RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-09-27_07:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.76 21.1297 0.779460 2 to 25 15.98 13.3960 0.290701 3 to 26 15.75 25.8610 0.922969 4 to 27 15.59 19.0698 0.675461 5 to 28 15.66 23.4844 0.865865 6 to 29 15.70 21.3036 0.786995 7 to 30 15.83 21.9030 0.811521 8 to 31 15.62 29.6569 0.971072 9 to 32 15.52 29.9815 0.973522 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.002778 Tough bday spacings test for dh-ranFile-2015-09-27_07:31: 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 37 62 90 98 88 52 40 12 9 4 (O-E)^2/E 0.1 0.0 1.7 0.6 0.0 1.2 0.0 3.5 0.6 0.9 0.0 Birthday Spacings: Sum(O-E)^2/E= 8.664, p= 0.436 RESULTS OF GCD FOR dh-ranFile-2015-09-27_07:31 Euclid's algorithm: p-value, steps to gcd: 0.149930 p-value, dist. of gcd's: 0.041896 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-09-27_07:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.391 0.829 0.080 0.884 0.749 0.166 0.093 0.165 Bits 8 to 15---> 0.959 0.573 0.095 0.403 0.306 0.584 0.699 0.466 Bits 16 to 23---> 0.652 0.736 0.374 0.113 0.207 0.648 0.311 0.076 Bits 24 to 31---> 0.154 0.655 0.106 0.692 0.765 0.869 0.971 0.219 KS test for the above 32 p values: 0.342 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-09-27_07:31, p-values for 5 runs: 0.5377, 0.2303, 0.6054, 0.0681, 0.8200 Rank test for binary matrices (31x31) for dh-ranFile-2015-09-27_07:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 233 211.4 2.203 2.203 r= 29 5252 5134.0 2.712 4.915 r= 30 23013 23103.0 0.351 5.266 r= 31 11502 11551.5 0.212 5.478 chi-square = 5.478 with df = 3; p-value = 0.860 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-09-27_07:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 221 211.4 0.434 0.434 r= 30 5125 5134.0 0.016 0.450 r= 31 23211 23103.0 0.504 0.955 r= 32 11443 11551.5 1.020 1.974 chi-square = 1.974 with df = 3; p-value = 0.422 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-09-27_07:31 b-rank test for bits 1 to 8, p=0.39739 b-rank test for bits 2 to 9, p=0.54369 b-rank test for bits 3 to 10, p=0.02893 b-rank test for bits 4 to 11, p=0.20753 b-rank test for bits 5 to 12, p=0.69412 b-rank test for bits 6 to 13, p=0.09547 b-rank test for bits 7 to 14, p=0.19004 b-rank test for bits 8 to 15, p=0.34164 b-rank test for bits 9 to 16, p=0.22866 b-rank test for bits 10 to 17, p=0.23100 b-rank test for bits 11 to 18, p=0.94047 b-rank test for bits 12 to 19, p=0.99052 b-rank test for bits 13 to 20, p=0.24114 b-rank test for bits 14 to 21, p=0.53844 b-rank test for bits 15 to 22, p=0.15272 b-rank test for bits 16 to 23, p=0.97935 b-rank test for bits 17 to 24, p=0.25259 b-rank test for bits 18 to 25, p=0.74726 b-rank test for bits 19 to 26, p=0.87213 b-rank test for bits 20 to 27, p=0.80167 b-rank test for bits 21 to 28, p=0.86679 b-rank test for bits 22 to 29, p=0.60066 b-rank test for bits 23 to 30, p=0.20039 b-rank test for bits 24 to 31, p=0.78008 b-rank test for bits 25 to 32, p=0.18945 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 = 0.580997 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-09-27_07:31 (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 142183 0.64 0.738724 2 141782 -0.30 0.383042 3 142619 1.66 0.951352 4 141505 -0.94 0.172407 5 141652 -0.60 0.273841 6 142163 0.59 0.723305 7 142483 1.34 0.909934 8 141853 -0.13 0.447646 9 142699 1.85 0.967483 10 141904 -0.01 0.495032 11 141701 -0.49 0.313217 12 141731 -0.42 0.338464 13 142007 0.23 0.590255 14 141322 -1.37 0.084990 15 141807 -0.24 0.405518 16 142519 1.42 0.922844 17 142188 0.65 0.742508 18 141608 -0.70 0.240703 19 142558 1.52 0.935188 20 141892 -0.04 0.483851 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-09-27_07:31 Bits used No. missing words z-score p-value 23 to 32 141997 0.3023 0.618792 22 to 31 141851 -0.2011 0.420295 21 to 30 142210 1.0368 0.850084 20 to 29 141516 -1.3563 0.087500 19 to 28 141994 0.2920 0.614844 18 to 27 141685 -0.7736 0.219598 17 to 26 141771 -0.4770 0.316681 16 to 25 141365 -1.8770 0.030259 15 to 24 141460 -1.5494 0.060641 14 to 23 142354 1.5333 0.937405 13 to 22 142051 0.4885 0.687408 12 to 21 141530 -1.3080 0.095431 11 to 20 142245 1.1575 0.876462 10 to 19 141880 -0.1011 0.459721 9 to 18 141753 -0.5391 0.294920 8 to 17 141736 -0.5977 0.275024 7 to 16 142039 0.4471 0.672612 6 to 15 141867 -0.1460 0.441974 5 to 14 141883 -0.0908 0.463829 4 to 13 141619 -1.0011 0.158380 3 to 12 141593 -1.0908 0.137682 2 to 11 141695 -0.7391 0.229933 1 to 10 141905 -0.0149 0.494044 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-09-27_07:31 Bits used No. missing words z-score p-value 28 to 32 142202 0.9921 0.839426 27 to 31 141980 0.2396 0.594664 26 to 30 141849 -0.2045 0.418978 25 to 29 141745 -0.5571 0.288746 24 to 28 141552 -1.2113 0.112893 23 to 27 141954 0.1514 0.560179 22 to 26 141871 -0.1299 0.448310 21 to 25 141817 -0.3130 0.377147 20 to 24 142124 0.7277 0.766600 19 to 23 141842 -0.2282 0.409731 18 to 22 141941 0.1074 0.542747 17 to 21 142066 0.5311 0.702320 16 to 20 141771 -0.4689 0.319565 15 to 19 140915 -3.3706 0.000375 14 to 18 142415 1.7141 0.956748 13 to 17 141369 -1.8316 0.033504 12 to 16 141756 -0.5198 0.301615 11 to 15 141972 0.2124 0.584118 10 to 14 142045 0.4599 0.677205 9 to 13 141856 -0.1808 0.428270 8 to 12 142107 0.6701 0.748593 7 to 11 142295 1.3074 0.904454 6 to 10 142001 0.3107 0.622003 5 to 9 141988 0.2667 0.605141 4 to 8 141849 -0.2045 0.418978 3 to 7 141441 -1.5876 0.056193 2 to 6 141831 -0.2655 0.395302 1 to 5 141728 -0.6147 0.269384 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-09-27_07:31 Bits used No. missing words z-score p-value 31 to 32 141390 -1.5319 0.062768 30 to 31 141732 -0.5231 0.300453 29 to 30 141634 -0.8122 0.208343 28 to 29 142160 0.7394 0.770180 27 to 28 141961 0.1524 0.560572 26 to 27 141943 0.0993 0.539559 25 to 26 142639 2.1524 0.984318 24 to 25 141673 -0.6971 0.242858 23 to 24 141510 -1.1780 0.119405 22 to 23 141891 -0.0541 0.478439 21 to 22 142123 0.6303 0.735749 20 to 21 141871 -0.1131 0.454988 19 to 20 141527 -1.1278 0.129699 18 to 19 141604 -0.9007 0.183880 17 to 18 141519 -1.1514 0.124781 16 to 17 141767 -0.4199 0.337297 15 to 16 142249 1.0020 0.841823 14 to 15 141470 -1.2960 0.097495 13 to 14 142711 2.3648 0.990980 12 to 13 142198 0.8515 0.802764 11 to 12 141739 -0.5024 0.307676 10 to 11 142723 2.4002 0.991807 9 to 10 141209 -2.0659 0.019420 8 to 9 141678 -0.6824 0.247496 7 to 8 142111 0.5949 0.724044 6 to 7 142272 1.0698 0.857651 5 to 6 141803 -0.3137 0.376891 4 to 5 141096 -2.3992 0.008215 3 to 4 141635 -0.8092 0.209191 2 to 3 141955 0.1347 0.553583 1 to 2 141684 -0.6647 0.253124 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-09-27_07:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2579.24 1.121 0.868767 Test results for specific bytes for dh-ranFile-2015-09-27_07:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2518.81 0.266 0.604859 2 to 9 2493.35 -0.094 0.462541 3 to 10 2335.08 -2.332 0.009843 4 to 11 2395.34 -1.480 0.069412 5 to 12 2398.07 -1.442 0.074716 6 to 13 2539.41 0.557 0.711368 7 to 14 2472.29 -0.392 0.347571 8 to 15 2576.24 1.078 0.859530 9 to 16 2648.87 2.105 0.982371 10 to 17 2376.47 -1.747 0.040315 11 to 18 2442.94 -0.807 0.209867 12 to 19 2553.87 0.762 0.776922 13 to 20 2483.13 -0.239 0.405718 14 to 21 2532.73 0.463 0.678291 15 to 22 2433.30 -0.943 0.172783 16 to 23 2461.46 -0.545 0.292851 17 to 24 2424.16 -1.073 0.141726 18 to 25 2462.57 -0.529 0.298263 19 to 26 2451.75 -0.682 0.247500 20 to 27 2506.41 0.091 0.536121 21 to 28 2577.01 1.089 0.861946 22 to 29 2563.59 0.899 0.815759 23 to 30 2593.39 1.321 0.906699 24 to 31 2471.44 -0.404 0.343133 25 to 32 2489.46 -0.149 0.440748 CDPARK for dh-ranFile-2015-09-27_07:31: 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 3468 -2.5114 0.006012 3577 2.4658 0.993164 3548 1.1416 0.873180 3540 0.7763 0.781201 3485 -1.7352 0.041356 3545 1.0046 0.842447 3543 0.9132 0.819442 3523 0.0000 0.500000 3512 -0.5023 0.307734 3516 -0.3196 0.374623 Square side=100, avg. no. parked=3525.70 sample std.=30.46 p-value of the KSTEST for those 10 p-values: 0.349844 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-09-27_07:31 0.6478,0.3683,0.6403,0.8189,0.6941,0.4945,0.1739,0.6527,0.1230,0.8131, The KS test for those 10 p-values: 0.593330 The 3DSPHERES test for dh-ranFile-2015-09-27_07:31 sample no r^3 equiv. uni. 1 9.100 0.261651 2 36.446 0.703255 3 82.229 0.935492 4 46.261 0.786056 5 9.922 0.281600 6 55.016 0.840207 7 45.830 0.782957 8 25.525 0.572943 9 4.055 0.126439 10 8.076 0.236007 11 5.524 0.168186 12 2.812 0.089488 13 11.304 0.313949 14 15.319 0.399875 15 61.202 0.869979 16 58.119 0.855906 17 14.512 0.383521 18 29.133 0.621336 19 8.024 0.234673 20 45.657 0.781701 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.818703 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-09-27_07:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 2.0 -0.7 1.3 -1.1 0.1 0.3 -1.4 0.8 -0.3 -0.0 0.9 -0.4 -0.5 0.5 -0.1 0.1 -0.4 -0.2 -1.3 1.6 -0.6 1.2 0.3 -1.0 -0.2 -0.4 1.9 1.1 -0.3 -0.3 -1.2 -0.2 -1.1 0.4 -0.6 0.4 0.5 -1.3 -0.4 -0.7 -0.6 -1.0 0.8 Chi-square with 42 degrees of freedom:32.461634 z-score=-1.040721, p-value=0.145110 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-09-27_07:31 Test no p-value 1 0.002883 2 0.861976 3 0.023730 4 0.039226 5 0.222078 6 0.203908 7 0.328644 8 0.083634 9 0.057404 10 0.129233 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000236 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-09-27_07:31: (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 66532 0.27 66644 0.01 3 25000.00 25103 0.42 24920 0.26 4 6666.67 6657 0.01 6757 1.22 5 1388.89 1402 0.12 1407 0.24 6 238.10 256 1.35 235 0.04 7 34.72 44 2.48 32 0.21 8 4.96 5 0.00 4 0.19 p=0.41207 p=0.09588 Number of rngs required: 687998, p-value: 0.320 RESULTS OF CRAPS TEST for dh-ranFile-2015-09-27_07:31 No. of wins: Observed Expected 99066 98585.9 z-score= 2.147, pvalue=0.98412 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66520 66666.7 0.323 0.323 2 37484 37654.3 0.770 1.093 3 27030 26954.7 0.210 1.303 4 19207 19313.5 0.587 1.890 5 14028 13851.4 2.251 4.141 6 9928 9943.5 0.024 4.165 7 7105 7145.0 0.224 4.390 8 5294 5139.1 4.671 9.060 9 3771 3699.9 1.368 10.428 10 2665 2666.3 0.001 10.429 11 1925 1923.3 0.001 10.430 12 1427 1388.7 1.054 11.484 13 1000 1003.7 0.014 11.498 14 708 726.1 0.453 11.951 15 501 525.8 1.173 13.124 16 389 381.2 0.162 13.286 17 291 276.5 0.756 14.042 18 190 200.8 0.584 14.626 19 142 146.0 0.109 14.735 20 109 106.2 0.073 14.808 21 286 287.1 0.004 14.812 Chisq= 14.81 for 20 degrees of freedom, p= 0.21294 SUMMARY of craptest p-value for no. of wins: 0.984122 p-value for throws/game: 0.212937 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-09-27_07:31 No. of wins: Observed Expected 98633 98585.9 z-score= 0.211, pvalue=0.58350 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66938 66666.7 1.104 1.104 2 37733 37654.3 0.164 1.269 3 26593 26954.7 4.854 6.123 4 19157 19313.5 1.268 7.391 5 14015 13851.4 1.932 9.323 6 9894 9943.5 0.247 9.569 7 7105 7145.0 0.224 9.794 8 5031 5139.1 2.273 12.066 9 3762 3699.9 1.043 13.110 10 2755 2666.3 2.951 16.061 11 1894 1923.3 0.447 16.508 12 1421 1388.7 0.749 17.257 13 996 1003.7 0.059 17.317 14 717 726.1 0.115 17.432 15 531 525.8 0.051 17.482 16 391 381.2 0.255 17.737 17 291 276.5 0.756 18.493 18 217 200.8 1.302 19.795 19 167 146.0 3.025 22.820 20 96 106.2 0.982 23.803 21 296 287.1 0.275 24.078 Chisq= 24.08 for 20 degrees of freedom, p= 0.76099 SUMMARY of craptest p-value for no. of wins: 0.583495 p-value for throws/game: 0.760995 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0002,0.0004,0.0028,0.0029,0.0060,0.0082,0.0098,0.0194,0.0237,0.0289, 0.0303,0.0335,0.0392,0.0403,0.0414,0.0419,0.0562,0.0574,0.0606,0.0628, 0.0681,0.0694,0.0747,0.0760,0.0797,0.0836,0.0850,0.0875,0.0895,0.0933, 0.0954,0.0955,0.0955,0.0959,0.0975,0.1059,0.1129,0.1131,0.1194,0.1230, 0.1248,0.1264,0.1292,0.1297,0.1377,0.1417,0.1451,0.1499,0.1527,0.1543, 0.1584,0.1649,0.1657,0.1682,0.1724,0.1728,0.1739,0.1839,0.1894,0.1900, 0.2004,0.2039,0.2067,0.2075,0.2083,0.2092,0.2099,0.2129,0.2192,0.2196, 0.2221,0.2287,0.2299,0.2303,0.2310,0.2347,0.2360,0.2407,0.2411,0.2429, 0.2475,0.2475,0.2526,0.2531,0.2617,0.2694,0.2738,0.2750,0.2816,0.2887, 0.2907,0.2929,0.2949,0.2983,0.3005,0.3016,0.3060,0.3077,0.3077,0.3107, 0.3132,0.3139,0.3167,0.3196,0.3204,0.3286,0.3373,0.3385,0.3416,0.3418, 0.3431,0.3476,0.3498,0.3683,0.3739,0.3746,0.3769,0.3771,0.3830,0.3835, 0.3912,0.3953,0.3974,0.3999,0.4028,0.4055,0.4057,0.4097,0.4121,0.4190, 0.4190,0.4203,0.4222,0.4283,0.4358,0.4407,0.4420,0.4476,0.4483,0.4550, 0.4597,0.4625,0.4638,0.4663,0.4784,0.4839,0.4940,0.4945,0.4950,0.5000, 0.5361,0.5377,0.5384,0.5396,0.5427,0.5437,0.5536,0.5602,0.5606,0.5729, 0.5734,0.5810,0.5835,0.5841,0.5842,0.5903,0.5933,0.5947,0.6007,0.6049, 0.6051,0.6054,0.6148,0.6188,0.6213,0.6220,0.6403,0.6478,0.6481,0.6520, 0.6527,0.6546,0.6726,0.6755,0.6772,0.6783,0.6874,0.6919,0.6941,0.6941, 0.6986,0.7023,0.7033,0.7114,0.7233,0.7240,0.7357,0.7361,0.7387,0.7425, 0.7473,0.7486,0.7493,0.7610,0.7652,0.7666,0.7702,0.7769,0.7795,0.7801, 0.7812,0.7817,0.7830,0.7861,0.7870,0.8017,0.8028,0.8115,0.8131,0.8158, 0.8187,0.8189,0.8194,0.8200,0.8287,0.8394,0.8402,0.8418,0.8424,0.8501, 0.8559,0.8577,0.8595,0.8600,0.8619,0.8620,0.8659,0.8668,0.8685,0.8688, 0.8700,0.8721,0.8732,0.8765,0.8839,0.9045,0.9067,0.9099,0.9228,0.9230, 0.9352,0.9355,0.9374,0.9405,0.9514,0.9567,0.9591,0.9675,0.9711,0.9713, 0.9735,0.9793,0.9824,0.9841,0.9843,0.9905,0.9910,0.9918,0.9932, Overall p-value after applying KStest on 269 p-values = 0.129974 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.