RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-10-10_23:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.78 9.7486 0.086182 2 to 25 15.69 13.9722 0.330931 3 to 26 16.04 8.5085 0.045567 4 to 27 15.61 16.6565 0.522136 5 to 28 15.85 20.3496 0.743260 6 to 29 15.88 21.5441 0.797107 7 to 30 15.72 15.0158 0.405654 8 to 31 15.75 20.0145 0.726510 9 to 32 15.70 19.8007 0.715448 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.807057 Tough bday spacings test for dh-ranFile-2016-10-10_23:31: 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 72 101 106 84 52 23 13 7 5 (O-E)^2/E 0.1 1.6 0.0 0.1 0.7 0.4 0.0 1.5 0.2 0.0 0.2 Birthday Spacings: Sum(O-E)^2/E= 5.032, p= 0.111 RESULTS OF GCD FOR dh-ranFile-2016-10-10_23:31 Euclid's algorithm: p-value, steps to gcd: 0.097347 p-value, dist. of gcd's: 0.576999 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-10-10_23:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.011 0.472 0.538 0.807 0.285 0.109 0.889 0.858 Bits 8 to 15---> 0.916 0.124 0.289 0.760 0.005 0.207 0.308 0.760 Bits 16 to 23---> 0.537 0.450 0.133 0.972 0.990 0.130 0.415 0.754 Bits 24 to 31---> 0.571 0.523 0.966 0.089 0.347 0.376 0.445 0.183 KS test for the above 32 p values: 0.261 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-10-10_23:31, p-values for 5 runs: 0.4942, 0.0801, 0.4340, 0.9956, 0.3803 Rank test for binary matrices (31x31) for dh-ranFile-2016-10-10_23:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 229 211.4 1.462 1.462 r= 29 5173 5134.0 0.296 1.758 r= 30 23160 23103.0 0.140 1.899 r= 31 11438 11551.5 1.116 3.014 chi-square = 3.014 with df = 3; p-value = 0.611 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-10-10_23:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 190 211.4 2.170 2.170 r= 30 5202 5134.0 0.900 3.070 r= 31 22893 23103.0 1.910 4.980 r= 32 11715 11551.5 2.314 7.293 chi-square = 7.293 with df = 3; p-value = 0.937 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-10-10_23:31 b-rank test for bits 1 to 8, p=0.19901 b-rank test for bits 2 to 9, p=0.83604 b-rank test for bits 3 to 10, p=0.03926 b-rank test for bits 4 to 11, p=0.24261 b-rank test for bits 5 to 12, p=0.19027 b-rank test for bits 6 to 13, p=0.52920 b-rank test for bits 7 to 14, p=0.62331 b-rank test for bits 8 to 15, p=0.10025 b-rank test for bits 9 to 16, p=0.09936 b-rank test for bits 10 to 17, p=0.27988 b-rank test for bits 11 to 18, p=0.15391 b-rank test for bits 12 to 19, p=0.09347 b-rank test for bits 13 to 20, p=0.08074 b-rank test for bits 14 to 21, p=0.44641 b-rank test for bits 15 to 22, p=0.31642 b-rank test for bits 16 to 23, p=0.90343 b-rank test for bits 17 to 24, p=0.84476 b-rank test for bits 18 to 25, p=0.26292 b-rank test for bits 19 to 26, p=0.32482 b-rank test for bits 20 to 27, p=0.61340 b-rank test for bits 21 to 28, p=0.63639 b-rank test for bits 22 to 29, p=0.18535 b-rank test for bits 23 to 30, p=0.60361 b-rank test for bits 24 to 31, p=0.98614 b-rank test for bits 25 to 32, p=0.36643 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 = 0.106156 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-10-10_23:31 (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 142076 0.39 0.651516 2 142143 0.55 0.707453 3 141348 -1.31 0.094841 4 142170 0.61 0.728752 5 141976 0.16 0.561893 6 141499 -0.96 0.168851 7 142289 0.89 0.812482 8 141651 -0.60 0.273063 9 141650 -0.61 0.272287 10 141896 -0.03 0.487577 11 141615 -0.69 0.245825 12 141941 0.07 0.529493 13 142013 0.24 0.595695 14 142041 0.31 0.620822 15 141600 -0.72 0.234922 16 142255 0.81 0.790351 17 142100 0.45 0.672017 18 141698 -0.49 0.310737 19 141831 -0.18 0.427394 20 140759 -2.69 0.003597 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-10-10_23:31 Bits used No. missing words z-score p-value 23 to 32 141705 -0.7046 0.240534 22 to 31 141744 -0.5701 0.284304 21 to 30 141603 -1.0563 0.145413 20 to 29 141656 -0.8736 0.191181 19 to 28 141233 -2.3322 0.009846 18 to 27 141365 -1.8770 0.030259 17 to 26 142089 0.6196 0.732224 16 to 25 142020 0.3816 0.648629 15 to 24 141945 0.1230 0.548947 14 to 23 142253 1.1851 0.882005 13 to 22 142284 1.2920 0.901815 12 to 21 142263 1.2196 0.888683 11 to 20 141883 -0.0908 0.463829 10 to 19 141827 -0.2839 0.388245 9 to 18 141700 -0.7218 0.235200 8 to 17 141969 0.2058 0.581510 7 to 16 141888 -0.0736 0.470684 6 to 15 142055 0.5023 0.692275 5 to 14 141584 -1.1218 0.130968 4 to 13 142070 0.5540 0.710222 3 to 12 142072 0.5609 0.712578 2 to 11 141744 -0.5701 0.284304 1 to 10 141567 -1.1804 0.118911 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-10-10_23:31 Bits used No. missing words z-score p-value 28 to 32 141832 -0.2621 0.396609 27 to 31 141779 -0.4418 0.329318 26 to 30 141409 -1.6960 0.044940 25 to 29 141792 -0.3977 0.345415 24 to 28 141741 -0.5706 0.284132 23 to 27 142170 0.8836 0.811551 22 to 26 142644 2.4904 0.993620 21 to 25 141781 -0.4350 0.331775 20 to 24 141886 -0.0791 0.468483 19 to 23 141765 -0.4893 0.312331 18 to 22 141879 -0.1028 0.459056 17 to 21 141871 -0.1299 0.448310 16 to 20 142064 0.5243 0.699967 15 to 19 141924 0.0497 0.519831 14 to 18 141920 0.0362 0.514426 13 to 17 141476 -1.4689 0.070928 12 to 16 141933 0.0802 0.531976 11 to 15 142193 0.9616 0.831873 10 to 14 141708 -0.6825 0.247470 9 to 13 142103 0.6565 0.744252 8 to 12 141842 -0.2282 0.409731 7 to 11 141690 -0.7435 0.228592 6 to 10 141922 0.0429 0.517129 5 to 9 141835 -0.2520 0.400534 4 to 8 141599 -1.0520 0.146408 3 to 7 141403 -1.7164 0.043047 2 to 6 141945 0.1209 0.548121 1 to 5 141755 -0.5232 0.300434 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-10-10_23:31 Bits used No. missing words z-score p-value 31 to 32 141766 -0.4228 0.336220 30 to 31 141998 0.2616 0.603171 29 to 30 142208 0.8810 0.810850 28 to 29 142256 1.0226 0.846758 27 to 28 142393 1.4268 0.923175 26 to 27 141991 0.2409 0.595189 25 to 26 141851 -0.1721 0.431693 24 to 25 142570 1.9489 0.974345 23 to 24 142012 0.3029 0.619002 22 to 23 141980 0.2085 0.582568 21 to 22 141710 -0.5880 0.278268 20 to 21 141815 -0.2783 0.390407 19 to 20 142117 0.6126 0.729928 18 to 19 141112 -2.3520 0.009336 17 to 18 141683 -0.6676 0.252182 16 to 17 141699 -0.6204 0.267483 15 to 16 141442 -1.3786 0.084016 14 to 15 141761 -0.4376 0.330856 13 to 14 141282 -1.8505 0.032119 12 to 13 141421 -1.4405 0.074863 11 to 12 142280 1.0934 0.862896 10 to 11 141313 -1.7591 0.039282 9 to 10 141869 -0.1190 0.452651 8 to 9 141863 -0.1367 0.445647 7 to 8 142138 0.6745 0.750017 6 to 7 141813 -0.2842 0.388144 5 to 6 142625 2.1111 0.982619 4 to 5 141617 -0.8623 0.194253 3 to 4 142531 1.8338 0.966661 2 to 3 141247 -1.9538 0.025364 1 to 2 142182 0.8043 0.789399 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-10-10_23:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2514.61 0.207 0.581866 Test results for specific bytes for dh-ranFile-2016-10-10_23:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2488.47 -0.163 0.435224 2 to 9 2437.19 -0.888 0.187184 3 to 10 2468.24 -0.449 0.326676 4 to 11 2593.70 1.325 0.907434 5 to 12 2434.64 -0.924 0.177648 6 to 13 2534.02 0.481 0.684761 7 to 14 2511.46 0.162 0.564367 8 to 15 2521.28 0.301 0.618290 9 to 16 2550.29 0.711 0.761502 10 to 17 2578.01 1.103 0.865050 11 to 18 2489.54 -0.148 0.441196 12 to 19 2403.46 -1.365 0.086074 13 to 20 2562.12 0.879 0.810165 14 to 21 2410.99 -1.259 0.104049 15 to 22 2535.32 0.499 0.691282 16 to 23 2520.82 0.294 0.615804 17 to 24 2427.20 -1.029 0.151625 18 to 25 2565.57 0.927 0.823104 19 to 26 2587.77 1.241 0.892754 20 to 27 2540.88 0.578 0.718392 21 to 28 2446.98 -0.750 0.226698 22 to 29 2444.95 -0.779 0.218115 23 to 30 2454.87 -0.638 0.261650 24 to 31 2502.85 0.040 0.516057 25 to 32 2419.75 -1.135 0.128198 CDPARK for dh-ranFile-2016-10-10_23:31: 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 3543 0.9132 0.819442 3535 0.5479 0.708135 3498 -1.1416 0.126820 3523 0.0000 0.500000 3539 0.7306 0.767486 3513 -0.4566 0.323972 3505 -0.8219 0.205562 3530 0.3196 0.625377 3535 0.5479 0.708135 3553 1.3699 0.914635 Square side=100, avg. no. parked=3527.40 sample std.=16.58 p-value of the KSTEST for those 10 p-values: 0.684356 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-10-10_23:31 0.0260,0.8256,0.6133,0.6435,0.6291,0.6571,0.4088,0.0634,0.6573,0.9862, The KS test for those 10 p-values: 0.444466 The 3DSPHERES test for dh-ranFile-2016-10-10_23:31 sample no r^3 equiv. uni. 1 34.935 0.687917 2 21.480 0.511294 3 3.016 0.095642 4 0.699 0.023032 5 49.293 0.806622 6 96.218 0.959533 7 3.468 0.109179 8 36.230 0.701108 9 4.207 0.130840 10 14.031 0.373554 11 30.390 0.636867 12 21.420 0.510313 13 61.433 0.870976 14 66.613 0.891438 15 38.527 0.723141 16 69.081 0.900012 17 0.132 0.004400 18 18.664 0.463201 19 16.078 0.414879 20 49.856 0.810216 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.600797 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-10-10_23:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 0.5 -0.1 0.2 0.6 -1.3 0.8 -1.8 0.1 -0.8 -1.3 -0.8 -0.9 -0.5 1.5 -0.4 0.8 -0.3 0.4 1.2 -1.0 -0.1 -1.0 -0.0 -0.9 0.6 2.7 -1.0 2.1 1.2 1.3 1.2 -1.7 1.2 0.3 1.3 0.5 -0.7 -1.2 -0.7 -0.6 0.0 -0.1 Chi-square with 42 degrees of freedom:44.848891 z-score=0.310839, p-value=0.646726 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-10-10_23:31 Test no p-value 1 0.310560 2 0.001267 3 0.230978 4 0.329141 5 0.569573 6 0.013501 7 0.972571 8 0.013306 9 0.292315 10 0.477466 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.016905 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-10-10_23:31: (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 66403 1.04 66518 0.33 3 25000.00 25112 0.50 25091 0.33 4 6666.67 6827 3.86 6776 1.79 5 1388.89 1379 0.07 1368 0.31 6 238.10 237 0.01 215 2.24 7 34.72 36 0.05 29 0.94 8 4.96 5 0.00 2 1.77 p=0.52137 p=0.74058 Number of rngs required: 688712, p-value: 0.639 RESULTS OF CRAPS TEST for dh-ranFile-2016-10-10_23:31 No. of wins: Observed Expected 98814 98585.9 z-score= 1.020, pvalue=0.84623 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66622 66666.7 0.030 0.030 2 37660 37654.3 0.001 0.031 3 26961 26954.7 0.001 0.032 4 19243 19313.5 0.257 0.289 5 13982 13851.4 1.231 1.520 6 9979 9943.5 0.126 1.647 7 7103 7145.0 0.247 1.894 8 5050 5139.1 1.544 3.438 9 3668 3699.9 0.274 3.712 10 2666 2666.3 0.000 3.712 11 1898 1923.3 0.334 4.046 12 1424 1388.7 0.895 4.941 13 1042 1003.7 1.460 6.401 14 702 726.1 0.803 7.204 15 575 525.8 4.597 11.801 16 397 381.2 0.659 12.460 17 267 276.5 0.329 12.789 18 207 200.8 0.190 12.978 19 143 146.0 0.061 13.039 20 117 106.2 1.095 14.134 21 294 287.1 0.165 14.300 Chisq= 14.30 for 20 degrees of freedom, p= 0.18501 SUMMARY of craptest p-value for no. of wins: 0.846226 p-value for throws/game: 0.185009 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-10-10_23:31 No. of wins: Observed Expected 98276 98585.9 z-score=-1.386, pvalue=0.08289 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66571 66666.7 0.137 0.137 2 37524 37654.3 0.451 0.588 3 26995 26954.7 0.060 0.648 4 19320 19313.5 0.002 0.651 5 13916 13851.4 0.301 0.952 6 9967 9943.5 0.055 1.007 7 7128 7145.0 0.041 1.048 8 5087 5139.1 0.528 1.575 9 3850 3699.9 6.092 7.668 10 2638 2666.3 0.300 7.968 11 1932 1923.3 0.039 8.007 12 1360 1388.7 0.595 8.602 13 1042 1003.7 1.460 10.062 14 705 726.1 0.615 10.678 15 529 525.8 0.019 10.697 16 389 381.2 0.162 10.858 17 278 276.5 0.008 10.866 18 199 200.8 0.017 10.883 19 164 146.0 2.223 13.106 20 120 106.2 1.789 14.895 21 286 287.1 0.004 14.899 Chisq= 14.90 for 20 degrees of freedom, p= 0.21786 SUMMARY of craptest p-value for no. of wins: 0.082894 p-value for throws/game: 0.217856 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0013,0.0036,0.0044,0.0052,0.0093,0.0098,0.0113,0.0133,0.0135,0.0169, 0.0230,0.0254,0.0260,0.0303,0.0321,0.0393,0.0393,0.0430,0.0449,0.0456, 0.0634,0.0709,0.0749,0.0801,0.0807,0.0829,0.0840,0.0861,0.0862,0.0892, 0.0935,0.0948,0.0956,0.0973,0.0994,0.1002,0.1040,0.1062,0.1088,0.1092, 0.1110,0.1189,0.1239,0.1268,0.1282,0.1301,0.1308,0.1310,0.1333,0.1454, 0.1464,0.1516,0.1539,0.1689,0.1776,0.1827,0.1850,0.1854,0.1872,0.1903, 0.1912,0.1943,0.1990,0.2056,0.2066,0.2179,0.2181,0.2267,0.2286,0.2310, 0.2349,0.2352,0.2405,0.2426,0.2458,0.2475,0.2522,0.2610,0.2617,0.2629, 0.2675,0.2723,0.2731,0.2783,0.2799,0.2841,0.2843,0.2843,0.2845,0.2890, 0.2923,0.3004,0.3082,0.3106,0.3107,0.3123,0.3164,0.3240,0.3248,0.3267, 0.3291,0.3293,0.3309,0.3309,0.3318,0.3362,0.3454,0.3474,0.3664,0.3736, 0.3764,0.3803,0.3881,0.3882,0.3904,0.3966,0.4005,0.4057,0.4088,0.4097, 0.4149,0.4153,0.4274,0.4317,0.4340,0.4352,0.4412,0.4445,0.4449,0.4456, 0.4464,0.4483,0.4503,0.4527,0.4591,0.4632,0.4638,0.4685,0.4707,0.4725, 0.4775,0.4876,0.4942,0.5000,0.5103,0.5113,0.5144,0.5161,0.5171,0.5198, 0.5214,0.5221,0.5226,0.5292,0.5295,0.5320,0.5369,0.5380,0.5481,0.5489, 0.5619,0.5644,0.5696,0.5706,0.5770,0.5815,0.5819,0.5826,0.5952,0.5957, 0.6008,0.6032,0.6036,0.6106,0.6133,0.6134,0.6158,0.6183,0.6190,0.6208, 0.6233,0.6254,0.6291,0.6364,0.6369,0.6390,0.6435,0.6467,0.6486,0.6515, 0.6571,0.6573,0.6720,0.6844,0.6848,0.6879,0.6913,0.6923,0.7000,0.7011, 0.7075,0.7081,0.7081,0.7102,0.7126,0.7154,0.7184,0.7231,0.7265,0.7288, 0.7299,0.7322,0.7406,0.7433,0.7443,0.7500,0.7537,0.7597,0.7603,0.7615, 0.7675,0.7894,0.7904,0.7971,0.8066,0.8071,0.8074,0.8102,0.8102,0.8108, 0.8116,0.8125,0.8194,0.8231,0.8256,0.8319,0.8360,0.8448,0.8462,0.8468, 0.8580,0.8629,0.8650,0.8710,0.8820,0.8887,0.8895,0.8914,0.8928,0.9000, 0.9018,0.9034,0.9074,0.9146,0.9157,0.9232,0.9369,0.9595,0.9662,0.9667, 0.9720,0.9726,0.9743,0.9826,0.9861,0.9862,0.9900,0.9936,0.9956, Overall p-value after applying KStest on 269 p-values = 0.078102 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.