RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-29_05:31 (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 17.5638 0.583154 2 to 25 15.73 19.0086 0.671960 3 to 26 15.76 16.4167 0.505489 4 to 27 15.85 20.6624 0.758242 5 to 28 15.77 21.7073 0.803762 6 to 29 15.57 12.9139 0.258068 7 to 30 15.80 16.0316 0.478405 8 to 31 15.77 11.1362 0.150603 9 to 32 16.03 12.2669 0.216290 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.812803 Tough bday spacings test for dh-ranFile-2018-06-29_05:31: 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 7 42 59 99 112 78 51 26 18 7 1 (O-E)^2/E 0.5 0.8 2.8 0.0 2.1 0.0 0.0 0.5 0.7 0.0 2.3 Birthday Spacings: Sum(O-E)^2/E= 9.675, p= 0.531 RESULTS OF GCD FOR dh-ranFile-2018-06-29_05:31 Euclid's algorithm: p-value, steps to gcd: 0.115285 p-value, dist. of gcd's: 0.555710 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-29_05:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.291 0.168 0.284 0.419 0.560 0.937 0.210 0.452 Bits 8 to 15---> 0.969 0.639 0.509 0.306 0.290 0.693 0.080 0.597 Bits 16 to 23---> 0.119 0.437 0.009 0.533 0.459 0.328 0.904 0.349 Bits 24 to 31---> 0.797 0.131 0.629 0.765 0.978 0.534 0.354 0.210 KS test for the above 32 p values: 0.384 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-29_05:31, p-values for 5 runs: 0.5341, 0.4150, 0.8350, 0.8605, 0.2503 Rank test for binary matrices (31x31) for dh-ranFile-2018-06-29_05:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 213 211.4 0.012 0.012 r= 29 5017 5134.0 2.667 2.679 r= 30 23379 23103.0 3.296 5.975 r= 31 11391 11551.5 2.231 8.205 chi-square = 8.205 with df = 3; p-value = 0.958 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-06-29_05:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 190 211.4 2.170 2.170 r= 30 5080 5134.0 0.568 2.738 r= 31 23220 23103.0 0.592 3.330 r= 32 11510 11551.5 0.149 3.479 chi-square = 3.479 with df = 3; p-value = 0.677 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-06-29_05:31 b-rank test for bits 1 to 8, p=0.61642 b-rank test for bits 2 to 9, p=0.70261 b-rank test for bits 3 to 10, p=0.99610 b-rank test for bits 4 to 11, p=0.25616 b-rank test for bits 5 to 12, p=0.81468 b-rank test for bits 6 to 13, p=0.53707 b-rank test for bits 7 to 14, p=0.94860 b-rank test for bits 8 to 15, p=0.20039 b-rank test for bits 9 to 16, p=0.85187 b-rank test for bits 10 to 17, p=0.12733 b-rank test for bits 11 to 18, p=0.04036 b-rank test for bits 12 to 19, p=0.58462 b-rank test for bits 13 to 20, p=0.09966 b-rank test for bits 14 to 21, p=0.60109 b-rank test for bits 15 to 22, p=0.31361 b-rank test for bits 16 to 23, p=0.06907 b-rank test for bits 17 to 24, p=0.52391 b-rank test for bits 18 to 25, p=0.54161 b-rank test for bits 19 to 26, p=0.85878 b-rank test for bits 20 to 27, p=0.41635 b-rank test for bits 21 to 28, p=0.29793 b-rank test for bits 22 to 29, p=0.26908 b-rank test for bits 23 to 30, p=0.22250 b-rank test for bits 24 to 31, p=0.97260 b-rank test for bits 25 to 32, p=0.17688 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 = 0.879578 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-29_05:31 (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 142590 1.59 0.944122 2 141755 -0.36 0.359205 3 141934 0.06 0.522982 4 141642 -0.62 0.266116 5 141987 0.18 0.572001 6 141902 -0.02 0.493168 7 141983 0.17 0.568331 8 141756 -0.36 0.360079 9 142058 0.35 0.635840 10 141696 -0.50 0.309089 11 142267 0.84 0.798332 12 141594 -0.74 0.230637 13 141973 0.15 0.559129 14 142479 1.33 0.908406 15 142360 1.05 0.853822 16 142024 0.27 0.605620 17 141638 -0.63 0.263057 18 141963 0.13 0.549895 19 141198 -1.66 0.048258 20 142127 0.51 0.694475 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-06-29_05:31 Bits used No. missing words z-score p-value 23 to 32 141796 -0.3908 0.347975 22 to 31 142077 0.5782 0.718426 21 to 30 142096 0.6437 0.740112 20 to 29 142060 0.5196 0.698312 19 to 28 142075 0.5713 0.716094 18 to 27 141643 -0.9184 0.179210 17 to 26 141761 -0.5115 0.304507 16 to 25 142219 1.0678 0.857201 15 to 24 141883 -0.0908 0.463829 14 to 23 142196 0.9885 0.838550 13 to 22 142252 1.1816 0.881322 12 to 21 142054 0.4989 0.691062 11 to 20 141643 -0.9184 0.179210 10 to 19 141752 -0.5425 0.293731 9 to 18 141524 -1.3287 0.091970 8 to 17 141952 0.1471 0.558488 7 to 16 141712 -0.6804 0.248110 6 to 15 141514 -1.3632 0.086409 5 to 14 141589 -1.1046 0.134669 4 to 13 141602 -1.0598 0.144627 3 to 12 142113 0.7023 0.758757 2 to 11 142002 0.3196 0.625346 1 to 10 142004 0.3264 0.627957 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-06-29_05:31 Bits used No. missing words z-score p-value 28 to 32 141793 -0.3943 0.346665 27 to 31 142062 0.5175 0.697605 26 to 30 142043 0.4531 0.674768 25 to 29 141717 -0.6520 0.257212 24 to 28 141820 -0.3028 0.381016 23 to 27 141538 -1.2587 0.104061 22 to 26 141819 -0.3062 0.379725 21 to 25 141761 -0.5028 0.307548 20 to 24 141840 -0.2350 0.407098 19 to 23 142081 0.5819 0.719694 18 to 22 142283 1.2667 0.897365 17 to 21 142008 0.3345 0.630989 16 to 20 141817 -0.3130 0.377147 15 to 19 142003 0.3175 0.624578 14 to 18 141626 -0.9604 0.168417 13 to 17 142177 0.9074 0.817891 12 to 16 142170 0.8836 0.811551 11 to 15 141865 -0.1503 0.440275 10 to 14 142171 0.8870 0.812465 9 to 13 142254 1.1684 0.878672 8 to 12 141931 0.0735 0.529279 7 to 11 141945 0.1209 0.548121 6 to 10 141914 0.0158 0.506315 5 to 9 142097 0.6362 0.737667 4 to 8 141850 -0.2011 0.420303 3 to 7 141982 0.2463 0.597290 2 to 6 141733 -0.5977 0.275010 1 to 5 141893 -0.0554 0.477928 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-06-29_05:31 Bits used No. missing words z-score p-value 31 to 32 141840 -0.2045 0.418976 30 to 31 142302 1.1583 0.876633 29 to 30 141786 -0.3638 0.358002 28 to 29 142157 0.7306 0.767485 27 to 28 141974 0.1908 0.575646 26 to 27 140934 -2.8771 0.002007 25 to 26 141799 -0.3255 0.372418 24 to 25 142292 1.1288 0.870513 23 to 24 141716 -0.5703 0.284239 22 to 23 142533 1.8397 0.967096 21 to 22 142081 0.5064 0.693713 20 to 21 142528 1.8250 0.965998 19 to 20 142429 1.5329 0.937356 18 to 19 141940 0.0905 0.536044 17 to 18 141858 -0.1514 0.439824 16 to 17 141827 -0.2429 0.404056 15 to 16 141781 -0.3786 0.352509 14 to 15 141809 -0.2960 0.383631 13 to 14 141970 0.1790 0.571018 12 to 13 142413 1.4858 0.931328 11 to 12 142674 2.2557 0.987954 10 to 11 142204 0.8692 0.807640 9 to 10 142073 0.4828 0.685382 8 to 9 141974 0.1908 0.575646 7 to 8 142331 1.2439 0.893225 6 to 7 141835 -0.2193 0.413223 5 to 6 141854 -0.1632 0.435174 4 to 5 141967 0.1701 0.567541 3 to 4 142313 1.1908 0.883127 2 to 3 141954 0.1318 0.552417 1 to 2 142451 1.5978 0.944961 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-29_05:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2345.10 -2.191 0.014238 Test results for specific bytes for dh-ranFile-2018-06-29_05:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2462.84 -0.526 0.299602 2 to 9 2560.86 0.861 0.805277 3 to 10 2449.93 -0.708 0.239425 4 to 11 2384.99 -1.626 0.051922 5 to 12 2432.29 -0.958 0.169143 6 to 13 2404.10 -1.356 0.087518 7 to 14 2496.80 -0.045 0.481960 8 to 15 2466.83 -0.469 0.319519 9 to 16 2417.73 -1.163 0.122323 10 to 17 2439.13 -0.861 0.194675 11 to 18 2599.82 1.412 0.920977 12 to 19 2460.29 -0.562 0.287194 13 to 20 2550.94 0.720 0.764373 14 to 21 2528.85 0.408 0.658349 15 to 22 2424.43 -1.069 0.142599 16 to 23 2408.74 -1.291 0.098429 17 to 24 2570.03 0.990 0.839014 18 to 25 2570.78 1.001 0.841597 19 to 26 2358.43 -2.002 0.022637 20 to 27 2490.03 -0.141 0.443945 21 to 28 2500.74 0.010 0.504189 22 to 29 2458.45 -0.588 0.278421 23 to 30 2564.27 0.909 0.818294 24 to 31 2545.04 0.637 0.737930 25 to 32 2520.70 0.293 0.615141 CDPARK for dh-ranFile-2018-06-29_05:31: 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 3487 -1.6438 0.050105 3495 -1.2785 0.100530 3509 -0.6393 0.261324 3539 0.7306 0.767486 3490 -1.5068 0.065925 3516 -0.3196 0.374623 3534 0.5023 0.692266 3527 0.1826 0.572463 3542 0.8676 0.807188 3530 0.3196 0.625377 Square side=100, avg. no. parked=3516.90 sample std.=19.61 p-value of the KSTEST for those 10 p-values: 0.606126 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-29_05:31 0.2287,0.8191,0.0069,0.3757,0.7273,0.8235,0.2353,0.7146,0.0047,0.3751, The KS test for those 10 p-values: 0.239989 The 3DSPHERES test for dh-ranFile-2018-06-29_05:31 sample no r^3 equiv. uni. 1 7.194 0.213220 2 19.518 0.478270 3 13.002 0.351701 4 52.418 0.825753 5 6.283 0.188961 6 44.995 0.776829 7 21.570 0.512764 8 0.023 0.000765 9 99.635 0.963889 10 89.347 0.949117 11 26.798 0.590689 12 2.178 0.070028 13 16.476 0.422586 14 93.834 0.956187 15 47.233 0.792876 16 7.562 0.222798 17 30.234 0.634978 18 53.788 0.833528 19 7.572 0.223072 20 1.760 0.056973 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.752638 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-29_05:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 0.1 -0.4 1.9 0.5 -2.0 0.4 1.2 -0.7 -1.3 -0.2 -0.3 -0.5 1.0 0.3 0.5 0.2 -0.7 -1.1 0.1 -0.7 1.7 -0.1 0.6 0.5 -1.2 1.8 0.6 -1.5 -1.0 -1.3 0.4 -0.5 0.4 1.5 2.0 -1.4 -0.1 0.9 -0.7 -0.6 1.0 -1.1 Chi-square with 42 degrees of freedom:42.296970 z-score=0.032402, p-value=0.541853 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-06-29_05:31 Test no p-value 1 0.966430 2 0.000900 3 0.447098 4 0.614819 5 0.065155 6 0.284494 7 0.095730 8 0.082299 9 0.591393 10 0.189987 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.055115 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-29_05:31: (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 66624 0.03 66856 0.54 3 25000.00 25066 0.17 24774 2.04 4 6666.67 6693 0.10 6727 0.55 5 1388.89 1342 1.58 1349 1.15 6 238.10 229 0.35 245 0.20 7 34.72 43 1.97 41 1.14 8 4.96 2 1.77 7 0.84 p=0.57424 p=0.62503 Number of rngs required: 687988, p-value: 0.316 RESULTS OF CRAPS TEST for dh-ranFile-2018-06-29_05:31 No. of wins: Observed Expected 98622 98585.9 z-score= 0.162, pvalue=0.56421 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66687 66666.7 0.006 0.006 2 37427 37654.3 1.372 1.379 3 26876 26954.7 0.230 1.609 4 19373 19313.5 0.184 1.792 5 13835 13851.4 0.019 1.812 6 10161 9943.5 4.756 6.567 7 7143 7145.0 0.001 6.568 8 5146 5139.1 0.009 6.577 9 3770 3699.9 1.329 7.907 10 2638 2666.3 0.300 8.207 11 1908 1923.3 0.122 8.329 12 1431 1388.7 1.286 9.615 13 1010 1003.7 0.039 9.654 14 696 726.1 1.251 10.905 15 514 525.8 0.266 11.172 16 390 381.2 0.205 11.377 17 263 276.5 0.663 12.040 18 187 200.8 0.952 12.993 19 137 146.0 0.553 13.545 20 124 106.2 2.978 16.523 21 284 287.1 0.034 16.557 Chisq= 16.56 for 20 degrees of freedom, p= 0.31849 SUMMARY of craptest p-value for no. of wins: 0.564207 p-value for throws/game: 0.318487 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-29_05:31 No. of wins: Observed Expected 98711 98585.9 z-score= 0.560, pvalue=0.71216 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66635 66666.7 0.015 0.015 2 37767 37654.3 0.337 0.352 3 26954 26954.7 0.000 0.352 4 19376 19313.5 0.203 0.555 5 13885 13851.4 0.081 0.636 6 9795 9943.5 2.219 2.855 7 7145 7145.0 0.000 2.855 8 5091 5139.1 0.450 3.305 9 3691 3699.9 0.021 3.326 10 2728 2666.3 1.428 4.754 11 1942 1923.3 0.181 4.935 12 1352 1388.7 0.972 5.907 13 991 1003.7 0.161 6.068 14 724 726.1 0.006 6.075 15 502 525.8 1.080 7.155 16 355 381.2 1.794 8.949 17 282 276.5 0.108 9.057 18 204 200.8 0.050 9.107 19 173 146.0 4.999 14.107 20 113 106.2 0.433 14.540 21 295 287.1 0.217 14.757 Chisq= 14.76 for 20 degrees of freedom, p= 0.20984 SUMMARY of craptest p-value for no. of wins: 0.712160 p-value for throws/game: 0.209840 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0008,0.0009,0.0020,0.0047,0.0069,0.0090,0.0142,0.0226,0.0404,0.0483, 0.0501,0.0519,0.0551,0.0570,0.0652,0.0659,0.0691,0.0700,0.0800,0.0823, 0.0864,0.0875,0.0920,0.0957,0.0984,0.0997,0.1005,0.1041,0.1153,0.1189, 0.1223,0.1273,0.1308,0.1347,0.1426,0.1446,0.1506,0.1678,0.1684,0.1691, 0.1769,0.1792,0.1792,0.1890,0.1900,0.1947,0.2004,0.2098,0.2098,0.2103, 0.2132,0.2163,0.2225,0.2228,0.2231,0.2287,0.2306,0.2353,0.2394,0.2400, 0.2481,0.2503,0.2562,0.2572,0.2581,0.2613,0.2631,0.2661,0.2691,0.2750, 0.2784,0.2842,0.2843,0.2845,0.2872,0.2897,0.2906,0.2937,0.2979,0.2996, 0.3045,0.3059,0.3075,0.3091,0.3136,0.3163,0.3185,0.3195,0.3285,0.3467, 0.3480,0.3493,0.3517,0.3525,0.3541,0.3580,0.3592,0.3601,0.3724,0.3746, 0.3751,0.3757,0.3771,0.3797,0.3810,0.3836,0.3845,0.4041,0.4071,0.4132, 0.4150,0.4163,0.4190,0.4194,0.4203,0.4226,0.4352,0.4373,0.4398,0.4403, 0.4439,0.4471,0.4523,0.4586,0.4638,0.4779,0.4783,0.4784,0.4820,0.4932, 0.5042,0.5055,0.5063,0.5089,0.5128,0.5230,0.5239,0.5293,0.5305,0.5326, 0.5339,0.5341,0.5360,0.5371,0.5416,0.5419,0.5481,0.5499,0.5524,0.5557, 0.5585,0.5591,0.5600,0.5642,0.5675,0.5683,0.5710,0.5720,0.5725,0.5742, 0.5756,0.5756,0.5832,0.5846,0.5907,0.5914,0.5969,0.5973,0.6011,0.6056, 0.6061,0.6148,0.6151,0.6164,0.6246,0.6250,0.6253,0.6254,0.6280,0.6286, 0.6310,0.6350,0.6358,0.6392,0.6583,0.6720,0.6748,0.6765,0.6854,0.6911, 0.6923,0.6931,0.6937,0.6945,0.6976,0.6983,0.7026,0.7122,0.7146,0.7161, 0.7184,0.7197,0.7273,0.7377,0.7379,0.7401,0.7526,0.7582,0.7588,0.7644, 0.7654,0.7675,0.7675,0.7768,0.7929,0.7970,0.7983,0.8038,0.8053,0.8072, 0.8076,0.8116,0.8125,0.8128,0.8147,0.8179,0.8183,0.8191,0.8235,0.8258, 0.8335,0.8350,0.8386,0.8390,0.8416,0.8519,0.8538,0.8572,0.8588,0.8605, 0.8705,0.8766,0.8787,0.8796,0.8813,0.8831,0.8932,0.8974,0.9044,0.9084, 0.9210,0.9313,0.9368,0.9374,0.9441,0.9450,0.9486,0.9491,0.9562,0.9580, 0.9639,0.9660,0.9664,0.9671,0.9694,0.9726,0.9780,0.9880,0.9961, Overall p-value after applying KStest on 269 p-values = 0.642005 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.