RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-03-24_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 15.97 17.5660 0.583298 2 to 25 15.99 12.0592 0.203458 3 to 26 16.15 9.0919 0.062667 4 to 27 16.23 26.9026 0.940489 5 to 28 15.92 24.4664 0.892693 6 to 29 15.67 16.3079 0.497877 7 to 30 15.58 21.6654 0.802068 8 to 31 15.59 21.5367 0.796799 9 to 32 16.01 7.9413 0.032215 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.662284 Tough bday spacings test for dh-ranFile-2018-03-24_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 9 42 57 97 116 77 44 31 14 8 5 (O-E)^2/E 0.0 0.8 3.6 0.0 3.4 0.0 1.3 0.1 0.1 0.3 0.2 Birthday Spacings: Sum(O-E)^2/E= 9.722, p= 0.535 RESULTS OF GCD FOR dh-ranFile-2018-03-24_02:31 Euclid's algorithm: p-value, steps to gcd: 0.751013 p-value, dist. of gcd's: 0.995205 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-03-24_02:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.194 0.669 0.635 0.388 0.149 0.414 0.019 0.737 Bits 8 to 15---> 0.248 0.891 0.437 0.938 0.544 0.403 0.789 0.192 Bits 16 to 23---> 0.306 0.166 0.948 0.992 0.716 0.569 0.722 0.151 Bits 24 to 31---> 0.784 0.028 0.766 0.952 0.890 0.433 0.581 0.313 KS test for the above 32 p values: 0.107 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-03-24_02:31, p-values for 5 runs: 0.9538, 0.0112, 0.9079, 0.3785, 0.4117 Rank test for binary matrices (31x31) for dh-ranFile-2018-03-24_02:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 222 211.4 0.530 0.530 r= 29 5145 5134.0 0.024 0.553 r= 30 23035 23103.0 0.200 0.754 r= 31 11598 11551.5 0.187 0.941 chi-square = 0.941 with df = 3; p-value = 0.184 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-03-24_02:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 203 211.4 0.335 0.335 r= 30 5005 5134.0 3.242 3.577 r= 31 23039 23103.0 0.178 3.755 r= 32 11753 11551.5 3.514 7.269 chi-square = 7.269 with df = 3; p-value = 0.936 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-03-24_02:31 b-rank test for bits 1 to 8, p=0.42993 b-rank test for bits 2 to 9, p=0.04306 b-rank test for bits 3 to 10, p=0.72134 b-rank test for bits 4 to 11, p=0.41703 b-rank test for bits 5 to 12, p=0.44952 b-rank test for bits 6 to 13, p=0.74012 b-rank test for bits 7 to 14, p=0.40948 b-rank test for bits 8 to 15, p=0.63149 b-rank test for bits 9 to 16, p=0.70637 b-rank test for bits 10 to 17, p=0.82715 b-rank test for bits 11 to 18, p=0.18327 b-rank test for bits 12 to 19, p=0.28179 b-rank test for bits 13 to 20, p=0.22148 b-rank test for bits 14 to 21, p=0.55287 b-rank test for bits 15 to 22, p=0.52674 b-rank test for bits 16 to 23, p=0.23933 b-rank test for bits 17 to 24, p=0.06752 b-rank test for bits 18 to 25, p=0.59031 b-rank test for bits 19 to 26, p=0.38353 b-rank test for bits 20 to 27, p=0.60993 b-rank test for bits 21 to 28, p=0.97905 b-rank test for bits 22 to 29, p=0.43332 b-rank test for bits 23 to 30, p=0.60314 b-rank test for bits 24 to 31, p=0.00160 b-rank test for bits 25 to 32, p=0.03577 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 = 0.341679 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-03-24_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 141775 -0.31 0.376816 2 142761 1.99 0.976698 3 142486 1.35 0.911068 4 142693 1.83 0.966450 5 142947 2.42 0.992334 6 141987 0.18 0.572001 7 142339 1.00 0.842287 8 141745 -0.38 0.350508 9 141868 -0.10 0.461536 10 142112 0.47 0.682082 11 142055 0.34 0.633204 12 142235 0.76 0.776645 13 142054 0.34 0.632324 14 141609 -0.70 0.241431 15 142457 1.28 0.899658 16 142101 0.45 0.672861 17 141186 -1.69 0.045512 18 142261 0.82 0.794364 19 141556 -0.83 0.204533 20 141789 -0.28 0.389300 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-03-24_02:31 Bits used No. missing words z-score p-value 23 to 32 142295 1.3299 0.908224 22 to 31 142410 1.7264 0.957867 21 to 30 142128 0.7540 0.774586 20 to 29 141678 -0.7977 0.212525 19 to 28 142367 1.5782 0.942737 18 to 27 142155 0.8471 0.801541 17 to 26 141389 -1.7942 0.036387 16 to 25 141947 0.1299 0.551676 15 to 24 142426 1.7816 0.962594 14 to 23 142030 0.4161 0.661333 13 to 22 142073 0.5644 0.713752 12 to 21 142043 0.4609 0.677576 11 to 20 142446 1.8506 0.967885 10 to 19 142230 1.1058 0.865585 9 to 18 142402 1.6989 0.955327 8 to 17 142283 1.2885 0.901217 7 to 16 141878 -0.1080 0.456984 6 to 15 141841 -0.2356 0.406864 5 to 14 142057 0.5092 0.694696 4 to 13 142286 1.2989 0.903004 3 to 12 142021 0.3851 0.649907 2 to 11 141637 -0.9391 0.173848 1 to 10 141852 -0.1977 0.421644 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-03-24_02:31 Bits used No. missing words z-score p-value 28 to 32 141870 -0.1333 0.446969 27 to 31 141883 -0.0893 0.464440 26 to 30 141761 -0.5028 0.307548 25 to 29 142121 0.7175 0.763475 24 to 28 142236 1.1074 0.865930 23 to 27 141920 0.0362 0.514426 22 to 26 142092 0.6192 0.732114 21 to 25 141836 -0.2486 0.401844 20 to 24 141871 -0.1299 0.448310 19 to 23 141937 0.0938 0.537365 18 to 22 141708 -0.6825 0.247470 17 to 21 142090 0.6124 0.729877 16 to 20 141946 0.1243 0.549463 15 to 19 142040 0.4429 0.671099 14 to 18 141542 -1.2452 0.106532 13 to 17 142191 0.9548 0.830164 12 to 16 142367 1.5514 0.939600 11 to 15 141478 -1.4621 0.071852 10 to 14 141485 -1.4384 0.075159 9 to 13 141589 -1.0859 0.138770 8 to 12 141881 -0.0960 0.461747 7 to 11 141692 -0.7367 0.230649 6 to 10 142216 1.0396 0.850728 5 to 9 141840 -0.2350 0.407098 4 to 8 142066 0.5311 0.702320 3 to 7 141876 -0.1130 0.455022 2 to 6 142261 1.1921 0.883389 1 to 5 141734 -0.5943 0.276143 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-03-24_02:31 Bits used No. missing words z-score p-value 31 to 32 141962 0.1554 0.561735 30 to 31 142112 0.5978 0.725029 29 to 30 141997 0.2586 0.602033 28 to 29 141862 -0.1396 0.444482 27 to 28 141950 0.1200 0.547747 26 to 27 141589 -0.9449 0.172348 25 to 26 141847 -0.1839 0.427060 24 to 25 142064 0.4563 0.675896 23 to 24 141865 -0.1308 0.447980 22 to 23 141185 -2.1367 0.016313 21 to 22 142210 0.8869 0.812442 20 to 21 142002 0.2734 0.607713 19 to 20 141690 -0.6470 0.258819 18 to 19 142227 0.9371 0.825641 17 to 18 142137 0.6716 0.749079 16 to 17 141615 -0.8682 0.192634 15 to 16 142035 0.3707 0.644573 14 to 15 142239 0.9725 0.834594 13 to 14 141337 -1.6883 0.045678 12 to 13 142123 0.6303 0.735749 11 to 12 141964 0.1613 0.564059 10 to 11 142302 1.1583 0.876633 9 to 10 142044 0.3973 0.654411 8 to 9 142036 0.3737 0.645671 7 to 8 141923 0.0403 0.516083 6 to 7 142069 0.4710 0.681181 5 to 6 141566 -1.0128 0.155584 4 to 5 142089 0.5300 0.701944 3 to 4 142186 0.8161 0.792789 2 to 3 141891 -0.0541 0.478439 1 to 2 142454 1.6067 0.945939 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-03-24_02:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2473.84 -0.370 0.355687 Test results for specific bytes for dh-ranFile-2018-03-24_02:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2480.82 -0.271 0.393091 2 to 9 2357.62 -2.014 0.022025 3 to 10 2383.69 -1.645 0.049993 4 to 11 2518.16 0.257 0.601343 5 to 12 2486.12 -0.196 0.422168 6 to 13 2469.38 -0.433 0.332505 7 to 14 2463.07 -0.522 0.300747 8 to 15 2586.79 1.227 0.890173 9 to 16 2384.10 -1.639 0.050593 10 to 17 2513.42 0.190 0.575257 11 to 18 2564.54 0.913 0.819315 12 to 19 2448.56 -0.727 0.233468 13 to 20 2513.25 0.187 0.574326 14 to 21 2435.58 -0.911 0.181128 15 to 22 2567.48 0.954 0.830026 16 to 23 2571.82 1.016 0.845126 17 to 24 2561.80 0.874 0.808918 18 to 25 2353.04 -2.078 0.018837 19 to 26 2496.27 -0.053 0.478968 20 to 27 2527.05 0.383 0.648997 21 to 28 2539.34 0.556 0.711008 22 to 29 2489.49 -0.149 0.440938 23 to 30 2579.82 1.129 0.870504 24 to 31 2479.39 -0.292 0.385328 25 to 32 2436.72 -0.895 0.185418 CDPARK for dh-ranFile-2018-03-24_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 3535 0.5479 0.708135 3530 0.3196 0.625377 3559 1.6438 0.949895 3518 -0.2283 0.409702 3541 0.8219 0.794438 3500 -1.0502 0.146807 3486 -1.6895 0.045562 3516 -0.3196 0.374623 3555 1.4612 0.928018 Square side=100, avg. no. parked=3525.70 sample std.=21.85 p-value of the KSTEST for those 10 p-values: 0.949918 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-03-24_02:31 0.4864,0.1387,0.5302,0.9004,0.3345,0.2724,0.9954,0.4362,0.4044,0.3911, The KS test for those 10 p-values: 0.455280 The 3DSPHERES test for dh-ranFile-2018-03-24_02:31 sample no r^3 equiv. uni. 1 3.920 0.122482 2 7.417 0.219041 3 39.459 0.731609 4 8.535 0.247604 5 10.655 0.298933 6 21.565 0.512673 7 4.741 0.146172 8 36.623 0.705000 9 22.394 0.525961 10 8.123 0.237218 11 25.215 0.568504 12 2.169 0.069741 13 35.931 0.698114 14 56.215 0.846465 15 16.082 0.414954 16 5.804 0.175916 17 64.785 0.884615 18 4.690 0.144727 19 50.609 0.814918 20 9.937 0.281957 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.399258 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-03-24_02:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.1 0.6 -1.0 0.1 0.0 -0.6 0.1 0.5 1.0 -0.7 -0.8 0.4 0.4 -0.6 -0.9 1.2 0.6 0.6 -0.2 -1.2 1.2 -0.7 -0.5 1.0 -0.1 0.1 0.1 -0.1 -0.7 -1.3 -1.1 1.1 0.1 1.0 -0.7 -1.6 0.8 -0.4 0.4 1.6 0.0 -1.1 Chi-square with 42 degrees of freedom:26.061108 z-score=-1.739076, p-value=0.025556 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-03-24_02:31 Test no p-value 1 0.688913 2 0.025429 3 0.121023 4 0.988744 5 0.637228 6 0.043689 7 0.849034 8 0.926134 9 0.119789 10 0.252479 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.278471 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-03-24_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 66501 0.41 66530 0.28 3 25000.00 25050 0.10 25240 2.30 4 6666.67 6785 2.10 6572 1.34 5 1388.89 1403 0.14 1382 0.03 6 238.10 218 1.70 231 0.21 7 34.72 34 0.01 40 0.80 8 4.96 8 1.86 4 0.19 p=0.61269 p=0.47691 Number of rngs required: 688401, p-value: 0.499 RESULTS OF CRAPS TEST for dh-ranFile-2018-03-24_02:31 No. of wins: Observed Expected 98675 98585.9 z-score= 0.399, pvalue=0.65494 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66403 66666.7 1.043 1.043 2 37600 37654.3 0.078 1.121 3 27004 26954.7 0.090 1.211 4 19528 19313.5 2.383 3.594 5 13738 13851.4 0.929 4.523 6 10063 9943.5 1.435 5.958 7 7216 7145.0 0.705 6.663 8 5056 5139.1 1.343 8.006 9 3857 3699.9 6.674 14.680 10 2673 2666.3 0.017 14.696 11 1839 1923.3 3.697 18.394 12 1382 1388.7 0.033 18.427 13 1035 1003.7 0.975 19.402 14 718 726.1 0.091 19.493 15 531 525.8 0.051 19.544 16 356 381.2 1.660 21.203 17 278 276.5 0.008 21.211 18 205 200.8 0.087 21.298 19 136 146.0 0.683 21.980 20 103 106.2 0.097 22.078 21 279 287.1 0.229 22.307 Chisq= 22.31 for 20 degrees of freedom, p= 0.67592 SUMMARY of craptest p-value for no. of wins: 0.654940 p-value for throws/game: 0.675920 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-03-24_02:31 No. of wins: Observed Expected 98761 98585.9 z-score= 0.783, pvalue=0.78328 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66538 66666.7 0.248 0.248 2 37766 37654.3 0.331 0.580 3 26955 26954.7 0.000 0.580 4 19451 19313.5 0.979 1.559 5 13778 13851.4 0.389 1.948 6 10072 9943.5 1.659 3.608 7 7111 7145.0 0.162 3.770 8 5105 5139.1 0.226 3.996 9 3659 3699.9 0.451 4.447 10 2559 2666.3 4.318 8.765 11 1927 1923.3 0.007 8.772 12 1505 1388.7 9.733 18.505 13 1007 1003.7 0.011 18.515 14 710 726.1 0.359 18.874 15 530 525.8 0.033 18.907 16 362 381.2 0.962 19.869 17 292 276.5 0.864 20.734 18 172 200.8 4.139 24.872 19 127 146.0 2.469 27.341 20 93 106.2 1.644 28.985 21 281 287.1 0.130 29.116 Chisq= 29.12 for 20 degrees of freedom, p= 0.91449 SUMMARY of craptest p-value for no. of wins: 0.783285 p-value for throws/game: 0.914491 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0016,0.0112,0.0163,0.0188,0.0188,0.0220,0.0254,0.0256,0.0281,0.0322, 0.0358,0.0364,0.0431,0.0437,0.0455,0.0456,0.0457,0.0500,0.0506,0.0627, 0.0675,0.0697,0.0719,0.0752,0.1065,0.1067,0.1198,0.1210,0.1225,0.1387, 0.1388,0.1447,0.1462,0.1468,0.1491,0.1511,0.1556,0.1659,0.1723,0.1738, 0.1759,0.1811,0.1833,0.1844,0.1854,0.1916,0.1926,0.1939,0.2035,0.2045, 0.2125,0.2190,0.2215,0.2306,0.2335,0.2372,0.2393,0.2414,0.2475,0.2476, 0.2478,0.2525,0.2588,0.2724,0.2761,0.2785,0.2818,0.2820,0.2989,0.3007, 0.3057,0.3075,0.3131,0.3325,0.3345,0.3417,0.3505,0.3557,0.3746,0.3768, 0.3785,0.3835,0.3853,0.3882,0.3893,0.3911,0.3921,0.3931,0.3993,0.4018, 0.4030,0.4044,0.4069,0.4071,0.4095,0.4097,0.4117,0.4136,0.4150,0.4170, 0.4216,0.4222,0.4271,0.4299,0.4332,0.4333,0.4362,0.4368,0.4409,0.4445, 0.4470,0.4480,0.4483,0.4495,0.4550,0.4553,0.4570,0.4615,0.4617,0.4644, 0.4769,0.4784,0.4790,0.4864,0.4979,0.4991,0.5127,0.5144,0.5161,0.5260, 0.5267,0.5302,0.5348,0.5374,0.5441,0.5477,0.5495,0.5517,0.5529,0.5617, 0.5641,0.5685,0.5685,0.5720,0.5743,0.5753,0.5806,0.5833,0.5903,0.6013, 0.6020,0.6031,0.6077,0.6099,0.6127,0.6254,0.6315,0.6323,0.6332,0.6349, 0.6372,0.6446,0.6457,0.6490,0.6499,0.6544,0.6549,0.6613,0.6623,0.6691, 0.6711,0.6729,0.6759,0.6759,0.6776,0.6812,0.6821,0.6889,0.6947,0.6981, 0.7019,0.7023,0.7050,0.7064,0.7081,0.7110,0.7138,0.7159,0.7213,0.7222, 0.7250,0.7299,0.7316,0.7321,0.7357,0.7370,0.7401,0.7491,0.7510,0.7635, 0.7662,0.7746,0.7766,0.7833,0.7844,0.7888,0.7928,0.7944,0.7944,0.7968, 0.8015,0.8021,0.8089,0.8124,0.8149,0.8193,0.8256,0.8272,0.8300,0.8302, 0.8346,0.8423,0.8451,0.8465,0.8490,0.8507,0.8656,0.8659,0.8705,0.8766, 0.8834,0.8846,0.8897,0.8902,0.8909,0.8927,0.8997,0.9004,0.9012,0.9030, 0.9079,0.9082,0.9111,0.9145,0.9261,0.9280,0.9362,0.9379,0.9396,0.9405, 0.9427,0.9459,0.9483,0.9499,0.9499,0.9524,0.9538,0.9553,0.9579,0.9626, 0.9665,0.9679,0.9767,0.9790,0.9887,0.9918,0.9923,0.9952,0.9954, Overall p-value after applying KStest on 269 p-values = 0.178198 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.