RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-04-16_20:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 16.01 19.2760 0.687079 2 to 25 15.87 13.2163 0.278412 3 to 26 15.86 25.2461 0.910665 4 to 27 15.69 13.3412 0.286936 5 to 28 15.72 26.7945 0.938848 6 to 29 15.71 13.6395 0.307566 7 to 30 15.75 21.0247 0.774812 8 to 31 15.91 17.3164 0.566865 9 to 32 15.87 11.9332 0.195832 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.782181 Tough bday spacings test for dh-ranFile-2018-04-16_20:31: 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 29 64 103 102 82 57 29 16 6 4 (O-E)^2/E 0.1 1.6 1.2 0.3 0.2 0.2 0.5 0.0 0.1 0.1 0.0 Birthday Spacings: Sum(O-E)^2/E= 4.200, p= 0.062 RESULTS OF GCD FOR dh-ranFile-2018-04-16_20:31 Euclid's algorithm: p-value, steps to gcd: 0.074232 p-value, dist. of gcd's: 0.129770 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-04-16_20:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.205 0.551 0.816 0.258 0.632 0.963 0.433 0.945 Bits 8 to 15---> 0.549 0.915 0.170 0.762 0.156 0.424 0.036 0.875 Bits 16 to 23---> 0.730 0.184 0.816 0.013 0.336 0.189 0.611 0.794 Bits 24 to 31---> 0.485 0.294 0.161 0.509 0.525 0.059 0.225 0.108 KS test for the above 32 p values: 0.238 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-04-16_20:31, p-values for 5 runs: 0.2776, 0.8871, 0.7266, 0.6695, 0.3758 Rank test for binary matrices (31x31) for dh-ranFile-2018-04-16_20:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 233 211.4 2.203 2.203 r= 29 5169 5134.0 0.238 2.442 r= 30 23083 23103.0 0.017 2.459 r= 31 11515 11551.5 0.115 2.574 chi-square = 2.574 with df = 3; p-value = 0.538 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-04-16_20:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 206 211.4 0.139 0.139 r= 30 5171 5134.0 0.267 0.405 r= 31 23202 23103.0 0.424 0.829 r= 32 11421 11551.5 1.475 2.304 chi-square = 2.304 with df = 3; p-value = 0.488 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-04-16_20:31 b-rank test for bits 1 to 8, p=0.57003 b-rank test for bits 2 to 9, p=0.26147 b-rank test for bits 3 to 10, p=0.81927 b-rank test for bits 4 to 11, p=0.96062 b-rank test for bits 5 to 12, p=0.17833 b-rank test for bits 6 to 13, p=0.39294 b-rank test for bits 7 to 14, p=0.94689 b-rank test for bits 8 to 15, p=0.27365 b-rank test for bits 9 to 16, p=0.38219 b-rank test for bits 10 to 17, p=0.86295 b-rank test for bits 11 to 18, p=0.32984 b-rank test for bits 12 to 19, p=0.76236 b-rank test for bits 13 to 20, p=0.22094 b-rank test for bits 14 to 21, p=0.77114 b-rank test for bits 15 to 22, p=0.19438 b-rank test for bits 16 to 23, p=0.05584 b-rank test for bits 17 to 24, p=0.17287 b-rank test for bits 18 to 25, p=0.73751 b-rank test for bits 19 to 26, p=0.92311 b-rank test for bits 20 to 27, p=0.48869 b-rank test for bits 21 to 28, p=0.23270 b-rank test for bits 22 to 29, p=0.53785 b-rank test for bits 23 to 30, p=0.02399 b-rank test for bits 24 to 31, p=0.51593 b-rank test for bits 25 to 32, p=0.76055 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 = 0.969013 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-04-16_20:31 (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 141930 0.05 0.519259 2 142692 1.83 0.966275 3 141510 -0.93 0.175406 4 141144 -1.79 0.036876 5 141736 -0.40 0.342747 6 142133 0.52 0.699371 7 141871 -0.09 0.464320 8 141733 -0.41 0.340175 9 141936 0.06 0.524843 10 141754 -0.36 0.358332 11 142393 1.13 0.870777 12 141347 -1.31 0.094447 13 142016 0.25 0.598408 14 142151 0.56 0.713844 15 142111 0.47 0.681248 16 141788 -0.28 0.388404 17 142282 0.87 0.808048 18 141943 0.08 0.531352 19 142362 1.06 0.854890 20 141720 -0.44 0.329114 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-04-16_20:31 Bits used No. missing words z-score p-value 23 to 32 141904 -0.0184 0.492668 22 to 31 141735 -0.6011 0.273874 21 to 30 142262 1.2161 0.888027 20 to 29 141909 -0.0011 0.499546 19 to 28 141712 -0.6804 0.248110 18 to 27 142050 0.4851 0.686186 17 to 26 141672 -0.8184 0.206570 16 to 25 142070 0.5540 0.710222 15 to 24 141792 -0.4046 0.342891 14 to 23 141455 -1.5667 0.058598 13 to 22 141109 -2.7598 0.002892 12 to 21 141372 -1.8529 0.031951 11 to 20 142108 0.6851 0.753350 10 to 19 141876 -0.1149 0.454250 9 to 18 141856 -0.1839 0.427047 8 to 17 142324 1.4299 0.923627 7 to 16 141623 -0.9873 0.161737 6 to 15 141884 -0.0873 0.465199 5 to 14 141996 0.2989 0.617477 4 to 13 142115 0.7092 0.760902 3 to 12 142117 0.7161 0.763036 2 to 11 141632 -0.9563 0.169458 1 to 10 141860 -0.1701 0.432464 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-04-16_20:31 Bits used No. missing words z-score p-value 28 to 32 141905 -0.0147 0.494145 27 to 31 141916 0.0226 0.509019 26 to 30 141845 -0.2181 0.413688 25 to 29 141701 -0.7062 0.240031 24 to 28 141728 -0.6147 0.269384 23 to 27 142017 0.3650 0.642438 22 to 26 141306 -2.0452 0.020418 21 to 25 141692 -0.7367 0.230649 20 to 24 141619 -0.9842 0.162516 19 to 23 141896 -0.0452 0.481979 18 to 22 141869 -0.1367 0.445629 17 to 21 142024 0.3887 0.651255 16 to 20 141002 -3.0757 0.001050 15 to 19 142023 0.3853 0.650001 14 to 18 142104 0.6599 0.745341 13 to 17 142486 1.9548 0.974697 12 to 16 141973 0.2158 0.585440 11 to 15 141477 -1.4655 0.071389 10 to 14 141847 -0.2113 0.416331 9 to 13 142398 1.6565 0.951191 8 to 12 141625 -0.9638 0.167565 7 to 11 141961 0.1752 0.569520 6 to 10 141828 -0.2757 0.391391 5 to 9 141362 -1.8554 0.031773 4 to 8 141993 0.2836 0.611652 3 to 7 141621 -0.9774 0.164188 2 to 6 142168 0.8768 0.809715 1 to 5 141717 -0.6520 0.257212 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-04-16_20:31 Bits used No. missing words z-score p-value 31 to 32 142038 0.3796 0.647863 30 to 31 141704 -0.6057 0.272359 29 to 30 141066 -2.4877 0.006429 28 to 29 141667 -0.7148 0.237355 27 to 28 141891 -0.0541 0.478439 26 to 27 142389 1.4150 0.921459 25 to 26 141474 -1.2842 0.099543 24 to 25 142001 0.2704 0.606579 23 to 24 141738 -0.5054 0.306640 22 to 23 141606 -0.8948 0.185453 21 to 22 141634 -0.8122 0.208343 20 to 21 142400 1.4474 0.926108 19 to 20 141620 -0.8535 0.196696 18 to 19 142095 0.5477 0.708051 17 to 18 141795 -0.3373 0.367962 16 to 17 142249 1.0020 0.841823 15 to 16 141763 -0.4317 0.332997 14 to 15 141907 -0.0069 0.497258 13 to 14 141750 -0.4700 0.319178 12 to 13 142000 0.2675 0.605444 11 to 12 142138 0.6745 0.750017 10 to 11 142579 1.9754 0.975890 9 to 10 141421 -1.4405 0.074863 8 to 9 141658 -0.7414 0.229230 7 to 8 142369 1.3560 0.912444 6 to 7 142464 1.6362 0.949101 5 to 6 142461 1.6273 0.948168 4 to 5 142232 0.9518 0.829408 3 to 4 141646 -0.7768 0.218643 2 to 3 141481 -1.2635 0.103203 1 to 2 141592 -0.9361 0.174617 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-04-16_20:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2412.45 -1.238 0.107834 Test results for specific bytes for dh-ranFile-2018-04-16_20:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2594.22 1.332 0.908638 2 to 9 2544.21 0.625 0.734093 3 to 10 2550.33 0.712 0.761692 4 to 11 2435.54 -0.912 0.180990 5 to 12 2454.19 -0.648 0.258541 6 to 13 2524.79 0.351 0.637048 7 to 14 2497.89 -0.030 0.488111 8 to 15 2628.11 1.812 0.964985 9 to 16 2427.10 -1.031 0.151270 10 to 17 2283.44 -3.063 0.001097 11 to 18 2588.28 1.248 0.894062 12 to 19 2409.11 -1.285 0.099319 13 to 20 2439.83 -0.851 0.197404 14 to 21 2520.66 0.292 0.614914 15 to 22 2498.40 -0.023 0.490994 16 to 23 2382.35 -1.664 0.048072 17 to 24 2406.21 -1.326 0.092344 18 to 25 2486.50 -0.191 0.424282 19 to 26 2433.62 -0.939 0.173931 20 to 27 2586.50 1.223 0.889402 21 to 28 2441.21 -0.831 0.202859 22 to 29 2351.86 -2.095 0.018088 23 to 30 2338.93 -2.278 0.011365 24 to 31 2600.80 1.426 0.923002 25 to 32 2481.88 -0.256 0.398894 CDPARK for dh-ranFile-2018-04-16_20:31: 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 3515 -0.3653 0.357445 3508 -0.6849 0.246694 3578 2.5114 0.993988 3550 1.2329 0.891189 3539 0.7306 0.767486 3509 -0.6393 0.261324 3513 -0.4566 0.323972 3509 -0.6393 0.261324 3536 0.5936 0.723613 3522 -0.0457 0.481790 Square side=100, avg. no. parked=3527.90 sample std.=21.73 p-value of the KSTEST for those 10 p-values: 0.595256 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-04-16_20:31 0.0274,0.8252,0.0384,0.5198,0.4300,0.6492,0.0882,0.5574,0.3383,0.9396, The KS test for those 10 p-values: 0.634643 The 3DSPHERES test for dh-ranFile-2018-04-16_20:31 sample no r^3 equiv. uni. 1 37.301 0.711585 2 63.933 0.881292 3 52.080 0.823775 4 36.001 0.698819 5 42.222 0.755224 6 28.168 0.608956 7 43.211 0.763157 8 21.687 0.514653 9 55.095 0.840626 10 63.540 0.879727 11 117.141 0.979853 12 7.007 0.208295 13 24.647 0.560264 14 41.553 0.749701 15 5.419 0.165267 16 37.218 0.710785 17 25.008 0.565513 18 40.454 0.740364 19 21.255 0.507611 20 22.198 0.522850 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.012146 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-04-16_20:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -1.2 -0.1 0.6 0.3 0.1 0.0 0.5 -1.0 -1.3 -2.7 -0.3 -0.9 -0.2 -0.0 -0.5 -1.0 -0.5 0.2 1.8 1.0 2.2 0.2 0.2 0.6 0.7 -0.3 0.5 -0.6 0.4 -0.4 -0.3 -0.5 1.4 -0.4 -1.4 -0.7 3.3 0.9 1.0 0.9 0.0 1.8 Chi-square with 42 degrees of freedom:47.588504 z-score=0.609756, p-value=0.744308 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-04-16_20:31 Test no p-value 1 0.941206 2 0.910266 3 0.682367 4 0.884901 5 0.510783 6 0.178560 7 0.087262 8 0.896819 9 0.029441 10 0.766380 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.228356 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-04-16_20:31: (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 66411 0.98 66725 0.05 3 25000.00 25222 1.97 24927 0.21 4 6666.67 6680 0.03 6686 0.06 5 1388.89 1393 0.01 1372 0.21 6 238.10 255 1.20 244 0.15 7 34.72 34 0.01 40 0.80 8 4.96 4 0.19 5 0.00 p=0.37617 p=0.03888 Number of rngs required: 687641, p-value: 0.189 RESULTS OF CRAPS TEST for dh-ranFile-2018-04-16_20:31 No. of wins: Observed Expected 98463 98585.9 z-score=-0.549, pvalue=0.29133 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66570 66666.7 0.140 0.140 2 37575 37654.3 0.167 0.307 3 27086 26954.7 0.639 0.947 4 19264 19313.5 0.127 1.073 5 13860 13851.4 0.005 1.079 6 9989 9943.5 0.208 1.286 7 7185 7145.0 0.224 1.510 8 5112 5139.1 0.143 1.653 9 3679 3699.9 0.118 1.770 10 2674 2666.3 0.022 1.792 11 1859 1923.3 2.152 3.944 12 1429 1388.7 1.167 5.111 13 1027 1003.7 0.540 5.651 14 709 726.1 0.405 6.056 15 569 525.8 3.543 9.599 16 370 381.2 0.326 9.925 17 298 276.5 1.665 11.591 18 202 200.8 0.007 11.598 19 152 146.0 0.248 11.846 20 105 106.2 0.014 11.859 21 286 287.1 0.004 11.864 Chisq= 11.86 for 20 degrees of freedom, p= 0.07932 SUMMARY of craptest p-value for no. of wins: 0.291333 p-value for throws/game: 0.079315 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-04-16_20:31 No. of wins: Observed Expected 98544 98585.9 z-score=-0.187, pvalue=0.42575 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66613 66666.7 0.043 0.043 2 37938 37654.3 2.137 2.180 3 26862 26954.7 0.319 2.499 4 19327 19313.5 0.009 2.509 5 13815 13851.4 0.096 2.605 6 10012 9943.5 0.471 3.076 7 7116 7145.0 0.118 3.194 8 5058 5139.1 1.279 4.473 9 3666 3699.9 0.310 4.783 10 2642 2666.3 0.221 5.004 11 1939 1923.3 0.128 5.132 12 1339 1388.7 1.782 6.913 13 1000 1003.7 0.014 6.927 14 739 726.1 0.228 7.155 15 525 525.8 0.001 7.156 16 371 381.2 0.270 7.427 17 306 276.5 3.139 10.565 18 198 200.8 0.040 10.605 19 151 146.0 0.172 10.777 20 111 106.2 0.216 10.993 21 272 287.1 0.796 11.788 Chisq= 11.79 for 20 degrees of freedom, p= 0.07683 SUMMARY of craptest p-value for no. of wins: 0.425746 p-value for throws/game: 0.076835 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0011,0.0011,0.0029,0.0064,0.0114,0.0121,0.0135,0.0181,0.0204,0.0240, 0.0274,0.0294,0.0318,0.0320,0.0359,0.0369,0.0384,0.0389,0.0481,0.0558, 0.0586,0.0594,0.0621,0.0714,0.0742,0.0749,0.0768,0.0793,0.0873,0.0882, 0.0923,0.0944,0.0993,0.0995,0.1032,0.1078,0.1081,0.1298,0.1513,0.1561, 0.1607,0.1617,0.1625,0.1642,0.1653,0.1676,0.1695,0.1704,0.1729,0.1739, 0.1746,0.1754,0.1783,0.1786,0.1810,0.1839,0.1855,0.1890,0.1892,0.1944, 0.1958,0.1967,0.1974,0.2029,0.2049,0.2066,0.2083,0.2083,0.2186,0.2209, 0.2249,0.2284,0.2292,0.2306,0.2327,0.2374,0.2383,0.2400,0.2467,0.2481, 0.2572,0.2580,0.2585,0.2613,0.2613,0.2615,0.2694,0.2724,0.2736,0.2739, 0.2776,0.2784,0.2869,0.2913,0.2943,0.3066,0.3076,0.3192,0.3240,0.3291, 0.3298,0.3330,0.3357,0.3383,0.3402,0.3427,0.3429,0.3574,0.3583,0.3680, 0.3758,0.3762,0.3822,0.3884,0.3914,0.3929,0.3989,0.4137,0.4163,0.4236, 0.4243,0.4257,0.4270,0.4300,0.4325,0.4330,0.4456,0.4542,0.4643,0.4652, 0.4784,0.4818,0.4820,0.4855,0.4881,0.4882,0.4887,0.4910,0.4927,0.4941, 0.4973,0.4995,0.5076,0.5090,0.5093,0.5108,0.5147,0.5159,0.5193,0.5198, 0.5228,0.5248,0.5252,0.5314,0.5378,0.5380,0.5489,0.5511,0.5574,0.5603, 0.5655,0.5669,0.5695,0.5700,0.5854,0.5953,0.5984,0.6054,0.6066,0.6090, 0.6110,0.6117,0.6149,0.6175,0.6322,0.6346,0.6370,0.6424,0.6479,0.6492, 0.6500,0.6513,0.6695,0.6812,0.6824,0.6862,0.6871,0.6988,0.6994,0.7081, 0.7102,0.7108,0.7116,0.7138,0.7236,0.7266,0.7301,0.7341,0.7375,0.7404, 0.7443,0.7453,0.7497,0.7500,0.7533,0.7552,0.7605,0.7609,0.7615,0.7617, 0.7624,0.7630,0.7632,0.7664,0.7675,0.7711,0.7748,0.7822,0.7941,0.8080, 0.8097,0.8158,0.8162,0.8193,0.8238,0.8252,0.8294,0.8406,0.8418,0.8549, 0.8629,0.8708,0.8748,0.8797,0.8813,0.8849,0.8871,0.8880,0.8894,0.8912, 0.8941,0.8968,0.9086,0.9103,0.9107,0.9124,0.9152,0.9215,0.9230,0.9231, 0.9236,0.9261,0.9388,0.9396,0.9412,0.9452,0.9469,0.9482,0.9491,0.9512, 0.9606,0.9627,0.9650,0.9663,0.9690,0.9747,0.9759,0.9799,0.9940, Overall p-value after applying KStest on 269 p-values = 0.287833 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.