RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-04-23_08:31 (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 9.9971 0.096267 2 to 25 15.97 18.9990 0.671413 3 to 26 15.99 21.1466 0.780197 4 to 27 15.67 25.2883 0.911560 5 to 28 15.72 15.1331 0.414107 6 to 29 15.76 15.8566 0.465977 7 to 30 15.93 10.5421 0.120647 8 to 31 15.86 14.3634 0.358765 9 to 32 15.69 16.9804 0.544307 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.982630 Tough bday spacings test for dh-ranFile-2016-04-23_08:31: 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 8 29 72 102 93 70 72 25 17 8 4 (O-E)^2/E 0.1 1.6 0.0 0.2 0.2 0.8 7.6 0.8 0.3 0.3 0.0 Birthday Spacings: Sum(O-E)^2/E= 11.981, p= 0.714 RESULTS OF GCD FOR dh-ranFile-2016-04-23_08:31 Euclid's algorithm: p-value, steps to gcd: 0.927082 p-value, dist. of gcd's: 0.738514 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-04-23_08:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.693 0.951 0.789 0.902 0.034 0.599 0.260 0.069 Bits 8 to 15---> 0.731 0.673 0.239 0.462 0.603 0.211 0.335 0.661 Bits 16 to 23---> 0.970 0.336 0.637 0.870 0.164 0.461 0.516 0.237 Bits 24 to 31---> 0.339 0.968 0.242 0.792 0.445 0.412 0.236 0.850 KS test for the above 32 p values: 0.106 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-04-23_08:31, p-values for 5 runs: 0.7590, 0.4478, 0.7216, 0.6562, 0.9003 Rank test for binary matrices (31x31) for dh-ranFile-2016-04-23_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 200 211.4 0.617 0.617 r= 29 5165 5134.0 0.187 0.804 r= 30 23034 23103.0 0.206 1.010 r= 31 11601 11551.5 0.212 1.222 chi-square = 1.222 with df = 3; p-value = 0.252 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-04-23_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 234 211.4 2.412 2.412 r= 30 5059 5134.0 1.096 3.508 r= 31 23139 23103.0 0.056 3.564 r= 32 11568 11551.5 0.024 3.587 chi-square = 3.587 with df = 3; p-value = 0.690 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-04-23_08:31 b-rank test for bits 1 to 8, p=0.59036 b-rank test for bits 2 to 9, p=0.61945 b-rank test for bits 3 to 10, p=0.56366 b-rank test for bits 4 to 11, p=0.59138 b-rank test for bits 5 to 12, p=0.76281 b-rank test for bits 6 to 13, p=0.94358 b-rank test for bits 7 to 14, p=0.96185 b-rank test for bits 8 to 15, p=0.79566 b-rank test for bits 9 to 16, p=0.90464 b-rank test for bits 10 to 17, p=0.42043 b-rank test for bits 11 to 18, p=0.58215 b-rank test for bits 12 to 19, p=0.00410 b-rank test for bits 13 to 20, p=0.66631 b-rank test for bits 14 to 21, p=0.55951 b-rank test for bits 15 to 22, p=0.74295 b-rank test for bits 16 to 23, p=0.18377 b-rank test for bits 17 to 24, p=0.59287 b-rank test for bits 18 to 25, p=0.38048 b-rank test for bits 19 to 26, p=0.00480 b-rank test for bits 20 to 27, p=0.21963 b-rank test for bits 21 to 28, p=0.51006 b-rank test for bits 22 to 29, p=0.76767 b-rank test for bits 23 to 30, p=0.61984 b-rank test for bits 24 to 31, p=0.92695 b-rank test for bits 25 to 32, p=0.18527 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 = 0.210721 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-04-23_08:31 (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 142165 0.60 0.724866 2 141684 -0.53 0.299280 3 141837 -0.17 0.432900 4 141919 0.02 0.509013 5 141766 -0.33 0.368857 6 141995 0.20 0.579324 7 142461 1.29 0.901292 8 142194 0.67 0.747012 9 142087 0.42 0.660972 10 142086 0.41 0.660116 11 141897 -0.03 0.488509 12 142053 0.34 0.631443 13 141985 0.18 0.570167 14 141580 -0.77 0.220809 15 142167 0.60 0.726424 16 141883 -0.06 0.475473 17 141812 -0.23 0.410054 18 141679 -0.54 0.295235 19 142476 1.32 0.907248 20 142372 1.08 0.860153 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-04-23_08:31 Bits used No. missing words z-score p-value 23 to 32 141797 -0.3873 0.349251 22 to 31 141952 0.1471 0.558488 21 to 30 141892 -0.0598 0.476174 20 to 29 142121 0.7299 0.767273 19 to 28 141757 -0.5253 0.299696 18 to 27 141795 -0.3942 0.346701 17 to 26 141430 -1.6529 0.049179 16 to 25 141730 -0.6184 0.268163 15 to 24 142333 1.4609 0.927983 14 to 23 141715 -0.6701 0.251396 13 to 22 141457 -1.5598 0.059408 12 to 21 142283 1.2885 0.901217 11 to 20 142238 1.1333 0.871465 10 to 19 142094 0.6368 0.737870 9 to 18 141730 -0.6184 0.268163 8 to 17 142357 1.5437 0.938668 7 to 16 142440 1.8299 0.966367 6 to 15 141820 -0.3080 0.379028 5 to 14 141760 -0.5149 0.303301 4 to 13 141994 0.2920 0.614844 3 to 12 142087 0.6127 0.729948 2 to 11 141854 -0.1908 0.424344 1 to 10 141599 -1.0701 0.142286 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-04-23_08:31 Bits used No. missing words z-score p-value 28 to 32 142276 1.2429 0.893057 27 to 31 141474 -1.4757 0.070013 26 to 30 142136 0.7684 0.778867 25 to 29 142327 1.4158 0.921587 24 to 28 142282 1.2633 0.896757 23 to 27 141938 0.0972 0.538711 22 to 26 141961 0.1752 0.569520 21 to 25 141717 -0.6520 0.257212 20 to 24 141997 0.2972 0.616838 19 to 23 141669 -0.8147 0.207628 18 to 22 142029 0.4057 0.657504 17 to 21 141787 -0.4147 0.339189 16 to 20 141574 -1.1367 0.127829 15 to 19 141967 0.1955 0.577496 14 to 18 142059 0.5074 0.694048 13 to 17 141657 -0.8554 0.196177 12 to 16 142434 1.7785 0.962343 11 to 15 142369 1.5582 0.940407 10 to 14 141543 -1.2418 0.107156 9 to 13 141973 0.2158 0.585440 8 to 12 142202 0.9921 0.839426 7 to 11 142105 0.6633 0.746427 6 to 10 142401 1.6667 0.952211 5 to 9 141820 -0.3028 0.381016 4 to 8 141919 0.0328 0.513075 3 to 7 142271 1.2260 0.889901 2 to 6 142493 1.9785 0.976066 1 to 5 141290 -2.0994 0.017890 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-04-23_08:31 Bits used No. missing words z-score p-value 31 to 32 142104 0.5742 0.717100 30 to 31 141975 0.1937 0.576801 29 to 30 141836 -0.2163 0.414372 28 to 29 142040 0.3855 0.650051 27 to 28 142604 2.0492 0.979777 26 to 27 142102 0.5683 0.715101 25 to 26 142539 1.8574 0.968375 24 to 25 142590 2.0079 0.977672 23 to 24 141753 -0.4612 0.322345 22 to 23 141744 -0.4877 0.312882 21 to 22 141592 -0.9361 0.174617 20 to 21 141894 -0.0452 0.481966 19 to 20 142062 0.4504 0.673772 18 to 19 142107 0.5831 0.720086 17 to 18 141340 -1.6794 0.046533 16 to 17 141898 -0.0334 0.486669 15 to 16 142138 0.6745 0.750017 14 to 15 141700 -0.6175 0.268455 13 to 14 141537 -1.0983 0.136033 12 to 13 141966 0.1672 0.566381 11 to 12 141906 -0.0098 0.496081 10 to 11 142330 1.2409 0.892681 9 to 10 141650 -0.7650 0.222140 8 to 9 141626 -0.8358 0.201639 7 to 8 141801 -0.3196 0.374652 6 to 7 142135 0.6657 0.747196 5 to 6 141782 -0.3756 0.353605 4 to 5 141697 -0.6263 0.265545 3 to 4 142257 1.0256 0.847454 2 to 3 141858 -0.1514 0.439824 1 to 2 141855 -0.1603 0.436336 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-04-23_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2515.58 0.220 0.587182 Test results for specific bytes for dh-ranFile-2016-04-23_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2616.91 1.653 0.950867 2 to 9 2419.64 -1.136 0.127881 3 to 10 2424.14 -1.073 0.141687 4 to 11 2492.85 -0.101 0.459730 5 to 12 2462.60 -0.529 0.298436 6 to 13 2522.28 0.315 0.623662 7 to 14 2540.89 0.578 0.718445 8 to 15 2506.29 0.089 0.535449 9 to 16 2576.90 1.088 0.861598 10 to 17 2672.38 2.438 0.992612 11 to 18 2425.87 -1.048 0.147234 12 to 19 2539.99 0.566 0.714155 13 to 20 2412.82 -1.233 0.108812 14 to 21 2463.55 -0.516 0.303085 15 to 22 2516.45 0.233 0.591979 16 to 23 2471.47 -0.403 0.343314 17 to 24 2377.69 -1.730 0.041834 18 to 25 2513.30 0.188 0.574589 19 to 26 2364.03 -1.923 0.027248 20 to 27 2487.52 -0.176 0.429963 21 to 28 2641.19 1.997 0.977076 22 to 29 2538.53 0.545 0.707108 23 to 30 2603.45 1.463 0.928264 24 to 31 2469.21 -0.435 0.331613 25 to 32 2552.50 0.742 0.771100 CDPARK for dh-ranFile-2016-04-23_08:31: 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 3524 0.0457 0.518210 3494 -1.3242 0.092718 3560 1.6895 0.954438 3553 1.3699 0.914635 3539 0.7306 0.767486 3506 -0.7763 0.218799 3505 -0.8219 0.205562 3566 1.9635 0.975204 3525 0.0913 0.536383 3537 0.6393 0.738676 Square side=100, avg. no. parked=3530.90 sample std.=23.25 p-value of the KSTEST for those 10 p-values: 0.397229 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-04-23_08:31 0.6127,0.6596,0.4136,0.9592,0.3100,0.1800,0.7102,0.0285,0.0227,0.2578, The KS test for those 10 p-values: 0.510472 The 3DSPHERES test for dh-ranFile-2016-04-23_08:31 sample no r^3 equiv. uni. 1 73.374 0.913344 2 8.854 0.255555 3 24.025 0.551046 4 93.855 0.956217 5 97.606 0.961362 6 6.014 0.181660 7 5.130 0.157191 8 49.128 0.805555 9 35.534 0.694092 10 3.279 0.103544 11 14.848 0.390393 12 25.116 0.567072 13 14.679 0.386948 14 73.449 0.913560 15 5.092 0.156098 16 19.542 0.478683 17 14.935 0.392156 18 15.316 0.399817 19 25.852 0.577574 20 12.459 0.339861 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.777630 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-04-23_08:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 -1.2 -0.1 -0.8 0.8 -1.1 -0.3 -0.6 -0.0 -0.6 -0.7 -0.6 1.0 1.6 0.6 0.3 1.8 -1.0 -2.0 0.6 -0.2 0.8 -0.1 -1.7 0.4 -2.5 0.1 0.6 -0.8 0.9 1.2 0.1 2.4 -0.1 0.8 0.2 1.0 -0.4 -1.2 -0.1 0.1 0.0 -0.1 Chi-square with 42 degrees of freedom:40.499762 z-score=-0.163689, p-value=0.463094 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-04-23_08:31 Test no p-value 1 0.487777 2 0.908383 3 0.220099 4 0.718266 5 0.030137 6 0.342852 7 0.045019 8 0.114070 9 0.534018 10 0.257106 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.245677 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-04-23_08:31: (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 66446 0.73 66557 0.18 3 25000.00 25091 0.33 25163 1.06 4 6666.67 6732 0.64 6560 1.71 5 1388.89 1448 2.52 1442 2.03 6 238.10 243 0.10 235 0.04 7 34.72 33 0.09 37 0.15 8 4.96 6 0.22 5 0.00 p=0.40686 p=0.47794 Number of rngs required: 688546, p-value: 0.565 RESULTS OF CRAPS TEST for dh-ranFile-2016-04-23_08:31 No. of wins: Observed Expected 98404 98585.9 z-score=-0.813, pvalue=0.20800 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66772 66666.7 0.166 0.166 2 37655 37654.3 0.000 0.166 3 27035 26954.7 0.239 0.405 4 19299 19313.5 0.011 0.416 5 13704 13851.4 1.569 1.985 6 9927 9943.5 0.028 2.013 7 7162 7145.0 0.040 2.053 8 5082 5139.1 0.634 2.687 9 3714 3699.9 0.054 2.741 10 2713 2666.3 0.818 3.559 11 1852 1923.3 2.645 6.204 12 1393 1388.7 0.013 6.217 13 996 1003.7 0.059 6.277 14 766 726.1 2.188 8.465 15 537 525.8 0.237 8.702 16 363 381.2 0.864 9.566 17 294 276.5 1.102 10.668 18 212 200.8 0.621 11.290 19 159 146.0 1.160 12.450 20 90 106.2 2.475 14.926 21 275 287.1 0.511 15.437 Chisq= 15.44 for 20 degrees of freedom, p= 0.24911 SUMMARY of craptest p-value for no. of wins: 0.208001 p-value for throws/game: 0.249107 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-04-23_08:31 No. of wins: Observed Expected 98720 98585.9 z-score= 0.600, pvalue=0.72573 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66779 66666.7 0.189 0.189 2 37624 37654.3 0.024 0.214 3 26892 26954.7 0.146 0.360 4 19391 19313.5 0.311 0.671 5 13757 13851.4 0.644 1.315 6 9992 9943.5 0.236 1.551 7 7119 7145.0 0.095 1.646 8 5164 5139.1 0.121 1.766 9 3625 3699.9 1.515 3.281 10 2613 2666.3 1.065 4.347 11 1888 1923.3 0.649 4.996 12 1379 1388.7 0.068 5.064 13 1076 1003.7 5.206 10.270 14 744 726.1 0.439 10.709 15 569 525.8 3.543 14.252 16 391 381.2 0.255 14.507 17 284 276.5 0.201 14.708 18 202 200.8 0.007 14.715 19 131 146.0 1.538 16.253 20 107 106.2 0.006 16.259 21 273 287.1 0.694 16.952 Chisq= 16.95 for 20 degrees of freedom, p= 0.34394 SUMMARY of craptest p-value for no. of wins: 0.725733 p-value for throws/game: 0.343942 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0041,0.0048,0.0179,0.0227,0.0272,0.0285,0.0301,0.0338,0.0418,0.0450, 0.0465,0.0492,0.0594,0.0693,0.0700,0.0927,0.0963,0.1035,0.1055,0.1072, 0.1088,0.1141,0.1206,0.1278,0.1279,0.1360,0.1417,0.1423,0.1472,0.1561, 0.1572,0.1636,0.1746,0.1800,0.1817,0.1838,0.1853,0.1962,0.2016,0.2056, 0.2076,0.2080,0.2107,0.2110,0.2188,0.2196,0.2201,0.2208,0.2221,0.2360, 0.2367,0.2391,0.2421,0.2457,0.2491,0.2514,0.2523,0.2556,0.2571,0.2572, 0.2578,0.2602,0.2655,0.2682,0.2682,0.2685,0.2952,0.2984,0.2993,0.2997, 0.3031,0.3033,0.3100,0.3129,0.3223,0.3316,0.3347,0.3355,0.3389,0.3392, 0.3399,0.3429,0.3433,0.3439,0.3467,0.3493,0.3536,0.3588,0.3689,0.3747, 0.3790,0.3805,0.3810,0.3869,0.3904,0.3922,0.3972,0.3998,0.4069,0.4101, 0.4117,0.4136,0.4141,0.4144,0.4204,0.4243,0.4300,0.4329,0.4363,0.4398, 0.4447,0.4478,0.4597,0.4615,0.4620,0.4631,0.4660,0.4755,0.4762,0.4779, 0.4787,0.4820,0.4867,0.4878,0.4885,0.4961,0.5090,0.5101,0.5105,0.5131, 0.5159,0.5182,0.5340,0.5354,0.5364,0.5387,0.5443,0.5510,0.5585,0.5595, 0.5637,0.5653,0.5664,0.5671,0.5695,0.5702,0.5746,0.5768,0.5775,0.5776, 0.5793,0.5821,0.5854,0.5872,0.5904,0.5914,0.5920,0.5929,0.5988,0.6033, 0.6127,0.6148,0.6168,0.6194,0.6198,0.6237,0.6314,0.6374,0.6501,0.6562, 0.6575,0.6596,0.6601,0.6608,0.6610,0.6663,0.6714,0.6733,0.6738,0.6904, 0.6926,0.6940,0.6941,0.7071,0.7102,0.7137,0.7142,0.7151,0.7171,0.7183, 0.7184,0.7201,0.7216,0.7249,0.7257,0.7264,0.7299,0.7307,0.7379,0.7385, 0.7387,0.7429,0.7464,0.7470,0.7472,0.7500,0.7590,0.7628,0.7673,0.7675, 0.7677,0.7711,0.7776,0.7789,0.7802,0.7886,0.7924,0.7957,0.8056,0.8394, 0.8475,0.8500,0.8602,0.8616,0.8701,0.8715,0.8899,0.8927,0.8931,0.8968, 0.9003,0.9012,0.9013,0.9016,0.9046,0.9072,0.9084,0.9116,0.9133,0.9136, 0.9146,0.9216,0.9270,0.9271,0.9280,0.9283,0.9387,0.9404,0.9436,0.9509, 0.9514,0.9522,0.9544,0.9562,0.9592,0.9614,0.9619,0.9623,0.9664,0.9684, 0.9684,0.9702,0.9752,0.9761,0.9771,0.9777,0.9798,0.9826,0.9926, Overall p-value after applying KStest on 269 p-values = 0.130597 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.