RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-05-07_22:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.70 24.6746 0.897766 2 to 25 15.92 11.1964 0.153827 3 to 26 15.59 21.1979 0.782439 4 to 27 15.77 22.7254 0.841595 5 to 28 15.93 12.4371 0.227023 6 to 29 15.64 20.2852 0.740100 7 to 30 15.70 18.0711 0.615632 8 to 31 15.82 21.2842 0.786165 9 to 32 15.92 15.8858 0.468054 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.344739 Tough bday spacings test for dh-ranFile-2016-05-07_22:31: 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 16 31 64 104 100 79 50 29 12 9 6 (O-E)^2/E 5.1 0.9 1.2 0.4 0.1 0.0 0.1 0.0 0.6 0.9 0.9 Birthday Spacings: Sum(O-E)^2/E= 10.064, p= 0.565 RESULTS OF GCD FOR dh-ranFile-2016-05-07_22:31 Euclid's algorithm: p-value, steps to gcd: 0.827093 p-value, dist. of gcd's: 0.782551 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-05-07_22:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.182 0.462 0.930 0.131 0.048 0.298 0.955 0.737 Bits 8 to 15---> 0.071 0.345 0.155 0.523 0.923 0.148 0.316 0.393 Bits 16 to 23---> 0.702 0.194 0.167 0.609 0.283 0.401 0.710 0.309 Bits 24 to 31---> 0.063 0.187 0.181 0.464 0.396 0.248 0.829 0.307 KS test for the above 32 p values: 0.956 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-05-07_22:31, p-values for 5 runs: 0.1147, 0.7111, 0.4459, 0.1704, 0.8555 Rank test for binary matrices (31x31) for dh-ranFile-2016-05-07_22:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 214 211.4 0.032 0.032 r= 29 5208 5134.0 1.066 1.098 r= 30 23097 23103.0 0.002 1.099 r= 31 11481 11551.5 0.431 1.530 chi-square = 1.530 with df = 3; p-value = 0.325 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-05-07_22:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 223 211.4 0.634 0.634 r= 30 5099 5134.0 0.239 0.873 r= 31 23111 23103.0 0.003 0.876 r= 32 11567 11551.5 0.021 0.897 chi-square = 0.897 with df = 3; p-value = 0.174 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-05-07_22:31 b-rank test for bits 1 to 8, p=0.99730 b-rank test for bits 2 to 9, p=0.23065 b-rank test for bits 3 to 10, p=0.89737 b-rank test for bits 4 to 11, p=0.65963 b-rank test for bits 5 to 12, p=0.86600 b-rank test for bits 6 to 13, p=0.92584 b-rank test for bits 7 to 14, p=0.96358 b-rank test for bits 8 to 15, p=0.71248 b-rank test for bits 9 to 16, p=0.42485 b-rank test for bits 10 to 17, p=0.76973 b-rank test for bits 11 to 18, p=0.61866 b-rank test for bits 12 to 19, p=0.82710 b-rank test for bits 13 to 20, p=0.81918 b-rank test for bits 14 to 21, p=0.61367 b-rank test for bits 15 to 22, p=0.69993 b-rank test for bits 16 to 23, p=0.51326 b-rank test for bits 17 to 24, p=0.41179 b-rank test for bits 18 to 25, p=0.36523 b-rank test for bits 19 to 26, p=0.58110 b-rank test for bits 20 to 27, p=0.41039 b-rank test for bits 21 to 28, p=0.89828 b-rank test for bits 22 to 29, p=0.22577 b-rank test for bits 23 to 30, p=0.20108 b-rank test for bits 24 to 31, p=0.65758 b-rank test for bits 25 to 32, p=0.64726 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 = 0.025762 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-05-07_22:31 (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 141508 -0.94 0.174203 2 141960 0.12 0.547120 3 142214 0.71 0.761720 4 141858 -0.12 0.452269 5 141252 -1.54 0.062292 6 141493 -0.97 0.165343 7 142184 0.64 0.739483 8 142604 1.62 0.947712 9 141263 -1.51 0.065507 10 141463 -1.04 0.148514 11 141163 -1.74 0.040600 12 141872 -0.09 0.465249 13 140807 -2.58 0.005004 14 143268 3.17 0.999249 15 141599 -0.73 0.234205 16 141923 0.03 0.512740 17 141508 -0.94 0.174203 18 142484 1.34 0.910313 19 142168 0.60 0.727201 20 141758 -0.35 0.361829 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-05-07_22:31 Bits used No. missing words z-score p-value 23 to 32 142053 0.4954 0.689846 22 to 31 142165 0.8816 0.811009 21 to 30 141954 0.1540 0.561209 20 to 29 141938 0.0989 0.539376 19 to 28 141840 -0.2391 0.405526 18 to 27 141821 -0.3046 0.380341 17 to 26 142138 0.7885 0.784803 16 to 25 142442 1.8368 0.966880 15 to 24 142228 1.0989 0.864086 14 to 23 141463 -1.5391 0.061894 13 to 22 141988 0.2713 0.606911 12 to 21 141838 -0.2460 0.402855 11 to 20 142193 0.9782 0.836006 10 to 19 141640 -0.9287 0.176516 9 to 18 141660 -0.8598 0.194961 8 to 17 141590 -1.1011 0.135418 7 to 16 141783 -0.4356 0.331556 6 to 15 141923 0.0471 0.518798 5 to 14 141979 0.2402 0.594928 4 to 13 142443 1.8402 0.967134 3 to 12 142071 0.5575 0.711401 2 to 11 141640 -0.9287 0.176516 1 to 10 142018 0.3747 0.646067 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-05-07_22:31 Bits used No. missing words z-score p-value 28 to 32 142237 1.1107 0.866661 27 to 31 141843 -0.2248 0.411049 26 to 30 142251 1.1582 0.876610 25 to 29 141672 -0.8045 0.210552 24 to 28 142043 0.4531 0.674768 23 to 27 141971 0.2091 0.582796 22 to 26 141837 -0.2452 0.403156 21 to 25 142120 0.7141 0.762428 20 to 24 142093 0.6226 0.733230 19 to 23 141931 0.0735 0.529279 18 to 22 142125 0.7311 0.767636 17 to 21 141470 -1.4893 0.068210 16 to 20 141965 0.1887 0.574841 15 to 19 141668 -0.8181 0.206659 14 to 18 141781 -0.4350 0.331775 13 to 17 142065 0.5277 0.701145 12 to 16 141841 -0.2316 0.408414 11 to 15 141572 -1.1435 0.126417 10 to 14 141688 -0.7503 0.226546 9 to 13 142167 0.8735 0.808793 8 to 12 141448 -1.5638 0.058929 7 to 11 142154 0.8294 0.796558 6 to 10 142129 0.7446 0.771757 5 to 9 142105 0.6633 0.746427 4 to 8 142243 1.1311 0.870990 3 to 7 142316 1.3785 0.915982 2 to 6 142543 2.1480 0.984144 1 to 5 142176 0.9040 0.816993 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-05-07_22:31 Bits used No. missing words z-score p-value 31 to 32 142108 0.5860 0.721078 30 to 31 142106 0.5801 0.719092 29 to 30 142810 2.6568 0.996056 28 to 29 141881 -0.0836 0.466699 27 to 28 141774 -0.3992 0.344872 26 to 27 142399 1.4445 0.925694 25 to 26 142155 0.7247 0.765679 24 to 25 141594 -0.9302 0.176140 23 to 24 141949 0.1170 0.546578 22 to 23 141570 -1.0010 0.158420 21 to 22 142241 0.9784 0.836056 20 to 21 142387 1.4091 0.920591 19 to 20 142068 0.4681 0.680127 18 to 19 141818 -0.2694 0.393807 17 to 18 142729 2.4179 0.992195 16 to 17 142354 1.3117 0.905191 15 to 16 141420 -1.4435 0.074447 14 to 15 141587 -0.9508 0.170846 13 to 14 142119 0.6185 0.731876 12 to 13 141914 0.0138 0.505496 11 to 12 142095 0.5477 0.708051 10 to 11 141599 -0.9154 0.179984 9 to 10 141572 -0.9951 0.159850 8 to 9 142074 0.4858 0.686429 7 to 8 142086 0.5212 0.698869 6 to 7 141796 -0.3343 0.369074 5 to 6 142649 2.1819 0.985442 4 to 5 141969 0.1760 0.569860 3 to 4 141614 -0.8712 0.191828 2 to 3 141730 -0.5290 0.298404 1 to 2 142268 1.0580 0.854978 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-05-07_22:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2401.42 -1.394 0.081649 Test results for specific bytes for dh-ranFile-2016-05-07_22:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2490.84 -0.129 0.448482 2 to 9 2487.37 -0.179 0.429131 3 to 10 2547.54 0.672 0.749307 4 to 11 2493.14 -0.097 0.461349 5 to 12 2461.65 -0.542 0.293802 6 to 13 2426.26 -1.043 0.148501 7 to 14 2479.90 -0.284 0.388094 8 to 15 2370.97 -1.825 0.034019 9 to 16 2562.47 0.883 0.811511 10 to 17 2532.60 0.461 0.677627 11 to 18 2515.26 0.216 0.585420 12 to 19 2413.42 -1.224 0.110390 13 to 20 2535.31 0.499 0.691229 14 to 21 2537.74 0.534 0.703218 15 to 22 2533.68 0.476 0.683089 16 to 23 2608.31 1.532 0.937207 17 to 24 2439.68 -0.853 0.196821 18 to 25 2593.29 1.319 0.906479 19 to 26 2542.89 0.606 0.727908 20 to 27 2362.26 -1.948 0.025715 21 to 28 2599.98 1.414 0.921306 22 to 29 2540.48 0.573 0.716512 23 to 30 2528.29 0.400 0.655442 24 to 31 2499.76 -0.003 0.498664 25 to 32 2536.20 0.512 0.695674 CDPARK for dh-ranFile-2016-05-07_22:31: 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 3548 1.1416 0.873180 3556 1.5068 0.934075 3534 0.5023 0.692266 3533 0.4566 0.676028 3554 1.4155 0.921543 3508 -0.6849 0.246694 3522 -0.0457 0.481790 3533 0.4566 0.676028 3540 0.7763 0.781201 3520 -0.1370 0.445521 Square side=100, avg. no. parked=3534.80 sample std.=14.59 p-value of the KSTEST for those 10 p-values: 0.092054 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-05-07_22:31 0.9142,0.9811,0.2295,0.7106,0.3170,0.1227,0.5657,0.0783,0.8402,0.7304, The KS test for those 10 p-values: 0.811735 The 3DSPHERES test for dh-ranFile-2016-05-07_22:31 sample no r^3 equiv. uni. 1 17.847 0.448381 2 145.261 0.992109 3 4.131 0.128645 4 5.996 0.181168 5 10.809 0.302530 6 66.299 0.890295 7 10.285 0.290246 8 16.244 0.418111 9 36.571 0.704481 10 110.384 0.974763 11 7.018 0.208596 12 45.820 0.782883 13 104.674 0.969473 14 57.560 0.853197 15 0.349 0.011552 16 9.602 0.273911 17 18.509 0.460413 18 7.813 0.229285 19 19.655 0.480652 20 51.783 0.822023 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.564136 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-05-07_22:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -0.3 -0.4 -0.8 -0.7 -0.3 -0.0 0.8 0.6 -1.0 -1.2 -0.3 1.6 0.0 1.0 0.1 -0.7 0.4 -1.5 0.6 0.4 -0.5 1.3 0.3 -0.2 -1.2 -0.3 -0.7 0.8 -2.2 0.6 1.4 1.4 -0.4 -0.1 -0.5 -0.7 -0.7 -0.4 -0.1 0.9 -1.0 -0.1 Chi-square with 42 degrees of freedom:29.634390 z-score=-1.349199, p-value=0.075560 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-05-07_22:31 Test no p-value 1 0.588505 2 0.415712 3 0.755231 4 0.164410 5 0.129365 6 0.839206 7 0.543128 8 0.188037 9 0.103899 10 0.373718 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.524083 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-05-07_22:31: (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 66417 0.94 66563 0.16 3 25000.00 25223 1.99 24934 0.17 4 6666.67 6694 0.11 6764 1.42 5 1388.89 1388 0.00 1443 2.11 6 238.10 237 0.01 253 0.93 7 34.72 37 0.15 37 0.15 8 4.96 3 0.77 5 0.00 p=0.31873 p=0.44945 Number of rngs required: 688533, p-value: 0.559 RESULTS OF CRAPS TEST for dh-ranFile-2016-05-07_22:31 No. of wins: Observed Expected 98760 98585.9 z-score= 0.779, pvalue=0.78197 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66358 66666.7 1.429 1.429 2 37716 37654.3 0.101 1.530 3 27139 26954.7 1.260 2.790 4 19200 19313.5 0.667 3.456 5 13796 13851.4 0.222 3.678 6 10110 9943.5 2.787 6.465 7 7217 7145.0 0.725 7.190 8 5047 5139.1 1.650 8.839 9 3777 3699.9 1.608 10.447 10 2702 2666.3 0.478 10.925 11 1966 1923.3 0.947 11.872 12 1405 1388.7 0.190 12.063 13 987 1003.7 0.278 12.341 14 691 726.1 1.701 14.041 15 534 525.8 0.127 14.168 16 380 381.2 0.003 14.172 17 280 276.5 0.043 14.215 18 188 200.8 0.820 15.035 19 146 146.0 0.000 15.035 20 86 106.2 3.847 18.882 21 275 287.1 0.511 19.393 Chisq= 19.39 for 20 degrees of freedom, p= 0.50358 SUMMARY of craptest p-value for no. of wins: 0.781969 p-value for throws/game: 0.503583 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-05-07_22:31 No. of wins: Observed Expected 98476 98585.9 z-score=-0.491, pvalue=0.31159 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66693 66666.7 0.010 0.010 2 37686 37654.3 0.027 0.037 3 27141 26954.7 1.287 1.324 4 19096 19313.5 2.449 3.773 5 13964 13851.4 0.915 4.688 6 9678 9943.5 7.091 11.779 7 7226 7145.0 0.918 12.697 8 5212 5139.1 1.035 13.732 9 3766 3699.9 1.182 14.914 10 2604 2666.3 1.456 16.369 11 1876 1923.3 1.165 17.534 12 1414 1388.7 0.459 17.994 13 1030 1003.7 0.688 18.682 14 706 726.1 0.559 19.241 15 505 525.8 0.826 20.066 16 372 381.2 0.220 20.286 17 254 276.5 1.837 22.123 18 205 200.8 0.087 22.210 19 147 146.0 0.007 22.217 20 108 106.2 0.030 22.247 21 317 287.1 3.111 25.357 Chisq= 25.36 for 20 degrees of freedom, p= 0.81190 SUMMARY of craptest p-value for no. of wins: 0.311589 p-value for throws/game: 0.811903 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0050,0.0116,0.0257,0.0258,0.0340,0.0406,0.0481,0.0589,0.0619,0.0623, 0.0632,0.0655,0.0682,0.0706,0.0744,0.0756,0.0783,0.0816,0.0921,0.1039, 0.1104,0.1147,0.1227,0.1264,0.1286,0.1294,0.1309,0.1354,0.1478,0.1485, 0.1485,0.1538,0.1554,0.1584,0.1599,0.1644,0.1653,0.1675,0.1704,0.1708, 0.1738,0.1742,0.1742,0.1761,0.1765,0.1765,0.1800,0.1809,0.1812,0.1823, 0.1871,0.1880,0.1918,0.1943,0.1950,0.1968,0.2011,0.2067,0.2086,0.2106, 0.2258,0.2265,0.2270,0.2293,0.2295,0.2306,0.2342,0.2467,0.2478,0.2739, 0.2831,0.2902,0.2938,0.2983,0.2984,0.3025,0.3073,0.3090,0.3116,0.3164, 0.3170,0.3187,0.3246,0.3316,0.3318,0.3447,0.3449,0.3452,0.3618,0.3652, 0.3691,0.3737,0.3803,0.3881,0.3933,0.3938,0.3958,0.4005,0.4029,0.4032, 0.4055,0.4084,0.4104,0.4110,0.4118,0.4157,0.4181,0.4249,0.4291,0.4455, 0.4459,0.4484,0.4485,0.4494,0.4523,0.4604,0.4613,0.4617,0.4644,0.4652, 0.4667,0.4681,0.4807,0.4818,0.4987,0.5036,0.5055,0.5127,0.5133,0.5188, 0.5226,0.5241,0.5293,0.5394,0.5431,0.5466,0.5471,0.5594,0.5612,0.5641, 0.5651,0.5657,0.5699,0.5748,0.5811,0.5828,0.5854,0.5885,0.5949,0.6069, 0.6094,0.6137,0.6156,0.6187,0.6461,0.6473,0.6554,0.6576,0.6596,0.6748, 0.6760,0.6760,0.6776,0.6801,0.6831,0.6864,0.6898,0.6912,0.6923,0.6957, 0.6989,0.6999,0.7011,0.7024,0.7032,0.7045,0.7081,0.7095,0.7106,0.7111, 0.7114,0.7125,0.7165,0.7191,0.7211,0.7272,0.7279,0.7304,0.7319,0.7332, 0.7366,0.7395,0.7401,0.7464,0.7493,0.7552,0.7617,0.7624,0.7657,0.7676, 0.7697,0.7718,0.7812,0.7820,0.7824,0.7826,0.7829,0.7848,0.7862,0.7966, 0.8088,0.8110,0.8115,0.8117,0.8119,0.8170,0.8192,0.8220,0.8271,0.8271, 0.8289,0.8360,0.8361,0.8392,0.8402,0.8416,0.8532,0.8550,0.8555,0.8641, 0.8660,0.8667,0.8710,0.8732,0.8766,0.8903,0.8974,0.8978,0.8983,0.9052, 0.9065,0.9103,0.9142,0.9160,0.9206,0.9213,0.9215,0.9225,0.9257,0.9258, 0.9304,0.9341,0.9372,0.9477,0.9553,0.9561,0.9636,0.9669,0.9671,0.9695, 0.9748,0.9811,0.9841,0.9854,0.9921,0.9922,0.9961,0.9973,0.9992, Overall p-value after applying KStest on 269 p-values = 0.163866 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.