RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-10-29_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 15.84 19.3826 0.692981 2 to 25 15.72 13.0464 0.266927 3 to 26 15.55 23.5600 0.868108 4 to 27 15.79 14.5489 0.372064 5 to 28 16.02 8.3780 0.042219 6 to 29 16.00 21.0793 0.777235 7 to 30 15.74 21.0779 0.777176 8 to 31 15.84 24.8856 0.902701 9 to 32 16.09 22.5238 0.834595 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.269644 Tough bday spacings test for dh-ranFile-2015-10-29_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 4 35 73 91 105 81 54 28 14 7 8 (O-E)^2/E 2.9 0.1 0.0 0.5 0.5 0.1 0.1 0.1 0.1 0.0 3.8 Birthday Spacings: Sum(O-E)^2/E= 8.144, p= 0.385 RESULTS OF GCD FOR dh-ranFile-2015-10-29_19:31 Euclid's algorithm: p-value, steps to gcd: 0.284195 p-value, dist. of gcd's: 0.568105 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-10-29_19:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.357 0.784 0.313 0.718 0.880 0.308 0.238 0.191 Bits 8 to 15---> 0.051 0.730 0.590 0.881 0.800 0.283 0.689 0.757 Bits 16 to 23---> 0.307 0.262 0.731 0.451 0.548 0.170 0.455 0.333 Bits 24 to 31---> 0.771 0.524 0.605 0.737 0.299 0.850 0.521 0.124 KS test for the above 32 p values: 0.563 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-10-29_19:31, p-values for 5 runs: 0.1892, 0.9710, 0.5314, 0.8383, 0.9139 Rank test for binary matrices (31x31) for dh-ranFile-2015-10-29_19:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 206 211.4 0.139 0.139 r= 29 5119 5134.0 0.044 0.183 r= 30 23118 23103.0 0.010 0.192 r= 31 11557 11551.5 0.003 0.195 chi-square = 0.195 with df = 3; p-value = 0.022 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-10-29_19:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 204 211.4 0.260 0.260 r= 30 5123 5134.0 0.024 0.284 r= 31 23042 23103.0 0.161 0.445 r= 32 11631 11551.5 0.547 0.992 chi-square = 0.992 with df = 3; p-value = 0.197 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-10-29_19:31 b-rank test for bits 1 to 8, p=0.37028 b-rank test for bits 2 to 9, p=0.20166 b-rank test for bits 3 to 10, p=0.51735 b-rank test for bits 4 to 11, p=0.69028 b-rank test for bits 5 to 12, p=0.10792 b-rank test for bits 6 to 13, p=0.41742 b-rank test for bits 7 to 14, p=0.17935 b-rank test for bits 8 to 15, p=0.22287 b-rank test for bits 9 to 16, p=0.38188 b-rank test for bits 10 to 17, p=0.38619 b-rank test for bits 11 to 18, p=0.82167 b-rank test for bits 12 to 19, p=0.77379 b-rank test for bits 13 to 20, p=0.92327 b-rank test for bits 14 to 21, p=0.66397 b-rank test for bits 15 to 22, p=0.53188 b-rank test for bits 16 to 23, p=0.32100 b-rank test for bits 17 to 24, p=0.92830 b-rank test for bits 18 to 25, p=0.11817 b-rank test for bits 19 to 26, p=0.16489 b-rank test for bits 20 to 27, p=0.73913 b-rank test for bits 21 to 28, p=0.52160 b-rank test for bits 22 to 29, p=0.89346 b-rank test for bits 23 to 30, p=0.59413 b-rank test for bits 24 to 31, p=0.40636 b-rank test for bits 25 to 32, p=0.83977 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 = 0.872960 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-10-29_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 142281 0.87 0.807409 2 142257 0.81 0.791694 3 142053 0.34 0.631443 4 142478 1.33 0.908021 5 141900 -0.02 0.491304 6 141936 0.06 0.524843 7 141671 -0.56 0.288816 8 141081 -1.94 0.026474 9 141701 -0.49 0.313217 10 142640 1.71 0.956105 11 142039 0.30 0.619043 12 141975 0.15 0.560972 13 142363 1.06 0.855422 14 141858 -0.12 0.452269 15 142160 0.59 0.720954 16 142303 0.92 0.821159 17 141679 -0.54 0.295235 18 141437 -1.10 0.134889 19 142516 1.42 0.921825 20 142195 0.67 0.747759 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-10-29_19:31 Bits used No. missing words z-score p-value 23 to 32 141525 -1.3253 0.092540 22 to 31 142043 0.4609 0.677576 21 to 30 142499 2.0333 0.978991 20 to 29 141972 0.2161 0.585547 19 to 28 141892 -0.0598 0.476174 18 to 27 141763 -0.5046 0.306925 17 to 26 141906 -0.0115 0.495419 16 to 25 141760 -0.5149 0.303301 15 to 24 141880 -0.1011 0.459721 14 to 23 141925 0.0540 0.521546 13 to 22 142027 0.4058 0.657540 12 to 21 141802 -0.3701 0.355653 11 to 20 142583 2.3230 0.989910 10 to 19 142705 2.7437 0.996962 9 to 18 141577 -1.1460 0.125905 8 to 17 141985 0.2609 0.602927 7 to 16 142099 0.6540 0.743455 6 to 15 141518 -1.3494 0.088602 5 to 14 142134 0.7747 0.780749 4 to 13 141959 0.1713 0.567997 3 to 12 142035 0.4333 0.667618 2 to 11 141641 -0.9253 0.177411 1 to 10 141754 -0.5356 0.296110 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-10-29_19:31 Bits used No. missing words z-score p-value 28 to 32 141876 -0.1130 0.455022 27 to 31 142792 2.9921 0.998615 26 to 30 141592 -1.0757 0.141032 25 to 29 141657 -0.8554 0.196177 24 to 28 142162 0.8565 0.804142 23 to 27 142002 0.3141 0.623291 22 to 26 142115 0.6972 0.757157 21 to 25 142045 0.4599 0.677205 20 to 24 141956 0.1582 0.562852 19 to 23 141404 -1.7130 0.043358 18 to 22 142106 0.6667 0.747511 17 to 21 142403 1.6735 0.952881 16 to 20 142254 1.1684 0.878672 15 to 19 141295 -2.0825 0.018650 14 to 18 141512 -1.3469 0.089009 13 to 17 141462 -1.5164 0.064713 12 to 16 142156 0.8362 0.798470 11 to 15 142173 0.8938 0.814285 10 to 14 142102 0.6531 0.743160 9 to 13 142261 1.1921 0.883389 8 to 12 141606 -1.0282 0.151919 7 to 11 141857 -0.1774 0.429601 6 to 10 141531 -1.2825 0.099838 5 to 9 141737 -0.5842 0.279553 4 to 8 141937 0.0938 0.537365 3 to 7 141266 -2.1808 0.014600 2 to 6 141602 -1.0418 0.148753 1 to 5 141867 -0.1435 0.442951 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-10-29_19:31 Bits used No. missing words z-score p-value 31 to 32 142310 1.1819 0.881381 30 to 31 141826 -0.2458 0.402914 29 to 30 142232 0.9518 0.829408 28 to 29 141493 -1.2281 0.109702 27 to 28 142291 1.1259 0.869890 26 to 27 141254 -1.9331 0.026610 25 to 26 141757 -0.4494 0.326589 24 to 25 141259 -1.9184 0.027532 23 to 24 141520 -1.1485 0.125388 22 to 23 142216 0.9046 0.817170 21 to 22 141545 -1.0747 0.141250 20 to 21 141202 -2.0865 0.018466 19 to 20 141452 -1.3491 0.088660 18 to 19 142700 2.3324 0.990159 17 to 18 141744 -0.4877 0.312882 16 to 17 141521 -1.1455 0.125998 15 to 16 142236 0.9636 0.832384 14 to 15 141680 -0.6765 0.249365 13 to 14 141323 -1.7296 0.041852 12 to 13 141721 -0.5555 0.289261 11 to 12 141879 -0.0895 0.464355 10 to 11 140946 -2.8417 0.002244 9 to 10 141547 -1.0688 0.142575 8 to 9 141598 -0.9184 0.179211 7 to 8 142029 0.3530 0.637959 6 to 7 142397 1.4386 0.924862 5 to 6 141690 -0.6470 0.258819 4 to 5 142049 0.4120 0.659832 3 to 4 142531 1.8338 0.966661 2 to 3 141752 -0.4641 0.321288 1 to 2 142302 1.1583 0.876633 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-10-29_19:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2514.77 0.209 0.582706 Test results for specific bytes for dh-ranFile-2015-10-29_19:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2485.10 -0.211 0.416575 2 to 9 2503.76 0.053 0.521219 3 to 10 2471.76 -0.399 0.344803 4 to 11 2605.47 1.492 0.932097 5 to 12 2477.14 -0.323 0.373226 6 to 13 2513.97 0.198 0.578285 7 to 14 2570.33 0.995 0.840026 8 to 15 2439.05 -0.862 0.194336 9 to 16 2497.38 -0.037 0.485229 10 to 17 2513.67 0.193 0.576634 11 to 18 2422.16 -1.101 0.135500 12 to 19 2508.38 0.119 0.547176 13 to 20 2494.59 -0.076 0.469511 14 to 21 2614.08 1.613 0.946667 15 to 22 2473.71 -0.372 0.355034 16 to 23 2515.76 0.223 0.588166 17 to 24 2581.20 1.148 0.874594 18 to 25 2534.52 0.488 0.687284 19 to 26 2469.55 -0.431 0.333392 20 to 27 2511.99 0.170 0.567332 21 to 28 2487.17 -0.181 0.428031 22 to 29 2500.08 0.001 0.500464 23 to 30 2436.31 -0.901 0.183872 24 to 31 2451.97 -0.679 0.248512 25 to 32 2346.21 -2.175 0.014820 CDPARK for dh-ranFile-2015-10-29_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 3528 0.2283 0.590298 3495 -1.2785 0.100530 3495 -1.2785 0.100530 3490 -1.5068 0.065925 3534 0.5023 0.692266 3539 0.7306 0.767486 3492 -1.4155 0.078457 3556 1.5068 0.934075 3528 0.2283 0.590298 3513 -0.4566 0.323972 Square side=100, avg. no. parked=3517.00 sample std.=22.08 p-value of the KSTEST for those 10 p-values: 0.398907 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-10-29_19:31 0.0395,0.5888,0.9368,0.8570,0.9261,0.7345,0.0248,0.4997,0.0193,0.6466, The KS test for those 10 p-values: 0.213042 The 3DSPHERES test for dh-ranFile-2015-10-29_19:31 sample no r^3 equiv. uni. 1 9.328 0.267244 2 22.190 0.522721 3 22.551 0.528433 4 8.133 0.237464 5 9.669 0.275530 6 26.292 0.583715 7 38.017 0.718390 8 5.974 0.180546 9 4.533 0.140242 10 22.683 0.530509 11 3.957 0.123558 12 3.796 0.118845 13 12.962 0.350840 14 2.491 0.079681 15 12.674 0.344564 16 9.266 0.265728 17 14.634 0.386034 18 2.349 0.075309 19 24.833 0.562980 20 43.173 0.762855 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.025648 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-10-29_19:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 -1.6 -1.1 0.9 0.2 -0.7 -0.3 -0.9 0.5 0.5 0.2 -0.9 1.9 0.1 0.5 0.3 -0.4 0.2 -1.1 1.1 0.2 -1.8 -0.4 0.8 0.7 0.1 0.1 -1.9 -0.7 -0.3 -0.5 1.0 -1.0 0.3 2.0 -1.6 -0.9 -1.0 -0.8 -1.3 1.6 -1.0 -0.1 Chi-square with 42 degrees of freedom:39.435449 z-score=-0.279815, p-value=0.415848 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-10-29_19:31 Test no p-value 1 0.620086 2 0.039469 3 0.433397 4 0.273610 5 0.740402 6 0.015117 7 0.378756 8 0.025341 9 0.961660 10 0.029766 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.037724 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-10-29_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 66524 0.31 66851 0.51 3 25000.00 25144 0.83 24924 0.23 4 6666.67 6627 0.24 6577 1.21 5 1388.89 1419 0.65 1386 0.01 6 238.10 245 0.20 226 0.61 7 34.72 38 0.31 33 0.09 8 4.96 2 1.77 2 1.77 p=0.36387 p=0.37982 Number of rngs required: 688780, p-value: 0.668 RESULTS OF CRAPS TEST for dh-ranFile-2015-10-29_19:31 No. of wins: Observed Expected 98759 98585.9 z-score= 0.774, pvalue=0.78065 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66696 66666.7 0.013 0.013 2 37568 37654.3 0.198 0.211 3 27208 26954.7 2.380 2.591 4 19147 19313.5 1.435 4.025 5 13710 13851.4 1.444 5.469 6 9914 9943.5 0.088 5.557 7 7160 7145.0 0.031 5.588 8 5099 5139.1 0.312 5.901 9 3745 3699.9 0.551 6.451 10 2766 2666.3 3.728 10.180 11 1886 1923.3 0.725 10.904 12 1415 1388.7 0.497 11.401 13 993 1003.7 0.114 11.515 14 742 726.1 0.346 11.861 15 528 525.8 0.009 11.870 16 383 381.2 0.009 11.879 17 287 276.5 0.396 12.275 18 208 200.8 0.256 12.531 19 161 146.0 1.544 14.075 20 106 106.2 0.000 14.076 21 278 287.1 0.289 14.365 Chisq= 14.37 for 20 degrees of freedom, p= 0.18849 SUMMARY of craptest p-value for no. of wins: 0.780650 p-value for throws/game: 0.188491 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-10-29_19:31 No. of wins: Observed Expected 98757 98585.9 z-score= 0.765, pvalue=0.77800 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66656 66666.7 0.002 0.002 2 37791 37654.3 0.496 0.498 3 26865 26954.7 0.299 0.797 4 19457 19313.5 1.067 1.863 5 13804 13851.4 0.162 2.026 6 9881 9943.5 0.393 2.419 7 7159 7145.0 0.027 2.446 8 5014 5139.1 3.044 5.490 9 3667 3699.9 0.292 5.782 10 2712 2666.3 0.783 6.566 11 1958 1923.3 0.625 7.191 12 1414 1388.7 0.459 7.650 13 980 1003.7 0.560 8.210 14 686 726.1 2.219 10.429 15 546 525.8 0.773 11.203 16 378 381.2 0.026 11.229 17 285 276.5 0.259 11.487 18 208 200.8 0.256 11.743 19 139 146.0 0.334 12.078 20 108 106.2 0.030 12.108 21 292 287.1 0.083 12.191 Chisq= 12.19 for 20 degrees of freedom, p= 0.09065 SUMMARY of craptest p-value for no. of wins: 0.777996 p-value for throws/game: 0.090646 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0022,0.0146,0.0148,0.0151,0.0185,0.0186,0.0193,0.0216,0.0248,0.0253, 0.0256,0.0265,0.0266,0.0275,0.0298,0.0377,0.0395,0.0395,0.0419,0.0422, 0.0434,0.0507,0.0647,0.0659,0.0753,0.0785,0.0797,0.0886,0.0887,0.0890, 0.0906,0.0925,0.0998,0.1005,0.1005,0.1079,0.1097,0.1182,0.1188,0.1236, 0.1239,0.1254,0.1259,0.1260,0.1349,0.1355,0.1402,0.1410,0.1413,0.1426, 0.1488,0.1519,0.1649,0.1695,0.1774,0.1792,0.1794,0.1805,0.1839,0.1885, 0.1892,0.1907,0.1943,0.1962,0.1968,0.2017,0.2130,0.2229,0.2375,0.2382, 0.2485,0.2494,0.2588,0.2619,0.2657,0.2669,0.2672,0.2696,0.2736,0.2755, 0.2796,0.2834,0.2842,0.2888,0.2893,0.2952,0.2961,0.2989,0.3033,0.3069, 0.3074,0.3076,0.3127,0.3129,0.3132,0.3210,0.3213,0.3240,0.3266,0.3334, 0.3334,0.3446,0.3448,0.3508,0.3550,0.3557,0.3568,0.3639,0.3703,0.3721, 0.3732,0.3788,0.3798,0.3819,0.3852,0.3860,0.3862,0.3989,0.4029,0.4064, 0.4158,0.4166,0.4174,0.4280,0.4296,0.4334,0.4430,0.4514,0.4523,0.4548, 0.4550,0.4597,0.4644,0.4695,0.4762,0.4852,0.4913,0.4954,0.4997,0.5005, 0.5174,0.5206,0.5212,0.5215,0.5216,0.5227,0.5235,0.5248,0.5284,0.5305, 0.5314,0.5319,0.5374,0.5472,0.5475,0.5610,0.5629,0.5630,0.5633,0.5673, 0.5680,0.5681,0.5766,0.5783,0.5827,0.5837,0.5855,0.5882,0.5888,0.5897, 0.5903,0.5903,0.5941,0.6029,0.6050,0.6190,0.6201,0.6233,0.6314,0.6380, 0.6466,0.6575,0.6598,0.6640,0.6676,0.6680,0.6772,0.6776,0.6873,0.6890, 0.6903,0.6923,0.6930,0.7180,0.7184,0.7210,0.7304,0.7307,0.7345,0.7366, 0.7391,0.7404,0.7432,0.7435,0.7475,0.7478,0.7567,0.7572,0.7629,0.7675, 0.7707,0.7738,0.7772,0.7772,0.7780,0.7806,0.7807,0.7836,0.7917,0.7985, 0.7996,0.8041,0.8074,0.8143,0.8172,0.8212,0.8217,0.8294,0.8324,0.8346, 0.8383,0.8398,0.8400,0.8497,0.8554,0.8570,0.8681,0.8699,0.8730,0.8746, 0.8766,0.8787,0.8803,0.8813,0.8814,0.8834,0.8935,0.9027,0.9080,0.9139, 0.9218,0.9233,0.9249,0.9261,0.9283,0.9321,0.9341,0.9368,0.9467,0.9529, 0.9561,0.9617,0.9667,0.9710,0.9790,0.9899,0.9902,0.9970,0.9986, Overall p-value after applying KStest on 269 p-values = 0.288741 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.