RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-11-01_10:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.50 18.8960 0.665464 2 to 25 15.26 27.0073 0.942039 3 to 26 15.83 15.9544 0.472928 4 to 27 15.89 7.3698 0.021765 5 to 28 15.92 20.7013 0.760062 6 to 29 16.03 9.1592 0.064867 7 to 30 15.96 27.1954 0.944737 8 to 31 15.99 16.6514 0.521783 9 to 32 15.93 17.9169 0.605896 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.568929 Tough bday spacings test for dh-ranFile-2016-11-01_10:31: 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 3 33 69 98 97 88 64 28 13 7 0 (O-E)^2/E 4.1 0.4 0.2 0.0 0.0 1.2 2.7 0.1 0.2 0.0 4.1 Birthday Spacings: Sum(O-E)^2/E= 13.148, p= 0.785 RESULTS OF GCD FOR dh-ranFile-2016-11-01_10:31 Euclid's algorithm: p-value, steps to gcd: 0.081002 p-value, dist. of gcd's: 0.922705 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-11-01_10:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.216 0.726 0.709 0.061 0.422 0.389 0.003 0.541 Bits 8 to 15---> 0.757 0.370 0.022 0.690 0.895 0.839 0.188 0.393 Bits 16 to 23---> 0.120 0.236 0.499 0.092 0.231 0.687 0.132 0.211 Bits 24 to 31---> 0.374 0.512 0.446 0.528 0.321 0.289 0.870 0.401 KS test for the above 32 p values: 0.878 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-11-01_10:31, p-values for 5 runs: 0.3086, 0.7603, 0.8166, 0.7750, 0.9134 Rank test for binary matrices (31x31) for dh-ranFile-2016-11-01_10:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 203 211.4 0.335 0.335 r= 29 5231 5134.0 1.832 2.167 r= 30 22992 23103.0 0.534 2.701 r= 31 11574 11551.5 0.044 2.745 chi-square = 2.745 with df = 3; p-value = 0.567 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-11-01_10:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 238 211.4 3.342 3.342 r= 30 5099 5134.0 0.239 3.581 r= 31 23148 23103.0 0.087 3.668 r= 32 11515 11551.5 0.115 3.784 chi-square = 3.784 with df = 3; p-value = 0.714 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-11-01_10:31 b-rank test for bits 1 to 8, p=0.27124 b-rank test for bits 2 to 9, p=0.66111 b-rank test for bits 3 to 10, p=0.38439 b-rank test for bits 4 to 11, p=0.55824 b-rank test for bits 5 to 12, p=0.42890 b-rank test for bits 6 to 13, p=0.34626 b-rank test for bits 7 to 14, p=0.65493 b-rank test for bits 8 to 15, p=0.22739 b-rank test for bits 9 to 16, p=0.20108 b-rank test for bits 10 to 17, p=0.53201 b-rank test for bits 11 to 18, p=0.49411 b-rank test for bits 12 to 19, p=0.37910 b-rank test for bits 13 to 20, p=0.18464 b-rank test for bits 14 to 21, p=0.43144 b-rank test for bits 15 to 22, p=0.83332 b-rank test for bits 16 to 23, p=0.62698 b-rank test for bits 17 to 24, p=0.30887 b-rank test for bits 18 to 25, p=0.24752 b-rank test for bits 19 to 26, p=0.22604 b-rank test for bits 20 to 27, p=0.95026 b-rank test for bits 21 to 28, p=0.89910 b-rank test for bits 22 to 29, p=0.30073 b-rank test for bits 23 to 30, p=0.58866 b-rank test for bits 24 to 31, p=0.58564 b-rank test for bits 25 to 32, p=0.11919 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 = 0.218280 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-11-01_10:31 (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 142715 1.88 0.970110 2 141405 -1.18 0.119330 3 142169 0.61 0.727977 4 141712 -0.46 0.322381 5 141415 -1.15 0.124050 6 142120 0.49 0.688718 7 142059 0.35 0.636717 8 141903 -0.01 0.494100 9 141615 -0.69 0.245825 10 141544 -0.85 0.196670 11 141185 -1.69 0.045289 12 142189 0.65 0.743262 13 141290 -1.45 0.073944 14 142288 0.88 0.811852 15 141886 -0.05 0.478265 16 140860 -2.45 0.007109 17 142024 0.27 0.605620 18 142553 1.50 0.933697 19 141802 -0.25 0.400996 20 141813 -0.23 0.410962 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-11-01_10:31 Bits used No. missing words z-score p-value 23 to 32 141975 0.2264 0.589574 22 to 31 142157 0.8540 0.803457 21 to 30 142307 1.3713 0.914856 20 to 29 142332 1.4575 0.927508 19 to 28 142223 1.0816 0.860289 18 to 27 142059 0.5161 0.697109 17 to 26 142077 0.5782 0.718426 16 to 25 141703 -0.7115 0.238393 15 to 24 141429 -1.6563 0.048830 14 to 23 142071 0.5575 0.711401 13 to 22 142363 1.5644 0.941136 12 to 21 141659 -0.8632 0.194012 11 to 20 141998 0.3058 0.620106 10 to 19 141306 -2.0804 0.018742 9 to 18 141788 -0.4184 0.337835 8 to 17 141777 -0.4563 0.324083 7 to 16 141697 -0.7322 0.232032 6 to 15 141552 -1.2322 0.108942 5 to 14 142644 2.5333 0.994351 4 to 13 142200 1.0023 0.841903 3 to 12 142136 0.7816 0.782781 2 to 11 142192 0.9747 0.835151 1 to 10 141905 -0.0149 0.494044 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-11-01_10:31 Bits used No. missing words z-score p-value 28 to 32 141847 -0.2113 0.416331 27 to 31 141544 -1.2384 0.107783 26 to 30 142019 0.3718 0.644965 25 to 29 142053 0.4870 0.686877 24 to 28 142405 1.6802 0.953544 23 to 27 141826 -0.2825 0.388790 22 to 26 141501 -1.3842 0.083153 21 to 25 142731 2.7853 0.997326 20 to 24 142317 1.3819 0.916504 19 to 23 141814 -0.3232 0.373290 18 to 22 141595 -1.0655 0.143319 17 to 21 141743 -0.5638 0.286435 16 to 20 142074 0.5582 0.711647 15 to 19 142100 0.6463 0.740970 14 to 18 141595 -1.0655 0.143319 13 to 17 141956 0.1582 0.562852 12 to 16 141652 -0.8723 0.191521 11 to 15 142081 0.5819 0.719694 10 to 14 141663 -0.8350 0.201854 9 to 13 141962 0.1785 0.570852 8 to 12 141793 -0.3943 0.346665 7 to 11 141904 -0.0181 0.492792 6 to 10 142137 0.7718 0.779873 5 to 9 141858 -0.1740 0.430933 4 to 8 142237 1.1107 0.866661 3 to 7 142279 1.2531 0.894919 2 to 6 142299 1.3209 0.906735 1 to 5 141335 -1.9469 0.025774 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-11-01_10:31 Bits used No. missing words z-score p-value 31 to 32 142189 0.8250 0.795310 30 to 31 141851 -0.1721 0.431693 29 to 30 141755 -0.4553 0.324464 28 to 29 141944 0.1023 0.540729 27 to 28 141891 -0.0541 0.478439 26 to 27 142163 0.7483 0.772857 25 to 26 141745 -0.4847 0.313927 24 to 25 142002 0.2734 0.607713 23 to 24 142140 0.6804 0.751888 22 to 23 142515 1.7866 0.963002 21 to 22 142358 1.3235 0.907167 20 to 21 141935 0.0757 0.530180 19 to 20 141644 -0.7827 0.216906 18 to 19 141812 -0.2871 0.387014 17 to 18 141932 0.0669 0.526659 16 to 17 141955 0.1347 0.553583 15 to 16 142351 1.3029 0.903689 14 to 15 142280 1.0934 0.862896 13 to 14 142081 0.5064 0.693713 12 to 13 141942 0.0964 0.538387 11 to 12 142151 0.7129 0.762043 10 to 11 142152 0.7158 0.762955 9 to 10 142697 2.3235 0.989924 8 to 9 142103 0.5713 0.716101 7 to 8 142179 0.7955 0.786835 6 to 7 142436 1.5536 0.939860 5 to 6 142228 0.9400 0.826399 4 to 5 142211 0.8899 0.813235 3 to 4 141836 -0.2163 0.414372 2 to 3 142405 1.4622 0.928150 1 to 2 142301 1.1554 0.876030 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-11-01_10:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2445.21 -0.775 0.219217 Test results for specific bytes for dh-ranFile-2016-11-01_10:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2416.65 -1.179 0.119255 2 to 9 2364.06 -1.922 0.027275 3 to 10 2510.59 0.150 0.559502 4 to 11 2487.67 -0.174 0.430761 5 to 12 2354.69 -2.055 0.019937 6 to 13 2568.92 0.975 0.835134 7 to 14 2511.61 0.164 0.565225 8 to 15 2462.49 -0.531 0.297870 9 to 16 2494.57 -0.077 0.469378 10 to 17 2473.39 -0.376 0.353317 11 to 18 2524.78 0.350 0.637004 12 to 19 2543.31 0.612 0.729883 13 to 20 2497.35 -0.038 0.485026 14 to 21 2619.65 1.692 0.954693 15 to 22 2578.33 1.108 0.866002 16 to 23 2440.97 -0.835 0.201923 17 to 24 2534.95 0.494 0.689445 18 to 25 2539.80 0.563 0.713223 19 to 26 2536.09 0.510 0.695119 20 to 27 2574.12 1.048 0.852743 21 to 28 2621.46 1.718 0.957072 22 to 29 2454.17 -0.648 0.258448 23 to 30 2528.84 0.408 0.658288 24 to 31 2534.61 0.489 0.687730 25 to 32 2461.86 -0.539 0.294809 CDPARK for dh-ranFile-2016-11-01_10:31: 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 3547 1.0959 0.863437 3489 -1.5525 0.060270 3517 -0.2740 0.392053 3537 0.6393 0.738676 3555 1.4612 0.928018 3531 0.3653 0.642555 3513 -0.4566 0.323972 3510 -0.5936 0.276387 3529 0.2740 0.607947 3540 0.7763 0.781201 Square side=100, avg. no. parked=3526.80 sample std.=18.71 p-value of the KSTEST for those 10 p-values: 0.855003 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-11-01_10:31 0.8165,0.0111,0.0067,0.1124,0.3337,0.2232,0.3718,0.5638,0.4369,0.8223, The KS test for those 10 p-values: 0.149203 The 3DSPHERES test for dh-ranFile-2016-11-01_10:31 sample no r^3 equiv. uni. 1 76.318 0.921444 2 42.098 0.754211 3 51.746 0.821804 4 29.667 0.628016 5 15.928 0.411942 6 13.069 0.353147 7 18.423 0.458868 8 34.403 0.682339 9 31.168 0.646169 10 47.754 0.796441 11 19.253 0.473631 12 10.836 0.303154 13 12.109 0.332118 14 20.018 0.486893 15 33.030 0.667462 16 60.490 0.866859 17 9.696 0.276181 18 81.115 0.933051 19 131.791 0.987637 20 42.130 0.754469 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.064838 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-11-01_10:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 0.1 0.8 -0.5 1.4 0.2 0.5 -1.5 -0.6 -0.9 0.1 1.7 0.9 0.8 0.8 0.7 -0.8 0.3 -1.5 1.3 -0.7 -1.0 -0.2 -0.6 -0.5 0.6 -2.1 -0.5 0.6 -0.5 -0.3 1.5 -0.0 0.4 1.0 1.0 0.3 -0.7 0.9 1.0 -0.6 0.0 0.8 Chi-square with 42 degrees of freedom:33.352287 z-score=-0.943543, p-value=0.172776 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-11-01_10:31 Test no p-value 1 0.069700 2 0.961638 3 0.162265 4 0.165091 5 0.021313 6 0.831428 7 0.140273 8 0.889069 9 0.085922 10 0.001618 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.007789 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-11-01_10:31: (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 66494 0.45 66312 1.89 3 25000.00 25114 0.52 25261 2.72 4 6666.67 6735 0.70 6739 0.78 5 1388.89 1374 0.16 1408 0.26 6 238.10 229 0.35 242 0.06 7 34.72 45 3.04 33 0.09 8 4.96 8 1.86 4 0.19 p=0.68662 p=0.57619 Number of rngs required: 688264, p-value: 0.436 RESULTS OF CRAPS TEST for dh-ranFile-2016-11-01_10:31 No. of wins: Observed Expected 99291 98585.9 z-score= 3.154, pvalue=0.99919 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66490 66666.7 0.468 0.468 2 37610 37654.3 0.052 0.520 3 27165 26954.7 1.640 2.161 4 19340 19313.5 0.036 2.197 5 13891 13851.4 0.113 2.310 6 9996 9943.5 0.277 2.587 7 7121 7145.0 0.081 2.668 8 5120 5139.1 0.071 2.738 9 3715 3699.9 0.062 2.800 10 2680 2666.3 0.070 2.871 11 1881 1923.3 0.932 3.802 12 1373 1388.7 0.178 3.981 13 958 1003.7 2.082 6.063 14 735 726.1 0.108 6.171 15 519 525.8 0.089 6.260 16 366 381.2 0.602 6.862 17 279 276.5 0.022 6.884 18 221 200.8 2.026 8.910 19 143 146.0 0.061 8.971 20 110 106.2 0.135 9.106 21 287 287.1 0.000 9.106 Chisq= 9.11 for 20 degrees of freedom, p= 0.01835 SUMMARY of craptest p-value for no. of wins: 0.999194 p-value for throws/game: 0.018349 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-11-01_10:31 No. of wins: Observed Expected 98195 98585.9 z-score=-1.748, pvalue=0.04022 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66771 66666.7 0.163 0.163 2 37471 37654.3 0.893 1.056 3 27122 26954.7 1.038 2.094 4 19393 19313.5 0.328 2.421 5 13921 13851.4 0.350 2.771 6 9980 9943.5 0.134 2.905 7 7058 7145.0 1.060 3.964 8 5083 5139.1 0.612 4.576 9 3697 3699.9 0.002 4.578 10 2610 2666.3 1.189 5.767 11 1916 1923.3 0.028 5.795 12 1365 1388.7 0.406 6.201 13 1006 1003.7 0.005 6.206 14 773 726.1 3.024 9.230 15 500 525.8 1.269 10.499 16 353 381.2 2.079 12.579 17 264 276.5 0.569 13.147 18 220 200.8 1.830 14.977 19 138 146.0 0.437 15.414 20 92 106.2 1.902 17.316 21 267 287.1 1.409 18.725 Chisq= 18.73 for 20 degrees of freedom, p= 0.46026 SUMMARY of craptest p-value for no. of wins: 0.040219 p-value for throws/game: 0.460261 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0016,0.0027,0.0067,0.0071,0.0078,0.0111,0.0183,0.0187,0.0199,0.0213, 0.0218,0.0222,0.0258,0.0273,0.0402,0.0453,0.0488,0.0603,0.0609,0.0648, 0.0649,0.0697,0.0739,0.0810,0.0832,0.0859,0.0921,0.1078,0.1089,0.1124, 0.1192,0.1193,0.1193,0.1195,0.1241,0.1324,0.1403,0.1433,0.1433,0.1492, 0.1623,0.1651,0.1728,0.1846,0.1884,0.1915,0.1940,0.1967,0.2011,0.2019, 0.2019,0.2106,0.2158,0.2169,0.2183,0.2192,0.2232,0.2260,0.2274,0.2307, 0.2320,0.2362,0.2384,0.2458,0.2475,0.2584,0.2712,0.2762,0.2764,0.2864, 0.2886,0.2948,0.2979,0.3007,0.3032,0.3086,0.3089,0.3139,0.3211,0.3224, 0.3240,0.3241,0.3245,0.3321,0.3337,0.3378,0.3463,0.3467,0.3531,0.3533, 0.3704,0.3718,0.3733,0.3738,0.3791,0.3844,0.3870,0.3888,0.3892,0.3921, 0.3929,0.4010,0.4013,0.4110,0.4119,0.4144,0.4163,0.4217,0.4289,0.4308, 0.4309,0.4314,0.4317,0.4365,0.4369,0.4458,0.4589,0.4603,0.4694,0.4729, 0.4736,0.4783,0.4784,0.4850,0.4869,0.4928,0.4940,0.4941,0.4941,0.4994, 0.5121,0.5218,0.5267,0.5275,0.5302,0.5320,0.5384,0.5407,0.5410,0.5536, 0.5582,0.5595,0.5629,0.5638,0.5652,0.5674,0.5689,0.5709,0.5762,0.5856, 0.5887,0.5896,0.6056,0.6059,0.6077,0.6079,0.6201,0.6270,0.6280,0.6367, 0.6370,0.6426,0.6450,0.6462,0.6549,0.6583,0.6611,0.6655,0.6675,0.6823, 0.6866,0.6868,0.6869,0.6877,0.6887,0.6894,0.6895,0.6937,0.6951,0.6971, 0.7094,0.7114,0.7116,0.7132,0.7142,0.7161,0.7184,0.7197,0.7264,0.7280, 0.7299,0.7387,0.7410,0.7433,0.7519,0.7542,0.7545,0.7567,0.7601,0.7603, 0.7620,0.7630,0.7729,0.7750,0.7799,0.7812,0.7828,0.7845,0.7868,0.7953, 0.7964,0.8035,0.8119,0.8132,0.8165,0.8166,0.8218,0.8223,0.8264,0.8314, 0.8333,0.8351,0.8352,0.8392,0.8419,0.8527,0.8550,0.8603,0.8629,0.8634, 0.8660,0.8667,0.8669,0.8705,0.8760,0.8783,0.8891,0.8949,0.8951,0.8991, 0.9037,0.9067,0.9072,0.9134,0.9149,0.9165,0.9214,0.9227,0.9275,0.9280, 0.9282,0.9331,0.9337,0.9399,0.9411,0.9420,0.9447,0.9503,0.9535,0.9547, 0.9571,0.9616,0.9630,0.9701,0.9876,0.9899,0.9944,0.9973,0.9992, Overall p-value after applying KStest on 269 p-values = 0.504220 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.