RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-08-02_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 15.61 32.6069 0.987364 2 to 25 15.73 8.2021 0.037967 3 to 26 15.89 20.3425 0.742915 4 to 27 15.71 16.0405 0.479037 5 to 28 15.69 16.6193 0.519564 6 to 29 15.71 21.1481 0.780265 7 to 30 15.80 32.2068 0.985818 8 to 31 15.57 13.8837 0.324681 9 to 32 15.75 21.1349 0.779684 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.173893 Tough bday spacings test for dh-ranFile-2016-08-02_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 11 44 71 88 102 66 62 32 17 5 2 (O-E)^2/E 0.4 1.5 0.1 1.0 0.2 1.9 1.9 0.2 0.3 0.4 1.0 Birthday Spacings: Sum(O-E)^2/E= 8.755, p= 0.445 RESULTS OF GCD FOR dh-ranFile-2016-08-02_16:31 Euclid's algorithm: p-value, steps to gcd: 0.320236 p-value, dist. of gcd's: 0.695910 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-08-02_16:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.057 0.713 0.185 0.802 0.724 0.293 0.420 0.456 Bits 8 to 15---> 0.316 0.247 0.330 0.268 0.932 0.794 0.092 0.515 Bits 16 to 23---> 0.710 0.703 0.336 0.738 0.957 0.645 0.885 0.997 Bits 24 to 31---> 0.122 0.095 0.220 0.313 0.615 0.638 0.592 0.608 KS test for the above 32 p values: 0.081 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-08-02_16:31, p-values for 5 runs: 0.4640, 0.0750, 0.8048, 0.6357, 0.9780 Rank test for binary matrices (31x31) for dh-ranFile-2016-08-02_16:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 188 211.4 2.594 2.594 r= 29 5055 5134.0 1.216 3.810 r= 30 23174 23103.0 0.218 4.028 r= 31 11583 11551.5 0.086 4.114 chi-square = 4.114 with df = 3; p-value = 0.751 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-08-02_16:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 208 211.4 0.055 0.055 r= 30 5042 5134.0 1.649 1.704 r= 31 23221 23103.0 0.602 2.306 r= 32 11529 11551.5 0.044 2.350 chi-square = 2.350 with df = 3; p-value = 0.497 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-08-02_16:31 b-rank test for bits 1 to 8, p=0.01056 b-rank test for bits 2 to 9, p=0.06270 b-rank test for bits 3 to 10, p=0.85282 b-rank test for bits 4 to 11, p=0.38474 b-rank test for bits 5 to 12, p=0.94103 b-rank test for bits 6 to 13, p=0.68654 b-rank test for bits 7 to 14, p=0.54513 b-rank test for bits 8 to 15, p=0.58419 b-rank test for bits 9 to 16, p=0.75996 b-rank test for bits 10 to 17, p=0.83800 b-rank test for bits 11 to 18, p=0.84545 b-rank test for bits 12 to 19, p=0.09687 b-rank test for bits 13 to 20, p=0.74184 b-rank test for bits 14 to 21, p=0.92387 b-rank test for bits 15 to 22, p=0.82863 b-rank test for bits 16 to 23, p=0.00773 b-rank test for bits 17 to 24, p=0.13428 b-rank test for bits 18 to 25, p=0.13238 b-rank test for bits 19 to 26, p=0.94971 b-rank test for bits 20 to 27, p=0.60573 b-rank test for bits 21 to 28, p=0.97031 b-rank test for bits 22 to 29, p=0.71481 b-rank test for bits 23 to 30, p=0.71855 b-rank test for bits 24 to 31, p=0.83691 b-rank test for bits 25 to 32, p=0.89813 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 = 0.028212 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-08-02_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 141933 0.06 0.522052 2 141862 -0.11 0.455973 3 141891 -0.04 0.482920 4 141945 0.08 0.533210 5 141935 0.06 0.523913 6 142535 1.46 0.928108 7 142113 0.48 0.682915 8 141666 -0.57 0.284838 9 141820 -0.21 0.417335 10 142192 0.66 0.745516 11 142422 1.20 0.884508 12 141166 -1.74 0.041215 13 141440 -1.10 0.136416 14 141832 -0.18 0.428310 15 141801 -0.25 0.400093 16 142096 0.44 0.668634 17 141386 -1.22 0.110715 18 141921 0.03 0.510876 19 141807 -0.24 0.405518 20 141344 -1.32 0.093273 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-08-02_16:31 Bits used No. missing words z-score p-value 23 to 32 141670 -0.8253 0.204608 22 to 31 141320 -2.0322 0.021068 21 to 30 142166 0.8851 0.811940 20 to 29 142250 1.1747 0.879947 19 to 28 141882 -0.0942 0.462459 18 to 27 142179 0.9299 0.823788 17 to 26 141659 -0.8632 0.194012 16 to 25 142265 1.2264 0.889985 15 to 24 142020 0.3816 0.648629 14 to 23 141984 0.2575 0.601597 13 to 22 141639 -0.9322 0.175624 12 to 21 142290 1.3127 0.905350 11 to 20 141998 0.3058 0.620106 10 to 19 142272 1.2506 0.894457 9 to 18 142213 1.0471 0.852482 8 to 17 142541 2.1782 0.985303 7 to 16 141911 0.0058 0.502297 6 to 15 141888 -0.0736 0.470684 5 to 14 142086 0.6092 0.728806 4 to 13 141522 -1.3356 0.090837 3 to 12 141772 -0.4736 0.317910 2 to 11 142270 1.2437 0.893193 1 to 10 142162 0.8713 0.808198 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-08-02_16:31 Bits used No. missing words z-score p-value 28 to 32 141511 -1.3503 0.088465 27 to 31 141628 -0.9537 0.170128 26 to 30 141849 -0.2045 0.418978 25 to 29 141532 -1.2791 0.100434 24 to 28 141822 -0.2960 0.383602 23 to 27 141284 -2.1198 0.017013 22 to 26 142340 1.4599 0.927841 21 to 25 141680 -0.7774 0.218464 20 to 24 141568 -1.1571 0.123626 19 to 23 141815 -0.3198 0.374574 18 to 22 142010 0.3413 0.633544 17 to 21 141700 -0.7096 0.238978 16 to 20 141832 -0.2621 0.396609 15 to 19 141855 -0.1842 0.426940 14 to 18 141609 -1.0181 0.154323 13 to 17 141764 -0.4926 0.311132 12 to 16 141995 0.2904 0.614248 11 to 15 141877 -0.1096 0.456366 10 to 14 141963 0.1819 0.572182 9 to 13 142161 0.8531 0.803203 8 to 12 142131 0.7514 0.773801 7 to 11 142280 1.2565 0.895534 6 to 10 141372 -1.8215 0.034269 5 to 9 142534 2.1175 0.982892 4 to 8 141870 -0.1333 0.446969 3 to 7 141429 -1.6282 0.051737 2 to 6 141958 0.1650 0.565521 1 to 5 141770 -0.4723 0.318355 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-08-02_16:31 Bits used No. missing words z-score p-value 31 to 32 142125 0.6362 0.737675 30 to 31 141486 -1.2488 0.105876 29 to 30 141237 -1.9833 0.023668 28 to 29 141655 -0.7502 0.226556 27 to 28 142216 0.9046 0.817170 26 to 27 141955 0.1347 0.553583 25 to 26 142166 0.7571 0.775517 24 to 25 142041 0.3884 0.651143 23 to 24 141559 -1.0334 0.150703 22 to 23 141466 -1.3078 0.095478 21 to 22 141496 -1.2193 0.111372 20 to 21 141534 -1.1072 0.134111 19 to 20 141784 -0.3697 0.355801 18 to 19 141842 -0.1986 0.421283 17 to 18 142541 1.8633 0.968792 16 to 17 142866 2.8220 0.997614 15 to 16 141468 -1.3019 0.096482 14 to 15 141500 -1.2075 0.113627 13 to 14 142069 0.4710 0.681181 12 to 13 141714 -0.5762 0.282242 11 to 12 142019 0.3235 0.626846 10 to 11 142403 1.4563 0.927339 9 to 10 142009 0.2940 0.615626 8 to 9 141599 -0.9154 0.179984 7 to 8 141790 -0.3520 0.362417 6 to 7 141723 -0.5496 0.291281 5 to 6 141893 -0.0482 0.480790 4 to 5 141959 0.1465 0.558244 3 to 4 141278 -1.8623 0.031278 2 to 3 142172 0.7748 0.780782 1 to 2 141705 -0.6027 0.273340 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-08-02_16:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2446.01 -0.764 0.222558 Test results for specific bytes for dh-ranFile-2016-08-02_16:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2421.97 -1.104 0.134899 2 to 9 2440.73 -0.838 0.200971 3 to 10 2407.01 -1.315 0.094248 4 to 11 2581.54 1.153 0.875584 5 to 12 2563.46 0.897 0.815268 6 to 13 2543.28 0.612 0.729766 7 to 14 2442.14 -0.818 0.206602 8 to 15 2672.98 2.446 0.992784 9 to 16 2591.95 1.300 0.903268 10 to 17 2425.75 -1.050 0.146862 11 to 18 2550.41 0.713 0.762061 12 to 19 2449.30 -0.717 0.236672 13 to 20 2532.05 0.453 0.674808 14 to 21 2368.10 -1.865 0.031062 15 to 22 2628.42 1.816 0.965322 16 to 23 2482.03 -0.254 0.399690 17 to 24 2531.89 0.451 0.674000 18 to 25 2412.66 -1.235 0.108384 19 to 26 2555.85 0.790 0.785183 20 to 27 2529.22 0.413 0.660275 21 to 28 2615.41 1.632 0.948674 22 to 29 2420.44 -1.125 0.130268 23 to 30 2460.95 -0.552 0.290379 24 to 31 2553.44 0.756 0.775082 25 to 32 2394.96 -1.485 0.068710 CDPARK for dh-ranFile-2016-08-02_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 3535 0.5479 0.708135 3555 1.4612 0.928018 3526 0.1370 0.554479 3521 -0.0913 0.463617 3514 -0.4110 0.340551 3500 -1.0502 0.146807 3499 -1.0959 0.136563 3532 0.4110 0.659449 3533 0.4566 0.676028 3507 -0.7306 0.232514 Square side=100, avg. no. parked=3522.20 sample std.=16.73 p-value of the KSTEST for those 10 p-values: 0.933618 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-08-02_16:31 0.8435,0.3570,0.6985,0.8636,0.6035,0.0394,0.9695,0.8317,0.8756,0.7899, The KS test for those 10 p-values: 0.041934 The 3DSPHERES test for dh-ranFile-2016-08-02_16:31 sample no r^3 equiv. uni. 1 69.872 0.902613 2 39.657 0.733374 3 87.819 0.946459 4 3.324 0.104894 5 11.102 0.309320 6 2.119 0.068195 7 29.715 0.628604 8 7.815 0.229346 9 1.999 0.064472 10 24.784 0.562254 11 28.098 0.608043 12 22.094 0.521199 13 0.614 0.020247 14 27.961 0.606249 15 9.062 0.260705 16 1.768 0.057236 17 88.794 0.948171 18 40.902 0.744208 19 13.470 0.361728 20 12.462 0.339933 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.622151 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-08-02_16:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -1.2 -0.4 0.9 0.1 -0.8 -1.0 1.2 -0.8 -1.1 0.3 1.1 -0.8 1.6 -0.7 -0.8 -1.3 -0.4 0.3 1.0 -0.1 -0.1 2.1 -1.1 -0.3 0.7 1.1 -1.4 0.3 0.4 0.3 -0.2 0.8 -0.6 -0.2 1.1 -1.2 -0.1 1.3 0.4 2.4 1.0 -0.1 Chi-square with 42 degrees of freedom:39.025337 z-score=-0.324562, p-value=0.397702 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-08-02_16:31 Test no p-value 1 0.826168 2 0.413996 3 0.216297 4 0.135844 5 0.545178 6 0.151553 7 0.857448 8 0.369017 9 0.175207 10 0.944921 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.776972 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-08-02_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 66673 0.00 66952 1.22 3 25000.00 24980 0.02 24653 4.82 4 6666.67 6650 0.04 6688 0.07 5 1388.89 1408 0.26 1412 0.38 6 238.10 243 0.10 250 0.60 7 34.72 39 0.53 38 0.31 8 4.96 6 0.22 6 0.22 p=0.02156 p=0.73219 Number of rngs required: 687658, p-value: 0.194 RESULTS OF CRAPS TEST for dh-ranFile-2016-08-02_16:31 No. of wins: Observed Expected 98442 98585.9 z-score=-0.643, pvalue=0.25998 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66851 66666.7 0.510 0.510 2 37583 37654.3 0.135 0.645 3 26958 26954.7 0.000 0.645 4 19555 19313.5 3.021 3.666 5 13928 13851.4 0.423 4.089 6 9844 9943.5 0.997 5.086 7 7113 7145.0 0.144 5.229 8 4994 5139.1 4.095 9.325 9 3722 3699.9 0.132 9.457 10 2559 2666.3 4.318 13.775 11 1887 1923.3 0.686 14.461 12 1385 1388.7 0.010 14.471 13 1022 1003.7 0.333 14.804 14 700 726.1 0.941 15.745 15 544 525.8 0.627 16.373 16 371 381.2 0.270 16.643 17 264 276.5 0.569 17.212 18 197 200.8 0.073 17.285 19 136 146.0 0.683 17.968 20 97 106.2 0.800 18.767 21 290 287.1 0.029 18.796 Chisq= 18.80 for 20 degrees of freedom, p= 0.46489 SUMMARY of craptest p-value for no. of wins: 0.259976 p-value for throws/game: 0.464889 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-08-02_16:31 No. of wins: Observed Expected 98703 98585.9 z-score= 0.524, pvalue=0.69983 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66662 66666.7 0.000 0.000 2 37706 37654.3 0.071 0.071 3 27127 26954.7 1.101 1.172 4 19240 19313.5 0.279 1.452 5 13658 13851.4 2.701 4.153 6 10080 9943.5 1.873 6.025 7 7047 7145.0 1.345 7.370 8 5123 5139.1 0.050 7.420 9 3652 3699.9 0.619 8.040 10 2678 2666.3 0.051 8.091 11 1958 1923.3 0.625 8.716 12 1408 1388.7 0.267 8.983 13 1018 1003.7 0.203 9.186 14 740 726.1 0.265 9.451 15 545 525.8 0.698 10.149 16 414 381.2 2.831 12.980 17 245 276.5 3.597 16.577 18 173 200.8 3.857 20.434 19 158 146.0 0.989 21.423 20 97 106.2 0.800 22.222 21 271 287.1 0.904 23.127 Chisq= 23.13 for 20 degrees of freedom, p= 0.71739 SUMMARY of craptest p-value for no. of wins: 0.699835 p-value for throws/game: 0.717390 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0077,0.0106,0.0170,0.0202,0.0211,0.0216,0.0237,0.0282,0.0311,0.0313, 0.0343,0.0380,0.0394,0.0412,0.0419,0.0517,0.0572,0.0572,0.0627,0.0645, 0.0682,0.0687,0.0750,0.0806,0.0885,0.0908,0.0916,0.0933,0.0942,0.0955, 0.0955,0.0965,0.0969,0.1004,0.1049,0.1059,0.1084,0.1107,0.1114,0.1136, 0.1218,0.1236,0.1303,0.1324,0.1341,0.1343,0.1349,0.1358,0.1364,0.1366, 0.1468,0.1469,0.1507,0.1516,0.1543,0.1701,0.1739,0.1752,0.1756,0.1800, 0.1853,0.1940,0.1944,0.2010,0.2046,0.2066,0.2163,0.2185,0.2204,0.2226, 0.2266,0.2293,0.2325,0.2367,0.2390,0.2472,0.2600,0.2607,0.2684,0.2733, 0.2822,0.2848,0.2904,0.2913,0.2930,0.3093,0.3111,0.3128,0.3164,0.3179, 0.3184,0.3202,0.3247,0.3295,0.3364,0.3399,0.3406,0.3558,0.3570,0.3617, 0.3624,0.3690,0.3746,0.3836,0.3847,0.3966,0.3977,0.3997,0.4001,0.4055, 0.4140,0.4173,0.4190,0.4196,0.4213,0.4269,0.4283,0.4445,0.4470,0.4556, 0.4560,0.4564,0.4625,0.4636,0.4640,0.4649,0.4707,0.4790,0.4808,0.4829, 0.4971,0.5023,0.5109,0.5152,0.5196,0.5212,0.5221,0.5239,0.5332,0.5451, 0.5452,0.5536,0.5545,0.5582,0.5623,0.5655,0.5722,0.5842,0.5922,0.6016, 0.6035,0.6057,0.6062,0.6080,0.6083,0.6142,0.6146,0.6156,0.6201,0.6222, 0.6268,0.6286,0.6335,0.6357,0.6381,0.6446,0.6486,0.6511,0.6594,0.6603, 0.6686,0.6740,0.6748,0.6760,0.6812,0.6829,0.6865,0.6959,0.6985,0.6998, 0.7029,0.7081,0.7103,0.7128,0.7148,0.7174,0.7185,0.7245,0.7288,0.7298, 0.7322,0.7334,0.7377,0.7379,0.7418,0.7429,0.7442,0.7455,0.7505,0.7600, 0.7621,0.7738,0.7751,0.7755,0.7770,0.7797,0.7803,0.7808,0.7852,0.7899, 0.7935,0.8019,0.8032,0.8048,0.8082,0.8119,0.8153,0.8172,0.8238,0.8262, 0.8286,0.8317,0.8369,0.8380,0.8435,0.8455,0.8525,0.8528,0.8574,0.8636, 0.8756,0.8756,0.8799,0.8845,0.8848,0.8900,0.8932,0.8945,0.8955,0.8981, 0.9026,0.9033,0.9054,0.9239,0.9273,0.9278,0.9280,0.9281,0.9321,0.9336, 0.9410,0.9449,0.9465,0.9482,0.9487,0.9497,0.9567,0.9653,0.9688,0.9695, 0.9703,0.9780,0.9829,0.9853,0.9858,0.9874,0.9928,0.9970,0.9976, Overall p-value after applying KStest on 269 p-values = 0.460347 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.