RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-01-11_19:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.80 11.1139 0.149416 2 to 25 15.97 21.7730 0.806391 3 to 26 15.61 28.8207 0.963784 4 to 27 15.45 29.2491 0.967703 5 to 28 15.65 32.3555 0.986412 6 to 29 15.87 9.5637 0.079097 7 to 30 15.90 11.4451 0.167489 8 to 31 15.79 24.8658 0.902246 9 to 32 15.77 23.6266 0.870058 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.015609 Tough bday spacings test for dh-ranFile-2017-01-11_19:31: 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 32 79 85 103 73 64 29 10 11 4 (O-E)^2/E 0.1 0.6 0.4 1.6 0.3 0.3 2.7 0.0 1.6 2.9 0.0 Birthday Spacings: Sum(O-E)^2/E= 10.637, p= 0.613 RESULTS OF GCD FOR dh-ranFile-2017-01-11_19:31 Euclid's algorithm: p-value, steps to gcd: 0.603052 p-value, dist. of gcd's: 0.687615 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-01-11_19:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.377 0.226 0.447 0.957 0.826 0.438 0.348 0.777 Bits 8 to 15---> 0.082 0.103 0.141 0.091 0.539 0.503 0.589 0.372 Bits 16 to 23---> 0.135 0.181 0.313 0.938 0.987 0.270 0.503 0.354 Bits 24 to 31---> 0.374 0.597 0.927 0.944 0.727 0.101 0.831 0.320 KS test for the above 32 p values: 0.362 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-01-11_19:31, p-values for 5 runs: 0.9784, 0.6180, 0.2131, 0.5023, 0.7334 Rank test for binary matrices (31x31) for dh-ranFile-2017-01-11_19:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 200 211.4 0.617 0.617 r= 29 5095 5134.0 0.296 0.913 r= 30 22888 23103.0 2.002 2.915 r= 31 11817 11551.5 6.101 9.016 chi-square = 9.016 with df = 3; p-value = 0.971 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2017-01-11_19:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 200 211.4 0.617 0.617 r= 30 5118 5134.0 0.050 0.667 r= 31 22973 23103.0 0.732 1.399 r= 32 11709 11551.5 2.147 3.545 chi-square = 3.545 with df = 3; p-value = 0.685 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2017-01-11_19:31 b-rank test for bits 1 to 8, p=0.68472 b-rank test for bits 2 to 9, p=0.67795 b-rank test for bits 3 to 10, p=0.93806 b-rank test for bits 4 to 11, p=0.50102 b-rank test for bits 5 to 12, p=0.78935 b-rank test for bits 6 to 13, p=0.59229 b-rank test for bits 7 to 14, p=0.15532 b-rank test for bits 8 to 15, p=0.42509 b-rank test for bits 9 to 16, p=0.03186 b-rank test for bits 10 to 17, p=0.63965 b-rank test for bits 11 to 18, p=0.02823 b-rank test for bits 12 to 19, p=0.84138 b-rank test for bits 13 to 20, p=0.68834 b-rank test for bits 14 to 21, p=0.89825 b-rank test for bits 15 to 22, p=0.69815 b-rank test for bits 16 to 23, p=0.47005 b-rank test for bits 17 to 24, p=0.13986 b-rank test for bits 18 to 25, p=0.83787 b-rank test for bits 19 to 26, p=0.35541 b-rank test for bits 20 to 27, p=0.91133 b-rank test for bits 21 to 28, p=0.04799 b-rank test for bits 22 to 29, p=0.95398 b-rank test for bits 23 to 30, p=0.99562 b-rank test for bits 24 to 31, p=0.84492 b-rank test for bits 25 to 32, p=0.54391 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 = 0.144155 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-01-11_19:31 (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 141536 -0.87 0.191532 2 142249 0.79 0.786292 3 141226 -1.60 0.055181 4 141643 -0.62 0.266883 5 141336 -1.34 0.090195 6 141898 -0.03 0.489440 7 142401 1.15 0.874673 8 142797 2.07 0.980960 9 141995 0.20 0.579324 10 140753 -2.70 0.003449 11 142193 0.66 0.746264 12 142224 0.74 0.768894 13 141269 -1.50 0.067314 14 141941 0.07 0.529493 15 142287 0.88 0.811222 16 141801 -0.25 0.400093 17 141918 0.02 0.508081 18 141843 -0.15 0.438420 19 141648 -0.61 0.270738 20 141713 -0.46 0.323219 ---------------------------------------------------------------- OPSO test for dh-ranFile-2017-01-11_19:31 Bits used No. missing words z-score p-value 23 to 32 142080 0.5885 0.721907 22 to 31 141798 -0.3839 0.350528 21 to 30 141778 -0.4529 0.325324 20 to 29 142361 1.5575 0.940322 19 to 28 141719 -0.6563 0.255812 18 to 27 141564 -1.1908 0.116867 17 to 26 142030 0.4161 0.661333 16 to 25 141965 0.1920 0.576115 15 to 24 142255 1.1920 0.883363 14 to 23 141646 -0.9080 0.181930 13 to 22 141976 0.2299 0.590914 12 to 21 142578 2.3058 0.989438 11 to 20 141405 -1.7391 0.041011 10 to 19 142244 1.1540 0.875757 9 to 18 141567 -1.1804 0.118911 8 to 17 142041 0.4540 0.675098 7 to 16 142388 1.6506 0.950588 6 to 15 142131 0.7644 0.777679 5 to 14 141993 0.2885 0.613525 4 to 13 141687 -0.7667 0.221643 3 to 12 142452 1.8713 0.969347 2 to 11 141517 -1.3529 0.088050 1 to 10 141815 -0.3253 0.372486 ----------------------------------------------------------------- OQSO test for dh-ranFile-2017-01-11_19:31 Bits used No. missing words z-score p-value 28 to 32 141872 -0.1265 0.449651 27 to 31 142309 1.3548 0.912262 26 to 30 141888 -0.0723 0.471180 25 to 29 141919 0.0328 0.513075 24 to 28 142120 0.7141 0.762428 23 to 27 141707 -0.6859 0.246399 22 to 26 141389 -1.7638 0.038880 21 to 25 142423 1.7413 0.959181 20 to 24 142387 1.6192 0.947300 19 to 23 142171 0.8870 0.812465 18 to 22 141720 -0.6418 0.260503 17 to 21 141962 0.1785 0.570852 16 to 20 141586 -1.0960 0.136532 15 to 19 141575 -1.1333 0.128540 14 to 18 141855 -0.1842 0.426940 13 to 17 141936 0.0904 0.536018 12 to 16 142497 1.9921 0.976820 11 to 15 141388 -1.7672 0.038596 10 to 14 142011 0.3446 0.634819 9 to 13 141571 -1.1469 0.125715 8 to 12 141800 -0.3706 0.355464 7 to 11 142057 0.5006 0.691665 6 to 10 142104 0.6599 0.745341 5 to 9 141868 -0.1401 0.444290 4 to 8 141658 -0.8520 0.197116 3 to 7 141446 -1.5706 0.058137 2 to 6 141886 -0.0791 0.468483 1 to 5 141781 -0.4350 0.331775 ----------------------------------------------------------------- DNA test for dh-ranFile-2017-01-11_19:31 Bits used No. missing words z-score p-value 31 to 32 141743 -0.4906 0.311837 30 to 31 141732 -0.5231 0.300453 29 to 30 142115 0.6067 0.727974 28 to 29 142336 1.2586 0.895915 27 to 28 141506 -1.1898 0.117070 26 to 27 141807 -0.3019 0.381380 25 to 26 142017 0.3176 0.624610 24 to 25 140797 -3.2812 0.000517 23 to 24 142026 0.3442 0.634637 22 to 23 141510 -1.1780 0.119405 21 to 22 142089 0.5300 0.701944 20 to 21 141533 -1.1101 0.133474 19 to 20 141845 -0.1898 0.424747 18 to 19 142424 1.5182 0.935518 17 to 18 141845 -0.1898 0.424747 16 to 17 142128 0.6450 0.740551 15 to 16 141626 -0.8358 0.201639 14 to 15 142429 1.5329 0.937356 13 to 14 142276 1.0816 0.860290 12 to 13 141090 -2.4169 0.007827 11 to 12 142109 0.5890 0.722068 10 to 11 142051 0.4179 0.661992 9 to 10 142166 0.7571 0.775517 8 to 9 142334 1.2527 0.894845 7 to 8 142109 0.5890 0.722068 6 to 7 142123 0.6303 0.735749 5 to 6 141713 -0.5791 0.281246 4 to 5 142384 1.4002 0.919274 3 to 4 141670 -0.7060 0.240098 2 to 3 142394 1.4297 0.923599 1 to 2 141931 0.0639 0.525484 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2017-01-11_19:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2436.17 -0.903 0.183330 Test results for specific bytes for dh-ranFile-2017-01-11_19:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2542.93 0.607 0.728127 2 to 9 2486.94 -0.185 0.426714 3 to 10 2382.60 -1.660 0.048423 4 to 11 2548.54 0.687 0.753801 5 to 12 2526.72 0.378 0.647243 6 to 13 2583.04 1.174 0.879878 7 to 14 2483.69 -0.231 0.408789 8 to 15 2567.04 0.948 0.828461 9 to 16 2393.19 -1.510 0.065459 10 to 17 2526.25 0.371 0.644748 11 to 18 2457.04 -0.608 0.271759 12 to 19 2536.74 0.520 0.698299 13 to 20 2405.13 -1.342 0.089842 14 to 21 2510.64 0.150 0.559780 15 to 22 2415.50 -1.195 0.116028 16 to 23 2464.72 -0.499 0.308916 17 to 24 2406.34 -1.325 0.092658 18 to 25 2506.58 0.093 0.537047 19 to 26 2505.71 0.081 0.532179 20 to 27 2515.67 0.222 0.587688 21 to 28 2346.49 -2.171 0.014969 22 to 29 2499.85 -0.002 0.499167 23 to 30 2511.28 0.160 0.563376 24 to 31 2504.18 0.059 0.523556 25 to 32 2464.49 -0.502 0.307792 CDPARK for dh-ranFile-2017-01-11_19:31: 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 3567 2.0091 0.977738 3532 0.4110 0.659449 3523 0.0000 0.500000 3478 -2.0548 0.019949 3538 0.6849 0.753306 3576 2.4201 0.992242 3542 0.8676 0.807188 3560 1.6895 0.954438 3525 0.0913 0.536383 3550 1.2329 0.891189 Square side=100, avg. no. parked=3539.10 sample std.=26.36 p-value of the KSTEST for those 10 p-values: 0.015696 Results for the MINIMUM DISTANCE test for dh-ranFile-2017-01-11_19:31 0.5852,0.2395,0.9835,0.3269,0.5627,0.1370,0.2414,0.0215,0.8345,0.5833, The KS test for those 10 p-values: 0.832327 The 3DSPHERES test for dh-ranFile-2017-01-11_19:31 sample no r^3 equiv. uni. 1 1.733 0.056125 2 30.076 0.633055 3 133.005 0.988127 4 41.436 0.748721 5 1.901 0.061407 6 10.270 0.289884 7 26.486 0.586401 8 16.433 0.421768 9 14.125 0.375513 10 15.807 0.409568 11 13.590 0.364276 12 46.537 0.788012 13 96.119 0.959399 14 4.600 0.142152 15 7.401 0.218617 16 22.158 0.522222 17 49.929 0.810674 18 85.431 0.942022 19 21.032 0.503946 20 26.756 0.590115 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.953542 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-01-11_19:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -0.3 -2.0 2.1 -1.3 -0.6 0.2 -0.8 0.7 1.1 -0.1 -1.0 1.0 0.7 0.1 -0.6 -0.4 -2.2 0.0 0.9 0.8 0.1 0.0 0.3 -0.9 1.0 0.6 -0.7 0.8 0.2 1.3 -1.6 -0.2 -0.4 -1.5 1.0 0.3 -0.1 -0.8 1.0 -1.3 -1.0 0.8 Chi-square with 42 degrees of freedom:38.293056 z-score=-0.404461, p-value=0.365557 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2017-01-11_19:31 Test no p-value 1 0.656131 2 0.697831 3 0.161691 4 0.048173 5 0.135756 6 0.623662 7 0.017905 8 0.360943 9 0.343861 10 0.341881 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.117362 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-01-11_19:31: (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 66657 0.00 66643 0.01 3 25000.00 24975 0.03 24914 0.30 4 6666.67 6683 0.04 6746 0.94 5 1388.89 1438 1.74 1423 0.84 6 238.10 212 2.86 241 0.04 7 34.72 29 0.94 26 2.19 8 4.96 5 0.00 6 0.22 p=0.53121 p=0.39459 Number of rngs required: 689531, p-value: 0.905 RESULTS OF CRAPS TEST for dh-ranFile-2017-01-11_19:31 No. of wins: Observed Expected 98829 98585.9 z-score= 1.087, pvalue=0.86159 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66669 66666.7 0.000 0.000 2 37838 37654.3 0.896 0.896 3 26837 26954.7 0.514 1.410 4 19389 19313.5 0.295 1.706 5 13797 13851.4 0.214 1.920 6 9917 9943.5 0.071 1.990 7 7160 7145.0 0.031 2.022 8 5074 5139.1 0.824 2.846 9 3617 3699.9 1.856 4.702 10 2749 2666.3 2.565 7.267 11 1895 1923.3 0.417 7.684 12 1378 1388.7 0.083 7.767 13 980 1003.7 0.560 8.328 14 753 726.1 0.994 9.321 15 503 525.8 0.992 10.313 16 394 381.2 0.433 10.746 17 304 276.5 2.727 13.473 18 189 200.8 0.697 14.170 19 140 146.0 0.245 14.415 20 103 106.2 0.097 14.512 21 314 287.1 2.518 17.030 Chisq= 17.03 for 20 degrees of freedom, p= 0.34897 SUMMARY of craptest p-value for no. of wins: 0.861585 p-value for throws/game: 0.348972 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2017-01-11_19:31 No. of wins: Observed Expected 98677 98585.9 z-score= 0.408, pvalue=0.65823 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66566 66666.7 0.152 0.152 2 37681 37654.3 0.019 0.171 3 26936 26954.7 0.013 0.184 4 19370 19313.5 0.166 0.349 5 13914 13851.4 0.283 0.632 6 9918 9943.5 0.066 0.698 7 7104 7145.0 0.236 0.933 8 5150 5139.1 0.023 0.957 9 3649 3699.9 0.699 1.656 10 2684 2666.3 0.118 1.773 11 1979 1923.3 1.611 3.385 12 1424 1388.7 0.895 4.280 13 986 1003.7 0.313 4.593 14 716 726.1 0.142 4.734 15 550 525.8 1.110 5.845 16 405 381.2 1.492 7.337 17 254 276.5 1.837 9.174 18 168 200.8 5.367 14.541 19 130 146.0 1.750 16.291 20 107 106.2 0.006 16.297 21 309 287.1 1.668 17.965 Chisq= 17.97 for 20 degrees of freedom, p= 0.41030 SUMMARY of craptest p-value for no. of wins: 0.658230 p-value for throws/game: 0.410298 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0005,0.0034,0.0078,0.0150,0.0156,0.0157,0.0179,0.0199,0.0215,0.0282, 0.0319,0.0386,0.0389,0.0410,0.0480,0.0482,0.0484,0.0552,0.0561,0.0581, 0.0614,0.0655,0.0673,0.0791,0.0824,0.0880,0.0898,0.0902,0.0909,0.0927, 0.1010,0.1031,0.1160,0.1169,0.1171,0.1174,0.1189,0.1194,0.1257,0.1285, 0.1335,0.1350,0.1358,0.1365,0.1370,0.1399,0.1412,0.1422,0.1442,0.1494, 0.1553,0.1617,0.1675,0.1814,0.1819,0.1833,0.1915,0.1971,0.2016,0.2131, 0.2186,0.2216,0.2259,0.2395,0.2401,0.2414,0.2464,0.2558,0.2605,0.2669, 0.2700,0.2707,0.2718,0.2812,0.2899,0.3005,0.3078,0.3089,0.3118,0.3130, 0.3196,0.3232,0.3253,0.3269,0.3318,0.3419,0.3439,0.3479,0.3490,0.3505, 0.3541,0.3554,0.3555,0.3609,0.3623,0.3643,0.3656,0.3723,0.3725,0.3737, 0.3755,0.3766,0.3814,0.3946,0.4001,0.4088,0.4096,0.4103,0.4218,0.4247, 0.4247,0.4251,0.4267,0.4269,0.4379,0.4384,0.4443,0.4470,0.4497,0.4685, 0.4700,0.4712,0.4894,0.4992,0.5000,0.5010,0.5023,0.5029,0.5030,0.5039, 0.5081,0.5131,0.5222,0.5236,0.5255,0.5295,0.5312,0.5322,0.5360,0.5364, 0.5370,0.5394,0.5439,0.5598,0.5627,0.5634,0.5709,0.5761,0.5793,0.5833, 0.5852,0.5864,0.5877,0.5889,0.5901,0.5909,0.5923,0.5971,0.6031,0.6135, 0.6135,0.6180,0.6237,0.6246,0.6331,0.6346,0.6348,0.6396,0.6447,0.6472, 0.6561,0.6582,0.6594,0.6613,0.6620,0.6751,0.6780,0.6847,0.6851,0.6876, 0.6883,0.6917,0.6978,0.6981,0.6983,0.7019,0.7219,0.7221,0.7221,0.7274, 0.7280,0.7281,0.7334,0.7357,0.7406,0.7453,0.7463,0.7487,0.7533,0.7538, 0.7624,0.7689,0.7755,0.7767,0.7777,0.7863,0.7880,0.7893,0.8064,0.8072, 0.8107,0.8112,0.8125,0.8256,0.8285,0.8306,0.8323,0.8345,0.8379,0.8414, 0.8449,0.8603,0.8616,0.8701,0.8747,0.8758,0.8799,0.8834,0.8912,0.8948, 0.8959,0.8982,0.9022,0.9055,0.9113,0.9123,0.9193,0.9236,0.9273,0.9355, 0.9374,0.9377,0.9381,0.9403,0.9420,0.9443,0.9473,0.9506,0.9535,0.9540, 0.9544,0.9570,0.9592,0.9594,0.9638,0.9677,0.9693,0.9709,0.9768,0.9777, 0.9784,0.9810,0.9835,0.9864,0.9870,0.9881,0.9894,0.9922,0.9956, Overall p-value after applying KStest on 269 p-values = 0.329614 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.