RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-03-12_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 15.65 12.4326 0.226735 2 to 25 15.44 37.5051 0.997127 3 to 26 15.30 26.6831 0.937117 4 to 27 15.73 27.9445 0.954409 5 to 28 15.85 13.7573 0.315799 6 to 29 15.74 11.9187 0.194964 7 to 30 15.68 22.3021 0.826621 8 to 31 15.72 22.7169 0.841306 9 to 32 15.56 22.2593 0.825047 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.028594 Tough bday spacings test for dh-ranFile-2016-03-12_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 15 33 69 99 76 89 50 39 16 8 6 (O-E)^2/E 3.7 0.4 0.2 0.0 4.8 1.5 0.1 2.9 0.1 0.3 0.9 Birthday Spacings: Sum(O-E)^2/E= 14.912, p= 0.865 RESULTS OF GCD FOR dh-ranFile-2016-03-12_01:31 Euclid's algorithm: p-value, steps to gcd: 0.021505 p-value, dist. of gcd's: 0.909902 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-03-12_01:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.470 0.983 0.361 0.842 0.739 0.828 0.689 0.620 Bits 8 to 15---> 0.689 0.606 0.827 0.918 0.098 0.450 0.715 0.903 Bits 16 to 23---> 0.161 0.662 0.444 0.630 0.214 0.932 0.600 0.762 Bits 24 to 31---> 0.185 0.288 0.879 0.723 0.671 0.308 0.166 0.430 KS test for the above 32 p values: 0.880 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-03-12_01:31, p-values for 5 runs: 0.3943, 0.4824, 0.0602, 0.7494, 0.1587 Rank test for binary matrices (31x31) for dh-ranFile-2016-03-12_01:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 221 211.4 0.434 0.434 r= 29 5129 5134.0 0.005 0.439 r= 30 23155 23103.0 0.117 0.556 r= 31 11495 11551.5 0.277 0.833 chi-square = 0.833 with df = 3; p-value = 0.158 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-03-12_01:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 204 211.4 0.260 0.260 r= 30 5100 5134.0 0.225 0.486 r= 31 23223 23103.0 0.623 1.108 r= 32 11473 11551.5 0.534 1.642 chi-square = 1.642 with df = 3; p-value = 0.350 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-03-12_01:31 b-rank test for bits 1 to 8, p=0.93799 b-rank test for bits 2 to 9, p=0.26530 b-rank test for bits 3 to 10, p=0.16477 b-rank test for bits 4 to 11, p=0.61374 b-rank test for bits 5 to 12, p=0.98489 b-rank test for bits 6 to 13, p=0.75675 b-rank test for bits 7 to 14, p=0.70203 b-rank test for bits 8 to 15, p=0.49068 b-rank test for bits 9 to 16, p=0.49091 b-rank test for bits 10 to 17, p=0.01059 b-rank test for bits 11 to 18, p=0.57001 b-rank test for bits 12 to 19, p=0.95094 b-rank test for bits 13 to 20, p=0.29980 b-rank test for bits 14 to 21, p=0.45509 b-rank test for bits 15 to 22, p=0.78406 b-rank test for bits 16 to 23, p=0.63620 b-rank test for bits 17 to 24, p=0.66889 b-rank test for bits 18 to 25, p=0.30800 b-rank test for bits 19 to 26, p=0.61586 b-rank test for bits 20 to 27, p=0.92731 b-rank test for bits 21 to 28, p=0.43861 b-rank test for bits 22 to 29, p=0.23035 b-rank test for bits 23 to 30, p=0.38975 b-rank test for bits 24 to 31, p=0.49181 b-rank test for bits 25 to 32, p=0.21173 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 = 0.644733 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-03-12_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 142359 1.05 0.853286 2 142152 0.57 0.714638 3 142244 0.78 0.782875 4 141361 -1.28 0.100071 5 141260 -1.52 0.064617 6 141615 -0.69 0.245825 7 142038 0.30 0.618152 8 142251 0.80 0.787650 9 141432 -1.12 0.132370 10 142702 1.85 0.967989 11 141920 0.02 0.509945 12 141613 -0.69 0.244356 13 141816 -0.22 0.413691 14 142076 0.39 0.651516 15 141515 -0.92 0.178439 16 141426 -1.13 0.129391 17 141574 -0.78 0.216672 18 141797 -0.26 0.396486 19 142115 0.48 0.684577 20 142690 1.82 0.965924 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-03-12_01:31 Bits used No. missing words z-score p-value 23 to 32 142118 0.7196 0.764100 22 to 31 142028 0.4092 0.658806 21 to 30 141876 -0.1149 0.454250 20 to 29 142363 1.5644 0.941136 19 to 28 142494 2.0161 0.978105 18 to 27 141833 -0.2632 0.396196 17 to 26 142179 0.9299 0.823788 16 to 25 142328 1.4437 0.925587 15 to 24 142244 1.1540 0.875757 14 to 23 142156 0.8506 0.802500 13 to 22 142013 0.3575 0.639635 12 to 21 141785 -0.4287 0.334062 11 to 20 142019 0.3782 0.647349 10 to 19 141546 -1.2529 0.105128 9 to 18 141761 -0.5115 0.304507 8 to 17 141879 -0.1046 0.458352 7 to 16 141603 -1.0563 0.145413 6 to 15 141949 0.1368 0.554403 5 to 14 141923 0.0471 0.518798 4 to 13 142163 0.8747 0.809138 3 to 12 141548 -1.2460 0.106389 2 to 11 141145 -2.6356 0.004199 1 to 10 141619 -1.0011 0.158380 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-03-12_01:31 Bits used No. missing words z-score p-value 28 to 32 141903 -0.0215 0.491440 27 to 31 142270 1.2226 0.889262 26 to 30 142315 1.3752 0.915458 25 to 29 141952 0.1446 0.557504 24 to 28 141745 -0.5571 0.288746 23 to 27 141789 -0.4079 0.341674 22 to 26 142162 0.8565 0.804142 21 to 25 142246 1.1413 0.873118 20 to 24 141698 -0.7164 0.236881 19 to 23 142455 1.8497 0.967824 18 to 22 141818 -0.3096 0.378435 17 to 21 141234 -2.2893 0.011032 16 to 20 142005 0.3243 0.627147 15 to 19 142112 0.6870 0.753964 14 to 18 141894 -0.0520 0.479278 13 to 17 142262 1.1955 0.884053 12 to 16 141844 -0.2215 0.412368 11 to 15 141913 0.0124 0.504963 10 to 14 141920 0.0362 0.514426 9 to 13 141593 -1.0723 0.141792 8 to 12 142182 0.9243 0.822336 7 to 11 142484 1.9480 0.974295 6 to 10 141840 -0.2350 0.407098 5 to 9 141987 0.2633 0.603836 4 to 8 142063 0.5209 0.698787 3 to 7 142447 1.8226 0.965819 2 to 6 141917 0.0260 0.510371 1 to 5 141639 -0.9164 0.179736 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-03-12_01:31 Bits used No. missing words z-score p-value 31 to 32 142032 0.3619 0.641271 30 to 31 142757 2.5005 0.993799 29 to 30 142090 0.5329 0.702966 28 to 29 141822 -0.2576 0.398354 27 to 28 142361 1.3324 0.908629 26 to 27 141642 -0.7886 0.215178 25 to 26 142024 0.3383 0.632416 24 to 25 141557 -1.0393 0.149328 23 to 24 141931 0.0639 0.525484 22 to 23 141988 0.2321 0.591756 21 to 22 142019 0.3235 0.626846 20 to 21 142171 0.7719 0.779910 19 to 20 142323 1.2203 0.888818 18 to 19 142214 0.8987 0.815602 17 to 18 141748 -0.4759 0.317073 16 to 17 141829 -0.2370 0.406343 15 to 16 141676 -0.6883 0.245635 14 to 15 141504 -1.1957 0.115914 13 to 14 141857 -0.1544 0.438661 12 to 13 142130 0.6509 0.742459 11 to 12 141282 -1.8505 0.032119 10 to 11 142353 1.3088 0.904692 9 to 10 142808 2.6509 0.995987 8 to 9 142141 0.6834 0.752821 7 to 8 142136 0.6686 0.748138 6 to 7 141490 -1.2370 0.108051 5 to 6 141290 -1.8269 0.033855 4 to 5 141655 -0.7502 0.226556 3 to 4 142203 0.8663 0.806833 2 to 3 141457 -1.3343 0.091052 1 to 2 141897 -0.0364 0.485493 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-03-12_01:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2584.91 1.201 0.885088 Test results for specific bytes for dh-ranFile-2016-03-12_01:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2490.77 -0.131 0.448076 2 to 9 2375.31 -1.763 0.038915 3 to 10 2574.54 1.054 0.854092 4 to 11 2453.38 -0.659 0.254838 5 to 12 2516.53 0.234 0.592444 6 to 13 2548.34 0.684 0.752916 7 to 14 2367.74 -1.870 0.030708 8 to 15 2427.84 -1.020 0.153756 9 to 16 2548.14 0.681 0.751982 10 to 17 2508.60 0.122 0.548411 11 to 18 2499.71 -0.004 0.498382 12 to 19 2430.65 -0.981 0.163349 13 to 20 2484.29 -0.222 0.412102 14 to 21 2562.42 0.883 0.811297 15 to 22 2506.30 0.089 0.535494 16 to 23 2645.32 2.055 0.980064 17 to 24 2493.97 -0.085 0.466045 18 to 25 2559.94 0.848 0.801698 19 to 26 2485.88 -0.200 0.420874 20 to 27 2462.37 -0.532 0.297313 21 to 28 2513.60 0.192 0.576234 22 to 29 2449.84 -0.709 0.239029 23 to 30 2391.15 -1.539 0.061854 24 to 31 2452.10 -0.677 0.249062 25 to 32 2667.37 2.367 0.991033 CDPARK for dh-ranFile-2016-03-12_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 3540 0.7763 0.781201 3501 -1.0046 0.157553 3554 1.4155 0.921543 3537 0.6393 0.738676 3534 0.5023 0.692266 3521 -0.0913 0.463617 3549 1.1872 0.882429 3476 -2.1461 0.015932 3499 -1.0959 0.136563 3491 -1.4612 0.071982 Square side=100, avg. no. parked=3520.20 sample std.=25.42 p-value of the KSTEST for those 10 p-values: 0.590213 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-03-12_01:31 0.8643,0.7071,0.9043,0.2608,0.2319,0.2302,0.5863,0.9264,0.4564,0.6725, The KS test for those 10 p-values: 0.559704 The 3DSPHERES test for dh-ranFile-2016-03-12_01:31 sample no r^3 equiv. uni. 1 6.800 0.202804 2 7.437 0.219566 3 22.669 0.530295 4 40.691 0.742409 5 0.535 0.017667 6 10.192 0.288047 7 21.886 0.517859 8 1.911 0.061714 9 93.096 0.955094 10 25.824 0.577177 11 3.342 0.105425 12 12.024 0.330224 13 35.511 0.693853 14 17.016 0.432880 15 33.220 0.669560 16 17.953 0.450324 17 4.378 0.135786 18 7.176 0.212754 19 4.748 0.146366 20 14.694 0.387256 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.125236 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-03-12_01:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 0.1 -0.6 -0.8 -2.0 1.3 -0.5 -0.5 1.1 0.5 -0.2 -0.5 -0.4 1.3 -0.2 0.7 -0.9 -0.2 0.1 0.2 0.3 -0.7 -0.1 -0.5 1.3 0.1 1.1 -0.7 -1.1 -2.6 -0.7 0.0 1.1 1.1 0.2 -0.1 -0.2 3.0 0.1 2.1 -0.6 1.0 0.8 Chi-square with 42 degrees of freedom:43.273883 z-score=0.138992, p-value=0.583264 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-03-12_01:31 Test no p-value 1 0.420453 2 0.703934 3 0.528550 4 0.545975 5 0.584644 6 0.022241 7 0.782255 8 0.221613 9 0.320720 10 0.251653 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.604112 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-03-12_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 66536 0.26 66655 0.00 3 25000.00 25192 1.47 24970 0.04 4 6666.67 6613 0.43 6746 0.94 5 1388.89 1378 0.09 1347 1.26 6 238.10 248 0.41 250 0.60 7 34.72 29 0.94 24 3.31 8 4.96 3 0.77 7 0.84 p=0.37421 p=0.67819 Number of rngs required: 687933, p-value: 0.294 RESULTS OF CRAPS TEST for dh-ranFile-2016-03-12_01:31 No. of wins: Observed Expected 98873 98585.9 z-score= 1.284, pvalue=0.90048 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66667 66666.7 0.000 0.000 2 37653 37654.3 0.000 0.000 3 27063 26954.7 0.435 0.435 4 19367 19313.5 0.148 0.583 5 13716 13851.4 1.324 1.907 6 9911 9943.5 0.107 2.014 7 7155 7145.0 0.014 2.028 8 5164 5139.1 0.121 2.149 9 3746 3699.9 0.575 2.724 10 2646 2666.3 0.155 2.878 11 1911 1923.3 0.079 2.957 12 1314 1388.7 4.022 6.980 13 1029 1003.7 0.637 7.617 14 727 726.1 0.001 7.618 15 546 525.8 0.773 8.391 16 397 381.2 0.659 9.050 17 234 276.5 6.544 15.594 18 219 200.8 1.644 17.238 19 147 146.0 0.007 17.245 20 91 106.2 2.180 19.424 21 297 287.1 0.340 19.765 Chisq= 19.76 for 20 degrees of freedom, p= 0.52728 SUMMARY of craptest p-value for no. of wins: 0.900475 p-value for throws/game: 0.527279 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-03-12_01:31 No. of wins: Observed Expected 98729 98585.9 z-score= 0.640, pvalue=0.73898 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66842 66666.7 0.461 0.461 2 37394 37654.3 1.800 2.261 3 26953 26954.7 0.000 2.261 4 19417 19313.5 0.555 2.816 5 13733 13851.4 1.012 3.828 6 10113 9943.5 2.888 6.716 7 7119 7145.0 0.095 6.811 8 5049 5139.1 1.579 8.390 9 3735 3699.9 0.334 8.723 10 2767 2666.3 3.803 12.527 11 1883 1923.3 0.846 13.372 12 1358 1388.7 0.680 14.053 13 976 1003.7 0.765 14.818 14 733 726.1 0.065 14.883 15 573 525.8 4.230 19.113 16 345 381.2 3.429 22.542 17 251 276.5 2.359 24.901 18 199 200.8 0.017 24.917 19 160 146.0 1.346 26.263 20 119 106.2 1.539 27.802 21 281 287.1 0.130 27.932 Chisq= 27.93 for 20 degrees of freedom, p= 0.88898 SUMMARY of craptest p-value for no. of wins: 0.738983 p-value for throws/game: 0.888983 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0042,0.0106,0.0110,0.0159,0.0177,0.0215,0.0222,0.0286,0.0307,0.0321, 0.0339,0.0389,0.0602,0.0617,0.0619,0.0646,0.0720,0.0911,0.0984,0.1001, 0.1051,0.1054,0.1064,0.1081,0.1159,0.1252,0.1294,0.1324,0.1358,0.1366, 0.1418,0.1454,0.1464,0.1493,0.1538,0.1576,0.1583,0.1584,0.1587,0.1613, 0.1633,0.1648,0.1663,0.1784,0.1797,0.1846,0.1950,0.2028,0.2117,0.2128, 0.2142,0.2152,0.2167,0.2196,0.2216,0.2266,0.2267,0.2302,0.2304,0.2319, 0.2369,0.2390,0.2444,0.2456,0.2458,0.2491,0.2517,0.2548,0.2608,0.2653, 0.2880,0.2883,0.2887,0.2940,0.2973,0.2998,0.3045,0.3079,0.3080,0.3158, 0.3171,0.3207,0.3302,0.3341,0.3417,0.3501,0.3611,0.3742,0.3784,0.3873, 0.3898,0.3943,0.3962,0.3965,0.3984,0.4063,0.4071,0.4121,0.4124,0.4137, 0.4205,0.4209,0.4300,0.4329,0.4386,0.4387,0.4441,0.4481,0.4496,0.4503, 0.4542,0.4551,0.4564,0.4584,0.4636,0.4660,0.4697,0.4793,0.4824,0.4855, 0.4907,0.4909,0.4914,0.4918,0.4984,0.5050,0.5099,0.5104,0.5144,0.5179, 0.5188,0.5255,0.5273,0.5286,0.5303,0.5355,0.5460,0.5484,0.5544,0.5575, 0.5597,0.5700,0.5762,0.5772,0.5833,0.5846,0.5863,0.5902,0.5918,0.5924, 0.6000,0.6038,0.6041,0.6060,0.6137,0.6159,0.6182,0.6201,0.6268,0.6271, 0.6296,0.6324,0.6362,0.6396,0.6413,0.6447,0.6473,0.6515,0.6588,0.6624, 0.6689,0.6696,0.6709,0.6725,0.6782,0.6846,0.6886,0.6891,0.6923,0.6939, 0.6988,0.7020,0.7030,0.7039,0.7071,0.7146,0.7155,0.7233,0.7387,0.7388, 0.7390,0.7424,0.7425,0.7481,0.7494,0.7520,0.7528,0.7529,0.7540,0.7567, 0.7624,0.7641,0.7799,0.7812,0.7823,0.7829,0.7841,0.7877,0.8017,0.8025, 0.8041,0.8068,0.8091,0.8113,0.8156,0.8223,0.8238,0.8250,0.8266,0.8267, 0.8279,0.8413,0.8423,0.8533,0.8541,0.8643,0.8647,0.8731,0.8758,0.8787, 0.8798,0.8824,0.8841,0.8851,0.8888,0.8890,0.8893,0.9005,0.9034,0.9043, 0.9047,0.9086,0.9099,0.9155,0.9177,0.9215,0.9256,0.9264,0.9273,0.9319, 0.9371,0.9380,0.9411,0.9509,0.9544,0.9551,0.9658,0.9659,0.9678,0.9680, 0.9743,0.9781,0.9801,0.9832,0.9849,0.9910,0.9938,0.9960,0.9971, Overall p-value after applying KStest on 269 p-values = 0.310637 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.