RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-23_06:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.76 19.8403 0.717523 2 to 25 15.91 14.1323 0.342281 3 to 26 15.54 20.3933 0.745390 4 to 27 15.71 17.8678 0.602771 5 to 28 15.93 11.1263 0.150074 6 to 29 15.89 22.2717 0.825507 7 to 30 15.81 19.1145 0.678000 8 to 31 15.89 18.6332 0.650014 9 to 32 15.98 15.9813 0.474841 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.378624 Tough bday spacings test for dh-ranFile-2018-06-23_06:31: 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 3 48 70 92 98 78 61 26 14 7 3 (O-E)^2/E 4.1 3.5 0.1 0.3 0.0 0.0 1.5 0.5 0.1 0.0 0.3 Birthday Spacings: Sum(O-E)^2/E= 10.499, p= 0.602 RESULTS OF GCD FOR dh-ranFile-2018-06-23_06:31 Euclid's algorithm: p-value, steps to gcd: 0.536468 p-value, dist. of gcd's: 0.805315 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-23_06:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.686 0.902 0.511 0.604 0.220 0.435 0.064 0.453 Bits 8 to 15---> 0.897 0.599 0.610 0.717 0.488 0.663 0.160 0.791 Bits 16 to 23---> 0.673 0.166 0.511 0.411 0.078 0.390 0.776 0.930 Bits 24 to 31---> 0.000 0.110 0.172 0.834 0.451 0.479 0.131 0.089 KS test for the above 32 p values: 0.439 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-23_06:31, p-values for 5 runs: 0.2962, 0.1020, 0.7744, 0.0854, 0.0486 Rank test for binary matrices (31x31) for dh-ranFile-2018-06-23_06:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 218 211.4 0.205 0.205 r= 29 5063 5134.0 0.982 1.187 r= 30 23234 23103.0 0.742 1.929 r= 31 11485 11551.5 0.383 2.312 chi-square = 2.312 with df = 3; p-value = 0.490 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-06-23_06:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 222 211.4 0.530 0.530 r= 30 5060 5134.0 1.067 1.597 r= 31 23134 23103.0 0.041 1.638 r= 32 11584 11551.5 0.091 1.729 chi-square = 1.729 with df = 3; p-value = 0.370 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-06-23_06:31 b-rank test for bits 1 to 8, p=0.42845 b-rank test for bits 2 to 9, p=0.07787 b-rank test for bits 3 to 10, p=0.23734 b-rank test for bits 4 to 11, p=0.53710 b-rank test for bits 5 to 12, p=0.57380 b-rank test for bits 6 to 13, p=0.34842 b-rank test for bits 7 to 14, p=0.98773 b-rank test for bits 8 to 15, p=0.34872 b-rank test for bits 9 to 16, p=0.31386 b-rank test for bits 10 to 17, p=0.20390 b-rank test for bits 11 to 18, p=0.52066 b-rank test for bits 12 to 19, p=0.49416 b-rank test for bits 13 to 20, p=0.70377 b-rank test for bits 14 to 21, p=0.08521 b-rank test for bits 15 to 22, p=0.94520 b-rank test for bits 16 to 23, p=0.26347 b-rank test for bits 17 to 24, p=0.26485 b-rank test for bits 18 to 25, p=0.69339 b-rank test for bits 19 to 26, p=0.98702 b-rank test for bits 20 to 27, p=0.36331 b-rank test for bits 21 to 28, p=0.76340 b-rank test for bits 22 to 29, p=0.20276 b-rank test for bits 23 to 30, p=0.97572 b-rank test for bits 24 to 31, p=0.96933 b-rank test for bits 25 to 32, p=0.02656 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 = 0.407115 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-23_06:31 (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 141427 -1.13 0.129884 2 141738 -0.40 0.344466 3 141364 -1.27 0.101308 4 142535 1.46 0.928108 5 141859 -0.12 0.453195 6 141935 0.06 0.523913 7 141591 -0.74 0.228510 8 142562 1.52 0.936362 9 142010 0.24 0.592977 10 141852 -0.13 0.446722 11 141691 -0.51 0.304985 12 141883 -0.06 0.475473 13 142130 0.52 0.696928 14 142229 0.75 0.772436 15 141499 -0.96 0.168851 16 142735 1.93 0.973143 17 142331 0.99 0.837740 18 141514 -0.92 0.177830 19 142238 0.77 0.778733 20 141795 -0.27 0.394686 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-06-23_06:31 Bits used No. missing words z-score p-value 23 to 32 141526 -1.3218 0.093113 22 to 31 141580 -1.1356 0.128058 21 to 30 142012 0.3540 0.638344 20 to 29 142167 0.8885 0.812869 19 to 28 142101 0.6609 0.745672 18 to 27 141802 -0.3701 0.355653 17 to 26 142274 1.2575 0.895711 16 to 25 142268 1.2368 0.891918 15 to 24 141973 0.2196 0.586890 14 to 23 141733 -0.6080 0.271582 13 to 22 141655 -0.8770 0.190243 12 to 21 141679 -0.7942 0.213528 11 to 20 142062 0.5264 0.700712 10 to 19 142198 0.9954 0.840233 9 to 18 141590 -1.1011 0.135418 8 to 17 141391 -1.7873 0.036941 7 to 16 141832 -0.2667 0.394867 6 to 15 142183 0.9437 0.827336 5 to 14 142166 0.8851 0.811940 4 to 13 142227 1.0954 0.863332 3 to 12 142592 2.3540 0.990715 2 to 11 142136 0.7816 0.782781 1 to 10 141726 -0.6322 0.263637 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-06-23_06:31 Bits used No. missing words z-score p-value 28 to 32 141555 -1.2011 0.114853 27 to 31 141421 -1.6554 0.048926 26 to 30 141596 -1.0621 0.144087 25 to 29 142213 1.0294 0.848352 24 to 28 141508 -1.3604 0.086845 23 to 27 141695 -0.7265 0.233753 22 to 26 141799 -0.3740 0.354202 21 to 25 141907 -0.0079 0.496849 20 to 24 142092 0.6192 0.732114 19 to 23 141966 0.1921 0.576169 18 to 22 141950 0.1379 0.554826 17 to 21 141968 0.1989 0.578822 16 to 20 141823 -0.2926 0.384897 15 to 19 142122 0.7209 0.764519 14 to 18 141466 -1.5028 0.066444 13 to 17 141919 0.0328 0.513075 12 to 16 141793 -0.3943 0.346665 11 to 15 141795 -0.3876 0.349171 10 to 14 142211 1.0226 0.846754 9 to 13 142287 1.2802 0.899769 8 to 12 142085 0.5955 0.724243 7 to 11 142313 1.3684 0.914402 6 to 10 142442 1.8057 0.964514 5 to 9 141653 -0.8689 0.192447 4 to 8 141948 0.1311 0.552146 3 to 7 141808 -0.3435 0.365614 2 to 6 141760 -0.5062 0.306357 1 to 5 142349 1.4904 0.931941 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-06-23_06:31 Bits used No. missing words z-score p-value 31 to 32 141830 -0.2340 0.407488 30 to 31 142099 0.5595 0.712089 29 to 30 142120 0.6214 0.732847 28 to 29 141611 -0.8800 0.189422 27 to 28 142005 0.2822 0.611110 26 to 27 141736 -0.5113 0.304571 25 to 26 142210 0.8869 0.812442 24 to 25 142059 0.4415 0.670576 23 to 24 141910 0.0020 0.500789 22 to 23 141665 -0.7207 0.235536 21 to 22 141845 -0.1898 0.424747 20 to 21 141536 -1.1013 0.135390 19 to 20 141659 -0.7384 0.230125 18 to 19 141717 -0.5673 0.285240 17 to 18 141963 0.1583 0.562897 16 to 17 141461 -1.3225 0.093000 15 to 16 142234 0.9577 0.830900 14 to 15 142216 0.9046 0.817170 13 to 14 142248 0.9990 0.841109 12 to 13 142035 0.3707 0.644573 11 to 12 142450 1.5949 0.944632 10 to 11 141897 -0.0364 0.485493 9 to 10 141518 -1.1544 0.124175 8 to 9 141534 -1.1072 0.134111 7 to 8 142060 0.4445 0.671643 6 to 7 142330 1.2409 0.892681 5 to 6 142011 0.2999 0.617878 4 to 5 141811 -0.2901 0.385886 3 to 4 141568 -1.0069 0.156998 2 to 3 141965 0.1642 0.565220 1 to 2 141973 0.1878 0.574490 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-23_06:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2560.84 0.860 0.805225 Test results for specific bytes for dh-ranFile-2018-06-23_06:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2428.46 -1.012 0.155831 2 to 9 2499.08 -0.013 0.494787 3 to 10 2431.23 -0.973 0.165375 4 to 11 2527.77 0.393 0.652729 5 to 12 2445.33 -0.773 0.219723 6 to 13 2577.59 1.097 0.863730 7 to 14 2523.63 0.334 0.630877 8 to 15 2546.16 0.653 0.743055 9 to 16 2452.41 -0.673 0.250478 10 to 17 2430.70 -0.980 0.163530 11 to 18 2558.84 0.832 0.797312 12 to 19 2637.89 1.950 0.974413 13 to 20 2564.69 0.915 0.819854 14 to 21 2485.51 -0.205 0.418810 15 to 22 2378.62 -1.717 0.043031 16 to 23 2571.52 1.011 0.844106 17 to 24 2444.81 -0.781 0.217537 18 to 25 2577.67 1.098 0.863993 19 to 26 2680.29 2.550 0.994610 20 to 27 2498.39 -0.023 0.490937 21 to 28 2523.85 0.337 0.632048 22 to 29 2541.40 0.586 0.720899 23 to 30 2469.47 -0.432 0.332979 24 to 31 2456.47 -0.616 0.269094 25 to 32 2564.65 0.914 0.819716 CDPARK for dh-ranFile-2018-06-23_06:31: 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 3539 0.7306 0.767486 3456 -3.0594 0.001109 3515 -0.3653 0.357445 3512 -0.5023 0.307734 3511 -0.5479 0.291865 3535 0.5479 0.708135 3501 -1.0046 0.157553 3544 0.9589 0.831196 3535 0.5479 0.708135 3484 -1.7808 0.037471 Square side=100, avg. no. parked=3513.20 sample std.=26.17 p-value of the KSTEST for those 10 p-values: 0.317649 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-23_06:31 0.7843,0.6194,0.2036,0.1208,0.2399,0.2975,0.5150,0.7804,0.7302,0.0155, The KS test for those 10 p-values: 0.676759 The 3DSPHERES test for dh-ranFile-2018-06-23_06:31 sample no r^3 equiv. uni. 1 6.026 0.181965 2 4.117 0.128226 3 59.547 0.862608 4 13.577 0.364012 5 9.205 0.264227 6 2.176 0.069957 7 0.346 0.011472 8 28.661 0.615330 9 17.913 0.449596 10 35.727 0.696056 11 15.117 0.395828 12 10.144 0.286900 13 17.199 0.436332 14 12.929 0.350119 15 0.645 0.021279 16 2.095 0.067465 17 12.136 0.332716 18 37.739 0.715768 19 8.641 0.250264 20 89.061 0.948631 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.075096 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-23_06:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 2.7 -1.2 1.1 0.5 -0.9 0.7 -1.0 1.8 -0.6 -2.2 0.3 0.7 0.1 0.1 0.3 0.8 -0.9 -0.3 -0.4 -0.7 0.4 0.7 0.1 1.4 -0.5 -0.8 -0.1 -2.6 0.1 1.0 1.9 1.1 -0.0 -0.5 0.3 0.6 -0.5 0.2 -1.2 1.0 2.4 -1.0 1.8 Chi-square with 42 degrees of freedom:53.416756 z-score=1.245670, p-value=0.888615 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-06-23_06:31 Test no p-value 1 0.690516 2 0.081836 3 0.166165 4 0.615137 5 0.312558 6 0.204025 7 0.236970 8 0.821455 9 0.280068 10 0.115655 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.145229 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-23_06:31: (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 66818 0.34 66595 0.08 3 25000.00 24943 0.13 24891 0.48 4 6666.67 6561 1.67 6869 6.14 5 1388.89 1392 0.01 1406 0.21 6 238.10 238 0.00 209 3.56 7 34.72 40 0.80 24 3.31 8 4.96 7 0.84 5 0.00 p=0.29593 p=0.96768 Number of rngs required: 688101, p-value: 0.364 RESULTS OF CRAPS TEST for dh-ranFile-2018-06-23_06:31 No. of wins: Observed Expected 98608 98585.9 z-score= 0.099, pvalue=0.53944 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66844 66666.7 0.472 0.472 2 37476 37654.3 0.844 1.316 3 26825 26954.7 0.624 1.941 4 19559 19313.5 3.122 5.062 5 13776 13851.4 0.411 5.473 6 10114 9943.5 2.922 8.395 7 7296 7145.0 3.190 11.585 8 4951 5139.1 6.883 18.468 9 3594 3699.9 3.029 21.497 10 2583 2666.3 2.602 24.099 11 1941 1923.3 0.162 24.262 12 1378 1388.7 0.083 24.345 13 988 1003.7 0.246 24.591 14 710 726.1 0.359 24.949 15 538 525.8 0.281 25.231 16 392 381.2 0.309 25.540 17 298 276.5 1.665 27.205 18 207 200.8 0.190 27.395 19 124 146.0 3.311 30.705 20 109 106.2 0.073 30.778 21 297 287.1 0.340 31.119 Chisq= 31.12 for 20 degrees of freedom, p= 0.94636 SUMMARY of craptest p-value for no. of wins: 0.539443 p-value for throws/game: 0.946358 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-23_06:31 No. of wins: Observed Expected 98981 98585.9 z-score= 1.767, pvalue=0.96141 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66506 66666.7 0.387 0.387 2 37804 37654.3 0.595 0.982 3 27043 26954.7 0.289 1.271 4 19338 19313.5 0.031 1.302 5 13987 13851.4 1.327 2.629 6 9888 9943.5 0.310 2.940 7 7119 7145.0 0.095 3.035 8 5094 5139.1 0.395 3.430 9 3621 3699.9 1.681 5.111 10 2610 2666.3 1.189 6.300 11 1930 1923.3 0.023 6.323 12 1344 1388.7 1.441 7.764 13 1033 1003.7 0.854 8.619 14 787 726.1 5.101 13.719 15 537 525.8 0.237 13.956 16 357 381.2 1.530 15.487 17 313 276.5 4.807 20.294 18 186 200.8 1.095 21.389 19 125 146.0 3.016 24.405 20 91 106.2 2.180 26.585 21 287 287.1 0.000 26.585 Chisq= 26.58 for 20 degrees of freedom, p= 0.85265 SUMMARY of craptest p-value for no. of wins: 0.961411 p-value for throws/game: 0.852645 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0001,0.0011,0.0115,0.0155,0.0213,0.0266,0.0369,0.0375,0.0430,0.0486, 0.0489,0.0636,0.0664,0.0675,0.0700,0.0751,0.0779,0.0781,0.0818,0.0852, 0.0854,0.0868,0.0887,0.0930,0.0931,0.1013,0.1020,0.1097,0.1149,0.1157, 0.1208,0.1242,0.1281,0.1282,0.1299,0.1308,0.1341,0.1354,0.1354,0.1441, 0.1452,0.1501,0.1558,0.1570,0.1576,0.1596,0.1635,0.1654,0.1655,0.1662, 0.1689,0.1723,0.1778,0.1820,0.1894,0.1902,0.1924,0.2028,0.2036,0.2039, 0.2040,0.2135,0.2175,0.2197,0.2202,0.2285,0.2301,0.2338,0.2355,0.2370, 0.2373,0.2399,0.2503,0.2505,0.2635,0.2636,0.2642,0.2648,0.2691,0.2716, 0.2801,0.2852,0.2869,0.2919,0.2959,0.2962,0.2975,0.3046,0.3050,0.3064, 0.3077,0.3126,0.3139,0.3176,0.3327,0.3330,0.3423,0.3445,0.3467,0.3484, 0.3487,0.3492,0.3501,0.3542,0.3557,0.3574,0.3633,0.3640,0.3640,0.3656, 0.3696,0.3786,0.3849,0.3859,0.3903,0.3947,0.3949,0.3958,0.4071,0.4075, 0.4112,0.4188,0.4247,0.4285,0.4349,0.4363,0.4392,0.4467,0.4496,0.4506, 0.4527,0.4532,0.4748,0.4755,0.4787,0.4855,0.4881,0.4899,0.4909,0.4942, 0.4948,0.4968,0.5008,0.5106,0.5114,0.5131,0.5150,0.5207,0.5239,0.5365, 0.5371,0.5394,0.5521,0.5548,0.5629,0.5652,0.5738,0.5745,0.5762,0.5788, 0.5869,0.5930,0.5990,0.6022,0.6028,0.6040,0.6097,0.6111,0.6151,0.6153, 0.6179,0.6194,0.6309,0.6320,0.6383,0.6446,0.6500,0.6527,0.6625,0.6706, 0.6716,0.6730,0.6768,0.6780,0.6857,0.6905,0.6934,0.6961,0.6969,0.7007, 0.7038,0.7081,0.7081,0.7121,0.7158,0.7171,0.7175,0.7209,0.7242,0.7302, 0.7321,0.7328,0.7431,0.7454,0.7457,0.7634,0.7645,0.7675,0.7724,0.7744, 0.7756,0.7787,0.7804,0.7828,0.7843,0.7909,0.7973,0.8052,0.8053,0.8119, 0.8124,0.8129,0.8172,0.8197,0.8199,0.8215,0.8255,0.8273,0.8309,0.8312, 0.8340,0.8377,0.8402,0.8411,0.8441,0.8468,0.8484,0.8526,0.8626,0.8633, 0.8637,0.8640,0.8886,0.8919,0.8927,0.8957,0.8966,0.8998,0.9016,0.9144, 0.9281,0.9303,0.9319,0.9364,0.9446,0.9452,0.9464,0.9486,0.9614,0.9645, 0.9677,0.9693,0.9731,0.9744,0.9757,0.9870,0.9877,0.9907,0.9946, Overall p-value after applying KStest on 269 p-values = 0.677587 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.