RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-07-23_03:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.47 21.3413 0.788604 2 to 25 15.67 22.0413 0.816864 3 to 26 16.09 13.7710 0.316762 4 to 27 15.57 24.8978 0.902979 5 to 28 15.75 17.6915 0.591455 6 to 29 15.76 24.6157 0.896353 7 to 30 15.63 16.6623 0.522536 8 to 31 15.72 10.9803 0.142416 9 to 32 15.84 15.1558 0.415743 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.525066 Tough bday spacings test for dh-ranFile-2015-07-23_03:31: 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 10 33 70 95 79 84 67 34 16 7 5 (O-E)^2/E 0.1 0.4 0.1 0.1 3.6 0.4 4.3 0.6 0.1 0.0 0.2 Birthday Spacings: Sum(O-E)^2/E= 9.852, p= 0.546 RESULTS OF GCD FOR dh-ranFile-2015-07-23_03:31 Euclid's algorithm: p-value, steps to gcd: 0.608420 p-value, dist. of gcd's: 0.303498 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-07-23_03:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.264 0.720 0.306 0.114 0.842 0.860 0.388 0.745 Bits 8 to 15---> 0.333 0.890 0.914 0.958 0.592 0.205 0.764 0.975 Bits 16 to 23---> 0.993 0.064 0.075 0.159 0.377 0.318 0.226 0.910 Bits 24 to 31---> 0.645 0.201 0.440 0.298 0.552 0.056 0.421 0.448 KS test for the above 32 p values: 0.184 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-07-23_03:31, p-values for 5 runs: 0.3378, 0.5182, 0.1795, 0.1465, 0.9197 Rank test for binary matrices (31x31) for dh-ranFile-2015-07-23_03:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 210 211.4 0.010 0.010 r= 29 5032 5134.0 2.027 2.036 r= 30 23010 23103.0 0.375 2.411 r= 31 11748 11551.5 3.342 5.753 chi-square = 5.753 with df = 3; p-value = 0.876 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-07-23_03:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 201 211.4 0.513 0.513 r= 30 5003 5134.0 3.343 3.857 r= 31 23125 23103.0 0.021 3.877 r= 32 11671 11551.5 1.236 5.113 chi-square = 5.113 with df = 3; p-value = 0.836 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-07-23_03:31 b-rank test for bits 1 to 8, p=0.19440 b-rank test for bits 2 to 9, p=0.14416 b-rank test for bits 3 to 10, p=0.01273 b-rank test for bits 4 to 11, p=0.06742 b-rank test for bits 5 to 12, p=0.26533 b-rank test for bits 6 to 13, p=0.47568 b-rank test for bits 7 to 14, p=0.59741 b-rank test for bits 8 to 15, p=0.08005 b-rank test for bits 9 to 16, p=0.50538 b-rank test for bits 10 to 17, p=0.97903 b-rank test for bits 11 to 18, p=0.08778 b-rank test for bits 12 to 19, p=0.65204 b-rank test for bits 13 to 20, p=0.82142 b-rank test for bits 14 to 21, p=0.77374 b-rank test for bits 15 to 22, p=0.48510 b-rank test for bits 16 to 23, p=0.02843 b-rank test for bits 17 to 24, p=0.68783 b-rank test for bits 18 to 25, p=0.40249 b-rank test for bits 19 to 26, p=0.29685 b-rank test for bits 20 to 27, p=0.31784 b-rank test for bits 21 to 28, p=0.52144 b-rank test for bits 22 to 29, p=0.61085 b-rank test for bits 23 to 30, p=0.53108 b-rank test for bits 24 to 31, p=0.81638 b-rank test for bits 25 to 32, p=0.90501 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 = 0.667018 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-07-23_03:31 (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 141770 -0.33 0.372387 2 142901 2.32 0.989748 3 142298 0.91 0.818089 4 141984 0.17 0.569249 5 141402 -1.19 0.117939 6 141254 -1.53 0.062867 7 141966 0.13 0.552669 8 142143 0.55 0.707453 9 141692 -0.51 0.305804 10 142422 1.20 0.884508 11 141397 -1.20 0.115647 12 142057 0.35 0.634962 13 141049 -2.01 0.022209 14 141804 -0.25 0.402803 15 141432 -1.12 0.132370 16 142289 0.89 0.812482 17 142278 0.86 0.805485 18 141186 -1.69 0.045512 19 141865 -0.10 0.458753 20 143269 3.18 0.999255 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-07-23_03:31 Bits used No. missing words z-score p-value 23 to 32 141836 -0.2529 0.400187 22 to 31 142341 1.4885 0.931693 21 to 30 142224 1.0851 0.861054 20 to 29 142404 1.7058 0.955973 19 to 28 142259 1.2058 0.886045 18 to 27 141458 -1.5563 0.059817 17 to 26 142551 2.2127 0.986539 16 to 25 142003 0.3230 0.626652 15 to 24 141231 -2.3391 0.009666 14 to 23 141751 -0.5460 0.292545 13 to 22 141874 -0.1218 0.451518 12 to 21 142099 0.6540 0.743455 11 to 20 142140 0.7954 0.786814 10 to 19 142258 1.2023 0.885378 9 to 18 141573 -1.1598 0.123074 8 to 17 141546 -1.2529 0.105128 7 to 16 142033 0.4264 0.665109 6 to 15 141763 -0.5046 0.306925 5 to 14 142684 2.6713 0.996222 4 to 13 142582 2.3196 0.989817 3 to 12 141756 -0.5287 0.298498 2 to 11 142165 0.8816 0.811009 1 to 10 141909 -0.0011 0.499546 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-07-23_03:31 Bits used No. missing words z-score p-value 28 to 32 142133 0.7582 0.775835 27 to 31 142494 1.9819 0.976257 26 to 30 141916 0.0226 0.509019 25 to 29 141732 -0.6011 0.273881 24 to 28 142091 0.6158 0.730997 23 to 27 141756 -0.5198 0.301615 22 to 26 141688 -0.7503 0.226546 21 to 25 142098 0.6396 0.738770 20 to 24 142168 0.8768 0.809715 19 to 23 142329 1.4226 0.922575 18 to 22 142154 0.8294 0.796558 17 to 21 142138 0.7752 0.780875 16 to 20 141660 -0.8452 0.199003 15 to 19 141176 -2.4859 0.006462 14 to 18 142286 1.2768 0.899172 13 to 17 142314 1.3718 0.914931 12 to 16 142145 0.7989 0.787820 11 to 15 142097 0.6362 0.737667 10 to 14 141884 -0.0859 0.465787 9 to 13 142331 1.4294 0.923554 8 to 12 142095 0.6294 0.735453 7 to 11 141989 0.2701 0.606446 6 to 10 142162 0.8565 0.804142 5 to 9 142522 2.0768 0.981092 4 to 8 141816 -0.3164 0.375860 3 to 7 141596 -1.0621 0.144087 2 to 6 141716 -0.6554 0.256119 1 to 5 142347 1.4836 0.931046 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-07-23_03:31 Bits used No. missing words z-score p-value 31 to 32 141805 -0.3078 0.379133 30 to 31 141633 -0.8151 0.207498 29 to 30 141950 0.1200 0.547747 28 to 29 142037 0.3766 0.646767 27 to 28 141358 -1.6263 0.051938 26 to 27 141649 -0.7679 0.221263 25 to 26 141825 -0.2488 0.401773 24 to 25 141547 -1.0688 0.142575 23 to 24 141528 -1.1249 0.130323 22 to 23 141596 -0.9243 0.177671 21 to 22 142194 0.8397 0.799471 20 to 21 141972 0.1849 0.573333 19 to 20 142155 0.7247 0.765679 18 to 19 141860 -0.1455 0.442152 17 to 18 141604 -0.9007 0.183880 16 to 17 141956 0.1377 0.554749 15 to 16 142191 0.8309 0.796981 14 to 15 142503 1.7512 0.960048 13 to 14 142206 0.8751 0.809249 12 to 13 141647 -0.7738 0.219514 11 to 12 141529 -1.1219 0.130949 10 to 11 141764 -0.4287 0.334070 9 to 10 141091 -2.4140 0.007890 8 to 9 141700 -0.6175 0.268455 7 to 8 142207 0.8781 0.810051 6 to 7 142663 2.2232 0.986899 5 to 6 141925 0.0462 0.518434 4 to 5 141923 0.0403 0.516083 3 to 4 141761 -0.4376 0.330856 2 to 3 142094 0.5447 0.707037 1 to 2 142838 2.7394 0.996923 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-07-23_03:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2514.78 0.209 0.582808 Test results for specific bytes for dh-ranFile-2015-07-23_03:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2526.49 0.375 0.646054 2 to 9 2461.14 -0.550 0.291323 3 to 10 2514.34 0.203 0.580336 4 to 11 2524.21 0.342 0.633987 5 to 12 2528.08 0.397 0.654359 6 to 13 2488.16 -0.167 0.433536 7 to 14 2481.17 -0.266 0.395025 8 to 15 2461.12 -0.550 0.291228 9 to 16 2494.35 -0.080 0.468132 10 to 17 2487.33 -0.179 0.428924 11 to 18 2567.63 0.956 0.830570 12 to 19 2606.28 1.503 0.933578 13 to 20 2368.86 -1.855 0.031831 14 to 21 2428.47 -1.012 0.155883 15 to 22 2412.14 -1.242 0.107028 16 to 23 2441.95 -0.821 0.205830 17 to 24 2589.35 1.264 0.896804 18 to 25 2432.58 -0.953 0.170169 19 to 26 2529.38 0.415 0.661108 20 to 27 2650.22 2.124 0.983184 21 to 28 2542.12 0.596 0.724290 22 to 29 2605.44 1.491 0.932034 23 to 30 2559.06 0.835 0.798203 24 to 31 2528.52 0.403 0.656671 25 to 32 2441.52 -0.827 0.204129 CDPARK for dh-ranFile-2015-07-23_03:31: 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 3502 -0.9589 0.168804 3490 -1.5068 0.065925 3515 -0.3653 0.357445 3550 1.2329 0.891189 3539 0.7306 0.767486 3545 1.0046 0.842447 3491 -1.4612 0.071982 3502 -0.9589 0.168804 3519 -0.1826 0.427537 3522 -0.0457 0.481790 Square side=100, avg. no. parked=3517.50 sample std.=20.60 p-value of the KSTEST for those 10 p-values: 0.609190 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-07-23_03:31 0.4332,0.8028,0.0571,0.6500,0.8734,0.5691,0.1317,0.3790,0.6471,0.7256, The KS test for those 10 p-values: 0.881461 The 3DSPHERES test for dh-ranFile-2015-07-23_03:31 sample no r^3 equiv. uni. 1 20.572 0.496279 2 16.216 0.417566 3 7.698 0.226320 4 0.532 0.017589 5 28.147 0.608685 6 42.762 0.759591 7 59.797 0.863745 8 6.350 0.190776 9 19.024 0.469603 10 41.973 0.753179 11 33.145 0.668732 12 14.478 0.382819 13 17.859 0.448602 14 26.052 0.580375 15 9.491 0.271201 16 28.397 0.611927 17 17.750 0.446595 18 5.455 0.166248 19 38.743 0.725120 20 32.841 0.665365 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.433014 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-07-23_03:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 0.1 -1.3 -1.3 -1.1 -0.6 -0.8 0.4 1.5 -0.6 -0.9 0.9 -1.9 -1.2 -0.1 -1.2 0.2 1.5 1.0 0.5 -0.6 0.7 0.8 -0.4 0.0 -1.1 1.0 0.2 1.3 1.7 -1.2 0.2 0.3 -1.1 0.1 -0.3 0.0 -1.7 0.9 -1.3 0.9 1.0 -0.1 Chi-square with 42 degrees of freedom:40.682860 z-score=-0.143712, p-value=0.471209 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-07-23_03:31 Test no p-value 1 0.187240 2 0.898751 3 0.685604 4 0.612841 5 0.043076 6 0.034060 7 0.083171 8 0.409373 9 0.071972 10 0.492912 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.101374 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-07-23_03:31: (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 66459 0.65 66378 1.25 3 25000.00 25149 0.89 25182 1.32 4 6666.67 6723 0.48 6818 3.44 5 1388.89 1380 0.06 1371 0.23 6 238.10 242 0.06 201 5.78 7 34.72 36 0.05 43 1.97 8 4.96 10 5.12 6 0.22 p=0.70604 p=0.97265 Number of rngs required: 689415, p-value: 0.880 RESULTS OF CRAPS TEST for dh-ranFile-2015-07-23_03:31 No. of wins: Observed Expected 98567 98585.9 z-score=-0.084, pvalue=0.46639 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66312 66666.7 1.887 1.887 2 37450 37654.3 1.109 2.996 3 27152 26954.7 1.444 4.439 4 19311 19313.5 0.000 4.440 5 14005 13851.4 1.703 6.142 6 9941 9943.5 0.001 6.143 7 7293 7145.0 3.065 9.208 8 5021 5139.1 2.713 11.920 9 3713 3699.9 0.047 11.967 10 2759 2666.3 3.223 15.190 11 1942 1923.3 0.181 15.371 12 1348 1388.7 1.195 16.567 13 1054 1003.7 2.519 19.086 14 706 726.1 0.559 19.644 15 529 525.8 0.019 19.663 16 412 381.2 2.497 22.160 17 287 276.5 0.396 22.556 18 207 200.8 0.190 22.746 19 155 146.0 0.557 23.302 20 118 106.2 1.308 24.610 21 285 287.1 0.016 24.625 Chisq= 24.63 for 20 degrees of freedom, p= 0.78386 SUMMARY of craptest p-value for no. of wins: 0.466390 p-value for throws/game: 0.783860 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-07-23_03:31 No. of wins: Observed Expected 98450 98585.9 z-score=-0.608, pvalue=0.27171 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66986 66666.7 1.530 1.530 2 37377 37654.3 2.042 3.572 3 26991 26954.7 0.049 3.621 4 19172 19313.5 1.036 4.657 5 13902 13851.4 0.185 4.842 6 10073 9943.5 1.685 6.527 7 7321 7145.0 4.334 10.861 8 5059 5139.1 1.248 12.109 9 3581 3699.9 3.819 15.928 10 2616 2666.3 0.949 16.876 11 1870 1923.3 1.479 18.355 12 1382 1388.7 0.033 18.388 13 983 1003.7 0.428 18.815 14 690 726.1 1.799 20.614 15 558 525.8 1.967 22.581 16 374 381.2 0.134 22.716 17 297 276.5 1.514 24.229 18 211 200.8 0.515 24.744 19 150 146.0 0.110 24.855 20 115 106.2 0.727 25.581 21 292 287.1 0.083 25.665 Chisq= 25.66 for 20 degrees of freedom, p= 0.82282 SUMMARY of craptest p-value for no. of wins: 0.271714 p-value for throws/game: 0.822823 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0065,0.0079,0.0097,0.0127,0.0176,0.0222,0.0284,0.0318,0.0341,0.0431, 0.0455,0.0519,0.0564,0.0571,0.0598,0.0629,0.0635,0.0659,0.0674,0.0720, 0.0720,0.0750,0.0801,0.0832,0.0878,0.1014,0.1051,0.1070,0.1137,0.1156, 0.1179,0.1231,0.1303,0.1309,0.1317,0.1324,0.1424,0.1426,0.1441,0.1442, 0.1465,0.1559,0.1593,0.1662,0.1688,0.1688,0.1702,0.1777,0.1795,0.1836, 0.1839,0.1872,0.1908,0.1944,0.1990,0.2013,0.2041,0.2053,0.2058,0.2075, 0.2195,0.2213,0.2259,0.2263,0.2265,0.2561,0.2637,0.2653,0.2685,0.2712, 0.2717,0.2739,0.2912,0.2913,0.2925,0.2969,0.2982,0.2985,0.3016,0.3035, 0.3058,0.3058,0.3069,0.3168,0.3176,0.3178,0.3309,0.3327,0.3341,0.3378, 0.3574,0.3724,0.3759,0.3774,0.3790,0.3791,0.3828,0.3884,0.3950,0.4002, 0.4018,0.4025,0.4028,0.4094,0.4157,0.4176,0.4206,0.4275,0.4289,0.4330, 0.4332,0.4335,0.4399,0.4422,0.4466,0.4477,0.4486,0.4515,0.4588,0.4658, 0.4664,0.4681,0.4696,0.4712,0.4757,0.4818,0.4851,0.4929,0.4963,0.4995, 0.5054,0.5090,0.5161,0.5182,0.5184,0.5214,0.5225,0.5251,0.5311,0.5465, 0.5477,0.5520,0.5527,0.5547,0.5691,0.5692,0.5733,0.5803,0.5804,0.5828, 0.5915,0.5923,0.5974,0.6064,0.6084,0.6087,0.6092,0.6108,0.6119,0.6128, 0.6267,0.6340,0.6350,0.6453,0.6461,0.6468,0.6471,0.6500,0.6520,0.6544, 0.6567,0.6611,0.6651,0.6654,0.6670,0.6687,0.6856,0.6878,0.7060,0.7070, 0.7075,0.7196,0.7243,0.7251,0.7256,0.7310,0.7355,0.7377,0.7388,0.7435, 0.7453,0.7532,0.7596,0.7638,0.7657,0.7675,0.7737,0.7758,0.7809,0.7839, 0.7868,0.7878,0.7886,0.7966,0.7970,0.7982,0.7995,0.8028,0.8041,0.8055, 0.8092,0.8097,0.8101,0.8110,0.8125,0.8164,0.8169,0.8181,0.8214,0.8228, 0.8306,0.8363,0.8416,0.8424,0.8604,0.8611,0.8637,0.8734,0.8757,0.8801, 0.8815,0.8845,0.8854,0.8860,0.8898,0.8912,0.8964,0.8968,0.8988,0.8992, 0.9030,0.9050,0.9096,0.9138,0.9149,0.9197,0.9226,0.9236,0.9310,0.9317, 0.9320,0.9336,0.9560,0.9581,0.9600,0.9727,0.9747,0.9763,0.9790,0.9811, 0.9832,0.9865,0.9869,0.9897,0.9898,0.9932,0.9962,0.9969,0.9993, Overall p-value after applying KStest on 269 p-values = 0.501136 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.