RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-03-27_23:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.60 14.9997 0.404494 2 to 25 15.77 21.6189 0.800179 3 to 26 15.90 10.6737 0.126985 4 to 27 15.70 13.4323 0.293201 5 to 28 15.84 17.1158 0.553454 6 to 29 15.82 11.4921 0.170131 7 to 30 15.71 17.1387 0.554994 8 to 31 15.51 21.3835 0.790394 9 to 32 15.96 10.9433 0.140502 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.637773 Tough bday spacings test for dh-ranFile-2018-03-27_23:31: 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 35 66 96 101 76 64 24 19 6 4 (O-E)^2/E 0.0 0.1 0.7 0.0 0.1 0.1 2.7 1.1 1.1 0.1 0.0 Birthday Spacings: Sum(O-E)^2/E= 6.029, p= 0.187 RESULTS OF GCD FOR dh-ranFile-2018-03-27_23:31 Euclid's algorithm: p-value, steps to gcd: 0.264150 p-value, dist. of gcd's: 0.359522 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-03-27_23:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.732 0.600 0.131 0.232 0.723 0.171 0.948 0.965 Bits 8 to 15---> 0.711 0.056 0.180 0.381 0.137 0.867 0.521 0.636 Bits 16 to 23---> 0.497 0.401 0.243 0.896 0.231 0.885 0.350 0.386 Bits 24 to 31---> 0.390 0.330 0.427 0.273 0.806 0.936 0.530 0.693 KS test for the above 32 p values: 0.106 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-03-27_23:31, p-values for 5 runs: 0.3209, 0.2720, 0.8030, 0.5487, 0.8036 Rank test for binary matrices (31x31) for dh-ranFile-2018-03-27_23:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 196 211.4 1.124 1.124 r= 29 5070 5134.0 0.798 1.922 r= 30 23173 23103.0 0.212 2.134 r= 31 11561 11551.5 0.008 2.142 chi-square = 2.142 with df = 3; p-value = 0.457 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-03-27_23:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 198 211.4 0.852 0.852 r= 30 5132 5134.0 0.001 0.852 r= 31 23157 23103.0 0.126 0.978 r= 32 11513 11551.5 0.128 1.107 chi-square = 1.107 with df = 3; p-value = 0.225 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-03-27_23:31 b-rank test for bits 1 to 8, p=0.69497 b-rank test for bits 2 to 9, p=0.77570 b-rank test for bits 3 to 10, p=0.01630 b-rank test for bits 4 to 11, p=0.35210 b-rank test for bits 5 to 12, p=0.13626 b-rank test for bits 6 to 13, p=0.01591 b-rank test for bits 7 to 14, p=0.04518 b-rank test for bits 8 to 15, p=0.70630 b-rank test for bits 9 to 16, p=0.69985 b-rank test for bits 10 to 17, p=0.89362 b-rank test for bits 11 to 18, p=0.91211 b-rank test for bits 12 to 19, p=0.43542 b-rank test for bits 13 to 20, p=0.88201 b-rank test for bits 14 to 21, p=0.99316 b-rank test for bits 15 to 22, p=0.13632 b-rank test for bits 16 to 23, p=0.96989 b-rank test for bits 17 to 24, p=0.35315 b-rank test for bits 18 to 25, p=0.95362 b-rank test for bits 19 to 26, p=0.91781 b-rank test for bits 20 to 27, p=0.59953 b-rank test for bits 21 to 28, p=0.04278 b-rank test for bits 22 to 29, p=0.11210 b-rank test for bits 23 to 30, p=0.32724 b-rank test for bits 24 to 31, p=0.92261 b-rank test for bits 25 to 32, p=0.16071 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 = 0.121992 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-03-27_23:31 (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 141525 -0.90 0.184602 2 141762 -0.34 0.365337 3 142221 0.73 0.766755 4 142204 0.69 0.754425 5 142775 2.02 0.978442 6 140552 -3.17 0.000759 7 142108 0.46 0.678741 8 141627 -0.66 0.254739 9 142232 0.75 0.774546 10 142022 0.26 0.603820 11 140521 -3.24 0.000590 12 141261 -1.51 0.064913 13 142199 0.68 0.750733 14 142490 1.36 0.912563 15 142141 0.54 0.705844 16 141818 -0.21 0.415512 17 141987 0.18 0.572001 18 140803 -2.58 0.004871 19 141404 -1.18 0.118865 20 142086 0.41 0.660116 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-03-27_23:31 Bits used No. missing words z-score p-value 23 to 32 141796 -0.3908 0.347975 22 to 31 142005 0.3299 0.629261 21 to 30 141708 -0.6942 0.243765 20 to 29 141901 -0.0287 0.488542 19 to 28 142037 0.4402 0.670119 18 to 27 141863 -0.1598 0.436536 17 to 26 142152 0.8368 0.798646 16 to 25 141574 -1.1563 0.123777 15 to 24 142207 1.0264 0.847660 14 to 23 142090 0.6230 0.733358 13 to 22 142349 1.5161 0.935253 12 to 21 141855 -0.1873 0.425695 11 to 20 141920 0.0368 0.514675 10 to 19 141763 -0.5046 0.306925 9 to 18 141840 -0.2391 0.405526 8 to 17 142090 0.6230 0.733358 7 to 16 142406 1.7127 0.956612 6 to 15 141652 -0.8873 0.187447 5 to 14 141641 -0.9253 0.177411 4 to 13 142051 0.4885 0.687408 3 to 12 141554 -1.2253 0.110236 2 to 11 141831 -0.2701 0.393540 1 to 10 142106 0.6782 0.751169 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-03-27_23:31 Bits used No. missing words z-score p-value 28 to 32 142006 0.3277 0.628429 27 to 31 142037 0.4328 0.667413 26 to 30 142280 1.2565 0.895534 25 to 29 141892 -0.0587 0.476577 24 to 28 141886 -0.0791 0.468483 23 to 27 142289 1.2870 0.900956 22 to 26 141813 -0.3265 0.372007 21 to 25 141920 0.0362 0.514426 20 to 24 141848 -0.2079 0.417654 19 to 23 141923 0.0463 0.518480 18 to 22 142090 0.6124 0.729877 17 to 21 141979 0.2362 0.593349 16 to 20 141919 0.0328 0.513075 15 to 19 142165 0.8667 0.806941 14 to 18 141671 -0.8079 0.209575 13 to 17 141761 -0.5028 0.307548 12 to 16 141811 -0.3333 0.369446 11 to 15 141474 -1.4757 0.070013 10 to 14 141706 -0.6893 0.245332 9 to 13 141727 -0.6181 0.268265 8 to 12 141809 -0.3401 0.366890 7 to 11 141722 -0.6350 0.262709 6 to 10 141456 -1.5367 0.062182 5 to 9 141685 -0.7604 0.223496 4 to 8 142067 0.5345 0.703493 3 to 7 141478 -1.4621 0.071852 2 to 6 141437 -1.6011 0.054675 1 to 5 141724 -0.6282 0.264924 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-03-27_23:31 Bits used No. missing words z-score p-value 31 to 32 141731 -0.5260 0.299428 30 to 31 141609 -0.8859 0.187828 29 to 30 141594 -0.9302 0.176140 28 to 29 141606 -0.8948 0.185453 27 to 28 142212 0.8928 0.814026 26 to 27 142314 1.1937 0.883706 25 to 26 142069 0.4710 0.681181 24 to 25 142057 0.4356 0.668438 23 to 24 142327 1.2321 0.891038 22 to 23 141284 -1.8446 0.032546 21 to 22 142064 0.4563 0.675896 20 to 21 141922 0.0374 0.514907 19 to 20 141793 -0.3432 0.365740 18 to 19 142209 0.8840 0.811647 17 to 18 142095 0.5477 0.708051 16 to 17 141451 -1.3520 0.088187 15 to 16 141841 -0.2016 0.420129 14 to 15 141621 -0.8505 0.197515 13 to 14 141979 0.2055 0.581416 12 to 13 141514 -1.1662 0.121774 11 to 12 142624 2.1082 0.982492 10 to 11 141836 -0.2163 0.414372 9 to 10 142160 0.7394 0.770180 8 to 9 141531 -1.1160 0.132207 7 to 8 141862 -0.1396 0.444482 6 to 7 141847 -0.1839 0.427060 5 to 6 141562 -1.0246 0.152783 4 to 5 141680 -0.6765 0.249365 3 to 4 142196 0.8456 0.801122 2 to 3 142319 1.2085 0.886566 1 to 2 141750 -0.4700 0.319178 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-03-27_23:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2522.91 0.324 0.627021 Test results for specific bytes for dh-ranFile-2018-03-27_23:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2546.85 0.663 0.746176 2 to 9 2596.02 1.358 0.912765 3 to 10 2389.28 -1.566 0.058695 4 to 11 2372.74 -1.800 0.035950 5 to 12 2537.39 0.529 0.701517 6 to 13 2537.10 0.525 0.700081 7 to 14 2505.48 0.078 0.530898 8 to 15 2472.67 -0.387 0.349544 9 to 16 2535.44 0.501 0.691897 10 to 17 2522.89 0.324 0.626908 11 to 18 2494.07 -0.084 0.466596 12 to 19 2577.80 1.100 0.864400 13 to 20 2421.92 -1.104 0.134739 14 to 21 2545.63 0.645 0.740624 15 to 22 2468.00 -0.453 0.325413 16 to 23 2580.02 1.132 0.871105 17 to 24 2619.78 1.694 0.954865 18 to 25 2574.21 1.049 0.853008 19 to 26 2458.82 -0.582 0.280151 20 to 27 2479.31 -0.293 0.384899 21 to 28 2536.80 0.520 0.698619 22 to 29 2587.55 1.238 0.892181 23 to 30 2450.88 -0.695 0.243651 24 to 31 2501.44 0.020 0.508141 25 to 32 2434.47 -0.927 0.177050 CDPARK for dh-ranFile-2018-03-27_23:31: 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 3504 -0.8676 0.192812 3524 0.0457 0.518210 3490 -1.5068 0.065925 3526 0.1370 0.554479 3486 -1.6895 0.045562 3521 -0.0913 0.463617 3531 0.3653 0.642555 3514 -0.4110 0.340551 3557 1.5525 0.939730 3476 -2.1461 0.015932 Square side=100, avg. no. parked=3512.90 sample std.=23.07 p-value of the KSTEST for those 10 p-values: 0.235293 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-03-27_23:31 0.1743,0.2632,0.6571,0.9051,0.4173,0.3518,0.1362,0.8980,0.5949,0.8865, The KS test for those 10 p-values: 0.878506 The 3DSPHERES test for dh-ranFile-2018-03-27_23:31 sample no r^3 equiv. uni. 1 52.445 0.825909 2 120.335 0.981888 3 165.523 0.995984 4 13.036 0.352442 5 2.690 0.085762 6 12.033 0.330420 7 26.717 0.589578 8 41.843 0.752109 9 97.840 0.961662 10 8.585 0.248852 11 35.180 0.690457 12 3.630 0.113976 13 50.754 0.815815 14 26.135 0.581541 15 4.889 0.150377 16 34.729 0.685771 17 17.695 0.445574 18 75.177 0.918399 19 24.284 0.554906 20 8.283 0.241255 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.432917 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-03-27_23:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 1.3 0.6 1.5 1.6 1.6 2.0 1.0 -0.3 -0.1 0.1 -0.4 0.0 1.1 -0.2 -0.0 0.6 0.2 -0.5 -1.2 -0.9 -0.1 0.4 -0.3 0.1 0.1 -0.8 -1.5 -0.3 0.2 0.3 0.6 0.8 0.9 -0.2 1.9 0.0 2.1 1.3 -0.7 -1.3 -1.0 -0.1 Chi-square with 42 degrees of freedom:37.160022 z-score=-0.528085, p-value=0.316926 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-03-27_23:31 Test no p-value 1 0.021313 2 0.004152 3 0.125452 4 0.020556 5 0.351001 6 0.160169 7 0.612335 8 0.318177 9 0.590045 10 0.667305 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.012469 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-03-27_23:31: (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 66665 0.00 66415 0.95 3 25000.00 25050 0.10 25184 1.35 4 6666.67 6619 0.34 6726 0.53 5 1388.89 1384 0.02 1389 0.00 6 238.10 242 0.06 245 0.20 7 34.72 37 0.15 39 0.53 8 4.96 2 1.77 1 3.16 p=0.12470 p=0.65266 Number of rngs required: 688263, p-value: 0.436 RESULTS OF CRAPS TEST for dh-ranFile-2018-03-27_23:31 No. of wins: Observed Expected 98663 98585.9 z-score= 0.345, pvalue=0.63496 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66669 66666.7 0.000 0.000 2 37670 37654.3 0.007 0.007 3 27051 26954.7 0.344 0.350 4 19155 19313.5 1.300 1.651 5 13933 13851.4 0.480 2.131 6 10126 9943.5 3.348 5.479 7 7089 7145.0 0.439 5.918 8 5102 5139.1 0.267 6.186 9 3745 3699.9 0.551 6.736 10 2561 2666.3 4.158 10.895 11 1811 1923.3 6.560 17.455 12 1361 1388.7 0.554 18.009 13 1039 1003.7 1.240 19.250 14 726 726.1 0.000 19.250 15 561 525.8 2.352 21.601 16 364 381.2 0.772 22.373 17 277 276.5 0.001 22.374 18 196 200.8 0.116 22.490 19 141 146.0 0.170 22.660 20 114 106.2 0.571 23.231 21 309 287.1 1.668 24.899 Chisq= 24.90 for 20 degrees of freedom, p= 0.79468 SUMMARY of craptest p-value for no. of wins: 0.634961 p-value for throws/game: 0.794676 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-03-27_23:31 No. of wins: Observed Expected 98518 98585.9 z-score=-0.304, pvalue=0.38075 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66514 66666.7 0.350 0.350 2 37831 37654.3 0.829 1.179 3 27073 26954.7 0.519 1.698 4 19376 19313.5 0.203 1.900 5 13799 13851.4 0.198 2.098 6 9765 9943.5 3.206 5.304 7 7202 7145.0 0.454 5.759 8 5070 5139.1 0.928 6.687 9 3777 3699.9 1.608 8.295 10 2632 2666.3 0.441 8.736 11 1938 1923.3 0.112 8.848 12 1378 1388.7 0.083 8.931 13 1035 1003.7 0.975 9.906 14 683 726.1 2.563 12.469 15 534 525.8 0.127 12.596 16 386 381.2 0.062 12.658 17 265 276.5 0.482 13.139 18 185 200.8 1.248 14.387 19 159 146.0 1.160 15.548 20 105 106.2 0.014 15.561 21 293 287.1 0.121 15.682 Chisq= 15.68 for 20 degrees of freedom, p= 0.26386 SUMMARY of craptest p-value for no. of wins: 0.380753 p-value for throws/game: 0.263860 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0006,0.0008,0.0042,0.0049,0.0125,0.0159,0.0159,0.0163,0.0206,0.0213, 0.0325,0.0359,0.0428,0.0452,0.0456,0.0547,0.0562,0.0587,0.0622,0.0649, 0.0659,0.0700,0.0719,0.0858,0.0882,0.1062,0.1102,0.1121,0.1140,0.1189, 0.1218,0.1220,0.1238,0.1247,0.1255,0.1270,0.1314,0.1322,0.1347,0.1362, 0.1363,0.1363,0.1369,0.1405,0.1504,0.1528,0.1602,0.1607,0.1701,0.1708, 0.1743,0.1761,0.1770,0.1774,0.1803,0.1846,0.1855,0.1872,0.1874,0.1878, 0.1928,0.1975,0.2096,0.2235,0.2246,0.2309,0.2316,0.2353,0.2413,0.2430, 0.2437,0.2438,0.2453,0.2489,0.2494,0.2547,0.2627,0.2632,0.2639,0.2641, 0.2649,0.2683,0.2720,0.2728,0.2802,0.2932,0.2994,0.3069,0.3075,0.3169, 0.3182,0.3192,0.3209,0.3254,0.3272,0.3300,0.3304,0.3406,0.3480,0.3495, 0.3503,0.3510,0.3518,0.3521,0.3524,0.3532,0.3595,0.3653,0.3657,0.3669, 0.3694,0.3720,0.3808,0.3812,0.3849,0.3858,0.3903,0.3935,0.4007,0.4045, 0.4055,0.4144,0.4155,0.4173,0.4177,0.4201,0.4257,0.4268,0.4271,0.4329, 0.4354,0.4360,0.4365,0.4445,0.4456,0.4565,0.4636,0.4666,0.4685,0.4766, 0.4885,0.4971,0.5081,0.5131,0.5144,0.5147,0.5149,0.5182,0.5185,0.5210, 0.5301,0.5309,0.5487,0.5535,0.5545,0.5549,0.5550,0.5720,0.5814,0.5815, 0.5896,0.5900,0.5933,0.5949,0.5995,0.5997,0.6038,0.6123,0.6269,0.6270, 0.6284,0.6293,0.6350,0.6356,0.6378,0.6426,0.6527,0.6571,0.6601,0.6673, 0.6674,0.6684,0.6701,0.6759,0.6787,0.6812,0.6858,0.6874,0.6905,0.6919, 0.6925,0.6950,0.6986,0.6998,0.7001,0.7015,0.7035,0.7058,0.7063,0.7081, 0.7105,0.7226,0.7299,0.7319,0.7334,0.7334,0.7406,0.7462,0.7507,0.7512, 0.7521,0.7544,0.7668,0.7702,0.7745,0.7757,0.7904,0.7947,0.7986,0.8002, 0.8011,0.8030,0.8036,0.8058,0.8069,0.8116,0.8140,0.8158,0.8259,0.8477, 0.8530,0.8644,0.8675,0.8711,0.8785,0.8820,0.8837,0.8848,0.8865,0.8866, 0.8910,0.8922,0.8936,0.8955,0.8961,0.8980,0.9010,0.9051,0.9121,0.9126, 0.9128,0.9178,0.9184,0.9226,0.9353,0.9362,0.9397,0.9476,0.9536,0.9549, 0.9566,0.9617,0.9654,0.9699,0.9784,0.9819,0.9825,0.9932,0.9960, Overall p-value after applying KStest on 269 p-values = 0.460977 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.