RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-04-22_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 15.44 27.2705 0.945782 2 to 25 15.59 30.2306 0.975271 3 to 26 15.74 21.8628 0.809947 4 to 27 15.87 12.9499 0.260463 5 to 28 15.80 22.0153 0.815870 6 to 29 15.79 13.8389 0.321530 7 to 30 15.89 13.2382 0.279900 8 to 31 15.78 17.8171 0.599533 9 to 32 15.94 22.6445 0.838814 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.149104 Tough bday spacings test for dh-ranFile-2017-04-22_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 12 40 68 102 98 76 48 32 9 9 6 (O-E)^2/E 0.9 0.3 0.4 0.2 0.0 0.1 0.3 0.2 2.3 0.9 0.9 Birthday Spacings: Sum(O-E)^2/E= 6.416, p= 0.221 RESULTS OF GCD FOR dh-ranFile-2017-04-22_00:31 Euclid's algorithm: p-value, steps to gcd: 0.457950 p-value, dist. of gcd's: 0.390361 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-04-22_00:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.746 0.362 0.605 0.656 0.458 0.182 0.449 0.494 Bits 8 to 15---> 0.819 0.838 0.727 0.379 0.311 0.239 0.024 0.277 Bits 16 to 23---> 0.299 0.334 0.359 0.012 0.326 0.204 0.826 0.547 Bits 24 to 31---> 0.548 0.982 0.903 0.683 0.221 0.154 0.037 0.154 KS test for the above 32 p values: 0.593 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-04-22_00:31, p-values for 5 runs: 0.2143, 0.1403, 0.5021, 0.1306, 0.6382 Rank test for binary matrices (31x31) for dh-ranFile-2017-04-22_00:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 204 211.4 0.260 0.260 r= 29 5230 5134.0 1.795 2.055 r= 30 23033 23103.0 0.212 2.267 r= 31 11533 11551.5 0.030 2.297 chi-square = 2.297 with df = 3; p-value = 0.487 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2017-04-22_00:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 242 211.4 4.424 4.424 r= 30 5100 5134.0 0.225 4.649 r= 31 23148 23103.0 0.087 4.737 r= 32 11510 11551.5 0.149 4.886 chi-square = 4.886 with df = 3; p-value = 0.820 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2017-04-22_00:31 b-rank test for bits 1 to 8, p=0.85468 b-rank test for bits 2 to 9, p=0.88754 b-rank test for bits 3 to 10, p=0.94452 b-rank test for bits 4 to 11, p=0.73391 b-rank test for bits 5 to 12, p=0.62149 b-rank test for bits 6 to 13, p=0.11691 b-rank test for bits 7 to 14, p=0.58030 b-rank test for bits 8 to 15, p=0.00477 b-rank test for bits 9 to 16, p=0.85441 b-rank test for bits 10 to 17, p=0.63659 b-rank test for bits 11 to 18, p=0.28505 b-rank test for bits 12 to 19, p=0.81124 b-rank test for bits 13 to 20, p=0.38201 b-rank test for bits 14 to 21, p=0.52932 b-rank test for bits 15 to 22, p=0.27854 b-rank test for bits 16 to 23, p=0.50697 b-rank test for bits 17 to 24, p=0.24556 b-rank test for bits 18 to 25, p=0.12404 b-rank test for bits 19 to 26, p=0.10289 b-rank test for bits 20 to 27, p=0.57224 b-rank test for bits 21 to 28, p=0.30111 b-rank test for bits 22 to 29, p=0.09088 b-rank test for bits 23 to 30, p=0.56708 b-rank test for bits 24 to 31, p=0.77394 b-rank test for bits 25 to 32, p=0.41920 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 = 0.969935 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-04-22_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 141918 0.02 0.508081 2 141851 -0.14 0.445798 3 142385 1.11 0.866797 4 141909 -0.00 0.499692 5 141901 -0.02 0.492236 6 141867 -0.10 0.460608 7 141619 -0.68 0.248778 8 141437 -1.10 0.134889 9 141528 -0.89 0.186476 10 142454 1.27 0.898419 11 140973 -2.19 0.014346 12 141463 -1.04 0.148514 13 141921 0.03 0.510876 14 141896 -0.03 0.487577 15 141383 -1.23 0.109397 16 141846 -0.15 0.441184 17 140899 -2.36 0.009123 18 142233 0.76 0.775247 19 142114 0.48 0.683746 20 141534 -0.88 0.190260 ---------------------------------------------------------------- OPSO test for dh-ranFile-2017-04-22_00:31 Bits used No. missing words z-score p-value 23 to 32 141418 -1.6942 0.045110 22 to 31 141817 -0.3184 0.375099 21 to 30 141578 -1.1425 0.126620 20 to 29 141959 0.1713 0.567997 19 to 28 141960 0.1747 0.569352 18 to 27 142383 1.6333 0.948802 17 to 26 141952 0.1471 0.558488 16 to 25 141541 -1.2701 0.102024 15 to 24 142221 1.0747 0.858751 14 to 23 142093 0.6333 0.736746 13 to 22 142012 0.3540 0.638344 12 to 21 141963 0.1851 0.573413 11 to 20 142014 0.3609 0.640925 10 to 19 141803 -0.3667 0.356938 9 to 18 141582 -1.1287 0.129507 8 to 17 142000 0.3127 0.622729 7 to 16 142139 0.7920 0.785810 6 to 15 142244 1.1540 0.875757 5 to 14 141969 0.2058 0.581510 4 to 13 141295 -2.1184 0.017071 3 to 12 141853 -0.1942 0.422994 2 to 11 141796 -0.3908 0.347975 1 to 10 141904 -0.0184 0.492668 ----------------------------------------------------------------- OQSO test for dh-ranFile-2017-04-22_00:31 Bits used No. missing words z-score p-value 28 to 32 142806 3.0396 0.998815 27 to 31 141765 -0.4893 0.312331 26 to 30 141554 -1.2045 0.114197 25 to 29 142079 0.5752 0.717406 24 to 28 141905 -0.0147 0.494145 23 to 27 142100 0.6463 0.740970 22 to 26 142048 0.4701 0.680847 21 to 25 141815 -0.3198 0.374574 20 to 24 142143 0.7921 0.785849 19 to 23 141967 0.1955 0.577496 18 to 22 142189 0.9480 0.828444 17 to 21 141511 -1.3503 0.088465 16 to 20 142356 1.5141 0.935004 15 to 19 142070 0.5446 0.707001 14 to 18 141643 -0.9028 0.183312 13 to 17 141921 0.0396 0.515778 12 to 16 141689 -0.7469 0.227568 11 to 15 141659 -0.8486 0.198059 10 to 14 142073 0.5548 0.710489 9 to 13 142044 0.4565 0.675988 8 to 12 141654 -0.8655 0.193375 7 to 11 141728 -0.6147 0.269384 6 to 10 141791 -0.4011 0.344166 5 to 9 141912 0.0091 0.503611 4 to 8 141550 -1.2181 0.111599 3 to 7 142071 0.5480 0.708166 2 to 6 141967 0.1955 0.577496 1 to 5 141992 0.2802 0.610352 ----------------------------------------------------------------- DNA test for dh-ranFile-2017-04-22_00:31 Bits used No. missing words z-score p-value 31 to 32 142205 0.8722 0.808446 30 to 31 140974 -2.7591 0.002898 29 to 30 141471 -1.2930 0.098004 28 to 29 142232 0.9518 0.829408 27 to 28 141491 -1.2340 0.108599 26 to 27 142006 0.2852 0.612240 25 to 26 142203 0.8663 0.806833 24 to 25 141996 0.2557 0.600895 23 to 24 141795 -0.3373 0.367962 22 to 23 141612 -0.8771 0.190222 21 to 22 141346 -1.6617 0.048282 20 to 21 142122 0.6273 0.734784 19 to 20 142111 0.5949 0.724044 18 to 19 142435 1.5506 0.939507 17 to 18 141868 -0.1219 0.451482 16 to 17 142127 0.6421 0.739594 15 to 16 142174 0.7807 0.782522 14 to 15 142100 0.5624 0.713095 13 to 14 142142 0.6863 0.753751 12 to 13 141532 -1.1131 0.132840 11 to 12 142362 1.3353 0.909113 10 to 11 141716 -0.5703 0.284239 9 to 10 142006 0.2852 0.612240 8 to 9 141882 -0.0806 0.467872 7 to 8 141631 -0.8210 0.205814 6 to 7 141761 -0.4376 0.330856 5 to 6 141864 -0.1337 0.446813 4 to 5 141717 -0.5673 0.285240 3 to 4 141638 -0.8004 0.211744 2 to 3 142180 0.7984 0.787691 1 to 2 142208 0.8810 0.810850 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2017-04-22_00:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2488.11 -0.168 0.433226 Test results for specific bytes for dh-ranFile-2017-04-22_00:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2519.55 0.276 0.608886 2 to 9 2514.70 0.208 0.582332 3 to 10 2497.92 -0.029 0.488273 4 to 11 2450.68 -0.697 0.242747 5 to 12 2558.02 0.820 0.794023 6 to 13 2557.03 0.806 0.790011 7 to 14 2584.72 1.198 0.884561 8 to 15 2538.59 0.546 0.707399 9 to 16 2452.11 -0.677 0.249123 10 to 17 2369.46 -1.846 0.032441 11 to 18 2428.87 -1.006 0.157223 12 to 19 2405.81 -1.332 0.091414 13 to 20 2451.49 -0.686 0.246359 14 to 21 2559.73 0.845 0.800873 15 to 22 2528.48 0.403 0.656447 16 to 23 2603.90 1.469 0.929135 17 to 24 2518.09 0.256 0.600934 18 to 25 2427.30 -1.028 0.151945 19 to 26 2448.40 -0.730 0.232757 20 to 27 2398.14 -1.441 0.074857 21 to 28 2474.29 -0.364 0.358073 22 to 29 2582.56 1.168 0.878505 23 to 30 2624.15 1.756 0.960439 24 to 31 2554.44 0.770 0.779318 25 to 32 2699.29 2.818 0.997586 CDPARK for dh-ranFile-2017-04-22_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 3542 0.8676 0.807188 3517 -0.2740 0.392053 3552 1.3242 0.907282 3521 -0.0913 0.463617 3549 1.1872 0.882429 3532 0.4110 0.659449 3538 0.6849 0.753306 3539 0.7306 0.767486 3495 -1.2785 0.100530 3514 -0.4110 0.340551 Square side=100, avg. no. parked=3529.90 sample std.=16.94 p-value of the KSTEST for those 10 p-values: 0.388842 Results for the MINIMUM DISTANCE test for dh-ranFile-2017-04-22_00:31 0.7373,0.4005,0.5843,0.8629,0.0215,0.7965,0.4383,0.2206,0.5606,0.1422, The KS test for those 10 p-values: 0.974486 The 3DSPHERES test for dh-ranFile-2017-04-22_00:31 sample no r^3 equiv. uni. 1 38.985 0.727332 2 12.137 0.332730 3 12.974 0.351104 4 23.236 0.539074 5 0.182 0.006039 6 32.695 0.663732 7 46.087 0.784807 8 2.930 0.093053 9 71.021 0.906274 10 45.343 0.779409 11 19.393 0.476089 12 37.735 0.715729 13 45.949 0.783818 14 22.114 0.521511 15 14.341 0.379990 16 14.334 0.379847 17 0.006 0.000206 18 50.095 0.811724 19 8.372 0.243512 20 17.208 0.436513 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.427008 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-04-22_00:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -0.3 -3.0 -0.3 -0.8 1.1 2.1 -0.2 1.0 2.0 -0.1 -2.2 0.9 1.5 -1.6 -0.6 -0.9 1.2 0.6 -0.1 0.3 -1.1 0.1 1.1 0.5 -0.8 -0.2 -1.1 0.2 -1.0 -0.2 -0.3 0.5 0.3 -0.8 0.4 0.0 -1.3 -1.6 -0.7 -0.6 -1.0 0.8 Chi-square with 42 degrees of freedom:47.419229 z-score=0.591286, p-value=0.738811 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2017-04-22_00:31 Test no p-value 1 0.013410 2 0.984939 3 0.004394 4 0.015941 5 0.215980 6 0.832583 7 0.098150 8 0.260496 9 0.041269 10 0.004966 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000072 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-04-22_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 66447 0.72 66500 0.42 3 25000.00 25168 1.13 25205 1.68 4 6666.67 6734 0.68 6666 0.00 5 1388.89 1387 0.00 1349 1.15 6 238.10 227 0.52 239 0.00 7 34.72 30 0.64 37 0.15 8 4.96 6 0.22 3 0.77 p=0.31143 p=0.34647 Number of rngs required: 688790, p-value: 0.672 RESULTS OF CRAPS TEST for dh-ranFile-2017-04-22_00:31 No. of wins: Observed Expected 98335 98585.9 z-score=-1.122, pvalue=0.13093 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66573 66666.7 0.132 0.132 2 37687 37654.3 0.028 0.160 3 26938 26954.7 0.010 0.170 4 19294 19313.5 0.020 0.190 5 13975 13851.4 1.103 1.293 6 9912 9943.5 0.100 1.393 7 7253 7145.0 1.632 3.024 8 5049 5139.1 1.579 4.603 9 3731 3699.9 0.262 4.865 10 2726 2666.3 1.337 6.202 11 1962 1923.3 0.778 6.979 12 1306 1388.7 4.930 11.909 13 961 1003.7 1.818 13.727 14 767 726.1 2.299 16.026 15 512 525.8 0.364 16.390 16 382 381.2 0.002 16.392 17 247 276.5 3.155 19.547 18 200 200.8 0.003 19.551 19 140 146.0 0.245 19.796 20 103 106.2 0.097 19.893 21 282 287.1 0.091 19.984 Chisq= 19.98 for 20 degrees of freedom, p= 0.54109 SUMMARY of craptest p-value for no. of wins: 0.130934 p-value for throws/game: 0.541092 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2017-04-22_00:31 No. of wins: Observed Expected 98789 98585.9 z-score= 0.909, pvalue=0.81821 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67006 66666.7 1.727 1.727 2 37675 37654.3 0.011 1.739 3 26836 26954.7 0.523 2.262 4 19280 19313.5 0.058 2.320 5 13836 13851.4 0.017 2.337 6 9874 9943.5 0.486 2.823 7 7127 7145.0 0.045 2.869 8 5158 5139.1 0.070 2.938 9 3702 3699.9 0.001 2.939 10 2650 2666.3 0.100 3.039 11 1939 1923.3 0.128 3.167 12 1353 1388.7 0.920 4.087 13 978 1003.7 0.659 4.745 14 709 726.1 0.405 5.150 15 507 525.8 0.675 5.825 16 367 381.2 0.525 6.350 17 264 276.5 0.569 6.919 18 211 200.8 0.515 7.434 19 141 146.0 0.170 7.604 20 111 106.2 0.216 7.819 21 276 287.1 0.430 8.250 Chisq= 8.25 for 20 degrees of freedom, p= 0.00992 SUMMARY of craptest p-value for no. of wins: 0.818211 p-value for throws/game: 0.009917 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0001,0.0002,0.0029,0.0044,0.0048,0.0050,0.0060,0.0091,0.0099,0.0117, 0.0134,0.0143,0.0159,0.0171,0.0215,0.0242,0.0324,0.0373,0.0413,0.0451, 0.0483,0.0749,0.0885,0.0909,0.0914,0.0931,0.0980,0.0982,0.1005,0.1020, 0.1029,0.1086,0.1094,0.1116,0.1142,0.1169,0.1240,0.1266,0.1295,0.1306, 0.1309,0.1328,0.1349,0.1403,0.1422,0.1485,0.1491,0.1519,0.1541,0.1543, 0.1572,0.1818,0.1833,0.1865,0.1902,0.1903,0.1934,0.1981,0.2042,0.2058, 0.2117,0.2143,0.2160,0.2206,0.2208,0.2211,0.2276,0.2328,0.2388,0.2427, 0.2435,0.2456,0.2464,0.2488,0.2491,0.2605,0.2605,0.2694,0.2766,0.2785, 0.2799,0.2842,0.2851,0.2852,0.2992,0.3011,0.3107,0.3114,0.3123,0.3215, 0.3255,0.3309,0.3327,0.3343,0.3406,0.3442,0.3465,0.3480,0.3511,0.3569, 0.3581,0.3590,0.3621,0.3680,0.3746,0.3751,0.3794,0.3798,0.3800,0.3820, 0.3888,0.3904,0.3921,0.4005,0.4192,0.4230,0.4270,0.4332,0.4365,0.4383, 0.4412,0.4458,0.4468,0.4493,0.4515,0.4579,0.4579,0.4606,0.4636,0.4679, 0.4761,0.4869,0.4876,0.4883,0.4922,0.4927,0.4941,0.4941,0.4997,0.5021, 0.5036,0.5070,0.5081,0.5109,0.5158,0.5215,0.5293,0.5391,0.5411,0.5473, 0.5480,0.5585,0.5606,0.5671,0.5680,0.5694,0.5722,0.5734,0.5775,0.5775, 0.5803,0.5815,0.5823,0.5843,0.5932,0.5995,0.6009,0.6009,0.6049,0.6089, 0.6104,0.6122,0.6122,0.6215,0.6227,0.6366,0.6382,0.6383,0.6409,0.6564, 0.6564,0.6594,0.6637,0.6721,0.6760,0.6808,0.6832,0.6837,0.7070,0.7074, 0.7082,0.7105,0.7131,0.7157,0.7174,0.7240,0.7273,0.7274,0.7339,0.7348, 0.7367,0.7373,0.7388,0.7396,0.7410,0.7463,0.7533,0.7538,0.7675,0.7739, 0.7752,0.7793,0.7794,0.7825,0.7838,0.7848,0.7858,0.7858,0.7877,0.7900, 0.7940,0.7965,0.8009,0.8068,0.8072,0.8084,0.8099,0.8108,0.8112,0.8117, 0.8159,0.8182,0.8191,0.8196,0.8256,0.8284,0.8294,0.8326,0.8385,0.8388, 0.8544,0.8547,0.8588,0.8629,0.8668,0.8758,0.8785,0.8824,0.8846,0.8875, 0.8984,0.9025,0.9063,0.9073,0.9091,0.9291,0.9350,0.9395,0.9445,0.9458, 0.9488,0.9604,0.9699,0.9745,0.9753,0.9820,0.9849,0.9976,0.9988, Overall p-value after applying KStest on 269 p-values = 0.225411 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.