RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-04-10_14:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.65 13.5157 0.298959 2 to 25 15.47 17.2229 0.560632 3 to 26 15.48 18.9154 0.666590 4 to 27 15.76 11.9493 0.196800 5 to 28 15.75 15.9003 0.469085 6 to 29 15.82 18.8657 0.663707 7 to 30 15.82 27.3250 0.946530 8 to 31 15.78 16.6172 0.519421 9 to 32 15.80 28.0950 0.956160 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.499398 Tough bday spacings test for dh-ranFile-2016-04-10_14:31: 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 7 27 67 104 104 80 53 33 16 5 4 (O-E)^2/E 0.5 2.5 0.5 0.4 0.4 0.0 0.0 0.4 0.1 0.4 0.0 Birthday Spacings: Sum(O-E)^2/E= 5.282, p= 0.128 RESULTS OF GCD FOR dh-ranFile-2016-04-10_14:31 Euclid's algorithm: p-value, steps to gcd: 0.188805 p-value, dist. of gcd's: 0.365114 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-04-10_14:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.931 0.025 0.832 0.836 0.957 0.547 0.925 0.746 Bits 8 to 15---> 0.813 0.960 0.064 0.060 0.556 0.183 0.413 0.028 Bits 16 to 23---> 0.251 0.096 0.443 0.227 0.944 0.253 0.677 0.079 Bits 24 to 31---> 0.938 0.344 0.416 0.572 0.002 0.580 0.024 0.324 KS test for the above 32 p values: 0.803 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-04-10_14:31, p-values for 5 runs: 0.5781, 0.7162, 0.2049, 0.1918, 0.2867 Rank test for binary matrices (31x31) for dh-ranFile-2016-04-10_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 224 211.4 0.749 0.749 r= 29 5042 5134.0 1.649 2.398 r= 30 23023 23103.0 0.277 2.675 r= 31 11711 11551.5 2.202 4.877 chi-square = 4.877 with df = 3; p-value = 0.819 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-04-10_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 196 211.4 1.124 1.124 r= 30 5079 5134.0 0.589 1.714 r= 31 23234 23103.0 0.742 2.456 r= 32 11491 11551.5 0.317 2.773 chi-square = 2.773 with df = 3; p-value = 0.572 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-04-10_14:31 b-rank test for bits 1 to 8, p=0.48329 b-rank test for bits 2 to 9, p=0.64349 b-rank test for bits 3 to 10, p=0.19633 b-rank test for bits 4 to 11, p=0.58314 b-rank test for bits 5 to 12, p=0.16811 b-rank test for bits 6 to 13, p=0.25003 b-rank test for bits 7 to 14, p=0.14643 b-rank test for bits 8 to 15, p=0.46891 b-rank test for bits 9 to 16, p=0.63415 b-rank test for bits 10 to 17, p=0.39063 b-rank test for bits 11 to 18, p=0.51152 b-rank test for bits 12 to 19, p=0.73869 b-rank test for bits 13 to 20, p=0.63544 b-rank test for bits 14 to 21, p=0.04691 b-rank test for bits 15 to 22, p=0.39639 b-rank test for bits 16 to 23, p=0.45756 b-rank test for bits 17 to 24, p=0.21699 b-rank test for bits 18 to 25, p=0.09904 b-rank test for bits 19 to 26, p=0.21845 b-rank test for bits 20 to 27, p=0.51936 b-rank test for bits 21 to 28, p=0.55190 b-rank test for bits 22 to 29, p=0.94342 b-rank test for bits 23 to 30, p=0.48638 b-rank test for bits 24 to 31, p=0.03712 b-rank test for bits 25 to 32, p=0.01357 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 = 0.076263 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-04-10_14:31 (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 142456 1.28 0.899246 2 141959 0.12 0.546194 3 141245 -1.55 0.060310 4 141862 -0.11 0.455973 5 142455 1.27 0.898833 6 142144 0.55 0.708255 7 142211 0.70 0.759544 8 142807 2.10 0.982019 9 141935 0.06 0.523913 10 142580 1.57 0.941441 11 142186 0.65 0.740998 12 142302 0.92 0.820547 13 142243 0.78 0.782188 14 141995 0.20 0.579324 15 141523 -0.90 0.183358 16 141370 -1.26 0.103814 17 141979 0.16 0.564654 18 142319 0.96 0.830760 19 142192 0.66 0.745516 20 142677 1.79 0.963563 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-04-10_14:31 Bits used No. missing words z-score p-value 23 to 32 142343 1.4954 0.932597 22 to 31 141370 -1.8598 0.031460 21 to 30 142314 1.3954 0.918554 20 to 29 141765 -0.4977 0.309351 19 to 28 141427 -1.6632 0.048136 18 to 27 141849 -0.2080 0.417601 17 to 26 141497 -1.4218 0.077538 16 to 25 142010 0.3471 0.635756 15 to 24 141938 0.0989 0.539376 14 to 23 141926 0.0575 0.522920 13 to 22 141746 -0.5632 0.286647 12 to 21 142011 0.3506 0.637051 11 to 20 142256 1.1954 0.884037 10 to 19 142208 1.0299 0.848471 9 to 18 141869 -0.1391 0.444698 8 to 17 141837 -0.2494 0.401520 7 to 16 141697 -0.7322 0.232032 6 to 15 142008 0.3402 0.633163 5 to 14 141931 0.0747 0.529783 4 to 13 141595 -1.0839 0.139205 3 to 12 141743 -0.5736 0.283136 2 to 11 142169 0.8954 0.814717 1 to 10 142112 0.6989 0.757681 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-04-10_14:31 Bits used No. missing words z-score p-value 28 to 32 142423 1.7413 0.959181 27 to 31 141640 -0.9130 0.180626 26 to 30 141819 -0.3062 0.379725 25 to 29 141844 -0.2215 0.412368 24 to 28 141713 -0.6655 0.252857 23 to 27 141724 -0.6282 0.264924 22 to 26 142037 0.4328 0.667413 21 to 25 141776 -0.4520 0.325647 20 to 24 142053 0.4870 0.686877 19 to 23 142038 0.4362 0.668643 18 to 22 141249 -2.2384 0.012597 17 to 21 141694 -0.7299 0.232716 16 to 20 142285 1.2735 0.898572 15 to 19 141503 -1.3774 0.084196 14 to 18 141549 -1.2215 0.110956 13 to 17 141659 -0.8486 0.198059 12 to 16 141745 -0.5571 0.288746 11 to 15 141896 -0.0452 0.481979 10 to 14 141911 0.0057 0.502258 9 to 13 142074 0.5582 0.711647 8 to 12 141539 -1.2554 0.104675 7 to 11 142050 0.4768 0.683265 6 to 10 141563 -1.1740 0.120198 5 to 9 141808 -0.3435 0.365614 4 to 8 141705 -0.6926 0.244267 3 to 7 141507 -1.3638 0.086310 2 to 6 142098 0.6396 0.738770 1 to 5 141331 -1.9604 0.024972 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-04-10_14:31 Bits used No. missing words z-score p-value 31 to 32 142416 1.4946 0.932491 30 to 31 142324 1.2232 0.889376 29 to 30 141356 -1.6322 0.051314 28 to 29 141475 -1.2812 0.100060 27 to 28 141782 -0.3756 0.353605 26 to 27 142242 0.9813 0.836784 25 to 26 141680 -0.6765 0.249365 24 to 25 142113 0.6008 0.726012 23 to 24 141616 -0.8653 0.193443 22 to 23 141796 -0.3343 0.369074 21 to 22 142793 2.6067 0.995429 20 to 21 141894 -0.0452 0.481966 19 to 20 141308 -1.7738 0.038045 18 to 19 142194 0.8397 0.799471 17 to 18 141571 -0.9980 0.159134 16 to 17 141897 -0.0364 0.485493 15 to 16 141914 0.0138 0.505496 14 to 15 141756 -0.4523 0.325526 13 to 14 142255 1.0197 0.846059 12 to 13 142045 0.4002 0.655498 11 to 12 141347 -1.6588 0.048579 10 to 11 141473 -1.2871 0.099028 9 to 10 141746 -0.4818 0.314974 8 to 9 142105 0.5772 0.718097 7 to 8 141697 -0.6263 0.265545 6 to 7 142248 0.9990 0.841109 5 to 6 141984 0.2203 0.587168 4 to 5 142119 0.6185 0.731876 3 to 4 141493 -1.2281 0.109702 2 to 3 142028 0.3501 0.636853 1 to 2 141654 -0.7532 0.225669 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-04-10_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2455.70 -0.627 0.265489 Test results for specific bytes for dh-ranFile-2016-04-10_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2468.55 -0.445 0.328246 2 to 9 2457.46 -0.602 0.273704 3 to 10 2519.93 0.282 0.610950 4 to 11 2439.05 -0.862 0.194351 5 to 12 2511.79 0.167 0.566234 6 to 13 2508.54 0.121 0.548041 7 to 14 2451.75 -0.682 0.247489 8 to 15 2506.05 0.085 0.534065 9 to 16 2389.34 -1.565 0.058801 10 to 17 2541.42 0.586 0.720972 11 to 18 2500.47 0.007 0.502662 12 to 19 2483.49 -0.233 0.407715 13 to 20 2464.81 -0.498 0.309343 14 to 21 2409.12 -1.285 0.099351 15 to 22 2529.63 0.419 0.662393 16 to 23 2444.45 -0.786 0.216053 17 to 24 2542.52 0.601 0.726208 18 to 25 2481.41 -0.263 0.396310 19 to 26 2640.60 1.988 0.976615 20 to 27 2509.38 0.133 0.552787 21 to 28 2642.67 2.018 0.978186 22 to 29 2420.65 -1.122 0.130897 23 to 30 2527.53 0.389 0.651463 24 to 31 2457.68 -0.599 0.274749 25 to 32 2530.25 0.428 0.665598 CDPARK for dh-ranFile-2016-04-10_14:31: 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 3539 0.7306 0.767486 3551 1.2785 0.899470 3511 -0.5479 0.291865 3535 0.5479 0.708135 3530 0.3196 0.625377 3541 0.8219 0.794438 3569 2.1005 0.982156 3500 -1.0502 0.146807 3517 -0.2740 0.392053 3516 -0.3196 0.374623 Square side=100, avg. no. parked=3530.90 sample std.=19.51 p-value of the KSTEST for those 10 p-values: 0.522306 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-04-10_14:31 0.1284,0.4201,0.6550,0.6041,0.8461,0.6263,0.4340,0.2166,0.6748,0.8619, The KS test for those 10 p-values: 0.684822 The 3DSPHERES test for dh-ranFile-2016-04-10_14:31 sample no r^3 equiv. uni. 1 27.994 0.606684 2 20.172 0.489514 3 55.186 0.841110 4 13.964 0.372162 5 59.223 0.861116 6 9.335 0.267403 7 37.286 0.711440 8 8.023 0.234669 9 10.911 0.304903 10 4.026 0.125579 11 29.404 0.624740 12 16.672 0.426353 13 33.530 0.672961 14 20.822 0.500458 15 11.744 0.323944 16 28.325 0.611001 17 17.658 0.444901 18 13.780 0.368298 19 45.421 0.779976 20 14.251 0.378126 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.285180 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-04-10_14:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.9 0.3 0.8 0.4 -0.1 0.6 1.0 -1.1 -0.4 2.0 0.0 -0.0 -0.4 -0.1 0.5 -1.1 -0.6 -0.9 0.9 0.3 1.2 0.3 -0.8 0.8 0.2 -0.8 -1.2 0.8 1.1 -0.9 -0.1 -1.8 -0.9 0.2 0.1 -0.9 -0.4 1.3 -0.7 0.1 -1.0 -1.1 Chi-square with 42 degrees of freedom:28.858349 z-score=-1.433872, p-value=0.061339 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-04-10_14:31 Test no p-value 1 0.773985 2 0.042932 3 0.003314 4 0.867318 5 0.265634 6 0.117705 7 0.800070 8 0.979717 9 0.002004 10 0.070713 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.014965 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-04-10_14:31: (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 66433 0.82 66833 0.41 3 25000.00 25119 0.57 24850 0.90 4 6666.67 6779 1.89 6656 0.02 5 1388.89 1394 0.02 1373 0.18 6 238.10 230 0.28 254 1.06 7 34.72 40 0.80 30 0.64 8 4.96 4 0.19 3 0.77 p=0.39878 p=0.32231 Number of rngs required: 688009, p-value: 0.325 RESULTS OF CRAPS TEST for dh-ranFile-2016-04-10_14:31 No. of wins: Observed Expected 98994 98585.9 z-score= 1.825, pvalue=0.96603 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66808 66666.7 0.300 0.300 2 37854 37654.3 1.059 1.359 3 26978 26954.7 0.020 1.379 4 19276 19313.5 0.073 1.451 5 13756 13851.4 0.657 2.109 6 9710 9943.5 5.485 7.594 7 7036 7145.0 1.664 9.257 8 5169 5139.1 0.174 9.432 9 3788 3699.9 2.099 11.531 10 2678 2666.3 0.051 11.583 11 1906 1923.3 0.156 11.739 12 1374 1388.7 0.156 11.895 13 1017 1003.7 0.176 12.071 14 705 726.1 0.615 12.686 15 519 525.8 0.089 12.775 16 419 381.2 3.759 16.534 17 279 276.5 0.022 16.556 18 170 200.8 4.733 21.289 19 159 146.0 1.160 22.449 20 108 106.2 0.030 22.479 21 291 287.1 0.053 22.532 Chisq= 22.53 for 20 degrees of freedom, p= 0.68762 SUMMARY of craptest p-value for no. of wins: 0.966033 p-value for throws/game: 0.687624 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-04-10_14:31 No. of wins: Observed Expected 99131 98585.9 z-score= 2.438, pvalue=0.99262 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66581 66666.7 0.110 0.110 2 37650 37654.3 0.000 0.111 3 27118 26954.7 0.989 1.100 4 19190 19313.5 0.789 1.889 5 13892 13851.4 0.119 2.008 6 10024 9943.5 0.651 2.659 7 7202 7145.0 0.454 3.113 8 5108 5139.1 0.188 3.301 9 3658 3699.9 0.474 3.775 10 2601 2666.3 1.599 5.374 11 1910 1923.3 0.092 5.466 12 1384 1388.7 0.016 5.482 13 1036 1003.7 1.038 6.521 14 732 726.1 0.047 6.568 15 530 525.8 0.033 6.601 16 356 381.2 1.660 8.261 17 248 276.5 2.945 11.206 18 201 200.8 0.000 11.206 19 152 146.0 0.248 11.454 20 110 106.2 0.135 11.589 21 317 287.1 3.111 14.700 Chisq= 14.70 for 20 degrees of freedom, p= 0.20667 SUMMARY of craptest p-value for no. of wins: 0.992620 p-value for throws/game: 0.206670 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0020,0.0021,0.0033,0.0126,0.0136,0.0150,0.0242,0.0250,0.0254,0.0280, 0.0315,0.0371,0.0380,0.0429,0.0469,0.0481,0.0486,0.0513,0.0588,0.0601, 0.0603,0.0613,0.0635,0.0707,0.0763,0.0775,0.0793,0.0842,0.0863,0.0955, 0.0990,0.0990,0.0994,0.1001,0.1038,0.1047,0.1097,0.1110,0.1177,0.1202, 0.1256,0.1284,0.1284,0.1309,0.1392,0.1464,0.1468,0.1591,0.1681,0.1806, 0.1826,0.1834,0.1888,0.1918,0.1934,0.1944,0.1963,0.1968,0.1981,0.2049, 0.2067,0.2161,0.2166,0.2170,0.2185,0.2257,0.2275,0.2320,0.2327,0.2347, 0.2443,0.2475,0.2494,0.2500,0.2512,0.2529,0.2530,0.2649,0.2655,0.2655, 0.2656,0.2674,0.2737,0.2747,0.2831,0.2852,0.2866,0.2867,0.2887,0.2919, 0.2990,0.3049,0.3093,0.3094,0.3150,0.3223,0.3239,0.3244,0.3249,0.3255, 0.3256,0.3282,0.3438,0.3536,0.3651,0.3656,0.3683,0.3691,0.3722,0.3746, 0.3781,0.3797,0.3906,0.3921,0.3963,0.3964,0.3988,0.4015,0.4077,0.4124, 0.4132,0.4160,0.4176,0.4201,0.4264,0.4340,0.4430,0.4447,0.4449,0.4560, 0.4576,0.4689,0.4691,0.4820,0.4820,0.4833,0.4855,0.4864,0.4895,0.4994, 0.5005,0.5023,0.5027,0.5055,0.5115,0.5194,0.5194,0.5223,0.5229,0.5239, 0.5298,0.5341,0.5394,0.5462,0.5469,0.5480,0.5519,0.5528,0.5563,0.5606, 0.5647,0.5662,0.5717,0.5721,0.5781,0.5793,0.5799,0.5831,0.5872,0.6041, 0.6067,0.6110,0.6110,0.6247,0.6254,0.6263,0.6332,0.6341,0.6354,0.6358, 0.6369,0.6371,0.6435,0.6515,0.6550,0.6555,0.6624,0.6637,0.6656,0.6666, 0.6674,0.6686,0.6730,0.6748,0.6771,0.6833,0.6848,0.6869,0.6876,0.7081, 0.7083,0.7114,0.7116,0.7162,0.7181,0.7210,0.7260,0.7262,0.7319,0.7387, 0.7388,0.7410,0.7455,0.7462,0.7577,0.7595,0.7675,0.7740,0.7800,0.7822, 0.7944,0.7995,0.8001,0.8031,0.8127,0.8147,0.8190,0.8205,0.8308,0.8318, 0.8356,0.8368,0.8411,0.8411,0.8461,0.8461,0.8485,0.8611,0.8619,0.8673, 0.8840,0.8894,0.8986,0.8988,0.8992,0.8995,0.9186,0.9248,0.9310,0.9325, 0.9326,0.9381,0.9414,0.9434,0.9436,0.9465,0.9562,0.9571,0.9592,0.9603, 0.9636,0.9660,0.9766,0.9782,0.9797,0.9820,0.9822,0.9926,0.9954, Overall p-value after applying KStest on 269 p-values = 0.304364 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.