RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-02-23_05:31 (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 20.4208 0.746724 2 to 25 15.71 13.5427 0.300833 3 to 26 15.86 15.4810 0.439124 4 to 27 15.68 16.6480 0.521549 5 to 28 15.65 24.8530 0.901951 6 to 29 15.81 15.5970 0.447435 7 to 30 15.62 17.4612 0.576430 8 to 31 15.65 13.2992 0.284060 9 to 32 15.51 28.0783 0.955968 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.555931 Tough bday spacings test for dh-ranFile-2016-02-23_05:31: 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 6 28 72 100 106 78 55 30 15 7 3 (O-E)^2/E 1.1 2.0 0.0 0.1 0.7 0.0 0.2 0.0 0.0 0.0 0.3 Birthday Spacings: Sum(O-E)^2/E= 4.374, p= 0.071 RESULTS OF GCD FOR dh-ranFile-2016-02-23_05:31 Euclid's algorithm: p-value, steps to gcd: 0.105983 p-value, dist. of gcd's: 0.552075 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-02-23_05:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.081 0.826 0.984 0.664 0.427 0.150 0.065 0.504 Bits 8 to 15---> 0.606 0.191 0.259 0.170 0.122 0.864 0.341 0.603 Bits 16 to 23---> 0.524 0.510 0.004 0.793 0.059 0.223 0.283 0.524 Bits 24 to 31---> 0.924 0.030 0.253 0.985 0.284 0.955 0.688 0.214 KS test for the above 32 p values: 0.696 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-02-23_05:31, p-values for 5 runs: 0.1025, 0.2616, 0.1732, 0.3399, 0.4678 Rank test for binary matrices (31x31) for dh-ranFile-2016-02-23_05:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 204 211.4 0.260 0.260 r= 29 5120 5134.0 0.038 0.299 r= 30 23258 23103.0 1.039 1.338 r= 31 11418 11551.5 1.543 2.881 chi-square = 2.881 with df = 3; p-value = 0.590 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-02-23_05:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 212 211.4 0.002 0.002 r= 30 5238 5134.0 2.106 2.108 r= 31 23148 23103.0 0.087 2.195 r= 32 11402 11551.5 1.935 4.131 chi-square = 4.131 with df = 3; p-value = 0.752 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-02-23_05:31 b-rank test for bits 1 to 8, p=0.74332 b-rank test for bits 2 to 9, p=0.72411 b-rank test for bits 3 to 10, p=0.24887 b-rank test for bits 4 to 11, p=0.30536 b-rank test for bits 5 to 12, p=0.88758 b-rank test for bits 6 to 13, p=0.38837 b-rank test for bits 7 to 14, p=0.57354 b-rank test for bits 8 to 15, p=0.61749 b-rank test for bits 9 to 16, p=0.20631 b-rank test for bits 10 to 17, p=0.27308 b-rank test for bits 11 to 18, p=0.13703 b-rank test for bits 12 to 19, p=0.05101 b-rank test for bits 13 to 20, p=0.87179 b-rank test for bits 14 to 21, p=0.34548 b-rank test for bits 15 to 22, p=0.28208 b-rank test for bits 16 to 23, p=0.06500 b-rank test for bits 17 to 24, p=0.40357 b-rank test for bits 18 to 25, p=0.46957 b-rank test for bits 19 to 26, p=0.14492 b-rank test for bits 20 to 27, p=0.22715 b-rank test for bits 21 to 28, p=0.30069 b-rank test for bits 22 to 29, p=0.89059 b-rank test for bits 23 to 30, p=0.86735 b-rank test for bits 24 to 31, p=0.69040 b-rank test for bits 25 to 32, p=0.33636 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 = 0.386147 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-02-23_05:31 (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 142297 0.91 0.817471 2 142070 0.38 0.646317 3 142107 0.46 0.677904 4 142359 1.05 0.853286 5 142606 1.63 0.948209 6 141673 -0.55 0.290415 7 140922 -2.31 0.010532 8 141366 -1.27 0.102138 9 141808 -0.24 0.406425 10 141284 -1.46 0.072001 11 141833 -0.18 0.429228 12 141624 -0.67 0.252495 13 142333 0.99 0.838884 14 142233 0.76 0.775247 15 141686 -0.52 0.300905 16 141674 -0.55 0.291216 17 142120 0.49 0.688718 18 142725 1.91 0.971660 19 142235 0.76 0.776645 20 141832 -0.18 0.428310 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-02-23_05:31 Bits used No. missing words z-score p-value 23 to 32 142086 0.6092 0.728806 22 to 31 142446 1.8506 0.967885 21 to 30 142306 1.3678 0.914317 20 to 29 141555 -1.2218 0.110886 19 to 28 142576 2.2989 0.989244 18 to 27 141892 -0.0598 0.476174 17 to 26 141812 -0.3356 0.368579 16 to 25 142159 0.8609 0.805362 15 to 24 142203 1.0127 0.844388 14 to 23 142271 1.2471 0.893827 13 to 22 141491 -1.4425 0.074578 12 to 21 142150 0.8299 0.796701 11 to 20 142014 0.3609 0.640925 10 to 19 141753 -0.5391 0.294920 9 to 18 142173 0.9092 0.818380 8 to 17 141815 -0.3253 0.372486 7 to 16 142098 0.6506 0.742343 6 to 15 141657 -0.8701 0.192122 5 to 14 141443 -1.6080 0.053914 4 to 13 141404 -1.7425 0.040709 3 to 12 142024 0.3954 0.653731 2 to 11 142008 0.3402 0.633163 1 to 10 141953 0.1506 0.559849 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-02-23_05:31 Bits used No. missing words z-score p-value 28 to 32 141962 0.1785 0.570852 27 to 31 141848 -0.2079 0.417654 26 to 30 142242 1.1277 0.870276 25 to 29 141712 -0.6689 0.251775 24 to 28 141632 -0.9401 0.173583 23 to 27 142101 0.6497 0.742066 22 to 26 141895 -0.0486 0.480629 21 to 25 141596 -1.0621 0.144087 20 to 24 141652 -0.8723 0.191521 19 to 23 141726 -0.6215 0.267149 18 to 22 141774 -0.4587 0.323208 17 to 21 142023 0.3853 0.650001 16 to 20 142198 0.9785 0.836097 15 to 19 142693 2.6565 0.996052 14 to 18 142286 1.2768 0.899172 13 to 17 141569 -1.1537 0.124320 12 to 16 142309 1.3548 0.912262 11 to 15 141961 0.1752 0.569520 10 to 14 141819 -0.3062 0.379725 9 to 13 142183 0.9277 0.823217 8 to 12 141712 -0.6689 0.251775 7 to 11 141966 0.1921 0.576169 6 to 10 141950 0.1379 0.554826 5 to 9 142135 0.7650 0.777859 4 to 8 141222 -2.3299 0.009905 3 to 7 141956 0.1582 0.562852 2 to 6 141545 -1.2350 0.108412 1 to 5 141806 -0.3503 0.363068 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-02-23_05:31 Bits used No. missing words z-score p-value 31 to 32 141289 -1.8299 0.033634 30 to 31 141420 -1.4435 0.074447 29 to 30 141820 -0.2635 0.396079 28 to 29 142216 0.9046 0.817170 27 to 28 141894 -0.0452 0.481966 26 to 27 141377 -1.5703 0.058173 25 to 26 141853 -0.1662 0.434014 24 to 25 142186 0.8161 0.792789 23 to 24 141637 -0.8033 0.210891 22 to 23 141492 -1.2311 0.109150 21 to 22 142015 0.3117 0.622370 20 to 21 142186 0.8161 0.792789 19 to 20 141811 -0.2901 0.385886 18 to 19 141701 -0.6145 0.269428 17 to 18 142036 0.3737 0.645671 16 to 17 141836 -0.2163 0.414372 15 to 16 141634 -0.8122 0.208343 14 to 15 142289 1.1200 0.868637 13 to 14 141773 -0.4022 0.343786 12 to 13 141973 0.1878 0.574490 11 to 12 142484 1.6952 0.954980 10 to 11 141577 -0.9803 0.163463 9 to 10 141591 -0.9390 0.173859 8 to 9 142155 0.7247 0.765679 7 to 8 141720 -0.5585 0.288253 6 to 7 141882 -0.0806 0.467872 5 to 6 141858 -0.1514 0.439824 4 to 5 141873 -0.1072 0.457328 3 to 4 142209 0.8840 0.811647 2 to 3 141547 -1.0688 0.142575 1 to 2 142237 0.9666 0.833123 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-02-23_05:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2600.16 1.417 0.921690 Test results for specific bytes for dh-ranFile-2016-02-23_05:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2442.64 -0.811 0.208642 2 to 9 2419.86 -1.133 0.128544 3 to 10 2580.55 1.139 0.872694 4 to 11 2559.82 0.846 0.801200 5 to 12 2533.94 0.480 0.684382 6 to 13 2527.89 0.394 0.653385 7 to 14 2556.05 0.793 0.786022 8 to 15 2463.99 -0.509 0.305296 9 to 16 2533.86 0.479 0.683955 10 to 17 2571.41 1.010 0.843727 11 to 18 2517.13 0.242 0.595692 12 to 19 2577.59 1.097 0.863755 13 to 20 2483.57 -0.232 0.408116 14 to 21 2568.85 0.974 0.834888 15 to 22 2608.92 1.540 0.938262 16 to 23 2467.16 -0.464 0.321185 17 to 24 2406.49 -1.322 0.093008 18 to 25 2534.74 0.491 0.688371 19 to 26 2488.04 -0.169 0.432869 20 to 27 2487.72 -0.174 0.431074 21 to 28 2495.13 -0.069 0.472569 22 to 29 2524.86 0.352 0.637437 23 to 30 2466.18 -0.478 0.316246 24 to 31 2539.31 0.556 0.710874 25 to 32 2603.60 1.465 0.928561 CDPARK for dh-ranFile-2016-02-23_05:31: 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 3493 -1.3699 0.085365 3544 0.9589 0.831196 3487 -1.6438 0.050105 3490 -1.5068 0.065925 3539 0.7306 0.767486 3530 0.3196 0.625377 3515 -0.3653 0.357445 3570 2.1461 0.984068 3548 1.1416 0.873180 3512 -0.5023 0.307734 Square side=100, avg. no. parked=3522.80 sample std.=26.55 p-value of the KSTEST for those 10 p-values: 0.615441 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-02-23_05:31 0.4690,0.3071,0.5231,0.6198,0.4375,0.8699,0.5879,0.7361,0.1499,0.6420, The KS test for those 10 p-values: 0.517060 The 3DSPHERES test for dh-ranFile-2016-02-23_05:31 sample no r^3 equiv. uni. 1 1.432 0.046606 2 42.490 0.757395 3 100.257 0.964631 4 4.543 0.140539 5 69.155 0.900256 6 171.998 0.996763 7 97.649 0.961418 8 71.961 0.909163 9 5.610 0.170561 10 2.906 0.092331 11 1.673 0.054226 12 17.422 0.440506 13 12.284 0.336004 14 1.979 0.063829 15 32.367 0.660026 16 16.263 0.418479 17 199.068 0.998687 18 36.741 0.706151 19 91.334 0.952378 20 36.878 0.707494 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.041002 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-02-23_05:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 -0.3 0.1 2.1 0.4 -1.2 -0.5 -0.4 0.0 -0.3 -0.1 -1.2 -0.2 -0.3 1.2 0.1 0.5 -0.2 0.9 0.4 0.4 -0.3 -0.2 -0.2 -0.6 0.4 0.2 0.5 -1.7 -2.0 -1.0 0.7 0.5 -0.8 -0.9 0.4 1.2 0.5 -0.8 0.4 0.9 1.0 -0.1 Chi-square with 42 degrees of freedom:28.548310 z-score=-1.467700, p-value=0.056217 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-02-23_05:31 Test no p-value 1 0.568482 2 0.116008 3 0.059134 4 0.697409 5 0.734449 6 0.494571 7 0.157305 8 0.673101 9 0.067144 10 0.468636 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.337774 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-02-23_05:31: (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 66811 0.31 66583 0.11 3 25000.00 24898 0.42 24958 0.07 4 6666.67 6583 1.05 6735 0.70 5 1388.89 1413 0.42 1427 1.05 6 238.10 241 0.04 259 1.84 7 34.72 47 4.34 33 0.09 8 4.96 6 0.22 4 0.19 p=0.65968 p=0.32712 Number of rngs required: 687499, p-value: 0.147 RESULTS OF CRAPS TEST for dh-ranFile-2016-02-23_05:31 No. of wins: Observed Expected 98858 98585.9 z-score= 1.217, pvalue=0.88823 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66533 66666.7 0.268 0.268 2 37864 37654.3 1.168 1.436 3 27044 26954.7 0.296 1.731 4 19027 19313.5 4.249 5.980 5 14112 13851.4 4.902 10.882 6 9970 9943.5 0.070 10.953 7 7074 7145.0 0.706 11.659 8 5171 5139.1 0.198 11.857 9 3716 3699.9 0.070 11.927 10 2629 2666.3 0.522 12.449 11 1901 1923.3 0.259 12.708 12 1364 1388.7 0.441 13.149 13 1008 1003.7 0.018 13.167 14 719 726.1 0.070 13.238 15 490 525.8 2.442 15.680 16 379 381.2 0.012 15.692 17 278 276.5 0.008 15.700 18 195 200.8 0.169 15.869 19 117 146.0 5.755 21.624 20 89 106.2 2.790 24.414 21 320 287.1 3.767 28.181 Chisq= 28.18 for 20 degrees of freedom, p= 0.89481 SUMMARY of craptest p-value for no. of wins: 0.888231 p-value for throws/game: 0.894808 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-02-23_05:31 No. of wins: Observed Expected 98819 98585.9 z-score= 1.043, pvalue=0.85147 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66498 66666.7 0.427 0.427 2 37775 37654.3 0.387 0.813 3 27341 26954.7 5.535 6.349 4 19213 19313.5 0.523 6.871 5 13911 13851.4 0.256 7.128 6 9825 9943.5 1.413 8.541 7 7033 7145.0 1.756 10.297 8 5065 5139.1 1.068 11.365 9 3686 3699.9 0.052 11.417 10 2668 2666.3 0.001 11.418 11 1903 1923.3 0.215 11.633 12 1396 1388.7 0.038 11.671 13 990 1003.7 0.187 11.858 14 745 726.1 0.490 12.348 15 528 525.8 0.009 12.357 16 405 381.2 1.492 13.849 17 297 276.5 1.514 15.363 18 203 200.8 0.023 15.387 19 136 146.0 0.683 16.069 20 98 106.2 0.635 16.705 21 284 287.1 0.034 16.739 Chisq= 16.74 for 20 degrees of freedom, p= 0.33012 SUMMARY of craptest p-value for no. of wins: 0.851467 p-value for throws/game: 0.330121 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0044,0.0099,0.0105,0.0295,0.0336,0.0407,0.0410,0.0466,0.0501,0.0510, 0.0539,0.0542,0.0562,0.0582,0.0591,0.0595,0.0638,0.0646,0.0650,0.0659, 0.0671,0.0711,0.0720,0.0744,0.0746,0.0805,0.0854,0.0923,0.0930,0.1021, 0.1025,0.1060,0.1084,0.1091,0.1109,0.1160,0.1217,0.1243,0.1285,0.1370, 0.1405,0.1426,0.1441,0.1449,0.1473,0.1499,0.1500,0.1573,0.1635,0.1695, 0.1706,0.1732,0.1736,0.1739,0.1908,0.1915,0.1921,0.2063,0.2083,0.2086, 0.2109,0.2138,0.2230,0.2271,0.2489,0.2518,0.2518,0.2525,0.2530,0.2591, 0.2616,0.2671,0.2694,0.2731,0.2821,0.2830,0.2839,0.2841,0.2883,0.2904, 0.2912,0.2949,0.3007,0.3008,0.3009,0.3053,0.3054,0.3071,0.3077,0.3162, 0.3212,0.3232,0.3271,0.3301,0.3360,0.3364,0.3378,0.3399,0.3412,0.3438, 0.3455,0.3574,0.3631,0.3686,0.3725,0.3797,0.3859,0.3861,0.3884,0.3961, 0.4036,0.4064,0.4081,0.4144,0.4177,0.4185,0.4267,0.4283,0.4292,0.4311, 0.4329,0.4340,0.4375,0.4391,0.4398,0.4405,0.4474,0.4573,0.4678,0.4679, 0.4686,0.4690,0.4696,0.4726,0.4762,0.4806,0.4820,0.4946,0.5035,0.5100, 0.5171,0.5215,0.5231,0.5235,0.5244,0.5521,0.5548,0.5559,0.5598,0.5629, 0.5685,0.5695,0.5709,0.5735,0.5745,0.5762,0.5764,0.5879,0.5897,0.5957, 0.6035,0.6055,0.6154,0.6175,0.6198,0.6224,0.6254,0.6332,0.6374,0.6409, 0.6420,0.6457,0.6463,0.6500,0.6534,0.6537,0.6597,0.6600,0.6635,0.6731, 0.6779,0.6840,0.6844,0.6882,0.6884,0.6887,0.6904,0.6964,0.6974,0.7062, 0.7075,0.7109,0.7241,0.7288,0.7344,0.7361,0.7421,0.7423,0.7433,0.7467, 0.7523,0.7574,0.7657,0.7675,0.7752,0.7766,0.7779,0.7860,0.7928,0.7928, 0.7930,0.7967,0.8012,0.8054,0.8116,0.8172,0.8175,0.8184,0.8232,0.8261, 0.8312,0.8331,0.8349,0.8361,0.8389,0.8437,0.8444,0.8515,0.8533,0.8638, 0.8638,0.8673,0.8686,0.8699,0.8703,0.8718,0.8727,0.8732,0.8876,0.8882, 0.8906,0.8938,0.8948,0.8992,0.9003,0.9020,0.9092,0.9123,0.9143,0.9217, 0.9237,0.9286,0.9383,0.9482,0.9524,0.9550,0.9550,0.9560,0.9614,0.9646, 0.9679,0.9717,0.9841,0.9841,0.9847,0.9892,0.9961,0.9968,0.9987, Overall p-value after applying KStest on 269 p-values = 0.937220 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.