RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-04-07_04:31 (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 6.7119 0.013018 2 to 25 15.73 12.4090 0.225235 3 to 26 15.71 13.8681 0.323583 4 to 27 15.57 23.8124 0.875378 5 to 28 15.62 26.1461 0.928161 6 to 29 15.87 24.2741 0.887822 7 to 30 16.03 10.3394 0.111224 8 to 31 15.71 21.7638 0.806026 9 to 32 15.61 20.5146 0.751242 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.405378 Tough bday spacings test for dh-ranFile-2016-04-07_04:31: 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 46 79 84 88 82 58 33 13 6 2 (O-E)^2/E 0.0 2.4 0.4 1.9 1.0 0.2 0.7 0.4 0.2 0.1 1.0 Birthday Spacings: Sum(O-E)^2/E= 8.280, p= 0.398 RESULTS OF GCD FOR dh-ranFile-2016-04-07_04:31 Euclid's algorithm: p-value, steps to gcd: 0.822586 p-value, dist. of gcd's: 0.424958 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-04-07_04:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.883 0.456 0.269 0.538 0.949 0.433 0.426 0.612 Bits 8 to 15---> 0.528 0.760 0.929 0.320 0.573 0.893 0.913 0.831 Bits 16 to 23---> 0.771 0.213 0.869 0.233 0.265 0.021 0.738 0.476 Bits 24 to 31---> 0.674 0.487 0.283 0.398 0.698 0.569 0.509 0.219 KS test for the above 32 p values: 0.698 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-04-07_04:31, p-values for 5 runs: 0.1947, 0.4318, 0.3244, 0.2769, 0.5836 Rank test for binary matrices (31x31) for dh-ranFile-2016-04-07_04:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 210 211.4 0.010 0.010 r= 29 5165 5134.0 0.187 0.197 r= 30 23021 23103.0 0.291 0.488 r= 31 11604 11551.5 0.238 0.726 chi-square = 0.726 with df = 3; p-value = 0.133 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-04-07_04:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 233 211.4 2.203 2.203 r= 30 5151 5134.0 0.056 2.259 r= 31 23035 23103.0 0.200 2.460 r= 32 11581 11551.5 0.075 2.535 chi-square = 2.535 with df = 3; p-value = 0.531 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-04-07_04:31 b-rank test for bits 1 to 8, p=0.64003 b-rank test for bits 2 to 9, p=0.02625 b-rank test for bits 3 to 10, p=0.01624 b-rank test for bits 4 to 11, p=0.11919 b-rank test for bits 5 to 12, p=0.09189 b-rank test for bits 6 to 13, p=0.45682 b-rank test for bits 7 to 14, p=0.25229 b-rank test for bits 8 to 15, p=0.89716 b-rank test for bits 9 to 16, p=0.98961 b-rank test for bits 10 to 17, p=0.77884 b-rank test for bits 11 to 18, p=0.07007 b-rank test for bits 12 to 19, p=0.16995 b-rank test for bits 13 to 20, p=0.43748 b-rank test for bits 14 to 21, p=0.70845 b-rank test for bits 15 to 22, p=0.98878 b-rank test for bits 16 to 23, p=0.85099 b-rank test for bits 17 to 24, p=0.93517 b-rank test for bits 18 to 25, p=0.03220 b-rank test for bits 19 to 26, p=0.49824 b-rank test for bits 20 to 27, p=0.28256 b-rank test for bits 21 to 28, p=0.40858 b-rank test for bits 22 to 29, p=0.08808 b-rank test for bits 23 to 30, p=0.00751 b-rank test for bits 24 to 31, p=0.85225 b-rank test for bits 25 to 32, p=0.50907 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 = 0.106449 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-04-07_04:31 (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 141724 -0.43 0.332502 2 141945 0.08 0.533210 3 142669 1.77 0.962045 4 141249 -1.54 0.061436 5 141871 -0.09 0.464320 6 142119 0.49 0.687892 7 141907 -0.01 0.497828 8 142173 0.62 0.731070 9 141723 -0.44 0.331654 10 141244 -1.55 0.060031 11 141869 -0.09 0.462464 12 141767 -0.33 0.369738 13 141727 -0.43 0.335052 14 141923 0.03 0.512740 15 141902 -0.02 0.493168 16 141806 -0.24 0.404613 17 141859 -0.12 0.453195 18 141928 0.04 0.517397 19 142386 1.11 0.867299 20 142013 0.24 0.595695 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-04-07_04:31 Bits used No. missing words z-score p-value 23 to 32 141906 -0.0115 0.495419 22 to 31 141806 -0.3563 0.360804 21 to 30 142285 1.2954 0.902411 20 to 29 141981 0.2471 0.597599 19 to 28 141677 -0.8011 0.211526 18 to 27 141517 -1.3529 0.088050 17 to 26 142255 1.1920 0.883363 16 to 25 142384 1.6368 0.949163 15 to 24 141303 -2.0908 0.018273 14 to 23 142029 0.4127 0.660070 13 to 22 142167 0.8885 0.812869 12 to 21 142601 2.3851 0.991462 11 to 20 142062 0.5264 0.700712 10 to 19 141832 -0.2667 0.394867 9 to 18 141528 -1.3149 0.094267 8 to 17 141710 -0.6873 0.245933 7 to 16 141627 -0.9736 0.165140 6 to 15 142274 1.2575 0.895711 5 to 14 141698 -0.7287 0.233085 4 to 13 141714 -0.6736 0.250298 3 to 12 141504 -1.3977 0.081103 2 to 11 141926 0.0575 0.522920 1 to 10 141732 -0.6115 0.270440 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-04-07_04:31 Bits used No. missing words z-score p-value 28 to 32 141527 -1.2960 0.097482 27 to 31 141876 -0.1130 0.455022 26 to 30 141751 -0.5367 0.295733 25 to 29 141993 0.2836 0.611652 24 to 28 142005 0.3243 0.627147 23 to 27 141627 -0.9571 0.169271 22 to 26 141743 -0.5638 0.286435 21 to 25 141861 -0.1638 0.434932 20 to 24 141682 -0.7706 0.220469 19 to 23 141143 -2.5977 0.004692 18 to 22 141448 -1.5638 0.058929 17 to 21 141461 -1.5198 0.064285 16 to 20 141535 -1.2689 0.102236 15 to 19 142094 0.6260 0.734343 14 to 18 141574 -1.1367 0.127829 13 to 17 141923 0.0463 0.518480 12 to 16 141558 -1.1909 0.116837 11 to 15 141456 -1.5367 0.062182 10 to 14 141925 0.0531 0.521181 9 to 13 141472 -1.4825 0.069107 8 to 12 141926 0.0565 0.522532 7 to 11 141918 0.0294 0.511723 6 to 10 141683 -0.7672 0.221475 5 to 9 141647 -0.8893 0.186933 4 to 8 141886 -0.0791 0.468483 3 to 7 141462 -1.5164 0.064713 2 to 6 141446 -1.5706 0.058137 1 to 5 141964 0.1853 0.573512 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-04-07_04:31 Bits used No. missing words z-score p-value 31 to 32 141759 -0.4435 0.328720 30 to 31 142503 1.7512 0.960048 29 to 30 141420 -1.4435 0.074447 28 to 29 141546 -1.0718 0.141912 27 to 28 141962 0.1554 0.561735 26 to 27 141934 0.0728 0.529007 25 to 26 141404 -1.4906 0.068027 24 to 25 142031 0.3589 0.640168 23 to 24 141857 -0.1544 0.438661 22 to 23 141536 -1.1013 0.135390 21 to 22 141301 -1.7945 0.036368 20 to 21 141906 -0.0098 0.496081 19 to 20 142360 1.3294 0.908144 18 to 19 142298 1.1465 0.874210 17 to 18 141598 -0.9184 0.179211 16 to 17 142226 0.9341 0.824882 15 to 16 141676 -0.6883 0.245635 14 to 15 141514 -1.1662 0.121774 13 to 14 141612 -0.8771 0.190222 12 to 13 142228 0.9400 0.826399 11 to 12 142022 0.3324 0.630191 10 to 11 142383 1.3973 0.918832 9 to 10 142705 2.3471 0.990540 8 to 9 142162 0.7453 0.771967 7 to 8 142272 1.0698 0.857651 6 to 7 141836 -0.2163 0.414372 5 to 6 142144 0.6922 0.755607 4 to 5 142388 1.4120 0.921026 3 to 4 141701 -0.6145 0.269428 2 to 3 142145 0.6952 0.756532 1 to 2 141243 -1.9656 0.024674 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-04-07_04:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2544.84 0.634 0.737007 Test results for specific bytes for dh-ranFile-2016-04-07_04:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2609.63 1.550 0.939484 2 to 9 2537.84 0.535 0.703729 3 to 10 2421.06 -1.116 0.132117 4 to 11 2615.64 1.635 0.949010 5 to 12 2465.10 -0.493 0.310832 6 to 13 2439.31 -0.858 0.195367 7 to 14 2468.52 -0.445 0.328090 8 to 15 2410.61 -1.264 0.103077 9 to 16 2465.92 -0.482 0.314933 10 to 17 2529.17 0.413 0.660017 11 to 18 2466.27 -0.477 0.316663 12 to 19 2362.40 -1.946 0.025829 13 to 20 2574.19 1.049 0.852973 14 to 21 2426.25 -1.043 0.148475 15 to 22 2337.08 -2.304 0.010610 16 to 23 2368.88 -1.854 0.031849 17 to 24 2495.95 -0.057 0.477176 18 to 25 2466.97 -0.467 0.320221 19 to 26 2580.58 1.140 0.872774 20 to 27 2410.32 -1.268 0.102357 21 to 28 2606.06 1.500 0.933182 22 to 29 2372.16 -1.808 0.035308 23 to 30 2568.46 0.968 0.833535 24 to 31 2390.43 -1.550 0.060621 25 to 32 2426.66 -1.037 0.149818 CDPARK for dh-ranFile-2016-04-07_04:31: 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 3507 -0.7306 0.232514 3504 -0.8676 0.192812 3511 -0.5479 0.291865 3541 0.8219 0.794438 3504 -0.8676 0.192812 3493 -1.3699 0.085365 3563 1.8265 0.966111 3514 -0.4110 0.340551 3525 0.0913 0.536383 3475 -2.1918 0.014198 Square side=100, avg. no. parked=3513.70 sample std.=23.39 p-value of the KSTEST for those 10 p-values: 0.184421 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-04-07_04:31 0.5048,0.0259,0.8038,0.7967,0.8325,0.8659,0.6872,0.3577,0.4100,0.6394, The KS test for those 10 p-values: 0.376972 The 3DSPHERES test for dh-ranFile-2016-04-07_04:31 sample no r^3 equiv. uni. 1 21.586 0.513020 2 8.308 0.241904 3 55.021 0.840232 4 17.823 0.447941 5 19.284 0.474188 6 2.867 0.091131 7 56.527 0.848055 8 73.230 0.912926 9 21.488 0.511430 10 19.873 0.484399 11 30.300 0.635785 12 16.100 0.415308 13 15.941 0.412192 14 33.368 0.671188 15 18.840 0.466340 16 15.291 0.399324 17 46.893 0.790515 18 1.622 0.052646 19 19.935 0.485468 20 3.708 0.116268 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.481526 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-04-07_04:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 0.1 1.3 -0.5 -0.5 0.5 -1.4 3.3 -0.5 0.4 0.4 0.6 -0.5 -1.1 -0.2 -1.7 -0.4 0.1 -0.5 3.6 0.3 -0.3 -0.2 -0.4 0.3 0.7 -0.7 -1.0 -1.6 0.4 1.1 0.1 -0.0 -0.9 -1.2 0.8 0.3 -0.7 0.1 -0.7 -1.3 -1.0 1.8 Chi-square with 42 degrees of freedom:50.742046 z-score=0.953835, p-value=0.833060 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-04-07_04:31 Test no p-value 1 0.005989 2 0.000720 3 0.042865 4 0.225709 5 0.711041 6 0.145074 7 0.037443 8 0.306320 9 0.350002 10 0.129005 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000253 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-04-07_04:31: (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 66446 0.73 66662 0.00 3 25000.00 25223 1.99 24999 0.00 4 6666.67 6664 0.00 6613 0.43 5 1388.89 1382 0.03 1418 0.61 6 238.10 237 0.01 259 1.84 7 34.72 40 0.80 42 1.53 8 4.96 7 0.84 6 0.22 p=0.37754 p=0.40694 Number of rngs required: 689363, p-value: 0.867 RESULTS OF CRAPS TEST for dh-ranFile-2016-04-07_04:31 No. of wins: Observed Expected 98835 98585.9 z-score= 1.114, pvalue=0.86743 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66618 66666.7 0.036 0.036 2 37678 37654.3 0.015 0.050 3 26816 26954.7 0.714 0.764 4 19267 19313.5 0.112 0.876 5 13806 13851.4 0.149 1.025 6 10027 9943.5 0.700 1.726 7 7309 7145.0 3.763 5.489 8 5196 5139.1 0.631 6.119 9 3644 3699.9 0.844 6.963 10 2667 2666.3 0.000 6.963 11 1899 1923.3 0.308 7.271 12 1422 1388.7 0.797 8.067 13 1017 1003.7 0.176 8.243 14 724 726.1 0.006 8.250 15 537 525.8 0.237 8.487 16 376 381.2 0.070 8.556 17 285 276.5 0.259 8.815 18 195 200.8 0.169 8.984 19 154 146.0 0.440 9.424 20 102 106.2 0.167 9.592 21 261 287.1 2.375 11.967 Chisq= 11.97 for 20 degrees of freedom, p= 0.08279 SUMMARY of craptest p-value for no. of wins: 0.867426 p-value for throws/game: 0.082785 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-04-07_04:31 No. of wins: Observed Expected 98613 98585.9 z-score= 0.121, pvalue=0.54831 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66736 66666.7 0.072 0.072 2 37861 37654.3 1.134 1.207 3 26818 26954.7 0.694 1.900 4 19367 19313.5 0.148 2.049 5 13768 13851.4 0.502 2.551 6 9982 9943.5 0.149 2.700 7 7067 7145.0 0.852 3.552 8 5026 5139.1 2.488 6.040 9 3748 3699.9 0.626 6.666 10 2703 2666.3 0.505 7.171 11 1923 1923.3 0.000 7.171 12 1333 1388.7 2.237 9.408 13 1009 1003.7 0.028 9.436 14 720 726.1 0.052 9.488 15 461 525.8 7.994 17.482 16 423 381.2 4.595 22.077 17 279 276.5 0.022 22.099 18 193 200.8 0.305 22.405 19 156 146.0 0.687 23.092 20 114 106.2 0.571 23.662 21 313 287.1 2.334 25.996 Chisq= 26.00 for 20 degrees of freedom, p= 0.83406 SUMMARY of craptest p-value for no. of wins: 0.548310 p-value for throws/game: 0.834061 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0003,0.0007,0.0047,0.0060,0.0075,0.0106,0.0130,0.0142,0.0162,0.0183, 0.0214,0.0247,0.0258,0.0259,0.0262,0.0318,0.0322,0.0353,0.0364,0.0374, 0.0429,0.0526,0.0581,0.0589,0.0600,0.0606,0.0614,0.0622,0.0643,0.0647, 0.0680,0.0691,0.0701,0.0744,0.0811,0.0828,0.0854,0.0880,0.0881,0.0911, 0.0919,0.0943,0.0975,0.1022,0.1024,0.1031,0.1064,0.1112,0.1163,0.1168, 0.1192,0.1218,0.1278,0.1290,0.1321,0.1330,0.1354,0.1419,0.1451,0.1485, 0.1498,0.1651,0.1693,0.1699,0.1792,0.1844,0.1869,0.1902,0.1928,0.1928, 0.1947,0.1954,0.2115,0.2129,0.2188,0.2205,0.2215,0.2252,0.2257,0.2325, 0.2329,0.2331,0.2419,0.2456,0.2459,0.2503,0.2523,0.2648,0.2691,0.2694, 0.2704,0.2769,0.2826,0.2834,0.2864,0.2919,0.2957,0.3063,0.3108,0.3149, 0.3167,0.3200,0.3202,0.3236,0.3244,0.3281,0.3287,0.3317,0.3325,0.3351, 0.3406,0.3500,0.3577,0.3608,0.3697,0.3770,0.3775,0.3949,0.3980,0.3985, 0.3993,0.4046,0.4054,0.4069,0.4086,0.4100,0.4122,0.4144,0.4153,0.4250, 0.4255,0.4318,0.4326,0.4349,0.4375,0.4387,0.4479,0.4532,0.4550,0.4562, 0.4568,0.4625,0.4643,0.4663,0.4685,0.4742,0.4759,0.4772,0.4815,0.4844, 0.4855,0.4866,0.4932,0.4954,0.4961,0.4978,0.4982,0.5048,0.5087,0.5091, 0.5114,0.5117,0.5127,0.5130,0.5174,0.5185,0.5212,0.5225,0.5229,0.5277, 0.5290,0.5310,0.5332,0.5364,0.5383,0.5483,0.5617,0.5690,0.5725,0.5735, 0.5836,0.5957,0.5976,0.6117,0.6117,0.6271,0.6302,0.6358,0.6394,0.6400, 0.6402,0.6600,0.6601,0.6712,0.6739,0.6872,0.6879,0.6977,0.6983,0.7007, 0.7037,0.7084,0.7110,0.7311,0.7343,0.7370,0.7384,0.7512,0.7556,0.7565, 0.7601,0.7705,0.7720,0.7788,0.7905,0.7944,0.7967,0.8038,0.8060,0.8129, 0.8226,0.8249,0.8264,0.8315,0.8325,0.8331,0.8335,0.8341,0.8402,0.8481, 0.8510,0.8523,0.8530,0.8577,0.8659,0.8673,0.8674,0.8674,0.8691,0.8728, 0.8742,0.8754,0.8828,0.8834,0.8878,0.8927,0.8957,0.8972,0.9024,0.9081, 0.9129,0.9131,0.9188,0.9210,0.9282,0.9289,0.9332,0.9352,0.9395,0.9487, 0.9490,0.9492,0.9600,0.9620,0.9661,0.9888,0.9896,0.9905,0.9915, Overall p-value after applying KStest on 269 p-values = 0.003669 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.