RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-04-25_18:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.75 19.2607 0.686224 2 to 25 15.83 14.5693 0.373530 3 to 26 15.48 23.7435 0.873427 4 to 27 15.83 15.3454 0.429380 5 to 28 15.68 15.6516 0.451348 6 to 29 15.60 26.2236 0.929518 7 to 30 15.92 32.0632 0.985222 8 to 31 15.70 22.8501 0.845805 9 to 32 15.77 14.0423 0.335897 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.139529 Tough bday spacings test for dh-ranFile-2016-04-25_18:31: 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 5 41 80 98 98 72 49 34 11 9 3 (O-E)^2/E 1.9 0.5 0.6 0.0 0.0 0.5 0.2 0.6 1.0 0.9 0.3 Birthday Spacings: Sum(O-E)^2/E= 6.452, p= 0.224 RESULTS OF GCD FOR dh-ranFile-2016-04-25_18:31 Euclid's algorithm: p-value, steps to gcd: 0.965495 p-value, dist. of gcd's: 0.504247 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-04-25_18:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.758 0.789 0.581 0.068 0.909 0.658 0.600 0.824 Bits 8 to 15---> 0.734 0.733 0.708 0.262 0.738 0.486 0.956 0.999 Bits 16 to 23---> 0.010 0.029 0.143 0.494 0.024 0.816 0.815 0.012 Bits 24 to 31---> 0.374 0.072 0.170 0.012 0.757 0.120 0.040 0.973 KS test for the above 32 p values: 0.940 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-04-25_18:31, p-values for 5 runs: 0.8999, 0.0113, 0.5206, 0.5742, 0.6025 Rank test for binary matrices (31x31) for dh-ranFile-2016-04-25_18:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 203 211.4 0.335 0.335 r= 29 5133 5134.0 0.000 0.335 r= 30 22973 23103.0 0.732 1.067 r= 31 11691 11551.5 1.684 2.751 chi-square = 2.751 with df = 3; p-value = 0.568 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-04-25_18:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 198 211.4 0.852 0.852 r= 30 5193 5134.0 0.678 1.529 r= 31 22923 23103.0 1.403 2.933 r= 32 11686 11551.5 1.565 4.498 chi-square = 4.498 with df = 3; p-value = 0.788 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-04-25_18:31 b-rank test for bits 1 to 8, p=0.15875 b-rank test for bits 2 to 9, p=0.03738 b-rank test for bits 3 to 10, p=0.52488 b-rank test for bits 4 to 11, p=0.12023 b-rank test for bits 5 to 12, p=0.86981 b-rank test for bits 6 to 13, p=0.17627 b-rank test for bits 7 to 14, p=0.44391 b-rank test for bits 8 to 15, p=0.71368 b-rank test for bits 9 to 16, p=0.46244 b-rank test for bits 10 to 17, p=0.64861 b-rank test for bits 11 to 18, p=0.33125 b-rank test for bits 12 to 19, p=0.31462 b-rank test for bits 13 to 20, p=0.25031 b-rank test for bits 14 to 21, p=0.71274 b-rank test for bits 15 to 22, p=0.55917 b-rank test for bits 16 to 23, p=0.71974 b-rank test for bits 17 to 24, p=0.21670 b-rank test for bits 18 to 25, p=0.73130 b-rank test for bits 19 to 26, p=0.36933 b-rank test for bits 20 to 27, p=0.83649 b-rank test for bits 21 to 28, p=0.67205 b-rank test for bits 22 to 29, p=0.93290 b-rank test for bits 23 to 30, p=0.66618 b-rank test for bits 24 to 31, p=0.89728 b-rank test for bits 25 to 32, p=0.79364 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 = 0.820031 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-04-25_18:31 (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 142000 0.21 0.583886 2 142184 0.64 0.739483 3 143213 3.05 0.998840 4 142202 0.68 0.752952 5 141738 -0.40 0.344466 6 142031 0.28 0.611900 7 142745 1.95 0.974561 8 141760 -0.35 0.363582 9 142733 1.92 0.972852 10 141446 -1.08 0.139505 11 141666 -0.57 0.284838 12 142179 0.63 0.735676 13 142129 0.51 0.696111 14 141609 -0.70 0.241431 15 141810 -0.23 0.408238 16 142223 0.73 0.768182 17 141686 -0.52 0.300905 18 141904 -0.01 0.495032 19 142245 0.78 0.783561 20 142030 0.28 0.611005 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-04-25_18:31 Bits used No. missing words z-score p-value 23 to 32 141767 -0.4908 0.311786 22 to 31 141879 -0.1046 0.458352 21 to 30 141453 -1.5736 0.057796 20 to 29 142021 0.3851 0.649907 19 to 28 141635 -0.9460 0.172083 18 to 27 141670 -0.8253 0.204608 17 to 26 141788 -0.4184 0.337835 16 to 25 142055 0.5023 0.692275 15 to 24 142107 0.6816 0.752261 14 to 23 141913 0.0127 0.505049 13 to 22 141923 0.0471 0.518798 12 to 21 141875 -0.1184 0.452884 11 to 20 141998 0.3058 0.620106 10 to 19 141784 -0.4322 0.332808 9 to 18 142075 0.5713 0.716094 8 to 17 141398 -1.7632 0.038933 7 to 16 141908 -0.0046 0.498170 6 to 15 141746 -0.5632 0.286647 5 to 14 141829 -0.2770 0.390890 4 to 13 142340 1.4851 0.931237 3 to 12 141375 -1.8425 0.032700 2 to 11 141504 -1.3977 0.081103 1 to 10 141907 -0.0080 0.496795 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-04-25_18:31 Bits used No. missing words z-score p-value 28 to 32 141587 -1.0926 0.137275 27 to 31 142199 0.9819 0.836933 26 to 30 141602 -1.0418 0.148753 25 to 29 141857 -0.1774 0.429601 24 to 28 141636 -0.9265 0.177082 23 to 27 141693 -0.7333 0.231681 22 to 26 142001 0.3107 0.622003 21 to 25 141612 -1.0079 0.156752 20 to 24 141950 0.1379 0.554826 19 to 23 141794 -0.3909 0.347917 18 to 22 141929 0.0667 0.526581 17 to 21 142467 1.8904 0.970648 16 to 20 142318 1.3853 0.917023 15 to 19 141909 -0.0011 0.499554 14 to 18 141956 0.1582 0.562852 13 to 17 142072 0.5514 0.709328 12 to 16 141388 -1.7672 0.038596 11 to 15 142019 0.3718 0.644965 10 to 14 142251 1.1582 0.876610 9 to 13 142009 0.3379 0.632267 8 to 12 142115 0.6972 0.757157 7 to 11 141810 -0.3367 0.368167 6 to 10 141853 -0.1909 0.424283 5 to 9 142062 0.5175 0.697605 4 to 8 141471 -1.4859 0.068658 3 to 7 141449 -1.5604 0.059328 2 to 6 142177 0.9074 0.817891 1 to 5 141763 -0.4960 0.309935 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-04-25_18:31 Bits used No. missing words z-score p-value 31 to 32 142325 1.2262 0.889932 30 to 31 141961 0.1524 0.560572 29 to 30 142113 0.6008 0.726012 28 to 29 141947 0.1111 0.544240 27 to 28 142355 1.3147 0.905688 26 to 27 141916 0.0197 0.507849 25 to 26 141936 0.0787 0.531354 24 to 25 141609 -0.8859 0.187828 23 to 24 142038 0.3796 0.647863 22 to 23 142007 0.2881 0.613370 21 to 22 141715 -0.5732 0.283240 20 to 21 141930 0.0610 0.524310 19 to 20 142239 0.9725 0.834594 18 to 19 141583 -0.9626 0.167868 17 to 18 141662 -0.7296 0.232821 16 to 17 141967 0.1701 0.567541 15 to 16 142145 0.6952 0.756532 14 to 15 141623 -0.8446 0.199158 13 to 14 141627 -0.8328 0.202470 12 to 13 142173 0.7778 0.781653 11 to 12 142115 0.6067 0.727974 10 to 11 141239 -1.9774 0.024000 9 to 10 141660 -0.7355 0.231022 8 to 9 141947 0.1111 0.544240 7 to 8 141253 -1.9361 0.026429 6 to 7 142506 1.7601 0.960804 5 to 6 141864 -0.1337 0.446813 4 to 5 141879 -0.0895 0.464355 3 to 4 141569 -1.0039 0.157708 2 to 3 142100 0.5624 0.713095 1 to 2 141466 -1.3078 0.095478 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-04-25_18:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2567.57 0.956 0.830371 Test results for specific bytes for dh-ranFile-2016-04-25_18:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2417.46 -1.167 0.121560 2 to 9 2549.91 0.706 0.759854 3 to 10 2541.35 0.585 0.720660 4 to 11 2476.67 -0.330 0.370748 5 to 12 2554.96 0.777 0.781474 6 to 13 2456.47 -0.616 0.269065 7 to 14 2335.67 -2.324 0.010064 8 to 15 2425.15 -1.058 0.144915 9 to 16 2415.37 -1.197 0.115688 10 to 17 2525.35 0.359 0.640033 11 to 18 2500.09 0.001 0.500499 12 to 19 2450.43 -0.701 0.241659 13 to 20 2554.80 0.775 0.780814 14 to 21 2587.09 1.232 0.890954 15 to 22 2635.86 1.921 0.972652 16 to 23 2462.00 -0.537 0.295508 17 to 24 2470.32 -0.420 0.337335 18 to 25 2569.80 0.987 0.838191 19 to 26 2459.71 -0.570 0.284409 20 to 27 2481.59 -0.260 0.397303 21 to 28 2500.13 0.002 0.500753 22 to 29 2622.51 1.733 0.958413 23 to 30 2382.77 -1.658 0.048670 24 to 31 2438.53 -0.869 0.192339 25 to 32 2417.34 -1.169 0.121214 CDPARK for dh-ranFile-2016-04-25_18:31: 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 3524 0.0457 0.518210 3518 -0.2283 0.409702 3569 2.1005 0.982156 3552 1.3242 0.907282 3519 -0.1826 0.427537 3504 -0.8676 0.192812 3511 -0.5479 0.291865 3531 0.3653 0.642555 3527 0.1826 0.572463 3503 -0.9132 0.180558 Square side=100, avg. no. parked=3525.80 sample std.=19.76 p-value of the KSTEST for those 10 p-values: 0.825701 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-04-25_18:31 0.5216,0.2389,0.3240,0.1407,0.6012,0.1902,0.5734,0.2113,0.9633,0.0215, The KS test for those 10 p-values: 0.283128 The 3DSPHERES test for dh-ranFile-2016-04-25_18:31 sample no r^3 equiv. uni. 1 43.847 0.768127 2 3.595 0.112943 3 64.325 0.882833 4 2.814 0.089525 5 8.999 0.259167 6 0.543 0.017936 7 13.701 0.366628 8 99.685 0.963949 9 19.494 0.477853 10 26.666 0.588882 11 5.419 0.165272 12 18.819 0.465968 13 16.820 0.429174 14 13.979 0.372477 15 13.791 0.368518 16 109.622 0.974115 17 37.181 0.710435 18 6.232 0.187571 19 8.094 0.236461 20 10.822 0.302824 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.501839 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-04-25_18:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.1 -1.6 2.4 0.6 0.1 -1.9 0.1 0.8 0.0 -0.7 1.3 0.0 -0.1 -0.3 -1.0 1.5 1.1 -0.6 -0.5 0.3 -1.7 -1.6 -0.8 2.3 0.6 0.5 -0.7 1.3 1.2 -0.3 -0.7 0.6 -2.1 0.2 -0.1 -0.2 -0.7 -0.8 -0.7 0.1 1.0 -0.1 Chi-square with 42 degrees of freedom:43.928379 z-score=0.210403, p-value=0.610190 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-04-25_18:31 Test no p-value 1 0.300795 2 0.082127 3 0.863661 4 0.616265 5 0.382687 6 0.003532 7 0.999584 8 0.421874 9 0.528480 10 0.501318 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.442548 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-04-25_18:31: (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 66867 0.60 66860 0.56 3 25000.00 24810 1.44 24862 0.76 4 6666.67 6626 0.25 6593 0.81 5 1388.89 1413 0.42 1421 0.74 6 238.10 245 0.20 219 1.53 7 34.72 28 1.30 34 0.01 8 4.96 10 5.12 10 5.12 p=0.84439 p=0.85491 Number of rngs required: 688347, p-value: 0.474 RESULTS OF CRAPS TEST for dh-ranFile-2016-04-25_18:31 No. of wins: Observed Expected 98265 98585.9 z-score=-1.435, pvalue=0.07563 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66448 66666.7 0.717 0.717 2 38141 37654.3 6.290 7.008 3 26802 26954.7 0.865 7.873 4 19338 19313.5 0.031 7.904 5 13940 13851.4 0.566 8.471 6 9967 9943.5 0.055 8.526 7 7031 7145.0 1.820 10.346 8 5101 5139.1 0.282 10.628 9 3654 3699.9 0.569 11.196 10 2692 2666.3 0.248 11.444 11 1965 1923.3 0.903 12.347 12 1396 1388.7 0.038 12.385 13 993 1003.7 0.114 12.499 14 685 726.1 2.331 14.830 15 494 525.8 1.927 16.758 16 401 381.2 1.034 17.791 17 237 276.5 5.653 23.445 18 201 200.8 0.000 23.445 19 145 146.0 0.007 23.451 20 102 106.2 0.167 23.619 21 267 287.1 1.409 25.028 Chisq= 25.03 for 20 degrees of freedom, p= 0.79963 SUMMARY of craptest p-value for no. of wins: 0.075634 p-value for throws/game: 0.799628 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-04-25_18:31 No. of wins: Observed Expected 98640 98585.9 z-score= 0.242, pvalue=0.59567 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66613 66666.7 0.043 0.043 2 37974 37654.3 2.714 2.757 3 26787 26954.7 1.044 3.801 4 19421 19313.5 0.599 4.400 5 13632 13851.4 3.476 7.876 6 9954 9943.5 0.011 7.887 7 7192 7145.0 0.309 8.195 8 5114 5139.1 0.122 8.318 9 3669 3699.9 0.257 8.575 10 2646 2666.3 0.155 8.730 11 1981 1923.3 1.729 10.459 12 1404 1388.7 0.168 10.627 13 981 1003.7 0.514 11.141 14 734 726.1 0.085 11.226 15 523 525.8 0.015 11.241 16 379 381.2 0.012 11.253 17 264 276.5 0.569 11.822 18 200 200.8 0.003 11.825 19 146 146.0 0.000 11.825 20 91 106.2 2.180 14.005 21 295 287.1 0.217 14.221 Chisq= 14.22 for 20 degrees of freedom, p= 0.18091 SUMMARY of craptest p-value for no. of wins: 0.595669 p-value for throws/game: 0.180905 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0035,0.0101,0.0103,0.0113,0.0121,0.0123,0.0179,0.0215,0.0240,0.0242, 0.0264,0.0291,0.0327,0.0374,0.0386,0.0389,0.0395,0.0487,0.0578,0.0593, 0.0680,0.0687,0.0718,0.0756,0.0811,0.0821,0.0895,0.0955,0.1129,0.1157, 0.1202,0.1203,0.1212,0.1216,0.1373,0.1395,0.1395,0.1407,0.1426,0.1449, 0.1488,0.1568,0.1577,0.1587,0.1653,0.1679,0.1705,0.1721,0.1763,0.1771, 0.1806,0.1809,0.1876,0.1878,0.1902,0.1923,0.1928,0.1992,0.2025,0.2046, 0.2113,0.2167,0.2240,0.2310,0.2317,0.2328,0.2365,0.2389,0.2414,0.2417, 0.2503,0.2592,0.2623,0.2691,0.2831,0.2832,0.2844,0.2848,0.2866,0.2919, 0.2955,0.3008,0.3009,0.3028,0.3099,0.3118,0.3146,0.3240,0.3312,0.3328, 0.3359,0.3373,0.3378,0.3445,0.3479,0.3636,0.3666,0.3682,0.3685,0.3693, 0.3707,0.3725,0.3735,0.3738,0.3827,0.3909,0.3973,0.4082,0.4097,0.4219, 0.4243,0.4275,0.4292,0.4294,0.4296,0.4425,0.4439,0.4468,0.4513,0.4529, 0.4584,0.4624,0.4644,0.4660,0.4743,0.4779,0.4861,0.4944,0.4950,0.4968, 0.4982,0.4996,0.5005,0.5008,0.5013,0.5018,0.5042,0.5050,0.5078,0.5182, 0.5188,0.5206,0.5216,0.5243,0.5249,0.5266,0.5285,0.5314,0.5442,0.5442, 0.5548,0.5592,0.5606,0.5629,0.5675,0.5685,0.5725,0.5734,0.5742,0.5807, 0.5839,0.5889,0.5957,0.6001,0.6012,0.6025,0.6102,0.6110,0.6119,0.6134, 0.6163,0.6201,0.6220,0.6323,0.6400,0.6426,0.6450,0.6479,0.6486,0.6499, 0.6578,0.6662,0.6720,0.6862,0.6923,0.6961,0.6976,0.7081,0.7093,0.7104, 0.7127,0.7131,0.7137,0.7161,0.7197,0.7207,0.7260,0.7280,0.7313,0.7332, 0.7337,0.7357,0.7383,0.7395,0.7523,0.7530,0.7565,0.7572,0.7574,0.7584, 0.7599,0.7681,0.7682,0.7808,0.7815,0.7817,0.7836,0.7875,0.7895,0.7936, 0.7996,0.8146,0.8159,0.8179,0.8200,0.8238,0.8257,0.8304,0.8346,0.8365, 0.8369,0.8382,0.8444,0.8458,0.8549,0.8637,0.8698,0.8734,0.8766,0.8828, 0.8899,0.8910,0.8973,0.8999,0.9057,0.9073,0.9093,0.9170,0.9295,0.9312, 0.9329,0.9404,0.9562,0.9584,0.9608,0.9633,0.9639,0.9655,0.9706,0.9727, 0.9729,0.9734,0.9741,0.9746,0.9822,0.9852,0.9986,0.9988,0.9996, Overall p-value after applying KStest on 269 p-values = 0.936573 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.