RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-27_20:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.86 21.0933 0.777855 2 to 25 15.46 23.8544 0.876556 3 to 26 15.78 20.1236 0.732044 4 to 27 15.67 17.7504 0.595250 5 to 28 15.60 22.1901 0.822480 6 to 29 15.89 16.9468 0.542021 7 to 30 15.63 20.9772 0.772690 8 to 31 15.64 26.5577 0.935119 9 to 32 15.73 15.7526 0.458560 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.027212 Tough bday spacings test for dh-ranFile-2018-06-27_20:31: 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 15 29 70 92 106 75 58 31 15 7 2 (O-E)^2/E 3.7 1.6 0.1 0.3 0.7 0.1 0.7 0.1 0.0 0.0 1.0 Birthday Spacings: Sum(O-E)^2/E= 8.420, p= 0.412 RESULTS OF GCD FOR dh-ranFile-2018-06-27_20:31 Euclid's algorithm: p-value, steps to gcd: 0.143394 p-value, dist. of gcd's: 0.875567 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-27_20:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.321 0.158 0.235 0.390 0.924 0.423 0.601 0.242 Bits 8 to 15---> 0.325 0.837 0.600 0.464 0.846 0.314 0.071 0.089 Bits 16 to 23---> 0.959 0.180 0.406 0.733 0.913 0.898 0.285 0.062 Bits 24 to 31---> 0.911 0.229 0.141 0.242 0.107 0.775 0.809 0.126 KS test for the above 32 p values: 0.652 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-27_20:31, p-values for 5 runs: 0.4755, 0.8189, 0.5146, 0.2150, 0.3392 Rank test for binary matrices (31x31) for dh-ranFile-2018-06-27_20:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 212 211.4 0.002 0.002 r= 29 5176 5134.0 0.343 0.345 r= 30 23040 23103.0 0.172 0.517 r= 31 11572 11551.5 0.036 0.553 chi-square = 0.553 with df = 3; p-value = 0.093 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-06-27_20:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 178 211.4 5.282 5.282 r= 30 5217 5134.0 1.341 6.624 r= 31 23107 23103.0 0.001 6.624 r= 32 11498 11551.5 0.248 6.872 chi-square = 6.872 with df = 3; p-value = 0.924 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-06-27_20:31 b-rank test for bits 1 to 8, p=0.21815 b-rank test for bits 2 to 9, p=0.56643 b-rank test for bits 3 to 10, p=0.96995 b-rank test for bits 4 to 11, p=0.14217 b-rank test for bits 5 to 12, p=0.83588 b-rank test for bits 6 to 13, p=0.88339 b-rank test for bits 7 to 14, p=0.96003 b-rank test for bits 8 to 15, p=0.87907 b-rank test for bits 9 to 16, p=0.87662 b-rank test for bits 10 to 17, p=0.65466 b-rank test for bits 11 to 18, p=0.58129 b-rank test for bits 12 to 19, p=0.63517 b-rank test for bits 13 to 20, p=0.47156 b-rank test for bits 14 to 21, p=0.31363 b-rank test for bits 15 to 22, p=0.82365 b-rank test for bits 16 to 23, p=0.12576 b-rank test for bits 17 to 24, p=0.35087 b-rank test for bits 18 to 25, p=0.06605 b-rank test for bits 19 to 26, p=0.00454 b-rank test for bits 20 to 27, p=0.18765 b-rank test for bits 21 to 28, p=0.76355 b-rank test for bits 22 to 29, p=0.47545 b-rank test for bits 23 to 30, p=0.17931 b-rank test for bits 24 to 31, p=0.26406 b-rank test for bits 25 to 32, p=0.39361 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 = 0.973895 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-27_20:31 (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 141565 -0.80 0.210551 2 141537 -0.87 0.192169 3 142239 0.77 0.779426 4 142283 0.87 0.808685 5 141894 -0.04 0.485714 6 141515 -0.92 0.178439 7 141970 0.14 0.556362 8 141202 -1.65 0.049202 9 142057 0.35 0.634962 10 142453 1.27 0.898003 11 141480 -1.00 0.157905 12 141691 -0.51 0.304985 13 141806 -0.24 0.404613 14 142472 1.31 0.905686 15 141840 -0.16 0.435658 16 142218 0.72 0.764604 17 142088 0.42 0.661827 18 142449 1.26 0.896330 19 142636 1.70 0.955230 20 142098 0.44 0.670328 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-06-27_20:31 Bits used No. missing words z-score p-value 23 to 32 141952 0.1471 0.558488 22 to 31 141798 -0.3839 0.350528 21 to 30 141918 0.0299 0.511925 20 to 29 142137 0.7851 0.783793 19 to 28 141753 -0.5391 0.294920 18 to 27 142218 1.0644 0.856422 17 to 26 141216 -2.3908 0.008406 16 to 25 141544 -1.2598 0.103878 15 to 24 141942 0.1127 0.544848 14 to 23 142162 0.8713 0.808198 13 to 22 141801 -0.3736 0.354369 12 to 21 141708 -0.6942 0.243765 11 to 20 142010 0.3471 0.635756 10 to 19 141875 -0.1184 0.452884 9 to 18 141627 -0.9736 0.165140 8 to 17 141586 -1.1149 0.132440 7 to 16 142028 0.4092 0.658806 6 to 15 141738 -0.5908 0.277330 5 to 14 141933 0.0816 0.532526 4 to 13 141900 -0.0322 0.487167 3 to 12 141730 -0.6184 0.268163 2 to 11 142573 2.2885 0.988946 1 to 10 142002 0.3196 0.625346 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-06-27_20:31 Bits used No. missing words z-score p-value 28 to 32 142239 1.1175 0.868115 27 to 31 142014 0.3548 0.638635 26 to 30 141736 -0.5876 0.278414 25 to 29 141967 0.1955 0.577496 24 to 28 141851 -0.1977 0.421629 23 to 27 142023 0.3853 0.650001 22 to 26 141821 -0.2994 0.382308 21 to 25 142176 0.9040 0.816993 20 to 24 142326 1.4124 0.921090 19 to 23 142028 0.4023 0.656258 18 to 22 140973 -3.1740 0.000752 17 to 21 141341 -1.9265 0.027018 16 to 20 142106 0.6667 0.747511 15 to 19 142470 1.9006 0.971321 14 to 18 141732 -0.6011 0.273881 13 to 17 141967 0.1955 0.577496 12 to 16 141737 -0.5842 0.279553 11 to 15 141649 -0.8825 0.188760 10 to 14 142551 2.1752 0.985191 9 to 13 142148 0.8091 0.790757 8 to 12 141900 -0.0316 0.487385 7 to 11 141538 -1.2587 0.104061 6 to 10 141461 -1.5198 0.064285 5 to 9 142190 0.9514 0.829305 4 to 8 141717 -0.6520 0.257212 3 to 7 141573 -1.1401 0.127122 2 to 6 141984 0.2531 0.599912 1 to 5 142160 0.8497 0.802262 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-06-27_20:31 Bits used No. missing words z-score p-value 31 to 32 141546 -1.0718 0.141912 30 to 31 141818 -0.2694 0.393807 29 to 30 141317 -1.7473 0.040294 28 to 29 141613 -0.8741 0.191024 27 to 28 141438 -1.3904 0.082211 26 to 27 141941 0.0934 0.537216 25 to 26 142150 0.7099 0.761130 24 to 25 141640 -0.7945 0.213457 23 to 24 142057 0.4356 0.668438 22 to 23 141615 -0.8682 0.192634 21 to 22 142130 0.6509 0.742459 20 to 21 141934 0.0728 0.529007 19 to 20 142095 0.5477 0.708051 18 to 19 141661 -0.7325 0.231921 17 to 18 141847 -0.1839 0.427060 16 to 17 142062 0.4504 0.673772 15 to 16 141775 -0.3963 0.345959 14 to 15 141218 -2.0393 0.020709 13 to 14 141148 -2.2458 0.012358 12 to 13 142093 0.5418 0.706022 11 to 12 141753 -0.4612 0.322345 10 to 11 141823 -0.2547 0.399493 9 to 10 141740 -0.4995 0.308714 8 to 9 141303 -1.7886 0.036841 7 to 8 141872 -0.1101 0.456158 6 to 7 142014 0.3088 0.621248 5 to 6 141472 -1.2901 0.098515 4 to 5 141765 -0.4258 0.335144 3 to 4 142735 2.4356 0.992567 2 to 3 141995 0.2527 0.599755 1 to 2 141255 -1.9302 0.026792 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-27_20:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2470.05 -0.423 0.335968 Test results for specific bytes for dh-ranFile-2018-06-27_20:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2544.98 0.636 0.737654 2 to 9 2461.31 -0.547 0.292142 3 to 10 2455.00 -0.636 0.262276 4 to 11 2461.99 -0.537 0.295470 5 to 12 2525.09 0.355 0.638652 6 to 13 2525.21 0.356 0.639260 7 to 14 2495.82 -0.059 0.476443 8 to 15 2467.38 -0.461 0.322306 9 to 16 2501.21 0.017 0.506843 10 to 17 2458.45 -0.588 0.278388 11 to 18 2463.39 -0.518 0.302317 12 to 19 2576.19 1.077 0.859356 13 to 20 2591.62 1.296 0.902465 14 to 21 2526.80 0.379 0.647673 15 to 22 2599.51 1.407 0.920333 16 to 23 2590.57 1.281 0.899876 17 to 24 2467.26 -0.463 0.321658 18 to 25 2340.22 -2.260 0.011921 19 to 26 2644.56 2.044 0.979545 20 to 27 2609.14 1.543 0.938636 21 to 28 2464.25 -0.506 0.306582 22 to 29 2519.85 0.281 0.610534 23 to 30 2455.84 -0.624 0.266166 24 to 31 2466.88 -0.468 0.319762 25 to 32 2380.93 -1.684 0.046100 CDPARK for dh-ranFile-2018-06-27_20:31: 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 3474 -2.2374 0.012629 3493 -1.3699 0.085365 3525 0.0913 0.536383 3527 0.1826 0.572463 3561 1.7352 0.958644 3519 -0.1826 0.427537 3518 -0.2283 0.409702 3526 0.1370 0.554479 3537 0.6393 0.738676 3522 -0.0457 0.481790 Square side=100, avg. no. parked=3520.20 sample std.=22.21 p-value of the KSTEST for those 10 p-values: 0.670997 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-27_20:31 0.3206,0.3589,0.0452,0.9037,0.1540,0.0053,0.1953,0.2914,0.2249,0.6085, The KS test for those 10 p-values: 0.049264 The 3DSPHERES test for dh-ranFile-2018-06-27_20:31 sample no r^3 equiv. uni. 1 5.299 0.161926 2 53.848 0.833864 3 33.232 0.669695 4 38.085 0.719030 5 1.986 0.064056 6 2.461 0.078745 7 80.253 0.931100 8 4.471 0.138462 9 154.991 0.994295 10 30.511 0.638339 11 28.390 0.611845 12 75.736 0.919904 13 38.550 0.723352 14 12.065 0.331141 15 17.326 0.438710 16 31.971 0.655511 17 11.122 0.309767 18 20.313 0.491906 19 13.876 0.370323 20 7.039 0.209143 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.985397 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-27_20:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -1.6 -1.1 -0.8 1.2 -0.2 -0.0 -1.1 1.1 -1.7 -0.2 0.0 1.8 -0.2 0.9 0.3 0.1 -2.1 1.6 -0.6 -0.6 0.8 -0.0 -1.4 0.1 0.1 0.2 1.1 -1.7 0.8 1.5 -1.0 1.8 -1.0 2.0 -2.1 -1.4 0.5 -0.8 -1.8 0.1 -1.0 0.8 Chi-square with 42 degrees of freedom:55.283775 z-score=1.449379, p-value=0.917862 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-06-27_20:31 Test no p-value 1 0.964425 2 0.541388 3 0.339852 4 0.641393 5 0.101524 6 0.331345 7 0.038108 8 0.793981 9 0.299488 10 0.114008 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.618673 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-27_20:31: (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 66767 0.15 66700 0.02 3 25000.00 24970 0.04 25125 0.62 4 6666.67 6640 0.11 6519 3.27 5 1388.89 1366 0.38 1393 0.01 6 238.10 218 1.70 226 0.61 7 34.72 33 0.09 34 0.01 8 4.96 5 0.00 2 1.77 p=0.12625 p=0.61175 Number of rngs required: 687356, p-value: 0.112 RESULTS OF CRAPS TEST for dh-ranFile-2018-06-27_20:31 No. of wins: Observed Expected 98498 98585.9 z-score=-0.393, pvalue=0.34718 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66738 66666.7 0.076 0.076 2 37934 37654.3 2.077 2.154 3 26884 26954.7 0.186 2.339 4 19246 19313.5 0.236 2.575 5 13683 13851.4 2.048 4.623 6 9981 9943.5 0.141 4.764 7 7232 7145.0 1.059 5.823 8 5062 5139.1 1.156 6.978 9 3616 3699.9 1.901 8.879 10 2652 2666.3 0.077 8.956 11 1984 1923.3 1.914 10.870 12 1351 1388.7 1.026 11.896 13 1022 1003.7 0.333 12.229 14 730 726.1 0.021 12.249 15 540 525.8 0.382 12.631 16 350 381.2 2.546 15.177 17 282 276.5 0.108 15.284 18 207 200.8 0.190 15.474 19 130 146.0 1.750 17.224 20 81 106.2 5.986 23.210 21 295 287.1 0.217 23.427 Chisq= 23.43 for 20 degrees of freedom, p= 0.73167 SUMMARY of craptest p-value for no. of wins: 0.347176 p-value for throws/game: 0.731671 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-27_20:31 No. of wins: Observed Expected 98378 98585.9 z-score=-0.930, pvalue=0.17627 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66427 66666.7 0.862 0.862 2 37418 37654.3 1.483 2.345 3 27234 26954.7 2.893 5.238 4 19495 19313.5 1.706 6.945 5 13602 13851.4 4.491 11.436 6 10050 9943.5 1.140 12.576 7 7181 7145.0 0.181 12.757 8 5204 5139.1 0.820 13.577 9 3692 3699.9 0.017 13.594 10 2664 2666.3 0.002 13.596 11 1969 1923.3 1.084 14.680 12 1352 1388.7 0.972 15.652 13 1022 1003.7 0.333 15.985 14 714 726.1 0.203 16.188 15 550 525.8 1.110 17.299 16 405 381.2 1.492 18.791 17 274 276.5 0.023 18.814 18 173 200.8 3.857 22.671 19 173 146.0 4.999 27.670 20 118 106.2 1.308 28.978 21 283 287.1 0.059 29.037 Chisq= 29.04 for 20 degrees of freedom, p= 0.91296 SUMMARY of craptest p-value for no. of wins: 0.176272 p-value for throws/game: 0.912962 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0008,0.0045,0.0053,0.0084,0.0119,0.0124,0.0126,0.0207,0.0268,0.0270, 0.0272,0.0368,0.0381,0.0403,0.0452,0.0461,0.0492,0.0493,0.0618,0.0641, 0.0643,0.0661,0.0711,0.0787,0.0822,0.0854,0.0889,0.0930,0.0985,0.1015, 0.1039,0.1041,0.1071,0.1118,0.1140,0.1257,0.1258,0.1263,0.1271,0.1324, 0.1385,0.1408,0.1419,0.1422,0.1434,0.1540,0.1576,0.1579,0.1619,0.1651, 0.1763,0.1784,0.1793,0.1801,0.1876,0.1888,0.1910,0.1922,0.1926,0.1953, 0.2091,0.2106,0.2135,0.2150,0.2181,0.2249,0.2288,0.2319,0.2353,0.2415, 0.2422,0.2438,0.2572,0.2623,0.2641,0.2662,0.2682,0.2739,0.2773,0.2784, 0.2784,0.2796,0.2852,0.2914,0.2921,0.2949,0.2955,0.2995,0.3023,0.3050, 0.3066,0.3087,0.3098,0.3136,0.3142,0.3198,0.3206,0.3211,0.3217,0.3223, 0.3223,0.3255,0.3311,0.3313,0.3351,0.3360,0.3392,0.3399,0.3460,0.3472, 0.3505,0.3509,0.3544,0.3589,0.3703,0.3823,0.3896,0.3936,0.3938,0.3995, 0.4046,0.4061,0.4097,0.4121,0.4216,0.4230,0.4271,0.4275,0.4357,0.4387, 0.4529,0.4562,0.4586,0.4642,0.4716,0.4754,0.4755,0.4764,0.4818,0.4857, 0.4872,0.4874,0.4919,0.5068,0.5119,0.5146,0.5290,0.5325,0.5364,0.5372, 0.5414,0.5420,0.5448,0.5545,0.5564,0.5585,0.5664,0.5725,0.5775,0.5775, 0.5813,0.5953,0.5996,0.5998,0.5999,0.6013,0.6085,0.6105,0.6117,0.6118, 0.6187,0.6212,0.6253,0.6350,0.6352,0.6358,0.6383,0.6386,0.6387,0.6393, 0.6414,0.6477,0.6500,0.6521,0.6547,0.6555,0.6563,0.6588,0.6618,0.6684, 0.6697,0.6703,0.6710,0.6738,0.7060,0.7081,0.7190,0.7234,0.7317,0.7320, 0.7329,0.7377,0.7387,0.7425,0.7475,0.7611,0.7635,0.7646,0.7727,0.7753, 0.7779,0.7794,0.7838,0.7908,0.7940,0.8023,0.8082,0.8087,0.8088,0.8170, 0.8189,0.8225,0.8237,0.8293,0.8339,0.8359,0.8365,0.8462,0.8564,0.8594, 0.8681,0.8756,0.8766,0.8766,0.8791,0.8834,0.8963,0.8980,0.8984,0.8999, 0.9025,0.9037,0.9057,0.9110,0.9129,0.9130,0.9179,0.9199,0.9203,0.9211, 0.9239,0.9243,0.9311,0.9351,0.9386,0.9552,0.9586,0.9587,0.9600,0.9644, 0.9700,0.9713,0.9739,0.9795,0.9852,0.9854,0.9889,0.9926,0.9943, Overall p-value after applying KStest on 269 p-values = 0.469785 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.