RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-06-04_19:31 (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 12.0739 0.204356 2 to 25 15.74 17.1119 0.553190 3 to 26 15.32 22.1551 0.821171 4 to 27 15.77 19.4780 0.698204 5 to 28 15.47 25.0416 0.906219 6 to 29 15.76 27.4539 0.948262 7 to 30 15.83 16.8381 0.534614 8 to 31 15.46 21.7769 0.806548 9 to 32 15.25 39.4839 0.998470 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.026687 Tough bday spacings test for dh-ranFile-2015-06-04_19:31: 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 17 40 88 102 95 66 46 23 14 5 4 (O-E)^2/E 6.7 0.3 3.0 0.2 0.1 1.9 0.7 1.5 0.1 0.4 0.0 Birthday Spacings: Sum(O-E)^2/E= 14.844, p= 0.862 RESULTS OF GCD FOR dh-ranFile-2015-06-04_19:31 Euclid's algorithm: p-value, steps to gcd: 0.191038 p-value, dist. of gcd's: 0.478230 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-06-04_19:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.283 0.197 0.721 0.670 0.184 0.301 0.890 0.576 Bits 8 to 15---> 0.285 0.410 0.296 0.217 0.807 0.646 0.285 0.522 Bits 16 to 23---> 0.021 0.627 0.228 0.882 0.577 0.015 0.706 0.039 Bits 24 to 31---> 0.114 0.875 0.018 0.608 0.654 0.475 0.546 0.424 KS test for the above 32 p values: 0.712 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-06-04_19:31, p-values for 5 runs: 0.5677, 0.1162, 0.0003, 0.0805, 0.0106 Rank test for binary matrices (31x31) for dh-ranFile-2015-06-04_19:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 212 211.4 0.002 0.002 r= 29 5202 5134.0 0.900 0.902 r= 30 23096 23103.0 0.002 0.904 r= 31 11490 11551.5 0.328 1.232 chi-square = 1.232 with df = 3; p-value = 0.255 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-06-04_19:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 183 211.4 3.820 3.820 r= 30 5028 5134.0 2.189 6.009 r= 31 23276 23103.0 1.295 7.304 r= 32 11513 11551.5 0.128 7.432 chi-square = 7.432 with df = 3; p-value = 0.941 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-06-04_19:31 b-rank test for bits 1 to 8, p=0.98699 b-rank test for bits 2 to 9, p=0.81733 b-rank test for bits 3 to 10, p=0.15923 b-rank test for bits 4 to 11, p=0.21987 b-rank test for bits 5 to 12, p=0.76022 b-rank test for bits 6 to 13, p=0.10357 b-rank test for bits 7 to 14, p=0.06718 b-rank test for bits 8 to 15, p=0.25977 b-rank test for bits 9 to 16, p=0.60476 b-rank test for bits 10 to 17, p=0.22253 b-rank test for bits 11 to 18, p=0.97096 b-rank test for bits 12 to 19, p=0.95072 b-rank test for bits 13 to 20, p=0.15037 b-rank test for bits 14 to 21, p=0.06696 b-rank test for bits 15 to 22, p=0.42579 b-rank test for bits 16 to 23, p=0.76978 b-rank test for bits 17 to 24, p=0.90687 b-rank test for bits 18 to 25, p=0.70514 b-rank test for bits 19 to 26, p=0.50477 b-rank test for bits 20 to 27, p=0.60467 b-rank test for bits 21 to 28, p=0.26787 b-rank test for bits 22 to 29, p=0.04005 b-rank test for bits 23 to 30, p=0.31185 b-rank test for bits 24 to 31, p=0.76209 b-rank test for bits 25 to 32, p=0.86873 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 = 0.695269 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-06-04_19:31 (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 141943 0.08 0.531352 3 142267 0.84 0.798332 4 142061 0.35 0.638469 5 141257 -1.52 0.063737 6 142615 1.65 0.950402 7 141781 -0.30 0.382151 8 141684 -0.53 0.299280 9 141766 -0.33 0.368857 10 141877 -0.08 0.469894 11 141970 0.14 0.556362 12 142004 0.22 0.587528 13 141837 -0.17 0.432900 14 141690 -0.51 0.304167 15 141762 -0.34 0.365337 16 141368 -1.26 0.102973 17 141377 -1.24 0.106794 18 141703 -0.48 0.314875 19 142455 1.27 0.898833 20 142201 0.68 0.752214 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-06-04_19:31 Bits used No. missing words z-score p-value 23 to 32 141953 0.1506 0.559849 22 to 31 141676 -0.8046 0.210529 21 to 30 141743 -0.5736 0.283136 20 to 29 141413 -1.7115 0.043496 19 to 28 141954 0.1540 0.561209 18 to 27 141922 0.0437 0.517424 17 to 26 141863 -0.1598 0.436536 16 to 25 142094 0.6368 0.737870 15 to 24 142226 1.0920 0.862576 14 to 23 141998 0.3058 0.620106 13 to 22 141801 -0.3736 0.354369 12 to 21 141753 -0.5391 0.294920 11 to 20 142370 1.5885 0.943915 10 to 19 142145 0.8127 0.791792 9 to 18 141557 -1.2149 0.112196 8 to 17 141893 -0.0563 0.477547 7 to 16 141439 -1.6218 0.052420 6 to 15 141887 -0.0770 0.469312 5 to 14 141999 0.3092 0.621418 4 to 13 141627 -0.9736 0.165140 3 to 12 141435 -1.6356 0.050960 2 to 11 142112 0.6989 0.757681 1 to 10 141492 -1.4391 0.075066 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-06-04_19:31 Bits used No. missing words z-score p-value 28 to 32 141893 -0.0554 0.477928 27 to 31 141385 -1.7774 0.037752 26 to 30 141737 -0.5842 0.279553 25 to 29 142190 0.9514 0.829305 24 to 28 141699 -0.7130 0.237928 23 to 27 142422 1.7379 0.958883 22 to 26 141808 -0.3435 0.365614 21 to 25 142151 0.8192 0.793670 20 to 24 142574 2.2531 0.987874 19 to 23 141741 -0.5706 0.284132 18 to 22 141390 -1.7604 0.039167 17 to 21 142444 1.8124 0.965041 16 to 20 142331 1.4294 0.923554 15 to 19 142058 0.5040 0.692857 14 to 18 142167 0.8735 0.808793 13 to 17 141985 0.2565 0.601221 12 to 16 141738 -0.5808 0.280695 11 to 15 141755 -0.5232 0.300434 10 to 14 142028 0.4023 0.656258 9 to 13 141587 -1.0926 0.137275 8 to 12 141688 -0.7503 0.226546 7 to 11 142001 0.3107 0.622003 6 to 10 141441 -1.5876 0.056193 5 to 9 141660 -0.8452 0.199003 4 to 8 141421 -1.6554 0.048926 3 to 7 141684 -0.7638 0.222484 2 to 6 142246 1.1413 0.873118 1 to 5 141959 0.1684 0.566855 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-06-04_19:31 Bits used No. missing words z-score p-value 31 to 32 141907 -0.0069 0.497258 30 to 31 142358 1.3235 0.907167 29 to 30 141403 -1.4936 0.067640 28 to 29 141861 -0.1426 0.443316 27 to 28 141714 -0.5762 0.282242 26 to 27 141661 -0.7325 0.231921 25 to 26 141850 -0.1750 0.430534 24 to 25 141862 -0.1396 0.444482 23 to 24 141969 0.1760 0.569860 22 to 23 141849 -0.1780 0.429375 21 to 22 141299 -1.8004 0.035900 20 to 21 141539 -1.0924 0.137325 19 to 20 141320 -1.7384 0.041067 18 to 19 142129 0.6480 0.741506 17 to 18 141970 0.1790 0.571018 16 to 17 141882 -0.0806 0.467872 15 to 16 141800 -0.3225 0.373534 14 to 15 141632 -0.8181 0.206655 13 to 14 141878 -0.0924 0.463183 12 to 13 141915 0.0167 0.506672 11 to 12 141633 -0.8151 0.207498 10 to 11 141863 -0.1367 0.445647 9 to 10 141828 -0.2399 0.405199 8 to 9 141972 0.1849 0.573333 7 to 8 141960 0.1495 0.559408 6 to 7 141311 -1.7650 0.038783 5 to 6 142144 0.6922 0.755607 4 to 5 142121 0.6244 0.733816 3 to 4 141935 0.0757 0.530180 2 to 3 141956 0.1377 0.554749 1 to 2 141473 -1.2871 0.099028 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-06-04_19:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2557.29 0.810 0.791102 Test results for specific bytes for dh-ranFile-2015-06-04_19:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2591.05 1.288 0.901059 2 to 9 2582.20 1.163 0.877487 3 to 10 2623.44 1.746 0.959564 4 to 11 2491.16 -0.125 0.450252 5 to 12 2564.91 0.918 0.820686 6 to 13 2624.12 1.755 0.960398 7 to 14 2492.09 -0.112 0.455465 8 to 15 2564.14 0.907 0.817832 9 to 16 2424.78 -1.064 0.143715 10 to 17 2424.39 -1.069 0.142454 11 to 18 2422.68 -1.093 0.137096 12 to 19 2534.93 0.494 0.689348 13 to 20 2432.45 -0.955 0.169722 14 to 21 2533.73 0.477 0.683341 15 to 22 2526.50 0.375 0.646091 16 to 23 2501.60 0.023 0.509052 17 to 24 2695.43 2.764 0.997143 18 to 25 2568.61 0.970 0.834038 19 to 26 2512.70 0.180 0.571254 20 to 27 2505.40 0.076 0.530453 21 to 28 2464.13 -0.507 0.305958 22 to 29 2549.61 0.702 0.758533 23 to 30 2475.81 -0.342 0.366151 24 to 31 2593.72 1.325 0.907475 25 to 32 2515.19 0.215 0.585058 CDPARK for dh-ranFile-2015-06-04_19:31: 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 3508 -0.6849 0.246694 3522 -0.0457 0.481790 3526 0.1370 0.554479 3520 -0.1370 0.445521 3520 -0.1370 0.445521 3523 0.0000 0.500000 3551 1.2785 0.899470 3514 -0.4110 0.340551 3541 0.8219 0.794438 3552 1.3242 0.907282 Square side=100, avg. no. parked=3527.70 sample std.=14.36 p-value of the KSTEST for those 10 p-values: 0.440929 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-06-04_19:31 0.9712,0.6557,0.6653,0.3115,0.7362,0.3907,0.9170,0.3562,0.5515,0.8006, The KS test for those 10 p-values: 0.226785 The 3DSPHERES test for dh-ranFile-2015-06-04_19:31 sample no r^3 equiv. uni. 1 26.387 0.585041 2 8.726 0.252396 3 24.106 0.552253 4 68.808 0.899099 5 22.733 0.531287 6 15.068 0.394838 7 53.261 0.830577 8 7.410 0.218865 9 6.879 0.204899 10 27.564 0.601008 11 47.590 0.795327 12 95.685 0.958808 13 21.656 0.514153 14 0.696 0.022933 15 1.558 0.050612 16 52.255 0.824798 17 60.491 0.866862 18 22.431 0.526548 19 69.153 0.900250 20 136.397 0.989397 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.349870 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-06-04_19:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 -1.6 1.1 -0.7 -0.6 -0.4 0.6 0.7 -0.5 -1.2 -1.1 0.6 0.5 -0.3 0.0 1.4 1.3 -1.5 -1.2 0.2 -0.3 0.0 -1.7 1.7 0.7 -0.7 1.9 0.1 1.3 0.6 -0.9 -1.6 0.7 -1.2 0.6 -0.7 -1.4 -0.4 -0.8 -1.3 0.9 1.0 -0.1 Chi-square with 42 degrees of freedom:41.884355 z-score=-0.012618, p-value=0.524005 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-06-04_19:31 Test no p-value 1 0.004999 2 0.817994 3 0.437553 4 0.658034 5 0.001168 6 0.054108 7 0.106655 8 0.554241 9 0.035881 10 0.186273 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.004308 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-06-04_19:31: (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 66631 0.02 66684 0.00 3 25000.00 25038 0.06 25055 0.12 4 6666.67 6674 0.01 6633 0.17 5 1388.89 1386 0.01 1345 1.39 6 238.10 233 0.11 233 0.11 7 34.72 32 0.21 43 1.97 8 4.96 5 0.00 6 0.22 p=0.00126 p=0.32119 Number of rngs required: 687449, p-value: 0.134 RESULTS OF CRAPS TEST for dh-ranFile-2015-06-04_19:31 No. of wins: Observed Expected 98789 98585.9 z-score= 0.909, pvalue=0.81821 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66833 66666.7 0.415 0.415 2 37374 37654.3 2.087 2.502 3 26998 26954.7 0.069 2.571 4 19550 19313.5 2.897 5.468 5 13770 13851.4 0.479 5.947 6 10002 9943.5 0.344 6.291 7 7138 7145.0 0.007 6.297 8 5151 5139.1 0.028 6.325 9 3626 3699.9 1.475 7.800 10 2686 2666.3 0.146 7.945 11 1915 1923.3 0.036 7.981 12 1350 1388.7 1.081 9.062 13 972 1003.7 1.002 10.064 14 782 726.1 4.297 14.361 15 513 525.8 0.313 14.675 16 323 381.2 8.872 23.546 17 273 276.5 0.045 23.592 18 203 200.8 0.023 23.615 19 147 146.0 0.007 23.622 20 100 106.2 0.364 23.986 21 294 287.1 0.165 24.151 Chisq= 24.15 for 20 degrees of freedom, p= 0.76415 SUMMARY of craptest p-value for no. of wins: 0.818211 p-value for throws/game: 0.764147 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-06-04_19:31 No. of wins: Observed Expected 98564 98585.9 z-score=-0.098, pvalue=0.46106 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66461 66666.7 0.634 0.634 2 37925 37654.3 1.946 2.580 3 26954 26954.7 0.000 2.580 4 19223 19313.5 0.424 3.004 5 13946 13851.4 0.646 3.650 6 10069 9943.5 1.583 5.233 7 7082 7145.0 0.556 5.789 8 5201 5139.1 0.746 6.535 9 3621 3699.9 1.681 8.216 10 2658 2666.3 0.026 8.242 11 1897 1923.3 0.360 8.602 12 1340 1388.7 1.711 10.313 13 974 1003.7 0.880 11.193 14 708 726.1 0.453 11.646 15 496 525.8 1.693 13.339 16 386 381.2 0.062 13.400 17 286 276.5 0.324 13.724 18 219 200.8 1.644 15.368 19 130 146.0 1.750 17.118 20 101 106.2 0.256 17.374 21 323 287.1 4.485 21.860 Chisq= 21.86 for 20 degrees of freedom, p= 0.65182 SUMMARY of craptest p-value for no. of wins: 0.461060 p-value for throws/game: 0.651817 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0003,0.0012,0.0013,0.0043,0.0050,0.0106,0.0146,0.0184,0.0213,0.0229, 0.0267,0.0359,0.0359,0.0378,0.0386,0.0388,0.0392,0.0400,0.0411,0.0435, 0.0489,0.0506,0.0510,0.0524,0.0541,0.0562,0.0637,0.0670,0.0672,0.0676, 0.0751,0.0805,0.0990,0.1030,0.1036,0.1067,0.1068,0.1122,0.1139,0.1162, 0.1341,0.1371,0.1373,0.1373,0.1425,0.1437,0.1504,0.1592,0.1651,0.1697, 0.1838,0.1846,0.1863,0.1910,0.1973,0.1990,0.2044,0.2049,0.2067,0.2075, 0.2105,0.2172,0.2189,0.2199,0.2225,0.2225,0.2265,0.2268,0.2277,0.2319, 0.2379,0.2467,0.2524,0.2546,0.2598,0.2679,0.2796,0.2807,0.2822,0.2831, 0.2834,0.2841,0.2846,0.2847,0.2949,0.2964,0.2993,0.3004,0.3010,0.3042, 0.3060,0.3115,0.3119,0.3149,0.3212,0.3406,0.3499,0.3544,0.3562,0.3653, 0.3656,0.3662,0.3689,0.3735,0.3822,0.3907,0.3948,0.4052,0.4097,0.4238, 0.4258,0.4294,0.4305,0.4329,0.4365,0.4376,0.4409,0.4433,0.4445,0.4455, 0.4455,0.4456,0.4503,0.4555,0.4611,0.4632,0.4679,0.4693,0.4699,0.4751, 0.4775,0.4779,0.4782,0.4818,0.4973,0.5000,0.5048,0.5067,0.5091,0.5142, 0.5174,0.5215,0.5240,0.5265,0.5302,0.5305,0.5313,0.5314,0.5346,0.5464, 0.5515,0.5523,0.5532,0.5542,0.5545,0.5547,0.5564,0.5594,0.5598,0.5612, 0.5669,0.5677,0.5699,0.5710,0.5713,0.5733,0.5756,0.5774,0.5850,0.5851, 0.5875,0.6010,0.6012,0.6047,0.6048,0.6085,0.6201,0.6214,0.6220,0.6269, 0.6385,0.6461,0.6462,0.6518,0.6541,0.6557,0.6563,0.6580,0.6653,0.6701, 0.6833,0.6893,0.6929,0.6953,0.6982,0.7051,0.7060,0.7124,0.7208,0.7338, 0.7362,0.7379,0.7415,0.7522,0.7556,0.7577,0.7585,0.7602,0.7621,0.7641, 0.7698,0.7911,0.7918,0.7937,0.7944,0.7953,0.7983,0.8006,0.8065,0.8068, 0.8088,0.8173,0.8178,0.8180,0.8182,0.8207,0.8212,0.8248,0.8293,0.8306, 0.8340,0.8621,0.8626,0.8669,0.8687,0.8731,0.8752,0.8775,0.8821,0.8896, 0.8988,0.8991,0.8995,0.9002,0.9011,0.9062,0.9069,0.9072,0.9073,0.9075, 0.9170,0.9236,0.9407,0.9439,0.9483,0.9504,0.9507,0.9588,0.9589,0.9596, 0.9604,0.9650,0.9710,0.9712,0.9870,0.9879,0.9894,0.9971,0.9985, Overall p-value after applying KStest on 269 p-values = 0.421486 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.