RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-07-10_02:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.91 14.0009 0.332965 2 to 25 15.75 19.1642 0.680814 3 to 26 15.67 12.7470 0.247046 4 to 27 15.44 16.4909 0.510662 5 to 28 15.65 15.9774 0.474563 6 to 29 15.37 30.9997 0.980026 7 to 30 15.53 39.8337 0.998634 8 to 31 15.61 15.2474 0.422334 9 to 32 15.85 14.7574 0.387049 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.220369 Tough bday spacings test for dh-ranFile-2015-07-10_02:31: 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 38 71 98 98 83 43 34 16 7 1 (O-E)^2/E 0.4 0.1 0.1 0.0 0.0 0.3 1.6 0.6 0.1 0.0 2.3 Birthday Spacings: Sum(O-E)^2/E= 5.403, p= 0.137 RESULTS OF GCD FOR dh-ranFile-2015-07-10_02:31 Euclid's algorithm: p-value, steps to gcd: 0.375701 p-value, dist. of gcd's: 0.741383 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-07-10_02:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.981 0.365 0.589 0.952 0.258 0.991 0.884 0.126 Bits 8 to 15---> 0.716 0.514 0.650 0.334 0.505 0.248 0.247 0.513 Bits 16 to 23---> 0.885 0.109 0.474 0.712 0.135 0.675 0.728 0.684 Bits 24 to 31---> 0.638 0.606 0.505 0.679 0.018 0.813 0.552 0.245 KS test for the above 32 p values: 0.462 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-07-10_02:31, p-values for 5 runs: 0.7981, 0.9720, 0.8402, 0.5150, 0.4519 Rank test for binary matrices (31x31) for dh-ranFile-2015-07-10_02:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 238 211.4 3.342 3.342 r= 29 5075 5134.0 0.678 4.020 r= 30 23109 23103.0 0.002 4.022 r= 31 11578 11551.5 0.061 4.083 chi-square = 4.083 with df = 3; p-value = 0.747 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-07-10_02:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 213 211.4 0.012 0.012 r= 30 5043 5134.0 1.613 1.625 r= 31 23202 23103.0 0.424 2.049 r= 32 11542 11551.5 0.008 2.057 chi-square = 2.057 with df = 3; p-value = 0.439 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-07-10_02:31 b-rank test for bits 1 to 8, p=0.13907 b-rank test for bits 2 to 9, p=0.39838 b-rank test for bits 3 to 10, p=0.29915 b-rank test for bits 4 to 11, p=0.51829 b-rank test for bits 5 to 12, p=0.32130 b-rank test for bits 6 to 13, p=0.89548 b-rank test for bits 7 to 14, p=0.96953 b-rank test for bits 8 to 15, p=0.57643 b-rank test for bits 9 to 16, p=0.90986 b-rank test for bits 10 to 17, p=0.04381 b-rank test for bits 11 to 18, p=0.23325 b-rank test for bits 12 to 19, p=0.83975 b-rank test for bits 13 to 20, p=0.07854 b-rank test for bits 14 to 21, p=0.62643 b-rank test for bits 15 to 22, p=0.22987 b-rank test for bits 16 to 23, p=0.09094 b-rank test for bits 17 to 24, p=0.90265 b-rank test for bits 18 to 25, p=0.17381 b-rank test for bits 19 to 26, p=0.93795 b-rank test for bits 20 to 27, p=0.76787 b-rank test for bits 21 to 28, p=0.11307 b-rank test for bits 22 to 29, p=0.25787 b-rank test for bits 23 to 30, p=0.64251 b-rank test for bits 24 to 31, p=0.14350 b-rank test for bits 25 to 32, p=0.88001 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 = 0.509983 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-07-10_02:31 (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 141711 -0.46 0.321543 2 141929 0.05 0.518328 3 142512 1.41 0.920450 4 142551 1.50 0.933093 5 140972 -2.19 0.014261 6 142403 1.15 0.875634 7 142097 0.44 0.669481 8 141192 -1.68 0.046869 9 141568 -0.80 0.212580 10 142604 1.62 0.947712 11 141228 -1.59 0.055704 12 141880 -0.07 0.472683 13 141646 -0.62 0.269193 14 142488 1.35 0.911818 15 141534 -0.88 0.190260 16 142292 0.89 0.814363 17 141924 0.03 0.513671 18 141366 -1.27 0.102138 19 142318 0.95 0.830170 20 141164 -1.74 0.040805 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-07-10_02:31 Bits used No. missing words z-score p-value 23 to 32 142023 0.3920 0.652458 22 to 31 141756 -0.5287 0.298498 21 to 30 142316 1.4023 0.919589 20 to 29 142017 0.3713 0.644784 19 to 28 142147 0.8196 0.793764 18 to 27 142329 1.4471 0.926071 17 to 26 142040 0.4506 0.673856 16 to 25 142208 1.0299 0.848471 15 to 24 141886 -0.0804 0.467940 14 to 23 141833 -0.2632 0.396196 13 to 22 142138 0.7885 0.784803 12 to 21 141929 0.0678 0.527039 11 to 20 141918 0.0299 0.511925 10 to 19 142083 0.5989 0.725368 9 to 18 141596 -1.0804 0.139971 8 to 17 141360 -1.8942 0.029096 7 to 16 141960 0.1747 0.569352 6 to 15 141645 -0.9115 0.181021 5 to 14 141741 -0.5804 0.280806 4 to 13 142197 0.9920 0.839393 3 to 12 141837 -0.2494 0.401520 2 to 11 142019 0.3782 0.647349 1 to 10 141894 -0.0529 0.478921 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-07-10_02:31 Bits used No. missing words z-score p-value 28 to 32 142028 0.4023 0.656258 27 to 31 142317 1.3819 0.916504 26 to 30 141986 0.2599 0.602529 25 to 29 142072 0.5514 0.709328 24 to 28 141677 -0.7876 0.215477 23 to 27 142235 1.1040 0.865196 22 to 26 141412 -1.6859 0.045911 21 to 25 141981 0.2429 0.595978 20 to 24 142146 0.8023 0.788802 19 to 23 141793 -0.3943 0.346665 18 to 22 142167 0.8735 0.808793 17 to 21 141547 -1.2282 0.109679 16 to 20 141529 -1.2893 0.098655 15 to 19 141826 -0.2825 0.388790 14 to 18 142002 0.3141 0.623291 13 to 17 142187 0.9413 0.826713 12 to 16 142256 1.1752 0.880033 11 to 15 142277 1.2463 0.893680 10 to 14 142163 0.8599 0.805077 9 to 13 142109 0.6768 0.750749 8 to 12 141920 0.0362 0.514426 7 to 11 142229 1.0836 0.860735 6 to 10 142136 0.7684 0.778867 5 to 9 141963 0.1819 0.572182 4 to 8 142135 0.7650 0.777859 3 to 7 142190 0.9514 0.829305 2 to 6 142021 0.3785 0.647486 1 to 5 141493 -1.4113 0.079080 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-07-10_02:31 Bits used No. missing words z-score p-value 31 to 32 142007 0.2881 0.613370 30 to 31 142654 2.1967 0.985978 29 to 30 142013 0.3058 0.620126 28 to 29 141736 -0.5113 0.304571 27 to 28 141925 0.0462 0.518434 26 to 27 142018 0.3206 0.625728 25 to 26 141968 0.1731 0.568701 24 to 25 142369 1.3560 0.912444 23 to 24 142314 1.1937 0.883706 22 to 23 141810 -0.2930 0.384758 21 to 22 142297 1.1436 0.873599 20 to 21 141945 0.1052 0.541900 19 to 20 141701 -0.6145 0.269428 18 to 19 141845 -0.1898 0.424747 17 to 18 141918 0.0256 0.510202 16 to 17 142161 0.7424 0.771074 15 to 16 142323 1.2203 0.888818 14 to 15 142334 1.2527 0.894845 13 to 14 141635 -0.8092 0.209191 12 to 13 141343 -1.6706 0.047401 11 to 12 141617 -0.8623 0.194253 10 to 11 142197 0.8486 0.801944 9 to 10 141524 -1.1367 0.127839 8 to 9 141800 -0.3225 0.373534 7 to 8 142352 1.3058 0.904192 6 to 7 142428 1.5300 0.936992 5 to 6 141437 -1.3933 0.081764 4 to 5 141770 -0.4110 0.340535 3 to 4 142196 0.8456 0.801122 2 to 3 141471 -1.2930 0.098004 1 to 2 142067 0.4651 0.679071 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-07-10_02:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2488.40 -0.164 0.434856 Test results for specific bytes for dh-ranFile-2015-07-10_02:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2536.19 0.512 0.695614 2 to 9 2497.03 -0.042 0.483226 3 to 10 2582.81 1.171 0.879231 4 to 11 2580.69 1.141 0.873105 5 to 12 2568.98 0.976 0.835366 6 to 13 2558.17 0.823 0.794653 7 to 14 2432.49 -0.955 0.169845 8 to 15 2469.77 -0.428 0.334485 9 to 16 2377.64 -1.730 0.041774 10 to 17 2517.89 0.253 0.599873 11 to 18 2270.20 -3.250 0.000577 12 to 19 2434.02 -0.933 0.175384 13 to 20 2451.86 -0.681 0.247998 14 to 21 2433.05 -0.947 0.171867 15 to 22 2467.14 -0.465 0.321057 16 to 23 2461.94 -0.538 0.295191 17 to 24 2616.97 1.654 0.950952 18 to 25 2583.36 1.179 0.880768 19 to 26 2470.07 -0.423 0.336062 20 to 27 2554.14 0.766 0.778040 21 to 28 2353.38 -2.073 0.019064 22 to 29 2567.82 0.959 0.831249 23 to 30 2575.01 1.061 0.855594 24 to 31 2499.09 -0.013 0.494885 25 to 32 2445.96 -0.764 0.222379 CDPARK for dh-ranFile-2015-07-10_02:31: 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 3517 -0.2740 0.392053 3552 1.3242 0.907282 3537 0.6393 0.738676 3527 0.1826 0.572463 3522 -0.0457 0.481790 3469 -2.4658 0.006836 3504 -0.8676 0.192812 3544 0.9589 0.831196 3522 -0.0457 0.481790 3513 -0.4566 0.323972 Square side=100, avg. no. parked=3520.70 sample std.=22.04 p-value of the KSTEST for those 10 p-values: 0.927250 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-07-10_02:31 0.5820,0.8365,0.2756,0.5866,0.8307,0.8479,0.5404,0.0544,0.0661,0.0250, The KS test for those 10 p-values: 0.492837 The 3DSPHERES test for dh-ranFile-2015-07-10_02:31 sample no r^3 equiv. uni. 1 24.565 0.559054 2 23.895 0.549101 3 7.200 0.213382 4 9.052 0.260454 5 23.840 0.548270 6 10.106 0.285997 7 41.666 0.750641 8 49.393 0.807264 9 20.699 0.498403 10 3.060 0.096984 11 16.834 0.429432 12 61.847 0.872744 13 1.938 0.062560 14 3.576 0.112363 15 51.252 0.818843 16 16.013 0.413611 17 3.542 0.111367 18 12.689 0.344896 19 26.001 0.579666 20 4.322 0.134182 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.342651 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-07-10_02:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 1.3 0.6 -0.1 0.2 -1.0 -0.8 -1.0 0.4 0.6 0.1 -1.1 0.1 -1.3 -1.6 0.5 0.6 1.8 0.4 -0.1 0.8 0.2 -0.8 0.7 0.1 0.7 -1.6 -0.3 0.4 0.4 -0.7 -0.9 -0.2 0.5 1.2 -0.1 0.5 -1.7 -2.4 -0.1 0.9 -1.0 -1.1 Chi-square with 42 degrees of freedom:34.905758 z-score=-0.774045, p-value=0.227048 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-07-10_02:31 Test no p-value 1 0.270334 2 0.027603 3 0.299853 4 0.122285 5 0.234696 6 0.909109 7 0.115145 8 0.757490 9 0.123004 10 0.514025 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.095599 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-07-10_02:31: (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 66596 0.07 66628 0.02 3 25000.00 25132 0.70 25054 0.12 4 6666.67 6611 0.46 6657 0.01 5 1388.89 1384 0.02 1371 0.23 6 238.10 237 0.01 244 0.15 7 34.72 38 0.31 36 0.05 8 4.96 1 3.16 9 3.29 p=0.42118 p=0.30544 Number of rngs required: 690205, p-value: 0.984 RESULTS OF CRAPS TEST for dh-ranFile-2015-07-10_02:31 No. of wins: Observed Expected 98723 98585.9 z-score= 0.613, pvalue=0.73019 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66471 66666.7 0.574 0.574 2 37806 37654.3 0.611 1.185 3 26960 26954.7 0.001 1.186 4 19365 19313.5 0.138 1.324 5 13840 13851.4 0.009 1.333 6 9947 9943.5 0.001 1.334 7 7263 7145.0 1.948 3.282 8 5147 5139.1 0.012 3.295 9 3643 3699.9 0.874 4.169 10 2623 2666.3 0.703 4.872 11 1927 1923.3 0.007 4.879 12 1369 1388.7 0.281 5.159 13 983 1003.7 0.428 5.587 14 763 726.1 1.871 7.458 15 516 525.8 0.184 7.642 16 376 381.2 0.070 7.711 17 262 276.5 0.764 8.476 18 210 200.8 0.419 8.895 19 142 146.0 0.109 9.003 20 104 106.2 0.046 9.050 21 283 287.1 0.059 9.108 Chisq= 9.11 for 20 degrees of freedom, p= 0.01838 SUMMARY of craptest p-value for no. of wins: 0.730186 p-value for throws/game: 0.018383 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-07-10_02:31 No. of wins: Observed Expected 98865 98585.9 z-score= 1.248, pvalue=0.89407 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66880 66666.7 0.683 0.683 2 37711 37654.3 0.085 0.768 3 26830 26954.7 0.577 1.345 4 19555 19313.5 3.021 4.366 5 13563 13851.4 6.006 10.371 6 9853 9943.5 0.824 11.196 7 7078 7145.0 0.629 11.825 8 5079 5139.1 0.702 12.527 9 3758 3699.9 0.913 13.440 10 2674 2666.3 0.022 13.463 11 1972 1923.3 1.232 14.694 12 1396 1388.7 0.038 14.732 13 1035 1003.7 0.975 15.707 14 672 726.1 4.037 19.744 15 579 525.8 5.375 25.119 16 384 381.2 0.021 25.140 17 280 276.5 0.043 25.184 18 207 200.8 0.190 25.373 19 122 146.0 3.940 29.314 20 93 106.2 1.644 30.958 21 279 287.1 0.229 31.187 Chisq= 31.19 for 20 degrees of freedom, p= 0.94723 SUMMARY of craptest p-value for no. of wins: 0.894073 p-value for throws/game: 0.947235 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0006,0.0068,0.0143,0.0180,0.0184,0.0191,0.0250,0.0276,0.0291,0.0408, 0.0418,0.0438,0.0459,0.0469,0.0474,0.0544,0.0557,0.0626,0.0661,0.0785, 0.0791,0.0818,0.0909,0.0956,0.0970,0.0980,0.0987,0.1021,0.1090,0.1097, 0.1114,0.1124,0.1131,0.1151,0.1223,0.1230,0.1265,0.1278,0.1342,0.1351, 0.1373,0.1391,0.1400,0.1435,0.1698,0.1719,0.1738,0.1754,0.1810,0.1903, 0.1928,0.1943,0.2092,0.2126,0.2134,0.2155,0.2204,0.2224,0.2270,0.2299, 0.2332,0.2347,0.2454,0.2470,0.2474,0.2475,0.2480,0.2579,0.2583,0.2605, 0.2692,0.2694,0.2703,0.2756,0.2808,0.2860,0.2952,0.2985,0.2992,0.2999, 0.3046,0.3054,0.3211,0.3213,0.3215,0.3240,0.3330,0.3345,0.3345,0.3361, 0.3405,0.3427,0.3449,0.3467,0.3648,0.3735,0.3757,0.3848,0.3870,0.3888, 0.3921,0.3962,0.3984,0.4015,0.4136,0.4212,0.4223,0.4247,0.4294,0.4349, 0.4393,0.4519,0.4619,0.4679,0.4727,0.4742,0.4746,0.4789,0.4818,0.4818, 0.4832,0.4928,0.4949,0.4984,0.5046,0.5048,0.5100,0.5102,0.5107,0.5119, 0.5133,0.5136,0.5137,0.5140,0.5144,0.5150,0.5183,0.5183,0.5184,0.5270, 0.5404,0.5419,0.5483,0.5491,0.5519,0.5591,0.5687,0.5694,0.5722,0.5725, 0.5764,0.5797,0.5820,0.5866,0.5895,0.5960,0.5999,0.6025,0.6058,0.6134, 0.6201,0.6233,0.6257,0.6264,0.6379,0.6425,0.6448,0.6473,0.6475,0.6497, 0.6525,0.6563,0.6695,0.6739,0.6746,0.6785,0.6791,0.6808,0.6839,0.6956, 0.7093,0.7116,0.7164,0.7254,0.7277,0.7302,0.7387,0.7414,0.7473,0.7506, 0.7507,0.7575,0.7679,0.7711,0.7779,0.7780,0.7789,0.7848,0.7888,0.7938, 0.7947,0.7981,0.8011,0.8019,0.8051,0.8073,0.8088,0.8134,0.8144,0.8188, 0.8267,0.8293,0.8302,0.8307,0.8312,0.8312,0.8354,0.8365,0.8394,0.8398, 0.8402,0.8479,0.8485,0.8556,0.8607,0.8652,0.8727,0.8731,0.8736,0.8756, 0.8792,0.8800,0.8800,0.8808,0.8836,0.8837,0.8854,0.8888,0.8937,0.8941, 0.8948,0.8955,0.9027,0.9042,0.9073,0.9091,0.9099,0.9118,0.9124,0.9165, 0.9196,0.9205,0.9261,0.9272,0.9331,0.9370,0.9379,0.9472,0.9477,0.9510, 0.9516,0.9695,0.9720,0.9800,0.9812,0.9835,0.9860,0.9914,0.9986, Overall p-value after applying KStest on 269 p-values = 0.458656 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.