RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-10-12_01:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.87 12.5617 0.235002 2 to 25 15.44 18.1112 0.618142 3 to 26 15.69 17.4118 0.573177 4 to 27 15.67 23.0511 0.852407 5 to 28 15.83 15.6964 0.454552 6 to 29 15.83 24.9275 0.903657 7 to 30 15.92 15.7727 0.459996 8 to 31 16.08 12.7733 0.248776 9 to 32 15.78 21.0317 0.775126 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.671982 Tough bday spacings test for dh-ranFile-2016-10-12_01:31: 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 13 28 62 103 101 72 65 24 17 7 8 (O-E)^2/E 1.6 2.0 1.7 0.3 0.1 0.5 3.2 1.1 0.3 0.0 3.8 Birthday Spacings: Sum(O-E)^2/E= 14.705, p= 0.857 RESULTS OF GCD FOR dh-ranFile-2016-10-12_01:31 Euclid's algorithm: p-value, steps to gcd: 0.597346 p-value, dist. of gcd's: 0.102730 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-10-12_01:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.957 0.625 0.491 0.224 0.365 0.085 0.725 0.884 Bits 8 to 15---> 0.332 0.169 0.621 0.643 0.731 0.545 0.606 0.141 Bits 16 to 23---> 0.216 0.934 0.040 0.897 0.493 0.189 0.638 0.577 Bits 24 to 31---> 0.159 0.138 0.343 0.670 0.433 0.108 0.161 0.873 KS test for the above 32 p values: 0.276 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-10-12_01:31, p-values for 5 runs: 0.6469, 0.5291, 0.8718, 0.6377, 0.6662 Rank test for binary matrices (31x31) for dh-ranFile-2016-10-12_01:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 214 211.4 0.032 0.032 r= 29 5158 5134.0 0.112 0.144 r= 30 23053 23103.0 0.108 0.252 r= 31 11575 11551.5 0.048 0.300 chi-square = 0.300 with df = 3; p-value = 0.040 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-10-12_01:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 193 211.4 1.605 1.605 r= 30 5106 5134.0 0.153 1.757 r= 31 23069 23103.0 0.050 1.808 r= 32 11632 11551.5 0.561 2.368 chi-square = 2.368 with df = 3; p-value = 0.500 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-10-12_01:31 b-rank test for bits 1 to 8, p=0.99670 b-rank test for bits 2 to 9, p=0.37127 b-rank test for bits 3 to 10, p=0.02943 b-rank test for bits 4 to 11, p=0.24752 b-rank test for bits 5 to 12, p=0.89008 b-rank test for bits 6 to 13, p=0.81939 b-rank test for bits 7 to 14, p=0.16864 b-rank test for bits 8 to 15, p=0.69020 b-rank test for bits 9 to 16, p=0.76081 b-rank test for bits 10 to 17, p=0.73272 b-rank test for bits 11 to 18, p=0.94097 b-rank test for bits 12 to 19, p=0.38442 b-rank test for bits 13 to 20, p=0.47869 b-rank test for bits 14 to 21, p=0.24076 b-rank test for bits 15 to 22, p=0.35034 b-rank test for bits 16 to 23, p=0.86762 b-rank test for bits 17 to 24, p=0.43863 b-rank test for bits 18 to 25, p=0.68513 b-rank test for bits 19 to 26, p=0.83837 b-rank test for bits 20 to 27, p=0.69188 b-rank test for bits 21 to 28, p=0.67750 b-rank test for bits 22 to 29, p=0.21256 b-rank test for bits 23 to 30, p=0.27587 b-rank test for bits 24 to 31, p=0.90596 b-rank test for bits 25 to 32, p=0.43316 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 = 0.413388 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-10-12_01:31 (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 141887 -0.05 0.479196 2 141935 0.06 0.523913 3 141261 -1.51 0.064913 4 142164 0.60 0.724086 5 141827 -0.19 0.423730 6 142026 0.27 0.607417 7 142530 1.45 0.926494 8 142200 0.68 0.751474 9 142073 0.38 0.648920 10 141902 -0.02 0.493168 11 142285 0.88 0.809956 12 141928 0.04 0.517397 13 142022 0.26 0.603820 14 141970 0.14 0.556362 15 142276 0.86 0.804196 16 141571 -0.79 0.214621 17 141623 -0.67 0.251749 18 141636 -0.64 0.261535 19 141414 -1.16 0.123572 20 142410 1.17 0.878957 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-10-12_01:31 Bits used No. missing words z-score p-value 23 to 32 141848 -0.2115 0.416255 22 to 31 141831 -0.2701 0.393540 21 to 30 141596 -1.0804 0.139971 20 to 29 141504 -1.3977 0.081103 19 to 28 141789 -0.4149 0.339096 18 to 27 141804 -0.3632 0.358225 17 to 26 142266 1.2299 0.890632 16 to 25 142027 0.4058 0.657540 15 to 24 141485 -1.4632 0.071705 14 to 23 142546 2.1954 0.985933 13 to 22 141576 -1.1494 0.125193 12 to 21 141933 0.0816 0.532526 11 to 20 141525 -1.3253 0.092540 10 to 19 141531 -1.3046 0.096017 9 to 18 142153 0.8402 0.799614 8 to 17 141847 -0.2149 0.414911 7 to 16 141647 -0.9046 0.182842 6 to 15 142128 0.7540 0.774586 5 to 14 142113 0.7023 0.758757 4 to 13 141502 -1.4046 0.080072 3 to 12 142632 2.4920 0.993648 2 to 11 142013 0.3575 0.639635 1 to 10 142321 1.4196 0.922131 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-10-12_01:31 Bits used No. missing words z-score p-value 28 to 32 141964 0.1853 0.573512 27 to 31 141873 -0.1232 0.450993 26 to 30 141775 -0.4554 0.324427 25 to 29 141931 0.0735 0.529279 24 to 28 141424 -1.6452 0.049966 23 to 27 141766 -0.4859 0.313532 22 to 26 141902 -0.0248 0.490088 21 to 25 142052 0.4836 0.685675 20 to 24 142054 0.4904 0.688077 19 to 23 142089 0.6091 0.728755 18 to 22 142211 1.0226 0.846754 17 to 21 141807 -0.3469 0.364340 16 to 20 141405 -1.7096 0.043671 15 to 19 141617 -0.9909 0.160855 14 to 18 141896 -0.0452 0.481979 13 to 17 141698 -0.7164 0.236881 12 to 16 142439 1.7955 0.963712 11 to 15 141997 0.2972 0.616838 10 to 14 141732 -0.6011 0.273881 9 to 13 141901 -0.0282 0.488737 8 to 12 141770 -0.4723 0.318355 7 to 11 142049 0.4735 0.682057 6 to 10 142017 0.3650 0.642438 5 to 9 141530 -1.2859 0.099245 4 to 8 142086 0.5989 0.725374 3 to 7 142338 1.4531 0.926905 2 to 6 141662 -0.8384 0.200901 1 to 5 142163 0.8599 0.805077 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-10-12_01:31 Bits used No. missing words z-score p-value 31 to 32 141818 -0.2694 0.393807 30 to 31 142350 1.2999 0.903184 29 to 30 141786 -0.3638 0.358002 28 to 29 141761 -0.4376 0.330856 27 to 28 141733 -0.5201 0.301480 26 to 27 141858 -0.1514 0.439824 25 to 26 142082 0.5094 0.694747 24 to 25 141878 -0.0924 0.463183 23 to 24 142285 1.1082 0.866106 22 to 23 141407 -1.4818 0.069197 21 to 22 142182 0.8043 0.789399 20 to 21 141846 -0.1868 0.425903 19 to 20 142287 1.1141 0.867376 18 to 19 141569 -1.0039 0.157708 17 to 18 142155 0.7247 0.765679 16 to 17 141672 -0.7001 0.241936 15 to 16 142400 1.4474 0.926108 14 to 15 141595 -0.9272 0.176904 13 to 14 141809 -0.2960 0.383631 12 to 13 141732 -0.5231 0.300453 11 to 12 141870 -0.1160 0.453819 10 to 11 141895 -0.0423 0.483141 9 to 10 142310 1.1819 0.881381 8 to 9 141481 -1.2635 0.103203 7 to 8 141307 -1.7768 0.037802 6 to 7 141513 -1.1691 0.121179 5 to 6 141679 -0.6794 0.248430 4 to 5 141855 -0.1603 0.436336 3 to 4 141776 -0.3933 0.347048 2 to 3 141671 -0.7030 0.241016 1 to 2 142058 0.4386 0.669508 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-10-12_01:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2477.21 -0.322 0.373599 Test results for specific bytes for dh-ranFile-2016-10-12_01:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2383.94 -1.641 0.050367 2 to 9 2574.31 1.051 0.853347 3 to 10 2510.35 0.146 0.558177 4 to 11 2527.32 0.386 0.650375 5 to 12 2519.06 0.270 0.606234 6 to 13 2448.75 -0.725 0.234277 7 to 14 2436.13 -0.903 0.183200 8 to 15 2709.77 2.967 0.998494 9 to 16 2654.69 2.188 0.985652 10 to 17 2371.81 -1.813 0.034928 11 to 18 2430.19 -0.987 0.161757 12 to 19 2619.97 1.697 0.955117 13 to 20 2566.24 0.937 0.825579 14 to 21 2564.95 0.919 0.820842 15 to 22 2567.63 0.956 0.830568 16 to 23 2452.32 -0.674 0.250061 17 to 24 2380.94 -1.684 0.046120 18 to 25 2342.16 -2.232 0.012803 19 to 26 2430.83 -0.978 0.163971 20 to 27 2472.65 -0.387 0.349480 21 to 28 2518.00 0.255 0.600490 22 to 29 2603.66 1.466 0.928663 23 to 30 2519.57 0.277 0.609008 24 to 31 2565.42 0.925 0.822547 25 to 32 2549.68 0.703 0.758839 CDPARK for dh-ranFile-2016-10-12_01:31: 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 3530 0.3196 0.625377 3512 -0.5023 0.307734 3541 0.8219 0.794438 3508 -0.6849 0.246694 3502 -0.9589 0.168804 3530 0.3196 0.625377 3528 0.2283 0.590298 3491 -1.4612 0.071982 3572 2.2374 0.987371 3523 0.0000 0.500000 Square side=100, avg. no. parked=3523.70 sample std.=21.57 p-value of the KSTEST for those 10 p-values: 0.958980 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-10-12_01:31 0.2408,0.6421,0.6032,0.5903,0.1811,0.9560,0.2046,0.6464,0.2862,0.5234, The KS test for those 10 p-values: 0.677266 The 3DSPHERES test for dh-ranFile-2016-10-12_01:31 sample no r^3 equiv. uni. 1 28.136 0.608534 2 4.035 0.125846 3 3.235 0.102208 4 5.198 0.159076 5 43.030 0.761728 6 50.424 0.813775 7 34.243 0.680643 8 11.153 0.310492 9 29.975 0.631811 10 6.072 0.183229 11 23.699 0.546136 12 131.639 0.987574 13 5.361 0.163652 14 30.698 0.640581 15 65.712 0.888128 16 9.096 0.261539 17 3.317 0.104662 18 59.925 0.864326 19 51.507 0.820381 20 11.275 0.313282 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.825667 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-10-12_01:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 0.5 0.1 -0.5 -0.5 0.1 1.2 1.2 -0.7 1.1 0.6 -0.2 -1.2 -0.9 1.6 -0.1 -0.6 -2.0 1.1 0.3 1.0 1.5 -0.4 0.8 -1.5 0.1 -0.7 -1.5 0.4 -0.5 -1.0 -0.2 1.7 -1.0 -0.6 -0.7 -0.5 -0.4 -0.4 0.4 -0.6 0.0 -1.1 Chi-square with 42 degrees of freedom:34.566046 z-score=-0.811111, p-value=0.214571 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-10-12_01:31 Test no p-value 1 0.117393 2 0.730262 3 0.409385 4 0.935803 5 0.035589 6 0.400614 7 0.041039 8 0.016440 9 0.565872 10 0.066015 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.033941 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-10-12_01:31: (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 66626 0.02 66487 0.48 3 25000.00 25075 0.23 25237 2.25 4 6666.67 6617 0.37 6578 1.18 5 1388.89 1388 0.00 1438 1.74 6 238.10 259 1.84 227 0.52 7 34.72 28 1.30 26 2.19 8 4.96 6 0.22 6 0.22 p=0.31989 p=0.80088 Number of rngs required: 688618, p-value: 0.598 RESULTS OF CRAPS TEST for dh-ranFile-2016-10-12_01:31 No. of wins: Observed Expected 98348 98585.9 z-score=-1.064, pvalue=0.14370 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66645 66666.7 0.007 0.007 2 37816 37654.3 0.694 0.701 3 27135 26954.7 1.206 1.907 4 19601 19313.5 4.281 6.188 5 13607 13851.4 4.313 10.501 6 9851 9943.5 0.861 11.362 7 6943 7145.0 5.712 17.074 8 5135 5139.1 0.003 17.077 9 3705 3699.9 0.007 17.085 10 2625 2666.3 0.640 17.724 11 1943 1923.3 0.201 17.925 12 1376 1388.7 0.117 18.042 13 999 1003.7 0.022 18.064 14 673 726.1 3.889 21.953 15 524 525.8 0.006 21.960 16 375 381.2 0.099 22.059 17 289 276.5 0.561 22.621 18 189 200.8 0.697 23.317 19 151 146.0 0.172 23.490 20 125 106.2 3.322 26.812 21 293 287.1 0.121 26.933 Chisq= 26.93 for 20 degrees of freedom, p= 0.86283 SUMMARY of craptest p-value for no. of wins: 0.143700 p-value for throws/game: 0.862828 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-10-12_01:31 No. of wins: Observed Expected 98563 98585.9 z-score=-0.102, pvalue=0.45928 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66864 66666.7 0.584 0.584 2 37728 37654.3 0.144 0.728 3 26762 26954.7 1.378 2.106 4 19203 19313.5 0.632 2.738 5 13708 13851.4 1.485 4.223 6 10093 9943.5 2.246 6.470 7 7081 7145.0 0.574 7.043 8 5196 5139.1 0.631 7.674 9 3698 3699.9 0.001 7.675 10 2625 2666.3 0.640 8.314 11 1869 1923.3 1.535 9.849 12 1394 1388.7 0.020 9.869 13 1068 1003.7 4.117 13.986 14 767 726.1 2.299 16.285 15 489 525.8 2.580 18.866 16 387 381.2 0.090 18.956 17 284 276.5 0.201 19.157 18 202 200.8 0.007 19.164 19 150 146.0 0.110 19.274 20 120 106.2 1.789 21.063 21 312 287.1 2.157 23.220 Chisq= 23.22 for 20 degrees of freedom, p= 0.72189 SUMMARY of craptest p-value for no. of wins: 0.459284 p-value for throws/game: 0.721889 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0128,0.0164,0.0294,0.0339,0.0349,0.0356,0.0378,0.0399,0.0402,0.0410, 0.0437,0.0461,0.0500,0.0504,0.0649,0.0660,0.0692,0.0717,0.0720,0.0801, 0.0811,0.0846,0.0925,0.0960,0.0992,0.1022,0.1027,0.1032,0.1047,0.1083, 0.1174,0.1212,0.1236,0.1252,0.1258,0.1381,0.1400,0.1411,0.1437,0.1577, 0.1588,0.1591,0.1609,0.1614,0.1618,0.1637,0.1640,0.1686,0.1688,0.1691, 0.1769,0.1811,0.1828,0.1832,0.1832,0.1891,0.2009,0.2046,0.2126,0.2146, 0.2146,0.2162,0.2239,0.2343,0.2350,0.2369,0.2408,0.2408,0.2410,0.2419, 0.2467,0.2475,0.2484,0.2488,0.2501,0.2517,0.2615,0.2615,0.2739,0.2759, 0.2760,0.2862,0.3005,0.3015,0.3077,0.3105,0.3133,0.3135,0.3184,0.3199, 0.3244,0.3309,0.3320,0.3391,0.3430,0.3470,0.3495,0.3503,0.3580,0.3582, 0.3643,0.3652,0.3713,0.3736,0.3836,0.3844,0.3935,0.3938,0.4006,0.4094, 0.4134,0.4149,0.4163,0.4237,0.4259,0.4327,0.4332,0.4363,0.4386,0.4398, 0.4510,0.4538,0.4546,0.4593,0.4600,0.4632,0.4787,0.4792,0.4820,0.4831, 0.4887,0.4901,0.4915,0.4932,0.4932,0.5000,0.5004,0.5174,0.5234,0.5239, 0.5291,0.5293,0.5325,0.5448,0.5461,0.5564,0.5582,0.5659,0.5732,0.5735, 0.5765,0.5903,0.5903,0.5973,0.5977,0.6005,0.6032,0.6038,0.6062,0.6062, 0.6074,0.6085,0.6090,0.6168,0.6181,0.6209,0.6247,0.6254,0.6254,0.6318, 0.6377,0.6382,0.6396,0.6406,0.6421,0.6424,0.6434,0.6464,0.6469,0.6489, 0.6504,0.6575,0.6662,0.6695,0.6700,0.6720,0.6773,0.6775,0.6806,0.6821, 0.6851,0.6857,0.6881,0.6902,0.6919,0.6947,0.7219,0.7241,0.7250,0.7254, 0.7288,0.7303,0.7311,0.7327,0.7515,0.7588,0.7588,0.7608,0.7617,0.7657, 0.7746,0.7751,0.7894,0.7944,0.7996,0.8009,0.8042,0.8051,0.8100,0.8138, 0.8194,0.8204,0.8208,0.8225,0.8256,0.8257,0.8306,0.8384,0.8468,0.8524, 0.8533,0.8568,0.8628,0.8643,0.8661,0.8674,0.8676,0.8718,0.8728,0.8790, 0.8814,0.8841,0.8881,0.8901,0.8906,0.8968,0.9032,0.9037,0.9060,0.9221, 0.9261,0.9265,0.9269,0.9287,0.9339,0.9358,0.9410,0.9551,0.9560,0.9567, 0.9590,0.9637,0.9857,0.9859,0.9874,0.9876,0.9936,0.9967,0.9985, Overall p-value after applying KStest on 269 p-values = 0.913561 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.