RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-01-31_03:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.69 17.9314 0.606816 2 to 25 15.95 12.3492 0.221452 3 to 26 15.70 23.0446 0.852196 4 to 27 15.60 22.5952 0.837102 5 to 28 15.84 22.1966 0.822722 6 to 29 15.55 19.9988 0.725712 7 to 30 15.88 9.4877 0.076292 8 to 31 15.83 12.5763 0.235946 9 to 32 15.92 12.2838 0.217345 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.752913 Tough bday spacings test for dh-ranFile-2016-01-31_03:31: 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 70 94 99 84 48 35 12 8 4 (O-E)^2/E 0.0 0.0 0.1 0.1 0.0 0.4 0.3 0.9 0.6 0.3 0.0 Birthday Spacings: Sum(O-E)^2/E= 2.838, p= 0.015 RESULTS OF GCD FOR dh-ranFile-2016-01-31_03:31 Euclid's algorithm: p-value, steps to gcd: 0.216985 p-value, dist. of gcd's: 0.648717 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-01-31_03:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.411 0.576 0.905 0.491 0.489 0.043 0.497 0.615 Bits 8 to 15---> 0.949 0.070 0.554 0.817 0.935 0.744 0.142 0.164 Bits 16 to 23---> 0.284 0.085 0.716 0.733 0.731 0.043 0.424 0.557 Bits 24 to 31---> 0.627 0.562 0.911 0.666 0.202 0.879 0.814 0.594 KS test for the above 32 p values: 0.437 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-01-31_03:31, p-values for 5 runs: 0.3434, 0.1258, 0.1799, 0.4453, 0.9556 Rank test for binary matrices (31x31) for dh-ranFile-2016-01-31_03:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 226 211.4 1.006 1.006 r= 29 5181 5134.0 0.430 1.436 r= 30 23051 23103.0 0.117 1.553 r= 31 11542 11551.5 0.008 1.561 chi-square = 1.561 with df = 3; p-value = 0.332 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-01-31_03:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 211 211.4 0.001 0.001 r= 30 5148 5134.0 0.038 0.039 r= 31 23084 23103.0 0.016 0.055 r= 32 11557 11551.5 0.003 0.057 chi-square = 0.057 with df = 3; p-value = 0.004 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-01-31_03:31 b-rank test for bits 1 to 8, p=0.19509 b-rank test for bits 2 to 9, p=0.94807 b-rank test for bits 3 to 10, p=0.97065 b-rank test for bits 4 to 11, p=0.19354 b-rank test for bits 5 to 12, p=0.89589 b-rank test for bits 6 to 13, p=0.63794 b-rank test for bits 7 to 14, p=0.63210 b-rank test for bits 8 to 15, p=0.85870 b-rank test for bits 9 to 16, p=0.81649 b-rank test for bits 10 to 17, p=0.29682 b-rank test for bits 11 to 18, p=0.77212 b-rank test for bits 12 to 19, p=0.46421 b-rank test for bits 13 to 20, p=0.30974 b-rank test for bits 14 to 21, p=0.18953 b-rank test for bits 15 to 22, p=0.65794 b-rank test for bits 16 to 23, p=0.08087 b-rank test for bits 17 to 24, p=0.59659 b-rank test for bits 18 to 25, p=0.00619 b-rank test for bits 19 to 26, p=0.87384 b-rank test for bits 20 to 27, p=0.11492 b-rank test for bits 21 to 28, p=0.75815 b-rank test for bits 22 to 29, p=0.99143 b-rank test for bits 23 to 30, p=0.19092 b-rank test for bits 24 to 31, p=0.21714 b-rank test for bits 25 to 32, p=0.29692 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 = 0.643385 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-01-31_03:31 (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 141915 0.01 0.505285 2 141875 -0.08 0.468035 3 143144 2.88 0.998041 4 142322 0.96 0.832523 5 141818 -0.21 0.415512 6 141870 -0.09 0.463392 7 141860 -0.12 0.454121 8 141884 -0.06 0.476404 9 141574 -0.78 0.216672 10 142098 0.44 0.670328 11 143177 2.96 0.998471 12 141521 -0.91 0.182121 13 142356 1.04 0.851670 14 141781 -0.30 0.382151 15 141443 -1.09 0.137954 16 142569 1.54 0.938376 17 142161 0.59 0.721739 18 141786 -0.29 0.386614 19 142343 1.01 0.844529 20 142266 0.83 0.797674 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-01-31_03:31 Bits used No. missing words z-score p-value 23 to 32 142288 1.3058 0.904183 22 to 31 142058 0.5127 0.695904 21 to 30 141748 -0.5563 0.288999 20 to 29 141887 -0.0770 0.469312 19 to 28 142035 0.4333 0.667618 18 to 27 141703 -0.7115 0.238393 17 to 26 142136 0.7816 0.782781 16 to 25 141878 -0.1080 0.456984 15 to 24 141906 -0.0115 0.495419 14 to 23 142003 0.3230 0.626652 13 to 22 142271 1.2471 0.893827 12 to 21 142086 0.6092 0.728806 11 to 20 141853 -0.1942 0.422994 10 to 19 141950 0.1402 0.555765 9 to 18 141749 -0.5529 0.290179 8 to 17 142518 2.0989 0.982085 7 to 16 142100 0.6575 0.744565 6 to 15 142109 0.6885 0.754436 5 to 14 141328 -2.0046 0.022504 4 to 13 141274 -2.1908 0.014233 3 to 12 142704 2.7402 0.996930 2 to 11 142181 0.9368 0.825568 1 to 10 142217 1.0609 0.855639 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-01-31_03:31 Bits used No. missing words z-score p-value 28 to 32 142136 0.7684 0.778867 27 to 31 142206 1.0057 0.842711 26 to 30 141647 -0.8893 0.186933 25 to 29 141739 -0.5774 0.281838 24 to 28 141733 -0.5977 0.275010 23 to 27 141611 -1.0113 0.155939 22 to 26 142125 0.7311 0.767636 21 to 25 141620 -0.9808 0.163351 20 to 24 142084 0.5921 0.723109 19 to 23 141260 -2.2011 0.013864 18 to 22 142161 0.8531 0.803203 17 to 21 142130 0.7480 0.772780 16 to 20 141839 -0.2384 0.405783 15 to 19 142274 1.2362 0.891802 14 to 18 141685 -0.7604 0.223496 13 to 17 141489 -1.4248 0.077101 12 to 16 141565 -1.1672 0.121561 11 to 15 141908 -0.0045 0.498201 10 to 14 141324 -1.9842 0.023618 9 to 13 142074 0.5582 0.711647 8 to 12 142233 1.0972 0.863720 7 to 11 141812 -0.3299 0.370726 6 to 10 142076 0.5650 0.713957 5 to 9 142153 0.8260 0.795598 4 to 8 141815 -0.3198 0.374574 3 to 7 141809 -0.3401 0.366890 2 to 6 142200 0.9853 0.837767 1 to 5 142378 1.5887 0.943937 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-01-31_03:31 Bits used No. missing words z-score p-value 31 to 32 141929 0.0580 0.523135 30 to 31 142019 0.3235 0.626846 29 to 30 141864 -0.1337 0.446813 28 to 29 142323 1.2203 0.888818 27 to 28 142058 0.4386 0.669508 26 to 27 141800 -0.3225 0.373534 25 to 26 141935 0.0757 0.530180 24 to 25 141348 -1.6558 0.048877 23 to 24 141698 -0.6234 0.266513 22 to 23 141937 0.0816 0.532527 21 to 22 142662 2.2203 0.986800 20 to 21 141979 0.2055 0.581416 19 to 20 142378 1.3825 0.916592 18 to 19 141635 -0.8092 0.209191 17 to 18 142284 1.1052 0.865468 16 to 17 142488 1.7070 0.956088 15 to 16 141524 -1.1367 0.127839 14 to 15 141593 -0.9331 0.175377 13 to 14 142225 0.9312 0.824120 12 to 13 142117 0.6126 0.729928 11 to 12 141884 -0.0747 0.470219 10 to 11 141889 -0.0600 0.476090 9 to 10 141989 0.2350 0.592901 8 to 9 141392 -1.5260 0.063499 7 to 8 142112 0.5978 0.725029 6 to 7 141712 -0.5821 0.280252 5 to 6 141256 -1.9272 0.026976 4 to 5 142327 1.2321 0.891038 3 to 4 141896 -0.0393 0.484317 2 to 3 141866 -0.1278 0.449147 1 to 2 141307 -1.7768 0.037802 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-01-31_03:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2609.02 1.542 0.938432 Test results for specific bytes for dh-ranFile-2016-01-31_03:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2419.46 -1.139 0.127352 2 to 9 2465.65 -0.486 0.313551 3 to 10 2549.75 0.704 0.759162 4 to 11 2521.53 0.305 0.619645 5 to 12 2473.82 -0.370 0.355595 6 to 13 2608.86 1.540 0.938165 7 to 14 2500.84 0.012 0.504718 8 to 15 2442.27 -0.816 0.207118 9 to 16 2484.09 -0.225 0.410970 10 to 17 2610.14 1.558 0.940342 11 to 18 2462.64 -0.528 0.298622 12 to 19 2523.79 0.336 0.631705 13 to 20 2551.15 0.723 0.765283 14 to 21 2361.54 -1.958 0.025112 15 to 22 2465.32 -0.490 0.311901 16 to 23 2394.00 -1.499 0.066936 17 to 24 2497.98 -0.029 0.488621 18 to 25 2597.19 1.375 0.915362 19 to 26 2427.65 -1.023 0.153100 20 to 27 2400.83 -1.402 0.080395 21 to 28 2525.54 0.361 0.641004 22 to 29 2422.36 -1.098 0.136093 23 to 30 2478.42 -0.305 0.380110 24 to 31 2459.31 -0.575 0.282480 25 to 32 2488.32 -0.165 0.434414 CDPARK for dh-ranFile-2016-01-31_03:31: 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 3550 1.2329 0.891189 3530 0.3196 0.625377 3520 -0.1370 0.445521 3475 -2.1918 0.014198 3526 0.1370 0.554479 3492 -1.4155 0.078457 3486 -1.6895 0.045562 3522 -0.0457 0.481790 3514 -0.4110 0.340551 3529 0.2740 0.607947 Square side=100, avg. no. parked=3514.40 sample std.=21.93 p-value of the KSTEST for those 10 p-values: 0.356804 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-01-31_03:31 0.3999,0.4324,0.7343,0.1930,0.2210,0.9696,0.6200,0.7454,0.4777,0.3037, The KS test for those 10 p-values: 0.837569 The 3DSPHERES test for dh-ranFile-2016-01-31_03:31 sample no r^3 equiv. uni. 1 31.885 0.654526 2 65.999 0.889192 3 28.683 0.615608 4 38.972 0.727211 5 14.841 0.390249 6 17.028 0.433118 7 56.292 0.846859 8 31.118 0.645579 9 52.776 0.827820 10 5.631 0.171136 11 9.355 0.267905 12 2.722 0.086742 13 38.458 0.722499 14 38.397 0.721939 15 29.522 0.626217 16 4.828 0.148663 17 31.172 0.646220 18 38.052 0.718717 19 5.548 0.168840 20 49.930 0.810682 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.288297 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-01-31_03:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.5 -0.4 0.0 1.9 1.1 -0.2 0.9 0.2 -1.5 0.1 0.9 -0.8 -0.0 1.3 -1.0 -1.7 0.7 0.2 2.4 -0.4 -0.1 -0.3 -0.6 -1.2 0.1 -0.6 -1.1 0.2 0.4 1.9 -0.2 0.9 -0.2 -0.4 -0.5 -1.4 1.8 0.9 -0.1 -1.3 -1.0 2.7 Chi-square with 42 degrees of freedom:47.133582 z-score=0.560120, p-value=0.729370 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-01-31_03:31 Test no p-value 1 0.908265 2 0.457257 3 0.027081 4 0.005898 5 0.035603 6 0.394004 7 0.000970 8 0.363647 9 0.809858 10 0.003959 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000643 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-01-31_03:31: (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 66766 0.15 66359 1.42 3 25000.00 24954 0.08 25223 1.99 4 6666.67 6625 0.26 6702 0.19 5 1388.89 1369 0.28 1422 0.79 6 238.10 236 0.02 237 0.01 7 34.72 48 5.08 52 8.60 8 4.96 1 3.16 4 0.19 p=0.82852 p=0.95969 Number of rngs required: 689762, p-value: 0.944 RESULTS OF CRAPS TEST for dh-ranFile-2016-01-31_03:31 No. of wins: Observed Expected 98692 98585.9 z-score= 0.475, pvalue=0.68251 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66949 66666.7 1.196 1.196 2 37261 37654.3 4.108 5.304 3 26882 26954.7 0.196 5.500 4 19296 19313.5 0.016 5.516 5 13835 13851.4 0.019 5.536 6 9955 9943.5 0.013 5.549 7 7285 7145.0 2.742 8.291 8 5125 5139.1 0.039 8.330 9 3663 3699.9 0.367 8.697 10 2696 2666.3 0.331 9.028 11 1909 1923.3 0.107 9.135 12 1414 1388.7 0.459 9.594 13 1041 1003.7 1.385 10.979 14 724 726.1 0.006 10.985 15 535 525.8 0.160 11.145 16 386 381.2 0.062 11.207 17 313 276.5 4.807 16.014 18 208 200.8 0.256 16.270 19 148 146.0 0.028 16.298 20 103 106.2 0.097 16.395 21 272 287.1 0.796 17.191 Chisq= 17.19 for 20 degrees of freedom, p= 0.35944 SUMMARY of craptest p-value for no. of wins: 0.682509 p-value for throws/game: 0.359437 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-01-31_03:31 No. of wins: Observed Expected 98563 98585.9 z-score=-0.102, pvalue=0.45928 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66474 66666.7 0.557 0.557 2 37624 37654.3 0.024 0.581 3 26972 26954.7 0.011 0.592 4 19446 19313.5 0.910 1.502 5 13816 13851.4 0.091 1.592 6 10022 9943.5 0.619 2.211 7 7091 7145.0 0.409 2.620 8 5119 5139.1 0.078 2.698 9 3767 3699.9 1.218 3.917 10 2654 2666.3 0.057 3.973 11 1975 1923.3 1.388 5.361 12 1420 1388.7 0.704 6.065 13 994 1003.7 0.094 6.159 14 696 726.1 1.251 7.410 15 503 525.8 0.992 8.402 16 373 381.2 0.174 8.576 17 298 276.5 1.665 10.242 18 200 200.8 0.003 10.245 19 146 146.0 0.000 10.245 20 108 106.2 0.030 10.275 21 302 287.1 0.772 11.047 Chisq= 11.05 for 20 degrees of freedom, p= 0.05500 SUMMARY of craptest p-value for no. of wins: 0.459284 p-value for throws/game: 0.055000 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0006,0.0010,0.0036,0.0040,0.0059,0.0062,0.0139,0.0142,0.0142,0.0150, 0.0225,0.0236,0.0251,0.0270,0.0271,0.0356,0.0378,0.0430,0.0434,0.0456, 0.0489,0.0550,0.0635,0.0669,0.0700,0.0763,0.0771,0.0785,0.0804,0.0809, 0.0847,0.0867,0.1149,0.1216,0.1258,0.1274,0.1278,0.1361,0.1380,0.1421, 0.1487,0.1531,0.1559,0.1634,0.1636,0.1688,0.1711,0.1754,0.1799,0.1821, 0.1869,0.1895,0.1909,0.1930,0.1935,0.1951,0.2017,0.2071,0.2092,0.2167, 0.2170,0.2171,0.2173,0.2210,0.2215,0.2235,0.2359,0.2384,0.2665,0.2679, 0.2750,0.2803,0.2818,0.2825,0.2839,0.2883,0.2890,0.2902,0.2968,0.2969, 0.2986,0.3037,0.3097,0.3119,0.3136,0.3317,0.3406,0.3434,0.3556,0.3568, 0.3594,0.3636,0.3669,0.3707,0.3735,0.3746,0.3801,0.3822,0.3866,0.3902, 0.3940,0.3999,0.4058,0.4107,0.4110,0.4155,0.4230,0.4236,0.4324,0.4331, 0.4344,0.4372,0.4453,0.4455,0.4468,0.4491,0.4541,0.4570,0.4573,0.4593, 0.4634,0.4642,0.4680,0.4693,0.4702,0.4761,0.4764,0.4777,0.4818,0.4843, 0.4886,0.4887,0.4906,0.4954,0.4969,0.4982,0.5047,0.5053,0.5231,0.5302, 0.5325,0.5538,0.5545,0.5558,0.5568,0.5618,0.5759,0.5814,0.5929,0.5939, 0.5966,0.6068,0.6079,0.6150,0.6156,0.6196,0.6200,0.6254,0.6262,0.6267, 0.6268,0.6274,0.6317,0.6321,0.6379,0.6410,0.6434,0.6456,0.6462,0.6487, 0.6545,0.6579,0.6658,0.6676,0.6695,0.6703,0.6825,0.6959,0.7116,0.7140, 0.7165,0.7187,0.7217,0.7219,0.7225,0.7231,0.7250,0.7257,0.7272,0.7288, 0.7294,0.7299,0.7308,0.7333,0.7343,0.7443,0.7446,0.7454,0.7529,0.7544, 0.7582,0.7592,0.7653,0.7676,0.7721,0.7728,0.7789,0.7828,0.7956,0.7977, 0.8032,0.8099,0.8107,0.8142,0.8165,0.8168,0.8227,0.8241,0.8256,0.8278, 0.8285,0.8325,0.8371,0.8376,0.8378,0.8427,0.8445,0.8469,0.8517,0.8522, 0.8556,0.8587,0.8637,0.8655,0.8738,0.8785,0.8888,0.8892,0.8910,0.8912, 0.8918,0.8938,0.8959,0.9042,0.9050,0.9083,0.9112,0.9154,0.9166,0.9354, 0.9382,0.9384,0.9384,0.9403,0.9439,0.9441,0.9481,0.9493,0.9556,0.9561, 0.9597,0.9696,0.9707,0.9821,0.9868,0.9914,0.9969,0.9980,0.9985, Overall p-value after applying KStest on 269 p-values = 0.505478 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.