RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-01-24_19:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.83 9.5852 0.079903 2 to 25 15.53 21.5067 0.795560 3 to 26 15.76 15.6828 0.453577 4 to 27 15.93 7.1700 0.018761 5 to 28 15.66 25.7276 0.920432 6 to 29 15.81 21.9688 0.814077 7 to 30 15.73 17.2320 0.561243 8 to 31 15.66 18.9033 0.665892 9 to 32 15.88 20.2552 0.738614 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.560794 Tough bday spacings test for dh-ranFile-2017-01-24_19:31: 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 10 47 58 100 94 87 47 33 15 7 2 (O-E)^2/E 0.1 2.9 3.2 0.1 0.1 1.0 0.5 0.4 0.0 0.0 1.0 Birthday Spacings: Sum(O-E)^2/E= 9.311, p= 0.497 RESULTS OF GCD FOR dh-ranFile-2017-01-24_19:31 Euclid's algorithm: p-value, steps to gcd: 0.910436 p-value, dist. of gcd's: 0.961536 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-01-24_19:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.488 0.430 0.184 0.043 0.345 0.026 0.658 0.836 Bits 8 to 15---> 0.243 0.217 0.311 0.747 0.653 0.137 0.421 0.160 Bits 16 to 23---> 0.800 0.771 0.614 0.867 0.031 0.621 0.040 0.710 Bits 24 to 31---> 0.266 0.582 0.952 0.493 0.433 0.662 0.131 0.770 KS test for the above 32 p values: 0.403 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-01-24_19:31, p-values for 5 runs: 0.3466, 0.1652, 0.3424, 0.7722, 0.6827 Rank test for binary matrices (31x31) for dh-ranFile-2017-01-24_19:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 224 211.4 0.749 0.749 r= 29 5110 5134.0 0.112 0.861 r= 30 23008 23103.0 0.391 1.252 r= 31 11658 11551.5 0.981 2.234 chi-square = 2.234 with df = 3; p-value = 0.475 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2017-01-24_19:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 200 211.4 0.617 0.617 r= 30 5118 5134.0 0.050 0.667 r= 31 23128 23103.0 0.027 0.694 r= 32 11554 11551.5 0.001 0.694 chi-square = 0.694 with df = 3; p-value = 0.125 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2017-01-24_19:31 b-rank test for bits 1 to 8, p=0.95393 b-rank test for bits 2 to 9, p=0.58902 b-rank test for bits 3 to 10, p=0.40336 b-rank test for bits 4 to 11, p=0.70535 b-rank test for bits 5 to 12, p=0.57454 b-rank test for bits 6 to 13, p=0.49734 b-rank test for bits 7 to 14, p=0.89873 b-rank test for bits 8 to 15, p=0.41620 b-rank test for bits 9 to 16, p=0.20792 b-rank test for bits 10 to 17, p=0.77269 b-rank test for bits 11 to 18, p=0.95348 b-rank test for bits 12 to 19, p=0.36328 b-rank test for bits 13 to 20, p=0.73055 b-rank test for bits 14 to 21, p=0.12961 b-rank test for bits 15 to 22, p=0.91246 b-rank test for bits 16 to 23, p=0.03124 b-rank test for bits 17 to 24, p=0.72387 b-rank test for bits 18 to 25, p=0.92787 b-rank test for bits 19 to 26, p=0.37561 b-rank test for bits 20 to 27, p=0.07926 b-rank test for bits 21 to 28, p=0.00700 b-rank test for bits 22 to 29, p=0.56649 b-rank test for bits 23 to 30, p=0.17410 b-rank test for bits 24 to 31, p=0.36944 b-rank test for bits 25 to 32, p=0.07371 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 = 0.899799 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-01-24_19:31 (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 142243 0.78 0.782188 2 141983 0.17 0.568331 3 141739 -0.40 0.345327 4 141522 -0.90 0.182739 5 141398 -1.19 0.116103 6 141850 -0.14 0.444875 7 142571 1.55 0.938943 8 141532 -0.88 0.188993 9 142179 0.63 0.735676 10 143106 2.80 0.997413 11 141289 -1.45 0.073617 12 141757 -0.36 0.360954 13 142783 2.04 0.979389 14 142420 1.19 0.883596 15 141650 -0.61 0.272287 16 141875 -0.08 0.468035 17 142804 2.09 0.981707 18 141052 -2.00 0.022583 19 141668 -0.56 0.286426 20 141761 -0.35 0.364459 ---------------------------------------------------------------- OPSO test for dh-ranFile-2017-01-24_19:31 Bits used No. missing words z-score p-value 23 to 32 142004 0.3264 0.627957 22 to 31 142271 1.2471 0.893827 21 to 30 142270 1.2437 0.893193 20 to 29 141841 -0.2356 0.406864 19 to 28 142026 0.4023 0.656272 18 to 27 141775 -0.4632 0.321608 17 to 26 142111 0.6954 0.756602 16 to 25 142333 1.4609 0.927983 15 to 24 141671 -0.8218 0.205588 14 to 23 142072 0.5609 0.712578 13 to 22 141694 -0.7425 0.228887 12 to 21 142225 1.0885 0.861817 11 to 20 141950 0.1402 0.555765 10 to 19 141779 -0.4494 0.326567 9 to 18 142360 1.5540 0.939912 8 to 17 141741 -0.5804 0.280806 7 to 16 141873 -0.1253 0.450153 6 to 15 141242 -2.3011 0.010692 5 to 14 141972 0.2161 0.585547 4 to 13 141340 -1.9632 0.024811 3 to 12 142221 1.0747 0.858751 2 to 11 141925 0.0540 0.521546 1 to 10 141593 -1.0908 0.137682 ----------------------------------------------------------------- OQSO test for dh-ranFile-2017-01-24_19:31 Bits used No. missing words z-score p-value 28 to 32 141722 -0.6350 0.262709 27 to 31 141562 -1.1774 0.119520 26 to 30 141840 -0.2350 0.407098 25 to 29 141746 -0.5537 0.289905 24 to 28 142120 0.7141 0.762428 23 to 27 141294 -2.0859 0.018495 22 to 26 141904 -0.0181 0.492792 21 to 25 141604 -1.0350 0.150331 20 to 24 141907 -0.0079 0.496849 19 to 23 142147 0.8057 0.789781 18 to 22 141979 0.2362 0.593349 17 to 21 141670 -0.8113 0.208600 16 to 20 142188 0.9446 0.827580 15 to 19 141797 -0.3808 0.351683 14 to 18 141371 -1.8248 0.034012 13 to 17 141405 -1.7096 0.043671 12 to 16 142399 1.6599 0.951533 11 to 15 141841 -0.2316 0.408414 10 to 14 142188 0.9446 0.827580 9 to 13 141440 -1.5909 0.055811 8 to 12 142235 1.1040 0.865196 7 to 11 141786 -0.4181 0.337949 6 to 10 141692 -0.7367 0.230649 5 to 9 142276 1.2429 0.893057 4 to 8 141808 -0.3435 0.365614 3 to 7 141662 -0.8384 0.200901 2 to 6 142268 1.2158 0.887975 1 to 5 141361 -1.8587 0.031532 ----------------------------------------------------------------- DNA test for dh-ranFile-2017-01-24_19:31 Bits used No. missing words z-score p-value 31 to 32 142282 1.0993 0.864186 30 to 31 142198 0.8515 0.802764 29 to 30 142291 1.1259 0.869890 28 to 29 141528 -1.1249 0.130323 27 to 28 142575 1.9636 0.975213 26 to 27 141870 -0.1160 0.453819 25 to 26 142110 0.5919 0.723057 24 to 25 142111 0.5949 0.724044 23 to 24 141945 0.1052 0.541900 22 to 23 142461 1.6273 0.948168 21 to 22 142132 0.6568 0.744359 20 to 21 142319 1.2085 0.886566 19 to 20 141669 -0.7089 0.239182 18 to 19 141565 -1.0157 0.154881 17 to 18 141392 -1.5260 0.063499 16 to 17 142211 0.8899 0.813235 15 to 16 141578 -0.9774 0.164192 14 to 15 141680 -0.6765 0.249365 13 to 14 141539 -1.0924 0.137325 12 to 13 142000 0.2675 0.605444 11 to 12 142229 0.9430 0.827154 10 to 11 142367 1.3501 0.911501 9 to 10 142117 0.6126 0.729928 8 to 9 141746 -0.4818 0.314974 7 to 8 141725 -0.5437 0.293308 6 to 7 142008 0.2911 0.614498 5 to 6 141843 -0.1957 0.422437 4 to 5 141684 -0.6647 0.253124 3 to 4 141462 -1.3196 0.093491 2 to 3 142150 0.7099 0.761130 1 to 2 141748 -0.4759 0.317073 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2017-01-24_19:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2563.74 0.901 0.816318 Test results for specific bytes for dh-ranFile-2017-01-24_19:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2494.59 -0.077 0.469500 2 to 9 2507.20 0.102 0.540557 3 to 10 2557.11 0.808 0.790365 4 to 11 2488.78 -0.159 0.436989 5 to 12 2450.26 -0.703 0.240882 6 to 13 2471.32 -0.406 0.342499 7 to 14 2499.18 -0.012 0.495399 8 to 15 2617.41 1.660 0.951586 9 to 16 2445.18 -0.775 0.219092 10 to 17 2596.53 1.365 0.913903 11 to 18 2535.77 0.506 0.693500 12 to 19 2443.98 -0.792 0.214105 13 to 20 2383.44 -1.648 0.049636 14 to 21 2442.77 -0.809 0.209174 15 to 22 2469.10 -0.437 0.331067 16 to 23 2478.60 -0.303 0.381104 17 to 24 2302.34 -2.795 0.002592 18 to 25 2463.63 -0.514 0.303496 19 to 26 2449.29 -0.717 0.236648 20 to 27 2538.52 0.545 0.707062 21 to 28 2472.18 -0.393 0.347017 22 to 29 2404.63 -1.349 0.088710 23 to 30 2568.77 0.973 0.834614 24 to 31 2478.74 -0.301 0.381856 25 to 32 2428.00 -1.018 0.154296 CDPARK for dh-ranFile-2017-01-24_19:31: 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 3575 2.3744 0.991212 3546 1.0502 0.853193 3563 1.8265 0.966111 3542 0.8676 0.807188 3508 -0.6849 0.246694 3556 1.5068 0.934075 3499 -1.0959 0.136563 3498 -1.1416 0.126820 3518 -0.2283 0.409702 3520 -0.1370 0.445521 Square side=100, avg. no. parked=3532.50 sample std.=26.15 p-value of the KSTEST for those 10 p-values: 0.198123 Results for the MINIMUM DISTANCE test for dh-ranFile-2017-01-24_19:31 0.2092,0.0186,0.4194,0.2959,0.7399,0.7131,0.1019,0.2993,0.6607,0.0824, The KS test for those 10 p-values: 0.178723 The 3DSPHERES test for dh-ranFile-2017-01-24_19:31 sample no r^3 equiv. uni. 1 21.418 0.510293 2 58.855 0.859402 3 2.124 0.068363 4 13.717 0.366959 5 45.918 0.783594 6 29.650 0.627804 7 14.107 0.375136 8 0.109 0.003629 9 20.596 0.496681 10 25.278 0.569409 11 11.560 0.319781 12 53.393 0.831322 13 28.374 0.611632 14 0.920 0.030210 15 1.075 0.035198 16 51.570 0.820758 17 4.292 0.133297 18 14.997 0.393410 19 9.882 0.280640 20 19.784 0.482865 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.318351 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-01-24_19:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 0.5 -0.6 -1.4 0.5 -0.1 1.6 -0.6 0.1 0.2 -1.2 -0.4 -0.0 -1.4 1.4 1.0 -1.8 0.4 1.7 0.1 -2.4 1.0 -0.7 -0.3 1.1 0.1 0.0 1.1 0.5 0.2 -1.6 1.1 -0.4 1.1 -1.0 1.5 1.7 -0.4 0.5 0.4 0.9 0.0 -1.1 Chi-square with 42 degrees of freedom:43.038429 z-score=0.113302, p-value=0.573407 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2017-01-24_19:31 Test no p-value 1 0.153246 2 0.932322 3 0.804840 4 0.034085 5 0.422892 6 0.011784 7 0.802493 8 0.219679 9 0.203765 10 0.019113 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.053510 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-01-24_19:31: (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 66572 0.13 66769 0.16 3 25000.00 25042 0.07 24832 1.13 4 6666.67 6714 0.34 6742 0.85 5 1388.89 1354 0.88 1371 0.23 6 238.10 281 7.73 236 0.02 7 34.72 32 0.21 42 1.53 8 4.96 4 0.19 7 0.84 p=0.85497 p=0.42395 Number of rngs required: 689994, p-value: 0.969 RESULTS OF CRAPS TEST for dh-ranFile-2017-01-24_19:31 No. of wins: Observed Expected 98236 98585.9 z-score=-1.565, pvalue=0.05882 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66654 66666.7 0.002 0.002 2 37605 37654.3 0.065 0.067 3 27212 26954.7 2.455 2.522 4 19186 19313.5 0.841 3.364 5 13860 13851.4 0.005 3.369 6 10034 9943.5 0.823 4.192 7 7028 7145.0 1.917 6.109 8 5137 5139.1 0.001 6.109 9 3650 3699.9 0.672 6.782 10 2684 2666.3 0.118 6.899 11 1881 1923.3 0.932 7.831 12 1381 1388.7 0.043 7.874 13 1000 1003.7 0.014 7.888 14 757 726.1 1.311 9.199 15 508 525.8 0.605 9.804 16 381 381.2 0.000 9.804 17 304 276.5 2.727 12.531 18 204 200.8 0.050 12.581 19 143 146.0 0.061 12.642 20 92 106.2 1.902 14.544 21 299 287.1 0.492 15.036 Chisq= 15.04 for 20 degrees of freedom, p= 0.22568 SUMMARY of craptest p-value for no. of wins: 0.058818 p-value for throws/game: 0.225682 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2017-01-24_19:31 No. of wins: Observed Expected 98397 98585.9 z-score=-0.845, pvalue=0.19914 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66393 66666.7 1.123 1.123 2 37562 37654.3 0.226 1.350 3 26810 26954.7 0.777 2.127 4 19337 19313.5 0.029 2.156 5 13931 13851.4 0.457 2.613 6 10099 9943.5 2.430 5.043 7 7282 7145.0 2.626 7.669 8 5268 5139.1 3.235 10.904 9 3822 3699.9 4.032 14.935 10 2559 2666.3 4.318 19.253 11 1920 1923.3 0.006 19.259 12 1353 1388.7 0.920 20.179 13 1006 1003.7 0.005 20.184 14 724 726.1 0.006 20.190 15 552 525.8 1.302 21.492 16 366 381.2 0.602 22.094 17 289 276.5 0.561 22.656 18 208 200.8 0.256 22.912 19 138 146.0 0.437 23.349 20 106 106.2 0.000 23.349 21 275 287.1 0.511 23.860 Chisq= 23.86 for 20 degrees of freedom, p= 0.75144 SUMMARY of craptest p-value for no. of wins: 0.199143 p-value for throws/game: 0.751442 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0026,0.0036,0.0070,0.0107,0.0118,0.0185,0.0186,0.0188,0.0191,0.0226, 0.0248,0.0265,0.0302,0.0312,0.0313,0.0315,0.0340,0.0341,0.0352,0.0396, 0.0430,0.0437,0.0496,0.0535,0.0558,0.0588,0.0635,0.0684,0.0736,0.0737, 0.0793,0.0799,0.0824,0.0887,0.0935,0.1019,0.1161,0.1195,0.1254,0.1268, 0.1296,0.1303,0.1313,0.1333,0.1366,0.1372,0.1373,0.1377,0.1503,0.1532, 0.1543,0.1549,0.1604,0.1642,0.1652,0.1741,0.1787,0.1827,0.1842,0.1890, 0.1981,0.1991,0.2009,0.2038,0.2056,0.2079,0.2086,0.2092,0.2092,0.2141, 0.2173,0.2191,0.2197,0.2257,0.2289,0.2306,0.2366,0.2392,0.2409,0.2431, 0.2467,0.2494,0.2531,0.2627,0.2661,0.2723,0.2806,0.2808,0.2864,0.2899, 0.2933,0.2959,0.2993,0.3035,0.3107,0.3150,0.3171,0.3184,0.3198,0.3216, 0.3266,0.3311,0.3379,0.3424,0.3425,0.3451,0.3453,0.3466,0.3470,0.3517, 0.3610,0.3633,0.3645,0.3656,0.3670,0.3694,0.3751,0.3756,0.3811,0.3819, 0.3934,0.4032,0.4034,0.4069,0.4071,0.4084,0.4097,0.4162,0.4194,0.4210, 0.4224,0.4229,0.4240,0.4302,0.4328,0.4370,0.4449,0.4455,0.4502,0.4536, 0.4538,0.4680,0.4695,0.4746,0.4829,0.4878,0.4928,0.4930,0.4954,0.4967, 0.4968,0.4971,0.4973,0.5103,0.5215,0.5406,0.5419,0.5558,0.5608,0.5612, 0.5665,0.5683,0.5694,0.5734,0.5745,0.5818,0.5855,0.5890,0.5933,0.6054, 0.6116,0.6136,0.6145,0.6208,0.6278,0.6280,0.6532,0.6563,0.6576,0.6607, 0.6618,0.6659,0.6827,0.6935,0.7054,0.7071,0.7103,0.7126,0.7131,0.7231, 0.7239,0.7240,0.7299,0.7305,0.7357,0.7386,0.7399,0.7444,0.7465,0.7514, 0.7566,0.7611,0.7624,0.7700,0.7713,0.7722,0.7727,0.7822,0.7836,0.7898, 0.7904,0.7956,0.8005,0.8025,0.8028,0.8048,0.8072,0.8132,0.8141,0.8163, 0.8208,0.8272,0.8276,0.8276,0.8313,0.8346,0.8357,0.8532,0.8550,0.8588, 0.8594,0.8618,0.8642,0.8652,0.8672,0.8699,0.8836,0.8866,0.8880,0.8931, 0.8932,0.8938,0.8987,0.8998,0.9104,0.9115,0.9125,0.9139,0.9204,0.9279, 0.9280,0.9323,0.9341,0.9389,0.9399,0.9482,0.9515,0.9516,0.9523,0.9535, 0.9539,0.9615,0.9661,0.9694,0.9752,0.9794,0.9817,0.9912,0.9974, Overall p-value after applying KStest on 269 p-values = 0.100117 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.