RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-12-18_15:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.68 24.5332 0.894344 2 to 25 15.79 20.5029 0.750682 3 to 26 15.47 30.3158 0.975845 4 to 27 15.69 18.4048 0.636255 5 to 28 15.85 18.2631 0.627575 6 to 29 15.88 16.2769 0.495703 7 to 30 15.74 14.2392 0.349899 8 to 31 15.65 14.5527 0.372333 9 to 32 15.76 24.1029 0.883334 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.144963 Tough bday spacings test for dh-ranFile-2015-12-18_15:31: 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 14 30 85 97 100 90 43 21 8 6 6 (O-E)^2/E 2.6 1.2 1.9 0.0 0.1 1.8 1.6 2.6 3.2 0.1 0.9 Birthday Spacings: Sum(O-E)^2/E= 15.833, p= 0.895 RESULTS OF GCD FOR dh-ranFile-2015-12-18_15:31 Euclid's algorithm: p-value, steps to gcd: 0.913575 p-value, dist. of gcd's: 0.519618 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-12-18_15:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.845 0.604 0.961 0.461 0.868 0.711 0.865 0.853 Bits 8 to 15---> 0.901 0.635 0.108 0.809 0.648 0.075 0.423 0.441 Bits 16 to 23---> 0.804 0.224 0.187 0.668 0.556 0.797 0.950 0.494 Bits 24 to 31---> 0.661 0.898 0.885 0.353 0.434 0.344 0.953 0.621 KS test for the above 32 p values: 0.980 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-12-18_15:31, p-values for 5 runs: 0.0259, 0.4090, 0.4169, 0.5510, 0.8805 Rank test for binary matrices (31x31) for dh-ranFile-2015-12-18_15:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 229 211.4 1.462 1.462 r= 29 5152 5134.0 0.063 1.525 r= 30 23158 23103.0 0.131 1.656 r= 31 11461 11551.5 0.709 2.365 chi-square = 2.365 with df = 3; p-value = 0.500 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-12-18_15:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 198 211.4 0.852 0.852 r= 30 5087 5134.0 0.430 1.282 r= 31 23175 23103.0 0.224 1.506 r= 32 11540 11551.5 0.011 1.518 chi-square = 1.518 with df = 3; p-value = 0.322 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-12-18_15:31 b-rank test for bits 1 to 8, p=0.68055 b-rank test for bits 2 to 9, p=0.67368 b-rank test for bits 3 to 10, p=0.57678 b-rank test for bits 4 to 11, p=0.50526 b-rank test for bits 5 to 12, p=0.04443 b-rank test for bits 6 to 13, p=0.37795 b-rank test for bits 7 to 14, p=0.54765 b-rank test for bits 8 to 15, p=0.41009 b-rank test for bits 9 to 16, p=0.32160 b-rank test for bits 10 to 17, p=0.88877 b-rank test for bits 11 to 18, p=0.25641 b-rank test for bits 12 to 19, p=0.31270 b-rank test for bits 13 to 20, p=0.87117 b-rank test for bits 14 to 21, p=0.03328 b-rank test for bits 15 to 22, p=0.37784 b-rank test for bits 16 to 23, p=0.93206 b-rank test for bits 17 to 24, p=0.79869 b-rank test for bits 18 to 25, p=0.58582 b-rank test for bits 19 to 26, p=0.14788 b-rank test for bits 20 to 27, p=0.36674 b-rank test for bits 21 to 28, p=0.24617 b-rank test for bits 22 to 29, p=0.34322 b-rank test for bits 23 to 30, p=0.87972 b-rank test for bits 24 to 31, p=0.27673 b-rank test for bits 25 to 32, p=0.69558 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 = 0.791692 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-12-18_15:31 (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 141731 -0.42 0.338464 2 141676 -0.55 0.292821 3 142073 0.38 0.648920 4 141745 -0.38 0.350508 5 141403 -1.18 0.118402 6 142240 0.77 0.780119 7 142028 0.28 0.609212 8 141482 -1.00 0.159034 9 142107 0.46 0.677904 10 141919 0.02 0.509013 11 141692 -0.51 0.305804 12 141500 -0.96 0.169441 13 141794 -0.27 0.393787 14 141168 -1.73 0.041630 15 141456 -1.06 0.144758 16 142253 0.80 0.789003 17 141966 0.13 0.552669 18 142017 0.25 0.599312 19 141702 -0.48 0.314045 20 141913 0.01 0.503421 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-12-18_15:31 Bits used No. missing words z-score p-value 23 to 32 142085 0.6058 0.727663 22 to 31 142441 1.8333 0.966624 21 to 30 142218 1.0644 0.856422 20 to 29 142472 1.9402 0.973825 19 to 28 142122 0.7333 0.768326 18 to 27 141898 -0.0391 0.484418 17 to 26 141513 -1.3667 0.085867 16 to 25 141480 -1.4804 0.069377 15 to 24 141705 -0.7046 0.240534 14 to 23 141747 -0.5598 0.287822 13 to 22 141802 -0.3701 0.355653 12 to 21 142378 1.6161 0.946964 11 to 20 142131 0.7644 0.777679 10 to 19 142184 0.9471 0.828216 9 to 18 141979 0.2402 0.594928 8 to 17 141960 0.1747 0.569352 7 to 16 141987 0.2678 0.605584 6 to 15 142094 0.6368 0.737870 5 to 14 141870 -0.1356 0.446061 4 to 13 142093 0.6333 0.736746 3 to 12 142316 1.4023 0.919589 2 to 11 141775 -0.4632 0.321608 1 to 10 141906 -0.0115 0.495419 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-12-18_15:31 Bits used No. missing words z-score p-value 28 to 32 141730 -0.6079 0.271628 27 to 31 141790 -0.4045 0.342919 26 to 30 142136 0.7684 0.778867 25 to 29 142267 1.2124 0.887328 24 to 28 141926 0.0565 0.522532 23 to 27 142023 0.3853 0.650001 22 to 26 141076 -2.8248 0.002365 21 to 25 141800 -0.3706 0.355464 20 to 24 142166 0.8701 0.807868 19 to 23 142177 0.9074 0.817891 18 to 22 142080 0.5785 0.718551 17 to 21 142127 0.7379 0.769702 16 to 20 141693 -0.7333 0.231681 15 to 19 141962 0.1785 0.570852 14 to 18 142406 1.6836 0.953873 13 to 17 142199 0.9819 0.836933 12 to 16 141471 -1.4859 0.068658 11 to 15 141752 -0.5333 0.296905 10 to 14 141955 0.1548 0.561516 9 to 13 142087 0.6023 0.726503 8 to 12 141924 0.0497 0.519831 7 to 11 141565 -1.1672 0.121561 6 to 10 141913 0.0124 0.504963 5 to 9 141711 -0.6723 0.250695 4 to 8 141774 -0.4587 0.323208 3 to 7 141855 -0.1842 0.426940 2 to 6 141971 0.2091 0.582796 1 to 5 141968 0.1989 0.578822 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-12-18_15:31 Bits used No. missing words z-score p-value 31 to 32 141873 -0.1072 0.457328 30 to 31 141653 -0.7561 0.224784 29 to 30 141805 -0.3078 0.379133 28 to 29 142033 0.3648 0.642373 27 to 28 141873 -0.1072 0.457328 26 to 27 142075 0.4887 0.687474 25 to 26 141970 0.1790 0.571018 24 to 25 141584 -0.9597 0.168609 23 to 24 142048 0.4091 0.658751 22 to 23 141488 -1.2429 0.106959 21 to 22 141792 -0.3461 0.364632 20 to 21 141799 -0.3255 0.372418 19 to 20 142377 1.3796 0.916139 18 to 19 141945 0.1052 0.541900 17 to 18 141673 -0.6971 0.242858 16 to 17 142070 0.4740 0.682233 15 to 16 142276 1.0816 0.860290 14 to 15 142056 0.4327 0.667367 13 to 14 141870 -0.1160 0.453819 12 to 13 142295 1.1377 0.872371 11 to 12 141485 -1.2517 0.105338 10 to 11 141883 -0.0777 0.469045 9 to 10 141676 -0.6883 0.245635 8 to 9 141769 -0.4140 0.339454 7 to 8 141996 0.2557 0.600895 6 to 7 141900 -0.0275 0.489022 5 to 6 142182 0.8043 0.789399 4 to 5 141898 -0.0334 0.486669 3 to 4 141752 -0.4641 0.321288 2 to 3 142029 0.3530 0.637959 1 to 2 141695 -0.6322 0.263614 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-12-18_15:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2541.17 0.582 0.719808 Test results for specific bytes for dh-ranFile-2015-12-18_15:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2459.96 -0.566 0.285601 2 to 9 2496.91 -0.044 0.482597 3 to 10 2622.05 1.726 0.957835 4 to 11 2541.16 0.582 0.719733 5 to 12 2526.84 0.380 0.647876 6 to 13 2453.55 -0.657 0.255605 7 to 14 2497.85 -0.030 0.487888 8 to 15 2389.91 -1.557 0.059750 9 to 16 2482.32 -0.250 0.401289 10 to 17 2624.42 1.760 0.960764 11 to 18 2352.50 -2.086 0.018494 12 to 19 2365.64 -1.900 0.028705 13 to 20 2429.79 -0.993 0.160358 14 to 21 2588.60 1.253 0.894890 15 to 22 2497.97 -0.029 0.488563 16 to 23 2527.33 0.387 0.650447 17 to 24 2477.07 -0.324 0.372850 18 to 25 2452.35 -0.674 0.250214 19 to 26 2482.35 -0.250 0.401464 20 to 27 2471.96 -0.397 0.345834 21 to 28 2392.16 -1.525 0.063627 22 to 29 2438.92 -0.864 0.193839 23 to 30 2440.62 -0.840 0.200537 24 to 31 2513.45 0.190 0.575425 25 to 32 2473.52 -0.375 0.354009 CDPARK for dh-ranFile-2015-12-18_15:31: 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 3510 -0.5936 0.276387 3491 -1.4612 0.071982 3536 0.5936 0.723613 3546 1.0502 0.853193 3535 0.5479 0.708135 3570 2.1461 0.984068 3534 0.5023 0.692266 3558 1.5982 0.944998 3504 -0.8676 0.192812 3520 -0.1370 0.445521 Square side=100, avg. no. parked=3530.40 sample std.=23.26 p-value of the KSTEST for those 10 p-values: 0.504528 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-12-18_15:31 0.6451,0.6361,0.9642,0.8615,0.3245,0.3969,0.3635,0.9829,0.0374,0.8154, The KS test for those 10 p-values: 0.363828 The 3DSPHERES test for dh-ranFile-2015-12-18_15:31 sample no r^3 equiv. uni. 1 2.081 0.067020 2 8.403 0.244286 3 25.286 0.569532 4 21.410 0.510147 5 82.921 0.936964 6 29.915 0.631081 7 5.933 0.179447 8 52.829 0.828121 9 36.099 0.699800 10 11.190 0.311334 11 114.523 0.978016 12 2.628 0.083884 13 20.570 0.496253 14 38.768 0.725355 15 19.914 0.485103 16 82.041 0.935087 17 20.877 0.501370 18 53.297 0.830780 19 34.078 0.678876 20 21.848 0.517249 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.576112 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-12-18_15:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 0.1 0.6 1.5 -1.6 1.6 -1.1 -0.8 -0.9 2.3 -0.8 0.2 2.0 0.2 -1.0 0.1 0.2 -0.9 -0.6 -0.4 0.2 -0.7 0.9 -0.3 0.7 -0.1 1.5 -0.2 -2.1 0.4 -0.4 -0.8 0.2 0.9 1.5 0.1 -0.7 1.1 0.9 -1.3 1.6 -1.0 -1.1 Chi-square with 42 degrees of freedom:45.354267 z-score=0.365980, p-value=0.666045 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-12-18_15:31 Test no p-value 1 0.534005 2 0.615430 3 0.902214 4 0.327426 5 0.508357 6 0.828935 7 0.355464 8 0.242909 9 0.071930 10 0.007199 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.771637 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-12-18_15:31: (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 66985 1.52 66418 0.93 3 25000.00 24773 2.06 25174 1.21 4 6666.67 6624 0.27 6770 1.60 5 1388.89 1345 1.39 1370 0.26 6 238.10 226 0.61 231 0.21 7 34.72 41 1.14 32 0.21 8 4.96 5 0.00 4 0.19 p=0.67840 p=0.40494 Number of rngs required: 688270, p-value: 0.439 RESULTS OF CRAPS TEST for dh-ranFile-2015-12-18_15:31 No. of wins: Observed Expected 98630 98585.9 z-score= 0.197, pvalue=0.57825 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66690 66666.7 0.008 0.008 2 37695 37654.3 0.044 0.052 3 26914 26954.7 0.062 0.114 4 19377 19313.5 0.209 0.323 5 13935 13851.4 0.504 0.827 6 9773 9943.5 2.925 3.752 7 7176 7145.0 0.134 3.886 8 5153 5139.1 0.038 3.924 9 3655 3699.9 0.544 4.468 10 2584 2666.3 2.540 7.008 11 2022 1923.3 5.062 12.070 12 1379 1388.7 0.068 12.139 13 1011 1003.7 0.053 12.191 14 693 726.1 1.513 13.704 15 531 525.8 0.051 13.755 16 391 381.2 0.255 14.009 17 268 276.5 0.264 14.273 18 205 200.8 0.087 14.360 19 144 146.0 0.027 14.386 20 100 106.2 0.364 14.750 21 304 287.1 0.993 15.743 Chisq= 15.74 for 20 degrees of freedom, p= 0.26758 SUMMARY of craptest p-value for no. of wins: 0.578253 p-value for throws/game: 0.267583 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-12-18_15:31 No. of wins: Observed Expected 98482 98585.9 z-score=-0.465, pvalue=0.32114 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66405 66666.7 1.027 1.027 2 37851 37654.3 1.027 2.054 3 26957 26954.7 0.000 2.055 4 19299 19313.5 0.011 2.065 5 13795 13851.4 0.230 2.295 6 9939 9943.5 0.002 2.297 7 7183 7145.0 0.202 2.499 8 5140 5139.1 0.000 2.499 9 3679 3699.9 0.118 2.617 10 2711 2666.3 0.749 3.366 11 1932 1923.3 0.039 3.405 12 1399 1388.7 0.076 3.481 13 982 1003.7 0.470 3.951 14 800 726.1 7.513 11.464 15 553 525.8 1.403 12.867 16 377 381.2 0.045 12.912 17 260 276.5 0.989 13.901 18 168 200.8 5.367 19.268 19 164 146.0 2.223 21.491 20 100 106.2 0.364 21.855 21 306 287.1 1.242 23.097 Chisq= 23.10 for 20 degrees of freedom, p= 0.71596 SUMMARY of craptest p-value for no. of wins: 0.321139 p-value for throws/game: 0.715960 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0024,0.0072,0.0185,0.0259,0.0287,0.0333,0.0374,0.0416,0.0444,0.0597, 0.0636,0.0670,0.0687,0.0694,0.0719,0.0720,0.0748,0.0839,0.0859,0.1053, 0.1070,0.1084,0.1184,0.1216,0.1448,0.1450,0.1479,0.1590,0.1604,0.1686, 0.1694,0.1794,0.1871,0.1928,0.1938,0.2005,0.2242,0.2248,0.2317,0.2405, 0.2429,0.2429,0.2443,0.2456,0.2462,0.2502,0.2507,0.2556,0.2564,0.2636, 0.2676,0.2716,0.2764,0.2767,0.2856,0.2878,0.2928,0.2969,0.3058,0.3113, 0.3127,0.3140,0.3211,0.3213,0.3216,0.3216,0.3218,0.3232,0.3245,0.3274, 0.3385,0.3395,0.3429,0.3432,0.3441,0.3458,0.3499,0.3505,0.3527,0.3540, 0.3555,0.3555,0.3557,0.3635,0.3638,0.3646,0.3667,0.3723,0.3724,0.3728, 0.3778,0.3779,0.3791,0.3938,0.3969,0.4013,0.4015,0.4049,0.4090,0.4101, 0.4169,0.4233,0.4269,0.4336,0.4392,0.4410,0.4455,0.4461,0.4538,0.4573, 0.4573,0.4610,0.4690,0.4826,0.4844,0.4851,0.4867,0.4879,0.4886,0.4890, 0.4939,0.4954,0.4957,0.4963,0.4999,0.5014,0.5034,0.5045,0.5050,0.5053, 0.5084,0.5090,0.5101,0.5172,0.5196,0.5198,0.5225,0.5340,0.5419,0.5476, 0.5510,0.5527,0.5565,0.5615,0.5694,0.5695,0.5709,0.5710,0.5754,0.5761, 0.5768,0.5783,0.5788,0.5828,0.5858,0.5949,0.5993,0.6009,0.6045,0.6056, 0.6092,0.6154,0.6206,0.6276,0.6311,0.6347,0.6361,0.6363,0.6380,0.6424, 0.6451,0.6478,0.6479,0.6489,0.6500,0.6504,0.6588,0.6611,0.6660,0.6674, 0.6682,0.6737,0.6779,0.6784,0.6789,0.6805,0.6822,0.6875,0.6923,0.6956, 0.6998,0.7081,0.7108,0.7160,0.7186,0.7197,0.7198,0.7236,0.7254,0.7265, 0.7277,0.7367,0.7379,0.7507,0.7683,0.7697,0.7716,0.7777,0.7789,0.7801, 0.7890,0.7894,0.7917,0.7972,0.7987,0.8035,0.8079,0.8094,0.8154,0.8179, 0.8281,0.8282,0.8289,0.8308,0.8369,0.8450,0.8528,0.8532,0.8564,0.8603, 0.8615,0.8647,0.8683,0.8712,0.8724,0.8797,0.8805,0.8833,0.8854,0.8873, 0.8888,0.8943,0.8949,0.8955,0.8977,0.9014,0.9022,0.9136,0.9161,0.9196, 0.9321,0.9351,0.9370,0.9450,0.9470,0.9495,0.9531,0.9539,0.9578,0.9607, 0.9608,0.9642,0.9666,0.9738,0.9758,0.9780,0.9801,0.9829,0.9841, Overall p-value after applying KStest on 269 p-values = 0.045940 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.