RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-10-19_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 15.96 20.0859 0.730142 2 to 25 15.96 29.7986 0.972165 3 to 26 15.76 14.5261 0.370424 4 to 27 15.85 17.5199 0.580284 5 to 28 15.63 18.7963 0.659652 6 to 29 15.83 23.3760 0.862595 7 to 30 15.67 24.6552 0.897302 8 to 31 15.75 16.7246 0.526828 9 to 32 15.66 14.8457 0.393403 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.143565 Tough bday spacings test for dh-ranFile-2016-10-19_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 3 48 70 90 99 81 48 39 14 5 3 (O-E)^2/E 4.1 3.5 0.1 0.6 0.0 0.1 0.3 2.9 0.1 0.4 0.3 Birthday Spacings: Sum(O-E)^2/E= 12.451, p= 0.744 RESULTS OF GCD FOR dh-ranFile-2016-10-19_17:31 Euclid's algorithm: p-value, steps to gcd: 0.576712 p-value, dist. of gcd's: 0.303937 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-10-19_17:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.188 0.057 0.181 0.961 0.590 0.980 0.393 0.859 Bits 8 to 15---> 0.241 0.614 0.774 0.745 0.824 0.157 0.157 0.088 Bits 16 to 23---> 0.522 0.670 0.308 0.496 0.153 0.517 0.725 0.312 Bits 24 to 31---> 0.018 0.928 0.084 0.869 0.237 0.901 0.164 0.626 KS test for the above 32 p values: 0.192 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-10-19_17:31, p-values for 5 runs: 0.1174, 0.9890, 0.1946, 0.1839, 0.8312 Rank test for binary matrices (31x31) for dh-ranFile-2016-10-19_17:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 208 211.4 0.055 0.055 r= 29 5175 5134.0 0.327 0.383 r= 30 23138 23103.0 0.053 0.435 r= 31 11479 11551.5 0.455 0.891 chi-square = 0.891 with df = 3; p-value = 0.172 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-10-19_17:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 207 211.4 0.092 0.092 r= 30 5047 5134.0 1.475 1.567 r= 31 23147 23103.0 0.084 1.651 r= 32 11599 11551.5 0.195 1.846 chi-square = 1.846 with df = 3; p-value = 0.395 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-10-19_17:31 b-rank test for bits 1 to 8, p=0.57195 b-rank test for bits 2 to 9, p=0.61189 b-rank test for bits 3 to 10, p=0.35622 b-rank test for bits 4 to 11, p=0.32551 b-rank test for bits 5 to 12, p=0.73619 b-rank test for bits 6 to 13, p=0.98209 b-rank test for bits 7 to 14, p=0.57801 b-rank test for bits 8 to 15, p=0.76982 b-rank test for bits 9 to 16, p=0.83930 b-rank test for bits 10 to 17, p=0.40933 b-rank test for bits 11 to 18, p=0.85982 b-rank test for bits 12 to 19, p=0.33679 b-rank test for bits 13 to 20, p=0.93130 b-rank test for bits 14 to 21, p=0.46139 b-rank test for bits 15 to 22, p=0.51104 b-rank test for bits 16 to 23, p=0.16607 b-rank test for bits 17 to 24, p=0.66840 b-rank test for bits 18 to 25, p=0.28009 b-rank test for bits 19 to 26, p=0.26933 b-rank test for bits 20 to 27, p=0.74661 b-rank test for bits 21 to 28, p=0.28324 b-rank test for bits 22 to 29, p=0.73961 b-rank test for bits 23 to 30, p=0.26244 b-rank test for bits 24 to 31, p=0.82844 b-rank test for bits 25 to 32, p=0.72356 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 = 0.229731 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-10-19_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 141728 -0.42 0.335904 2 142055 0.34 0.633204 3 141531 -0.88 0.188362 4 141669 -0.56 0.287222 5 142442 1.24 0.893353 6 142590 1.59 0.944122 7 141524 -0.90 0.183979 8 141983 0.17 0.568331 9 141474 -1.02 0.154547 10 141981 0.17 0.566493 11 141533 -0.88 0.189626 12 141735 -0.41 0.341889 13 142702 1.85 0.967989 14 141725 -0.43 0.333351 15 141516 -0.92 0.179049 16 142263 0.83 0.795692 17 141774 -0.32 0.375929 18 141365 -1.27 0.101722 19 141650 -0.61 0.272287 20 142254 0.81 0.789678 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-10-19_17:31 Bits used No. missing words z-score p-value 23 to 32 141871 -0.1322 0.447424 22 to 31 142470 1.9333 0.973403 21 to 30 142100 0.6575 0.744565 20 to 29 142179 0.9299 0.823788 19 to 28 142248 1.1678 0.878562 18 to 27 142414 1.7402 0.959092 17 to 26 142125 0.7437 0.771468 16 to 25 142371 1.5920 0.944304 15 to 24 142158 0.8575 0.804411 14 to 23 142279 1.2747 0.898797 13 to 22 142087 0.6127 0.729948 12 to 21 141750 -0.5494 0.291361 11 to 20 141706 -0.7011 0.241609 10 to 19 141675 -0.8080 0.209535 9 to 18 141548 -1.2460 0.106389 8 to 17 141425 -1.6701 0.047449 7 to 16 141993 0.2885 0.613525 6 to 15 141498 -1.4184 0.078040 5 to 14 141718 -0.6598 0.254704 4 to 13 141494 -1.4322 0.076047 3 to 12 141763 -0.5046 0.306925 2 to 11 141626 -0.9770 0.164285 1 to 10 142369 1.5851 0.943525 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-10-19_17:31 Bits used No. missing words z-score p-value 28 to 32 142090 0.6124 0.729877 27 to 31 141811 -0.3333 0.369446 26 to 30 141694 -0.7299 0.232716 25 to 29 141733 -0.5977 0.275010 24 to 28 141987 0.2633 0.603836 23 to 27 142155 0.8328 0.797516 22 to 26 142164 0.8633 0.806011 21 to 25 141513 -1.3435 0.089556 20 to 24 141505 -1.3706 0.085248 19 to 23 142071 0.5480 0.708166 18 to 22 141741 -0.5706 0.284132 17 to 21 141781 -0.4350 0.331775 16 to 20 142593 2.3175 0.989762 15 to 19 141903 -0.0215 0.491440 14 to 18 141994 0.2870 0.612950 13 to 17 142076 0.5650 0.713957 12 to 16 141704 -0.6960 0.243204 11 to 15 142300 1.3243 0.907299 10 to 14 141621 -0.9774 0.164188 9 to 13 141999 0.3040 0.619423 8 to 12 141276 -2.1469 0.015901 7 to 11 142148 0.8091 0.790757 6 to 10 142237 1.1107 0.866661 5 to 9 142142 0.7887 0.784860 4 to 8 141726 -0.6215 0.267149 3 to 7 141559 -1.1876 0.117504 2 to 6 141820 -0.3028 0.381016 1 to 5 141856 -0.1808 0.428270 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-10-19_17:31 Bits used No. missing words z-score p-value 31 to 32 142109 0.5890 0.722068 30 to 31 142377 1.3796 0.916139 29 to 30 142504 1.7542 0.960301 28 to 29 141633 -0.8151 0.207498 27 to 28 142064 0.4563 0.675896 26 to 27 141642 -0.7886 0.215178 25 to 26 142279 1.0905 0.862247 24 to 25 142005 0.2822 0.611110 23 to 24 142301 1.1554 0.876030 22 to 23 142446 1.5831 0.943300 21 to 22 141049 -2.5378 0.005577 20 to 21 141680 -0.6765 0.249365 19 to 20 142604 2.0492 0.979777 18 to 19 141414 -1.4612 0.071987 17 to 18 141295 -1.8122 0.034979 16 to 17 141903 -0.0187 0.492551 15 to 16 142456 1.6126 0.946584 14 to 15 141467 -1.3048 0.095979 13 to 14 141693 -0.6381 0.261691 12 to 13 141617 -0.8623 0.194253 11 to 12 141872 -0.1101 0.456158 10 to 11 142006 0.2852 0.612240 9 to 10 142165 0.7542 0.774632 8 to 9 142061 0.4474 0.672708 7 to 8 142091 0.5359 0.703986 6 to 7 141904 -0.0157 0.493728 5 to 6 141677 -0.6853 0.246565 4 to 5 141989 0.2350 0.592901 3 to 4 141890 -0.0570 0.477264 2 to 3 141673 -0.6971 0.242858 1 to 2 141931 0.0639 0.525484 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-10-19_17:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2541.88 0.592 0.723181 Test results for specific bytes for dh-ranFile-2016-10-19_17:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2489.89 -0.143 0.443151 2 to 9 2607.73 1.524 0.936191 3 to 10 2548.30 0.683 0.752734 4 to 11 2617.39 1.660 0.951551 5 to 12 2425.71 -1.051 0.146719 6 to 13 2490.75 -0.131 0.447951 7 to 14 2526.08 0.369 0.643890 8 to 15 2488.30 -0.165 0.434306 9 to 16 2547.05 0.665 0.747093 10 to 17 2500.20 0.003 0.501147 11 to 18 2517.21 0.243 0.596172 12 to 19 2511.24 0.159 0.563173 13 to 20 2530.99 0.438 0.669408 14 to 21 2510.47 0.148 0.558854 15 to 22 2503.40 0.048 0.519195 16 to 23 2466.66 -0.472 0.318636 17 to 24 2458.64 -0.585 0.279308 18 to 25 2526.96 0.381 0.648522 19 to 26 2420.03 -1.131 0.129030 20 to 27 2500.22 0.003 0.501267 21 to 28 2464.48 -0.502 0.307701 22 to 29 2596.15 1.360 0.913051 23 to 30 2473.75 -0.371 0.355215 24 to 31 2463.82 -0.512 0.304447 25 to 32 2443.77 -0.795 0.213247 CDPARK for dh-ranFile-2016-10-19_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 3518 -0.2283 0.409702 3545 1.0046 0.842447 3526 0.1370 0.554479 3490 -1.5068 0.065925 3514 -0.4110 0.340551 3494 -1.3242 0.092718 3471 -2.3744 0.008788 3498 -1.1416 0.126820 3546 1.0502 0.853193 3542 0.8676 0.807188 Square side=100, avg. no. parked=3514.40 sample std.=24.51 p-value of the KSTEST for those 10 p-values: 0.318499 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-10-19_17:31 0.0378,0.0116,0.7308,0.5034,0.7388,0.1300,0.9228,0.3406,0.5678,0.8109, The KS test for those 10 p-values: 0.724709 The 3DSPHERES test for dh-ranFile-2016-10-19_17:31 sample no r^3 equiv. uni. 1 0.492 0.016258 2 29.460 0.625439 3 88.879 0.948318 4 31.022 0.644442 5 23.246 0.539232 6 23.029 0.535895 7 33.803 0.675917 8 1.148 0.037540 9 4.380 0.135842 10 23.297 0.540013 11 8.067 0.235775 12 55.320 0.841815 13 25.264 0.569213 14 14.736 0.388099 15 38.425 0.722191 16 26.370 0.584802 17 45.615 0.781395 18 20.615 0.496994 19 102.240 0.966893 20 101.962 0.966584 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.380832 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-10-19_17:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 0.5 0.3 1.4 -1.3 0.6 0.8 1.2 0.2 0.0 0.8 -0.5 -0.4 -1.6 0.4 -0.8 -0.4 -1.4 -1.1 1.5 0.4 0.3 0.1 0.9 -0.6 2.5 1.9 -1.6 -0.6 0.5 -0.5 1.6 0.6 1.3 0.1 0.2 0.0 0.8 0.1 1.0 -1.3 -1.0 0.8 Chi-square with 42 degrees of freedom:41.372542 z-score=-0.068461, p-value=0.501638 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-10-19_17:31 Test no p-value 1 0.936576 2 0.063537 3 0.062453 4 0.180935 5 0.373015 6 0.048932 7 0.007386 8 0.790265 9 0.430463 10 0.788285 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.076242 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-10-19_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 66561 0.17 66604 0.06 3 25000.00 25038 0.06 25018 0.01 4 6666.67 6728 0.56 6705 0.22 5 1388.89 1412 0.38 1383 0.02 6 238.10 213 2.65 250 0.60 7 34.72 39 0.53 33 0.09 8 4.96 8 1.86 6 0.22 p=0.59990 p=0.02390 Number of rngs required: 690734, p-value: 0.997 RESULTS OF CRAPS TEST for dh-ranFile-2016-10-19_17:31 No. of wins: Observed Expected 98684 98585.9 z-score= 0.439, pvalue=0.66965 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66492 66666.7 0.458 0.458 2 37648 37654.3 0.001 0.459 3 27140 26954.7 1.273 1.732 4 19355 19313.5 0.089 1.821 5 13861 13851.4 0.007 1.828 6 9981 9943.5 0.141 1.969 7 7171 7145.0 0.094 2.064 8 5118 5139.1 0.086 2.150 9 3695 3699.9 0.006 2.156 10 2618 2666.3 0.875 3.031 11 1903 1923.3 0.215 3.246 12 1392 1388.7 0.008 3.254 13 1012 1003.7 0.068 3.322 14 706 726.1 0.559 3.881 15 508 525.8 0.605 4.486 16 371 381.2 0.270 4.756 17 283 276.5 0.151 4.907 18 210 200.8 0.419 5.326 19 154 146.0 0.440 5.766 20 98 106.2 0.635 6.401 21 284 287.1 0.034 6.435 Chisq= 6.44 for 20 degrees of freedom, p= 0.00183 SUMMARY of craptest p-value for no. of wins: 0.669650 p-value for throws/game: 0.001832 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-10-19_17:31 No. of wins: Observed Expected 98581 98585.9 z-score=-0.022, pvalue=0.49133 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67005 66666.7 1.717 1.717 2 38050 37654.3 4.158 5.875 3 26780 26954.7 1.133 7.008 4 19370 19313.5 0.166 7.173 5 13662 13851.4 2.590 9.763 6 9817 9943.5 1.610 11.374 7 7046 7145.0 1.372 12.746 8 5006 5139.1 3.446 16.192 9 3667 3699.9 0.292 16.484 10 2740 2666.3 2.037 18.521 11 1879 1923.3 1.022 19.543 12 1342 1388.7 1.573 21.116 13 1020 1003.7 0.264 21.380 14 710 726.1 0.359 21.739 15 531 525.8 0.051 21.790 16 375 381.2 0.099 21.889 17 260 276.5 0.989 22.878 18 212 200.8 0.621 23.500 19 145 146.0 0.007 23.506 20 106 106.2 0.000 23.507 21 277 287.1 0.356 23.863 Chisq= 23.86 for 20 degrees of freedom, p= 0.75157 SUMMARY of craptest p-value for no. of wins: 0.491331 p-value for throws/game: 0.751570 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0018,0.0056,0.0074,0.0088,0.0116,0.0159,0.0163,0.0182,0.0239,0.0350, 0.0375,0.0378,0.0474,0.0489,0.0571,0.0625,0.0635,0.0659,0.0720,0.0760, 0.0762,0.0780,0.0839,0.0852,0.0876,0.0896,0.0927,0.0960,0.1017,0.1064, 0.1174,0.1175,0.1268,0.1290,0.1300,0.1358,0.1436,0.1467,0.1525,0.1545, 0.1567,0.1569,0.1638,0.1642,0.1643,0.1661,0.1723,0.1790,0.1807,0.1809, 0.1839,0.1840,0.1881,0.1884,0.1896,0.1918,0.1943,0.1946,0.2075,0.2095, 0.2132,0.2152,0.2297,0.2327,0.2358,0.2368,0.2408,0.2416,0.2429,0.2432, 0.2466,0.2494,0.2547,0.2617,0.2624,0.2671,0.2693,0.2723,0.2750,0.2793, 0.2801,0.2832,0.2841,0.2872,0.2914,0.3039,0.3044,0.3069,0.3077,0.3082, 0.3123,0.3185,0.3186,0.3255,0.3318,0.3334,0.3359,0.3368,0.3406,0.3406, 0.3419,0.3552,0.3562,0.3694,0.3704,0.3730,0.3759,0.3808,0.3810,0.3881, 0.3931,0.3934,0.3950,0.4093,0.4097,0.4283,0.4305,0.4343,0.4432,0.4474, 0.4480,0.4562,0.4614,0.4773,0.4913,0.4914,0.4926,0.4937,0.4959,0.4970, 0.5011,0.5013,0.5016,0.5034,0.5110,0.5168,0.5192,0.5219,0.5255,0.5268, 0.5359,0.5392,0.5400,0.5545,0.5589,0.5632,0.5665,0.5678,0.5683,0.5692, 0.5720,0.5767,0.5780,0.5803,0.5848,0.5899,0.5929,0.5962,0.5999,0.6038, 0.6111,0.6119,0.6122,0.6130,0.6135,0.6141,0.6194,0.6254,0.6261,0.6332, 0.6439,0.6444,0.6485,0.6597,0.6684,0.6694,0.6696,0.6698,0.6727,0.6759, 0.6759,0.7040,0.7082,0.7140,0.7221,0.7222,0.7232,0.7236,0.7247,0.7251, 0.7299,0.7299,0.7301,0.7308,0.7362,0.7388,0.7396,0.7440,0.7446,0.7453, 0.7466,0.7471,0.7516,0.7527,0.7698,0.7715,0.7737,0.7746,0.7814,0.7849, 0.7883,0.7897,0.7903,0.7908,0.7957,0.7975,0.8044,0.8060,0.8072,0.8109, 0.8238,0.8244,0.8284,0.8312,0.8393,0.8418,0.8424,0.8532,0.8593,0.8598, 0.8622,0.8626,0.8667,0.8694,0.8760,0.8786,0.8934,0.8973,0.8988,0.9008, 0.9073,0.9131,0.9161,0.9228,0.9282,0.9313,0.9362,0.9366,0.9433,0.9435, 0.9441,0.9443,0.9466,0.9483,0.9516,0.9591,0.9603,0.9611,0.9666,0.9669, 0.9680,0.9722,0.9734,0.9798,0.9802,0.9821,0.9890,0.9898,0.9974, Overall p-value after applying KStest on 269 p-values = 0.945943 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.