RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-05-08_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 15.60 29.5160 0.969945 2 to 25 15.34 27.6332 0.950589 3 to 26 15.55 30.9795 0.979913 4 to 27 15.93 14.3314 0.356480 5 to 28 15.75 17.1082 0.552944 6 to 29 15.64 17.4149 0.573386 7 to 30 15.98 26.5127 0.934388 8 to 31 16.24 18.0066 0.611575 9 to 32 15.73 17.7768 0.596949 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.013510 Tough bday spacings test for dh-ranFile-2016-05-08_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 16 38 79 104 101 75 38 24 16 5 4 (O-E)^2/E 5.1 0.1 0.4 0.4 0.1 0.1 3.8 1.1 0.1 0.4 0.0 Birthday Spacings: Sum(O-E)^2/E= 11.673, p= 0.692 RESULTS OF GCD FOR dh-ranFile-2016-05-08_05:31 Euclid's algorithm: p-value, steps to gcd: 0.848106 p-value, dist. of gcd's: 0.037234 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-05-08_05:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.625 0.980 0.864 0.895 0.400 0.409 0.246 0.123 Bits 8 to 15---> 0.238 0.070 0.901 0.163 0.411 0.731 0.421 0.788 Bits 16 to 23---> 0.142 0.594 0.325 0.112 0.728 0.374 0.768 0.937 Bits 24 to 31---> 0.582 0.907 0.441 0.260 0.286 0.962 0.834 0.090 KS test for the above 32 p values: 0.177 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-05-08_05:31, p-values for 5 runs: 0.9669, 0.4897, 0.0986, 0.1859, 0.6146 Rank test for binary matrices (31x31) for dh-ranFile-2016-05-08_05:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 238 211.4 3.342 3.342 r= 29 5050 5134.0 1.375 4.717 r= 30 23167 23103.0 0.177 4.894 r= 31 11545 11551.5 0.004 4.898 chi-square = 4.898 with df = 3; p-value = 0.821 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-05-08_05:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 229 211.4 1.462 1.462 r= 30 5195 5134.0 0.725 2.187 r= 31 22927 23103.0 1.342 3.528 r= 32 11649 11551.5 0.823 4.351 chi-square = 4.351 with df = 3; p-value = 0.774 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-05-08_05:31 b-rank test for bits 1 to 8, p=0.94181 b-rank test for bits 2 to 9, p=0.16530 b-rank test for bits 3 to 10, p=0.15994 b-rank test for bits 4 to 11, p=0.65643 b-rank test for bits 5 to 12, p=0.01938 b-rank test for bits 6 to 13, p=0.57785 b-rank test for bits 7 to 14, p=0.59812 b-rank test for bits 8 to 15, p=0.62246 b-rank test for bits 9 to 16, p=0.23310 b-rank test for bits 10 to 17, p=0.90768 b-rank test for bits 11 to 18, p=0.17649 b-rank test for bits 12 to 19, p=0.77079 b-rank test for bits 13 to 20, p=0.98246 b-rank test for bits 14 to 21, p=0.00297 b-rank test for bits 15 to 22, p=0.54155 b-rank test for bits 16 to 23, p=0.20303 b-rank test for bits 17 to 24, p=0.67821 b-rank test for bits 18 to 25, p=0.40236 b-rank test for bits 19 to 26, p=0.42984 b-rank test for bits 20 to 27, p=0.96137 b-rank test for bits 21 to 28, p=0.13041 b-rank test for bits 22 to 29, p=0.21442 b-rank test for bits 23 to 30, p=0.66563 b-rank test for bits 24 to 31, p=0.69256 b-rank test for bits 25 to 32, p=0.08889 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 = 0.643775 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-05-08_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 141578 -0.77 0.219425 2 142392 1.13 0.870284 3 141471 -1.02 0.152886 4 142027 0.27 0.608315 5 141174 -1.72 0.042893 6 142451 1.27 0.897169 7 141918 0.02 0.508081 8 141363 -1.28 0.100894 9 141109 -1.87 0.030747 10 141512 -0.93 0.176615 11 141671 -0.56 0.288816 12 142046 0.32 0.625259 13 141568 -0.80 0.212580 14 142609 1.63 0.948949 15 141840 -0.16 0.435658 16 141685 -0.52 0.300092 17 141246 -1.55 0.060590 18 142206 0.69 0.755894 19 142342 1.01 0.843971 20 141479 -1.01 0.157342 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-05-08_05:31 Bits used No. missing words z-score p-value 23 to 32 141614 -1.0184 0.154249 22 to 31 142377 1.6127 0.946590 21 to 30 141834 -0.2598 0.397525 20 to 29 142015 0.3644 0.642213 19 to 28 142025 0.3989 0.655003 18 to 27 141990 0.2782 0.609560 17 to 26 141684 -0.7770 0.218579 16 to 25 142065 0.5368 0.704295 15 to 24 142060 0.5196 0.698312 14 to 23 142315 1.3989 0.919073 13 to 22 141983 0.2540 0.600266 12 to 21 141317 -2.0425 0.020550 11 to 20 142098 0.6506 0.742343 10 to 19 141929 0.0678 0.527039 9 to 18 142296 1.3333 0.908791 8 to 17 142332 1.4575 0.927508 7 to 16 142050 0.4851 0.686186 6 to 15 142388 1.6506 0.950588 5 to 14 141996 0.2989 0.617477 4 to 13 142020 0.3816 0.648629 3 to 12 141233 -2.3322 0.009846 2 to 11 141930 0.0713 0.528411 1 to 10 141590 -1.1011 0.135418 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-05-08_05:31 Bits used No. missing words z-score p-value 28 to 32 141779 -0.4418 0.329318 27 to 31 142045 0.4599 0.677205 26 to 30 141245 -2.2520 0.012162 25 to 29 141581 -1.1130 0.132858 24 to 28 142340 1.4599 0.927841 23 to 27 141432 -1.6181 0.052824 22 to 26 141766 -0.4859 0.313532 21 to 25 142148 0.8091 0.790757 20 to 24 141880 -0.0994 0.460401 19 to 23 141702 -0.7028 0.241086 18 to 22 142201 0.9887 0.838598 17 to 21 142276 1.2429 0.893057 16 to 20 141615 -0.9977 0.159205 15 to 19 141636 -0.9265 0.177082 14 to 18 141586 -1.0960 0.136532 13 to 17 142179 0.9141 0.819677 12 to 16 141846 -0.2147 0.415009 11 to 15 141819 -0.3062 0.379725 10 to 14 141681 -0.7740 0.219465 9 to 13 141738 -0.5808 0.280695 8 to 12 141853 -0.1909 0.424283 7 to 11 141465 -1.5062 0.066008 6 to 10 142591 2.3107 0.989577 5 to 9 141727 -0.6181 0.268265 4 to 8 141928 0.0633 0.525232 3 to 7 141987 0.2633 0.603836 2 to 6 141642 -0.9062 0.182414 1 to 5 141706 -0.6893 0.245332 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-05-08_05:31 Bits used No. missing words z-score p-value 31 to 32 141844 -0.1927 0.423592 30 to 31 141757 -0.4494 0.326589 29 to 30 141925 0.0462 0.518434 28 to 29 141520 -1.1485 0.125388 27 to 28 141678 -0.6824 0.247496 26 to 27 141729 -0.5319 0.297381 25 to 26 142136 0.6686 0.748138 24 to 25 141726 -0.5408 0.294324 23 to 24 141826 -0.2458 0.402914 22 to 23 142050 0.4150 0.660913 21 to 22 141846 -0.1868 0.425903 20 to 21 141701 -0.6145 0.269428 19 to 20 142196 0.8456 0.801122 18 to 19 142080 0.5035 0.692677 17 to 18 142373 1.3678 0.914306 16 to 17 141850 -0.1750 0.430534 15 to 16 141931 0.0639 0.525484 14 to 15 141734 -0.5172 0.302509 13 to 14 141581 -0.9685 0.166391 12 to 13 141497 -1.2163 0.111933 11 to 12 141886 -0.0688 0.472566 10 to 11 141738 -0.5054 0.306640 9 to 10 141710 -0.5880 0.278268 8 to 9 142177 0.7896 0.785116 7 to 8 142337 1.2616 0.896447 6 to 7 142103 0.5713 0.716101 5 to 6 141525 -1.1337 0.128457 4 to 5 142199 0.8545 0.803582 3 to 4 141987 0.2291 0.590610 2 to 3 142303 1.1613 0.877234 1 to 2 141443 -1.3756 0.084472 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-05-08_05:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2542.66 0.603 0.726854 Test results for specific bytes for dh-ranFile-2016-05-08_05:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2534.91 0.494 0.689236 2 to 9 2506.09 0.086 0.534329 3 to 10 2534.60 0.489 0.687693 4 to 11 2622.57 1.733 0.958485 5 to 12 2368.93 -1.854 0.031901 6 to 13 2373.49 -1.789 0.036798 7 to 14 2421.64 -1.108 0.133892 8 to 15 2609.29 1.546 0.938899 9 to 16 2406.35 -1.324 0.092674 10 to 17 2453.30 -0.660 0.254502 11 to 18 2606.46 1.506 0.933918 12 to 19 2499.61 -0.006 0.497788 13 to 20 2306.47 -2.737 0.003100 14 to 21 2601.77 1.439 0.924956 15 to 22 2485.02 -0.212 0.416090 16 to 23 2629.93 1.838 0.966933 17 to 24 2436.96 -0.891 0.186334 18 to 25 2489.96 -0.142 0.443567 19 to 26 2414.30 -1.212 0.112747 20 to 27 2520.70 0.293 0.615165 21 to 28 2520.26 0.286 0.612745 22 to 29 2581.00 1.146 0.874014 23 to 30 2601.66 1.438 0.924733 24 to 31 2436.07 -0.904 0.182977 25 to 32 2497.92 -0.029 0.488274 CDPARK for dh-ranFile-2016-05-08_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 3540 0.7763 0.781201 3482 -1.8721 0.030593 3557 1.5525 0.939730 3537 0.6393 0.738676 3510 -0.5936 0.276387 3516 -0.3196 0.374623 3520 -0.1370 0.445521 3525 0.0913 0.536383 3490 -1.5068 0.065925 3513 -0.4566 0.323972 Square side=100, avg. no. parked=3519.00 sample std.=21.41 p-value of the KSTEST for those 10 p-values: 0.910957 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-05-08_05:31 0.1619,0.0459,0.1941,0.3261,0.1652,0.6640,0.7048,0.8505,0.1976,0.6380, The KS test for those 10 p-values: 0.334056 The 3DSPHERES test for dh-ranFile-2016-05-08_05:31 sample no r^3 equiv. uni. 1 63.541 0.879731 2 50.930 0.816892 3 49.265 0.806437 4 47.883 0.797311 5 56.903 0.849945 6 60.734 0.867935 7 128.498 0.986202 8 13.702 0.366651 9 13.798 0.368664 10 9.402 0.269040 11 13.846 0.369689 12 1.157 0.037831 13 15.848 0.410372 14 46.813 0.789955 15 1.894 0.061176 16 37.335 0.711914 17 6.442 0.193245 18 7.265 0.215076 19 9.427 0.269649 20 13.812 0.368965 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.629536 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-05-08_05:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 1.8 -1.1 -1.6 -1.9 -1.2 -1.3 -1.7 -0.4 0.6 1.3 0.8 1.1 1.2 0.2 -0.6 0.6 -1.2 0.2 -0.1 -0.3 -0.2 0.3 -1.5 -0.5 0.4 1.1 -0.2 -2.2 1.3 1.2 -0.4 1.5 -1.6 -0.6 -0.5 1.0 2.1 -2.0 -1.3 -1.3 -1.0 -0.1 Chi-square with 42 degrees of freedom:56.173977 z-score=1.546508, p-value=0.929401 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-05-08_05:31 Test no p-value 1 0.626081 2 0.012461 3 0.247329 4 0.038709 5 0.960575 6 0.915653 7 0.742704 8 0.955901 9 0.059542 10 0.049617 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.069230 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-05-08_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 66707 0.02 66658 0.00 3 25000.00 24999 0.00 25075 0.23 4 6666.67 6673 0.01 6590 0.88 5 1388.89 1344 1.45 1403 0.14 6 238.10 244 0.15 227 0.52 7 34.72 27 1.72 44 2.48 8 4.96 5 0.00 2 1.77 p=0.23549 p=0.57850 Number of rngs required: 688332, p-value: 0.467 RESULTS OF CRAPS TEST for dh-ranFile-2016-05-08_05:31 No. of wins: Observed Expected 98233 98585.9 z-score=-1.578, pvalue=0.05726 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66471 66666.7 0.574 0.574 2 37928 37654.3 1.989 2.563 3 26965 26954.7 0.004 2.567 4 19292 19313.5 0.024 2.591 5 13823 13851.4 0.058 2.650 6 10034 9943.5 0.823 3.472 7 7091 7145.0 0.409 3.881 8 5202 5139.1 0.771 4.651 9 3592 3699.9 3.145 7.796 10 2641 2666.3 0.240 8.036 11 1896 1923.3 0.388 8.424 12 1386 1388.7 0.005 8.430 13 980 1003.7 0.560 8.990 14 712 726.1 0.275 9.266 15 540 525.8 0.382 9.647 16 395 381.2 0.503 10.150 17 307 276.5 3.355 13.506 18 200 200.8 0.003 13.509 19 150 146.0 0.110 13.619 20 113 106.2 0.433 14.053 21 282 287.1 0.091 14.144 Chisq= 14.14 for 20 degrees of freedom, p= 0.17687 SUMMARY of craptest p-value for no. of wins: 0.057261 p-value for throws/game: 0.176874 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-05-08_05:31 No. of wins: Observed Expected 98730 98585.9 z-score= 0.645, pvalue=0.74043 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67108 66666.7 2.922 2.922 2 37661 37654.3 0.001 2.923 3 26819 26954.7 0.683 3.606 4 19118 19313.5 1.978 5.584 5 13754 13851.4 0.685 6.270 6 9940 9943.5 0.001 6.271 7 7106 7145.0 0.213 6.484 8 5136 5139.1 0.002 6.486 9 3764 3699.9 1.112 7.598 10 2609 2666.3 1.231 8.829 11 1888 1923.3 0.649 9.478 12 1354 1388.7 0.869 10.347 13 1033 1003.7 0.854 11.201 14 710 726.1 0.359 11.560 15 529 525.8 0.019 11.579 16 408 381.2 1.891 13.471 17 289 276.5 0.561 14.032 18 192 200.8 0.388 14.420 19 155 146.0 0.557 14.977 20 117 106.2 1.095 16.072 21 310 287.1 1.824 17.896 Chisq= 17.90 for 20 degrees of freedom, p= 0.40576 SUMMARY of craptest p-value for no. of wins: 0.740434 p-value for throws/game: 0.405762 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0030,0.0031,0.0098,0.0122,0.0125,0.0135,0.0194,0.0206,0.0306,0.0307, 0.0319,0.0368,0.0372,0.0378,0.0387,0.0429,0.0459,0.0496,0.0528,0.0573, 0.0595,0.0606,0.0612,0.0659,0.0660,0.0692,0.0698,0.0845,0.0889,0.0901, 0.0927,0.0986,0.1009,0.1117,0.1119,0.1127,0.1228,0.1254,0.1285,0.1304, 0.1329,0.1339,0.1354,0.1365,0.1416,0.1529,0.1542,0.1573,0.1592,0.1599, 0.1619,0.1633,0.1652,0.1653,0.1664,0.1765,0.1766,0.1769,0.1771,0.1774, 0.1824,0.1830,0.1859,0.1863,0.1932,0.1941,0.1976,0.2030,0.2126,0.2144, 0.2151,0.2186,0.2194,0.2195,0.2331,0.2355,0.2381,0.2411,0.2453,0.2458, 0.2473,0.2475,0.2545,0.2605,0.2683,0.2690,0.2694,0.2696,0.2764,0.2783, 0.2807,0.2861,0.2888,0.2943,0.2974,0.3001,0.3025,0.3066,0.3135,0.3240, 0.3250,0.3261,0.3266,0.3293,0.3341,0.3565,0.3667,0.3687,0.3690,0.3697, 0.3741,0.3746,0.3797,0.3975,0.4004,0.4024,0.4029,0.4058,0.4091,0.4104, 0.4106,0.4150,0.4161,0.4211,0.4236,0.4243,0.4259,0.4298,0.4305,0.4357, 0.4405,0.4436,0.4455,0.4604,0.4675,0.4726,0.4883,0.4897,0.4978,0.5081, 0.5184,0.5252,0.5255,0.5270,0.5284,0.5343,0.5364,0.5416,0.5529,0.5734, 0.5778,0.5785,0.5821,0.5906,0.5938,0.5969,0.5981,0.6003,0.6038,0.6083, 0.6096,0.6116,0.6127,0.6146,0.6152,0.6175,0.6225,0.6251,0.6253,0.6261, 0.6295,0.6380,0.6422,0.6438,0.6486,0.6550,0.6564,0.6609,0.6640,0.6656, 0.6772,0.6782,0.6862,0.6877,0.6892,0.6924,0.6926,0.6927,0.6983,0.7043, 0.7048,0.7119,0.7161,0.7269,0.7280,0.7306,0.7387,0.7404,0.7423,0.7427, 0.7481,0.7559,0.7678,0.7708,0.7740,0.7812,0.7851,0.7877,0.7900,0.7908, 0.7973,0.8011,0.8036,0.8064,0.8169,0.8197,0.8206,0.8343,0.8386,0.8440, 0.8481,0.8499,0.8505,0.8636,0.8679,0.8703,0.8740,0.8772,0.8797,0.8931, 0.8953,0.8964,0.8972,0.9008,0.9068,0.9077,0.9088,0.9110,0.9143,0.9157, 0.9191,0.9247,0.9250,0.9275,0.9278,0.9294,0.9339,0.9344,0.9370,0.9389, 0.9397,0.9418,0.9466,0.9489,0.9506,0.9506,0.9559,0.9585,0.9606,0.9614, 0.9618,0.9669,0.9669,0.9699,0.9797,0.9799,0.9825,0.9862,0.9896, Overall p-value after applying KStest on 269 p-values = 0.212894 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.