RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-04-10_00:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.98 15.7627 0.459285 2 to 25 15.85 11.3376 0.161515 3 to 26 15.64 12.0009 0.199914 4 to 27 15.82 17.6684 0.589958 5 to 28 15.69 30.0604 0.974087 6 to 29 15.83 18.4276 0.637643 7 to 30 15.64 24.1141 0.883632 8 to 31 15.47 24.7433 0.899395 9 to 32 15.99 24.0929 0.883066 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.225279 Tough bday spacings test for dh-ranFile-2018-04-10_00:31: 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 42 62 112 105 78 54 17 15 6 1 (O-E)^2/E 0.1 0.8 1.7 2.1 0.5 0.0 0.1 5.5 0.0 0.1 2.3 Birthday Spacings: Sum(O-E)^2/E= 13.229, p= 0.789 RESULTS OF GCD FOR dh-ranFile-2018-04-10_00:31 Euclid's algorithm: p-value, steps to gcd: 0.435721 p-value, dist. of gcd's: 0.427838 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-04-10_00:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.971 0.129 0.139 0.819 0.105 0.122 0.418 0.260 Bits 8 to 15---> 0.971 0.589 0.447 0.636 0.082 0.655 0.970 0.583 Bits 16 to 23---> 0.390 0.895 0.692 0.765 0.721 0.303 0.120 0.761 Bits 24 to 31---> 0.579 0.328 0.953 0.627 0.845 0.748 0.745 0.233 KS test for the above 32 p values: 0.543 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-04-10_00:31, p-values for 5 runs: 0.9088, 0.7421, 0.4060, 0.6362, 0.6795 Rank test for binary matrices (31x31) for dh-ranFile-2018-04-10_00:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 224 211.4 0.749 0.749 r= 29 5020 5134.0 2.532 3.281 r= 30 23203 23103.0 0.432 3.713 r= 31 11553 11551.5 0.000 3.713 chi-square = 3.713 with df = 3; p-value = 0.706 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-04-10_00:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 226 211.4 1.006 1.006 r= 30 5099 5134.0 0.239 1.245 r= 31 23114 23103.0 0.005 1.250 r= 32 11561 11551.5 0.008 1.257 chi-square = 1.257 with df = 3; p-value = 0.261 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-04-10_00:31 b-rank test for bits 1 to 8, p=0.31371 b-rank test for bits 2 to 9, p=0.64558 b-rank test for bits 3 to 10, p=0.76151 b-rank test for bits 4 to 11, p=0.75388 b-rank test for bits 5 to 12, p=0.72177 b-rank test for bits 6 to 13, p=0.32334 b-rank test for bits 7 to 14, p=0.12054 b-rank test for bits 8 to 15, p=0.85296 b-rank test for bits 9 to 16, p=0.61789 b-rank test for bits 10 to 17, p=0.60623 b-rank test for bits 11 to 18, p=0.49051 b-rank test for bits 12 to 19, p=0.31238 b-rank test for bits 13 to 20, p=0.25595 b-rank test for bits 14 to 21, p=0.68242 b-rank test for bits 15 to 22, p=0.41062 b-rank test for bits 16 to 23, p=0.63092 b-rank test for bits 17 to 24, p=0.53697 b-rank test for bits 18 to 25, p=0.41713 b-rank test for bits 19 to 26, p=0.16729 b-rank test for bits 20 to 27, p=0.40516 b-rank test for bits 21 to 28, p=0.84723 b-rank test for bits 22 to 29, p=0.55144 b-rank test for bits 23 to 30, p=0.14883 b-rank test for bits 24 to 31, p=0.93844 b-rank test for bits 25 to 32, p=0.81127 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 = 0.438510 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-04-10_00:31 (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 142001 0.21 0.584798 2 141727 -0.43 0.335052 3 141927 0.04 0.516466 4 141710 -0.47 0.320706 5 141925 0.04 0.514603 6 141701 -0.49 0.313217 7 141841 -0.16 0.436579 8 141339 -1.33 0.091340 9 141221 -1.61 0.053890 10 141640 -0.63 0.264584 11 141894 -0.04 0.485714 12 141787 -0.29 0.387509 13 142294 0.90 0.815610 14 142286 0.88 0.810589 15 141451 -1.07 0.142115 16 141523 -0.90 0.183358 17 142073 0.38 0.648920 18 142877 2.26 0.988118 19 142207 0.70 0.756626 20 141932 0.05 0.521121 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-04-10_00:31 Bits used No. missing words z-score p-value 23 to 32 141750 -0.5494 0.291361 22 to 31 142194 0.9816 0.836857 21 to 30 142325 1.4333 0.924120 20 to 29 141080 -2.8598 0.002120 19 to 28 141995 0.2954 0.616161 18 to 27 142201 1.0058 0.842734 17 to 26 141977 0.2333 0.592253 16 to 25 141963 0.1851 0.573413 15 to 24 141659 -0.8632 0.194012 14 to 23 142453 1.8747 0.969585 13 to 22 142059 0.5161 0.697109 12 to 21 141983 0.2540 0.600266 11 to 20 141599 -1.0701 0.142286 10 to 19 141699 -0.7253 0.234141 9 to 18 141846 -0.2184 0.413567 8 to 17 141151 -2.6149 0.004462 7 to 16 142082 0.5954 0.724217 6 to 15 142267 1.2333 0.891276 5 to 14 141632 -0.9563 0.169458 4 to 13 142218 1.0644 0.856422 3 to 12 141812 -0.3356 0.368579 2 to 11 141901 -0.0287 0.488542 1 to 10 142127 0.7506 0.773549 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-04-10_00:31 Bits used No. missing words z-score p-value 28 to 32 141569 -1.1537 0.124320 27 to 31 141591 -1.0791 0.140275 26 to 30 142150 0.8158 0.792702 25 to 29 142176 0.9040 0.816993 24 to 28 141601 -1.0452 0.147968 23 to 27 141751 -0.5367 0.295733 22 to 26 142052 0.4836 0.685675 21 to 25 141872 -0.1265 0.449651 20 to 24 141958 0.1650 0.565521 19 to 23 141701 -0.7062 0.240031 18 to 22 142387 1.6192 0.947300 17 to 21 141829 -0.2723 0.392694 16 to 20 141810 -0.3367 0.368167 15 to 19 141544 -1.2384 0.107783 14 to 18 142163 0.8599 0.805077 13 to 17 142316 1.3785 0.915982 12 to 16 142059 0.5074 0.694048 11 to 15 142283 1.2667 0.897365 10 to 14 141751 -0.5367 0.295733 9 to 13 142096 0.6328 0.736561 8 to 12 141285 -2.1164 0.017157 7 to 11 142304 1.3379 0.909530 6 to 10 141907 -0.0079 0.496849 5 to 9 141983 0.2497 0.598602 4 to 8 142441 1.8023 0.964249 3 to 7 142227 1.0768 0.859226 2 to 6 142336 1.4463 0.925959 1 to 5 142707 2.7040 0.996574 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-04-10_00:31 Bits used No. missing words z-score p-value 31 to 32 142320 1.2114 0.887132 30 to 31 141829 -0.2370 0.406343 29 to 30 142627 2.1170 0.982871 28 to 29 142021 0.3294 0.629077 27 to 28 142330 1.2409 0.892681 26 to 27 141796 -0.3343 0.369074 25 to 26 141613 -0.8741 0.191024 24 to 25 140851 -3.1219 0.000898 23 to 24 141710 -0.5880 0.278268 22 to 23 142270 1.0639 0.856318 21 to 22 142491 1.7158 0.956904 20 to 21 141841 -0.2016 0.420129 19 to 20 141887 -0.0659 0.473741 18 to 19 141820 -0.2635 0.396079 17 to 18 142130 0.6509 0.742459 16 to 17 141771 -0.4081 0.341617 15 to 16 142078 0.4976 0.690600 14 to 15 141479 -1.2694 0.102147 13 to 14 141863 -0.1367 0.445647 12 to 13 141779 -0.3845 0.350321 11 to 12 141610 -0.8830 0.188624 10 to 11 141716 -0.5703 0.284239 9 to 10 140744 -3.4376 0.000293 8 to 9 141951 0.1229 0.548915 7 to 8 141800 -0.3225 0.373534 6 to 7 141594 -0.9302 0.176140 5 to 6 141751 -0.4671 0.320232 4 to 5 141813 -0.2842 0.388144 3 to 4 142041 0.3884 0.651143 2 to 3 142216 0.9046 0.817170 1 to 2 142277 1.0846 0.860944 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-04-10_00:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2513.62 0.193 0.576359 Test results for specific bytes for dh-ranFile-2018-04-10_00:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2539.07 0.552 0.709693 2 to 9 2512.34 0.175 0.569274 3 to 10 2594.53 1.337 0.909358 4 to 11 2546.74 0.661 0.745681 5 to 12 2487.82 -0.172 0.431615 6 to 13 2442.83 -0.808 0.209417 7 to 14 2546.35 0.656 0.743931 8 to 15 2430.37 -0.985 0.162398 9 to 16 2552.49 0.742 0.771063 10 to 17 2616.65 1.650 0.950489 11 to 18 2477.31 -0.321 0.374131 12 to 19 2489.71 -0.146 0.442153 13 to 20 2457.00 -0.608 0.271539 14 to 21 2459.33 -0.575 0.282609 15 to 22 2497.31 -0.038 0.484813 16 to 23 2470.82 -0.413 0.339938 17 to 24 2560.58 0.857 0.804202 18 to 25 2465.72 -0.485 0.313892 19 to 26 2469.97 -0.425 0.335529 20 to 27 2474.21 -0.365 0.357641 21 to 28 2477.40 -0.320 0.374646 22 to 29 2461.16 -0.549 0.291410 23 to 30 2445.74 -0.767 0.221455 24 to 31 2502.73 0.039 0.515383 25 to 32 2433.54 -0.940 0.173649 CDPARK for dh-ranFile-2018-04-10_00:31: 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 3525 0.0913 0.536383 3514 -0.4110 0.340551 3516 -0.3196 0.374623 3541 0.8219 0.794438 3531 0.3653 0.642555 3535 0.5479 0.708135 3504 -0.8676 0.192812 3497 -1.1872 0.117571 3500 -1.0502 0.146807 3519 -0.1826 0.427537 Square side=100, avg. no. parked=3518.20 sample std.=14.20 p-value of the KSTEST for those 10 p-values: 0.601237 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-04-10_00:31 0.6290,0.1653,0.8510,0.6519,0.0650,0.9326,0.9289,0.6354,0.9078,0.8794, The KS test for those 10 p-values: 0.060299 The 3DSPHERES test for dh-ranFile-2018-04-10_00:31 sample no r^3 equiv. uni. 1 5.056 0.155104 2 11.195 0.311441 3 25.505 0.572651 4 10.702 0.300033 5 20.547 0.495860 6 9.404 0.269092 7 11.038 0.307831 8 21.098 0.505039 9 12.572 0.342333 10 76.108 0.920891 11 63.053 0.877759 12 1.258 0.041053 13 7.131 0.211562 14 7.271 0.215226 15 23.564 0.544088 16 83.156 0.937454 17 76.759 0.922588 18 10.564 0.296810 19 5.820 0.176339 20 6.112 0.184312 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.204842 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-04-10_00:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 0.5 1.3 1.2 0.1 -1.2 2.2 0.1 -1.3 0.5 -0.1 1.6 0.9 0.0 -0.3 -0.8 -0.6 -0.5 -1.3 -0.2 -0.1 -0.6 2.1 0.2 0.1 0.8 -0.4 0.5 -0.3 -0.4 1.6 -1.2 0.4 0.8 -0.9 -0.3 1.0 0.2 0.5 1.0 -1.3 1.0 0.8 Chi-square with 42 degrees of freedom:36.007013 z-score=-0.653889, p-value=0.269560 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-04-10_00:31 Test no p-value 1 0.693177 2 0.331207 3 0.116225 4 0.808522 5 0.013977 6 0.811725 7 0.011340 8 0.152126 9 0.039433 10 0.220222 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.022650 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-04-10_00:31: (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 66538 0.25 66809 0.30 3 25000.00 25211 1.78 25025 0.03 4 6666.67 6590 0.88 6540 2.41 5 1388.89 1364 0.45 1345 1.39 6 238.10 244 0.15 233 0.11 7 34.72 40 0.80 42 1.53 8 4.96 12 9.99 5 0.00 p=0.97353 p=0.54921 Number of rngs required: 688233, p-value: 0.422 RESULTS OF CRAPS TEST for dh-ranFile-2018-04-10_00:31 No. of wins: Observed Expected 98589 98585.9 z-score= 0.014, pvalue=0.50561 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66273 66666.7 2.325 2.325 2 37916 37654.3 1.819 4.143 3 27000 26954.7 0.076 4.219 4 19184 19313.5 0.868 5.087 5 13944 13851.4 0.619 5.706 6 10057 9943.5 1.295 7.000 7 7197 7145.0 0.378 7.378 8 5157 5139.1 0.063 7.441 9 3680 3699.9 0.107 7.548 10 2612 2666.3 1.106 8.653 11 1954 1923.3 0.489 9.142 12 1422 1388.7 0.797 9.939 13 983 1003.7 0.428 10.367 14 680 726.1 2.932 13.298 15 540 525.8 0.382 13.680 16 384 381.2 0.021 13.701 17 288 276.5 0.475 14.176 18 178 200.8 2.595 16.771 19 166 146.0 2.744 19.516 20 117 106.2 1.095 20.611 21 268 287.1 1.272 21.883 Chisq= 21.88 for 20 degrees of freedom, p= 0.65312 SUMMARY of craptest p-value for no. of wins: 0.505605 p-value for throws/game: 0.653120 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-04-10_00:31 No. of wins: Observed Expected 98505 98585.9 z-score=-0.362, pvalue=0.35881 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66387 66666.7 1.173 1.173 2 37837 37654.3 0.886 2.059 3 27089 26954.7 0.669 2.728 4 19349 19313.5 0.065 2.794 5 13916 13851.4 0.301 3.095 6 10095 9943.5 2.307 5.402 7 7009 7145.0 2.590 7.991 8 5133 5139.1 0.007 7.999 9 3659 3699.9 0.451 8.450 10 2683 2666.3 0.105 8.555 11 1974 1923.3 1.335 9.889 12 1334 1388.7 2.158 12.047 13 939 1003.7 4.173 16.220 14 706 726.1 0.559 16.778 15 536 525.8 0.196 16.975 16 369 381.2 0.387 17.362 17 272 276.5 0.075 17.437 18 183 200.8 1.583 19.020 19 148 146.0 0.028 19.047 20 95 106.2 1.184 20.232 21 287 287.1 0.000 20.232 Chisq= 20.23 for 20 degrees of freedom, p= 0.55648 SUMMARY of craptest p-value for no. of wins: 0.358808 p-value for throws/game: 0.556478 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0003,0.0009,0.0021,0.0045,0.0113,0.0140,0.0172,0.0226,0.0394,0.0411, 0.0539,0.0603,0.0650,0.0820,0.0913,0.1021,0.1046,0.1078,0.1162,0.1176, 0.1196,0.1205,0.1215,0.1243,0.1286,0.1388,0.1403,0.1421,0.1423,0.1468, 0.1480,0.1488,0.1521,0.1551,0.1615,0.1624,0.1653,0.1673,0.1695,0.1736, 0.1761,0.1763,0.1834,0.1843,0.1886,0.1910,0.1928,0.1940,0.1999,0.2048, 0.2094,0.2116,0.2152,0.2202,0.2215,0.2253,0.2330,0.2341,0.2400,0.2559, 0.2599,0.2607,0.2646,0.2691,0.2696,0.2715,0.2783,0.2826,0.2842,0.2914, 0.2914,0.2957,0.2957,0.2968,0.3000,0.3033,0.3078,0.3114,0.3124,0.3132, 0.3137,0.3139,0.3202,0.3207,0.3233,0.3279,0.3312,0.3351,0.3355,0.3399, 0.3406,0.3416,0.3423,0.3503,0.3576,0.3588,0.3682,0.3686,0.3691,0.3735, 0.3741,0.3746,0.3746,0.3875,0.3881,0.3902,0.3927,0.3961,0.4052,0.4060, 0.4063,0.4106,0.4136,0.4171,0.4177,0.4201,0.4225,0.4275,0.4278,0.4316, 0.4357,0.4366,0.4385,0.4422,0.4456,0.4470,0.4497,0.4593,0.4737,0.4848, 0.4857,0.4885,0.4905,0.4959,0.4968,0.5050,0.5056,0.5146,0.5154,0.5165, 0.5211,0.5364,0.5370,0.5431,0.5441,0.5489,0.5492,0.5514,0.5565,0.5655, 0.5693,0.5727,0.5734,0.5764,0.5794,0.5835,0.5848,0.5889,0.5900,0.5923, 0.5986,0.6003,0.6012,0.6062,0.6162,0.6179,0.6273,0.6290,0.6291,0.6309, 0.6354,0.6358,0.6362,0.6376,0.6426,0.6456,0.6489,0.6511,0.6519,0.6531, 0.6547,0.6795,0.6824,0.6857,0.6906,0.6916,0.6932,0.6940,0.6971,0.7059, 0.7081,0.7097,0.7213,0.7218,0.7242,0.7366,0.7421,0.7425,0.7439,0.7450, 0.7457,0.7477,0.7539,0.7566,0.7610,0.7615,0.7649,0.7711,0.7735,0.7888, 0.7927,0.7944,0.8042,0.8051,0.8085,0.8106,0.8113,0.8117,0.8156,0.8170, 0.8172,0.8194,0.8369,0.8427,0.8451,0.8472,0.8510,0.8530,0.8563,0.8564, 0.8592,0.8609,0.8778,0.8794,0.8831,0.8836,0.8871,0.8913,0.8927,0.8952, 0.8974,0.8994,0.9078,0.9088,0.9094,0.9095,0.9160,0.9209,0.9226,0.9241, 0.9260,0.9289,0.9326,0.9375,0.9384,0.9473,0.9505,0.9528,0.9569,0.9642, 0.9696,0.9702,0.9705,0.9706,0.9735,0.9741,0.9829,0.9881,0.9966, Overall p-value after applying KStest on 269 p-values = 0.584528 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.