RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-09-09_05:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.82 15.1193 0.413111 2 to 25 15.99 19.9020 0.720728 3 to 26 15.78 19.4618 0.697320 4 to 27 15.77 26.5167 0.934453 5 to 28 15.84 19.5323 0.701155 6 to 29 16.03 17.1010 0.552454 7 to 30 15.86 10.4479 0.116213 8 to 31 16.06 16.2954 0.497002 9 to 32 16.34 26.1845 0.928835 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.343846 Tough bday spacings test for dh-ranFile-2016-09-09_05:31: 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 40 71 97 90 81 53 42 13 2 4 (O-E)^2/E 0.5 0.3 0.1 0.0 0.6 0.1 0.0 5.0 0.2 3.2 0.0 Birthday Spacings: Sum(O-E)^2/E= 10.101, p= 0.568 RESULTS OF GCD FOR dh-ranFile-2016-09-09_05:31 Euclid's algorithm: p-value, steps to gcd: 0.694114 p-value, dist. of gcd's: 0.576066 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-09-09_05:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.665 0.244 0.042 0.830 0.201 0.819 0.162 0.188 Bits 8 to 15---> 0.289 0.921 0.456 0.808 0.762 0.783 0.535 0.314 Bits 16 to 23---> 0.062 0.511 0.273 0.822 0.917 0.447 0.126 0.460 Bits 24 to 31---> 0.594 0.812 0.638 0.078 0.974 0.089 0.761 0.202 KS test for the above 32 p values: 0.088 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-09-09_05:31, p-values for 5 runs: 0.0491, 0.7470, 0.7240, 0.1954, 0.5482 Rank test for binary matrices (31x31) for dh-ranFile-2016-09-09_05:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 227 211.4 1.148 1.148 r= 29 5225 5134.0 1.613 2.761 r= 30 23077 23103.0 0.029 2.790 r= 31 11471 11551.5 0.561 3.352 chi-square = 3.352 with df = 3; p-value = 0.659 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-09-09_05:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 194 211.4 1.435 1.435 r= 30 5079 5134.0 0.589 2.024 r= 31 23079 23103.0 0.025 2.049 r= 32 11648 11551.5 0.806 2.855 chi-square = 2.855 with df = 3; p-value = 0.586 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-09-09_05:31 b-rank test for bits 1 to 8, p=0.45432 b-rank test for bits 2 to 9, p=0.52264 b-rank test for bits 3 to 10, p=0.64374 b-rank test for bits 4 to 11, p=0.98468 b-rank test for bits 5 to 12, p=0.31721 b-rank test for bits 6 to 13, p=0.25813 b-rank test for bits 7 to 14, p=0.97058 b-rank test for bits 8 to 15, p=0.72388 b-rank test for bits 9 to 16, p=0.12556 b-rank test for bits 10 to 17, p=0.85120 b-rank test for bits 11 to 18, p=0.82077 b-rank test for bits 12 to 19, p=0.51850 b-rank test for bits 13 to 20, p=0.37192 b-rank test for bits 14 to 21, p=0.42855 b-rank test for bits 15 to 22, p=0.33948 b-rank test for bits 16 to 23, p=0.22190 b-rank test for bits 17 to 24, p=0.71479 b-rank test for bits 18 to 25, p=0.75199 b-rank test for bits 19 to 26, p=0.38123 b-rank test for bits 20 to 27, p=0.22537 b-rank test for bits 21 to 28, p=0.06019 b-rank test for bits 22 to 29, p=0.49633 b-rank test for bits 23 to 30, p=0.60835 b-rank test for bits 24 to 31, p=0.33687 b-rank test for bits 25 to 32, p=0.71149 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 = 0.732269 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-09-09_05:31 (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 142465 1.30 0.902907 2 141986 0.18 0.571084 3 141991 0.19 0.575666 4 141869 -0.09 0.462464 5 141770 -0.33 0.372387 6 141819 -0.21 0.416424 7 141753 -0.37 0.357460 8 141270 -1.49 0.067619 9 140980 -2.17 0.014953 10 141448 -1.08 0.140545 11 141877 -0.08 0.469894 12 141178 -1.71 0.043752 13 141614 -0.69 0.245090 14 141403 -1.18 0.118402 15 141513 -0.93 0.177222 16 141339 -1.33 0.091340 17 141541 -0.86 0.194734 18 141947 0.09 0.535067 19 141530 -0.89 0.187732 20 141952 0.10 0.539707 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-09-09_05:31 Bits used No. missing words z-score p-value 23 to 32 141940 0.1058 0.542113 22 to 31 141936 0.0920 0.536637 21 to 30 141585 -1.1184 0.131703 20 to 29 142349 1.5161 0.935253 19 to 28 141946 0.1264 0.550312 18 to 27 141393 -1.7804 0.037501 17 to 26 141700 -0.7218 0.235200 16 to 25 141623 -0.9873 0.161737 15 to 24 142327 1.4402 0.925100 14 to 23 142026 0.4023 0.656272 13 to 22 142181 0.9368 0.825568 12 to 21 141674 -0.8115 0.208544 11 to 20 141735 -0.6011 0.273874 10 to 19 141529 -1.3115 0.094847 9 to 18 141698 -0.7287 0.233085 8 to 17 142039 0.4471 0.672612 7 to 16 142128 0.7540 0.774586 6 to 15 141933 0.0816 0.532526 5 to 14 141710 -0.6873 0.245933 4 to 13 141847 -0.2149 0.414911 3 to 12 142297 1.3368 0.909355 2 to 11 142335 1.4678 0.928924 1 to 10 141760 -0.5149 0.303301 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-09-09_05:31 Bits used No. missing words z-score p-value 28 to 32 141970 0.2057 0.581472 27 to 31 141249 -2.2384 0.012597 26 to 30 141464 -1.5096 0.065574 25 to 29 141452 -1.5503 0.060538 24 to 28 141393 -1.7503 0.040036 23 to 27 141982 0.2463 0.597290 22 to 26 142350 1.4938 0.932386 21 to 25 141844 -0.2215 0.412368 20 to 24 142088 0.6057 0.727630 19 to 23 141521 -1.3164 0.094024 18 to 22 141720 -0.6418 0.260503 17 to 21 141878 -0.1062 0.457711 16 to 20 141582 -1.1096 0.133587 15 to 19 141790 -0.4045 0.342919 14 to 18 141841 -0.2316 0.408414 13 to 17 141763 -0.4960 0.309935 12 to 16 141702 -0.7028 0.241086 11 to 15 141847 -0.2113 0.416331 10 to 14 141687 -0.7537 0.225526 9 to 13 141773 -0.4621 0.321992 8 to 12 141946 0.1243 0.549463 7 to 11 141697 -0.7198 0.235836 6 to 10 141587 -1.0926 0.137275 5 to 9 141999 0.3040 0.619423 4 to 8 141565 -1.1672 0.121561 3 to 7 141910 0.0023 0.500906 2 to 6 141452 -1.5503 0.060538 1 to 5 141444 -1.5774 0.057353 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-09-09_05:31 Bits used No. missing words z-score p-value 31 to 32 141671 -0.7030 0.241016 30 to 31 141848 -0.1809 0.428217 29 to 30 142034 0.3678 0.643473 28 to 29 141874 -0.1042 0.458498 27 to 28 141936 0.0787 0.531354 26 to 27 142148 0.7040 0.759297 25 to 26 141933 0.0698 0.527833 24 to 25 141491 -1.2340 0.108599 23 to 24 141730 -0.5290 0.298404 22 to 23 142305 1.1672 0.878429 21 to 22 141842 -0.1986 0.421283 20 to 21 141668 -0.7119 0.238267 19 to 20 142143 0.6893 0.754680 18 to 19 142374 1.3707 0.914767 17 to 18 141956 0.1377 0.554749 16 to 17 141795 -0.3373 0.367962 15 to 16 142299 1.1495 0.874819 14 to 15 142245 0.9902 0.838956 13 to 14 141665 -0.7207 0.235536 12 to 13 142075 0.4887 0.687474 11 to 12 141836 -0.2163 0.414372 10 to 11 141641 -0.7915 0.214316 9 to 10 141923 0.0403 0.516083 8 to 9 141751 -0.4671 0.320232 7 to 8 141665 -0.7207 0.235536 6 to 7 142077 0.4946 0.689559 5 to 6 142348 1.2940 0.902169 4 to 5 141764 -0.4287 0.334070 3 to 4 141356 -1.6322 0.051314 2 to 3 141664 -0.7237 0.234629 1 to 2 142042 0.3914 0.652233 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-09-09_05:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2439.29 -0.859 0.195272 Test results for specific bytes for dh-ranFile-2016-09-09_05:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2430.62 -0.981 0.163258 2 to 9 2425.78 -1.050 0.146940 3 to 10 2395.10 -1.484 0.068967 4 to 11 2444.64 -0.783 0.216859 5 to 12 2545.68 0.646 0.740849 6 to 13 2577.15 1.091 0.862389 7 to 14 2578.36 1.108 0.866110 8 to 15 2497.23 -0.039 0.484389 9 to 16 2481.04 -0.268 0.394285 10 to 17 2632.73 1.877 0.969751 11 to 18 2418.46 -1.153 0.124430 12 to 19 2441.30 -0.830 0.203244 13 to 20 2455.46 -0.630 0.264404 14 to 21 2412.44 -1.238 0.107806 15 to 22 2509.57 0.135 0.553835 16 to 23 2581.01 1.146 0.874036 17 to 24 2559.87 0.847 0.801424 18 to 25 2470.66 -0.415 0.339071 19 to 26 2431.06 -0.975 0.164787 20 to 27 2616.56 1.648 0.950371 21 to 28 2403.66 -1.362 0.086526 22 to 29 2542.41 0.600 0.725692 23 to 30 2527.12 0.384 0.649347 24 to 31 2546.85 0.663 0.746175 25 to 32 2543.22 0.611 0.729451 CDPARK for dh-ranFile-2016-09-09_05:31: 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 3556 1.5068 0.934075 3482 -1.8721 0.030593 3498 -1.1416 0.126820 3527 0.1826 0.572463 3527 0.1826 0.572463 3524 0.0457 0.518210 3514 -0.4110 0.340551 3513 -0.4566 0.323972 3501 -1.0046 0.157553 3517 -0.2740 0.392053 Square side=100, avg. no. parked=3515.90 sample std.=19.04 p-value of the KSTEST for those 10 p-values: 0.430363 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-09-09_05:31 0.4754,0.2629,0.2459,0.0121,0.2685,0.8336,0.8748,0.5523,0.0380,0.0101, The KS test for those 10 p-values: 0.076024 The 3DSPHERES test for dh-ranFile-2016-09-09_05:31 sample no r^3 equiv. uni. 1 42.657 0.758746 2 6.650 0.198830 3 32.316 0.659458 4 30.253 0.635209 5 27.024 0.593760 6 4.234 0.131621 7 26.510 0.586731 8 27.858 0.604897 9 14.580 0.384917 10 49.849 0.810168 11 30.756 0.641274 12 7.764 0.228011 13 129.359 0.986593 14 44.588 0.773786 15 1.000 0.032787 16 75.935 0.920434 17 80.588 0.931865 18 35.612 0.694883 19 22.516 0.527893 20 27.466 0.599700 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.233682 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-09-09_05:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 -0.7 -1.3 -1.3 0.5 0.8 0.4 -1.3 0.7 1.2 -1.0 -1.3 -0.5 2.1 -0.6 -1.3 -0.4 1.2 -0.8 0.3 -0.4 1.6 0.3 -0.0 0.4 -0.7 1.0 -0.4 -0.1 -0.6 -0.6 -0.1 -1.5 1.1 0.1 0.4 -0.2 1.1 2.5 0.4 0.9 1.0 -0.1 Chi-square with 42 degrees of freedom:39.043242 z-score=-0.322609, p-value=0.398492 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-09-09_05:31 Test no p-value 1 0.445329 2 0.711659 3 0.249221 4 0.174571 5 0.027788 6 0.453129 7 0.394187 8 0.230340 9 0.432165 10 0.230072 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.082042 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-09-09_05:31: (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 66517 0.34 66520 0.32 3 25000.00 25096 0.37 25248 2.46 4 6666.67 6685 0.05 6560 1.71 5 1388.89 1421 0.74 1401 0.11 6 238.10 234 0.07 225 0.72 7 34.72 43 1.97 37 0.15 8 4.96 3 0.77 8 1.86 p=0.36613 p=0.70846 Number of rngs required: 689611, p-value: 0.921 RESULTS OF CRAPS TEST for dh-ranFile-2016-09-09_05:31 No. of wins: Observed Expected 98731 98585.9 z-score= 0.649, pvalue=0.74188 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66869 66666.7 0.614 0.614 2 37596 37654.3 0.090 0.704 3 26908 26954.7 0.081 0.785 4 19234 19313.5 0.327 1.112 5 13921 13851.4 0.350 1.462 6 10037 9943.5 0.878 2.340 7 7059 7145.0 1.036 3.376 8 5283 5139.1 4.031 7.407 9 3587 3699.9 3.443 10.850 10 2669 2666.3 0.003 10.853 11 1877 1923.3 1.116 11.969 12 1363 1388.7 0.477 12.446 13 923 1003.7 6.491 18.937 14 762 726.1 1.771 20.707 15 547 525.8 0.852 21.559 16 364 381.2 0.772 22.331 17 251 276.5 2.359 24.690 18 220 200.8 1.830 26.519 19 139 146.0 0.334 26.854 20 90 106.2 2.475 29.329 21 301 287.1 0.672 30.001 Chisq= 30.00 for 20 degrees of freedom, p= 0.93016 SUMMARY of craptest p-value for no. of wins: 0.741882 p-value for throws/game: 0.930158 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-09-09_05:31 No. of wins: Observed Expected 98510 98585.9 z-score=-0.339, pvalue=0.36720 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66854 66666.7 0.526 0.526 2 37444 37654.3 1.175 1.701 3 26813 26954.7 0.745 2.446 4 19437 19313.5 0.790 3.237 5 14014 13851.4 1.908 5.145 6 9885 9943.5 0.345 5.490 7 7149 7145.0 0.002 5.492 8 5120 5139.1 0.071 5.563 9 3689 3699.9 0.032 5.594 10 2665 2666.3 0.001 5.595 11 1955 1923.3 0.522 6.117 12 1318 1388.7 3.603 9.720 13 1009 1003.7 0.028 9.748 14 751 726.1 0.851 10.599 15 496 525.8 1.693 12.292 16 371 381.2 0.270 12.562 17 262 276.5 0.764 13.327 18 213 200.8 0.737 14.064 19 147 146.0 0.007 14.071 20 104 106.2 0.046 14.117 21 304 287.1 0.993 15.110 Chisq= 15.11 for 20 degrees of freedom, p= 0.22995 SUMMARY of craptest p-value for no. of wins: 0.367198 p-value for throws/game: 0.229946 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0101,0.0121,0.0126,0.0150,0.0278,0.0306,0.0328,0.0375,0.0380,0.0400, 0.0419,0.0438,0.0491,0.0513,0.0574,0.0602,0.0605,0.0605,0.0616,0.0656, 0.0676,0.0690,0.0760,0.0782,0.0820,0.0865,0.0875,0.0894,0.0913,0.0940, 0.0948,0.1078,0.1086,0.1162,0.1184,0.1216,0.1244,0.1256,0.1257,0.1268, 0.1316,0.1317,0.1336,0.1373,0.1405,0.1469,0.1576,0.1617,0.1617,0.1633, 0.1648,0.1746,0.1772,0.1877,0.1884,0.1947,0.1953,0.1954,0.1988,0.2008, 0.2021,0.2032,0.2085,0.2143,0.2169,0.2219,0.2254,0.2255,0.2280,0.2299, 0.2301,0.2303,0.2331,0.2337,0.2346,0.2352,0.2355,0.2355,0.2358,0.2383, 0.2410,0.2411,0.2439,0.2451,0.2459,0.2459,0.2492,0.2581,0.2605,0.2629, 0.2644,0.2685,0.2734,0.2739,0.2892,0.2984,0.3033,0.3099,0.3144,0.3172, 0.3202,0.3220,0.3240,0.3341,0.3369,0.3391,0.3395,0.3406,0.3429,0.3438, 0.3575,0.3661,0.3672,0.3680,0.3719,0.3724,0.3812,0.3849,0.3921,0.3942, 0.3943,0.3985,0.4084,0.4124,0.4131,0.4144,0.4149,0.4163,0.4164,0.4213, 0.4282,0.4286,0.4304,0.4322,0.4453,0.4469,0.4531,0.4543,0.4564,0.4577, 0.4585,0.4599,0.4625,0.4699,0.4754,0.4844,0.4963,0.4970,0.5009,0.5111, 0.5161,0.5182,0.5185,0.5226,0.5278,0.5279,0.5314,0.5325,0.5351,0.5355, 0.5366,0.5397,0.5421,0.5482,0.5495,0.5503,0.5523,0.5525,0.5538,0.5547, 0.5683,0.5711,0.5725,0.5725,0.5757,0.5761,0.5815,0.5855,0.5867,0.5936, 0.5938,0.5973,0.5997,0.6049,0.6084,0.6194,0.6352,0.6380,0.6413,0.6435, 0.6437,0.6493,0.6522,0.6563,0.6595,0.6595,0.6653,0.6726,0.6875,0.6896, 0.6941,0.6949,0.6973,0.7012,0.7085,0.7115,0.7117,0.7148,0.7207,0.7239, 0.7240,0.7257,0.7276,0.7295,0.7323,0.7408,0.7419,0.7462,0.7470,0.7520, 0.7547,0.7587,0.7593,0.7606,0.7619,0.7738,0.7746,0.7828,0.8014,0.8078, 0.8102,0.8120,0.8195,0.8208,0.8221,0.8256,0.8303,0.8336,0.8390,0.8512, 0.8624,0.8661,0.8740,0.8748,0.8748,0.8784,0.9022,0.9029,0.9094,0.9148, 0.9168,0.9204,0.9206,0.9208,0.9251,0.9288,0.9289,0.9302,0.9319,0.9324, 0.9341,0.9345,0.9353,0.9504,0.9698,0.9706,0.9742,0.9847,0.9866, Overall p-value after applying KStest on 269 p-values = 0.019022 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.