RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-02-04_00:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.70 19.7795 0.714337 2 to 25 15.46 24.9695 0.904606 3 to 26 15.76 20.0738 0.729529 4 to 27 15.87 20.2805 0.739866 5 to 28 15.46 32.4188 0.986658 6 to 29 15.83 20.2189 0.736813 7 to 30 15.48 21.4933 0.795003 8 to 31 15.65 22.0066 0.815534 9 to 32 16.03 13.8042 0.319093 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.010487 Tough bday spacings test for dh-ranFile-2017-02-04_00:31: 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 31 70 107 95 73 48 38 17 5 7 (O-E)^2/E 0.0 0.9 0.1 0.9 0.1 0.3 0.3 2.3 0.3 0.4 2.1 Birthday Spacings: Sum(O-E)^2/E= 7.724, p= 0.344 RESULTS OF GCD FOR dh-ranFile-2017-02-04_00:31 Euclid's algorithm: p-value, steps to gcd: 0.239282 p-value, dist. of gcd's: 0.614316 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-02-04_00:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.483 0.228 0.531 0.344 0.922 0.488 0.848 0.318 Bits 8 to 15---> 0.370 0.150 0.053 0.829 0.833 0.371 0.293 0.537 Bits 16 to 23---> 0.223 0.144 0.982 0.864 0.587 0.587 0.109 0.316 Bits 24 to 31---> 0.688 0.800 0.811 0.485 0.566 0.106 0.390 0.436 KS test for the above 32 p values: 0.195 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-02-04_00:31, p-values for 5 runs: 0.9062, 0.7717, 0.4102, 0.8521, 0.3685 Rank test for binary matrices (31x31) for dh-ranFile-2017-02-04_00:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 205 211.4 0.195 0.195 r= 29 5064 5134.0 0.955 1.150 r= 30 23151 23103.0 0.100 1.249 r= 31 11580 11551.5 0.070 1.319 chi-square = 1.319 with df = 3; p-value = 0.275 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2017-02-04_00:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 217 211.4 0.147 0.147 r= 30 5065 5134.0 0.928 1.075 r= 31 23111 23103.0 0.003 1.078 r= 32 11607 11551.5 0.266 1.344 chi-square = 1.344 with df = 3; p-value = 0.281 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2017-02-04_00:31 b-rank test for bits 1 to 8, p=0.99808 b-rank test for bits 2 to 9, p=0.99961 b-rank test for bits 3 to 10, p=0.97646 b-rank test for bits 4 to 11, p=0.79665 b-rank test for bits 5 to 12, p=0.14250 b-rank test for bits 6 to 13, p=0.84891 b-rank test for bits 7 to 14, p=0.83723 b-rank test for bits 8 to 15, p=0.34888 b-rank test for bits 9 to 16, p=0.12396 b-rank test for bits 10 to 17, p=0.53412 b-rank test for bits 11 to 18, p=0.04845 b-rank test for bits 12 to 19, p=0.80209 b-rank test for bits 13 to 20, p=0.27134 b-rank test for bits 14 to 21, p=0.44780 b-rank test for bits 15 to 22, p=0.66495 b-rank test for bits 16 to 23, p=0.71729 b-rank test for bits 17 to 24, p=0.31898 b-rank test for bits 18 to 25, p=0.75924 b-rank test for bits 19 to 26, p=0.38529 b-rank test for bits 20 to 27, p=0.41762 b-rank test for bits 21 to 28, p=0.53326 b-rank test for bits 22 to 29, p=0.71633 b-rank test for bits 23 to 30, p=0.80055 b-rank test for bits 24 to 31, p=0.01159 b-rank test for bits 25 to 32, p=0.70830 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 = 0.204442 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-02-04_00:31 (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 142427 1.21 0.886766 2 141910 0.00 0.500625 3 141447 -1.08 0.140024 4 141834 -0.18 0.430145 5 142300 0.91 0.819321 6 142049 0.33 0.627913 7 142008 0.23 0.591163 8 141884 -0.06 0.476404 9 142327 0.98 0.835434 10 142619 1.66 0.951352 11 140836 -2.51 0.006075 12 141223 -1.60 0.054404 13 142223 0.73 0.768182 14 141764 -0.34 0.367095 15 142305 0.92 0.822377 16 142478 1.33 0.908021 17 141880 -0.07 0.472683 18 143537 3.80 0.999929 19 141329 -1.36 0.087564 20 141787 -0.29 0.387509 ---------------------------------------------------------------- OPSO test for dh-ranFile-2017-02-04_00:31 Bits used No. missing words z-score p-value 23 to 32 141906 -0.0115 0.495419 22 to 31 142371 1.5920 0.944304 21 to 30 142220 1.0713 0.857977 20 to 29 141914 0.0161 0.506424 19 to 28 142326 1.4368 0.924612 18 to 27 141786 -0.4253 0.335318 17 to 26 141860 -0.1701 0.432464 16 to 25 142210 1.0368 0.850084 15 to 24 141945 0.1230 0.548947 14 to 23 141956 0.1609 0.563926 13 to 22 141528 -1.3149 0.094267 12 to 21 141972 0.2161 0.585547 11 to 20 142321 1.4196 0.922131 10 to 19 141904 -0.0184 0.492668 9 to 18 142123 0.7368 0.769376 8 to 17 142044 0.4644 0.678812 7 to 16 141819 -0.3115 0.377717 6 to 15 141879 -0.1046 0.458352 5 to 14 142007 0.3368 0.631864 4 to 13 141842 -0.2322 0.408202 3 to 12 142053 0.4954 0.689846 2 to 11 141910 0.0023 0.500922 1 to 10 142073 0.5644 0.713752 ----------------------------------------------------------------- OQSO test for dh-ranFile-2017-02-04_00:31 Bits used No. missing words z-score p-value 28 to 32 141837 -0.2452 0.403156 27 to 31 141402 -1.7198 0.042738 26 to 30 142023 0.3853 0.650001 25 to 29 141951 0.1413 0.556166 24 to 28 142368 1.5548 0.940005 23 to 27 141966 0.1921 0.576169 22 to 26 141484 -1.4418 0.074680 21 to 25 142048 0.4701 0.680847 20 to 24 142195 0.9684 0.833571 19 to 23 141632 -0.9401 0.173583 18 to 22 141540 -1.2520 0.105291 17 to 21 141945 0.1209 0.548121 16 to 20 142213 1.0294 0.848352 15 to 19 141844 -0.2215 0.412368 14 to 18 141577 -1.1265 0.129968 13 to 17 141904 -0.0181 0.492792 12 to 16 141519 -1.3232 0.092892 11 to 15 141891 -0.0621 0.475227 10 to 14 142066 0.5311 0.702320 9 to 13 141731 -0.6045 0.272753 8 to 12 141825 -0.2859 0.387491 7 to 11 141641 -0.9096 0.181519 6 to 10 141891 -0.0621 0.475227 5 to 9 141501 -1.3842 0.083153 4 to 8 141776 -0.4520 0.325647 3 to 7 142116 0.7006 0.758216 2 to 6 142314 1.3718 0.914931 1 to 5 141927 0.0599 0.523882 ----------------------------------------------------------------- DNA test for dh-ranFile-2017-02-04_00:31 Bits used No. missing words z-score p-value 31 to 32 141598 -0.9184 0.179211 30 to 31 141705 -0.6027 0.273340 29 to 30 142093 0.5418 0.706022 28 to 29 142166 0.7571 0.775517 27 to 28 142254 1.0167 0.845358 26 to 27 141768 -0.4169 0.338375 25 to 26 142802 2.6332 0.995771 24 to 25 141523 -1.1396 0.127223 23 to 24 141571 -0.9980 0.159134 22 to 23 141771 -0.4081 0.341617 21 to 22 141715 -0.5732 0.283240 20 to 21 141700 -0.6175 0.268455 19 to 20 141955 0.1347 0.553583 18 to 19 141790 -0.3520 0.362417 17 to 18 142022 0.3324 0.630191 16 to 17 142067 0.4651 0.679071 15 to 16 142419 1.5035 0.933639 14 to 15 142515 1.7866 0.963002 13 to 14 141661 -0.7325 0.231921 12 to 13 142160 0.7394 0.770180 11 to 12 142253 1.0138 0.844655 10 to 11 141741 -0.4965 0.309754 9 to 10 141907 -0.0069 0.497258 8 to 9 141515 -1.1632 0.122371 7 to 8 141746 -0.4818 0.314974 6 to 7 141885 -0.0718 0.471393 5 to 6 142127 0.6421 0.739594 4 to 5 141456 -1.3373 0.090569 3 to 4 141809 -0.2960 0.383631 2 to 3 141584 -0.9597 0.168609 1 to 2 141747 -0.4788 0.316023 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2017-02-04_00:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2459.53 -0.572 0.283565 Test results for specific bytes for dh-ranFile-2017-02-04_00:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2537.65 0.532 0.702804 2 to 9 2579.23 1.120 0.868742 3 to 10 2415.50 -1.195 0.116030 4 to 11 2650.03 2.122 0.983071 5 to 12 2467.37 -0.462 0.322213 6 to 13 2558.27 0.824 0.795038 7 to 14 2592.94 1.314 0.905650 8 to 15 2515.70 0.222 0.587840 9 to 16 2478.63 -0.302 0.381223 10 to 17 2445.03 -0.777 0.218458 11 to 18 2520.98 0.297 0.616674 12 to 19 2539.01 0.552 0.709438 13 to 20 2526.18 0.370 0.644375 14 to 21 2663.82 2.317 0.989742 15 to 22 2733.13 3.297 0.999511 16 to 23 2535.73 0.505 0.693345 17 to 24 2455.01 -0.636 0.262288 18 to 25 2607.76 1.524 0.936242 19 to 26 2475.60 -0.345 0.365042 20 to 27 2437.89 -0.878 0.189856 21 to 28 2445.69 -0.768 0.221239 22 to 29 2618.86 1.681 0.953614 23 to 30 2524.78 0.350 0.636998 24 to 31 2622.82 1.737 0.958804 25 to 32 2526.03 0.368 0.643603 CDPARK for dh-ranFile-2017-02-04_00:31: 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 3525 0.0913 0.536383 3519 -0.1826 0.427537 3575 2.3744 0.991212 3547 1.0959 0.863437 3517 -0.2740 0.392053 3525 0.0913 0.536383 3519 -0.1826 0.427537 3568 2.0548 0.980051 3538 0.6849 0.753306 3508 -0.6849 0.246694 Square side=100, avg. no. parked=3534.10 sample std.=21.45 p-value of the KSTEST for those 10 p-values: 0.193364 Results for the MINIMUM DISTANCE test for dh-ranFile-2017-02-04_00:31 0.1178,0.8697,0.4441,0.0703,0.1278,0.0997,0.2747,0.4336,0.4244,0.3683, The KS test for those 10 p-values: 0.067974 The 3DSPHERES test for dh-ranFile-2017-02-04_00:31 sample no r^3 equiv. uni. 1 4.650 0.143599 2 48.176 0.799284 3 0.400 0.013236 4 18.417 0.458762 5 45.736 0.782280 6 98.731 0.962785 7 61.470 0.871138 8 122.143 0.982947 9 2.883 0.091622 10 100.491 0.964905 11 123.205 0.983540 12 18.802 0.465670 13 80.176 0.930924 14 37.715 0.715545 15 1.832 0.059232 16 6.918 0.205953 17 66.195 0.889915 18 13.129 0.354428 19 4.561 0.141039 20 42.295 0.755814 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.061049 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-02-04_00:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -2.0 -0.8 0.9 0.3 -0.2 -0.6 -1.1 0.7 0.2 2.4 1.0 1.1 0.7 -0.1 -0.5 -2.5 -0.8 -0.1 -0.4 0.8 -0.6 -0.5 0.5 0.5 -0.9 -0.1 -0.1 2.1 0.9 -0.9 1.0 0.1 0.0 -0.6 0.1 1.0 -0.7 0.9 -0.7 0.1 0.0 -1.1 Chi-square with 42 degrees of freedom:36.806137 z-score=-0.566697, p-value=0.302123 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2017-02-04_00:31 Test no p-value 1 0.053077 2 0.715347 3 0.158166 4 0.055243 5 0.001770 6 0.434979 7 0.790179 8 0.258540 9 0.846723 10 0.712259 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.188572 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-02-04_00:31: (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 66670 0.00 66779 0.19 3 25000.00 24960 0.06 24979 0.02 4 6666.67 6724 0.49 6608 0.52 5 1388.89 1368 0.31 1368 0.31 6 238.10 237 0.01 233 0.11 7 34.72 36 0.05 31 0.40 8 4.96 4 0.19 1 3.16 p=0.01888 p=0.41805 Number of rngs required: 687816, p-value: 0.249 RESULTS OF CRAPS TEST for dh-ranFile-2017-02-04_00:31 No. of wins: Observed Expected 98326 98585.9 z-score=-1.162, pvalue=0.12257 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66664 66666.7 0.000 0.000 2 37549 37654.3 0.295 0.295 3 27134 26954.7 1.192 1.487 4 19375 19313.5 0.196 1.683 5 13804 13851.4 0.162 1.845 6 9794 9943.5 2.249 4.094 7 7251 7145.0 1.572 5.666 8 5174 5139.1 0.237 5.904 9 3588 3699.9 3.382 9.286 10 2669 2666.3 0.003 9.289 11 1916 1923.3 0.028 9.316 12 1419 1388.7 0.659 9.976 13 1060 1003.7 3.156 13.132 14 717 726.1 0.115 13.247 15 506 525.8 0.748 13.995 16 381 381.2 0.000 13.995 17 281 276.5 0.072 14.067 18 209 200.8 0.332 14.400 19 138 146.0 0.437 14.836 20 92 106.2 1.902 16.739 21 279 287.1 0.229 16.968 Chisq= 16.97 for 20 degrees of freedom, p= 0.34496 SUMMARY of craptest p-value for no. of wins: 0.122569 p-value for throws/game: 0.344965 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2017-02-04_00:31 No. of wins: Observed Expected 98675 98585.9 z-score= 0.399, pvalue=0.65494 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66502 66666.7 0.407 0.407 2 37404 37654.3 1.664 2.071 3 26999 26954.7 0.073 2.144 4 19620 19313.5 4.865 7.009 5 13833 13851.4 0.024 7.033 6 10160 9943.5 4.712 11.745 7 7144 7145.0 0.000 11.745 8 5173 5139.1 0.224 11.969 9 3630 3699.9 1.319 13.289 10 2616 2666.3 0.949 14.237 11 2011 1923.3 3.996 18.234 12 1378 1388.7 0.083 18.317 13 944 1003.7 3.553 21.870 14 697 726.1 1.169 23.039 15 562 525.8 2.487 25.526 16 373 381.2 0.174 25.700 17 263 276.5 0.663 26.363 18 183 200.8 1.583 27.946 19 146 146.0 0.000 27.946 20 104 106.2 0.046 27.993 21 258 287.1 2.952 30.945 Chisq= 30.94 for 20 degrees of freedom, p= 0.94408 SUMMARY of craptest p-value for no. of wins: 0.654940 p-value for throws/game: 0.944076 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0018,0.0061,0.0105,0.0116,0.0132,0.0189,0.0427,0.0485,0.0529,0.0531, 0.0544,0.0552,0.0592,0.0610,0.0680,0.0703,0.0747,0.0832,0.0876,0.0906, 0.0916,0.0929,0.0943,0.0997,0.1053,0.1059,0.1092,0.1160,0.1178,0.1224, 0.1226,0.1240,0.1272,0.1278,0.1300,0.1400,0.1410,0.1425,0.1436,0.1437, 0.1503,0.1582,0.1591,0.1686,0.1736,0.1792,0.1815,0.1886,0.1899,0.1934, 0.1946,0.2044,0.2060,0.2185,0.2212,0.2230,0.2280,0.2319,0.2393,0.2467, 0.2490,0.2585,0.2623,0.2685,0.2713,0.2728,0.2733,0.2747,0.2754,0.2813, 0.2832,0.2836,0.2929,0.3021,0.3098,0.3150,0.3160,0.3163,0.3182,0.3190, 0.3191,0.3222,0.3256,0.3353,0.3384,0.3416,0.3441,0.3443,0.3450,0.3489, 0.3544,0.3624,0.3650,0.3671,0.3683,0.3685,0.3699,0.3714,0.3777,0.3812, 0.3836,0.3853,0.3875,0.3875,0.3902,0.3921,0.4032,0.4082,0.4102,0.4124, 0.4176,0.4181,0.4244,0.4275,0.4275,0.4301,0.4325,0.4336,0.4350,0.4356, 0.4441,0.4478,0.4584,0.4588,0.4657,0.4714,0.4727,0.4752,0.4752,0.4764, 0.4832,0.4847,0.4880,0.4927,0.4928,0.4954,0.4973,0.5006,0.5009,0.5064, 0.5239,0.5309,0.5333,0.5341,0.5364,0.5364,0.5372,0.5481,0.5489,0.5536, 0.5562,0.5639,0.5656,0.5762,0.5855,0.5872,0.5874,0.5878,0.5912,0.6143, 0.6167,0.6279,0.6302,0.6319,0.6370,0.6436,0.6444,0.6500,0.6549,0.6649, 0.6788,0.6791,0.6808,0.6880,0.6898,0.6933,0.7023,0.7028,0.7060,0.7083, 0.7094,0.7123,0.7138,0.7143,0.7153,0.7155,0.7163,0.7173,0.7295,0.7368, 0.7396,0.7399,0.7533,0.7558,0.7582,0.7592,0.7682,0.7694,0.7702,0.7717, 0.7755,0.7823,0.7902,0.7950,0.7950,0.7966,0.7993,0.7997,0.8005,0.8021, 0.8106,0.8155,0.8193,0.8224,0.8291,0.8327,0.8336,0.8354,0.8372,0.8447, 0.8454,0.8467,0.8480,0.8484,0.8489,0.8501,0.8521,0.8580,0.8634,0.8639, 0.8687,0.8697,0.8711,0.8868,0.8899,0.9046,0.9056,0.9062,0.9080,0.9149, 0.9221,0.9224,0.9246,0.9309,0.9336,0.9362,0.9400,0.9441,0.9443,0.9514, 0.9536,0.9588,0.9628,0.9630,0.9649,0.9765,0.9801,0.9822,0.9829,0.9831, 0.9835,0.9867,0.9897,0.9912,0.9958,0.9981,0.9995,0.9996,0.9999, Overall p-value after applying KStest on 269 p-values = 0.327961 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.