RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-08-11_16:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.80 12.9316 0.259246 2 to 25 15.64 19.6001 0.704810 3 to 26 16.06 14.2588 0.351292 4 to 27 15.76 12.2625 0.216010 5 to 28 15.66 22.4259 0.831110 6 to 29 15.66 23.8613 0.876746 7 to 30 15.54 15.6714 0.452761 8 to 31 15.50 18.3794 0.634706 9 to 32 15.83 20.2719 0.739439 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.703185 Tough bday spacings test for dh-ranFile-2015-08-11_16:31: 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 15 41 68 96 88 82 57 29 13 8 3 (O-E)^2/E 3.7 0.5 0.4 0.0 1.0 0.2 0.5 0.0 0.2 0.3 0.3 Birthday Spacings: Sum(O-E)^2/E= 7.094, p= 0.283 RESULTS OF GCD FOR dh-ranFile-2015-08-11_16:31 Euclid's algorithm: p-value, steps to gcd: 0.281621 p-value, dist. of gcd's: 0.513132 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-08-11_16:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.385 0.118 0.307 0.646 0.015 0.398 0.465 0.582 Bits 8 to 15---> 0.906 0.141 0.056 0.313 0.093 0.291 0.688 0.572 Bits 16 to 23---> 0.148 0.763 0.503 0.974 0.562 0.677 0.167 0.434 Bits 24 to 31---> 0.340 0.686 0.762 0.210 0.907 0.649 0.921 0.128 KS test for the above 32 p values: 0.190 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-08-11_16:31, p-values for 5 runs: 0.3246, 0.3524, 0.1987, 0.0067, 0.7455 Rank test for binary matrices (31x31) for dh-ranFile-2015-08-11_16:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 188 211.4 2.594 2.594 r= 29 5210 5134.0 1.125 3.719 r= 30 23078 23103.0 0.027 3.746 r= 31 11524 11551.5 0.066 3.811 chi-square = 3.811 with df = 3; p-value = 0.717 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-08-11_16:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 212 211.4 0.002 0.002 r= 30 5178 5134.0 0.377 0.379 r= 31 23102 23103.0 0.000 0.379 r= 32 11508 11551.5 0.164 0.543 chi-square = 0.543 with df = 3; p-value = 0.091 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-08-11_16:31 b-rank test for bits 1 to 8, p=0.68196 b-rank test for bits 2 to 9, p=0.38992 b-rank test for bits 3 to 10, p=0.26346 b-rank test for bits 4 to 11, p=0.15486 b-rank test for bits 5 to 12, p=0.55846 b-rank test for bits 6 to 13, p=0.24370 b-rank test for bits 7 to 14, p=0.74357 b-rank test for bits 8 to 15, p=0.84648 b-rank test for bits 9 to 16, p=0.70335 b-rank test for bits 10 to 17, p=0.46120 b-rank test for bits 11 to 18, p=0.71991 b-rank test for bits 12 to 19, p=0.06714 b-rank test for bits 13 to 20, p=0.01760 b-rank test for bits 14 to 21, p=0.91687 b-rank test for bits 15 to 22, p=0.94278 b-rank test for bits 16 to 23, p=0.11316 b-rank test for bits 17 to 24, p=0.09706 b-rank test for bits 18 to 25, p=0.92893 b-rank test for bits 19 to 26, p=0.45233 b-rank test for bits 20 to 27, p=0.50165 b-rank test for bits 21 to 28, p=0.91569 b-rank test for bits 22 to 29, p=0.82491 b-rank test for bits 23 to 30, p=0.99116 b-rank test for bits 24 to 31, p=0.86911 b-rank test for bits 25 to 32, p=0.29066 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 = 0.536444 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-08-11_16:31 (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 141596 -0.73 0.232060 2 142123 0.50 0.691191 3 142051 0.33 0.629680 4 142636 1.70 0.955230 5 142348 1.02 0.847302 6 141931 0.05 0.520190 7 141980 0.17 0.565574 8 142470 1.31 0.904898 9 142226 0.74 0.770315 10 142299 0.91 0.818706 11 141644 -0.62 0.267652 12 141666 -0.57 0.284838 13 141612 -0.69 0.243623 14 142605 1.63 0.947961 15 142151 0.56 0.713844 16 142127 0.51 0.694475 17 142410 1.17 0.878957 18 142172 0.61 0.730298 19 141415 -1.15 0.124050 20 141898 -0.03 0.489440 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-08-11_16:31 Bits used No. missing words z-score p-value 23 to 32 141323 -2.0218 0.021597 22 to 31 141910 0.0023 0.500922 21 to 30 142150 0.8299 0.796701 20 to 29 141487 -1.4563 0.072653 19 to 28 141898 -0.0391 0.484418 18 to 27 142103 0.6678 0.747878 17 to 26 141885 -0.0839 0.466569 16 to 25 141983 0.2540 0.600266 15 to 24 142004 0.3264 0.627957 14 to 23 141993 0.2885 0.613525 13 to 22 141972 0.2161 0.585547 12 to 21 141954 0.1540 0.561209 11 to 20 142146 0.8161 0.792780 10 to 19 141483 -1.4701 0.070767 9 to 18 141777 -0.4563 0.324083 8 to 17 141458 -1.5563 0.059817 7 to 16 141528 -1.3149 0.094267 6 to 15 141682 -0.7839 0.216550 5 to 14 142618 2.4437 0.992731 4 to 13 142539 2.1713 0.985045 3 to 12 141912 0.0092 0.503673 2 to 11 142374 1.6023 0.945457 1 to 10 141616 -1.0115 0.155893 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-08-11_16:31 Bits used No. missing words z-score p-value 28 to 32 141331 -1.9604 0.024972 27 to 31 141357 -1.8723 0.030582 26 to 30 141242 -2.2621 0.011845 25 to 29 141483 -1.4452 0.074203 24 to 28 141804 -0.3571 0.360527 23 to 27 141979 0.2362 0.593349 22 to 26 141261 -2.1977 0.013984 21 to 25 141811 -0.3333 0.369446 20 to 24 142386 1.6158 0.946935 19 to 23 142274 1.2362 0.891802 18 to 22 141731 -0.6045 0.272753 17 to 21 142086 0.5989 0.725374 16 to 20 142168 0.8768 0.809715 15 to 19 141799 -0.3740 0.354202 14 to 18 141502 -1.3808 0.083673 13 to 17 141939 0.1006 0.540057 12 to 16 141446 -1.5706 0.058137 11 to 15 141281 -2.1299 0.016589 10 to 14 142121 0.7175 0.763475 9 to 13 142039 0.4396 0.669872 8 to 12 142270 1.2226 0.889262 7 to 11 141917 0.0260 0.510371 6 to 10 141563 -1.1740 0.120198 5 to 9 142480 1.9345 0.973473 4 to 8 142466 1.8870 0.970421 3 to 7 141027 -2.9909 0.001391 2 to 6 141787 -0.4147 0.339189 1 to 5 142068 0.5379 0.704665 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-08-11_16:31 Bits used No. missing words z-score p-value 31 to 32 141736 -0.5113 0.304571 30 to 31 142413 1.4858 0.931328 29 to 30 141388 -1.5378 0.062043 28 to 29 141706 -0.5998 0.274322 27 to 28 142050 0.4150 0.660913 26 to 27 141861 -0.1426 0.443316 25 to 26 141482 -1.2606 0.103734 24 to 25 141938 0.0846 0.533699 23 to 24 142192 0.8338 0.797813 22 to 23 141747 -0.4788 0.316023 21 to 22 141739 -0.5024 0.307676 20 to 21 142476 1.6716 0.952698 19 to 20 142285 1.1082 0.866106 18 to 19 141748 -0.4759 0.317073 17 to 18 142320 1.2114 0.887132 16 to 17 141744 -0.4877 0.312882 15 to 16 141764 -0.4287 0.334070 14 to 15 141699 -0.6204 0.267483 13 to 14 141423 -1.4346 0.075700 12 to 13 141265 -1.9007 0.028672 11 to 12 141472 -1.2901 0.098515 10 to 11 141520 -1.1485 0.125388 9 to 10 141713 -0.5791 0.281246 8 to 9 142071 0.4769 0.683284 7 to 8 141758 -0.4464 0.327654 6 to 7 141837 -0.2134 0.415522 5 to 6 141775 -0.3963 0.345959 4 to 5 141817 -0.2724 0.392673 3 to 4 141999 0.2645 0.604308 2 to 3 141734 -0.5172 0.302509 1 to 2 141547 -1.0688 0.142575 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-08-11_16:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2548.02 0.679 0.751464 Test results for specific bytes for dh-ranFile-2015-08-11_16:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2686.63 2.639 0.995847 2 to 9 2560.98 0.862 0.805769 3 to 10 2558.15 0.822 0.794585 4 to 11 2403.40 -1.366 0.085941 5 to 12 2477.34 -0.320 0.374327 6 to 13 2546.21 0.654 0.743305 7 to 14 2564.25 0.909 0.818212 8 to 15 2598.42 1.392 0.918023 9 to 16 2562.38 0.882 0.811159 10 to 17 2481.02 -0.268 0.394212 11 to 18 2516.77 0.237 0.593731 12 to 19 2441.49 -0.827 0.204007 13 to 20 2553.43 0.756 0.775067 14 to 21 2535.90 0.508 0.694165 15 to 22 2423.63 -1.080 0.140058 16 to 23 2482.07 -0.254 0.399926 17 to 24 2511.28 0.160 0.563395 18 to 25 2359.75 -1.983 0.023661 19 to 26 2598.89 1.399 0.919026 20 to 27 2604.46 1.477 0.930209 21 to 28 2474.96 -0.354 0.361630 22 to 29 2444.15 -0.790 0.214792 23 to 30 2481.09 -0.267 0.394567 24 to 31 2430.50 -0.983 0.162824 25 to 32 2590.19 1.275 0.898919 CDPARK for dh-ranFile-2015-08-11_16:31: 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 3513 -0.4566 0.323972 3518 -0.2283 0.409702 3504 -0.8676 0.192812 3477 -2.1005 0.017844 3514 -0.4110 0.340551 3550 1.2329 0.891189 3539 0.7306 0.767486 3537 0.6393 0.738676 3495 -1.2785 0.100530 3545 1.0046 0.842447 Square side=100, avg. no. parked=3519.20 sample std.=22.33 p-value of the KSTEST for those 10 p-values: 0.870350 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-08-11_16:31 0.6102,0.7012,0.6535,0.1839,0.2279,0.0116,0.7163,0.3275,0.4158,0.3965, The KS test for those 10 p-values: 0.496733 The 3DSPHERES test for dh-ranFile-2015-08-11_16:31 sample no r^3 equiv. uni. 1 58.013 0.855398 2 9.601 0.273872 3 4.068 0.126802 4 39.791 0.734563 5 34.333 0.681597 6 9.956 0.282429 7 30.386 0.636819 8 50.812 0.816169 9 25.937 0.578764 10 61.985 0.873330 11 21.054 0.504313 12 1.667 0.054036 13 37.790 0.716247 14 32.918 0.666217 15 17.427 0.440607 16 28.080 0.607805 17 3.049 0.096654 18 38.659 0.724352 19 28.038 0.607259 20 8.600 0.249236 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.540771 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-08-11_16:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 0.5 0.8 -0.4 -0.5 1.4 0.4 0.6 -0.6 -0.3 0.0 -0.1 0.5 -0.1 -0.9 -0.1 0.5 0.6 1.1 0.7 -1.6 -0.1 0.3 -0.0 -0.2 -0.4 0.1 -1.2 0.0 -0.7 0.1 -0.2 -0.1 -0.3 0.6 -0.1 -1.4 -0.1 -1.2 1.5 0.1 -1.0 -0.1 Chi-square with 42 degrees of freedom:20.252369 z-score=-2.372861, p-value=0.001839 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-08-11_16:31 Test no p-value 1 0.089592 2 0.002077 3 0.003827 4 0.002144 5 0.143229 6 0.055696 7 0.045283 8 0.396672 9 0.005691 10 0.780282 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000000 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-08-11_16:31: (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 66646 0.01 66456 0.67 3 25000.00 25036 0.05 25228 2.08 4 6666.67 6673 0.01 6684 0.05 5 1388.89 1370 0.26 1374 0.16 6 238.10 232 0.16 211 3.08 7 34.72 38 0.31 42 1.53 8 4.96 4 0.19 4 0.19 p=0.01338 p=0.74265 Number of rngs required: 689097, p-value: 0.789 RESULTS OF CRAPS TEST for dh-ranFile-2015-08-11_16:31 No. of wins: Observed Expected 98735 98585.9 z-score= 0.667, pvalue=0.74763 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66821 66666.7 0.357 0.357 2 37760 37654.3 0.297 0.654 3 26960 26954.7 0.001 0.655 4 19398 19313.5 0.370 1.025 5 13825 13851.4 0.050 1.075 6 9805 9943.5 1.930 3.006 7 6978 7145.0 3.904 6.910 8 5191 5139.1 0.525 7.435 9 3687 3699.9 0.045 7.480 10 2675 2666.3 0.028 7.508 11 1939 1923.3 0.128 7.636 12 1356 1388.7 0.772 8.408 13 1031 1003.7 0.742 9.149 14 656 726.1 6.775 15.924 15 508 525.8 0.605 16.529 16 365 381.2 0.684 17.214 17 280 276.5 0.043 17.257 18 215 200.8 1.000 18.257 19 146 146.0 0.000 18.257 20 100 106.2 0.364 18.621 21 304 287.1 0.993 19.614 Chisq= 19.61 for 20 degrees of freedom, p= 0.51768 SUMMARY of craptest p-value for no. of wins: 0.747629 p-value for throws/game: 0.517679 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-08-11_16:31 No. of wins: Observed Expected 98710 98585.9 z-score= 0.555, pvalue=0.71063 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67164 66666.7 3.710 3.710 2 37599 37654.3 0.081 3.791 3 26751 26954.7 1.540 5.331 4 19140 19313.5 1.558 6.889 5 13581 13851.4 5.279 12.169 6 10133 9943.5 3.610 15.778 7 7174 7145.0 0.117 15.896 8 5125 5139.1 0.039 15.934 9 3683 3699.9 0.077 16.011 10 2763 2666.3 3.507 19.519 11 1924 1923.3 0.000 19.519 12 1337 1388.7 1.928 21.446 13 996 1003.7 0.059 21.506 14 682 726.1 2.683 24.189 15 549 525.8 1.020 25.209 16 391 381.2 0.255 25.464 17 279 276.5 0.022 25.486 18 198 200.8 0.040 25.526 19 141 146.0 0.170 25.696 20 118 106.2 1.308 27.003 21 272 287.1 0.796 27.799 Chisq= 27.80 for 20 degrees of freedom, p= 0.88576 SUMMARY of craptest p-value for no. of wins: 0.710632 p-value for throws/game: 0.885757 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0000,0.0014,0.0018,0.0021,0.0021,0.0038,0.0057,0.0067,0.0116,0.0118, 0.0134,0.0140,0.0152,0.0166,0.0176,0.0178,0.0216,0.0237,0.0250,0.0287, 0.0306,0.0453,0.0540,0.0557,0.0560,0.0581,0.0598,0.0620,0.0671,0.0708, 0.0727,0.0742,0.0757,0.0837,0.0859,0.0896,0.0906,0.0933,0.0943,0.0967, 0.0971,0.0985,0.1005,0.1037,0.1132,0.1176,0.1202,0.1241,0.1254,0.1268, 0.1280,0.1401,0.1406,0.1426,0.1432,0.1482,0.1549,0.1559,0.1628,0.1667, 0.1839,0.1900,0.1928,0.1987,0.2040,0.2104,0.2148,0.2160,0.2166,0.2279, 0.2321,0.2436,0.2437,0.2492,0.2592,0.2635,0.2675,0.2677,0.2728,0.2739, 0.2743,0.2812,0.2816,0.2824,0.2835,0.2848,0.2907,0.2915,0.3025,0.3046, 0.3069,0.3077,0.3128,0.3129,0.3160,0.3171,0.3240,0.3241,0.3246,0.3275, 0.3277,0.3341,0.3392,0.3396,0.3406,0.3460,0.3513,0.3524,0.3542,0.3605, 0.3616,0.3694,0.3743,0.3850,0.3899,0.3927,0.3942,0.3946,0.3965,0.3967, 0.3978,0.3999,0.4097,0.4155,0.4158,0.4339,0.4406,0.4433,0.4523,0.4528, 0.4612,0.4645,0.4666,0.4844,0.4894,0.4967,0.5009,0.5017,0.5030,0.5037, 0.5043,0.5104,0.5131,0.5177,0.5202,0.5337,0.5364,0.5401,0.5408,0.5585, 0.5612,0.5624,0.5634,0.5656,0.5721,0.5788,0.5823,0.5855,0.5933,0.5937, 0.6003,0.6043,0.6073,0.6078,0.6102,0.6135,0.6280,0.6297,0.6347,0.6368, 0.6457,0.6495,0.6535,0.6609,0.6662,0.6699,0.6770,0.6816,0.6820,0.6833, 0.6861,0.6877,0.6912,0.6942,0.6945,0.7012,0.7032,0.7033,0.7047,0.7048, 0.7106,0.7138,0.7162,0.7163,0.7174,0.7199,0.7244,0.7254,0.7303,0.7346, 0.7387,0.7394,0.7426,0.7433,0.7436,0.7455,0.7476,0.7479,0.7515,0.7624, 0.7633,0.7635,0.7675,0.7703,0.7751,0.7803,0.7887,0.7928,0.7946,0.7967, 0.7978,0.8058,0.8097,0.8112,0.8162,0.8182,0.8187,0.8249,0.8311,0.8424, 0.8465,0.8473,0.8554,0.8661,0.8691,0.8703,0.8733,0.8767,0.8790,0.8858, 0.8871,0.8893,0.8912,0.8918,0.8989,0.9049,0.9064,0.9066,0.9157,0.9169, 0.9180,0.9190,0.9214,0.9289,0.9302,0.9313,0.9428,0.9455,0.9469,0.9480, 0.9527,0.9552,0.9704,0.9735,0.9735,0.9850,0.9912,0.9927,0.9958, Overall p-value after applying KStest on 269 p-values = 0.062256 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.