RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-09-01_14:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.84 22.6958 0.840583 2 to 25 16.02 17.8883 0.604083 3 to 26 15.48 17.4408 0.575091 4 to 27 15.83 20.4150 0.746445 5 to 28 15.86 24.5595 0.894988 6 to 29 15.71 15.4157 0.434433 7 to 30 15.82 18.3683 0.634028 8 to 31 16.03 22.7949 0.843952 9 to 32 15.79 5.7422 0.005243 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.200042 Tough bday spacings test for dh-ranFile-2016-09-01_14:31: 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 37 68 93 106 71 56 31 14 9 6 (O-E)^2/E 0.0 0.0 0.4 0.2 0.7 0.7 0.3 0.1 0.1 0.9 0.9 Birthday Spacings: Sum(O-E)^2/E= 4.146, p= 0.059 RESULTS OF GCD FOR dh-ranFile-2016-09-01_14:31 Euclid's algorithm: p-value, steps to gcd: 0.247499 p-value, dist. of gcd's: 0.175421 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-09-01_14:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.637 0.492 0.695 0.995 0.075 0.523 0.700 0.530 Bits 8 to 15---> 0.441 0.308 0.940 0.711 0.430 0.125 0.297 0.954 Bits 16 to 23---> 0.061 0.008 0.254 0.269 0.007 0.674 0.260 0.547 Bits 24 to 31---> 0.588 0.156 0.221 0.500 0.839 0.562 0.274 0.016 KS test for the above 32 p values: 0.701 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-09-01_14:31, p-values for 5 runs: 0.2676, 0.0047, 0.4912, 0.3510, 0.0401 Rank test for binary matrices (31x31) for dh-ranFile-2016-09-01_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 196 211.4 1.124 1.124 r= 29 5088 5134.0 0.412 1.537 r= 30 23082 23103.0 0.019 1.556 r= 31 11634 11551.5 0.589 2.145 chi-square = 2.145 with df = 3; p-value = 0.457 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-09-01_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 201 211.4 0.513 0.513 r= 30 5115 5134.0 0.070 0.584 r= 31 23197 23103.0 0.382 0.966 r= 32 11487 11551.5 0.360 1.326 chi-square = 1.326 with df = 3; p-value = 0.277 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-09-01_14:31 b-rank test for bits 1 to 8, p=0.44099 b-rank test for bits 2 to 9, p=0.94124 b-rank test for bits 3 to 10, p=0.07179 b-rank test for bits 4 to 11, p=0.10078 b-rank test for bits 5 to 12, p=0.43523 b-rank test for bits 6 to 13, p=0.85403 b-rank test for bits 7 to 14, p=0.48231 b-rank test for bits 8 to 15, p=0.38031 b-rank test for bits 9 to 16, p=0.71162 b-rank test for bits 10 to 17, p=0.21541 b-rank test for bits 11 to 18, p=0.29707 b-rank test for bits 12 to 19, p=0.77259 b-rank test for bits 13 to 20, p=0.48812 b-rank test for bits 14 to 21, p=0.08666 b-rank test for bits 15 to 22, p=0.41311 b-rank test for bits 16 to 23, p=0.72147 b-rank test for bits 17 to 24, p=0.34225 b-rank test for bits 18 to 25, p=0.58514 b-rank test for bits 19 to 26, p=0.51531 b-rank test for bits 20 to 27, p=0.24654 b-rank test for bits 21 to 28, p=0.48723 b-rank test for bits 22 to 29, p=0.62721 b-rank test for bits 23 to 30, p=0.73869 b-rank test for bits 24 to 31, p=0.94082 b-rank test for bits 25 to 32, p=0.96354 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 = 0.857470 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-09-01_14:31 (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 142012 0.24 0.594790 2 142431 1.22 0.888550 3 141618 -0.68 0.248038 4 142174 0.62 0.731840 5 141894 -0.04 0.485714 6 142344 1.02 0.845086 7 141859 -0.12 0.453195 8 142386 1.11 0.867299 9 141895 -0.03 0.486645 10 142065 0.36 0.641965 11 141807 -0.24 0.405518 12 141567 -0.80 0.211903 13 141299 -1.43 0.076934 14 142198 0.67 0.749991 15 142102 0.45 0.673704 16 141724 -0.43 0.332502 17 142635 1.70 0.955009 18 141522 -0.90 0.182739 19 141706 -0.48 0.317369 20 142510 1.40 0.919756 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-09-01_14:31 Bits used No. missing words z-score p-value 23 to 32 142563 2.2540 0.987903 22 to 31 141900 -0.0322 0.487167 21 to 30 142198 0.9954 0.840233 20 to 29 142145 0.8127 0.791792 19 to 28 141988 0.2713 0.606911 18 to 27 141542 -1.2667 0.102639 17 to 26 141389 -1.7942 0.036387 16 to 25 141902 -0.0253 0.489918 15 to 24 142283 1.2885 0.901217 14 to 23 141553 -1.2287 0.109588 13 to 22 142284 1.2920 0.901815 12 to 21 141610 -1.0322 0.150996 11 to 20 142053 0.4954 0.689846 10 to 19 141590 -1.1011 0.135418 9 to 18 141765 -0.4977 0.309351 8 to 17 141624 -0.9839 0.162583 7 to 16 142333 1.4609 0.927983 6 to 15 141678 -0.7977 0.212525 5 to 14 141230 -2.3425 0.009577 4 to 13 141511 -1.3736 0.084790 3 to 12 141872 -0.1287 0.448788 2 to 11 141994 0.2920 0.614844 1 to 10 142160 0.8644 0.806310 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-09-01_14:31 Bits used No. missing words z-score p-value 28 to 32 142168 0.8768 0.809715 27 to 31 142518 2.0633 0.980457 26 to 30 142089 0.6091 0.728755 25 to 29 141902 -0.0248 0.490088 24 to 28 141827 -0.2791 0.390090 23 to 27 142124 0.7277 0.766600 22 to 26 142084 0.5921 0.723109 21 to 25 142319 1.3887 0.917540 20 to 24 142346 1.4802 0.930595 19 to 23 141459 -1.5265 0.063437 18 to 22 141589 -1.0859 0.138770 17 to 21 141912 0.0091 0.503611 16 to 20 142130 0.7480 0.772780 15 to 19 141947 0.1277 0.550805 14 to 18 141799 -0.3740 0.354202 13 to 17 141737 -0.5842 0.279553 12 to 16 141814 -0.3232 0.373290 11 to 15 141731 -0.6045 0.272753 10 to 14 142028 0.4023 0.656258 9 to 13 141862 -0.1604 0.436267 8 to 12 141882 -0.0926 0.463093 7 to 11 142380 1.5955 0.944699 6 to 10 141751 -0.5367 0.295733 5 to 9 141773 -0.4621 0.321992 4 to 8 141975 0.2226 0.588081 3 to 7 141832 -0.2621 0.396609 2 to 6 141938 0.0972 0.538711 1 to 5 141838 -0.2418 0.404469 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-09-01_14:31 Bits used No. missing words z-score p-value 31 to 32 142265 1.0492 0.852951 30 to 31 142212 0.8928 0.814026 29 to 30 142310 1.1819 0.881381 28 to 29 141710 -0.5880 0.278268 27 to 28 141861 -0.1426 0.443316 26 to 27 142144 0.6922 0.755607 25 to 26 141987 0.2291 0.590610 24 to 25 141951 0.1229 0.548915 23 to 24 140829 -3.1868 0.000719 22 to 23 142312 1.1878 0.882547 21 to 22 142163 0.7483 0.772857 20 to 21 141774 -0.3992 0.344872 19 to 20 141997 0.2586 0.602033 18 to 19 142114 0.6037 0.726994 17 to 18 141454 -1.3432 0.089611 16 to 17 141428 -1.4199 0.077825 15 to 16 141598 -0.9184 0.179211 14 to 15 141945 0.1052 0.541900 13 to 14 141817 -0.2724 0.392673 12 to 13 141605 -0.8977 0.184665 11 to 12 141940 0.0905 0.536044 10 to 11 141935 0.0757 0.530180 9 to 10 141204 -2.0806 0.018734 8 to 9 141796 -0.3343 0.369074 7 to 8 141846 -0.1868 0.425903 6 to 7 141718 -0.5644 0.286243 5 to 6 142147 0.7011 0.758377 4 to 5 141623 -0.8446 0.199158 3 to 4 141511 -1.1750 0.119994 2 to 3 142331 1.2439 0.893225 1 to 2 142286 1.1111 0.866742 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-09-01_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2502.91 0.041 0.516388 Test results for specific bytes for dh-ranFile-2016-09-01_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2503.86 0.055 0.521749 2 to 9 2515.93 0.225 0.589106 3 to 10 2580.56 1.139 0.872706 4 to 11 2589.73 1.269 0.897779 5 to 12 2440.80 -0.837 0.201231 6 to 13 2503.37 0.048 0.519006 7 to 14 2531.88 0.451 0.673951 8 to 15 2495.04 -0.070 0.472026 9 to 16 2445.03 -0.777 0.218474 10 to 17 2536.51 0.516 0.697207 11 to 18 2467.41 -0.461 0.322442 12 to 19 2542.84 0.606 0.727684 13 to 20 2545.56 0.644 0.740301 14 to 21 2351.63 -2.098 0.017938 15 to 22 2487.92 -0.171 0.432166 16 to 23 2509.84 0.139 0.555321 17 to 24 2406.92 -1.316 0.094023 18 to 25 2492.01 -0.113 0.455014 19 to 26 2471.71 -0.400 0.344557 20 to 27 2429.66 -0.995 0.159928 21 to 28 2435.52 -0.912 0.180922 22 to 29 2437.00 -0.891 0.186476 23 to 30 2410.16 -1.271 0.101938 24 to 31 2499.02 -0.014 0.494451 25 to 32 2570.87 1.002 0.841896 CDPARK for dh-ranFile-2016-09-01_14:31: 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 3545 1.0046 0.842447 3515 -0.3653 0.357445 3504 -0.8676 0.192812 3523 0.0000 0.500000 3515 -0.3653 0.357445 3492 -1.4155 0.078457 3533 0.4566 0.676028 3511 -0.5479 0.291865 3514 -0.4110 0.340551 3559 1.6438 0.949895 Square side=100, avg. no. parked=3521.10 sample std.=18.76 p-value of the KSTEST for those 10 p-values: 0.830097 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-09-01_14:31 0.2841,0.4148,0.8700,0.2505,0.9078,0.2355,0.3929,0.4650,0.3746,0.9966, The KS test for those 10 p-values: 0.387699 The 3DSPHERES test for dh-ranFile-2016-09-01_14:31 sample no r^3 equiv. uni. 1 42.543 0.757830 2 15.258 0.398661 3 26.034 0.580123 4 2.286 0.073376 5 38.616 0.723953 6 16.151 0.416293 7 47.230 0.792853 8 2.123 0.068317 9 9.753 0.277552 10 28.944 0.618940 11 1.893 0.061152 12 37.624 0.714678 13 36.649 0.705255 14 22.826 0.532745 15 22.471 0.527178 16 11.296 0.313754 17 58.947 0.859831 18 22.615 0.529444 19 73.140 0.912664 20 9.726 0.276890 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.779254 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-09-01_14:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 1.3 -0.6 -0.7 -1.3 -1.2 0.4 0.9 -0.6 2.2 0.6 1.8 -1.1 0.2 1.0 -0.2 -0.5 -0.9 0.1 -1.7 -2.1 1.4 2.7 0.1 -1.6 -0.8 -0.7 1.2 -0.1 1.0 0.7 0.4 -0.2 1.2 -1.5 0.6 -1.2 -0.4 -2.0 -0.1 -1.3 -1.0 -0.1 Chi-square with 42 degrees of freedom:57.110989 z-score=1.648744, p-value=0.940050 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-09-01_14:31 Test no p-value 1 0.143982 2 0.359062 3 0.005029 4 0.511602 5 0.832817 6 0.899303 7 0.183181 8 0.044320 9 0.049494 10 0.136697 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.028551 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-09-01_14:31: (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 66676 0.00 66801 0.27 3 25000.00 24997 0.00 24827 1.20 4 6666.67 6684 0.05 6703 0.20 5 1388.89 1368 0.31 1403 0.14 6 238.10 232 0.16 223 0.96 7 34.72 37 0.15 33 0.09 8 4.96 5 0.00 9 3.29 p=0.00482 p=0.59253 Number of rngs required: 687666, p-value: 0.197 RESULTS OF CRAPS TEST for dh-ranFile-2016-09-01_14:31 No. of wins: Observed Expected 98914 98585.9 z-score= 1.468, pvalue=0.92890 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66599 66666.7 0.069 0.069 2 37451 37654.3 1.098 1.167 3 27085 26954.7 0.630 1.796 4 19298 19313.5 0.012 1.808 5 13848 13851.4 0.001 1.809 6 9815 9943.5 1.662 3.471 7 7350 7145.0 5.880 9.351 8 5117 5139.1 0.095 9.446 9 3640 3699.9 0.969 10.415 10 2702 2666.3 0.478 10.893 11 1998 1923.3 2.899 13.792 12 1367 1388.7 0.340 14.132 13 1058 1003.7 2.936 17.068 14 734 726.1 0.085 17.153 15 555 525.8 1.618 18.771 16 379 381.2 0.012 18.783 17 298 276.5 1.665 20.448 18 185 200.8 1.248 21.696 19 153 146.0 0.337 22.033 20 90 106.2 2.475 24.509 21 278 287.1 0.289 24.798 Chisq= 24.80 for 20 degrees of freedom, p= 0.79073 SUMMARY of craptest p-value for no. of wins: 0.928899 p-value for throws/game: 0.790728 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-09-01_14:31 No. of wins: Observed Expected 98496 98585.9 z-score=-0.402, pvalue=0.34388 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66159 66666.7 3.866 3.866 2 37698 37654.3 0.051 3.917 3 26933 26954.7 0.018 3.934 4 19461 19313.5 1.127 5.061 5 14126 13851.4 5.443 10.504 6 9901 9943.5 0.182 10.686 7 7161 7145.0 0.036 10.722 8 5162 5139.1 0.102 10.824 9 3635 3699.9 1.137 11.961 10 2686 2666.3 0.146 12.107 11 1947 1923.3 0.291 12.398 12 1434 1388.7 1.475 13.873 13 979 1003.7 0.609 14.482 14 776 726.1 3.424 17.905 15 556 525.8 1.730 19.636 16 382 381.2 0.002 19.638 17 287 276.5 0.396 20.033 18 191 200.8 0.481 20.515 19 136 146.0 0.683 21.197 20 99 106.2 0.490 21.688 21 291 287.1 0.053 21.740 Chisq= 21.74 for 20 degrees of freedom, p= 0.64522 SUMMARY of craptest p-value for no. of wins: 0.343879 p-value for throws/game: 0.645222 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0007,0.0047,0.0048,0.0050,0.0052,0.0067,0.0083,0.0096,0.0164,0.0179, 0.0187,0.0286,0.0364,0.0401,0.0443,0.0495,0.0595,0.0612,0.0614,0.0634, 0.0683,0.0718,0.0734,0.0755,0.0769,0.0778,0.0785,0.0848,0.0867,0.0896, 0.0940,0.1008,0.1019,0.1026,0.1096,0.1200,0.1246,0.1354,0.1367,0.1388, 0.1440,0.1510,0.1565,0.1599,0.1626,0.1754,0.1792,0.1809,0.1827,0.1832, 0.1847,0.1865,0.1928,0.1970,0.1992,0.2000,0.2012,0.2119,0.2125,0.2154, 0.2185,0.2212,0.2355,0.2465,0.2475,0.2480,0.2505,0.2545,0.2605,0.2676, 0.2689,0.2728,0.2739,0.2769,0.2771,0.2776,0.2783,0.2796,0.2841,0.2862, 0.2919,0.2957,0.2971,0.2974,0.3083,0.3094,0.3138,0.3174,0.3220,0.3224, 0.3325,0.3406,0.3423,0.3439,0.3446,0.3449,0.3510,0.3542,0.3574,0.3574, 0.3591,0.3691,0.3733,0.3746,0.3803,0.3877,0.3901,0.3927,0.3929,0.3966, 0.3987,0.4045,0.4055,0.4131,0.4148,0.4163,0.4259,0.4297,0.4322,0.4344, 0.4352,0.4363,0.4410,0.4413,0.4433,0.4488,0.4532,0.4550,0.4571,0.4631, 0.4650,0.4720,0.4823,0.4857,0.4866,0.4872,0.4872,0.4881,0.4899,0.4901, 0.4912,0.4919,0.4945,0.5000,0.5003,0.5036,0.5116,0.5153,0.5164,0.5190, 0.5217,0.5232,0.5272,0.5294,0.5302,0.5302,0.5327,0.5360,0.5387,0.5419, 0.5467,0.5489,0.5508,0.5553,0.5624,0.5751,0.5801,0.5851,0.5876,0.5881, 0.5891,0.5906,0.5925,0.5948,0.6020,0.6041,0.6069,0.6148,0.6189,0.6272, 0.6340,0.6373,0.6420,0.6452,0.6563,0.6737,0.6740,0.6741,0.6760,0.6898, 0.6955,0.6972,0.7000,0.7010,0.7053,0.7107,0.7116,0.7147,0.7215,0.7231, 0.7240,0.7270,0.7277,0.7288,0.7318,0.7387,0.7403,0.7464,0.7500,0.7556, 0.7578,0.7584,0.7666,0.7726,0.7728,0.7729,0.7793,0.7907,0.7918,0.7929, 0.8063,0.8097,0.8140,0.8301,0.8328,0.8395,0.8402,0.8406,0.8419,0.8424, 0.8440,0.8451,0.8530,0.8540,0.8575,0.8598,0.8667,0.8673,0.8700,0.8727, 0.8814,0.8825,0.8886,0.8932,0.8950,0.8978,0.8993,0.9012,0.9018,0.9078, 0.9127,0.9175,0.9198,0.9280,0.9289,0.9306,0.9397,0.9401,0.9408,0.9412, 0.9447,0.9499,0.9544,0.9550,0.9635,0.9805,0.9879,0.9953,0.9966, Overall p-value after applying KStest on 269 p-values = 0.434214 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.