RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-12-24_07:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.59 15.8570 0.466009 2 to 25 15.66 19.7243 0.711429 3 to 26 15.65 16.6679 0.522923 4 to 27 15.68 16.1311 0.485439 5 to 28 15.84 20.7810 0.763761 6 to 29 15.34 32.7889 0.988014 7 to 30 15.66 14.6809 0.381545 8 to 31 15.57 15.8990 0.468995 9 to 32 15.38 24.0957 0.883142 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.195840 Tough bday spacings test for dh-ranFile-2015-12-24_07:31: 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 7 31 66 112 103 66 58 37 12 5 3 (O-E)^2/E 0.5 0.9 0.7 2.1 0.3 1.9 0.7 1.8 0.6 0.4 0.3 Birthday Spacings: Sum(O-E)^2/E= 10.027, p= 0.562 RESULTS OF GCD FOR dh-ranFile-2015-12-24_07:31 Euclid's algorithm: p-value, steps to gcd: 0.584301 p-value, dist. of gcd's: 0.146790 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-12-24_07:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.338 0.924 0.134 0.789 0.900 0.455 0.301 0.461 Bits 8 to 15---> 0.668 0.455 0.367 0.366 0.541 0.048 0.929 0.780 Bits 16 to 23---> 0.357 0.835 0.201 0.110 0.615 0.657 0.673 0.390 Bits 24 to 31---> 0.151 0.844 0.603 0.853 0.087 0.702 0.669 0.562 KS test for the above 32 p values: 0.220 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-12-24_07:31, p-values for 5 runs: 0.3702, 0.5719, 0.2938, 0.8947, 0.1889 Rank test for binary matrices (31x31) for dh-ranFile-2015-12-24_07:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 230 211.4 1.633 1.633 r= 29 5116 5134.0 0.063 1.696 r= 30 23238 23103.0 0.788 2.485 r= 31 11416 11551.5 1.590 4.075 chi-square = 4.075 with df = 3; p-value = 0.746 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-12-24_07:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 212 211.4 0.002 0.002 r= 30 5085 5134.0 0.468 0.469 r= 31 23026 23103.0 0.257 0.726 r= 32 11677 11551.5 1.363 2.089 chi-square = 2.089 with df = 3; p-value = 0.446 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-12-24_07:31 b-rank test for bits 1 to 8, p=0.81549 b-rank test for bits 2 to 9, p=0.25945 b-rank test for bits 3 to 10, p=0.44549 b-rank test for bits 4 to 11, p=0.61141 b-rank test for bits 5 to 12, p=0.80486 b-rank test for bits 6 to 13, p=0.64525 b-rank test for bits 7 to 14, p=0.48757 b-rank test for bits 8 to 15, p=0.51676 b-rank test for bits 9 to 16, p=0.08326 b-rank test for bits 10 to 17, p=0.42928 b-rank test for bits 11 to 18, p=0.41240 b-rank test for bits 12 to 19, p=0.11472 b-rank test for bits 13 to 20, p=0.30175 b-rank test for bits 14 to 21, p=0.42826 b-rank test for bits 15 to 22, p=0.29084 b-rank test for bits 16 to 23, p=0.73324 b-rank test for bits 17 to 24, p=0.41076 b-rank test for bits 18 to 25, p=0.65921 b-rank test for bits 19 to 26, p=0.47465 b-rank test for bits 20 to 27, p=0.16216 b-rank test for bits 21 to 28, p=0.37491 b-rank test for bits 22 to 29, p=0.48768 b-rank test for bits 23 to 30, p=0.98557 b-rank test for bits 24 to 31, p=0.73478 b-rank test for bits 25 to 32, p=0.95985 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 = 0.488240 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-12-24_07:31 (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 141596 -0.73 0.232060 2 141578 -0.77 0.219425 3 141698 -0.49 0.310737 4 141590 -0.75 0.227804 5 141885 -0.06 0.477334 6 141533 -0.88 0.189626 7 141848 -0.14 0.443029 8 142221 0.73 0.766755 9 142502 1.38 0.916934 10 142043 0.31 0.622599 11 141702 -0.48 0.314045 12 142030 0.28 0.611005 13 141380 -1.24 0.108090 14 141663 -0.58 0.282464 15 141442 -1.09 0.137440 16 141445 -1.08 0.138987 17 141622 -0.67 0.251005 18 141368 -1.26 0.102973 19 141926 0.04 0.515534 20 141396 -1.20 0.115192 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-12-24_07:31 Bits used No. missing words z-score p-value 23 to 32 141780 -0.4460 0.327811 22 to 31 142255 1.1920 0.883363 21 to 30 141770 -0.4804 0.315454 20 to 29 142217 1.0609 0.855639 19 to 28 142009 0.3437 0.634460 18 to 27 141967 0.1989 0.578815 17 to 26 142027 0.4058 0.657540 16 to 25 142204 1.0161 0.845210 15 to 24 141821 -0.3046 0.380341 14 to 23 142688 2.6851 0.996374 13 to 22 141944 0.1196 0.547581 12 to 21 141746 -0.5632 0.286647 11 to 20 141852 -0.1977 0.421644 10 to 19 141856 -0.1839 0.427047 9 to 18 142233 1.1161 0.867811 8 to 17 141897 -0.0425 0.483043 7 to 16 141672 -0.8184 0.206570 6 to 15 142318 1.4092 0.920613 5 to 14 142005 0.3299 0.629261 4 to 13 141572 -1.1632 0.122373 3 to 12 141879 -0.1046 0.458352 2 to 11 141996 0.2989 0.617477 1 to 10 142049 0.4816 0.684962 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-12-24_07:31 Bits used No. missing words z-score p-value 28 to 32 141541 -1.2486 0.105910 27 to 31 142204 0.9989 0.841074 26 to 30 142526 2.0904 0.981709 25 to 29 141804 -0.3571 0.360527 24 to 28 142508 2.0294 0.978791 23 to 27 141445 -1.5740 0.057744 22 to 26 142082 0.5853 0.720834 21 to 25 142228 1.0802 0.859982 20 to 24 141979 0.2362 0.593349 19 to 23 142321 1.3955 0.918566 18 to 22 141723 -0.6316 0.263815 17 to 21 141636 -0.9265 0.177082 16 to 20 141830 -0.2689 0.393998 15 to 19 141433 -1.6147 0.053190 14 to 18 142059 0.5074 0.694048 13 to 17 141475 -1.4723 0.070469 12 to 16 141491 -1.4181 0.078086 11 to 15 141846 -0.2147 0.415009 10 to 14 141804 -0.3571 0.360527 9 to 13 141648 -0.8859 0.187845 8 to 12 142534 2.1175 0.982892 7 to 11 141850 -0.2011 0.420303 6 to 10 141945 0.1209 0.548121 5 to 9 141731 -0.6045 0.272753 4 to 8 141862 -0.1604 0.436267 3 to 7 142296 1.3107 0.905028 2 to 6 141776 -0.4520 0.325647 1 to 5 141315 -2.0147 0.021969 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-12-24_07:31 Bits used No. missing words z-score p-value 31 to 32 142145 0.6952 0.756532 30 to 31 141908 -0.0039 0.498435 29 to 30 142266 1.0521 0.853629 28 to 29 142523 1.8102 0.964870 27 to 28 141478 -1.2724 0.101623 26 to 27 142628 2.1200 0.982996 25 to 26 142049 0.4120 0.659832 24 to 25 142068 0.4681 0.680127 23 to 24 142202 0.8633 0.806023 22 to 23 142090 0.5329 0.702966 21 to 22 142148 0.7040 0.759297 20 to 21 142137 0.6716 0.749079 19 to 20 142026 0.3442 0.634637 18 to 19 141717 -0.5673 0.285240 17 to 18 141995 0.2527 0.599755 16 to 17 141894 -0.0452 0.481966 15 to 16 142000 0.2675 0.605444 14 to 15 141677 -0.6853 0.246565 13 to 14 142427 1.5271 0.936626 12 to 13 141836 -0.2163 0.414372 11 to 12 142042 0.3914 0.652233 10 to 11 141686 -0.6588 0.255015 9 to 10 142091 0.5359 0.703986 8 to 9 141703 -0.6086 0.271381 7 to 8 142254 1.0167 0.845358 6 to 7 141910 0.0020 0.500789 5 to 6 141936 0.0787 0.531354 4 to 5 141882 -0.0806 0.467872 3 to 4 141473 -1.2871 0.099028 2 to 3 141589 -0.9449 0.172348 1 to 2 141630 -0.8240 0.204975 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-12-24_07:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2435.74 -0.909 0.181736 Test results for specific bytes for dh-ranFile-2015-12-24_07:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2536.83 0.521 0.698754 2 to 9 2558.47 0.827 0.795864 3 to 10 2592.06 1.302 0.903537 4 to 11 2543.95 0.621 0.732859 5 to 12 2474.63 -0.359 0.359890 6 to 13 2520.14 0.285 0.612135 7 to 14 2484.21 -0.223 0.411673 8 to 15 2478.70 -0.301 0.381634 9 to 16 2469.20 -0.436 0.331555 10 to 17 2655.77 2.203 0.986199 11 to 18 2474.46 -0.361 0.358979 12 to 19 2541.61 0.588 0.721889 13 to 20 2557.11 0.808 0.790345 14 to 21 2445.91 -0.765 0.222147 15 to 22 2524.83 0.351 0.637245 16 to 23 2452.96 -0.665 0.252929 17 to 24 2543.38 0.613 0.730210 18 to 25 2418.09 -1.158 0.123360 19 to 26 2495.51 -0.064 0.474674 20 to 27 2521.25 0.301 0.618103 21 to 28 2558.79 0.831 0.797116 22 to 29 2411.20 -1.256 0.104599 23 to 30 2587.86 1.243 0.892984 24 to 31 2447.12 -0.748 0.227266 25 to 32 2413.34 -1.226 0.110190 CDPARK for dh-ranFile-2015-12-24_07:31: 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 3511 -0.5479 0.291865 3542 0.8676 0.807188 3558 1.5982 0.944998 3557 1.5525 0.939730 3515 -0.3653 0.357445 3504 -0.8676 0.192812 3559 1.6438 0.949895 3527 0.1826 0.572463 3526 0.1370 0.554479 Square side=100, avg. no. parked=3530.50 sample std.=20.88 p-value of the KSTEST for those 10 p-values: 0.375574 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-12-24_07:31 0.3675,0.3190,0.9080,0.6204,0.4525,0.2206,0.0808,0.0145,0.9235,0.0652, The KS test for those 10 p-values: 0.328878 The 3DSPHERES test for dh-ranFile-2015-12-24_07:31 sample no r^3 equiv. uni. 1 58.252 0.856546 2 73.207 0.912860 3 3.467 0.109136 4 6.878 0.204891 5 1.880 0.060746 6 89.709 0.949727 7 24.274 0.554753 8 82.144 0.935310 9 14.435 0.381938 10 59.660 0.863121 11 29.617 0.627392 12 57.956 0.855121 13 96.924 0.960474 14 4.431 0.137320 15 70.925 0.905971 16 18.454 0.459432 17 28.569 0.614143 18 80.975 0.932739 19 23.833 0.548159 20 2.600 0.083032 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.073354 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-12-24_07:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 1.3 -2.0 -0.4 0.5 -0.4 0.9 -1.6 -0.1 0.9 0.6 1.6 0.7 0.2 0.5 -0.7 -0.3 -2.0 0.0 -0.3 1.5 0.0 -0.1 0.2 -0.3 -1.0 0.6 0.2 -0.3 -0.7 0.1 0.5 -1.2 0.4 0.2 -0.2 1.5 1.9 -0.1 -0.4 0.4 0.9 -1.0 -0.1 Chi-square with 42 degrees of freedom:32.708507 z-score=-1.013785, p-value=0.152511 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-12-24_07:31 Test no p-value 1 0.013519 2 0.006887 3 0.725482 4 0.154346 5 0.895160 6 0.983803 7 0.165650 8 0.024342 9 0.959172 10 0.059993 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.010137 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-12-24_07:31: (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 66690 0.01 66580 0.11 3 25000.00 25060 0.14 25070 0.20 4 6666.67 6600 0.67 6661 0.00 5 1388.89 1368 0.31 1394 0.02 6 238.10 237 0.01 257 1.50 7 34.72 39 0.53 30 0.64 8 4.96 5 0.00 7 0.84 p=0.05229 p=0.23148 Number of rngs required: 688319, p-value: 0.462 RESULTS OF CRAPS TEST for dh-ranFile-2015-12-24_07:31 No. of wins: Observed Expected 98743 98585.9 z-score= 0.703, pvalue=0.75892 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66721 66666.7 0.044 0.044 2 37595 37654.3 0.093 0.138 3 26892 26954.7 0.146 0.284 4 19218 19313.5 0.472 0.756 5 13774 13851.4 0.433 1.188 6 10027 9943.5 0.700 1.889 7 7062 7145.0 0.965 2.854 8 5227 5139.1 1.504 4.358 9 3757 3699.9 0.882 5.240 10 2603 2666.3 1.503 6.743 11 1966 1923.3 0.947 7.690 12 1461 1388.7 3.760 11.449 13 1008 1003.7 0.018 11.468 14 764 726.1 1.974 13.442 15 546 525.8 0.773 14.215 16 380 381.2 0.003 14.218 17 265 276.5 0.482 14.700 18 189 200.8 0.697 15.397 19 146 146.0 0.000 15.397 20 103 106.2 0.097 15.494 21 296 287.1 0.275 15.769 Chisq= 15.77 for 20 degrees of freedom, p= 0.26916 SUMMARY of craptest p-value for no. of wins: 0.758919 p-value for throws/game: 0.269157 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-12-24_07:31 No. of wins: Observed Expected 98466 98585.9 z-score=-0.536, pvalue=0.29595 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66461 66666.7 0.634 0.634 2 37820 37654.3 0.729 1.363 3 26933 26954.7 0.018 1.381 4 19177 19313.5 0.964 2.345 5 13873 13851.4 0.034 2.379 6 10003 9943.5 0.356 2.734 7 7094 7145.0 0.364 3.099 8 5174 5139.1 0.237 3.336 9 3658 3699.9 0.474 3.810 10 2718 2666.3 1.003 4.812 11 1976 1923.3 1.442 6.255 12 1426 1388.7 1.000 7.254 13 994 1003.7 0.094 7.349 14 771 726.1 2.771 10.120 15 506 525.8 0.748 10.868 16 407 381.2 1.753 12.621 17 274 276.5 0.023 12.644 18 184 200.8 1.410 14.055 19 168 146.0 3.320 17.375 20 113 106.2 0.433 17.808 21 270 287.1 1.020 18.829 Chisq= 18.83 for 20 degrees of freedom, p= 0.46700 SUMMARY of craptest p-value for no. of wins: 0.295952 p-value for throws/game: 0.467003 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0069,0.0101,0.0135,0.0145,0.0220,0.0243,0.0480,0.0523,0.0532,0.0577, 0.0600,0.0607,0.0652,0.0705,0.0734,0.0781,0.0808,0.0830,0.0833,0.0871, 0.0990,0.1016,0.1030,0.1046,0.1059,0.1081,0.1091,0.1097,0.1102,0.1147, 0.1152,0.1224,0.1234,0.1337,0.1373,0.1374,0.1390,0.1468,0.1514,0.1525, 0.1543,0.1622,0.1657,0.1723,0.1771,0.1817,0.1878,0.1889,0.1896,0.1928, 0.1958,0.2012,0.2049,0.2050,0.2066,0.2188,0.2194,0.2197,0.2206,0.2221, 0.2273,0.2278,0.2315,0.2321,0.2466,0.2510,0.2529,0.2550,0.2595,0.2638, 0.2692,0.2714,0.2728,0.2825,0.2852,0.2866,0.2908,0.2919,0.2938,0.2960, 0.3010,0.3018,0.3107,0.3140,0.3155,0.3190,0.3256,0.3278,0.3289,0.3316, 0.3377,0.3574,0.3575,0.3590,0.3599,0.3605,0.3605,0.3661,0.3666,0.3675, 0.3702,0.3749,0.3756,0.3803,0.3815,0.3816,0.3819,0.3897,0.3940,0.4108, 0.4117,0.4124,0.4144,0.4150,0.4203,0.4216,0.4270,0.4283,0.4293,0.4363, 0.4430,0.4455,0.4459,0.4525,0.4553,0.4553,0.4584,0.4594,0.4606,0.4615, 0.4660,0.4670,0.4679,0.4690,0.4746,0.4747,0.4773,0.4820,0.4830,0.4854, 0.4876,0.4877,0.4882,0.4984,0.5008,0.5155,0.5168,0.5229,0.5314,0.5409, 0.5476,0.5481,0.5482,0.5545,0.5548,0.5619,0.5622,0.5719,0.5725,0.5788, 0.5843,0.5933,0.5998,0.6035,0.6054,0.6110,0.6114,0.6121,0.6141,0.6153, 0.6175,0.6181,0.6204,0.6226,0.6274,0.6293,0.6345,0.6346,0.6372,0.6452, 0.6522,0.6574,0.6575,0.6592,0.6598,0.6680,0.6691,0.6729,0.6801,0.6850, 0.6940,0.6988,0.7018,0.7030,0.7040,0.7114,0.7208,0.7219,0.7255,0.7302, 0.7329,0.7332,0.7348,0.7465,0.7491,0.7565,0.7589,0.7593,0.7638,0.7668, 0.7799,0.7895,0.7903,0.7959,0.7971,0.8049,0.8060,0.8072,0.8155,0.8348, 0.8411,0.8442,0.8452,0.8454,0.8528,0.8536,0.8551,0.8556,0.8565,0.8600, 0.8631,0.8678,0.8831,0.8834,0.8930,0.8947,0.8952,0.8999,0.9035,0.9050, 0.9060,0.9080,0.9129,0.9169,0.9186,0.9206,0.9235,0.9236,0.9287,0.9327, 0.9353,0.9366,0.9397,0.9450,0.9497,0.9499,0.9592,0.9598,0.9605,0.9649, 0.9788,0.9817,0.9829,0.9830,0.9838,0.9856,0.9862,0.9880,0.9964, Overall p-value after applying KStest on 269 p-values = 0.846830 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.