RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-04-21_12:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.63 17.0827 0.551226 2 to 25 15.63 13.0939 0.270125 3 to 26 15.55 18.7952 0.659586 4 to 27 15.67 26.2540 0.930045 5 to 28 15.82 14.6638 0.380314 6 to 29 15.88 4.9826 0.002180 7 to 30 15.88 24.4443 0.892143 8 to 31 15.63 21.1189 0.778983 9 to 32 15.63 16.8637 0.536364 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.641835 Tough bday spacings test for dh-ranFile-2017-04-21_12:31: 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 47 75 83 106 68 54 24 20 5 7 (O-E)^2/E 0.4 2.9 0.0 2.2 0.7 1.3 0.1 1.1 1.8 0.4 2.1 Birthday Spacings: Sum(O-E)^2/E= 13.036, p= 0.778 RESULTS OF GCD FOR dh-ranFile-2017-04-21_12:31 Euclid's algorithm: p-value, steps to gcd: 0.141437 p-value, dist. of gcd's: 0.165867 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-04-21_12:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.632 0.521 0.400 0.602 0.779 0.300 0.808 0.007 Bits 8 to 15---> 0.609 0.369 0.289 0.013 0.265 0.817 0.036 0.129 Bits 16 to 23---> 0.880 0.069 0.229 0.027 0.669 0.370 0.033 0.216 Bits 24 to 31---> 0.272 0.706 0.829 0.658 0.956 0.740 0.606 0.669 KS test for the above 32 p values: 0.692 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-04-21_12:31, p-values for 5 runs: 0.3991, 0.4717, 0.1342, 0.2731, 0.4486 Rank test for binary matrices (31x31) for dh-ranFile-2017-04-21_12:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 234 211.4 2.412 2.412 r= 29 5181 5134.0 0.430 2.842 r= 30 22959 23103.0 0.898 3.740 r= 31 11626 11551.5 0.480 4.220 chi-square = 4.220 with df = 3; p-value = 0.761 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2017-04-21_12:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 210 211.4 0.010 0.010 r= 30 5191 5134.0 0.633 0.642 r= 31 22973 23103.0 0.732 1.374 r= 32 11626 11551.5 0.480 1.854 chi-square = 1.854 with df = 3; p-value = 0.397 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2017-04-21_12:31 b-rank test for bits 1 to 8, p=0.65138 b-rank test for bits 2 to 9, p=0.67088 b-rank test for bits 3 to 10, p=0.84960 b-rank test for bits 4 to 11, p=0.57655 b-rank test for bits 5 to 12, p=0.84081 b-rank test for bits 6 to 13, p=0.59357 b-rank test for bits 7 to 14, p=0.37817 b-rank test for bits 8 to 15, p=0.60698 b-rank test for bits 9 to 16, p=0.12216 b-rank test for bits 10 to 17, p=0.04829 b-rank test for bits 11 to 18, p=0.66693 b-rank test for bits 12 to 19, p=0.03683 b-rank test for bits 13 to 20, p=0.89948 b-rank test for bits 14 to 21, p=0.23973 b-rank test for bits 15 to 22, p=0.89335 b-rank test for bits 16 to 23, p=0.90519 b-rank test for bits 17 to 24, p=0.08947 b-rank test for bits 18 to 25, p=0.04844 b-rank test for bits 19 to 26, p=0.59266 b-rank test for bits 20 to 27, p=0.47046 b-rank test for bits 21 to 28, p=0.45239 b-rank test for bits 22 to 29, p=0.74177 b-rank test for bits 23 to 30, p=0.99143 b-rank test for bits 24 to 31, p=0.63210 b-rank test for bits 25 to 32, p=0.33916 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 = 0.642004 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-04-21_12:31 (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 142787 2.05 0.979849 2 141400 -1.19 0.117019 3 142031 0.28 0.611900 4 142019 0.26 0.601117 5 142057 0.35 0.634962 6 141751 -0.37 0.355717 7 142204 0.69 0.754425 8 141974 0.15 0.560051 9 141983 0.17 0.568331 10 142432 1.22 0.888993 11 141714 -0.46 0.324059 12 141928 0.04 0.517397 13 142022 0.26 0.603820 14 141920 0.02 0.509945 15 141573 -0.79 0.215987 16 142370 1.08 0.859111 17 142319 0.96 0.830760 18 141712 -0.46 0.322381 19 141806 -0.24 0.404613 20 140833 -2.51 0.005955 ---------------------------------------------------------------- OPSO test for dh-ranFile-2017-04-21_12:31 Bits used No. missing words z-score p-value 23 to 32 142074 0.5678 0.714924 22 to 31 141466 -1.5287 0.063166 21 to 30 141833 -0.2632 0.396196 20 to 29 141395 -1.7736 0.038069 19 to 28 141835 -0.2563 0.398856 18 to 27 141882 -0.0942 0.462459 17 to 26 141801 -0.3736 0.354369 16 to 25 142113 0.7023 0.758757 15 to 24 141591 -1.0977 0.136170 14 to 23 142251 1.1782 0.880636 13 to 22 141275 -2.1873 0.014359 12 to 21 141890 -0.0667 0.473428 11 to 20 142031 0.4196 0.662594 10 to 19 142334 1.4644 0.928455 9 to 18 142360 1.5540 0.939912 8 to 17 142402 1.6989 0.955327 7 to 16 142262 1.2161 0.888027 6 to 15 142631 2.4885 0.993586 5 to 14 142467 1.9230 0.972760 4 to 13 142136 0.7816 0.782781 3 to 12 142110 0.6920 0.755521 2 to 11 142264 1.2230 0.889335 1 to 10 142115 0.7092 0.760902 ----------------------------------------------------------------- OQSO test for dh-ranFile-2017-04-21_12:31 Bits used No. missing words z-score p-value 28 to 32 142057 0.5006 0.691665 27 to 31 141423 -1.6486 0.049617 26 to 30 142262 1.1955 0.884053 25 to 29 141969 0.2023 0.580148 24 to 28 141440 -1.5909 0.055811 23 to 27 141991 0.2768 0.609051 22 to 26 141515 -1.3367 0.090658 21 to 25 142096 0.6328 0.736561 20 to 24 141687 -0.7537 0.225526 19 to 23 142558 2.1989 0.986057 18 to 22 141524 -1.3062 0.095742 17 to 21 141673 -0.8011 0.211532 16 to 20 141847 -0.2113 0.416331 15 to 19 142349 1.4904 0.931941 14 to 18 141954 0.1514 0.560179 13 to 17 142119 0.7107 0.761379 12 to 16 142089 0.6091 0.728755 11 to 15 142019 0.3718 0.644965 10 to 14 141716 -0.6554 0.256119 9 to 13 141914 0.0158 0.506315 8 to 12 141663 -0.8350 0.201854 7 to 11 142000 0.3074 0.620714 6 to 10 141467 -1.4994 0.066882 5 to 9 141687 -0.7537 0.225526 4 to 8 142118 0.7074 0.760327 3 to 7 141827 -0.2791 0.390090 2 to 6 142108 0.6735 0.749672 1 to 5 141818 -0.3096 0.378435 ----------------------------------------------------------------- DNA test for dh-ranFile-2017-04-21_12:31 Bits used No. missing words z-score p-value 31 to 32 141921 0.0344 0.513731 30 to 31 141850 -0.1750 0.430534 29 to 30 142030 0.3560 0.639064 28 to 29 141971 0.1819 0.572176 27 to 28 142508 1.7660 0.961301 26 to 27 142151 0.7129 0.762043 25 to 26 141808 -0.2989 0.382505 24 to 25 141796 -0.3343 0.369074 23 to 24 141530 -1.1190 0.131577 22 to 23 142040 0.3855 0.650051 21 to 22 142106 0.5801 0.719092 20 to 21 141636 -0.8063 0.210040 19 to 20 142351 1.3029 0.903689 18 to 19 141919 0.0285 0.511378 17 to 18 141971 0.1819 0.572176 16 to 17 141961 0.1524 0.560572 15 to 16 141657 -0.7443 0.228337 14 to 15 142201 0.8604 0.805211 13 to 14 141876 -0.0983 0.460840 12 to 13 142753 2.4887 0.993589 11 to 12 142060 0.4445 0.671643 10 to 11 141728 -0.5349 0.296361 9 to 10 142184 0.8102 0.791098 8 to 9 141570 -1.0010 0.158420 7 to 8 142201 0.8604 0.805211 6 to 7 142616 2.0846 0.981446 5 to 6 141466 -1.3078 0.095478 4 to 5 142288 1.1170 0.868007 3 to 4 141953 0.1288 0.551250 2 to 3 141883 -0.0777 0.469045 1 to 2 141764 -0.4287 0.334070 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2017-04-21_12:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2472.01 -0.396 0.346116 Test results for specific bytes for dh-ranFile-2017-04-21_12:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2661.26 2.281 0.988714 2 to 9 2370.55 -1.831 0.033577 3 to 10 2476.80 -0.328 0.371427 4 to 11 2539.43 0.558 0.711469 5 to 12 2684.61 2.611 0.995483 6 to 13 2589.66 1.268 0.897597 7 to 14 2564.78 0.916 0.820188 8 to 15 2572.25 1.022 0.846559 9 to 16 2438.52 -0.869 0.192311 10 to 17 2593.14 1.317 0.906110 11 to 18 2555.62 0.787 0.784254 12 to 19 2528.29 0.400 0.655451 13 to 20 2456.28 -0.618 0.268210 14 to 21 2400.21 -1.411 0.079084 15 to 22 2469.72 -0.428 0.334238 16 to 23 2607.06 1.514 0.934994 17 to 24 2525.25 0.357 0.639502 18 to 25 2423.50 -1.082 0.139643 19 to 26 2450.12 -0.705 0.240291 20 to 27 2465.78 -0.484 0.314234 21 to 28 2648.84 2.105 0.982352 22 to 29 2523.94 0.339 0.632510 23 to 30 2373.12 -1.794 0.036374 24 to 31 2467.42 -0.461 0.322469 25 to 32 2411.77 -1.248 0.106069 CDPARK for dh-ranFile-2017-04-21_12:31: 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 3522 -0.0457 0.481790 3520 -0.1370 0.445521 3523 0.0000 0.500000 3516 -0.3196 0.374623 3488 -1.5982 0.055002 3517 -0.2740 0.392053 3495 -1.2785 0.100530 3495 -1.2785 0.100530 3546 1.0502 0.853193 3529 0.2740 0.607947 Square side=100, avg. no. parked=3515.10 sample std.=16.82 p-value of the KSTEST for those 10 p-values: 0.309422 Results for the MINIMUM DISTANCE test for dh-ranFile-2017-04-21_12:31 0.4637,0.0923,0.2519,0.6664,0.7361,0.7369,0.6790,0.3437,0.5068,0.3597, The KS test for those 10 p-values: 0.619852 The 3DSPHERES test for dh-ranFile-2017-04-21_12:31 sample no r^3 equiv. uni. 1 19.495 0.477869 2 33.463 0.672230 3 4.546 0.140605 4 4.755 0.146563 5 0.457 0.015117 6 6.549 0.196112 7 9.897 0.280994 8 14.101 0.375010 9 6.028 0.182021 10 19.445 0.477000 11 15.728 0.408012 12 41.051 0.745478 13 167.169 0.996198 14 63.624 0.880065 15 14.903 0.391495 16 54.394 0.836856 17 7.342 0.217087 18 55.269 0.841549 19 6.034 0.182208 20 31.727 0.652700 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.675652 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-04-21_12:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -2.0 0.3 0.6 -1.2 1.1 -0.2 -0.7 0.2 0.8 0.2 0.5 -0.6 0.2 -0.1 0.6 1.9 -1.3 -0.9 1.1 0.6 -1.6 0.0 0.6 -0.8 -0.3 -0.7 -1.1 0.0 0.1 1.9 -0.3 -1.5 0.7 0.2 -2.5 0.7 -2.6 -0.4 -0.1 0.9 1.0 -0.1 Chi-square with 42 degrees of freedom:43.665635 z-score=0.181736, p-value=0.599469 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2017-04-21_12:31 Test no p-value 1 0.448617 2 0.001096 3 0.761855 4 0.015114 5 0.581656 6 0.031724 7 0.861516 8 0.047398 9 0.676809 10 0.001648 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.002213 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-04-21_12:31: (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 66541 0.24 66751 0.11 3 25000.00 25045 0.08 24952 0.09 4 6666.67 6683 0.04 6580 1.13 5 1388.89 1440 1.88 1402 0.12 6 238.10 255 1.20 264 2.82 7 34.72 31 0.40 43 1.97 8 4.96 4 0.19 7 0.84 p=0.32648 p=0.68662 Number of rngs required: 687611, p-value: 0.180 RESULTS OF CRAPS TEST for dh-ranFile-2017-04-21_12:31 No. of wins: Observed Expected 98503 98585.9 z-score=-0.371, pvalue=0.35547 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66692 66666.7 0.010 0.010 2 37722 37654.3 0.122 0.131 3 27027 26954.7 0.194 0.325 4 19444 19313.5 0.882 1.207 5 13818 13851.4 0.081 1.288 6 9836 9943.5 1.163 2.451 7 7208 7145.0 0.555 3.006 8 5044 5139.1 1.759 4.765 9 3613 3699.9 2.039 6.804 10 2611 2666.3 1.147 7.951 11 1923 1923.3 0.000 7.951 12 1370 1388.7 0.253 8.204 13 1046 1003.7 1.781 9.986 14 748 726.1 0.658 10.644 15 522 525.8 0.028 10.672 16 365 381.2 0.684 11.356 17 282 276.5 0.108 11.464 18 163 200.8 7.126 18.590 19 147 146.0 0.007 18.597 20 120 106.2 1.789 20.386 21 299 287.1 0.492 20.878 Chisq= 20.88 for 20 degrees of freedom, p= 0.59564 SUMMARY of craptest p-value for no. of wins: 0.355471 p-value for throws/game: 0.595643 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2017-04-21_12:31 No. of wins: Observed Expected 98369 98585.9 z-score=-0.970, pvalue=0.16604 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66626 66666.7 0.025 0.025 2 37723 37654.3 0.125 0.150 3 26915 26954.7 0.059 0.209 4 19356 19313.5 0.094 0.302 5 13767 13851.4 0.515 0.817 6 9965 9943.5 0.046 0.863 7 7224 7145.0 0.873 1.736 8 5153 5139.1 0.038 1.774 9 3714 3699.9 0.054 1.828 10 2668 2666.3 0.001 1.829 11 1885 1923.3 0.764 2.593 12 1306 1388.7 4.930 7.522 13 1026 1003.7 0.495 8.017 14 755 726.1 1.147 9.164 15 522 525.8 0.028 9.192 16 397 381.2 0.659 9.851 17 261 276.5 0.873 10.724 18 190 200.8 0.584 11.308 19 127 146.0 2.469 13.777 20 103 106.2 0.097 13.874 21 317 287.1 3.111 16.985 Chisq= 16.99 for 20 degrees of freedom, p= 0.34608 SUMMARY of craptest p-value for no. of wins: 0.166044 p-value for throws/game: 0.346076 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0011,0.0016,0.0022,0.0022,0.0060,0.0070,0.0131,0.0144,0.0151,0.0151, 0.0274,0.0317,0.0333,0.0336,0.0363,0.0364,0.0368,0.0381,0.0474,0.0483, 0.0484,0.0496,0.0550,0.0558,0.0632,0.0669,0.0694,0.0791,0.0895,0.0907, 0.0923,0.0955,0.0957,0.1005,0.1005,0.1061,0.1170,0.1222,0.1286,0.1316, 0.1342,0.1362,0.1396,0.1406,0.1414,0.1466,0.1584,0.1659,0.1660,0.1797, 0.1820,0.1822,0.1923,0.1961,0.2019,0.2100,0.2115,0.2160,0.2164,0.2171, 0.2255,0.2255,0.2283,0.2292,0.2397,0.2403,0.2519,0.2561,0.2647,0.2682, 0.2701,0.2723,0.2731,0.2810,0.2885,0.2964,0.3002,0.3094,0.3142,0.3224, 0.3225,0.3241,0.3265,0.3341,0.3342,0.3392,0.3437,0.3461,0.3461,0.3544, 0.3555,0.3557,0.3597,0.3690,0.3691,0.3700,0.3714,0.3746,0.3750,0.3782, 0.3784,0.3803,0.3825,0.3901,0.3915,0.3921,0.3962,0.3968,0.3989,0.3991, 0.3999,0.4046,0.4080,0.4163,0.4305,0.4455,0.4486,0.4486,0.4524,0.4608, 0.4625,0.4637,0.4690,0.4705,0.4717,0.4734,0.4770,0.4779,0.4818,0.5000, 0.5063,0.5068,0.5099,0.5114,0.5137,0.5174,0.5213,0.5364,0.5512,0.5513, 0.5601,0.5602,0.5606,0.5683,0.5722,0.5722,0.5765,0.5801,0.5817,0.5927, 0.5936,0.5956,0.5995,0.6011,0.6023,0.6038,0.6063,0.6070,0.6079,0.6090, 0.6091,0.6119,0.6199,0.6207,0.6321,0.6322,0.6325,0.6350,0.6391,0.6395, 0.6418,0.6420,0.6450,0.6501,0.6514,0.6527,0.6555,0.6584,0.6596,0.6626, 0.6664,0.6669,0.6688,0.6692,0.6709,0.6716,0.6722,0.6757,0.6768,0.6790, 0.6866,0.6917,0.6920,0.7063,0.7115,0.7149,0.7191,0.7288,0.7361,0.7366, 0.7369,0.7399,0.7418,0.7455,0.7497,0.7544,0.7555,0.7588,0.7603,0.7609, 0.7614,0.7614,0.7619,0.7620,0.7784,0.7786,0.7790,0.7828,0.7843,0.7911, 0.8052,0.8052,0.8084,0.8169,0.8202,0.8286,0.8308,0.8369,0.8408,0.8415, 0.8466,0.8496,0.8532,0.8591,0.8615,0.8680,0.8797,0.8801,0.8806,0.8841, 0.8880,0.8890,0.8893,0.8921,0.8933,0.8976,0.8995,0.9037,0.9052,0.9061, 0.9285,0.9300,0.9319,0.9350,0.9399,0.9553,0.9556,0.9613,0.9728,0.9798, 0.9814,0.9824,0.9861,0.9887,0.9914,0.9936,0.9936,0.9955,0.9962, Overall p-value after applying KStest on 269 p-values = 0.531879 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.