RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-01-23_16:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 16.06 19.4354 0.695882 2 to 25 15.78 23.0990 0.853945 3 to 26 15.80 14.4774 0.366934 4 to 27 15.65 14.3042 0.354533 5 to 28 15.88 20.6972 0.759873 6 to 29 15.92 10.5669 0.121826 7 to 30 15.72 15.4409 0.436241 8 to 31 15.65 20.4969 0.750393 9 to 32 15.76 17.5459 0.581989 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.715192 Tough bday spacings test for dh-ranFile-2017-01-23_16:31: 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 8 25 75 86 109 93 47 30 14 8 5 (O-E)^2/E 0.1 3.7 0.0 1.4 1.3 2.8 0.5 0.0 0.1 0.3 0.2 Birthday Spacings: Sum(O-E)^2/E= 10.470, p= 0.600 RESULTS OF GCD FOR dh-ranFile-2017-01-23_16:31 Euclid's algorithm: p-value, steps to gcd: 0.752254 p-value, dist. of gcd's: 0.916610 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-01-23_16:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.602 0.058 0.902 0.596 0.759 0.160 0.433 0.457 Bits 8 to 15---> 0.732 0.777 0.653 0.528 0.757 0.221 0.699 0.906 Bits 16 to 23---> 0.381 0.997 0.769 0.202 0.824 0.525 0.733 0.265 Bits 24 to 31---> 0.040 0.220 0.453 0.485 0.577 0.203 0.311 0.613 KS test for the above 32 p values: 0.360 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-01-23_16:31, p-values for 5 runs: 0.8121, 0.0714, 0.2279, 0.3304, 0.6409 Rank test for binary matrices (31x31) for dh-ranFile-2017-01-23_16:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 237 211.4 3.095 3.095 r= 29 5117 5134.0 0.056 3.152 r= 30 23225 23103.0 0.644 3.796 r= 31 11421 11551.5 1.475 5.270 chi-square = 5.270 with df = 3; p-value = 0.847 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2017-01-23_16:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 209 211.4 0.028 0.028 r= 30 5073 5134.0 0.725 0.753 r= 31 23216 23103.0 0.552 1.305 r= 32 11502 11551.5 0.212 1.517 chi-square = 1.517 with df = 3; p-value = 0.322 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2017-01-23_16:31 b-rank test for bits 1 to 8, p=0.69186 b-rank test for bits 2 to 9, p=0.27198 b-rank test for bits 3 to 10, p=0.08708 b-rank test for bits 4 to 11, p=0.01501 b-rank test for bits 5 to 12, p=0.95177 b-rank test for bits 6 to 13, p=0.19965 b-rank test for bits 7 to 14, p=0.52614 b-rank test for bits 8 to 15, p=0.72056 b-rank test for bits 9 to 16, p=0.05365 b-rank test for bits 10 to 17, p=0.39001 b-rank test for bits 11 to 18, p=0.63769 b-rank test for bits 12 to 19, p=0.45557 b-rank test for bits 13 to 20, p=0.38760 b-rank test for bits 14 to 21, p=0.02000 b-rank test for bits 15 to 22, p=0.67941 b-rank test for bits 16 to 23, p=0.56968 b-rank test for bits 17 to 24, p=0.18890 b-rank test for bits 18 to 25, p=0.46359 b-rank test for bits 19 to 26, p=0.27966 b-rank test for bits 20 to 27, p=0.37284 b-rank test for bits 21 to 28, p=0.26973 b-rank test for bits 22 to 29, p=0.62518 b-rank test for bits 23 to 30, p=0.98520 b-rank test for bits 24 to 31, p=0.53464 b-rank test for bits 25 to 32, p=0.16711 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 = 0.266773 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-01-23_16:31 (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 141643 -0.62 0.266883 2 141730 -0.42 0.337610 3 141666 -0.57 0.284838 4 141798 -0.26 0.397387 5 142380 1.10 0.864268 6 141374 -1.25 0.105509 7 141818 -0.21 0.415512 8 142429 1.21 0.887661 9 140874 -2.42 0.007782 10 142077 0.39 0.652379 11 141975 0.15 0.560972 12 141490 -0.98 0.163607 13 141971 0.14 0.557285 14 141243 -1.56 0.059754 15 142386 1.11 0.867299 16 142255 0.81 0.790351 17 141724 -0.43 0.332502 18 141416 -1.15 0.124529 19 142588 1.59 0.943594 20 143068 2.71 0.996607 ---------------------------------------------------------------- OPSO test for dh-ranFile-2017-01-23_16:31 Bits used No. missing words z-score p-value 23 to 32 142153 0.8402 0.799614 22 to 31 142299 1.3437 0.910476 21 to 30 141862 -0.1632 0.435178 20 to 29 141934 0.0851 0.533897 19 to 28 142259 1.2058 0.886045 18 to 27 142334 1.4644 0.928455 17 to 26 142540 2.1747 0.985175 16 to 25 141814 -0.3287 0.371182 15 to 24 141880 -0.1011 0.459721 14 to 23 141487 -1.4563 0.072653 13 to 22 142230 1.1058 0.865585 12 to 21 141909 -0.0011 0.499546 11 to 20 142372 1.5954 0.944690 10 to 19 141661 -0.8563 0.195913 9 to 18 142234 1.1196 0.868548 8 to 17 142010 0.3471 0.635756 7 to 16 142509 2.0678 0.980672 6 to 15 142087 0.6127 0.729948 5 to 14 142391 1.6609 0.951636 4 to 13 142110 0.6920 0.755521 3 to 12 142105 0.6747 0.750075 2 to 11 141591 -1.0977 0.136170 1 to 10 141948 0.1333 0.553040 ----------------------------------------------------------------- OQSO test for dh-ranFile-2017-01-23_16:31 Bits used No. missing words z-score p-value 28 to 32 142335 1.4429 0.925483 27 to 31 141927 0.0599 0.523882 26 to 30 142336 1.4463 0.925959 25 to 29 141663 -0.8350 0.201854 24 to 28 141676 -0.7909 0.214487 23 to 27 142398 1.6565 0.951191 22 to 26 142015 0.3582 0.639905 21 to 25 142036 0.4294 0.666180 20 to 24 142119 0.7107 0.761379 19 to 23 142467 1.8904 0.970648 18 to 22 141865 -0.1503 0.440275 17 to 21 142998 3.6904 0.999888 16 to 20 141641 -0.9096 0.181519 15 to 19 142263 1.1989 0.884713 14 to 18 141984 0.2531 0.599912 13 to 17 141839 -0.2384 0.405783 12 to 16 142404 1.6768 0.953214 11 to 15 141743 -0.5638 0.286435 10 to 14 141585 -1.0994 0.135792 9 to 13 142416 1.7175 0.957058 8 to 12 142725 2.7650 0.997154 7 to 11 141887 -0.0757 0.469831 6 to 10 141695 -0.7265 0.233753 5 to 9 142219 1.0497 0.853079 4 to 8 141592 -1.0757 0.141032 3 to 7 142149 0.8124 0.791731 2 to 6 142209 1.0158 0.845145 1 to 5 142653 2.5209 0.994148 ----------------------------------------------------------------- DNA test for dh-ranFile-2017-01-23_16:31 Bits used No. missing words z-score p-value 31 to 32 142306 1.1701 0.879023 30 to 31 142576 1.9666 0.975384 29 to 30 141803 -0.3137 0.376891 28 to 29 142087 0.5241 0.699896 27 to 28 141496 -1.2193 0.111372 26 to 27 142188 0.8220 0.794472 25 to 26 141832 -0.2281 0.409780 24 to 25 142034 0.3678 0.643473 23 to 24 141870 -0.1160 0.453819 22 to 23 142311 1.1849 0.881965 21 to 22 141672 -0.7001 0.241936 20 to 21 141809 -0.2960 0.383631 19 to 20 141596 -0.9243 0.177671 18 to 19 141437 -1.3933 0.081764 17 to 18 141655 -0.7502 0.226556 16 to 17 142067 0.4651 0.679071 15 to 16 141497 -1.2163 0.111933 14 to 15 141628 -0.8299 0.203303 13 to 14 141739 -0.5024 0.307676 12 to 13 141611 -0.8800 0.189422 11 to 12 141572 -0.9951 0.159850 10 to 11 142026 0.3442 0.634637 9 to 10 141964 0.1613 0.564059 8 to 9 142085 0.5182 0.697841 7 to 8 141540 -1.0895 0.137974 6 to 7 142239 0.9725 0.834594 5 to 6 141430 -1.4140 0.078688 4 to 5 141652 -0.7591 0.223901 3 to 4 142214 0.8987 0.815602 2 to 3 142191 0.8309 0.796981 1 to 2 142296 1.1406 0.872986 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2017-01-23_16:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2503.30 0.047 0.518626 Test results for specific bytes for dh-ranFile-2017-01-23_16:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2639.24 1.969 0.975531 2 to 9 2426.91 -1.034 0.150637 3 to 10 2452.24 -0.675 0.249706 4 to 11 2507.60 0.107 0.542794 5 to 12 2513.80 0.195 0.577356 6 to 13 2465.16 -0.493 0.311126 7 to 14 2410.08 -1.272 0.101748 8 to 15 2467.64 -0.458 0.323631 9 to 16 2512.94 0.183 0.572620 10 to 17 2500.80 0.011 0.504507 11 to 18 2524.72 0.350 0.636696 12 to 19 2479.08 -0.296 0.383666 13 to 20 2363.72 -1.927 0.026971 14 to 21 2401.18 -1.398 0.081127 15 to 22 2434.83 -0.922 0.178353 16 to 23 2550.33 0.712 0.761699 17 to 24 2476.29 -0.335 0.368705 18 to 25 2556.30 0.796 0.787057 19 to 26 2466.46 -0.474 0.317638 20 to 27 2583.96 1.187 0.882455 21 to 28 2538.01 0.538 0.704546 22 to 29 2545.97 0.650 0.742212 23 to 30 2467.06 -0.466 0.320662 24 to 31 2463.64 -0.514 0.303576 25 to 32 2475.11 -0.352 0.362417 CDPARK for dh-ranFile-2017-01-23_16:31: 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 3572 2.2374 0.987371 3561 1.7352 0.958644 3502 -0.9589 0.168804 3500 -1.0502 0.146807 3521 -0.0913 0.463617 3520 -0.1370 0.445521 3547 1.0959 0.863437 3482 -1.8721 0.030593 3515 -0.3653 0.357445 3504 -0.8676 0.192812 Square side=100, avg. no. parked=3522.40 sample std.=27.40 p-value of the KSTEST for those 10 p-values: 0.464535 Results for the MINIMUM DISTANCE test for dh-ranFile-2017-01-23_16:31 0.5673,0.0281,0.0965,0.8260,0.9828,0.8955,0.1100,0.9187,0.2514,0.8512, The KS test for those 10 p-values: 0.233337 The 3DSPHERES test for dh-ranFile-2017-01-23_16:31 sample no r^3 equiv. uni. 1 49.726 0.809390 2 19.933 0.485428 3 48.387 0.800690 4 7.453 0.219980 5 35.318 0.691881 6 31.250 0.647133 7 47.385 0.793925 8 45.674 0.781826 9 30.711 0.640732 10 10.096 0.285762 11 6.924 0.206104 12 1.137 0.037187 13 2.866 0.091106 14 37.043 0.709094 15 36.309 0.701891 16 2.567 0.082014 17 56.799 0.849427 18 24.379 0.556314 19 48.331 0.800316 20 13.243 0.356884 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.473272 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-01-23_16:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 -0.3 0.3 1.2 -0.3 -1.8 -1.0 1.2 0.5 1.3 -0.4 -0.3 -0.6 0.5 0.2 -0.3 -1.6 -2.2 1.8 -1.1 0.4 1.3 0.4 2.4 -1.1 -0.2 0.3 1.1 0.1 -1.6 -0.5 0.1 1.5 -1.3 0.5 0.4 0.5 1.8 1.7 -0.1 0.1 1.0 0.8 Chi-square with 42 degrees of freedom:48.245883 z-score=0.681482, p-value=0.764951 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2017-01-23_16:31 Test no p-value 1 0.481883 2 0.674092 3 0.557861 4 0.359983 5 0.738347 6 0.675117 7 0.098055 8 0.235229 9 0.605573 10 0.243236 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.587371 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-01-23_16:31: (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 66500 0.42 66618 0.04 3 25000.00 25020 0.02 25151 0.91 4 6666.67 6737 0.74 6560 1.71 5 1388.89 1453 2.96 1396 0.04 6 238.10 243 0.10 227 0.52 7 34.72 32 0.21 38 0.31 8 4.96 14 16.48 9 3.29 p=0.99811 p=0.66106 Number of rngs required: 689291, p-value: 0.848 RESULTS OF CRAPS TEST for dh-ranFile-2017-01-23_16:31 No. of wins: Observed Expected 98648 98585.9 z-score= 0.278, pvalue=0.60947 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66562 66666.7 0.164 0.164 2 37716 37654.3 0.101 0.265 3 27189 26954.7 2.036 2.301 4 19194 19313.5 0.739 3.040 5 13957 13851.4 0.805 3.845 6 9918 9943.5 0.066 3.911 7 7267 7145.0 2.082 5.993 8 4988 5139.1 4.441 10.434 9 3718 3699.9 0.089 10.523 10 2680 2666.3 0.070 10.593 11 1861 1923.3 2.020 12.613 12 1407 1388.7 0.240 12.853 13 1016 1003.7 0.150 13.004 14 690 726.1 1.799 14.802 15 511 525.8 0.419 15.221 16 388 381.2 0.123 15.344 17 288 276.5 0.475 15.819 18 184 200.8 1.410 17.229 19 126 146.0 2.736 19.965 20 87 106.2 3.476 23.441 21 253 287.1 4.053 27.495 Chisq= 27.49 for 20 degrees of freedom, p= 0.87809 SUMMARY of craptest p-value for no. of wins: 0.609468 p-value for throws/game: 0.878088 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2017-01-23_16:31 No. of wins: Observed Expected 98957 98585.9 z-score= 1.660, pvalue=0.95154 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66720 66666.7 0.043 0.043 2 37617 37654.3 0.037 0.080 3 26913 26954.7 0.065 0.144 4 19295 19313.5 0.018 0.162 5 13879 13851.4 0.055 0.217 6 9993 9943.5 0.246 0.463 7 7049 7145.0 1.291 1.753 8 5175 5139.1 0.251 2.005 9 3714 3699.9 0.054 2.059 10 2635 2666.3 0.367 2.426 11 1900 1923.3 0.283 2.709 12 1409 1388.7 0.296 3.004 13 1027 1003.7 0.540 3.545 14 724 726.1 0.006 3.551 15 537 525.8 0.237 3.788 16 386 381.2 0.062 3.850 17 278 276.5 0.008 3.857 18 207 200.8 0.190 4.047 19 146 146.0 0.000 4.047 20 100 106.2 0.364 4.411 21 296 287.1 0.275 4.686 Chisq= 4.69 for 20 degrees of freedom, p= 0.00017 SUMMARY of craptest p-value for no. of wins: 0.951539 p-value for throws/game: 0.000167 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0002,0.0078,0.0150,0.0200,0.0270,0.0281,0.0306,0.0372,0.0404,0.0536, 0.0583,0.0598,0.0714,0.0727,0.0787,0.0811,0.0818,0.0820,0.0871,0.0911, 0.0965,0.0981,0.1017,0.1055,0.1100,0.1114,0.1119,0.1218,0.1245,0.1358, 0.1362,0.1380,0.1410,0.1468,0.1506,0.1599,0.1599,0.1636,0.1671,0.1688, 0.1777,0.1784,0.1815,0.1889,0.1894,0.1928,0.1959,0.1996,0.2017,0.2019, 0.2031,0.2033,0.2061,0.2145,0.2200,0.2202,0.2205,0.2239,0.2266,0.2279, 0.2333,0.2338,0.2352,0.2419,0.2432,0.2497,0.2514,0.2651,0.2668,0.2669, 0.2697,0.2720,0.2797,0.2848,0.2858,0.2864,0.3036,0.3077,0.3111,0.3111, 0.3176,0.3207,0.3217,0.3236,0.3304,0.3325,0.3376,0.3545,0.3569,0.3574, 0.3600,0.3603,0.3624,0.3669,0.3687,0.3712,0.3728,0.3769,0.3809,0.3836, 0.3837,0.3876,0.3900,0.3974,0.4058,0.4098,0.4155,0.4327,0.4352,0.4362, 0.4403,0.4455,0.4526,0.4538,0.4556,0.4570,0.4597,0.4636,0.4636,0.4645, 0.4698,0.4733,0.4819,0.4854,0.4855,0.4995,0.5045,0.5186,0.5239,0.5251, 0.5261,0.5285,0.5339,0.5346,0.5428,0.5530,0.5563,0.5573,0.5579,0.5610, 0.5641,0.5673,0.5697,0.5726,0.5765,0.5774,0.5820,0.5874,0.5957,0.5997, 0.5999,0.6022,0.6056,0.6095,0.6130,0.6252,0.6346,0.6358,0.6367,0.6377, 0.6399,0.6407,0.6409,0.6435,0.6471,0.6524,0.6528,0.6611,0.6662,0.6741, 0.6751,0.6791,0.6794,0.6919,0.6919,0.6959,0.6978,0.6991,0.6999,0.7019, 0.7045,0.7091,0.7152,0.7206,0.7299,0.7322,0.7329,0.7383,0.7422,0.7501, 0.7504,0.7523,0.7555,0.7568,0.7594,0.7599,0.7614,0.7617,0.7650,0.7688, 0.7774,0.7818,0.7871,0.7904,0.7917,0.7939,0.7945,0.7970,0.7996,0.8003, 0.8007,0.8094,0.8121,0.8156,0.8240,0.8260,0.8346,0.8451,0.8470,0.8483, 0.8494,0.8512,0.8531,0.8539,0.8634,0.8643,0.8656,0.8673,0.8685,0.8730, 0.8781,0.8790,0.8820,0.8825,0.8847,0.8860,0.8877,0.8955,0.9023,0.9063, 0.9105,0.9166,0.9187,0.9255,0.9260,0.9285,0.9436,0.9447,0.9512,0.9515, 0.9516,0.9518,0.9532,0.9571,0.9586,0.9706,0.9754,0.9755,0.9807,0.9828, 0.9852,0.9852,0.9874,0.9941,0.9965,0.9966,0.9972,0.9981,0.9999, Overall p-value after applying KStest on 269 p-values = 0.219212 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.