 0.196 0.897 5 13734 13851.4 0.995 1.892 6 9963 9943.5 0.038 1.930 7 7117 7145.0 0.110 2.040 8 5045 5139.1 1.722 3.762 9 3700 3699.9 0.000 3.762 10 2641 2666.3 0.240 4.002 11 1977 1923.3 1.498 5.500 12 1406 1388.7 0.215 5.714 13 1026 1003.7 0.495 6.209 14 755 726.1 1.147 7.356 15 465 525.8 7.038 14.394 16 360 381.2 1.174 15.568 17 262 276.5 0.764 16.333 18 181 200.8 1.958 18.291 19 148 146.0 0.028 18.318 20 111 106.2 0.216 18.534 21 320 287.1 3.767 22.301 Chisq= 22.30 for 20 degrees of freedom, p= 0.67558 SUMMARY of craptest p-value for no. of wins: 0.070666 p-value for throws/game: 0.675579 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0013,0.0042,0.0181,0.0200,0.0206,0.0238,0.0291,0.0320,0.0406,0.0446, 0.0463,0.0559,0.0559,0.0570,0.0578,0.0650,0.0671,0.0689,0.0707,0.0828, 0.0861,0.0893,0.0938,0.1089,0.1112,0.1162,0.1203,0.1224,0.1240,0.1255, 0.1278,0.1354,0.1373,0.1403,0.1405,0.1443,0.1458,0.1480,0.1543,0.1575, 0.1601,0.1617,0.1655,0.1660,0.1761,0.1799,0.1803,0.1876,0.1888,0.1974, 0.2025,0.2086,0.2122,0.2165,0.2250,0.2255,0.2285,0.2301,0.2358,0.2400, 0.2405,0.2429,0.2438,0.2442,0.2451,0.2467,0.2506,0.2519,0.2559,0.2579, 0.2580,0.2612,0.2665,0.2738,0.2817,0.2861,0.2872,0.2876,0.2928,0.2935, 0.2947,0.3027,0.3051,0.3052,0.3100,0.3131,0.3148,0.3150,0.3181,0.3211, 0.3243,0.3244,0.3309,0.3369,0.3456,0.3560,0.3566,0.3575,0.3613,0.3623, 0.3655,0.3657,0.3669,0.3704,0.3709,0.3713,0.3776,0.3786,0.3788,0.3820, 0.3921,0.3927,0.3937,0.3956,0.4022,0.4052,0.4097,0.4098,0.4109,0.4181, 0.4200,0.4230,0.4231,0.4243,0.4243,0.4275,0.4299,0.4305,0.4372,0.4436, 0.4550,0.4566,0.4597,0.4652,0.4663,0.4774,0.4793,0.4844,0.4865,0.4902, 0.4914,0.4929,0.5033,0.5086,0.5160,0.5164,0.5179,0.5219,0.5235,0.5274, 0.5312,0.5383,0.5477,0.5545,0.5563,0.5588,0.5631,0.5669,0.5783,0.5840, 0.5886,0.5889,0.5891,0.5912,0.5921,0.5949,0.6017,0.6106,0.6171,0.6220, 0.6247,0.6257,0.6257,0.6269,0.6342,0.6348,0.6353,0.6424,0.6457,0.6489, 0.6542,0.6550,0.6594,0.6644,0.6653,0.6676,0.6756,0.6771,0.6772,0.6833, 0.6854,0.6968,0.6987,0.7070,0.7081,0.7136,0.7176,0.7212,0.7225,0.7288, 0.7288,0.7337,0.7380,0.7399,0.7402,0.7475,0.7502,0.7506,0.7507,0.7541, 0.7543,0.7552,0.7566,0.7590,0.7604,0.7683,0.7705,0.7746,0.7948,0.7985, 0.7986,0.8116,0.8133,0.8156,0.8249,0.8287,0.8369,0.8409,0.8418,0.8425, 0.8478,0.8602,0.8634,0.8642,0.8672,0.8680,0.8703,0.8710,0.8806,0.8807, 0.8827,0.8920,0.8994,0.9064,0.9067,0.9073,0.9117,0.9211,0.9264,0.9328, 0.9380,0.9386,0.9391,0.9452,0.9456,0.9487,0.9515,0.9522,0.9561,0.9677, 0.9694,0.9706,0.9712,0.9719,0.9749,0.9782,0.9789,0.9873,0.9939, Overall p-value after applying KStest on 269 p-values = 0.786102 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.