RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-04-04_11:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.81 15.1103 0.412462 2 to 25 15.76 17.4267 0.574163 3 to 26 15.65 12.3535 0.221728 4 to 27 15.74 10.9001 0.138288 5 to 28 15.88 15.9076 0.469606 6 to 29 16.10 7.4652 0.023312 7 to 30 15.57 19.3559 0.691511 8 to 31 15.75 19.1602 0.680587 9 to 32 15.75 25.4307 0.914524 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.953495 Tough bday spacings test for dh-ranFile-2016-04-04_11:31: 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 4 40 81 105 91 75 44 32 14 10 4 (O-E)^2/E 2.9 0.3 0.8 0.5 0.5 0.1 1.3 0.2 0.1 1.7 0.0 Birthday Spacings: Sum(O-E)^2/E= 8.375, p= 0.408 RESULTS OF GCD FOR dh-ranFile-2016-04-04_11:31 Euclid's algorithm: p-value, steps to gcd: 0.920668 p-value, dist. of gcd's: 0.604510 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-04-04_11:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.310 0.783 0.547 0.121 0.736 0.021 0.531 0.523 Bits 8 to 15---> 0.671 0.257 0.964 0.494 0.308 0.324 0.444 0.877 Bits 16 to 23---> 0.619 0.795 0.658 0.642 0.103 0.249 0.161 0.763 Bits 24 to 31---> 0.957 0.527 0.088 0.552 0.199 0.683 0.876 0.690 KS test for the above 32 p values: 0.113 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-04-04_11:31, p-values for 5 runs: 0.8651, 0.5876, 0.3367, 0.7899, 0.7338 Rank test for binary matrices (31x31) for dh-ranFile-2016-04-04_11:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 212 211.4 0.002 0.002 r= 29 5183 5134.0 0.467 0.469 r= 30 23207 23103.0 0.468 0.937 r= 31 11398 11551.5 2.040 2.977 chi-square = 2.977 with df = 3; p-value = 0.605 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-04-04_11:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 207 211.4 0.092 0.092 r= 30 5116 5134.0 0.063 0.156 r= 31 22938 23103.0 1.179 1.335 r= 32 11739 11551.5 3.043 4.377 chi-square = 4.377 with df = 3; p-value = 0.776 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-04-04_11:31 b-rank test for bits 1 to 8, p=0.22263 b-rank test for bits 2 to 9, p=0.22250 b-rank test for bits 3 to 10, p=0.57439 b-rank test for bits 4 to 11, p=0.62557 b-rank test for bits 5 to 12, p=0.61234 b-rank test for bits 6 to 13, p=0.69834 b-rank test for bits 7 to 14, p=0.33889 b-rank test for bits 8 to 15, p=0.43901 b-rank test for bits 9 to 16, p=0.60566 b-rank test for bits 10 to 17, p=0.24100 b-rank test for bits 11 to 18, p=0.29418 b-rank test for bits 12 to 19, p=0.16964 b-rank test for bits 13 to 20, p=0.53266 b-rank test for bits 14 to 21, p=0.97346 b-rank test for bits 15 to 22, p=0.33177 b-rank test for bits 16 to 23, p=0.47276 b-rank test for bits 17 to 24, p=0.54782 b-rank test for bits 18 to 25, p=0.33697 b-rank test for bits 19 to 26, p=0.81737 b-rank test for bits 20 to 27, p=0.03637 b-rank test for bits 21 to 28, p=0.93086 b-rank test for bits 22 to 29, p=0.51202 b-rank test for bits 23 to 30, p=0.52369 b-rank test for bits 24 to 31, p=0.29755 b-rank test for bits 25 to 32, p=0.23403 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 = 0.298935 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-04-04_11:31 (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 142335 0.99 0.840024 2 141813 -0.23 0.410962 3 140705 -2.81 0.002448 4 141734 -0.41 0.341032 5 142079 0.40 0.654104 6 142421 1.20 0.884052 7 142594 1.60 0.945167 8 142578 1.56 0.940893 9 142163 0.59 0.723305 10 141744 -0.39 0.349643 11 142470 1.31 0.904898 12 141446 -1.08 0.139505 13 141950 0.10 0.537852 14 141391 -1.21 0.112938 15 141821 -0.21 0.418248 16 141453 -1.07 0.143169 17 141906 -0.01 0.496896 18 141836 -0.17 0.431981 19 142187 0.65 0.741754 20 141378 -1.24 0.107224 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-04-04_11:31 Bits used No. missing words z-score p-value 23 to 32 142012 0.3540 0.638344 22 to 31 141762 -0.5080 0.305715 21 to 30 142178 0.9264 0.822894 20 to 29 141811 -0.3391 0.367279 19 to 28 141708 -0.6942 0.243765 18 to 27 142003 0.3230 0.626652 17 to 26 141701 -0.7184 0.236262 16 to 25 142300 1.3471 0.911032 15 to 24 142517 2.0954 0.981933 14 to 23 142271 1.2471 0.893827 13 to 22 142146 0.8161 0.792780 12 to 21 141962 0.1816 0.572060 11 to 20 142423 1.7713 0.961743 10 to 19 141714 -0.6736 0.250298 9 to 18 142008 0.3402 0.633163 8 to 17 141896 -0.0460 0.481669 7 to 16 142213 1.0471 0.852482 6 to 15 141847 -0.2149 0.414911 5 to 14 141788 -0.4184 0.337835 4 to 13 141827 -0.2839 0.388245 3 to 12 141438 -1.6253 0.052052 2 to 11 141895 -0.0494 0.480295 1 to 10 142257 1.1989 0.884709 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-04-04_11:31 Bits used No. missing words z-score p-value 28 to 32 141935 0.0870 0.534671 27 to 31 142422 1.7379 0.958883 26 to 30 142112 0.6870 0.753964 25 to 29 142142 0.7887 0.784860 24 to 28 141949 0.1345 0.553486 23 to 27 141518 -1.3265 0.092330 22 to 26 142042 0.4497 0.673547 21 to 25 142209 1.0158 0.845145 20 to 24 141835 -0.2520 0.400534 19 to 23 141738 -0.5808 0.280695 18 to 22 141806 -0.3503 0.363068 17 to 21 142104 0.6599 0.745341 16 to 20 141993 0.2836 0.611652 15 to 19 142231 1.0904 0.862233 14 to 18 141776 -0.4520 0.325647 13 to 17 141538 -1.2587 0.104061 12 to 16 141917 0.0260 0.510371 11 to 15 141850 -0.2011 0.420303 10 to 14 141797 -0.3808 0.351683 9 to 13 141682 -0.7706 0.220469 8 to 12 142058 0.5040 0.692857 7 to 11 141499 -1.3909 0.082120 6 to 10 142231 1.0904 0.862233 5 to 9 142137 0.7718 0.779873 4 to 8 141752 -0.5333 0.296905 3 to 7 141400 -1.7265 0.042125 2 to 6 141722 -0.6350 0.262709 1 to 5 141504 -1.3740 0.084721 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-04-04_11:31 Bits used No. missing words z-score p-value 31 to 32 141947 0.1111 0.544240 30 to 31 141477 -1.2753 0.101100 29 to 30 141831 -0.2311 0.408633 28 to 29 142191 0.8309 0.796981 27 to 28 141701 -0.6145 0.269428 26 to 27 141487 -1.2458 0.106417 25 to 26 142336 1.2586 0.895915 24 to 25 142052 0.4209 0.663070 23 to 24 141902 -0.0216 0.491375 22 to 23 141883 -0.0777 0.469045 21 to 22 142021 0.3294 0.629077 20 to 21 141836 -0.2163 0.414372 19 to 20 141858 -0.1514 0.439824 18 to 19 141498 -1.2134 0.112496 17 to 18 142440 1.5654 0.941255 16 to 17 142042 0.3914 0.652233 15 to 16 140807 -3.2517 0.000574 14 to 15 142256 1.0226 0.846758 13 to 14 141816 -0.2753 0.391539 12 to 13 142182 0.8043 0.789399 11 to 12 142263 1.0433 0.851589 10 to 11 142120 0.6214 0.732847 9 to 10 141909 -0.0010 0.499612 8 to 9 141913 0.0108 0.504319 7 to 8 142044 0.3973 0.654411 6 to 7 142277 1.0846 0.860944 5 to 6 141383 -1.5526 0.060260 4 to 5 141760 -0.4405 0.329787 3 to 4 141578 -0.9774 0.164192 2 to 3 141444 -1.3727 0.084930 1 to 2 142184 0.8102 0.791098 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-04-04_11:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2398.52 -1.435 0.075615 Test results for specific bytes for dh-ranFile-2016-04-04_11:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2423.26 -1.085 0.138886 2 to 9 2409.12 -1.285 0.099362 3 to 10 2578.09 1.104 0.865274 4 to 11 2437.83 -0.879 0.189629 5 to 12 2409.34 -1.282 0.099909 6 to 13 2380.06 -1.696 0.044917 7 to 14 2476.68 -0.330 0.370798 8 to 15 2482.76 -0.244 0.403714 9 to 16 2477.16 -0.323 0.373361 10 to 17 2370.65 -1.829 0.033674 11 to 18 2567.89 0.960 0.831512 12 to 19 2531.95 0.452 0.674325 13 to 20 2302.51 -2.793 0.002612 14 to 21 2489.59 -0.147 0.441505 15 to 22 2464.77 -0.498 0.309164 16 to 23 2509.14 0.129 0.551419 17 to 24 2419.13 -1.144 0.126387 18 to 25 2464.23 -0.506 0.306476 19 to 26 2514.95 0.211 0.583742 20 to 27 2557.86 0.818 0.793399 21 to 28 2415.67 -1.193 0.116502 22 to 29 2466.79 -0.470 0.319321 23 to 30 2521.87 0.309 0.621443 24 to 31 2519.37 0.274 0.607921 25 to 32 2604.59 1.479 0.930450 CDPARK for dh-ranFile-2016-04-04_11:31: 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 3506 -0.7763 0.218799 3512 -0.5023 0.307734 3517 -0.2740 0.392053 3522 -0.0457 0.481790 3490 -1.5068 0.065925 3532 0.4110 0.659449 3492 -1.4155 0.078457 3537 0.6393 0.738676 3549 1.1872 0.882429 3504 -0.8676 0.192812 Square side=100, avg. no. parked=3516.10 sample std.=18.26 p-value of the KSTEST for those 10 p-values: 0.543929 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-04-04_11:31 0.1501,0.1247,0.7048,0.4124,0.5160,0.5089,0.5166,0.9150,0.6076,0.3872, The KS test for those 10 p-values: 0.689897 The 3DSPHERES test for dh-ranFile-2016-04-04_11:31 sample no r^3 equiv. uni. 1 19.285 0.474191 2 0.392 0.012995 3 27.680 0.602541 4 54.018 0.834798 5 44.931 0.776355 6 18.698 0.463817 7 38.729 0.724992 8 6.450 0.193471 9 15.659 0.406656 10 3.566 0.112061 11 29.859 0.630393 12 27.978 0.606474 13 9.877 0.280522 14 1.550 0.050370 15 4.979 0.152918 16 22.209 0.523036 17 43.660 0.766675 18 22.667 0.530259 19 59.412 0.861984 20 10.927 0.305268 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.765614 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-04-04_11:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 0.1 2.0 1.1 0.6 -0.6 -0.2 -1.6 0.8 -1.7 0.1 -0.2 -0.5 0.2 -0.5 -1.1 -0.0 -2.0 1.6 0.8 0.9 1.4 -0.9 -0.4 -0.9 1.3 1.3 0.4 -0.4 2.7 1.6 -0.3 -0.2 0.0 1.3 -0.3 -1.9 -0.7 1.7 -0.1 -0.6 0.0 -1.1 Chi-square with 42 degrees of freedom:50.386574 z-score=0.915050, p-value=0.824349 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-04-04_11:31 Test no p-value 1 0.222055 2 0.897476 3 0.737383 4 0.006365 5 0.810990 6 0.080390 7 0.026590 8 0.449735 9 0.178892 10 0.433401 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.193448 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-04-04_11:31: (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 66771 0.16 66729 0.06 3 25000.00 24875 0.62 24977 0.02 4 6666.67 6673 0.01 6644 0.08 5 1388.89 1414 0.45 1358 0.69 6 238.10 218 1.70 252 0.81 7 34.72 45 3.04 34 0.01 8 4.96 3 0.77 5 0.00 p=0.65663 p=0.05265 Number of rngs required: 688035, p-value: 0.336 RESULTS OF CRAPS TEST for dh-ranFile-2016-04-04_11:31 No. of wins: Observed Expected 98349 98585.9 z-score=-1.059, pvalue=0.14472 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66616 66666.7 0.039 0.039 2 37787 37654.3 0.468 0.506 3 26691 26954.7 2.580 3.086 4 19155 19313.5 1.300 4.387 5 13888 13851.4 0.097 4.483 6 10101 9943.5 2.493 6.977 7 7194 7145.0 0.336 7.312 8 5180 5139.1 0.326 7.638 9 3679 3699.9 0.118 7.756 10 2654 2666.3 0.057 7.813 11 1915 1923.3 0.036 7.849 12 1388 1388.7 0.000 7.849 13 1025 1003.7 0.451 8.300 14 720 726.1 0.052 8.352 15 560 525.8 2.220 10.572 16 377 381.2 0.045 10.617 17 275 276.5 0.009 10.626 18 197 200.8 0.073 10.699 19 171 146.0 4.287 14.985 20 93 106.2 1.644 16.630 21 334 287.1 7.657 24.286 Chisq= 24.29 for 20 degrees of freedom, p= 0.76989 SUMMARY of craptest p-value for no. of wins: 0.144716 p-value for throws/game: 0.769886 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-04-04_11:31 No. of wins: Observed Expected 98252 98585.9 z-score=-1.493, pvalue=0.06769 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66536 66666.7 0.256 0.256 2 37772 37654.3 0.368 0.624 3 26821 26954.7 0.663 1.287 4 19063 19313.5 3.248 4.535 5 13975 13851.4 1.103 5.638 6 9994 9943.5 0.256 5.894 7 7159 7145.0 0.027 5.921 8 5283 5139.1 4.031 9.952 9 3758 3699.9 0.913 10.866 10 2704 2666.3 0.533 11.399 11 1853 1923.3 2.572 13.971 12 1404 1388.7 0.168 14.138 13 1005 1003.7 0.002 14.140 14 727 726.1 0.001 14.141 15 533 525.8 0.098 14.239 16 386 381.2 0.062 14.300 17 263 276.5 0.663 14.963 18 202 200.8 0.007 14.970 19 139 146.0 0.334 15.304 20 112 106.2 0.315 15.619 21 311 287.1 1.987 17.606 Chisq= 17.61 for 20 degrees of freedom, p= 0.38667 SUMMARY of craptest p-value for no. of wins: 0.067691 p-value for throws/game: 0.386674 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0006,0.0024,0.0026,0.0064,0.0130,0.0208,0.0233,0.0266,0.0337,0.0364, 0.0421,0.0449,0.0504,0.0521,0.0526,0.0603,0.0659,0.0677,0.0756,0.0785, 0.0804,0.0821,0.0847,0.0849,0.0877,0.0923,0.0994,0.0999,0.1011,0.1028, 0.1041,0.1064,0.1072,0.1121,0.1125,0.1129,0.1129,0.1165,0.1214,0.1247, 0.1264,0.1383,0.1389,0.1395,0.1432,0.1447,0.1501,0.1529,0.1606,0.1642, 0.1696,0.1789,0.1896,0.1928,0.1934,0.1935,0.1986,0.2188,0.2205,0.2217, 0.2221,0.2225,0.2226,0.2340,0.2363,0.2410,0.2438,0.2490,0.2503,0.2565, 0.2627,0.2694,0.2805,0.2807,0.2942,0.2969,0.2976,0.2989,0.3053,0.3057, 0.3065,0.3077,0.3081,0.3092,0.3100,0.3193,0.3236,0.3256,0.3298,0.3318, 0.3358,0.3367,0.3370,0.3378,0.3389,0.3410,0.3496,0.3517,0.3631,0.3673, 0.3708,0.3734,0.3867,0.3872,0.3882,0.3915,0.3921,0.4005,0.4037,0.4067, 0.4077,0.4086,0.4110,0.4124,0.4125,0.4144,0.4149,0.4182,0.4203,0.4320, 0.4334,0.4390,0.4398,0.4415,0.4436,0.4497,0.4638,0.4690,0.4696,0.4728, 0.4742,0.4803,0.4817,0.4818,0.4914,0.4944,0.4969,0.4996,0.5043,0.5089, 0.5104,0.5120,0.5160,0.5166,0.5226,0.5230,0.5237,0.5271,0.5303,0.5309, 0.5327,0.5347,0.5379,0.5439,0.5442,0.5466,0.5478,0.5514,0.5516,0.5535, 0.5721,0.5742,0.5744,0.5837,0.5876,0.6025,0.6045,0.6048,0.6057,0.6065, 0.6076,0.6079,0.6117,0.6123,0.6194,0.6214,0.6256,0.6267,0.6291,0.6304, 0.6332,0.6383,0.6423,0.6522,0.6541,0.6544,0.6566,0.6582,0.6594,0.6631, 0.6710,0.6735,0.6743,0.6806,0.6829,0.6899,0.6900,0.6915,0.6929,0.6983, 0.7048,0.7233,0.7250,0.7328,0.7338,0.7356,0.7374,0.7387,0.7418,0.7453, 0.7540,0.7634,0.7656,0.7667,0.7699,0.7764,0.7765,0.7799,0.7825,0.7849, 0.7894,0.7899,0.7911,0.7928,0.7934,0.7945,0.7970,0.8110,0.8174,0.8229, 0.8243,0.8315,0.8348,0.8400,0.8451,0.8468,0.8516,0.8525,0.8609,0.8620, 0.8622,0.8622,0.8651,0.8653,0.8763,0.8766,0.8824,0.8841,0.8847,0.8938, 0.8959,0.8975,0.9049,0.9110,0.9145,0.9150,0.9207,0.9304,0.9309,0.9409, 0.9413,0.9452,0.9535,0.9568,0.9589,0.9617,0.9644,0.9735,0.9819, Overall p-value after applying KStest on 269 p-values = 0.308612 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.