RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-09-17_04:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.78 26.0952 0.927256 2 to 25 15.60 20.9649 0.772135 3 to 26 15.91 28.9768 0.965259 4 to 27 15.77 12.2284 0.213885 5 to 28 15.81 12.7533 0.247463 6 to 29 15.63 23.5176 0.866855 7 to 30 15.68 12.8459 0.253558 8 to 31 15.82 16.0721 0.481268 9 to 32 15.44 41.9710 0.999323 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.075379 Tough bday spacings test for dh-ranFile-2016-09-17_04:31: 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 8 40 75 110 82 62 57 38 22 4 2 (O-E)^2/E 0.1 0.3 0.0 1.6 2.5 3.3 0.5 2.3 3.4 1.0 1.0 Birthday Spacings: Sum(O-E)^2/E= 16.126, p= 0.904 RESULTS OF GCD FOR dh-ranFile-2016-09-17_04:31 Euclid's algorithm: p-value, steps to gcd: 0.743169 p-value, dist. of gcd's: 0.514563 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-09-17_04:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.923 0.591 0.689 0.614 0.695 0.208 0.058 0.181 Bits 8 to 15---> 0.102 0.538 0.190 0.101 0.073 0.738 0.111 0.104 Bits 16 to 23---> 0.567 0.628 0.008 0.212 0.807 0.619 0.835 0.974 Bits 24 to 31---> 0.303 0.186 0.578 0.215 0.790 0.782 0.433 0.278 KS test for the above 32 p values: 0.707 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-09-17_04:31, p-values for 5 runs: 0.6298, 0.2859, 0.4085, 0.7427, 0.4898 Rank test for binary matrices (31x31) for dh-ranFile-2016-09-17_04:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 212 211.4 0.002 0.002 r= 29 5115 5134.0 0.070 0.072 r= 30 23103 23103.0 0.000 0.072 r= 31 11570 11551.5 0.030 0.102 chi-square = 0.102 with df = 3; p-value = 0.008 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-09-17_04:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 211 211.4 0.001 0.001 r= 30 5078 5134.0 0.611 0.612 r= 31 23236 23103.0 0.765 1.377 r= 32 11475 11551.5 0.507 1.884 chi-square = 1.884 with df = 3; p-value = 0.403 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-09-17_04:31 b-rank test for bits 1 to 8, p=0.55243 b-rank test for bits 2 to 9, p=0.30721 b-rank test for bits 3 to 10, p=0.63583 b-rank test for bits 4 to 11, p=0.94066 b-rank test for bits 5 to 12, p=0.38916 b-rank test for bits 6 to 13, p=0.82924 b-rank test for bits 7 to 14, p=0.97484 b-rank test for bits 8 to 15, p=0.93649 b-rank test for bits 9 to 16, p=0.24595 b-rank test for bits 10 to 17, p=0.64551 b-rank test for bits 11 to 18, p=0.01502 b-rank test for bits 12 to 19, p=0.86106 b-rank test for bits 13 to 20, p=0.91469 b-rank test for bits 14 to 21, p=0.45041 b-rank test for bits 15 to 22, p=0.15841 b-rank test for bits 16 to 23, p=0.75222 b-rank test for bits 17 to 24, p=0.30540 b-rank test for bits 18 to 25, p=0.88064 b-rank test for bits 19 to 26, p=0.41961 b-rank test for bits 20 to 27, p=0.28415 b-rank test for bits 21 to 28, p=0.35153 b-rank test for bits 22 to 29, p=0.39716 b-rank test for bits 23 to 30, p=0.96900 b-rank test for bits 24 to 31, p=0.95196 b-rank test for bits 25 to 32, p=0.91787 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 = 0.056177 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-09-17_04:31 (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 141963 0.13 0.549895 2 141216 -1.62 0.052624 3 141885 -0.06 0.477334 4 141863 -0.11 0.456900 5 142109 0.47 0.679578 6 141560 -0.82 0.207195 7 141647 -0.61 0.269964 8 141903 -0.01 0.494100 9 142133 0.52 0.699371 10 142945 2.42 0.992235 11 142385 1.11 0.866797 12 142125 0.50 0.692835 13 141672 -0.55 0.289615 14 141857 -0.12 0.451344 15 141036 -2.04 0.020651 16 141476 -1.01 0.155661 17 141554 -0.83 0.203210 18 142305 0.92 0.822377 19 141997 0.20 0.581150 20 142273 0.85 0.802253 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-09-17_04:31 Bits used No. missing words z-score p-value 23 to 32 142190 0.9678 0.833435 22 to 31 141830 -0.2736 0.392215 21 to 30 141639 -0.9322 0.175624 20 to 29 142205 1.0196 0.846029 19 to 28 142043 0.4609 0.677576 18 to 27 141717 -0.6632 0.253599 17 to 26 142236 1.1264 0.870012 16 to 25 141560 -1.2046 0.114182 15 to 24 142071 0.5575 0.711401 14 to 23 142293 1.3230 0.907082 13 to 22 141825 -0.2908 0.385605 12 to 21 142131 0.7644 0.777679 11 to 20 141587 -1.1115 0.133180 10 to 19 142151 0.8333 0.797675 9 to 18 142325 1.4333 0.924120 8 to 17 141659 -0.8632 0.194012 7 to 16 141570 -1.1701 0.120980 6 to 15 141597 -1.0770 0.140740 5 to 14 141572 -1.1632 0.122373 4 to 13 141713 -0.6770 0.249203 3 to 12 141415 -1.7046 0.044136 2 to 11 141761 -0.5115 0.304507 1 to 10 141728 -0.6253 0.265895 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-09-17_04:31 Bits used No. missing words z-score p-value 28 to 32 141517 -1.3299 0.091770 27 to 31 141771 -0.4689 0.319565 26 to 30 141914 0.0158 0.506315 25 to 29 142164 0.8633 0.806011 24 to 28 141414 -1.6791 0.046568 23 to 27 142294 1.3040 0.903877 22 to 26 141289 -2.1028 0.017741 21 to 25 141770 -0.4723 0.318355 20 to 24 141612 -1.0079 0.156752 19 to 23 141696 -0.7232 0.234793 18 to 22 142549 2.1684 0.984935 17 to 21 141941 0.1074 0.542747 16 to 20 141669 -0.8147 0.207628 15 to 19 141800 -0.3706 0.355464 14 to 18 141995 0.2904 0.614248 13 to 17 141891 -0.0621 0.475227 12 to 16 142437 1.7887 0.963169 11 to 15 141754 -0.5265 0.299256 10 to 14 141971 0.2091 0.582796 9 to 13 141784 -0.4248 0.335474 8 to 12 142026 0.3955 0.653760 7 to 11 142315 1.3752 0.915458 6 to 10 141899 -0.0350 0.486033 5 to 9 141312 -2.0248 0.021442 4 to 8 141574 -1.1367 0.127829 3 to 7 141896 -0.0452 0.481979 2 to 6 142167 0.8735 0.808793 1 to 5 141920 0.0362 0.514426 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-09-17_04:31 Bits used No. missing words z-score p-value 31 to 32 142200 0.8574 0.804397 30 to 31 140968 -2.7768 0.002745 29 to 30 142218 0.9105 0.818729 28 to 29 142497 1.7335 0.958500 27 to 28 142400 1.4474 0.926108 26 to 27 141700 -0.6175 0.268455 25 to 26 141643 -0.7856 0.216041 24 to 25 141669 -0.7089 0.239182 23 to 24 142078 0.4976 0.690600 22 to 23 141996 0.2557 0.600895 21 to 22 141699 -0.6204 0.267483 20 to 21 141244 -1.9626 0.024845 19 to 20 142202 0.8633 0.806023 18 to 19 142190 0.8279 0.796146 17 to 18 141576 -0.9833 0.162736 16 to 17 141961 0.1524 0.560572 15 to 16 142046 0.4032 0.656583 14 to 15 141637 -0.8033 0.210891 13 to 14 141766 -0.4228 0.336220 12 to 13 141857 -0.1544 0.438661 11 to 12 141514 -1.1662 0.121774 10 to 11 141794 -0.3402 0.366851 9 to 10 142154 0.7217 0.764773 8 to 9 142014 0.3088 0.621248 7 to 8 141400 -1.5024 0.066491 6 to 7 141960 0.1495 0.559408 5 to 6 141965 0.1642 0.565220 4 to 5 142473 1.6627 0.951818 3 to 4 141883 -0.0777 0.469045 2 to 3 142338 1.2645 0.896977 1 to 2 141988 0.2321 0.591756 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-09-17_04:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2552.19 0.738 0.769750 Test results for specific bytes for dh-ranFile-2016-09-17_04:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2389.62 -1.561 0.059263 2 to 9 2553.03 0.750 0.773369 3 to 10 2609.73 1.552 0.939647 4 to 11 2444.76 -0.781 0.217332 5 to 12 2558.28 0.824 0.795107 6 to 13 2516.31 0.231 0.591229 7 to 14 2625.44 1.774 0.961962 8 to 15 2578.12 1.105 0.865369 9 to 16 2439.09 -0.861 0.194509 10 to 17 2656.86 2.218 0.986736 11 to 18 2504.02 0.057 0.522660 12 to 19 2642.61 2.017 0.978139 13 to 20 2640.88 1.992 0.976835 14 to 21 2474.33 -0.363 0.358314 15 to 22 2534.46 0.487 0.686970 16 to 23 2600.50 1.421 0.922374 17 to 24 2582.60 1.168 0.878623 18 to 25 2539.78 0.563 0.713123 19 to 26 2522.56 0.319 0.625164 20 to 27 2492.09 -0.112 0.455478 21 to 28 2431.83 -0.964 0.167508 22 to 29 2513.55 0.192 0.575959 23 to 30 2493.17 -0.097 0.461505 24 to 31 2559.23 0.838 0.798892 25 to 32 2410.61 -1.264 0.103083 CDPARK for dh-ranFile-2016-09-17_04:31: 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 3496 -1.2329 0.108811 3541 0.8219 0.794438 3487 -1.6438 0.050105 3530 0.3196 0.625377 3510 -0.5936 0.276387 3511 -0.5479 0.291865 3524 0.0457 0.518210 3509 -0.6393 0.261324 3508 -0.6849 0.246694 3545 1.0046 0.842447 Square side=100, avg. no. parked=3516.10 sample std.=17.72 p-value of the KSTEST for those 10 p-values: 0.458598 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-09-17_04:31 0.0929,0.8307,0.7184,0.0755,0.3217,0.5898,0.3816,0.9720,0.4482,0.4858, The KS test for those 10 p-values: 0.989525 The 3DSPHERES test for dh-ranFile-2016-09-17_04:31 sample no r^3 equiv. uni. 1 83.393 0.937947 2 16.579 0.424562 3 74.970 0.917832 4 1.714 0.055534 5 7.486 0.220831 6 4.661 0.143894 7 96.361 0.959725 8 6.362 0.191079 9 10.957 0.305959 10 20.587 0.496532 11 2.142 0.068898 12 6.542 0.195939 13 47.338 0.793596 14 26.933 0.592526 15 37.588 0.714336 16 30.964 0.643750 17 80.485 0.931632 18 12.021 0.330140 19 12.588 0.342699 20 13.001 0.351682 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.835914 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-09-17_04:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 2.2 0.1 -0.7 0.6 -0.8 0.7 0.6 0.5 0.8 -0.2 -1.0 0.3 1.6 0.1 0.4 -0.2 -0.5 -0.9 -0.2 -0.2 -0.9 1.3 0.3 0.6 -0.5 -1.2 -0.9 0.9 -1.0 0.4 -1.3 0.9 0.1 0.8 -0.3 0.0 -1.0 0.9 -0.1 0.1 1.0 -0.1 Chi-square with 42 degrees of freedom:26.982832 z-score=-1.638507, p-value=0.034896 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-09-17_04:31 Test no p-value 1 0.462857 2 0.348947 3 0.042729 4 0.039009 5 0.946174 6 0.464310 7 0.020091 8 0.034763 9 0.565057 10 0.200649 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.021789 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-09-17_04:31: (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 66721 0.04 66750 0.10 3 25000.00 24971 0.03 24903 0.38 4 6666.67 6622 0.30 6635 0.15 5 1388.89 1404 0.16 1443 2.11 6 238.10 239 0.00 237 0.01 7 34.72 37 0.15 31 0.40 8 4.96 5 0.00 0 4.96 p=0.00540 p=0.76932 Number of rngs required: 689003, p-value: 0.756 RESULTS OF CRAPS TEST for dh-ranFile-2016-09-17_04:31 No. of wins: Observed Expected 98601 98585.9 z-score= 0.068, pvalue=0.52700 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66515 66666.7 0.345 0.345 2 37819 37654.3 0.720 1.065 3 27088 26954.7 0.659 1.724 4 19349 19313.5 0.065 1.790 5 13937 13851.4 0.529 2.318 6 9855 9943.5 0.788 3.107 7 7048 7145.0 1.318 4.424 8 5147 5139.1 0.012 4.437 9 3622 3699.9 1.639 6.075 10 2657 2666.3 0.032 6.108 11 1897 1923.3 0.360 6.468 12 1356 1388.7 0.772 7.240 13 1041 1003.7 1.385 8.625 14 733 726.1 0.065 8.690 15 524 525.8 0.006 8.696 16 383 381.2 0.009 8.705 17 281 276.5 0.072 8.777 18 203 200.8 0.023 8.801 19 141 146.0 0.170 8.971 20 112 106.2 0.315 9.286 21 292 287.1 0.083 9.369 Chisq= 9.37 for 20 degrees of freedom, p= 0.02177 SUMMARY of craptest p-value for no. of wins: 0.526996 p-value for throws/game: 0.021773 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-09-17_04:31 No. of wins: Observed Expected 98394 98585.9 z-score=-0.858, pvalue=0.19542 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66107 66666.7 4.698 4.698 2 37975 37654.3 2.731 7.429 3 26944 26954.7 0.004 7.434 4 19456 19313.5 1.052 8.486 5 13787 13851.4 0.300 8.785 6 10152 9943.5 4.370 13.155 7 7166 7145.0 0.062 13.217 8 5168 5139.1 0.163 13.380 9 3625 3699.9 1.515 14.895 10 2637 2666.3 0.322 15.217 11 1961 1923.3 0.738 15.954 12 1377 1388.7 0.099 16.054 13 1032 1003.7 0.797 16.851 14 743 726.1 0.391 17.242 15 507 525.8 0.675 17.917 16 381 381.2 0.000 17.917 17 263 276.5 0.663 18.580 18 190 200.8 0.584 19.164 19 134 146.0 0.984 20.148 20 122 106.2 2.346 22.493 21 273 287.1 0.694 23.187 Chisq= 23.19 for 20 degrees of freedom, p= 0.72031 SUMMARY of craptest p-value for no. of wins: 0.195418 p-value for throws/game: 0.720308 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0027,0.0054,0.0078,0.0083,0.0150,0.0177,0.0201,0.0207,0.0214,0.0218, 0.0218,0.0248,0.0348,0.0349,0.0390,0.0427,0.0441,0.0466,0.0501,0.0526, 0.0555,0.0562,0.0580,0.0593,0.0665,0.0689,0.0726,0.0754,0.0755,0.0918, 0.0929,0.1015,0.1021,0.1031,0.1036,0.1088,0.1105,0.1142,0.1210,0.1218, 0.1224,0.1278,0.1332,0.1407,0.1439,0.1557,0.1568,0.1584,0.1627,0.1675, 0.1756,0.1811,0.1863,0.1899,0.1911,0.1940,0.1945,0.1954,0.1959,0.2006, 0.2032,0.2072,0.2076,0.2076,0.2109,0.2119,0.2139,0.2149,0.2160,0.2173, 0.2208,0.2348,0.2392,0.2460,0.2467,0.2475,0.2492,0.2536,0.2536,0.2613, 0.2659,0.2675,0.2685,0.2700,0.2764,0.2779,0.2841,0.2859,0.2896,0.2919, 0.2993,0.3026,0.3045,0.3054,0.3060,0.3072,0.3184,0.3196,0.3217,0.3301, 0.3355,0.3362,0.3427,0.3489,0.3515,0.3517,0.3555,0.3583,0.3669,0.3816, 0.3856,0.3892,0.3922,0.3972,0.4032,0.4085,0.4196,0.4246,0.4328,0.4387, 0.4482,0.4504,0.4513,0.4555,0.4569,0.4586,0.4615,0.4629,0.4643,0.4690, 0.4752,0.4773,0.4813,0.4820,0.4858,0.4860,0.4898,0.4941,0.4965,0.5063, 0.5144,0.5146,0.5182,0.5227,0.5270,0.5380,0.5427,0.5499,0.5524,0.5594, 0.5606,0.5651,0.5652,0.5669,0.5760,0.5780,0.5812,0.5828,0.5898,0.5912, 0.5914,0.5918,0.5925,0.6009,0.6142,0.6143,0.6188,0.6212,0.6252,0.6254, 0.6285,0.6298,0.6358,0.6438,0.6455,0.6538,0.6566,0.6776,0.6796,0.6870, 0.6886,0.6906,0.6928,0.6949,0.6994,0.7074,0.7114,0.7131,0.7143,0.7184, 0.7203,0.7375,0.7427,0.7432,0.7522,0.7557,0.7648,0.7693,0.7698,0.7721, 0.7734,0.7777,0.7824,0.7897,0.7936,0.7944,0.7951,0.7961,0.7977,0.7989, 0.8023,0.8044,0.8060,0.8060,0.8070,0.8088,0.8187,0.8224,0.8292,0.8307, 0.8334,0.8349,0.8359,0.8424,0.8460,0.8611,0.8654,0.8668,0.8669,0.8700, 0.8786,0.8806,0.8970,0.9039,0.9039,0.9071,0.9147,0.9155,0.9178,0.9179, 0.9224,0.9229,0.9241,0.9261,0.9273,0.9316,0.9365,0.9379,0.9396,0.9407, 0.9462,0.9518,0.9520,0.9585,0.9597,0.9620,0.9632,0.9653,0.9690,0.9720, 0.9739,0.9748,0.9768,0.9781,0.9849,0.9867,0.9895,0.9922,0.9993, Overall p-value after applying KStest on 269 p-values = 0.366162 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.