RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-12-22_15:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.46 23.1699 0.856198 2 to 25 15.69 17.3959 0.572132 3 to 26 15.56 27.9079 0.953974 4 to 27 15.59 31.4252 0.982280 5 to 28 16.04 9.4204 0.073858 6 to 29 15.79 22.0070 0.815550 7 to 30 15.61 14.8023 0.390280 8 to 31 15.55 29.1600 0.966921 9 to 32 15.52 21.6902 0.803072 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.019084 Tough bday spacings test for dh-ranFile-2016-12-22_15:31: 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 35 69 109 92 83 57 23 20 4 1 (O-E)^2/E 0.5 0.1 0.2 1.3 0.3 0.3 0.5 1.5 1.8 1.0 2.3 Birthday Spacings: Sum(O-E)^2/E= 9.877, p= 0.549 RESULTS OF GCD FOR dh-ranFile-2016-12-22_15:31 Euclid's algorithm: p-value, steps to gcd: 0.771968 p-value, dist. of gcd's: 0.252569 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-12-22_15:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.233 0.998 0.015 0.095 0.277 0.781 0.015 0.001 Bits 8 to 15---> 0.801 0.222 0.322 0.532 0.338 0.675 0.829 0.992 Bits 16 to 23---> 0.009 0.705 0.807 0.883 0.785 0.901 0.089 0.744 Bits 24 to 31---> 0.604 0.568 0.101 0.517 0.703 0.734 0.252 0.169 KS test for the above 32 p values: 0.755 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-12-22_15:31, p-values for 5 runs: 0.3227, 0.9725, 0.1712, 0.8963, 0.6659 Rank test for binary matrices (31x31) for dh-ranFile-2016-12-22_15:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 221 211.4 0.434 0.434 r= 29 5145 5134.0 0.024 0.458 r= 30 22957 23103.0 0.923 1.381 r= 31 11677 11551.5 1.363 2.744 chi-square = 2.744 with df = 3; p-value = 0.567 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-12-22_15:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 214 211.4 0.032 0.032 r= 30 5074 5134.0 0.701 0.733 r= 31 23192 23103.0 0.342 1.075 r= 32 11520 11551.5 0.086 1.162 chi-square = 1.162 with df = 3; p-value = 0.238 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-12-22_15:31 b-rank test for bits 1 to 8, p=0.33505 b-rank test for bits 2 to 9, p=0.96384 b-rank test for bits 3 to 10, p=0.34510 b-rank test for bits 4 to 11, p=0.65464 b-rank test for bits 5 to 12, p=0.93154 b-rank test for bits 6 to 13, p=0.18208 b-rank test for bits 7 to 14, p=0.03105 b-rank test for bits 8 to 15, p=0.52961 b-rank test for bits 9 to 16, p=0.85645 b-rank test for bits 10 to 17, p=0.72095 b-rank test for bits 11 to 18, p=0.17732 b-rank test for bits 12 to 19, p=0.31958 b-rank test for bits 13 to 20, p=0.33596 b-rank test for bits 14 to 21, p=0.55795 b-rank test for bits 15 to 22, p=0.58415 b-rank test for bits 16 to 23, p=0.26934 b-rank test for bits 17 to 24, p=0.65886 b-rank test for bits 18 to 25, p=0.42980 b-rank test for bits 19 to 26, p=0.69512 b-rank test for bits 20 to 27, p=0.94923 b-rank test for bits 21 to 28, p=0.32865 b-rank test for bits 22 to 29, p=0.94936 b-rank test for bits 23 to 30, p=0.60529 b-rank test for bits 24 to 31, p=0.12216 b-rank test for bits 25 to 32, p=0.67591 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 = 0.773609 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-12-22_15:31 (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 142023 0.27 0.604720 2 142210 0.70 0.758816 3 141541 -0.86 0.194734 4 142569 1.54 0.938376 5 141394 -1.20 0.114287 6 142137 0.53 0.702616 7 141931 0.05 0.520190 8 142350 1.03 0.848402 9 142686 1.81 0.965211 10 141524 -0.90 0.183979 11 141862 -0.11 0.455973 12 142314 0.95 0.827796 13 142011 0.24 0.593884 14 141748 -0.38 0.353109 15 141967 0.13 0.553593 16 141482 -1.00 0.159034 17 142516 1.42 0.921825 18 141905 -0.01 0.495964 19 141723 -0.44 0.331654 20 142541 1.48 0.930010 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-12-22_15:31 Bits used No. missing words z-score p-value 23 to 32 141925 0.0540 0.521546 22 to 31 142245 1.1575 0.876462 21 to 30 142088 0.6161 0.731087 20 to 29 142051 0.4885 0.687408 19 to 28 141960 0.1747 0.569352 18 to 27 141816 -0.3218 0.373792 17 to 26 142238 1.1333 0.871465 16 to 25 142099 0.6540 0.743455 15 to 24 142254 1.1885 0.882685 14 to 23 141743 -0.5736 0.283136 13 to 22 142612 2.4230 0.992304 12 to 21 142239 1.1368 0.872188 11 to 20 141991 0.2816 0.610883 10 to 19 141784 -0.4322 0.332808 9 to 18 142052 0.4920 0.688628 8 to 17 141832 -0.2667 0.394867 7 to 16 141682 -0.7839 0.216550 6 to 15 142003 0.3230 0.626652 5 to 14 142440 1.8299 0.966367 4 to 13 141446 -1.5977 0.055056 3 to 12 141852 -0.1977 0.421644 2 to 11 142524 2.1196 0.982978 1 to 10 142497 2.0264 0.978641 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-12-22_15:31 Bits used No. missing words z-score p-value 28 to 32 142198 0.9785 0.836097 27 to 31 142023 0.3853 0.650001 26 to 30 141543 -1.2418 0.107156 25 to 29 142348 1.4870 0.931495 24 to 28 141579 -1.1198 0.131407 23 to 27 141334 -1.9503 0.025572 22 to 26 141907 -0.0079 0.496849 21 to 25 141677 -0.7876 0.215477 20 to 24 142532 2.1107 0.982603 19 to 23 142347 1.4836 0.931046 18 to 22 141919 0.0328 0.513075 17 to 21 142013 0.3514 0.637365 16 to 20 142567 2.2294 0.987106 15 to 19 141882 -0.0926 0.463093 14 to 18 141780 -0.4384 0.330546 13 to 17 142216 1.0396 0.850728 12 to 16 141826 -0.2825 0.388790 11 to 15 141927 0.0599 0.523882 10 to 14 141801 -0.3672 0.356727 9 to 13 142173 0.8938 0.814285 8 to 12 142002 0.3141 0.623291 7 to 11 141708 -0.6825 0.247470 6 to 10 141577 -1.1265 0.129968 5 to 9 141886 -0.0791 0.468483 4 to 8 141894 -0.0520 0.479278 3 to 7 142104 0.6599 0.745341 2 to 6 142112 0.6870 0.753964 1 to 5 141739 -0.5774 0.281838 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-12-22_15:31 Bits used No. missing words z-score p-value 31 to 32 142207 0.8781 0.810051 30 to 31 141619 -0.8564 0.195880 29 to 30 141995 0.2527 0.599755 28 to 29 142231 0.9489 0.828659 27 to 28 142234 0.9577 0.830900 26 to 27 142335 1.2557 0.895381 25 to 26 141561 -1.0275 0.152087 24 to 25 142054 0.4268 0.665221 23 to 24 141840 -0.2045 0.418976 22 to 23 142449 1.5919 0.944302 21 to 22 142766 2.5271 0.994249 20 to 21 142214 0.8987 0.815602 19 to 20 141887 -0.0659 0.473741 18 to 19 142214 0.8987 0.815602 17 to 18 141114 -2.3461 0.009485 16 to 17 141133 -2.2901 0.011009 15 to 16 142624 2.1082 0.982492 14 to 15 141765 -0.4258 0.335144 13 to 14 142368 1.3530 0.911974 12 to 13 142087 0.5241 0.699896 11 to 12 141838 -0.2104 0.416673 10 to 11 141679 -0.6794 0.248430 9 to 10 142107 0.5831 0.720086 8 to 9 142415 1.4917 0.932105 7 to 8 142245 0.9902 0.838956 6 to 7 141073 -2.4671 0.006812 5 to 6 141715 -0.5732 0.283240 4 to 5 141417 -1.4523 0.073209 3 to 4 141636 -0.8063 0.210040 2 to 3 142658 2.2085 0.986394 1 to 2 141676 -0.6883 0.245635 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-12-22_15:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2497.64 -0.033 0.486662 Test results for specific bytes for dh-ranFile-2016-12-22_15:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2486.33 -0.193 0.423325 2 to 9 2515.24 0.216 0.585312 3 to 10 2451.55 -0.685 0.246600 4 to 11 2471.45 -0.404 0.343191 5 to 12 2569.53 0.983 0.837270 6 to 13 2501.04 0.015 0.505853 7 to 14 2526.67 0.377 0.646958 8 to 15 2557.00 0.806 0.789899 9 to 16 2493.55 -0.091 0.463683 10 to 17 2479.11 -0.295 0.383808 11 to 18 2520.38 0.288 0.613405 12 to 19 2520.32 0.287 0.613102 13 to 20 2509.87 0.140 0.555491 14 to 21 2303.77 -2.775 0.002759 15 to 22 2410.43 -1.267 0.102634 16 to 23 2443.94 -0.793 0.213955 17 to 24 2608.89 1.540 0.938211 18 to 25 2409.85 -1.275 0.101180 19 to 26 2496.13 -0.055 0.478201 20 to 27 2336.00 -2.319 0.010187 21 to 28 2460.54 -0.558 0.288426 22 to 29 2558.78 0.831 0.797081 23 to 30 2400.10 -1.413 0.078865 24 to 31 2641.00 1.994 0.976929 25 to 32 2438.08 -0.876 0.190588 CDPARK for dh-ranFile-2016-12-22_15:31: 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 3496 -1.2329 0.108811 3569 2.1005 0.982156 3516 -0.3196 0.374623 3515 -0.3653 0.357445 3516 -0.3196 0.374623 3494 -1.3242 0.092718 3487 -1.6438 0.050105 3558 1.5982 0.944998 3529 0.2740 0.607947 3506 -0.7763 0.218799 Square side=100, avg. no. parked=3518.60 sample std.=25.50 p-value of the KSTEST for those 10 p-values: 0.317726 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-12-22_15:31 0.3950,0.2620,0.6735,0.6592,0.5084,0.8862,0.7315,0.0685,0.3752,0.6637, The KS test for those 10 p-values: 0.789112 The 3DSPHERES test for dh-ranFile-2016-12-22_15:31 sample no r^3 equiv. uni. 1 82.703 0.936503 2 4.356 0.135138 3 14.124 0.375500 4 4.142 0.128963 5 14.229 0.377678 6 9.757 0.277630 7 15.789 0.409222 8 7.160 0.212335 9 85.216 0.941606 10 38.786 0.725521 11 26.615 0.588183 12 7.475 0.220546 13 71.658 0.908243 14 7.414 0.218953 15 6.586 0.197095 16 18.802 0.465673 17 53.725 0.833178 18 6.170 0.185891 19 13.262 0.357287 20 16.795 0.428688 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.309928 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-12-22_15:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 -0.7 1.1 -0.3 0.3 -0.4 0.2 0.5 -0.0 0.3 0.1 0.1 -0.1 -1.4 0.6 1.7 -2.0 -0.6 0.5 -0.1 1.4 0.3 -1.3 -0.0 -0.8 1.1 -0.0 -1.2 -0.4 0.8 0.6 1.8 1.7 0.1 0.9 -0.3 1.2 0.8 -1.6 0.4 -0.6 -1.0 1.8 Chi-square with 42 degrees of freedom:37.061833 z-score=-0.538798, p-value=0.312798 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-12-22_15:31 Test no p-value 1 0.002997 2 0.177365 3 0.370469 4 0.464745 5 0.003262 6 0.002246 7 0.003378 8 0.124308 9 0.348655 10 0.797329 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000049 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-12-22_15:31: (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 66584 0.10 66835 0.43 3 25000.00 25007 0.00 24856 0.83 4 6666.67 6752 1.09 6624 0.27 5 1388.89 1351 1.03 1415 0.49 6 238.10 262 2.40 226 0.61 7 34.72 37 0.15 39 0.53 8 4.96 6 0.22 4 0.19 p=0.45595 p=0.23570 Number of rngs required: 687498, p-value: 0.147 RESULTS OF CRAPS TEST for dh-ranFile-2016-12-22_15:31 No. of wins: Observed Expected 98063 98585.9 z-score=-2.339, pvalue=0.00968 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66567 66666.7 0.149 0.149 2 37773 37654.3 0.374 0.523 3 26807 26954.7 0.810 1.333 4 19379 19313.5 0.222 1.555 5 13747 13851.4 0.787 2.342 6 10022 9943.5 0.619 2.961 7 7123 7145.0 0.068 3.029 8 5196 5139.1 0.631 3.660 9 3655 3699.9 0.544 4.204 10 2647 2666.3 0.140 4.344 11 1953 1923.3 0.458 4.801 12 1392 1388.7 0.008 4.809 13 1028 1003.7 0.588 5.397 14 768 726.1 2.413 7.810 15 493 525.8 2.050 9.860 16 361 381.2 1.065 10.925 17 311 276.5 4.294 15.220 18 224 200.8 2.673 17.893 19 145 146.0 0.007 17.899 20 126 106.2 3.685 21.585 21 283 287.1 0.059 21.644 Chisq= 21.64 for 20 degrees of freedom, p= 0.63984 SUMMARY of craptest p-value for no. of wins: 0.009680 p-value for throws/game: 0.639844 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-12-22_15:31 No. of wins: Observed Expected 98813 98585.9 z-score= 1.016, pvalue=0.84516 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66678 66666.7 0.002 0.002 2 37797 37654.3 0.541 0.543 3 26809 26954.7 0.788 1.330 4 19381 19313.5 0.236 1.567 5 13869 13851.4 0.022 1.589 6 9776 9943.5 2.823 4.412 7 7205 7145.0 0.503 4.915 8 4990 5139.1 4.324 9.240 9 3698 3699.9 0.001 9.241 10 2668 2666.3 0.001 9.242 11 1960 1923.3 0.699 9.941 12 1412 1388.7 0.390 10.330 13 1008 1003.7 0.018 10.349 14 766 726.1 2.188 12.537 15 488 525.8 2.722 15.259 16 388 381.2 0.123 15.382 17 304 276.5 2.727 18.109 18 216 200.8 1.146 19.255 19 161 146.0 1.544 20.799 20 125 106.2 3.322 24.122 21 301 287.1 0.672 24.793 Chisq= 24.79 for 20 degrees of freedom, p= 0.79054 SUMMARY of craptest p-value for no. of wins: 0.845164 p-value for throws/game: 0.790541 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0000,0.0010,0.0022,0.0028,0.0030,0.0033,0.0034,0.0068,0.0088,0.0095, 0.0097,0.0102,0.0110,0.0146,0.0150,0.0191,0.0256,0.0310,0.0501,0.0551, 0.0685,0.0732,0.0739,0.0789,0.0894,0.0927,0.0947,0.1012,0.1013,0.1026, 0.1072,0.1088,0.1143,0.1222,0.1243,0.1290,0.1300,0.1314,0.1351,0.1470, 0.1521,0.1590,0.1694,0.1712,0.1773,0.1774,0.1821,0.1840,0.1859,0.1906, 0.1947,0.1959,0.1971,0.2100,0.2123,0.2140,0.2155,0.2166,0.2188,0.2190, 0.2205,0.2224,0.2329,0.2357,0.2377,0.2456,0.2466,0.2475,0.2484,0.2517, 0.2526,0.2620,0.2693,0.2768,0.2776,0.2818,0.2831,0.2832,0.2884,0.3099, 0.3128,0.3177,0.3196,0.3223,0.3227,0.3287,0.3305,0.3317,0.3328,0.3350, 0.3351,0.3360,0.3380,0.3432,0.3451,0.3487,0.3531,0.3567,0.3573,0.3574, 0.3705,0.3738,0.3746,0.3746,0.3752,0.3755,0.3777,0.3838,0.3888,0.3903, 0.3949,0.3950,0.4092,0.4167,0.4190,0.4216,0.4233,0.4287,0.4298,0.4560, 0.4560,0.4631,0.4637,0.4647,0.4657,0.4685,0.4737,0.4782,0.4793,0.4867, 0.4960,0.4968,0.5059,0.5084,0.5131,0.5169,0.5202,0.5215,0.5239,0.5296, 0.5315,0.5486,0.5536,0.5555,0.5580,0.5672,0.5678,0.5694,0.5721,0.5841, 0.5853,0.5882,0.5939,0.5998,0.6042,0.6047,0.6053,0.6079,0.6109,0.6131, 0.6134,0.6233,0.6267,0.6374,0.6398,0.6470,0.6500,0.6546,0.6589,0.6592, 0.6637,0.6652,0.6659,0.6735,0.6753,0.6759,0.6874,0.6886,0.6951,0.6999, 0.7025,0.7026,0.7054,0.7201,0.7210,0.7255,0.7311,0.7315,0.7341,0.7435, 0.7437,0.7453,0.7540,0.7546,0.7588,0.7720,0.7736,0.7808,0.7848,0.7891, 0.7899,0.7905,0.7971,0.7973,0.8012,0.8031,0.8070,0.8101,0.8143,0.8155, 0.8156,0.8156,0.8278,0.8287,0.8287,0.8309,0.8332,0.8361,0.8373,0.8390, 0.8452,0.8484,0.8507,0.8562,0.8565,0.8715,0.8722,0.8765,0.8827,0.8833, 0.8862,0.8954,0.8963,0.9012,0.9082,0.9120,0.9218,0.9300,0.9310,0.9315, 0.9315,0.9321,0.9365,0.9382,0.9384,0.9416,0.9443,0.9450,0.9492,0.9494, 0.9540,0.9638,0.9652,0.9664,0.9669,0.9725,0.9769,0.9786,0.9822,0.9823, 0.9825,0.9826,0.9830,0.9864,0.9871,0.9923,0.9924,0.9942,0.9983, Overall p-value after applying KStest on 269 p-values = 0.127016 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.