RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-05-31_08:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.69 12.9174 0.258303 2 to 25 15.74 29.6928 0.971353 3 to 26 15.51 30.7176 0.978389 4 to 27 15.72 12.8599 0.254485 5 to 28 15.89 11.0558 0.146350 6 to 29 15.95 15.8363 0.464530 7 to 30 15.88 19.4428 0.696283 8 to 31 15.53 29.6194 0.970775 9 to 32 16.21 11.7349 0.184083 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.180169 Tough bday spacings test for dh-ranFile-2016-05-31_08:31: 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 11 42 63 98 114 74 41 30 11 11 5 (O-E)^2/E 0.4 0.8 1.4 0.0 2.7 0.2 2.4 0.0 1.0 2.9 0.2 Birthday Spacings: Sum(O-E)^2/E= 12.042, p= 0.718 RESULTS OF GCD FOR dh-ranFile-2016-05-31_08:31 Euclid's algorithm: p-value, steps to gcd: 0.072395 p-value, dist. of gcd's: 0.523969 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-05-31_08:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.172 0.566 0.648 0.227 0.126 0.390 0.398 0.628 Bits 8 to 15---> 0.358 0.594 0.967 0.512 0.837 0.326 0.488 0.996 Bits 16 to 23---> 0.588 0.172 0.273 0.763 0.635 0.598 0.509 0.783 Bits 24 to 31---> 0.343 0.516 0.337 0.094 0.820 0.423 0.774 0.129 KS test for the above 32 p values: 0.497 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-05-31_08:31, p-values for 5 runs: 0.2739, 0.9332, 0.7490, 0.7959, 0.1691 Rank test for binary matrices (31x31) for dh-ranFile-2016-05-31_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 216 211.4 0.099 0.099 r= 29 5088 5134.0 0.412 0.512 r= 30 23203 23103.0 0.432 0.944 r= 31 11493 11551.5 0.297 1.241 chi-square = 1.241 with df = 3; p-value = 0.257 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-05-31_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 193 211.4 1.605 1.605 r= 30 5112 5134.0 0.094 1.699 r= 31 23151 23103.0 0.100 1.798 r= 32 11544 11551.5 0.005 1.803 chi-square = 1.803 with df = 3; p-value = 0.386 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-05-31_08:31 b-rank test for bits 1 to 8, p=0.43403 b-rank test for bits 2 to 9, p=0.39911 b-rank test for bits 3 to 10, p=0.84603 b-rank test for bits 4 to 11, p=0.95755 b-rank test for bits 5 to 12, p=0.18570 b-rank test for bits 6 to 13, p=0.81955 b-rank test for bits 7 to 14, p=0.34241 b-rank test for bits 8 to 15, p=0.17231 b-rank test for bits 9 to 16, p=0.41793 b-rank test for bits 10 to 17, p=0.07195 b-rank test for bits 11 to 18, p=0.68213 b-rank test for bits 12 to 19, p=0.04265 b-rank test for bits 13 to 20, p=0.76531 b-rank test for bits 14 to 21, p=0.28044 b-rank test for bits 15 to 22, p=0.35481 b-rank test for bits 16 to 23, p=0.19420 b-rank test for bits 17 to 24, p=0.41244 b-rank test for bits 18 to 25, p=0.70868 b-rank test for bits 19 to 26, p=0.27035 b-rank test for bits 20 to 27, p=0.66412 b-rank test for bits 21 to 28, p=0.08740 b-rank test for bits 22 to 29, p=0.35158 b-rank test for bits 23 to 30, p=0.94172 b-rank test for bits 24 to 31, p=0.18765 b-rank test for bits 25 to 32, p=0.19521 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 = 0.319547 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-05-31_08:31 (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 141746 -0.38 0.351375 2 142152 0.57 0.714638 3 142072 0.38 0.648053 4 141416 -1.15 0.124529 5 141566 -0.80 0.211227 6 141925 0.04 0.514603 7 142796 2.07 0.980851 8 141697 -0.50 0.309913 9 142261 0.82 0.794364 10 141823 -0.20 0.420073 11 142406 1.16 0.877066 12 141733 -0.41 0.340175 13 141427 -1.13 0.129884 14 142205 0.69 0.755160 15 141998 0.21 0.582063 16 141731 -0.42 0.338464 17 142323 0.97 0.833108 18 141678 -0.54 0.294429 19 141775 -0.31 0.376816 20 141608 -0.70 0.240703 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-05-31_08:31 Bits used No. missing words z-score p-value 23 to 32 141904 -0.0184 0.492668 22 to 31 142610 2.4161 0.992156 21 to 30 142014 0.3609 0.640925 20 to 29 142055 0.5023 0.692275 19 to 28 142000 0.3127 0.622729 18 to 27 141569 -1.1736 0.120287 17 to 26 141891 -0.0632 0.474801 16 to 25 141737 -0.5942 0.276175 15 to 24 142162 0.8713 0.808198 14 to 23 142159 0.8609 0.805362 13 to 22 141253 -2.2632 0.011811 12 to 21 141591 -1.0977 0.136170 11 to 20 142008 0.3402 0.633163 10 to 19 142042 0.4575 0.676338 9 to 18 141949 0.1368 0.554403 8 to 17 141692 -0.7494 0.226804 7 to 16 141713 -0.6770 0.249203 6 to 15 142151 0.8333 0.797675 5 to 14 142656 2.5747 0.994984 4 to 13 141776 -0.4598 0.322845 3 to 12 141146 -2.6322 0.004242 2 to 11 141652 -0.8873 0.187447 1 to 10 141734 -0.6046 0.272727 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-05-31_08:31 Bits used No. missing words z-score p-value 28 to 32 142398 1.6565 0.951191 27 to 31 142128 0.7413 0.770730 26 to 30 142211 1.0226 0.846754 25 to 29 141939 0.1006 0.540057 24 to 28 141469 -1.4926 0.067765 23 to 27 142156 0.8362 0.798470 22 to 26 141513 -1.3435 0.089556 21 to 25 142334 1.4396 0.925004 20 to 24 141525 -1.3028 0.096319 19 to 23 141746 -0.5537 0.289905 18 to 22 141132 -2.6350 0.004207 17 to 21 142171 0.8870 0.812465 16 to 20 141829 -0.2723 0.392694 15 to 19 142245 1.1379 0.872411 14 to 18 141558 -1.1909 0.116837 13 to 17 141894 -0.0520 0.479278 12 to 16 142250 1.1548 0.875917 11 to 15 141809 -0.3401 0.366890 10 to 14 141804 -0.3571 0.360527 9 to 13 141619 -0.9842 0.162516 8 to 12 141762 -0.4994 0.308741 7 to 11 141640 -0.9130 0.180626 6 to 10 141810 -0.3367 0.368167 5 to 9 141845 -0.2181 0.413688 4 to 8 141927 0.0599 0.523882 3 to 7 141681 -0.7740 0.219465 2 to 6 141631 -0.9435 0.172715 1 to 5 142025 0.3921 0.652509 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-05-31_08:31 Bits used No. missing words z-score p-value 31 to 32 141949 0.1170 0.546578 30 to 31 141423 -1.4346 0.075700 29 to 30 141339 -1.6824 0.046247 28 to 29 142273 1.0728 0.858314 27 to 28 141181 -2.1485 0.015838 26 to 27 141866 -0.1278 0.449147 25 to 26 141567 -1.0098 0.156290 24 to 25 141646 -0.7768 0.218643 23 to 24 141695 -0.6322 0.263614 22 to 23 141141 -2.2665 0.011712 21 to 22 141928 0.0551 0.521960 20 to 21 141754 -0.4582 0.323404 19 to 20 141262 -1.9095 0.028097 18 to 19 142196 0.8456 0.801122 17 to 18 141717 -0.5673 0.285240 16 to 17 142154 0.7217 0.764773 15 to 16 142151 0.7129 0.762043 14 to 15 141891 -0.0541 0.478439 13 to 14 142516 1.7896 0.963240 12 to 13 142360 1.3294 0.908144 11 to 12 141814 -0.2812 0.389275 10 to 11 142358 1.3235 0.907167 9 to 10 141799 -0.3255 0.372418 8 to 9 141446 -1.3668 0.085851 7 to 8 142322 1.2173 0.888258 6 to 7 142402 1.4533 0.926930 5 to 6 142522 1.8073 0.964641 4 to 5 141759 -0.4435 0.328720 3 to 4 141882 -0.0806 0.467872 2 to 3 142010 0.2970 0.616752 1 to 2 141801 -0.3196 0.374652 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-05-31_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2438.04 -0.876 0.190447 Test results for specific bytes for dh-ranFile-2016-05-31_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2607.64 1.522 0.936022 2 to 9 2467.44 -0.460 0.322601 3 to 10 2492.90 -0.100 0.459995 4 to 11 2506.89 0.097 0.538829 5 to 12 2467.35 -0.462 0.322140 6 to 13 2379.30 -1.707 0.043917 7 to 14 2546.68 0.660 0.745405 8 to 15 2386.39 -1.607 0.054068 9 to 16 2512.97 0.183 0.572790 10 to 17 2412.05 -1.244 0.106795 11 to 18 2565.08 0.920 0.821299 12 to 19 2447.42 -0.744 0.228563 13 to 20 2600.62 1.423 0.922634 14 to 21 2530.51 0.431 0.666920 15 to 22 2379.69 -1.701 0.044428 16 to 23 2543.39 0.614 0.730271 17 to 24 2543.33 0.613 0.729979 18 to 25 2565.81 0.931 0.824011 19 to 26 2564.43 0.911 0.818916 20 to 27 2557.87 0.818 0.793457 21 to 28 2467.06 -0.466 0.320656 22 to 29 2386.56 -1.604 0.054328 23 to 30 2544.44 0.628 0.735141 24 to 31 2509.48 0.134 0.553343 25 to 32 2380.20 -1.694 0.045110 CDPARK for dh-ranFile-2016-05-31_08:31: 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 3532 0.4110 0.659449 3527 0.1826 0.572463 3549 1.1872 0.882429 3537 0.6393 0.738676 3501 -1.0046 0.157553 3495 -1.2785 0.100530 3534 0.5023 0.692266 3504 -0.8676 0.192812 3580 2.6027 0.995376 3572 2.2374 0.987371 Square side=100, avg. no. parked=3533.10 sample std.=27.11 p-value of the KSTEST for those 10 p-values: 0.198891 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-05-31_08:31 0.9398,0.2646,0.8364,0.2448,0.3236,0.0007,0.3342,0.6069,0.2461,0.5393, The KS test for those 10 p-values: 0.408619 The 3DSPHERES test for dh-ranFile-2016-05-31_08:31 sample no r^3 equiv. uni. 1 12.977 0.351165 2 6.627 0.198209 3 112.900 0.976794 4 19.159 0.471986 5 3.484 0.109646 6 57.497 0.852888 7 20.508 0.495211 8 2.337 0.074946 9 29.633 0.627591 10 19.363 0.475557 11 44.847 0.775731 12 7.322 0.216559 13 14.030 0.373536 14 1.621 0.052597 15 80.873 0.932509 16 59.425 0.862045 17 65.074 0.885722 18 42.905 0.760732 19 80.680 0.932073 20 20.798 0.500054 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.693051 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-05-31_08:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 0.9 0.6 0.3 0.5 1.2 0.7 1.8 0.1 0.2 -0.3 -1.1 0.0 0.5 -1.2 -1.7 0.7 1.2 0.9 -0.6 -0.4 0.8 -2.4 1.0 0.5 1.2 0.6 0.4 -0.8 0.7 -0.6 -0.4 -0.9 0.9 -1.6 -0.1 0.3 -1.7 0.5 -0.7 0.9 1.0 1.8 Chi-square with 42 degrees of freedom:40.429845 z-score=-0.171318, p-value=0.459993 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-05-31_08:31 Test no p-value 1 0.969620 2 0.005165 3 0.414693 4 0.626778 5 0.036932 6 0.113866 7 0.962870 8 0.811408 9 0.949327 10 0.564915 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.183848 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-05-31_08:31: (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 66614 0.04 66806 0.29 3 25000.00 25063 0.16 24782 1.90 4 6666.67 6670 0.00 6731 0.62 5 1388.89 1379 0.07 1421 0.74 6 238.10 227 0.52 224 0.83 7 34.72 39 0.53 30 0.64 8 4.96 7 0.84 5 0.00 p=0.09521 p=0.46024 Number of rngs required: 688806, p-value: 0.679 RESULTS OF CRAPS TEST for dh-ranFile-2016-05-31_08:31 No. of wins: Observed Expected 98329 98585.9 z-score=-1.149, pvalue=0.12531 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66439 66666.7 0.777 0.777 2 37677 37654.3 0.014 0.791 3 26919 26954.7 0.047 0.839 4 19172 19313.5 1.036 1.875 5 14047 13851.4 2.762 4.636 6 9904 9943.5 0.157 4.793 7 7169 7145.0 0.080 4.874 8 5193 5139.1 0.566 5.440 9 3667 3699.9 0.292 5.732 10 2698 2666.3 0.377 6.109 11 1984 1923.3 1.914 8.023 12 1327 1388.7 2.745 10.767 13 1101 1003.7 9.429 20.197 14 757 726.1 1.311 21.508 15 545 525.8 0.698 22.207 16 395 381.2 0.503 22.710 17 262 276.5 0.764 23.474 18 196 200.8 0.116 23.590 19 145 146.0 0.007 23.597 20 89 106.2 2.790 26.387 21 314 287.1 2.518 28.905 Chisq= 28.90 for 20 degrees of freedom, p= 0.91035 SUMMARY of craptest p-value for no. of wins: 0.125315 p-value for throws/game: 0.910352 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-05-31_08:31 No. of wins: Observed Expected 98446 98585.9 z-score=-0.626, pvalue=0.26581 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66601 66666.7 0.065 0.065 2 37921 37654.3 1.889 1.953 3 26839 26954.7 0.497 2.450 4 19431 19313.5 0.715 3.166 5 13824 13851.4 0.054 3.220 6 9979 9943.5 0.126 3.346 7 6991 7145.0 3.320 6.667 8 5087 5139.1 0.528 7.194 9 3786 3699.9 2.005 9.200 10 2705 2666.3 0.562 9.761 11 1910 1923.3 0.092 9.854 12 1363 1388.7 0.477 10.331 13 973 1003.7 0.940 11.271 14 682 726.1 2.683 13.954 15 486 525.8 3.018 16.972 16 381 381.2 0.000 16.972 17 297 276.5 1.514 18.486 18 188 200.8 0.820 19.305 19 165 146.0 2.477 21.782 20 103 106.2 0.097 21.880 21 288 287.1 0.003 21.882 Chisq= 21.88 for 20 degrees of freedom, p= 0.65307 SUMMARY of craptest p-value for no. of wins: 0.265812 p-value for throws/game: 0.653070 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0007,0.0042,0.0042,0.0052,0.0117,0.0118,0.0158,0.0281,0.0369,0.0427, 0.0439,0.0444,0.0451,0.0462,0.0526,0.0541,0.0543,0.0678,0.0719,0.0724, 0.0749,0.0757,0.0859,0.0874,0.0896,0.0938,0.0952,0.0963,0.1005,0.1068, 0.1096,0.1139,0.1168,0.1203,0.1245,0.1253,0.1264,0.1294,0.1299,0.1362, 0.1463,0.1563,0.1576,0.1625,0.1691,0.1718,0.1722,0.1723,0.1727,0.1802, 0.1806,0.1838,0.1841,0.1857,0.1874,0.1877,0.1904,0.1928,0.1942,0.1952, 0.1982,0.1989,0.2112,0.2166,0.2186,0.2195,0.2266,0.2268,0.2286,0.2407, 0.2448,0.2461,0.2492,0.2545,0.2567,0.2583,0.2636,0.2646,0.2658,0.2704, 0.2727,0.2732,0.2739,0.2762,0.2804,0.2852,0.2899,0.2944,0.3087,0.3099, 0.3195,0.3207,0.3221,0.3226,0.3228,0.3234,0.3236,0.3258,0.3287,0.3342, 0.3366,0.3385,0.3402,0.3424,0.3430,0.3512,0.3514,0.3516,0.3548,0.3576, 0.3605,0.3669,0.3682,0.3724,0.3735,0.3747,0.3768,0.3858,0.3893,0.3899, 0.3927,0.3980,0.3991,0.4086,0.4124,0.4137,0.4147,0.4179,0.4201,0.4225, 0.4340,0.4491,0.4600,0.4600,0.4602,0.4645,0.4679,0.4720,0.4748,0.4756, 0.4784,0.4793,0.4879,0.4927,0.4952,0.4969,0.5001,0.5087,0.5119,0.5146, 0.5155,0.5220,0.5239,0.5240,0.5388,0.5393,0.5401,0.5466,0.5533,0.5544, 0.5649,0.5661,0.5725,0.5728,0.5821,0.5877,0.5941,0.5977,0.6069,0.6168, 0.6227,0.6268,0.6276,0.6283,0.6332,0.6347,0.6409,0.6476,0.6481,0.6525, 0.6531,0.6594,0.6641,0.6669,0.6763,0.6788,0.6821,0.6923,0.6923,0.6931, 0.6963,0.7087,0.7146,0.7177,0.7300,0.7303,0.7351,0.7387,0.7454,0.7490, 0.7552,0.7607,0.7620,0.7632,0.7648,0.7653,0.7707,0.7736,0.7757,0.7829, 0.7935,0.7944,0.7959,0.7977,0.7985,0.8011,0.8054,0.8082,0.8114,0.8125, 0.8189,0.8195,0.8201,0.8213,0.8240,0.8331,0.8364,0.8373,0.8460,0.8468, 0.8529,0.8583,0.8620,0.8724,0.8759,0.8771,0.8824,0.8857,0.8883,0.9072, 0.9081,0.9104,0.9226,0.9250,0.9269,0.9321,0.9325,0.9332,0.9360,0.9398, 0.9417,0.9493,0.9512,0.9576,0.9629,0.9632,0.9646,0.9670,0.9696,0.9708, 0.9714,0.9768,0.9784,0.9809,0.9874,0.9922,0.9950,0.9954,0.9957, Overall p-value after applying KStest on 269 p-values = 0.435810 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.