RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-11-06_13:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.97 16.1025 0.483416 2 to 25 15.80 15.3550 0.430070 3 to 26 15.97 28.1910 0.957245 4 to 27 15.73 12.3998 0.224653 5 to 28 15.63 18.4242 0.637437 6 to 29 15.50 14.9694 0.402315 7 to 30 15.95 8.7952 0.053530 8 to 31 15.73 23.4104 0.863639 9 to 32 15.55 19.7983 0.715325 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.992003 Tough bday spacings test for dh-ranFile-2016-11-06_13:31: 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 9 37 65 105 104 79 44 27 19 7 4 (O-E)^2/E 0.0 0.0 0.9 0.5 0.4 0.0 1.3 0.3 1.1 0.0 0.0 Birthday Spacings: Sum(O-E)^2/E= 4.581, p= 0.083 RESULTS OF GCD FOR dh-ranFile-2016-11-06_13:31 Euclid's algorithm: p-value, steps to gcd: 0.219740 p-value, dist. of gcd's: 0.822727 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-11-06_13:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.883 0.634 0.897 0.722 0.024 0.745 0.015 0.179 Bits 8 to 15---> 0.155 0.508 0.527 0.584 0.810 0.468 0.762 0.171 Bits 16 to 23---> 0.512 0.943 0.160 0.006 0.234 0.492 0.910 0.662 Bits 24 to 31---> 0.851 0.556 0.911 0.211 0.041 0.253 0.348 0.214 KS test for the above 32 p values: 0.303 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-11-06_13:31, p-values for 5 runs: 0.3466, 0.8561, 0.4149, 0.5417, 0.0951 Rank test for binary matrices (31x31) for dh-ranFile-2016-11-06_13:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 209 211.4 0.028 0.028 r= 29 5075 5134.0 0.678 0.706 r= 30 23095 23103.0 0.003 0.709 r= 31 11621 11551.5 0.418 1.127 chi-square = 1.127 with df = 3; p-value = 0.229 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-11-06_13:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 200 211.4 0.617 0.617 r= 30 5106 5134.0 0.153 0.769 r= 31 23151 23103.0 0.100 0.869 r= 32 11543 11551.5 0.006 0.875 chi-square = 0.875 with df = 3; p-value = 0.169 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-11-06_13:31 b-rank test for bits 1 to 8, p=0.58518 b-rank test for bits 2 to 9, p=0.37653 b-rank test for bits 3 to 10, p=0.19514 b-rank test for bits 4 to 11, p=0.95393 b-rank test for bits 5 to 12, p=0.60781 b-rank test for bits 6 to 13, p=0.95904 b-rank test for bits 7 to 14, p=0.07545 b-rank test for bits 8 to 15, p=0.44163 b-rank test for bits 9 to 16, p=0.38144 b-rank test for bits 10 to 17, p=0.45233 b-rank test for bits 11 to 18, p=0.33969 b-rank test for bits 12 to 19, p=0.55839 b-rank test for bits 13 to 20, p=0.91450 b-rank test for bits 14 to 21, p=0.97751 b-rank test for bits 15 to 22, p=0.90611 b-rank test for bits 16 to 23, p=0.80459 b-rank test for bits 17 to 24, p=0.96011 b-rank test for bits 18 to 25, p=0.55966 b-rank test for bits 19 to 26, p=0.30659 b-rank test for bits 20 to 27, p=0.34381 b-rank test for bits 21 to 28, p=0.93592 b-rank test for bits 22 to 29, p=0.87853 b-rank test for bits 23 to 30, p=0.33139 b-rank test for bits 24 to 31, p=0.41119 b-rank test for bits 25 to 32, p=0.56225 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 = 0.074148 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-11-06_13:31 (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 141983 0.17 0.568331 2 141988 0.18 0.572918 3 142346 1.02 0.846197 4 141839 -0.16 0.434739 5 141616 -0.69 0.246561 6 141318 -1.38 0.083545 7 141102 -1.89 0.029628 8 142349 1.03 0.847852 9 142002 0.22 0.585708 10 141619 -0.68 0.248778 11 141796 -0.26 0.395586 12 141953 0.10 0.540635 13 141528 -0.89 0.186476 14 141462 -1.05 0.147974 15 141807 -0.24 0.405518 16 141504 -0.95 0.171811 17 142134 0.52 0.700184 18 142314 0.95 0.827796 19 141468 -1.03 0.151236 20 142512 1.41 0.920450 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-11-06_13:31 Bits used No. missing words z-score p-value 23 to 32 142072 0.5609 0.712578 22 to 31 141989 0.2747 0.608236 21 to 30 141736 -0.5977 0.275024 20 to 29 141823 -0.2977 0.382970 19 to 28 141508 -1.3839 0.083195 18 to 27 142143 0.8058 0.789809 17 to 26 141756 -0.5287 0.298498 16 to 25 142308 1.3747 0.915392 15 to 24 142416 1.7471 0.959693 14 to 23 142331 1.4540 0.927032 13 to 22 141504 -1.3977 0.081103 12 to 21 141478 -1.4873 0.068462 11 to 20 141787 -0.4218 0.336575 10 to 19 141766 -0.4942 0.310568 9 to 18 141585 -1.1184 0.131703 8 to 17 142104 0.6713 0.748978 7 to 16 142295 1.3299 0.908224 6 to 15 141962 0.1816 0.572060 5 to 14 141992 0.2851 0.612204 4 to 13 141941 0.1092 0.543481 3 to 12 141755 -0.5322 0.297303 2 to 11 141808 -0.3494 0.363389 1 to 10 141860 -0.1701 0.432464 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-11-06_13:31 Bits used No. missing words z-score p-value 28 to 32 142300 1.3243 0.907299 27 to 31 142442 1.8057 0.964514 26 to 30 140803 -3.7503 0.000088 25 to 29 141851 -0.1977 0.421629 24 to 28 141697 -0.7198 0.235836 23 to 27 141828 -0.2757 0.391391 22 to 26 141981 0.2429 0.595978 21 to 25 142062 0.5175 0.697605 20 to 24 141691 -0.7401 0.229619 19 to 23 142124 0.7277 0.766600 18 to 22 142224 1.0667 0.856941 17 to 21 141548 -1.2248 0.110316 16 to 20 141797 -0.3808 0.351683 15 to 19 141775 -0.4554 0.324427 14 to 18 141855 -0.1842 0.426940 13 to 17 141900 -0.0316 0.487385 12 to 16 141814 -0.3232 0.373290 11 to 15 141954 0.1514 0.560179 10 to 14 141924 0.0497 0.519831 9 to 13 142300 1.3243 0.907299 8 to 12 141673 -0.8011 0.211532 7 to 11 141715 -0.6587 0.255030 6 to 10 141974 0.2192 0.586761 5 to 9 142152 0.8226 0.794635 4 to 8 142219 1.0497 0.853079 3 to 7 141818 -0.3096 0.378435 2 to 6 142159 0.8463 0.801318 1 to 5 142100 0.6463 0.740970 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-11-06_13:31 Bits used No. missing words z-score p-value 31 to 32 142339 1.2675 0.897505 30 to 31 141591 -0.9390 0.173859 29 to 30 141910 0.0020 0.500789 28 to 29 141950 0.1200 0.547747 27 to 28 141938 0.0846 0.533699 26 to 27 142192 0.8338 0.797813 25 to 26 142480 1.6834 0.953850 24 to 25 141457 -1.3343 0.091052 23 to 24 142093 0.5418 0.706022 22 to 23 142602 2.0433 0.979487 21 to 22 141843 -0.1957 0.422437 20 to 21 141143 -2.2606 0.011893 19 to 20 142049 0.4120 0.659832 18 to 19 141906 -0.0098 0.496081 17 to 18 141665 -0.7207 0.235536 16 to 17 141521 -1.1455 0.125998 15 to 16 142071 0.4769 0.683284 14 to 15 142236 0.9636 0.832384 13 to 14 142143 0.6893 0.754680 12 to 13 142043 0.3943 0.653323 11 to 12 141488 -1.2429 0.106959 10 to 11 141873 -0.1072 0.457328 9 to 10 141783 -0.3727 0.354703 8 to 9 142244 0.9872 0.838234 7 to 8 142131 0.6539 0.743410 6 to 7 141290 -1.8269 0.033855 5 to 6 141816 -0.2753 0.391539 4 to 5 141764 -0.4287 0.334070 3 to 4 141614 -0.8712 0.191828 2 to 3 141634 -0.8122 0.208343 1 to 2 141544 -1.0777 0.140591 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-11-06_13:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2631.57 1.861 0.968609 Test results for specific bytes for dh-ranFile-2016-11-06_13:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2634.99 1.909 0.971875 2 to 9 2392.20 -1.525 0.063690 3 to 10 2484.25 -0.223 0.411890 4 to 11 2540.23 0.569 0.715303 5 to 12 2478.60 -0.303 0.381078 6 to 13 2465.89 -0.482 0.314755 7 to 14 2442.57 -0.812 0.208355 8 to 15 2467.69 -0.457 0.323864 9 to 16 2471.82 -0.399 0.345102 10 to 17 2424.36 -1.070 0.142369 11 to 18 2346.99 -2.164 0.015239 12 to 19 2503.81 0.054 0.521462 13 to 20 2459.34 -0.575 0.282639 14 to 21 2614.91 1.625 0.947931 15 to 22 2447.06 -0.749 0.227010 16 to 23 2456.88 -0.610 0.271004 17 to 24 2478.39 -0.306 0.379955 18 to 25 2619.50 1.690 0.954491 19 to 26 2455.47 -0.630 0.264413 20 to 27 2587.02 1.231 0.890765 21 to 28 2563.81 0.902 0.816592 22 to 29 2533.26 0.470 0.680934 23 to 30 2525.10 0.355 0.638707 24 to 31 2503.57 0.051 0.520144 25 to 32 2551.66 0.731 0.767474 CDPARK for dh-ranFile-2016-11-06_13:31: 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 3482 -1.8721 0.030593 3493 -1.3699 0.085365 3526 0.1370 0.554479 3526 0.1370 0.554479 3539 0.7306 0.767486 3489 -1.5525 0.060270 3551 1.2785 0.899470 3503 -0.9132 0.180558 3509 -0.6393 0.261324 3547 1.0959 0.863437 Square side=100, avg. no. parked=3516.50 sample std.=23.55 p-value of the KSTEST for those 10 p-values: 0.458673 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-11-06_13:31 0.6028,0.3909,0.3196,0.5996,0.8362,0.7942,0.7608,0.3701,0.6340,0.0884, The KS test for those 10 p-values: 0.676088 The 3DSPHERES test for dh-ranFile-2016-11-06_13:31 sample no r^3 equiv. uni. 1 15.332 0.400137 2 33.970 0.677716 3 38.156 0.719694 4 38.834 0.725960 5 124.088 0.984018 6 1.276 0.041642 7 10.326 0.291216 8 32.744 0.664275 9 18.652 0.462979 10 15.647 0.406409 11 21.873 0.517654 12 3.219 0.101741 13 16.121 0.415720 14 31.353 0.648342 15 18.001 0.451203 16 13.947 0.371812 17 2.659 0.084811 18 29.829 0.630015 19 3.163 0.100059 20 14.546 0.384227 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.396249 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-11-06_13:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -0.7 -0.6 1.1 1.4 0.5 -0.4 -0.4 1.5 1.4 -0.7 0.2 0.8 0.7 -1.9 -0.2 -1.0 0.1 -1.3 -1.3 -0.7 0.7 0.6 1.0 0.2 -0.3 1.2 0.4 1.4 2.9 0.1 0.5 0.0 -1.3 0.5 0.8 1.0 0.8 0.9 1.0 -0.6 0.0 -0.1 Chi-square with 42 degrees of freedom:40.434945 z-score=-0.170762, p-value=0.460219 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-11-06_13:31 Test no p-value 1 0.002972 2 0.809446 3 0.006786 4 0.883159 5 0.003657 6 0.306941 7 0.745865 8 0.384716 9 0.134765 10 0.693517 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.025366 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-11-06_13:31: (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 66335 1.65 66808 0.30 3 25000.00 25276 3.05 24951 0.10 4 6666.67 6682 0.04 6565 1.55 5 1388.89 1403 0.14 1392 0.01 6 238.10 258 1.66 254 1.06 7 34.72 37 0.15 27 1.72 8 4.96 8 1.86 2 1.77 p=0.79966 p=0.63029 Number of rngs required: 689358, p-value: 0.866 RESULTS OF CRAPS TEST for dh-ranFile-2016-11-06_13:31 No. of wins: Observed Expected 98643 98585.9 z-score= 0.256, pvalue=0.60086 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66853 66666.7 0.521 0.521 2 37501 37654.3 0.624 1.145 3 26833 26954.7 0.550 1.695 4 19361 19313.5 0.117 1.812 5 13825 13851.4 0.050 1.862 6 9920 9943.5 0.056 1.918 7 7106 7145.0 0.213 2.131 8 5137 5139.1 0.001 2.132 9 3682 3699.9 0.086 2.218 10 2626 2666.3 0.609 2.827 11 1938 1923.3 0.112 2.939 12 1440 1388.7 1.892 4.831 13 1046 1003.7 1.781 6.613 14 784 726.1 4.610 11.223 15 539 525.8 0.330 11.552 16 418 381.2 3.563 15.115 17 264 276.5 0.569 15.684 18 191 200.8 0.481 16.165 19 149 146.0 0.062 16.227 20 98 106.2 0.635 16.862 21 289 287.1 0.012 16.875 Chisq= 16.87 for 20 degrees of freedom, p= 0.33892 SUMMARY of craptest p-value for no. of wins: 0.600858 p-value for throws/game: 0.338917 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-11-06_13:31 No. of wins: Observed Expected 98667 98585.9 z-score= 0.363, pvalue=0.64166 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66969 66666.7 1.371 1.371 2 37522 37654.3 0.465 1.836 3 26572 26954.7 5.434 7.271 4 19358 19313.5 0.103 7.373 5 13784 13851.4 0.328 7.701 6 10178 9943.5 5.528 13.230 7 7145 7145.0 0.000 13.230 8 5142 5139.1 0.002 13.231 9 3717 3699.9 0.079 13.311 10 2683 2666.3 0.105 13.415 11 1955 1923.3 0.522 13.937 12 1372 1388.7 0.202 14.139 13 971 1003.7 1.066 15.205 14 680 726.1 2.932 18.137 15 547 525.8 0.852 18.989 16 378 381.2 0.026 19.015 17 272 276.5 0.075 19.089 18 216 200.8 1.146 20.235 19 145 146.0 0.007 20.242 20 118 106.2 1.308 21.549 21 276 287.1 0.430 21.979 Chisq= 21.98 for 20 degrees of freedom, p= 0.65837 SUMMARY of craptest p-value for no. of wins: 0.641665 p-value for throws/game: 0.658373 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0001,0.0030,0.0037,0.0059,0.0068,0.0119,0.0150,0.0152,0.0236,0.0254, 0.0296,0.0306,0.0339,0.0413,0.0416,0.0535,0.0603,0.0637,0.0685,0.0741, 0.0754,0.0811,0.0827,0.0832,0.0835,0.0848,0.0854,0.0884,0.0911,0.0951, 0.1001,0.1017,0.1070,0.1103,0.1260,0.1317,0.1348,0.1406,0.1424,0.1480, 0.1512,0.1547,0.1601,0.1686,0.1714,0.1718,0.1739,0.1789,0.1806,0.1865, 0.1918,0.1951,0.2083,0.2084,0.2114,0.2115,0.2143,0.2197,0.2247,0.2270, 0.2293,0.2296,0.2344,0.2355,0.2358,0.2466,0.2488,0.2530,0.2550,0.2613, 0.2644,0.2710,0.2750,0.2826,0.2912,0.2973,0.2985,0.3033,0.3066,0.3069, 0.3106,0.3148,0.3196,0.3239,0.3244,0.3314,0.3341,0.3366,0.3389,0.3397, 0.3438,0.3451,0.3466,0.3479,0.3517,0.3547,0.3634,0.3701,0.3718,0.3733, 0.3765,0.3784,0.3800,0.3811,0.3814,0.3830,0.3842,0.3847,0.3909,0.3914, 0.3915,0.3956,0.3962,0.4001,0.4023,0.4055,0.4064,0.4112,0.4119,0.4149, 0.4157,0.4216,0.4224,0.4269,0.4301,0.4325,0.4347,0.4416,0.4512,0.4523, 0.4573,0.4587,0.4602,0.4630,0.4676,0.4834,0.4874,0.4923,0.4961,0.5008, 0.5082,0.5122,0.5177,0.5198,0.5201,0.5215,0.5269,0.5337,0.5406,0.5417, 0.5435,0.5477,0.5545,0.5545,0.5559,0.5584,0.5597,0.5602,0.5622,0.5683, 0.5721,0.5729,0.5837,0.5852,0.5857,0.5868,0.5960,0.5996,0.6009,0.6028, 0.6078,0.6082,0.6122,0.6300,0.6303,0.6340,0.6343,0.6374,0.6387,0.6417, 0.6483,0.6533,0.6584,0.6598,0.6621,0.6643,0.6761,0.6777,0.6809,0.6833, 0.6935,0.6976,0.7002,0.7060,0.7126,0.7153,0.7153,0.7197,0.7220,0.7260, 0.7410,0.7434,0.7447,0.7459,0.7490,0.7547,0.7608,0.7622,0.7666,0.7675, 0.7675,0.7898,0.7942,0.7946,0.7978,0.7997,0.8013,0.8046,0.8094,0.8096, 0.8166,0.8227,0.8278,0.8324,0.8362,0.8382,0.8462,0.8479,0.8512,0.8531, 0.8561,0.8569,0.8634,0.8636,0.8661,0.8785,0.8832,0.8832,0.8908,0.8969, 0.8975,0.8995,0.9061,0.9073,0.9073,0.9082,0.9102,0.9106,0.9145,0.9154, 0.9205,0.9270,0.9359,0.9430,0.9479,0.9539,0.9539,0.9545,0.9572,0.9590, 0.9597,0.9601,0.9645,0.9686,0.9719,0.9775,0.9795,0.9840,0.9920, Overall p-value after applying KStest on 269 p-values = 0.861541 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.