RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-03-17_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 16.00 17.3321 0.567907 2 to 25 15.96 20.4799 0.749581 3 to 26 15.75 14.1789 0.345596 4 to 27 15.70 15.4723 0.438500 5 to 28 15.76 15.7320 0.457090 6 to 29 15.90 8.3537 0.041611 7 to 30 15.87 14.6675 0.380584 8 to 31 15.89 11.4970 0.170405 9 to 32 15.59 17.2039 0.559361 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.400089 Tough bday spacings test for dh-ranFile-2018-03-17_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 11 32 64 84 104 80 52 31 26 7 9 (O-E)^2/E 0.4 0.6 1.2 1.9 0.4 0.0 0.0 0.1 8.3 0.0 6.0 Birthday Spacings: Sum(O-E)^2/E= 18.856, p= 0.958 RESULTS OF GCD FOR dh-ranFile-2018-03-17_13:31 Euclid's algorithm: p-value, steps to gcd: 0.936634 p-value, dist. of gcd's: 0.885019 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-03-17_13:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.618 0.599 0.624 0.842 0.380 0.014 0.311 0.311 Bits 8 to 15---> 0.492 0.089 0.616 0.616 0.014 0.587 0.848 0.368 Bits 16 to 23---> 0.040 0.888 0.201 0.414 0.874 0.575 0.244 0.549 Bits 24 to 31---> 0.713 0.552 0.671 0.851 0.330 0.762 0.809 0.597 KS test for the above 32 p values: 0.586 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-03-17_13:31, p-values for 5 runs: 0.9810, 0.2302, 0.4126, 0.8544, 0.8462 Rank test for binary matrices (31x31) for dh-ranFile-2018-03-17_13:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 197 211.4 0.983 0.983 r= 29 5013 5134.0 2.852 3.836 r= 30 23199 23103.0 0.399 4.234 r= 31 11591 11551.5 0.135 4.369 chi-square = 4.369 with df = 3; p-value = 0.776 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-03-17_13:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 226 211.4 1.006 1.006 r= 30 5259 5134.0 3.043 4.049 r= 31 23002 23103.0 0.442 4.491 r= 32 11513 11551.5 0.128 4.619 chi-square = 4.619 with df = 3; p-value = 0.798 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-03-17_13:31 b-rank test for bits 1 to 8, p=0.67389 b-rank test for bits 2 to 9, p=0.68657 b-rank test for bits 3 to 10, p=0.80458 b-rank test for bits 4 to 11, p=0.17219 b-rank test for bits 5 to 12, p=0.77569 b-rank test for bits 6 to 13, p=0.35868 b-rank test for bits 7 to 14, p=0.70436 b-rank test for bits 8 to 15, p=0.62539 b-rank test for bits 9 to 16, p=0.66879 b-rank test for bits 10 to 17, p=0.11754 b-rank test for bits 11 to 18, p=0.25208 b-rank test for bits 12 to 19, p=0.24988 b-rank test for bits 13 to 20, p=0.00520 b-rank test for bits 14 to 21, p=0.55207 b-rank test for bits 15 to 22, p=0.97206 b-rank test for bits 16 to 23, p=0.51939 b-rank test for bits 17 to 24, p=0.91183 b-rank test for bits 18 to 25, p=0.75496 b-rank test for bits 19 to 26, p=0.25792 b-rank test for bits 20 to 27, p=0.23711 b-rank test for bits 21 to 28, p=0.39852 b-rank test for bits 22 to 29, p=0.18590 b-rank test for bits 23 to 30, p=0.52499 b-rank test for bits 24 to 31, p=0.02535 b-rank test for bits 25 to 32, p=0.79563 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 = 0.916223 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-03-17_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 142065 0.36 0.641965 2 142075 0.39 0.650651 3 141200 -1.66 0.048728 4 141891 -0.04 0.482920 5 141389 -1.22 0.112045 6 142565 1.53 0.937231 7 141299 -1.43 0.076934 8 141586 -0.76 0.224991 9 141592 -0.74 0.229218 10 141084 -1.93 0.026906 11 141435 -1.11 0.133877 12 142419 1.19 0.883137 13 142172 0.61 0.730298 14 141848 -0.14 0.443029 15 141790 -0.28 0.390196 16 141866 -0.10 0.459681 17 142297 0.91 0.817471 18 141446 -1.08 0.139505 19 142277 0.86 0.804841 20 142174 0.62 0.731840 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-03-17_13:31 Bits used No. missing words z-score p-value 23 to 32 142080 0.5885 0.721907 22 to 31 142158 0.8575 0.804411 21 to 30 141519 -1.3460 0.089157 20 to 29 141496 -1.4253 0.077039 19 to 28 141913 0.0127 0.505049 18 to 27 141774 -0.4667 0.320373 17 to 26 141999 0.3092 0.621418 16 to 25 142323 1.4264 0.923131 15 to 24 141827 -0.2839 0.388245 14 to 23 142483 1.9782 0.976045 13 to 22 141795 -0.3942 0.346701 12 to 21 141738 -0.5908 0.277330 11 to 20 141399 -1.7598 0.039224 10 to 19 142254 1.1885 0.882685 9 to 18 141864 -0.1563 0.437894 8 to 17 142073 0.5644 0.713752 7 to 16 141710 -0.6873 0.245933 6 to 15 141970 0.2092 0.582857 5 to 14 142144 0.8092 0.790802 4 to 13 142335 1.4678 0.928924 3 to 12 142035 0.4333 0.667618 2 to 11 141502 -1.4046 0.080072 1 to 10 141899 -0.0356 0.485792 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-03-17_13:31 Bits used No. missing words z-score p-value 28 to 32 141966 0.1921 0.576169 27 to 31 141858 -0.1740 0.430933 26 to 30 141778 -0.4452 0.328093 25 to 29 141593 -1.0723 0.141792 24 to 28 141949 0.1345 0.553486 23 to 27 141851 -0.1977 0.421629 22 to 26 142134 0.7616 0.776849 21 to 25 142197 0.9752 0.835258 20 to 24 142155 0.8328 0.797516 19 to 23 141654 -0.8655 0.193375 18 to 22 141468 -1.4960 0.067322 17 to 21 142041 0.4463 0.672324 16 to 20 141666 -0.8248 0.204729 15 to 19 141633 -0.9367 0.174453 14 to 18 142046 0.4633 0.678421 13 to 17 141763 -0.4960 0.309935 12 to 16 142142 0.7887 0.784860 11 to 15 141983 0.2497 0.598602 10 to 14 141706 -0.6893 0.245332 9 to 13 141730 -0.6079 0.271628 8 to 12 141913 0.0124 0.504963 7 to 11 141047 -2.9232 0.001733 6 to 10 141948 0.1311 0.552146 5 to 9 141672 -0.8045 0.210552 4 to 8 142397 1.6531 0.950847 3 to 7 141745 -0.5571 0.288746 2 to 6 141793 -0.3943 0.346665 1 to 5 141925 0.0531 0.521181 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-03-17_13:31 Bits used No. missing words z-score p-value 31 to 32 141785 -0.3668 0.356901 30 to 31 142434 1.5477 0.939153 29 to 30 141447 -1.3638 0.086314 28 to 29 141925 0.0462 0.518434 27 to 28 141885 -0.0718 0.471393 26 to 27 141829 -0.2370 0.406343 25 to 26 141802 -0.3166 0.375771 24 to 25 141579 -0.9744 0.164923 23 to 24 142123 0.6303 0.735749 22 to 23 141936 0.0787 0.531354 21 to 22 142070 0.4740 0.682233 20 to 21 141839 -0.2075 0.417824 19 to 20 141736 -0.5113 0.304571 18 to 19 141543 -1.0806 0.139933 17 to 18 141983 0.2173 0.586019 16 to 17 142977 3.1495 0.999182 15 to 16 141586 -0.9538 0.170099 14 to 15 142559 1.9164 0.972345 13 to 14 141838 -0.2104 0.416673 12 to 13 142291 1.1259 0.869890 11 to 12 141545 -1.0747 0.141250 10 to 11 141881 -0.0836 0.466699 9 to 10 141737 -0.5083 0.305605 8 to 9 141691 -0.6440 0.259774 7 to 8 141866 -0.1278 0.449147 6 to 7 142406 1.4651 0.928554 5 to 6 142247 0.9961 0.840394 4 to 5 142164 0.7512 0.773746 3 to 4 141999 0.2645 0.604308 2 to 3 142200 0.8574 0.804397 1 to 2 142154 0.7217 0.764773 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-03-17_13:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2476.16 -0.337 0.367993 Test results for specific bytes for dh-ranFile-2018-03-17_13:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2590.39 1.278 0.899437 2 to 9 2490.90 -0.129 0.448795 3 to 10 2505.49 0.078 0.530934 4 to 11 2497.67 -0.033 0.486868 5 to 12 2555.30 0.782 0.782902 6 to 13 2428.76 -1.008 0.156837 7 to 14 2602.66 1.452 0.926719 8 to 15 2432.90 -0.949 0.171315 9 to 16 2418.51 -1.152 0.124559 10 to 17 2493.08 -0.098 0.461034 11 to 18 2591.61 1.296 0.902445 12 to 19 2472.83 -0.384 0.350399 13 to 20 2457.37 -0.603 0.273296 14 to 21 2379.01 -1.711 0.043531 15 to 22 2424.69 -1.065 0.143415 16 to 23 2458.40 -0.588 0.278173 17 to 24 2448.28 -0.731 0.232277 18 to 25 2464.58 -0.501 0.308235 19 to 26 2466.92 -0.468 0.319980 20 to 27 2491.93 -0.114 0.454591 21 to 28 2547.75 0.675 0.750246 22 to 29 2602.13 1.444 0.925675 23 to 30 2493.42 -0.093 0.462925 24 to 31 2578.00 1.103 0.865004 25 to 32 2469.22 -0.435 0.331690 CDPARK for dh-ranFile-2018-03-17_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 3534 0.5023 0.692266 3495 -1.2785 0.100530 3540 0.7763 0.781201 3502 -0.9589 0.168804 3513 -0.4566 0.323972 3487 -1.6438 0.050105 3537 0.6393 0.738676 3530 0.3196 0.625377 3503 -0.9132 0.180558 3502 -0.9589 0.168804 Square side=100, avg. no. parked=3514.30 sample std.=18.33 p-value of the KSTEST for those 10 p-values: 0.249979 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-03-17_13:31 0.9873,0.1085,0.3791,0.2338,0.8171,0.0563,0.3886,0.0877,0.0768,0.6438, The KS test for those 10 p-values: 0.171001 The 3DSPHERES test for dh-ranFile-2018-03-17_13:31 sample no r^3 equiv. uni. 1 51.056 0.817656 2 9.264 0.265679 3 7.981 0.233585 4 48.341 0.800387 5 35.817 0.696959 6 3.150 0.099668 7 18.771 0.465117 8 42.521 0.757646 9 5.605 0.170429 10 33.486 0.672479 11 140.478 0.990745 12 56.240 0.846595 13 39.995 0.736361 14 1.865 0.060278 15 6.295 0.189290 16 16.868 0.430086 17 165.775 0.996017 18 7.929 0.232264 19 4.717 0.145492 20 20.501 0.495078 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.704287 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-03-17_13:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -0.3 -0.6 1.2 -0.1 1.5 1.4 0.4 -1.2 0.8 -1.2 0.1 -1.0 0.9 -0.1 0.3 0.7 -0.9 0.6 0.9 -1.0 -1.0 1.9 -0.3 -0.8 0.7 -1.2 -0.2 0.9 -0.2 -2.5 -0.4 0.6 0.7 0.2 1.3 -1.6 -0.7 -2.0 1.0 0.1 -1.0 -0.1 Chi-square with 42 degrees of freedom:40.721991 z-score=-0.139442, p-value=0.472942 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-03-17_13:31 Test no p-value 1 0.106166 2 0.280978 3 0.274222 4 0.006755 5 0.308062 6 0.499617 7 0.216363 8 0.936629 9 0.880965 10 0.274698 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.183965 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-03-17_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 66684 0.00 66584 0.10 3 25000.00 24897 0.42 25067 0.18 4 6666.67 6751 1.07 6643 0.08 5 1388.89 1377 0.10 1435 1.53 6 238.10 250 0.60 223 0.96 7 34.72 31 0.40 42 1.53 8 4.96 9 3.29 5 0.00 p=0.56344 p=0.37470 Number of rngs required: 688160, p-value: 0.390 RESULTS OF CRAPS TEST for dh-ranFile-2018-03-17_13:31 No. of wins: Observed Expected 98601 98585.9 z-score= 0.068, pvalue=0.52700 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66807 66666.7 0.295 0.295 2 37605 37654.3 0.065 0.360 3 26803 26954.7 0.854 1.214 4 19477 19313.5 1.385 2.599 5 13739 13851.4 0.912 3.511 6 9973 9943.5 0.087 3.599 7 7200 7145.0 0.423 4.022 8 5211 5139.1 1.007 5.028 9 3664 3699.9 0.348 5.376 10 2582 2666.3 2.665 8.041 11 1873 1923.3 1.317 9.358 12 1364 1388.7 0.441 9.799 13 1018 1003.7 0.203 10.002 14 725 726.1 0.002 10.004 15 521 525.8 0.044 10.048 16 401 381.2 1.034 11.082 17 254 276.5 1.837 12.919 18 211 200.8 0.515 13.434 19 169 146.0 3.629 17.063 20 112 106.2 0.315 17.378 21 291 287.1 0.053 17.430 Chisq= 17.43 for 20 degrees of freedom, p= 0.37513 SUMMARY of craptest p-value for no. of wins: 0.526996 p-value for throws/game: 0.375128 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-03-17_13:31 No. of wins: Observed Expected 98348 98585.9 z-score=-1.064, pvalue=0.14370 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66720 66666.7 0.043 0.043 2 37823 37654.3 0.756 0.798 3 27111 26954.7 0.906 1.704 4 19294 19313.5 0.020 1.724 5 13739 13851.4 0.912 2.636 6 9869 9943.5 0.559 3.195 7 7063 7145.0 0.942 4.137 8 5126 5139.1 0.033 4.170 9 3792 3699.9 2.294 6.464 10 2590 2666.3 2.183 8.648 11 1932 1923.3 0.039 8.687 12 1300 1388.7 5.670 14.357 13 1029 1003.7 0.637 14.994 14 739 726.1 0.228 15.222 15 514 525.8 0.266 15.488 16 378 381.2 0.026 15.514 17 260 276.5 0.989 16.504 18 203 200.8 0.023 16.527 19 149 146.0 0.062 16.589 20 132 106.2 6.260 22.849 21 237 287.1 8.747 31.596 Chisq= 31.60 for 20 degrees of freedom, p= 0.95220 SUMMARY of craptest p-value for no. of wins: 0.143700 p-value for throws/game: 0.952201 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0017,0.0052,0.0068,0.0140,0.0143,0.0254,0.0269,0.0392,0.0399,0.0416, 0.0435,0.0487,0.0501,0.0563,0.0603,0.0673,0.0768,0.0769,0.0770,0.0801, 0.0863,0.0877,0.0889,0.0892,0.0997,0.1005,0.1062,0.1085,0.1120,0.1175, 0.1246,0.1339,0.1395,0.1399,0.1413,0.1418,0.1434,0.1437,0.1455,0.1568, 0.1649,0.1688,0.1688,0.1701,0.1704,0.1704,0.1710,0.1713,0.1722,0.1745, 0.1806,0.1840,0.1859,0.1893,0.1934,0.2011,0.2047,0.2106,0.2164,0.2250, 0.2292,0.2302,0.2323,0.2323,0.2336,0.2338,0.2371,0.2444,0.2453,0.2459, 0.2499,0.2500,0.2521,0.2579,0.2598,0.2657,0.2716,0.2733,0.2742,0.2747, 0.2773,0.2782,0.2810,0.2887,0.3046,0.3056,0.3081,0.3082,0.3099,0.3108, 0.3109,0.3200,0.3204,0.3240,0.3281,0.3302,0.3317,0.3456,0.3467,0.3467, 0.3504,0.3569,0.3587,0.3675,0.3680,0.3747,0.3751,0.3758,0.3791,0.3799, 0.3806,0.3882,0.3886,0.3899,0.3902,0.3985,0.4001,0.4063,0.4126,0.4135, 0.4167,0.4178,0.4216,0.4301,0.4309,0.4379,0.4385,0.4430,0.4488,0.4491, 0.4546,0.4571,0.4597,0.4610,0.4629,0.4651,0.4667,0.4714,0.4729,0.4829, 0.4858,0.4869,0.4922,0.4951,0.4996,0.5050,0.5050,0.5184,0.5194,0.5212, 0.5250,0.5270,0.5309,0.5314,0.5487,0.5521,0.5521,0.5524,0.5535,0.5594, 0.5634,0.5679,0.5753,0.5762,0.5829,0.5857,0.5860,0.5868,0.5970,0.5986, 0.5988,0.6043,0.6156,0.6157,0.6182,0.6214,0.6239,0.6254,0.6254,0.6420, 0.6438,0.6507,0.6676,0.6688,0.6711,0.6723,0.6725,0.6739,0.6784,0.6822, 0.6866,0.6923,0.6970,0.7043,0.7044,0.7134,0.7138,0.7219,0.7303,0.7318, 0.7357,0.7364,0.7387,0.7496,0.7502,0.7550,0.7576,0.7620,0.7648,0.7737, 0.7757,0.7757,0.7768,0.7812,0.7829,0.7849,0.7908,0.7956,0.7975,0.7981, 0.8004,0.8044,0.8044,0.8046,0.8048,0.8086,0.8171,0.8175,0.8177,0.8353, 0.8404,0.8416,0.8462,0.8466,0.8477,0.8507,0.8544,0.8650,0.8699,0.8736, 0.8810,0.8827,0.8831,0.8850,0.8876,0.8994,0.9024,0.9118,0.9162,0.9231, 0.9257,0.9267,0.9286,0.9289,0.9366,0.9366,0.9372,0.9392,0.9508,0.9522, 0.9579,0.9721,0.9723,0.9760,0.9810,0.9873,0.9907,0.9960,0.9992, Overall p-value after applying KStest on 269 p-values = 0.621333 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.