RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-12-15_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 15.64 26.5857 0.935569 2 to 25 15.68 24.6723 0.897711 3 to 26 15.57 25.3388 0.912621 4 to 27 16.05 11.7705 0.186168 5 to 28 15.85 27.3565 0.946958 6 to 29 15.63 13.0397 0.266476 7 to 30 15.73 12.8841 0.256092 8 to 31 15.88 10.6118 0.123981 9 to 32 15.55 17.3151 0.566777 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.257338 Tough bday spacings test for dh-ranFile-2015-12-15_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 12 32 68 94 88 96 55 31 14 6 4 (O-E)^2/E 0.9 0.6 0.4 0.1 1.0 4.1 0.2 0.1 0.1 0.1 0.0 Birthday Spacings: Sum(O-E)^2/E= 7.347, p= 0.308 RESULTS OF GCD FOR dh-ranFile-2015-12-15_14:31 Euclid's algorithm: p-value, steps to gcd: 0.101006 p-value, dist. of gcd's: 0.079604 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-12-15_14:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.513 0.625 0.711 0.462 0.547 0.058 0.407 0.088 Bits 8 to 15---> 0.069 0.677 0.707 0.622 0.085 0.985 0.794 0.153 Bits 16 to 23---> 0.197 0.187 0.219 0.298 0.592 0.092 0.943 0.300 Bits 24 to 31---> 0.165 0.808 0.314 0.941 0.901 0.862 0.520 0.371 KS test for the above 32 p values: 0.081 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-12-15_14:31, p-values for 5 runs: 0.3722, 0.8150, 0.0975, 0.9307, 0.6922 Rank test for binary matrices (31x31) for dh-ranFile-2015-12-15_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 224 211.4 0.749 0.749 r= 29 5231 5134.0 1.832 2.581 r= 30 23068 23103.0 0.053 2.634 r= 31 11477 11551.5 0.481 3.115 chi-square = 3.115 with df = 3; p-value = 0.626 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-12-15_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 201 211.4 0.513 0.513 r= 30 5084 5134.0 0.487 1.001 r= 31 23124 23103.0 0.019 1.020 r= 32 11591 11551.5 0.135 1.154 chi-square = 1.154 with df = 3; p-value = 0.236 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-12-15_14:31 b-rank test for bits 1 to 8, p=0.45175 b-rank test for bits 2 to 9, p=0.04665 b-rank test for bits 3 to 10, p=0.07784 b-rank test for bits 4 to 11, p=0.90332 b-rank test for bits 5 to 12, p=0.58460 b-rank test for bits 6 to 13, p=0.33341 b-rank test for bits 7 to 14, p=0.22989 b-rank test for bits 8 to 15, p=0.86346 b-rank test for bits 9 to 16, p=0.04179 b-rank test for bits 10 to 17, p=0.68842 b-rank test for bits 11 to 18, p=0.96970 b-rank test for bits 12 to 19, p=0.83294 b-rank test for bits 13 to 20, p=0.82621 b-rank test for bits 14 to 21, p=0.67395 b-rank test for bits 15 to 22, p=0.25023 b-rank test for bits 16 to 23, p=0.67446 b-rank test for bits 17 to 24, p=0.64152 b-rank test for bits 18 to 25, p=0.68726 b-rank test for bits 19 to 26, p=0.94794 b-rank test for bits 20 to 27, p=0.89514 b-rank test for bits 21 to 28, p=0.77036 b-rank test for bits 22 to 29, p=0.57290 b-rank test for bits 23 to 30, p=0.02341 b-rank test for bits 24 to 31, p=0.89548 b-rank test for bits 25 to 32, p=0.15876 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 = 0.264925 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-12-15_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 141763 -0.34 0.366216 2 141625 -0.66 0.253242 3 141961 0.12 0.548045 4 142080 0.40 0.654966 5 141530 -0.89 0.187732 6 142370 1.08 0.859111 7 141361 -1.28 0.100071 8 142419 1.19 0.883137 9 141641 -0.63 0.265350 10 141396 -1.20 0.115192 11 140922 -2.31 0.010532 12 142438 1.24 0.891624 13 142343 1.01 0.844529 14 141921 0.03 0.510876 15 141506 -0.94 0.173004 16 141776 -0.31 0.377703 17 142201 0.68 0.752214 18 141365 -1.27 0.101722 19 141352 -1.30 0.096429 20 141639 -0.63 0.263820 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-12-15_14:31 Bits used No. missing words z-score p-value 23 to 32 141898 -0.0391 0.484418 22 to 31 141435 -1.6356 0.050960 21 to 30 141657 -0.8701 0.192122 20 to 29 141807 -0.3529 0.362096 19 to 28 141819 -0.3115 0.377717 18 to 27 142159 0.8609 0.805362 17 to 26 141583 -1.1253 0.130236 16 to 25 142162 0.8713 0.808198 15 to 24 142305 1.3644 0.913776 14 to 23 141832 -0.2667 0.394867 13 to 22 142473 1.9437 0.974034 12 to 21 142120 0.7264 0.766218 11 to 20 142133 0.7713 0.779728 10 to 19 141493 -1.4356 0.075555 9 to 18 141758 -0.5218 0.300895 8 to 17 142004 0.3264 0.627957 7 to 16 141998 0.3058 0.620106 6 to 15 141763 -0.5046 0.306925 5 to 14 141282 -2.1632 0.015263 4 to 13 141621 -0.9942 0.160053 3 to 12 141491 -1.4425 0.074578 2 to 11 142155 0.8471 0.801541 1 to 10 141663 -0.8494 0.197826 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-12-15_14:31 Bits used No. missing words z-score p-value 28 to 32 142067 0.5345 0.703493 27 to 31 141278 -2.1401 0.016173 26 to 30 141513 -1.3435 0.089556 25 to 29 142008 0.3345 0.630989 24 to 28 141844 -0.2215 0.412368 23 to 27 142717 2.7379 0.996908 22 to 26 142130 0.7480 0.772780 21 to 25 142074 0.5582 0.711647 20 to 24 141790 -0.4045 0.342919 19 to 23 142416 1.7175 0.957058 18 to 22 141867 -0.1435 0.442951 17 to 21 141569 -1.1537 0.124320 16 to 20 141851 -0.1977 0.421629 15 to 19 141645 -0.8960 0.185117 14 to 18 141721 -0.6384 0.261605 13 to 17 141845 -0.2181 0.413688 12 to 16 141946 0.1243 0.549463 11 to 15 141893 -0.0554 0.477928 10 to 14 141686 -0.7571 0.224510 9 to 13 142034 0.4226 0.663710 8 to 12 142391 1.6328 0.948742 7 to 11 142427 1.7548 0.960354 6 to 10 141606 -1.0282 0.151919 5 to 9 141864 -0.1537 0.438939 4 to 8 142239 1.1175 0.868115 3 to 7 141907 -0.0079 0.496849 2 to 6 141615 -0.9977 0.159205 1 to 5 142170 0.8836 0.811551 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-12-15_14:31 Bits used No. missing words z-score p-value 31 to 32 142260 1.0344 0.849531 30 to 31 141828 -0.2399 0.405199 29 to 30 141786 -0.3638 0.358002 28 to 29 141601 -0.9095 0.181536 27 to 28 142194 0.8397 0.799471 26 to 27 142225 0.9312 0.824120 25 to 26 142638 2.1495 0.984201 24 to 25 142333 1.2498 0.894307 23 to 24 142227 0.9371 0.825641 22 to 23 142242 0.9813 0.836784 21 to 22 141896 -0.0393 0.484317 20 to 21 141791 -0.3491 0.363524 19 to 20 141571 -0.9980 0.159134 18 to 19 142115 0.6067 0.727974 17 to 18 141878 -0.0924 0.463183 16 to 17 142005 0.2822 0.611110 15 to 16 142512 1.7778 0.962281 14 to 15 142782 2.5742 0.994977 13 to 14 141621 -0.8505 0.197515 12 to 13 141720 -0.5585 0.288253 11 to 12 141817 -0.2724 0.392673 10 to 11 142034 0.3678 0.643473 9 to 10 141529 -1.1219 0.130949 8 to 9 141793 -0.3432 0.365740 7 to 8 141783 -0.3727 0.354703 6 to 7 142053 0.4238 0.664146 5 to 6 141881 -0.0836 0.466699 4 to 5 141912 0.0079 0.503142 3 to 4 141762 -0.4346 0.331926 2 to 3 142108 0.5860 0.721078 1 to 2 141057 -2.5142 0.005964 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-12-15_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2491.34 -0.122 0.451288 Test results for specific bytes for dh-ranFile-2015-12-15_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2473.26 -0.378 0.352674 2 to 9 2521.84 0.309 0.621270 3 to 10 2505.55 0.078 0.531271 4 to 11 2420.53 -1.124 0.130535 5 to 12 2427.60 -1.024 0.152929 6 to 13 2536.39 0.515 0.696601 7 to 14 2378.59 -1.717 0.042987 8 to 15 2431.72 -0.966 0.167117 9 to 16 2480.60 -0.274 0.391909 10 to 17 2341.51 -2.241 0.012500 11 to 18 2528.58 0.404 0.656985 12 to 19 2554.15 0.766 0.778085 13 to 20 2436.13 -0.903 0.183182 14 to 21 2469.30 -0.434 0.332079 15 to 22 2493.16 -0.097 0.461444 16 to 23 2470.14 -0.422 0.336388 17 to 24 2536.48 0.516 0.697047 18 to 25 2492.64 -0.104 0.458575 19 to 26 2586.32 1.221 0.888908 20 to 27 2549.95 0.706 0.760029 21 to 28 2578.26 1.107 0.865805 22 to 29 2583.52 1.181 0.881239 23 to 30 2568.22 0.965 0.832656 24 to 31 2390.80 -1.544 0.061247 25 to 32 2446.33 -0.759 0.223923 CDPARK for dh-ranFile-2015-12-15_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 3546 1.0502 0.853193 3501 -1.0046 0.157553 3501 -1.0046 0.157553 3518 -0.2283 0.409702 3548 1.1416 0.873180 3484 -1.7808 0.037471 3571 2.1918 0.985802 3528 0.2283 0.590298 3512 -0.5023 0.307734 3509 -0.6393 0.261324 Square side=100, avg. no. parked=3521.80 sample std.=25.10 p-value of the KSTEST for those 10 p-values: 0.754535 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-12-15_14:31 0.2381,0.1399,0.5417,0.3924,0.5773,0.2650,0.2027,0.9920,0.9359,0.4727, The KS test for those 10 p-values: 0.624895 The 3DSPHERES test for dh-ranFile-2015-12-15_14:31 sample no r^3 equiv. uni. 1 15.928 0.411935 2 124.524 0.984248 3 69.281 0.900677 4 29.411 0.624829 5 68.170 0.896929 6 33.203 0.669379 7 72.946 0.912099 8 35.477 0.693504 9 85.078 0.941336 10 21.616 0.513502 11 23.577 0.544285 12 26.784 0.590492 13 29.052 0.620309 14 41.153 0.746343 15 1.310 0.042732 16 91.115 0.952029 17 9.746 0.277382 18 86.356 0.943784 19 0.314 0.010408 20 15.020 0.393876 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.038315 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-12-15_14:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -0.3 1.5 -0.1 -0.4 1.6 1.2 -0.1 -0.9 -0.1 -0.4 -1.0 -0.5 1.2 -0.7 0.0 -0.7 1.3 0.5 -0.6 -0.2 -1.2 0.4 -0.6 1.3 2.5 -0.4 -0.0 -0.0 -0.8 -0.5 -0.8 0.8 -0.2 0.2 0.2 -0.7 -0.1 -0.8 -0.1 -0.6 -1.0 -1.1 Chi-square with 42 degrees of freedom:29.279270 z-score=-1.387945, p-value=0.068800 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-12-15_14:31 Test no p-value 1 0.699357 2 0.767480 3 0.953708 4 0.151791 5 0.275733 6 0.628422 7 0.441304 8 0.459802 9 0.307459 10 0.630951 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.845013 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-12-15_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 67009 1.76 66516 0.34 3 25000.00 24704 3.50 25311 3.87 4 6666.67 6660 0.01 6555 1.87 5 1388.89 1330 2.50 1342 1.58 6 238.10 246 0.26 240 0.02 7 34.72 45 3.04 28 1.30 8 4.96 5 0.00 7 0.84 p=0.91384 p=0.86746 Number of rngs required: 687570, p-value: 0.167 RESULTS OF CRAPS TEST for dh-ranFile-2015-12-15_14:31 No. of wins: Observed Expected 98742 98585.9 z-score= 0.698, pvalue=0.75752 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66544 66666.7 0.226 0.226 2 37692 37654.3 0.038 0.263 3 27193 26954.7 2.106 2.370 4 19443 19313.5 0.869 3.238 5 13833 13851.4 0.024 3.263 6 9758 9943.5 3.462 6.725 7 7072 7145.0 0.746 7.471 8 5056 5139.1 1.343 8.814 9 3698 3699.9 0.001 8.815 10 2761 2666.3 3.364 12.179 11 1857 1923.3 2.287 14.466 12 1448 1388.7 2.529 16.995 13 1007 1003.7 0.011 17.006 14 717 726.1 0.115 17.121 15 537 525.8 0.237 17.358 16 377 381.2 0.045 17.403 17 254 276.5 1.837 19.240 18 207 200.8 0.190 19.430 19 166 146.0 2.744 22.174 20 98 106.2 0.635 22.809 21 282 287.1 0.091 22.901 Chisq= 22.90 for 20 degrees of freedom, p= 0.70630 SUMMARY of craptest p-value for no. of wins: 0.757523 p-value for throws/game: 0.706297 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-12-15_14:31 No. of wins: Observed Expected 98951 98585.9 z-score= 1.633, pvalue=0.94878 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67069 66666.7 2.428 2.428 2 37244 37654.3 4.471 6.899 3 26849 26954.7 0.415 7.314 4 19602 19313.5 4.311 11.625 5 13819 13851.4 0.076 11.701 6 9811 9943.5 1.767 13.467 7 7131 7145.0 0.028 13.495 8 5134 5139.1 0.005 13.500 9 3726 3699.9 0.185 13.685 10 2720 2666.3 1.082 14.766 11 1897 1923.3 0.360 15.127 12 1391 1388.7 0.004 15.130 13 996 1003.7 0.059 15.190 14 686 726.1 2.219 17.409 15 526 525.8 0.000 17.409 16 372 381.2 0.220 17.628 17 283 276.5 0.151 17.779 18 182 200.8 1.765 19.545 19 143 146.0 0.061 19.606 20 109 106.2 0.073 19.679 21 310 287.1 1.824 21.503 Chisq= 21.50 for 20 degrees of freedom, p= 0.63192 SUMMARY of craptest p-value for no. of wins: 0.948779 p-value for throws/game: 0.631924 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0060,0.0104,0.0105,0.0125,0.0153,0.0162,0.0234,0.0375,0.0383,0.0418, 0.0427,0.0430,0.0467,0.0510,0.0577,0.0612,0.0688,0.0694,0.0746,0.0756, 0.0778,0.0796,0.0806,0.0845,0.0876,0.0896,0.0920,0.0964,0.0975,0.1001, 0.1010,0.1017,0.1152,0.1240,0.1243,0.1302,0.1305,0.1309,0.1399,0.1518, 0.1519,0.1529,0.1531,0.1576,0.1576,0.1588,0.1591,0.1592,0.1601,0.1654, 0.1671,0.1674,0.1730,0.1815,0.1832,0.1851,0.1862,0.1869,0.1877,0.1921, 0.1974,0.1975,0.1978,0.2027,0.2191,0.2239,0.2245,0.2299,0.2360,0.2381, 0.2502,0.2532,0.2561,0.2573,0.2613,0.2616,0.2638,0.2649,0.2650,0.2653, 0.2665,0.2757,0.2774,0.2883,0.2980,0.3005,0.3009,0.3069,0.3075,0.3076, 0.3077,0.3136,0.3319,0.3321,0.3334,0.3364,0.3429,0.3527,0.3547,0.3580, 0.3621,0.3635,0.3657,0.3662,0.3709,0.3722,0.3777,0.3777,0.3919,0.3924, 0.3927,0.3939,0.3949,0.4052,0.4071,0.4097,0.4119,0.4124,0.4137,0.4216, 0.4389,0.4413,0.4430,0.4513,0.4518,0.4586,0.4598,0.4614,0.4624,0.4632, 0.4667,0.4727,0.4779,0.4843,0.4844,0.4968,0.5031,0.5109,0.5133,0.5135, 0.5195,0.5313,0.5417,0.5443,0.5473,0.5480,0.5495,0.5668,0.5729,0.5773, 0.5846,0.5903,0.5905,0.5919,0.6111,0.6201,0.6203,0.6213,0.6223,0.6246, 0.6248,0.6249,0.6258,0.6280,0.6284,0.6310,0.6310,0.6319,0.6415,0.6435, 0.6550,0.6570,0.6637,0.6641,0.6694,0.6740,0.6745,0.6773,0.6873,0.6884, 0.6922,0.6935,0.6966,0.6970,0.6994,0.7035,0.7063,0.7069,0.7113,0.7116, 0.7211,0.7280,0.7463,0.7522,0.7545,0.7575,0.7600,0.7662,0.7675,0.7704, 0.7728,0.7781,0.7797,0.7936,0.7995,0.8015,0.8054,0.8082,0.8083,0.8116, 0.8150,0.8241,0.8256,0.8262,0.8327,0.8329,0.8368,0.8445,0.8450,0.8495, 0.8532,0.8591,0.8622,0.8635,0.8658,0.8675,0.8681,0.8732,0.8812,0.8831, 0.8889,0.8916,0.8943,0.8951,0.8955,0.8969,0.8977,0.9006,0.9007,0.9033, 0.9121,0.9126,0.9138,0.9138,0.9307,0.9356,0.9359,0.9412,0.9413,0.9426, 0.9438,0.9470,0.9479,0.9487,0.9488,0.9520,0.9537,0.9571,0.9604,0.9623, 0.9697,0.9740,0.9842,0.9842,0.9848,0.9858,0.9920,0.9950,0.9969, Overall p-value after applying KStest on 269 p-values = 0.557774 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.