RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-12-10_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 15.66 11.6642 0.179968 2 to 25 15.74 31.2936 0.981609 3 to 26 15.85 9.6623 0.082829 4 to 27 15.82 10.5695 0.121952 5 to 28 15.65 12.8457 0.253548 6 to 29 15.66 16.3432 0.500352 7 to 30 15.57 29.3018 0.968157 8 to 31 15.70 17.1211 0.553811 9 to 32 15.53 15.9250 0.470844 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.494255 Tough bday spacings test for dh-ranFile-2015-12-10_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 11 39 88 85 95 76 48 26 18 8 6 (O-E)^2/E 0.4 0.2 3.0 1.6 0.1 0.1 0.3 0.5 0.7 0.3 0.9 Birthday Spacings: Sum(O-E)^2/E= 7.929, p= 0.364 RESULTS OF GCD FOR dh-ranFile-2015-12-10_17:31 Euclid's algorithm: p-value, steps to gcd: 0.215784 p-value, dist. of gcd's: 0.681355 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-12-10_17:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.594 0.193 0.105 0.432 0.291 0.455 0.222 0.080 Bits 8 to 15---> 0.372 0.580 0.376 0.897 0.313 0.163 0.916 0.515 Bits 16 to 23---> 0.675 0.015 0.402 0.524 0.600 0.946 0.729 0.931 Bits 24 to 31---> 0.127 0.651 0.606 0.106 0.714 0.942 0.224 0.973 KS test for the above 32 p values: 0.055 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-12-10_17:31, p-values for 5 runs: 0.1558, 0.5649, 0.6107, 0.1349, 0.6803 Rank test for binary matrices (31x31) for dh-ranFile-2015-12-10_17:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 224 211.4 0.749 0.749 r= 29 5320 5134.0 6.738 7.487 r= 30 23088 23103.0 0.010 7.496 r= 31 11368 11551.5 2.916 10.412 chi-square = 10.412 with df = 3; p-value = 0.985 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-12-10_17:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 209 211.4 0.028 0.028 r= 30 5186 5134.0 0.526 0.554 r= 31 23167 23103.0 0.177 0.731 r= 32 11438 11551.5 1.116 1.847 chi-square = 1.847 with df = 3; p-value = 0.395 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-12-10_17:31 b-rank test for bits 1 to 8, p=0.30069 b-rank test for bits 2 to 9, p=0.64663 b-rank test for bits 3 to 10, p=0.75667 b-rank test for bits 4 to 11, p=0.24254 b-rank test for bits 5 to 12, p=0.92622 b-rank test for bits 6 to 13, p=0.01409 b-rank test for bits 7 to 14, p=0.35521 b-rank test for bits 8 to 15, p=0.27780 b-rank test for bits 9 to 16, p=0.69478 b-rank test for bits 10 to 17, p=0.07848 b-rank test for bits 11 to 18, p=0.31774 b-rank test for bits 12 to 19, p=0.83201 b-rank test for bits 13 to 20, p=0.82029 b-rank test for bits 14 to 21, p=0.96397 b-rank test for bits 15 to 22, p=0.90800 b-rank test for bits 16 to 23, p=0.69484 b-rank test for bits 17 to 24, p=0.13460 b-rank test for bits 18 to 25, p=0.30583 b-rank test for bits 19 to 26, p=0.20677 b-rank test for bits 20 to 27, p=0.65662 b-rank test for bits 21 to 28, p=0.73376 b-rank test for bits 22 to 29, p=0.58173 b-rank test for bits 23 to 30, p=0.92725 b-rank test for bits 24 to 31, p=0.27015 b-rank test for bits 25 to 32, p=0.73245 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 = 0.702648 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-12-10_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 142706 1.86 0.968655 2 141608 -0.70 0.240703 3 142063 0.36 0.640218 4 142298 0.91 0.818089 5 141811 -0.23 0.409146 6 141840 -0.16 0.435658 7 142682 1.81 0.964486 8 142389 1.12 0.868797 9 141266 -1.50 0.066406 10 142288 0.88 0.811852 11 142544 1.48 0.930946 12 142112 0.47 0.682082 13 142065 0.36 0.641965 14 141467 -1.03 0.150689 15 141779 -0.30 0.380370 16 142664 1.76 0.961071 17 142536 1.46 0.928428 18 141574 -0.78 0.216672 19 141157 -1.76 0.039392 20 142298 0.91 0.818089 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-12-10_17:31 Bits used No. missing words z-score p-value 23 to 32 142311 1.3851 0.916984 22 to 31 141684 -0.7770 0.218579 21 to 30 142077 0.5782 0.718426 20 to 29 141716 -0.6667 0.252496 19 to 28 141685 -0.7736 0.219598 18 to 27 141990 0.2782 0.609560 17 to 26 142284 1.2920 0.901815 16 to 25 141994 0.2920 0.614844 15 to 24 141812 -0.3356 0.368579 14 to 23 141638 -0.9356 0.174734 13 to 22 142216 1.0575 0.854854 12 to 21 141811 -0.3391 0.367279 11 to 20 141612 -1.0253 0.152617 10 to 19 141737 -0.5942 0.276175 9 to 18 142501 2.0402 0.979337 8 to 17 141669 -0.8287 0.203630 7 to 16 142497 2.0264 0.978641 6 to 15 142130 0.7609 0.776651 5 to 14 142031 0.4196 0.662594 4 to 13 141597 -1.0770 0.140740 3 to 12 141616 -1.0115 0.155893 2 to 11 141928 0.0644 0.525666 1 to 10 141206 -2.4253 0.007648 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-12-10_17:31 Bits used No. missing words z-score p-value 28 to 32 141048 -2.9198 0.001751 27 to 31 141384 -1.7808 0.037474 26 to 30 142105 0.6633 0.746427 25 to 29 141836 -0.2486 0.401844 24 to 28 141969 0.2023 0.580148 23 to 27 141229 -2.3062 0.010550 22 to 26 141468 -1.4960 0.067322 21 to 25 141937 0.0938 0.537365 20 to 24 142062 0.5175 0.697605 19 to 23 141650 -0.8791 0.189678 18 to 22 141973 0.2158 0.585440 17 to 21 141900 -0.0316 0.487385 16 to 20 141432 -1.6181 0.052824 15 to 19 141636 -0.9265 0.177082 14 to 18 141758 -0.5130 0.303982 13 to 17 142186 0.9379 0.825843 12 to 16 142399 1.6599 0.951533 11 to 15 141597 -1.0587 0.144858 10 to 14 141867 -0.1435 0.442951 9 to 13 141744 -0.5604 0.287589 8 to 12 141735 -0.5909 0.277277 7 to 11 141926 0.0565 0.522532 6 to 10 142176 0.9040 0.816993 5 to 9 141743 -0.5638 0.286435 4 to 8 142035 0.4260 0.664946 3 to 7 141592 -1.0757 0.141032 2 to 6 141747 -0.5503 0.291067 1 to 5 141117 -2.6859 0.003617 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-12-10_17:31 Bits used No. missing words z-score p-value 31 to 32 141922 0.0374 0.514907 30 to 31 142147 0.7011 0.758377 29 to 30 141649 -0.7679 0.221263 28 to 29 142190 0.8279 0.796146 27 to 28 142082 0.5094 0.694747 26 to 27 141654 -0.7532 0.225669 25 to 26 141457 -1.3343 0.091052 24 to 25 141381 -1.5585 0.059558 23 to 24 141995 0.2527 0.599755 22 to 23 141874 -0.1042 0.458498 21 to 22 141956 0.1377 0.554749 20 to 21 141512 -1.1721 0.120586 19 to 20 141631 -0.8210 0.205814 18 to 19 142034 0.3678 0.643473 17 to 18 141996 0.2557 0.600895 16 to 17 142412 1.4828 0.930937 15 to 16 141942 0.0964 0.538387 14 to 15 141733 -0.5201 0.301480 13 to 14 142218 0.9105 0.818729 12 to 13 142223 0.9253 0.822590 11 to 12 141385 -1.5467 0.060968 10 to 11 141638 -0.8004 0.211744 9 to 10 142705 2.3471 0.990540 8 to 9 142002 0.2734 0.607713 7 to 8 141655 -0.7502 0.226556 6 to 7 142251 1.0079 0.843243 5 to 6 141625 -0.8387 0.200810 4 to 5 141949 0.1170 0.546578 3 to 4 141589 -0.9449 0.172348 2 to 3 141563 -1.0216 0.153480 1 to 2 142795 2.6126 0.995507 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-12-10_17:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2465.52 -0.488 0.312890 Test results for specific bytes for dh-ranFile-2015-12-10_17:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2389.80 -1.558 0.059559 2 to 9 2450.91 -0.694 0.243783 3 to 10 2564.14 0.907 0.817798 4 to 11 2469.32 -0.434 0.332211 5 to 12 2455.60 -0.628 0.265040 6 to 13 2622.20 1.728 0.958021 7 to 14 2479.29 -0.293 0.384788 8 to 15 2651.36 2.141 0.983846 9 to 16 2554.30 0.768 0.778731 10 to 17 2475.10 -0.352 0.362342 11 to 18 2513.68 0.193 0.576698 12 to 19 2487.69 -0.174 0.430887 13 to 20 2503.99 0.056 0.522478 14 to 21 2521.60 0.305 0.619975 15 to 22 2286.16 -3.024 0.001247 16 to 23 2565.88 0.932 0.824254 17 to 24 2554.21 0.767 0.778338 18 to 25 2295.18 -2.897 0.001886 19 to 26 2415.97 -1.188 0.117356 20 to 27 2501.09 0.015 0.506171 21 to 28 2383.01 -1.655 0.049012 22 to 29 2539.05 0.552 0.709601 23 to 30 2497.36 -0.037 0.485103 24 to 31 2472.57 -0.388 0.349059 25 to 32 2529.80 0.421 0.663263 CDPARK for dh-ranFile-2015-12-10_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 3577 2.4658 0.993164 3513 -0.4566 0.323972 3514 -0.4110 0.340551 3520 -0.1370 0.445521 3510 -0.5936 0.276387 3521 -0.0913 0.463617 3536 0.5936 0.723613 3505 -0.8219 0.205562 3536 0.5936 0.723613 3515 -0.3653 0.357445 Square side=100, avg. no. parked=3524.70 sample std.=19.94 p-value of the KSTEST for those 10 p-values: 0.466249 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-12-10_17:31 0.2741,0.7495,0.4043,0.2195,0.8225,0.4361,0.8086,0.5915,0.8659,0.6141, The KS test for those 10 p-values: 0.498424 The 3DSPHERES test for dh-ranFile-2015-12-10_17:31 sample no r^3 equiv. uni. 1 5.842 0.176952 2 55.468 0.842596 3 5.529 0.168303 4 24.473 0.557704 5 80.954 0.932692 6 16.742 0.427685 7 12.851 0.348428 8 51.817 0.822227 9 0.758 0.024936 10 47.221 0.792795 11 15.370 0.400900 12 5.048 0.154863 13 52.722 0.827504 14 26.488 0.586432 15 15.559 0.404659 16 41.444 0.748790 17 0.101 0.003366 18 92.925 0.954838 19 13.814 0.369003 20 57.159 0.851222 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.759373 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-12-10_17:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 0.5 -0.8 -0.3 1.0 1.1 -0.8 0.9 0.2 1.4 0.4 -1.3 -0.3 -0.8 -0.7 0.8 0.1 -0.4 1.2 -1.7 0.9 -0.3 0.2 1.1 1.2 -1.6 0.4 0.3 -0.7 -0.6 -0.4 -0.1 0.8 1.2 -0.1 -0.8 -1.4 0.2 1.3 -0.1 -0.6 -1.0 -0.1 Chi-square with 42 degrees of freedom:30.744076 z-score=-1.228122, p-value=0.099497 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-12-10_17:31 Test no p-value 1 0.008843 2 0.117179 3 0.225929 4 0.756684 5 0.281495 6 0.042595 7 0.000413 8 0.340089 9 0.938725 10 0.000773 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000559 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-12-10_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 66744 0.09 66597 0.07 3 25000.00 25001 0.00 25162 1.05 4 6666.67 6601 0.65 6523 3.10 5 1388.89 1404 0.16 1408 0.26 6 238.10 218 1.70 268 3.76 7 34.72 28 1.30 35 0.00 8 4.96 3 0.77 6 0.22 p=0.41351 p=0.79357 Number of rngs required: 687730, p-value: 0.218 RESULTS OF CRAPS TEST for dh-ranFile-2015-12-10_17:31 No. of wins: Observed Expected 98590 98585.9 z-score= 0.019, pvalue=0.50739 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66442 66666.7 0.757 0.757 2 37574 37654.3 0.171 0.928 3 27133 26954.7 1.179 2.107 4 19266 19313.5 0.117 2.224 5 13948 13851.4 0.673 2.897 6 10108 9943.5 2.720 5.617 7 7235 7145.0 1.133 6.750 8 4979 5139.1 4.986 11.736 9 3645 3699.9 0.814 12.550 10 2627 2666.3 0.579 13.129 11 1969 1923.3 1.084 14.214 12 1445 1388.7 2.279 16.493 13 971 1003.7 1.066 17.559 14 733 726.1 0.065 17.624 15 555 525.8 1.618 19.241 16 360 381.2 1.174 20.415 17 299 276.5 1.824 22.239 18 213 200.8 0.737 22.977 19 135 146.0 0.827 23.803 20 90 106.2 2.475 26.279 21 273 287.1 0.694 26.973 Chisq= 26.97 for 20 degrees of freedom, p= 0.86397 SUMMARY of craptest p-value for no. of wins: 0.507389 p-value for throws/game: 0.863965 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-12-10_17:31 No. of wins: Observed Expected 98600 98585.9 z-score= 0.063, pvalue=0.52522 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66612 66666.7 0.045 0.045 2 37730 37654.3 0.152 0.197 3 27016 26954.7 0.139 0.336 4 19415 19313.5 0.534 0.870 5 13705 13851.4 1.548 2.418 6 9984 9943.5 0.165 2.582 7 7264 7145.0 1.981 4.563 8 5188 5139.1 0.466 5.029 9 3560 3699.9 5.287 10.317 10 2606 2666.3 1.364 11.680 11 2025 1923.3 5.375 17.055 12 1355 1388.7 0.820 17.874 13 947 1003.7 3.205 21.079 14 711 726.1 0.316 21.395 15 529 525.8 0.019 21.414 16 376 381.2 0.070 21.483 17 248 276.5 2.945 24.429 18 195 200.8 0.169 24.598 19 136 146.0 0.683 25.281 20 96 106.2 0.982 26.263 21 302 287.1 0.772 27.035 Chisq= 27.04 for 20 degrees of freedom, p= 0.86572 SUMMARY of craptest p-value for no. of wins: 0.525216 p-value for throws/game: 0.865722 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0004,0.0006,0.0008,0.0012,0.0018,0.0019,0.0034,0.0036,0.0076,0.0088, 0.0105,0.0141,0.0150,0.0249,0.0375,0.0394,0.0426,0.0490,0.0528,0.0550, 0.0596,0.0596,0.0610,0.0664,0.0673,0.0785,0.0798,0.0828,0.0911,0.0995, 0.1054,0.1061,0.1172,0.1174,0.1206,0.1220,0.1271,0.1346,0.1349,0.1407, 0.1410,0.1449,0.1507,0.1526,0.1535,0.1549,0.1558,0.1559,0.1632,0.1683, 0.1723,0.1747,0.1770,0.1771,0.1800,0.1897,0.1929,0.2008,0.2036,0.2056, 0.2058,0.2068,0.2117,0.2158,0.2167,0.2184,0.2186,0.2195,0.2196,0.2213, 0.2217,0.2241,0.2257,0.2259,0.2266,0.2407,0.2425,0.2438,0.2525,0.2535, 0.2650,0.2701,0.2741,0.2762,0.2764,0.2773,0.2778,0.2815,0.2864,0.2876, 0.2908,0.2911,0.3007,0.3015,0.3040,0.3058,0.3129,0.3130,0.3177,0.3240, 0.3322,0.3401,0.3406,0.3484,0.3491,0.3552,0.3574,0.3623,0.3642,0.3673, 0.3686,0.3690,0.3724,0.3763,0.3804,0.3848,0.3952,0.4009,0.4018,0.4018, 0.4043,0.4047,0.4091,0.4135,0.4277,0.4309,0.4318,0.4357,0.4361,0.4430, 0.4455,0.4550,0.4585,0.4636,0.4662,0.4708,0.4851,0.4874,0.4943,0.4984, 0.5004,0.5062,0.5074,0.5145,0.5149,0.5225,0.5225,0.5245,0.5252,0.5257, 0.5374,0.5384,0.5466,0.5538,0.5547,0.5577,0.5649,0.5767,0.5797,0.5801, 0.5817,0.5854,0.5864,0.5915,0.5943,0.5998,0.5999,0.6009,0.6061,0.6077, 0.6096,0.6107,0.6141,0.6148,0.6200,0.6402,0.6420,0.6435,0.6466,0.6511, 0.6566,0.6626,0.6633,0.6649,0.6746,0.6803,0.6814,0.6821,0.6947,0.6948, 0.6948,0.6976,0.7026,0.7096,0.7144,0.7184,0.7236,0.7236,0.7285,0.7325, 0.7338,0.7464,0.7488,0.7495,0.7567,0.7567,0.7584,0.7594,0.7767,0.7783, 0.7787,0.7928,0.7936,0.7961,0.8086,0.8119,0.8170,0.8178,0.8181,0.8181, 0.8187,0.8203,0.8222,0.8225,0.8226,0.8243,0.8258,0.8275,0.8320,0.8426, 0.8432,0.8512,0.8549,0.8640,0.8657,0.8659,0.8688,0.8973,0.9018,0.9080, 0.9164,0.9170,0.9262,0.9273,0.9284,0.9309,0.9309,0.9309,0.9327,0.9387, 0.9424,0.9460,0.9515,0.9548,0.9580,0.9611,0.9640,0.9645,0.9682,0.9687, 0.9733,0.9786,0.9793,0.9816,0.9838,0.9846,0.9905,0.9932,0.9955, Overall p-value after applying KStest on 269 p-values = 0.194549 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.