RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-01-19_14:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.65 23.0716 0.853066 2 to 25 15.63 32.7976 0.988044 3 to 26 15.60 32.2854 0.986135 4 to 27 15.79 10.3540 0.111886 5 to 28 15.69 26.6627 0.936797 6 to 29 15.49 22.2605 0.825091 7 to 30 15.95 13.4960 0.297597 8 to 31 15.64 17.1649 0.556750 9 to 32 15.77 25.5777 0.917495 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.009160 Tough bday spacings test for dh-ranFile-2017-01-19_14:31: 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 8 36 77 134 74 66 56 26 14 6 3 (O-E)^2/E 0.1 0.0 0.2 13.5 5.7 1.9 0.3 0.5 0.1 0.1 0.3 Birthday Spacings: Sum(O-E)^2/E= 22.639, p= 0.988 RESULTS OF GCD FOR dh-ranFile-2017-01-19_14:31 Euclid's algorithm: p-value, steps to gcd: 0.447588 p-value, dist. of gcd's: 0.374059 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-01-19_14:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.662 0.605 0.395 0.040 0.427 0.373 0.027 0.914 Bits 8 to 15---> 0.618 0.941 0.650 0.340 0.232 0.989 0.948 0.301 Bits 16 to 23---> 0.286 0.728 0.638 0.858 0.921 0.763 0.521 0.825 Bits 24 to 31---> 0.979 0.455 0.190 0.711 0.108 0.325 0.565 0.044 KS test for the above 32 p values: 0.342 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-01-19_14:31, p-values for 5 runs: 0.5863, 0.4328, 0.2711, 0.7316, 0.6831 Rank test for binary matrices (31x31) for dh-ranFile-2017-01-19_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 217 211.4 0.147 0.147 r= 29 5102 5134.0 0.200 0.347 r= 30 23139 23103.0 0.056 0.403 r= 31 11542 11551.5 0.008 0.411 chi-square = 0.411 with df = 3; p-value = 0.062 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2017-01-19_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 215 211.4 0.061 0.061 r= 30 5178 5134.0 0.377 0.438 r= 31 22878 23103.0 2.192 2.630 r= 32 11729 11551.5 2.727 5.357 chi-square = 5.357 with df = 3; p-value = 0.853 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2017-01-19_14:31 b-rank test for bits 1 to 8, p=0.72210 b-rank test for bits 2 to 9, p=0.81399 b-rank test for bits 3 to 10, p=0.63482 b-rank test for bits 4 to 11, p=0.43517 b-rank test for bits 5 to 12, p=0.29040 b-rank test for bits 6 to 13, p=0.03478 b-rank test for bits 7 to 14, p=0.25801 b-rank test for bits 8 to 15, p=0.22436 b-rank test for bits 9 to 16, p=0.96926 b-rank test for bits 10 to 17, p=0.11050 b-rank test for bits 11 to 18, p=0.29782 b-rank test for bits 12 to 19, p=0.22272 b-rank test for bits 13 to 20, p=0.14527 b-rank test for bits 14 to 21, p=0.58882 b-rank test for bits 15 to 22, p=0.17465 b-rank test for bits 16 to 23, p=0.65256 b-rank test for bits 17 to 24, p=0.84179 b-rank test for bits 18 to 25, p=0.59631 b-rank test for bits 19 to 26, p=0.10927 b-rank test for bits 20 to 27, p=0.23337 b-rank test for bits 21 to 28, p=0.85982 b-rank test for bits 22 to 29, p=0.46104 b-rank test for bits 23 to 30, p=0.47578 b-rank test for bits 24 to 31, p=0.95042 b-rank test for bits 25 to 32, p=0.97109 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 = 0.883636 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-01-19_14:31 (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 142118 0.49 0.687065 2 141781 -0.30 0.382151 3 141963 0.13 0.549895 4 142559 1.52 0.935483 5 142326 0.97 0.834855 6 142442 1.24 0.893353 7 141934 0.06 0.522982 8 141377 -1.24 0.106794 9 141908 -0.00 0.498760 10 141903 -0.01 0.494100 11 142102 0.45 0.673704 12 141847 -0.15 0.442106 13 142419 1.19 0.883137 14 141470 -1.03 0.152335 15 141649 -0.61 0.271512 16 141533 -0.88 0.189626 17 141513 -0.93 0.177222 18 141625 -0.66 0.253242 19 142131 0.52 0.697743 20 141617 -0.68 0.247299 ---------------------------------------------------------------- OPSO test for dh-ranFile-2017-01-19_14:31 Bits used No. missing words z-score p-value 23 to 32 141881 -0.0977 0.461089 22 to 31 142013 0.3575 0.639635 21 to 30 141756 -0.5287 0.298498 20 to 29 141380 -1.8253 0.033980 19 to 28 141921 0.0402 0.516050 18 to 27 141500 -1.4115 0.079051 17 to 26 142129 0.7575 0.775620 16 to 25 141957 0.1644 0.565284 15 to 24 142037 0.4402 0.670119 14 to 23 142478 1.9609 0.975056 13 to 22 142018 0.3747 0.646067 12 to 21 142800 3.0713 0.998934 11 to 20 142271 1.2471 0.893827 10 to 19 141734 -0.6046 0.272727 9 to 18 141971 0.2127 0.584202 8 to 17 141927 0.0609 0.524293 7 to 16 141692 -0.7494 0.226804 6 to 15 141918 0.0299 0.511925 5 to 14 142061 0.5230 0.699513 4 to 13 142091 0.6264 0.734490 3 to 12 142444 1.8437 0.967386 2 to 11 141944 0.1196 0.547581 1 to 10 142080 0.5885 0.721907 ----------------------------------------------------------------- OQSO test for dh-ranFile-2017-01-19_14:31 Bits used No. missing words z-score p-value 28 to 32 141674 -0.7977 0.212514 27 to 31 141442 -1.5842 0.056578 26 to 30 141832 -0.2621 0.396609 25 to 29 141814 -0.3232 0.373290 24 to 28 142394 1.6429 0.949803 23 to 27 142035 0.4260 0.664946 22 to 26 141933 0.0802 0.531976 21 to 25 141955 0.1548 0.561516 20 to 24 141812 -0.3299 0.370726 19 to 23 141768 -0.4791 0.315939 18 to 22 141422 -1.6520 0.049271 17 to 21 142421 1.7345 0.958583 16 to 20 142075 0.5616 0.712803 15 to 19 141760 -0.5062 0.306357 14 to 18 141764 -0.4926 0.311132 13 to 17 141863 -0.1571 0.437602 12 to 16 141862 -0.1604 0.436267 11 to 15 141831 -0.2655 0.395302 10 to 14 141692 -0.7367 0.230649 9 to 13 141742 -0.5672 0.285282 8 to 12 142156 0.8362 0.798470 7 to 11 141984 0.2531 0.599912 6 to 10 142194 0.9650 0.832723 5 to 9 141425 -1.6418 0.050316 4 to 8 141888 -0.0723 0.471180 3 to 7 141475 -1.4723 0.070469 2 to 6 141947 0.1277 0.550805 1 to 5 141877 -0.1096 0.456366 ----------------------------------------------------------------- DNA test for dh-ranFile-2017-01-19_14:31 Bits used No. missing words z-score p-value 31 to 32 141731 -0.5260 0.299428 30 to 31 141927 0.0521 0.520785 29 to 30 141706 -0.5998 0.274322 28 to 29 141787 -0.3609 0.359104 27 to 28 141362 -1.6145 0.053205 26 to 27 141833 -0.2252 0.410927 25 to 26 141761 -0.4376 0.330856 24 to 25 141959 0.1465 0.558244 23 to 24 141802 -0.3166 0.375771 22 to 23 141939 0.0875 0.534872 21 to 22 141792 -0.3461 0.364632 20 to 21 141745 -0.4847 0.313927 19 to 20 141557 -1.0393 0.149328 18 to 19 142001 0.2704 0.606579 17 to 18 141395 -1.5172 0.064608 16 to 17 141526 -1.1308 0.129077 15 to 16 142350 1.2999 0.903184 14 to 15 141981 0.2114 0.583719 13 to 14 141847 -0.1839 0.427060 12 to 13 141989 0.2350 0.592901 11 to 12 142181 0.8014 0.788546 10 to 11 142023 0.3353 0.631304 9 to 10 141507 -1.1868 0.117650 8 to 9 141867 -0.1249 0.450314 7 to 8 142224 0.9282 0.823356 6 to 7 141850 -0.1750 0.430534 5 to 6 142012 0.3029 0.619002 4 to 5 141073 -2.4671 0.006812 3 to 4 141874 -0.1042 0.458498 2 to 3 142530 1.8309 0.966441 1 to 2 142170 0.7689 0.779035 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2017-01-19_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2510.20 0.144 0.557366 Test results for specific bytes for dh-ranFile-2017-01-19_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2549.32 0.697 0.757247 2 to 9 2652.33 2.154 0.984393 3 to 10 2374.45 -1.776 0.037903 4 to 11 2498.03 -0.028 0.488896 5 to 12 2484.16 -0.224 0.411371 6 to 13 2413.83 -1.219 0.111498 7 to 14 2520.74 0.293 0.615346 8 to 15 2492.57 -0.105 0.458143 9 to 16 2445.33 -0.773 0.219734 10 to 17 2441.79 -0.823 0.205204 11 to 18 2553.19 0.752 0.774052 12 to 19 2606.95 1.513 0.934803 13 to 20 2457.14 -0.606 0.272225 14 to 21 2604.41 1.477 0.930108 15 to 22 2496.72 -0.046 0.481502 16 to 23 2472.31 -0.392 0.347654 17 to 24 2583.94 1.187 0.882399 18 to 25 2504.13 0.058 0.523277 19 to 26 2528.34 0.401 0.655700 20 to 27 2423.12 -1.087 0.138479 21 to 28 2385.94 -1.613 0.053362 22 to 29 2598.50 1.393 0.918187 23 to 30 2508.52 0.120 0.547933 24 to 31 2562.99 0.891 0.813497 25 to 32 2643.20 2.025 0.978571 CDPARK for dh-ranFile-2017-01-19_14:31: 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 3526 0.1370 0.554479 3514 -0.4110 0.340551 3488 -1.5982 0.055002 3555 1.4612 0.928018 3521 -0.0913 0.463617 3533 0.4566 0.676028 3510 -0.5936 0.276387 3506 -0.7763 0.218799 3557 1.5525 0.939730 3488 -1.5982 0.055002 Square side=100, avg. no. parked=3519.80 sample std.=22.76 p-value of the KSTEST for those 10 p-values: 0.800949 Results for the MINIMUM DISTANCE test for dh-ranFile-2017-01-19_14:31 0.5968,0.0049,0.5296,0.2605,0.5381,0.3169,0.5753,0.7810,0.0229,0.2117, The KS test for those 10 p-values: 0.205919 The 3DSPHERES test for dh-ranFile-2017-01-19_14:31 sample no r^3 equiv. uni. 1 24.644 0.560210 2 27.727 0.603165 3 51.217 0.818635 4 5.313 0.162291 5 32.485 0.661368 6 20.083 0.487995 7 2.321 0.074440 8 53.617 0.832578 9 13.157 0.355046 10 25.858 0.577660 11 8.517 0.247158 12 10.767 0.301566 13 15.028 0.394033 14 10.022 0.283988 15 4.167 0.129689 16 39.270 0.729914 17 9.911 0.281351 18 2.099 0.067567 19 7.105 0.210887 20 17.665 0.445027 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.224539 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-01-19_14:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -0.3 -0.1 1.5 -0.4 2.4 1.0 0.6 0.5 -0.5 1.4 -1.9 -0.1 -0.8 -2.5 0.3 0.8 0.6 0.2 0.8 0.1 -0.7 0.5 -0.4 -1.0 1.8 0.3 -1.8 0.6 1.5 0.5 0.6 0.0 0.1 -0.1 -1.2 -0.5 0.5 -0.4 -0.1 2.4 -1.0 -0.1 Chi-square with 42 degrees of freedom:44.703029 z-score=0.294925, p-value=0.641049 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2017-01-19_14:31 Test no p-value 1 0.091211 2 0.549189 3 0.826333 4 0.852017 5 0.213998 6 0.897546 7 0.011095 8 0.785472 9 0.056910 10 0.083821 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.185578 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-01-19_14:31: (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 66939 1.11 66343 1.57 3 25000.00 24818 1.32 25250 2.50 4 6666.67 6564 1.58 6737 0.74 5 1388.89 1369 0.28 1386 0.01 6 238.10 271 4.55 246 0.26 7 34.72 32 0.21 31 0.40 8 4.96 6 0.22 6 0.22 p=0.84167 p=0.54220 Number of rngs required: 689321, p-value: 0.856 RESULTS OF CRAPS TEST for dh-ranFile-2017-01-19_14:31 No. of wins: Observed Expected 98303 98585.9 z-score=-1.265, pvalue=0.10292 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66727 66666.7 0.055 0.055 2 37645 37654.3 0.002 0.057 3 27078 26954.7 0.564 0.621 4 19412 19313.5 0.503 1.123 5 13709 13851.4 1.464 2.588 6 9941 9943.5 0.001 2.588 7 7363 7145.0 6.650 9.238 8 4936 5139.1 8.024 17.263 9 3648 3699.9 0.727 17.990 10 2630 2666.3 0.494 18.484 11 1925 1923.3 0.001 18.485 12 1372 1388.7 0.202 18.687 13 979 1003.7 0.609 19.296 14 749 726.1 0.720 20.015 15 503 525.8 0.992 21.007 16 361 381.2 1.065 22.072 17 295 276.5 1.232 23.305 18 194 200.8 0.232 23.537 19 137 146.0 0.553 24.090 20 102 106.2 0.167 24.257 21 294 287.1 0.165 24.422 Chisq= 24.42 for 20 degrees of freedom, p= 0.77557 SUMMARY of craptest p-value for no. of wins: 0.102916 p-value for throws/game: 0.775566 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2017-01-19_14:31 No. of wins: Observed Expected 98534 98585.9 z-score=-0.232, pvalue=0.40829 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66421 66666.7 0.905 0.905 2 37699 37654.3 0.053 0.958 3 26931 26954.7 0.021 0.979 4 19336 19313.5 0.026 1.005 5 13895 13851.4 0.137 1.143 6 9998 9943.5 0.298 1.441 7 7188 7145.0 0.258 1.699 8 5193 5139.1 0.566 2.265 9 3706 3699.9 0.010 2.275 10 2686 2666.3 0.146 2.421 11 1881 1923.3 0.932 3.353 12 1423 1388.7 0.845 4.198 13 973 1003.7 0.940 5.138 14 747 726.1 0.599 5.737 15 558 525.8 1.967 7.704 16 366 381.2 0.602 8.307 17 271 276.5 0.111 8.417 18 215 200.8 1.000 9.417 19 120 146.0 4.625 14.042 20 111 106.2 0.216 14.258 21 282 287.1 0.091 14.349 Chisq= 14.35 for 20 degrees of freedom, p= 0.18763 SUMMARY of craptest p-value for no. of wins: 0.408292 p-value for throws/game: 0.187631 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0049,0.0068,0.0092,0.0111,0.0229,0.0271,0.0340,0.0348,0.0379,0.0396, 0.0438,0.0493,0.0503,0.0532,0.0534,0.0550,0.0550,0.0566,0.0569,0.0620, 0.0646,0.0676,0.0705,0.0744,0.0791,0.0838,0.0912,0.1029,0.1068,0.1076, 0.1093,0.1105,0.1115,0.1119,0.1177,0.1291,0.1297,0.1385,0.1453,0.1493, 0.1523,0.1623,0.1746,0.1772,0.1856,0.1876,0.1896,0.1901,0.2052,0.2059, 0.2109,0.2117,0.2125,0.2140,0.2188,0.2197,0.2227,0.2244,0.2245,0.2268, 0.2306,0.2318,0.2334,0.2472,0.2473,0.2532,0.2580,0.2605,0.2711,0.2715, 0.2722,0.2727,0.2743,0.2764,0.2814,0.2840,0.2853,0.2862,0.2904,0.2976, 0.2978,0.2985,0.2994,0.3012,0.3016,0.3064,0.3111,0.3139,0.3159,0.3169, 0.3249,0.3309,0.3397,0.3406,0.3417,0.3477,0.3550,0.3591,0.3646,0.3707, 0.3727,0.3733,0.3741,0.3758,0.3822,0.3940,0.3950,0.3953,0.3966,0.4083, 0.4109,0.4114,0.4266,0.4271,0.4305,0.4328,0.4352,0.4363,0.4376,0.4421, 0.4450,0.4476,0.4503,0.4548,0.4564,0.4581,0.4585,0.4610,0.4611,0.4636, 0.4712,0.4758,0.4815,0.4880,0.4889,0.4941,0.4988,0.5119,0.5160,0.5208, 0.5212,0.5230,0.5233,0.5243,0.5296,0.5320,0.5349,0.5381,0.5422,0.5476, 0.5479,0.5492,0.5499,0.5508,0.5545,0.5567,0.5574,0.5582,0.5602,0.5615, 0.5652,0.5653,0.5753,0.5777,0.5837,0.5842,0.5863,0.5888,0.5929,0.5963, 0.5968,0.5999,0.6032,0.6046,0.6066,0.6153,0.6175,0.6190,0.6313,0.6348, 0.6383,0.6396,0.6410,0.6461,0.6502,0.6526,0.6557,0.6614,0.6621,0.6649, 0.6701,0.6737,0.6760,0.6831,0.6871,0.6977,0.6995,0.7105,0.7128,0.7219, 0.7221,0.7283,0.7299,0.7316,0.7345,0.7572,0.7634,0.7741,0.7756,0.7756, 0.7790,0.7810,0.7855,0.7885,0.7985,0.8009,0.8135,0.8140,0.8186,0.8234, 0.8246,0.8251,0.8263,0.8326,0.8327,0.8349,0.8417,0.8418,0.8520,0.8525, 0.8531,0.8565,0.8579,0.8598,0.8824,0.8831,0.8836,0.8934,0.8938,0.8975, 0.9032,0.9142,0.9175,0.9182,0.9212,0.9280,0.9301,0.9348,0.9355,0.9368, 0.9397,0.9410,0.9480,0.9498,0.9504,0.9586,0.9664,0.9674,0.9693,0.9711, 0.9751,0.9786,0.9794,0.9844,0.9861,0.9878,0.9880,0.9886,0.9989, Overall p-value after applying KStest on 269 p-values = 0.836697 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.