RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-12-13_07:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.38 28.0339 0.955456 2 to 25 15.44 24.8651 0.902231 3 to 26 15.78 16.2934 0.496862 4 to 27 15.89 18.2882 0.629121 5 to 28 15.65 19.3673 0.692138 6 to 29 15.52 22.2832 0.825927 7 to 30 15.75 13.1693 0.275216 8 to 31 15.47 28.0197 0.955292 9 to 32 15.68 16.1858 0.489295 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.072688 Tough bday spacings test for dh-ranFile-2016-12-13_07:31: 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 27 70 98 107 88 53 28 12 4 4 (O-E)^2/E 0.0 2.5 0.1 0.0 0.9 1.2 0.0 0.1 0.6 1.0 0.0 Birthday Spacings: Sum(O-E)^2/E= 6.528, p= 0.231 RESULTS OF GCD FOR dh-ranFile-2016-12-13_07:31 Euclid's algorithm: p-value, steps to gcd: 0.913487 p-value, dist. of gcd's: 0.386192 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-12-13_07:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.012 0.640 0.178 0.828 0.159 0.882 0.417 0.972 Bits 8 to 15---> 0.580 0.564 0.001 0.891 0.308 0.618 0.175 0.461 Bits 16 to 23---> 0.910 0.673 0.228 0.855 0.039 0.643 0.646 0.993 Bits 24 to 31---> 0.130 0.301 0.060 0.051 0.126 0.029 0.963 0.217 KS test for the above 32 p values: 0.845 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-12-13_07:31, p-values for 5 runs: 0.8733, 0.7157, 0.7036, 0.6278, 0.0869 Rank test for binary matrices (31x31) for dh-ranFile-2016-12-13_07:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 205 211.4 0.195 0.195 r= 29 5015 5134.0 2.759 2.954 r= 30 23126 23103.0 0.023 2.976 r= 31 11654 11551.5 0.909 3.885 chi-square = 3.885 with df = 3; p-value = 0.726 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-12-13_07:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 211 211.4 0.001 0.001 r= 30 5083 5134.0 0.507 0.508 r= 31 23000 23103.0 0.460 0.967 r= 32 11706 11551.5 2.066 3.033 chi-square = 3.033 with df = 3; p-value = 0.613 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-12-13_07:31 b-rank test for bits 1 to 8, p=0.20944 b-rank test for bits 2 to 9, p=0.44977 b-rank test for bits 3 to 10, p=0.02677 b-rank test for bits 4 to 11, p=0.15013 b-rank test for bits 5 to 12, p=0.47254 b-rank test for bits 6 to 13, p=0.91538 b-rank test for bits 7 to 14, p=0.26183 b-rank test for bits 8 to 15, p=0.35034 b-rank test for bits 9 to 16, p=0.54832 b-rank test for bits 10 to 17, p=0.58083 b-rank test for bits 11 to 18, p=0.28893 b-rank test for bits 12 to 19, p=0.76321 b-rank test for bits 13 to 20, p=0.88218 b-rank test for bits 14 to 21, p=0.35097 b-rank test for bits 15 to 22, p=0.41805 b-rank test for bits 16 to 23, p=0.03494 b-rank test for bits 17 to 24, p=0.82418 b-rank test for bits 18 to 25, p=0.26196 b-rank test for bits 19 to 26, p=0.05782 b-rank test for bits 20 to 27, p=0.82524 b-rank test for bits 21 to 28, p=0.56321 b-rank test for bits 22 to 29, p=0.42915 b-rank test for bits 23 to 30, p=0.90931 b-rank test for bits 24 to 31, p=0.74953 b-rank test for bits 25 to 32, p=0.06434 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 = 0.711247 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-12-13_07:31 (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 142352 1.03 0.849496 2 141845 -0.15 0.440263 3 142911 2.34 0.990367 4 142681 1.80 0.964303 5 141374 -1.25 0.105509 6 142168 0.60 0.727201 7 141416 -1.15 0.124529 8 141041 -2.03 0.021239 9 141798 -0.26 0.397387 10 142023 0.27 0.604720 11 141947 0.09 0.535067 12 141587 -0.75 0.225693 13 142358 1.05 0.852749 14 142655 1.74 0.959265 15 142081 0.40 0.655826 16 141249 -1.54 0.061436 17 142065 0.36 0.641965 18 141962 0.12 0.548971 19 142294 0.90 0.815610 20 141020 -2.08 0.018860 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-12-13_07:31 Bits used No. missing words z-score p-value 23 to 32 141280 -2.1701 0.015000 22 to 31 141300 -2.1011 0.017814 21 to 30 141960 0.1747 0.569352 20 to 29 142408 1.7196 0.957243 19 to 28 141549 -1.2425 0.107023 18 to 27 141919 0.0333 0.513300 17 to 26 142281 1.2816 0.900012 16 to 25 141860 -0.1701 0.432464 15 to 24 141698 -0.7287 0.233085 14 to 23 141319 -2.0356 0.020894 13 to 22 141836 -0.2529 0.400187 12 to 21 142076 0.5747 0.717261 11 to 20 141957 0.1644 0.565284 10 to 19 142276 1.2644 0.896953 9 to 18 142228 1.0989 0.864086 8 to 17 141934 0.0851 0.533897 7 to 16 141781 -0.4425 0.329058 6 to 15 142322 1.4230 0.922632 5 to 14 142772 2.9747 0.998534 4 to 13 142247 1.1644 0.877865 3 to 12 142251 1.1782 0.880636 2 to 11 141165 -2.5667 0.005134 1 to 10 141891 -0.0632 0.474801 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-12-13_07:31 Bits used No. missing words z-score p-value 28 to 32 142045 0.4599 0.677205 27 to 31 141812 -0.3299 0.370726 26 to 30 142160 0.8497 0.802262 25 to 29 141929 0.0667 0.526581 24 to 28 141965 0.1887 0.574841 23 to 27 142157 0.8396 0.799422 22 to 26 141904 -0.0181 0.492792 21 to 25 141940 0.1040 0.541402 20 to 24 141993 0.2836 0.611652 19 to 23 141686 -0.7571 0.224510 18 to 22 141718 -0.6486 0.258306 17 to 21 141950 0.1379 0.554826 16 to 20 141932 0.0768 0.530628 15 to 19 141525 -1.3028 0.096319 14 to 18 142044 0.4565 0.675988 13 to 17 141622 -0.9740 0.165028 12 to 16 141812 -0.3299 0.370726 11 to 15 141932 0.0768 0.530628 10 to 14 141809 -0.3401 0.366890 9 to 13 141679 -0.7808 0.217466 8 to 12 141684 -0.7638 0.222484 7 to 11 141763 -0.4960 0.309935 6 to 10 142116 0.7006 0.758216 5 to 9 142166 0.8701 0.807868 4 to 8 142203 0.9955 0.840251 3 to 7 142136 0.7684 0.778867 2 to 6 142410 1.6972 0.955169 1 to 5 141791 -0.4011 0.344166 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-12-13_07:31 Bits used No. missing words z-score p-value 31 to 32 142149 0.7070 0.760214 30 to 31 142385 1.4032 0.919715 29 to 30 142295 1.1377 0.872371 28 to 29 142020 0.3265 0.627962 27 to 28 141750 -0.4700 0.319178 26 to 27 142401 1.4504 0.926520 25 to 26 142291 1.1259 0.869890 24 to 25 141983 0.2173 0.586019 23 to 24 141694 -0.6352 0.262652 22 to 23 141708 -0.5939 0.276292 21 to 22 142102 0.5683 0.715101 20 to 21 141820 -0.2635 0.396079 19 to 20 141184 -2.1396 0.016193 18 to 19 142751 2.4828 0.993482 17 to 18 142050 0.4150 0.660913 16 to 17 141799 -0.3255 0.372418 15 to 16 141383 -1.5526 0.060260 14 to 15 142312 1.1878 0.882547 13 to 14 142145 0.6952 0.756532 12 to 13 141713 -0.5791 0.281246 11 to 12 142086 0.5212 0.698869 10 to 11 142423 1.5153 0.935146 9 to 10 142039 0.3825 0.648958 8 to 9 142156 0.7276 0.766583 7 to 8 141962 0.1554 0.561735 6 to 7 141915 0.0167 0.506672 5 to 6 141950 0.1200 0.547747 4 to 5 142098 0.5565 0.711082 3 to 4 141802 -0.3166 0.375771 2 to 3 141636 -0.8063 0.210040 1 to 2 142303 1.1613 0.877234 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-12-13_07:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2615.56 1.634 0.948905 Test results for specific bytes for dh-ranFile-2016-12-13_07:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2429.72 -0.994 0.160128 2 to 9 2525.65 0.363 0.641623 3 to 10 2342.04 -2.234 0.012744 4 to 11 2430.66 -0.981 0.163379 5 to 12 2540.39 0.571 0.716061 6 to 13 2476.79 -0.328 0.371383 7 to 14 2372.99 -1.796 0.036226 8 to 15 2506.38 0.090 0.535968 9 to 16 2389.86 -1.558 0.059667 10 to 17 2522.48 0.318 0.624727 11 to 18 2413.14 -1.228 0.109662 12 to 19 2559.76 0.845 0.801000 13 to 20 2548.06 0.680 0.751647 14 to 21 2473.83 -0.370 0.355652 15 to 22 2375.36 -1.763 0.038977 16 to 23 2401.82 -1.388 0.082495 17 to 24 2498.10 -0.027 0.489296 18 to 25 2489.80 -0.144 0.442638 19 to 26 2582.62 1.168 0.878688 20 to 27 2378.13 -1.723 0.042404 21 to 28 2504.38 0.062 0.524724 22 to 29 2478.73 -0.301 0.381774 23 to 30 2480.77 -0.272 0.392813 24 to 31 2629.78 1.835 0.966771 25 to 32 2458.21 -0.591 0.277246 CDPARK for dh-ranFile-2016-12-13_07:31: 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 3480 -1.9635 0.024796 3532 0.4110 0.659449 3511 -0.5479 0.291865 3538 0.6849 0.753306 3479 -2.0091 0.022262 3548 1.1416 0.873180 3491 -1.4612 0.071982 3534 0.5023 0.692266 3515 -0.3653 0.357445 Square side=100, avg. no. parked=3517.10 sample std.=24.74 p-value of the KSTEST for those 10 p-values: 0.415773 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-12-13_07:31 0.0669,0.2167,0.0938,0.2014,0.3059,0.0162,0.3181,0.6311,0.9589,0.0323, The KS test for those 10 p-values: 0.014560 The 3DSPHERES test for dh-ranFile-2016-12-13_07:31 sample no r^3 equiv. uni. 1 28.770 0.616724 2 38.930 0.726834 3 36.138 0.700183 4 84.370 0.939935 5 8.298 0.241648 6 62.361 0.874907 7 11.957 0.328727 8 33.073 0.667934 9 9.870 0.280355 10 47.380 0.793886 11 38.970 0.727199 12 22.957 0.534776 13 1.549 0.050334 14 20.556 0.496019 15 11.327 0.314482 16 29.328 0.623782 17 39.080 0.728193 18 45.159 0.778047 19 40.212 0.738260 20 60.704 0.867805 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.111117 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-12-13_07:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -0.3 -0.8 -0.3 -0.6 -0.6 0.3 -1.2 0.6 1.4 0.2 1.0 -1.4 -0.6 -0.5 -1.3 0.3 -0.3 2.2 0.5 0.7 -1.4 0.3 -1.2 0.9 -0.4 -0.7 0.8 -0.2 0.3 0.7 -0.3 1.3 -1.0 -0.2 0.1 1.0 0.5 1.7 1.0 0.1 -1.0 0.8 Chi-square with 42 degrees of freedom:32.962031 z-score=-0.986123, p-value=0.160327 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-12-13_07:31 Test no p-value 1 0.870317 2 0.050670 3 0.886799 4 0.833099 5 0.241787 6 0.319486 7 0.082090 8 0.036970 9 0.303951 10 0.021964 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.059964 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-12-13_07:31: (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 66790 0.23 66528 0.29 3 25000.00 24818 1.32 24969 0.04 4 6666.67 6740 0.81 6823 3.67 5 1388.89 1355 0.83 1391 0.00 6 238.10 255 1.20 252 0.81 7 34.72 32 0.21 32 0.21 8 4.96 9 3.29 4 0.19 p=0.75377 p=0.48243 Number of rngs required: 688360, p-value: 0.480 RESULTS OF CRAPS TEST for dh-ranFile-2016-12-13_07:31 No. of wins: Observed Expected 98585 98585.9 z-score=-0.004, pvalue=0.49847 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66735 66666.7 0.070 0.070 2 37785 37654.3 0.454 0.524 3 26823 26954.7 0.644 1.167 4 19184 19313.5 0.868 2.035 5 13939 13851.4 0.554 2.589 6 10018 9943.5 0.558 3.146 7 7234 7145.0 1.108 4.254 8 5087 5139.1 0.528 4.782 9 3636 3699.9 1.102 5.884 10 2594 2666.3 1.960 7.845 11 1878 1923.3 1.068 8.913 12 1356 1388.7 0.772 9.685 13 1065 1003.7 3.742 13.427 14 717 726.1 0.115 13.542 15 523 525.8 0.015 13.557 16 398 381.2 0.745 14.302 17 265 276.5 0.482 14.784 18 219 200.8 1.644 16.428 19 143 146.0 0.061 16.489 20 109 106.2 0.073 16.562 21 292 287.1 0.083 16.645 Chisq= 16.64 for 20 degrees of freedom, p= 0.32410 SUMMARY of craptest p-value for no. of wins: 0.498468 p-value for throws/game: 0.324096 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-12-13_07:31 No. of wins: Observed Expected 98616 98585.9 z-score= 0.135, pvalue=0.55362 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66772 66666.7 0.166 0.166 2 37487 37654.3 0.744 0.910 3 26680 26954.7 2.800 3.710 4 19443 19313.5 0.869 4.579 5 13909 13851.4 0.239 4.818 6 10049 9943.5 1.118 5.937 7 7336 7145.0 5.104 11.041 8 5102 5139.1 0.267 11.309 9 3692 3699.9 0.017 11.325 10 2577 2666.3 2.991 14.316 11 1898 1923.3 0.334 14.650 12 1407 1388.7 0.240 14.890 13 1002 1003.7 0.003 14.893 14 672 726.1 4.037 18.929 15 539 525.8 0.330 19.259 16 399 381.2 0.836 20.095 17 287 276.5 0.396 20.490 18 182 200.8 1.765 22.256 19 142 146.0 0.109 22.365 20 114 106.2 0.571 22.935 21 311 287.1 1.987 24.922 Chisq= 24.92 for 20 degrees of freedom, p= 0.79558 SUMMARY of craptest p-value for no. of wins: 0.553619 p-value for throws/game: 0.795582 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0007,0.0051,0.0117,0.0127,0.0146,0.0150,0.0162,0.0162,0.0178,0.0189, 0.0209,0.0212,0.0220,0.0223,0.0248,0.0268,0.0294,0.0323,0.0349,0.0362, 0.0370,0.0390,0.0390,0.0424,0.0503,0.0507,0.0512,0.0578,0.0597,0.0598, 0.0600,0.0603,0.0614,0.0643,0.0669,0.0720,0.0727,0.0821,0.0825,0.0869, 0.0938,0.0963,0.1055,0.1070,0.1097,0.1111,0.1245,0.1263,0.1299,0.1501, 0.1593,0.1601,0.1603,0.1634,0.1650,0.1751,0.1777,0.2014,0.2094,0.2100, 0.2165,0.2167,0.2175,0.2225,0.2245,0.2257,0.2283,0.2308,0.2331,0.2416, 0.2418,0.2583,0.2618,0.2620,0.2627,0.2752,0.2763,0.2772,0.2804,0.2812, 0.2889,0.2919,0.3015,0.3040,0.3059,0.3084,0.3099,0.3145,0.3181,0.3192, 0.3195,0.3241,0.3287,0.3291,0.3442,0.3503,0.3510,0.3557,0.3574,0.3669, 0.3707,0.3707,0.3714,0.3724,0.3758,0.3818,0.3862,0.3928,0.3961,0.3974, 0.4002,0.4158,0.4169,0.4181,0.4291,0.4325,0.4403,0.4426,0.4498,0.4610, 0.4725,0.4748,0.4803,0.4824,0.4893,0.4893,0.4928,0.4960,0.4969,0.4985, 0.5067,0.5133,0.5247,0.5266,0.5306,0.5306,0.5339,0.5348,0.5351,0.5360, 0.5414,0.5477,0.5483,0.5490,0.5536,0.5548,0.5617,0.5632,0.5645,0.5653, 0.5694,0.5748,0.5800,0.5808,0.5860,0.6047,0.6117,0.6134,0.6167,0.6181, 0.6238,0.6247,0.6278,0.6280,0.6291,0.6311,0.6400,0.6416,0.6420,0.6425, 0.6462,0.6490,0.6558,0.6594,0.6609,0.6679,0.6726,0.6760,0.6772,0.6921, 0.6923,0.6989,0.7002,0.7036,0.7111,0.7112,0.7151,0.7157,0.7161,0.7173, 0.7259,0.7268,0.7272,0.7272,0.7282,0.7383,0.7495,0.7516,0.7533,0.7538, 0.7565,0.7582,0.7602,0.7632,0.7666,0.7780,0.7789,0.7939,0.7956,0.7994, 0.8010,0.8023,0.8079,0.8156,0.8194,0.8242,0.8252,0.8259,0.8277,0.8331, 0.8403,0.8451,0.8495,0.8527,0.8553,0.8641,0.8678,0.8699,0.8703,0.8724, 0.8732,0.8733,0.8749,0.8772,0.8779,0.8787,0.8806,0.8822,0.8823,0.8825, 0.8868,0.8914,0.8970,0.9000,0.9022,0.9093,0.9101,0.9135,0.9154,0.9197, 0.9226,0.9265,0.9351,0.9399,0.9489,0.9552,0.9553,0.9555,0.9572,0.9589, 0.9593,0.9627,0.9643,0.9668,0.9722,0.9904,0.9929,0.9935,0.9985, Overall p-value after applying KStest on 269 p-values = 0.143852 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.