RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-03-23_02:31 (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 24.9432 0.904012 2 to 25 15.64 18.4847 0.641103 3 to 26 15.73 15.1294 0.413838 4 to 27 15.59 11.6733 0.180498 5 to 28 15.76 17.9048 0.605129 6 to 29 16.14 12.2233 0.213569 7 to 30 15.72 16.0684 0.481011 8 to 31 15.88 12.2978 0.218220 9 to 32 15.94 13.9889 0.332116 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.620431 Tough bday spacings test for dh-ranFile-2018-03-23_02:31: 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 10 36 68 93 88 95 59 20 17 13 1 (O-E)^2/E 0.1 0.0 0.4 0.2 1.0 3.6 0.9 3.2 0.3 6.2 2.3 Birthday Spacings: Sum(O-E)^2/E= 18.180, p= 0.948 RESULTS OF GCD FOR dh-ranFile-2018-03-23_02:31 Euclid's algorithm: p-value, steps to gcd: 0.335639 p-value, dist. of gcd's: 0.691012 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-03-23_02:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.052 0.872 0.043 0.720 0.336 0.967 0.770 0.141 Bits 8 to 15---> 0.705 0.505 0.645 0.604 0.705 0.942 0.838 0.164 Bits 16 to 23---> 0.089 0.083 0.640 0.006 0.932 0.763 0.308 0.447 Bits 24 to 31---> 0.265 0.941 0.438 0.575 0.301 0.625 0.224 0.746 KS test for the above 32 p values: 0.081 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-03-23_02:31, p-values for 5 runs: 0.0369, 0.0440, 0.2805, 0.6729, 0.4286 Rank test for binary matrices (31x31) for dh-ranFile-2018-03-23_02:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 216 211.4 0.099 0.099 r= 29 5091 5134.0 0.360 0.460 r= 30 23205 23103.0 0.450 0.910 r= 31 11488 11551.5 0.349 1.259 chi-square = 1.259 with df = 3; p-value = 0.261 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-03-23_02:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 218 211.4 0.205 0.205 r= 30 5118 5134.0 0.050 0.255 r= 31 23064 23103.0 0.066 0.321 r= 32 11600 11551.5 0.203 0.524 chi-square = 0.524 with df = 3; p-value = 0.086 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-03-23_02:31 b-rank test for bits 1 to 8, p=0.55907 b-rank test for bits 2 to 9, p=0.26292 b-rank test for bits 3 to 10, p=0.98426 b-rank test for bits 4 to 11, p=0.95036 b-rank test for bits 5 to 12, p=0.61035 b-rank test for bits 6 to 13, p=0.13939 b-rank test for bits 7 to 14, p=0.09280 b-rank test for bits 8 to 15, p=0.07734 b-rank test for bits 9 to 16, p=0.86941 b-rank test for bits 10 to 17, p=0.87158 b-rank test for bits 11 to 18, p=0.05553 b-rank test for bits 12 to 19, p=0.47289 b-rank test for bits 13 to 20, p=0.06586 b-rank test for bits 14 to 21, p=0.29493 b-rank test for bits 15 to 22, p=0.97538 b-rank test for bits 16 to 23, p=0.93635 b-rank test for bits 17 to 24, p=0.33697 b-rank test for bits 18 to 25, p=0.52088 b-rank test for bits 19 to 26, p=0.20943 b-rank test for bits 20 to 27, p=0.87950 b-rank test for bits 21 to 28, p=0.15537 b-rank test for bits 22 to 29, p=0.81517 b-rank test for bits 23 to 30, p=0.52123 b-rank test for bits 24 to 31, p=0.57094 b-rank test for bits 25 to 32, p=0.13811 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 = 0.452744 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-03-23_02:31 (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 141188 -1.69 0.045960 2 142290 0.89 0.813110 3 141776 -0.31 0.377703 4 141610 -0.70 0.242161 5 142186 0.65 0.740998 6 142157 0.58 0.718594 7 141592 -0.74 0.229218 8 142087 0.42 0.660972 9 142664 1.76 0.961071 10 142393 1.13 0.870777 11 142081 0.40 0.655826 12 141991 0.19 0.575666 13 141660 -0.58 0.280099 14 142734 1.93 0.972998 15 142056 0.34 0.634083 16 142317 0.95 0.829578 17 142180 0.63 0.736439 18 141320 -1.38 0.084266 19 141150 -1.77 0.038020 20 141809 -0.23 0.407331 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-03-23_02:31 Bits used No. missing words z-score p-value 23 to 32 141271 -2.2011 0.013863 22 to 31 142033 0.4264 0.665109 21 to 30 141406 -1.7356 0.041315 20 to 29 141958 0.1678 0.566641 19 to 28 142434 1.8092 0.964791 18 to 27 142184 0.9471 0.828216 17 to 26 142035 0.4333 0.667618 16 to 25 142129 0.7575 0.775620 15 to 24 141391 -1.7873 0.036941 14 to 23 142269 1.2402 0.892557 13 to 22 141822 -0.3011 0.381655 12 to 21 141587 -1.1115 0.133180 11 to 20 142118 0.7196 0.764100 10 to 19 141848 -0.2115 0.416255 9 to 18 141980 0.2437 0.596264 8 to 17 141699 -0.7253 0.234141 7 to 16 141466 -1.5287 0.063166 6 to 15 141608 -1.0391 0.149386 5 to 14 141611 -1.0287 0.151805 4 to 13 141688 -0.7632 0.222670 3 to 12 141767 -0.4908 0.311786 2 to 11 142228 1.0989 0.864086 1 to 10 142571 2.2816 0.988744 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-03-23_02:31 Bits used No. missing words z-score p-value 28 to 32 142167 0.8735 0.808793 27 to 31 141700 -0.7096 0.238978 26 to 30 142475 1.9175 0.972414 25 to 29 141969 0.2023 0.580148 24 to 28 142154 0.8294 0.796558 23 to 27 141676 -0.7909 0.214487 22 to 26 141637 -0.9232 0.177964 21 to 25 141803 -0.3604 0.359259 20 to 24 141708 -0.6825 0.247470 19 to 23 141640 -0.9130 0.180626 18 to 22 142133 0.7582 0.775835 17 to 21 141817 -0.3130 0.377147 16 to 20 142148 0.8091 0.790757 15 to 19 142329 1.4226 0.922575 14 to 18 142390 1.6294 0.948385 13 to 17 141728 -0.6147 0.269384 12 to 16 141971 0.2091 0.582796 11 to 15 141691 -0.7401 0.229619 10 to 14 141817 -0.3130 0.377147 9 to 13 142133 0.7582 0.775835 8 to 12 141834 -0.2554 0.399224 7 to 11 142037 0.4328 0.667413 6 to 10 141965 0.1887 0.574841 5 to 9 141771 -0.4689 0.319565 4 to 8 141757 -0.5164 0.302797 3 to 7 142047 0.4667 0.679635 2 to 6 142293 1.3006 0.903298 1 to 5 142253 1.1650 0.877987 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-03-23_02:31 Bits used No. missing words z-score p-value 31 to 32 141718 -0.5644 0.286243 30 to 31 141611 -0.8800 0.189422 29 to 30 142082 0.5094 0.694747 28 to 29 142128 0.6450 0.740551 27 to 28 141669 -0.7089 0.239182 26 to 27 141017 -2.6322 0.004241 25 to 26 141851 -0.1721 0.431693 24 to 25 142229 0.9430 0.827154 23 to 24 141759 -0.4435 0.328720 22 to 23 141916 0.0197 0.507849 21 to 22 141469 -1.2989 0.096988 20 to 21 142141 0.6834 0.752821 19 to 20 141932 0.0669 0.526659 18 to 19 141339 -1.6824 0.046247 17 to 18 142329 1.2380 0.892135 16 to 17 141211 -2.0600 0.019701 15 to 16 141324 -1.7266 0.042116 14 to 15 141846 -0.1868 0.425903 13 to 14 141533 -1.1101 0.133474 12 to 13 142025 0.3412 0.633527 11 to 12 142100 0.5624 0.713095 10 to 11 141772 -0.4051 0.342701 9 to 10 142526 1.8191 0.965551 8 to 9 141141 -2.2665 0.011712 7 to 8 141925 0.0462 0.518434 6 to 7 141675 -0.6912 0.244708 5 to 6 142008 0.2911 0.614498 4 to 5 142007 0.2881 0.613370 3 to 4 142353 1.3088 0.904692 2 to 3 141935 0.0757 0.530180 1 to 2 141407 -1.4818 0.069197 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-03-23_02:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2356.72 -2.026 0.021370 Test results for specific bytes for dh-ranFile-2018-03-23_02:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2580.09 1.133 0.871306 2 to 9 2518.02 0.255 0.600592 3 to 10 2488.96 -0.156 0.437971 4 to 11 2506.98 0.099 0.539297 5 to 12 2470.91 -0.411 0.340406 6 to 13 2398.92 -1.429 0.076441 7 to 14 2342.36 -2.229 0.012893 8 to 15 2481.36 -0.264 0.396065 9 to 16 2527.63 0.391 0.652014 10 to 17 2404.19 -1.355 0.087710 11 to 18 2541.13 0.582 0.719598 12 to 19 2476.95 -0.326 0.372242 13 to 20 2719.73 3.107 0.999056 14 to 21 2520.17 0.285 0.612276 15 to 22 2430.79 -0.979 0.163841 16 to 23 2545.99 0.650 0.742271 17 to 24 2499.51 -0.007 0.497214 18 to 25 2377.98 -1.726 0.042210 19 to 26 2543.54 0.616 0.730947 20 to 27 2486.83 -0.186 0.426111 21 to 28 2503.44 0.049 0.519424 22 to 29 2510.56 0.149 0.559376 23 to 30 2537.54 0.531 0.702236 24 to 31 2545.11 0.638 0.738265 25 to 32 2452.66 -0.669 0.251604 CDPARK for dh-ranFile-2018-03-23_02:31: 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 3521 -0.0913 0.463617 3502 -0.9589 0.168804 3545 1.0046 0.842447 3546 1.0502 0.853193 3552 1.3242 0.907282 3514 -0.4110 0.340551 3544 0.9589 0.831196 3551 1.2785 0.899470 3499 -1.0959 0.136563 3515 -0.3653 0.357445 Square side=100, avg. no. parked=3528.90 sample std.=19.74 p-value of the KSTEST for those 10 p-values: 0.372325 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-03-23_02:31 0.3661,0.8346,0.3252,0.4212,0.1147,0.9897,0.2525,0.7953,0.8694,0.6126, The KS test for those 10 p-values: 0.766937 The 3DSPHERES test for dh-ranFile-2018-03-23_02:31 sample no r^3 equiv. uni. 1 8.434 0.245068 2 0.688 0.022674 3 45.576 0.781114 4 11.740 0.323839 5 51.633 0.821129 6 49.107 0.805419 7 98.477 0.962468 8 38.818 0.725813 9 8.359 0.243173 10 55.179 0.841069 11 83.640 0.938456 12 3.076 0.097448 13 3.134 0.099202 14 17.746 0.446521 15 52.919 0.828638 16 58.045 0.855553 17 46.716 0.789274 18 3.653 0.114654 19 105.888 0.970683 20 82.957 0.937039 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.063311 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-03-23_02:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 1.3 0.1 0.1 0.8 -0.9 -0.1 0.4 -0.0 0.9 0.3 0.0 -0.9 0.3 -0.5 -0.5 -0.7 0.2 -0.4 -0.2 -0.3 0.5 -0.3 1.8 -0.9 0.2 1.7 1.0 -0.9 0.3 0.7 -1.8 0.1 1.2 -0.6 1.0 1.3 2.1 -0.4 0.5 -0.1 -1.3 -1.0 -0.1 Chi-square with 42 degrees of freedom:31.848372 z-score=-1.107633, p-value=0.127633 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-03-23_02:31 Test no p-value 1 0.325740 2 0.007432 3 0.258601 4 0.000951 5 0.377531 6 0.145938 7 0.418799 8 0.920829 9 0.110732 10 0.024802 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.003182 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-03-23_02:31: (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 66502 0.41 66463 0.62 3 25000.00 25123 0.61 25189 1.43 4 6666.67 6692 0.10 6591 0.86 5 1388.89 1417 0.57 1469 4.62 6 238.10 234 0.07 254 1.06 7 34.72 31 0.40 29 0.94 8 4.96 0 4.96 4 0.19 p=0.68885 p=0.86311 Number of rngs required: 689588, p-value: 0.916 RESULTS OF CRAPS TEST for dh-ranFile-2018-03-23_02:31 No. of wins: Observed Expected 98458 98585.9 z-score=-0.572, pvalue=0.28371 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66797 66666.7 0.255 0.255 2 37659 37654.3 0.001 0.255 3 26851 26954.7 0.399 0.655 4 19212 19313.5 0.533 1.188 5 13894 13851.4 0.131 1.319 6 9952 9943.5 0.007 1.326 7 7210 7145.0 0.591 1.917 8 5187 5139.1 0.447 2.364 9 3578 3699.9 4.014 6.377 10 2711 2666.3 0.749 7.127 11 1899 1923.3 0.308 7.435 12 1367 1388.7 0.340 7.775 13 990 1003.7 0.187 7.962 14 727 726.1 0.001 7.963 15 533 525.8 0.098 8.061 16 372 381.2 0.220 8.281 17 281 276.5 0.072 8.353 18 225 200.8 2.909 11.262 19 147 146.0 0.007 11.269 20 120 106.2 1.789 13.058 21 288 287.1 0.003 13.060 Chisq= 13.06 for 20 degrees of freedom, p= 0.12522 SUMMARY of craptest p-value for no. of wins: 0.283709 p-value for throws/game: 0.125223 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-03-23_02:31 No. of wins: Observed Expected 98869 98585.9 z-score= 1.266, pvalue=0.89731 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66625 66666.7 0.026 0.026 2 37690 37654.3 0.034 0.060 3 27003 26954.7 0.086 0.146 4 19343 19313.5 0.045 0.191 5 13937 13851.4 0.529 0.720 6 9848 9943.5 0.918 1.638 7 7229 7145.0 0.987 2.625 8 5103 5139.1 0.253 2.878 9 3578 3699.9 4.014 6.892 10 2695 2666.3 0.309 7.201 11 1953 1923.3 0.458 7.659 12 1363 1388.7 0.477 8.136 13 964 1003.7 1.571 9.708 14 743 726.1 0.391 10.099 15 549 525.8 1.020 11.119 16 372 381.2 0.220 11.339 17 282 276.5 0.108 11.447 18 208 200.8 0.256 11.703 19 125 146.0 3.016 14.719 20 105 106.2 0.014 14.733 21 285 287.1 0.016 14.749 Chisq= 14.75 for 20 degrees of freedom, p= 0.20940 SUMMARY of craptest p-value for no. of wins: 0.897310 p-value for throws/game: 0.209403 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0010,0.0032,0.0042,0.0062,0.0074,0.0117,0.0129,0.0139,0.0197,0.0214, 0.0227,0.0248,0.0369,0.0369,0.0380,0.0413,0.0421,0.0422,0.0429,0.0440, 0.0460,0.0462,0.0523,0.0555,0.0632,0.0633,0.0659,0.0692,0.0764,0.0773, 0.0809,0.0828,0.0843,0.0865,0.0877,0.0886,0.0928,0.0970,0.0974,0.0992, 0.1107,0.1147,0.1147,0.1252,0.1276,0.1332,0.1335,0.1366,0.1381,0.1394, 0.1408,0.1459,0.1494,0.1518,0.1554,0.1638,0.1638,0.1688,0.1780,0.1805, 0.1806,0.1894,0.2094,0.2094,0.2136,0.2145,0.2182,0.2227,0.2235,0.2292, 0.2296,0.2341,0.2390,0.2392,0.2422,0.2432,0.2447,0.2451,0.2475,0.2516, 0.2525,0.2586,0.2611,0.2629,0.2648,0.2694,0.2801,0.2805,0.2837,0.2862, 0.2949,0.3012,0.3028,0.3079,0.3118,0.3196,0.3238,0.3252,0.3257,0.3287, 0.3321,0.3355,0.3356,0.3370,0.3404,0.3406,0.3427,0.3574,0.3593,0.3661, 0.3722,0.3723,0.3771,0.3771,0.3775,0.3777,0.3817,0.3961,0.3992,0.4073, 0.4138,0.4163,0.4188,0.4212,0.4259,0.4261,0.4286,0.4317,0.4380,0.4382, 0.4465,0.4466,0.4527,0.4636,0.4729,0.4810,0.4972,0.5048,0.5078,0.5184, 0.5194,0.5209,0.5212,0.5267,0.5302,0.5393,0.5591,0.5594,0.5666,0.5709, 0.5748,0.5748,0.5757,0.5801,0.5828,0.5963,0.6006,0.6041,0.6051,0.6103, 0.6123,0.6126,0.6134,0.6145,0.6204,0.6253,0.6335,0.6341,0.6396,0.6411, 0.6452,0.6520,0.6558,0.6610,0.6651,0.6674,0.6676,0.6729,0.6796,0.6889, 0.6910,0.6947,0.7022,0.7047,0.7055,0.7131,0.7186,0.7196,0.7198,0.7258, 0.7309,0.7364,0.7383,0.7406,0.7410,0.7423,0.7460,0.7528,0.7631,0.7641, 0.7669,0.7698,0.7756,0.7758,0.7758,0.7811,0.7893,0.7908,0.7953,0.7966, 0.8054,0.8088,0.8131,0.8152,0.8211,0.8272,0.8282,0.8286,0.8296,0.8312, 0.8346,0.8378,0.8411,0.8424,0.8532,0.8556,0.8631,0.8641,0.8694,0.8694, 0.8708,0.8713,0.8716,0.8721,0.8780,0.8795,0.8921,0.8926,0.8973,0.8995, 0.9033,0.9040,0.9047,0.9073,0.9164,0.9208,0.9226,0.9319,0.9364,0.9370, 0.9385,0.9413,0.9420,0.9480,0.9484,0.9504,0.9611,0.9625,0.9648,0.9656, 0.9673,0.9707,0.9724,0.9730,0.9754,0.9843,0.9887,0.9897,0.9991, Overall p-value after applying KStest on 269 p-values = 0.173789 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.