RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-02-14_20:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.83 20.6925 0.759652 2 to 25 15.62 23.9057 0.877981 3 to 26 15.99 18.6030 0.648209 4 to 27 15.80 16.1159 0.484367 5 to 28 15.65 15.8411 0.464875 6 to 29 15.88 15.5624 0.444956 7 to 30 15.99 16.3868 0.503400 8 to 31 15.90 19.3605 0.691764 9 to 32 15.78 22.3271 0.827535 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.141913 Tough bday spacings test for dh-ranFile-2017-02-14_20:31: 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 33 71 104 106 77 49 26 13 6 8 (O-E)^2/E 0.5 0.4 0.1 0.4 0.7 0.0 0.2 0.5 0.2 0.1 3.8 Birthday Spacings: Sum(O-E)^2/E= 6.835, p= 0.259 RESULTS OF GCD FOR dh-ranFile-2017-02-14_20:31 Euclid's algorithm: p-value, steps to gcd: 0.490993 p-value, dist. of gcd's: 0.676250 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-02-14_20:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.022 0.346 0.512 0.881 0.516 0.824 0.291 0.897 Bits 8 to 15---> 0.778 0.561 0.192 0.957 0.910 0.235 0.530 0.028 Bits 16 to 23---> 0.835 0.941 0.245 0.620 0.884 0.635 0.461 0.592 Bits 24 to 31---> 0.650 0.093 0.011 0.265 0.722 0.926 0.887 0.542 KS test for the above 32 p values: 0.683 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-02-14_20:31, p-values for 5 runs: 0.0161, 0.3273, 0.6367, 0.0032, 0.2768 Rank test for binary matrices (31x31) for dh-ranFile-2017-02-14_20:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 193 211.4 1.605 1.605 r= 29 5008 5134.0 3.093 4.697 r= 30 23093 23103.0 0.004 4.702 r= 31 11706 11551.5 2.066 6.768 chi-square = 6.768 with df = 3; p-value = 0.920 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2017-02-14_20:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 209 211.4 0.028 0.028 r= 30 5066 5134.0 0.901 0.929 r= 31 23154 23103.0 0.112 1.041 r= 32 11571 11551.5 0.033 1.074 chi-square = 1.074 with df = 3; p-value = 0.217 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2017-02-14_20:31 b-rank test for bits 1 to 8, p=0.92739 b-rank test for bits 2 to 9, p=0.12198 b-rank test for bits 3 to 10, p=0.43082 b-rank test for bits 4 to 11, p=0.39862 b-rank test for bits 5 to 12, p=0.06545 b-rank test for bits 6 to 13, p=0.94499 b-rank test for bits 7 to 14, p=0.48225 b-rank test for bits 8 to 15, p=0.30541 b-rank test for bits 9 to 16, p=0.83594 b-rank test for bits 10 to 17, p=0.45872 b-rank test for bits 11 to 18, p=0.22655 b-rank test for bits 12 to 19, p=0.35942 b-rank test for bits 13 to 20, p=0.67348 b-rank test for bits 14 to 21, p=0.70999 b-rank test for bits 15 to 22, p=0.07972 b-rank test for bits 16 to 23, p=0.93684 b-rank test for bits 17 to 24, p=0.74977 b-rank test for bits 18 to 25, p=0.41390 b-rank test for bits 19 to 26, p=0.15884 b-rank test for bits 20 to 27, p=0.29532 b-rank test for bits 21 to 28, p=0.97067 b-rank test for bits 22 to 29, p=0.41620 b-rank test for bits 23 to 30, p=0.29466 b-rank test for bits 24 to 31, p=0.87637 b-rank test for bits 25 to 32, p=0.93462 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 = 0.624349 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-02-14_20:31 (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 141643 -0.62 0.266883 2 141521 -0.91 0.182121 3 142472 1.31 0.905686 4 141464 -1.04 0.149056 5 141926 0.04 0.515534 6 142087 0.42 0.660972 7 141667 -0.57 0.285632 8 141994 0.20 0.578410 9 142067 0.37 0.643708 10 142227 0.74 0.771023 11 142156 0.58 0.717805 12 142351 1.03 0.848950 13 141695 -0.50 0.308266 14 141221 -1.61 0.053890 15 142241 0.77 0.780809 16 141835 -0.17 0.431063 17 142033 0.29 0.613690 18 141510 -0.93 0.175406 19 141524 -0.90 0.183979 20 141318 -1.38 0.083545 ---------------------------------------------------------------- OPSO test for dh-ranFile-2017-02-14_20:31 Bits used No. missing words z-score p-value 23 to 32 141782 -0.4391 0.330306 22 to 31 141908 -0.0046 0.498170 21 to 30 141561 -1.2011 0.114849 20 to 29 141926 0.0575 0.522920 19 to 28 142270 1.2437 0.893193 18 to 27 141640 -0.9287 0.176516 17 to 26 141921 0.0402 0.516050 16 to 25 141874 -0.1218 0.451518 15 to 24 141630 -0.9632 0.167722 14 to 23 141957 0.1644 0.565284 13 to 22 142095 0.6402 0.738992 12 to 21 141595 -1.0839 0.139205 11 to 20 141579 -1.1391 0.127337 10 to 19 141674 -0.8115 0.208544 9 to 18 142142 0.8023 0.788813 8 to 17 141978 0.2368 0.593591 7 to 16 142070 0.5540 0.710222 6 to 15 141556 -1.2184 0.111540 5 to 14 142282 1.2851 0.900616 4 to 13 142026 0.4023 0.656272 3 to 12 141743 -0.5736 0.283136 2 to 11 141913 0.0127 0.505049 1 to 10 141529 -1.3115 0.094847 ----------------------------------------------------------------- OQSO test for dh-ranFile-2017-02-14_20:31 Bits used No. missing words z-score p-value 28 to 32 141801 -0.3672 0.356727 27 to 31 141769 -0.4757 0.317146 26 to 30 141671 -0.8079 0.209575 25 to 29 141963 0.1819 0.572182 24 to 28 141808 -0.3435 0.365614 23 to 27 142129 0.7446 0.771757 22 to 26 142283 1.2667 0.897365 21 to 25 141530 -1.2859 0.099245 20 to 24 141760 -0.5062 0.306357 19 to 23 141891 -0.0621 0.475227 18 to 22 141745 -0.5571 0.288746 17 to 21 141893 -0.0554 0.477928 16 to 20 141947 0.1277 0.550805 15 to 19 142149 0.8124 0.791731 14 to 18 142584 2.2870 0.988903 13 to 17 142163 0.8599 0.805077 12 to 16 141824 -0.2893 0.386193 11 to 15 141921 0.0396 0.515778 10 to 14 142126 0.7345 0.768670 9 to 13 141537 -1.2621 0.103450 8 to 12 142270 1.2226 0.889262 7 to 11 141988 0.2667 0.605141 6 to 10 141942 0.1107 0.544091 5 to 9 141619 -0.9842 0.162516 4 to 8 141814 -0.3232 0.373290 3 to 7 142328 1.4192 0.922083 2 to 6 142129 0.7446 0.771757 1 to 5 142091 0.6158 0.730997 ----------------------------------------------------------------- DNA test for dh-ranFile-2017-02-14_20:31 Bits used No. missing words z-score p-value 31 to 32 142249 1.0020 0.841823 30 to 31 142249 1.0020 0.841823 29 to 30 142225 0.9312 0.824120 28 to 29 141593 -0.9331 0.175377 27 to 28 141742 -0.4936 0.310795 26 to 27 142531 1.8338 0.966661 25 to 26 142210 0.8869 0.812442 24 to 25 142101 0.5654 0.714099 23 to 24 142168 0.7630 0.777280 22 to 23 141516 -1.1603 0.122970 21 to 22 141592 -0.9361 0.174617 20 to 21 141929 0.0580 0.523135 19 to 20 141652 -0.7591 0.223901 18 to 19 141363 -1.6116 0.053525 17 to 18 141638 -0.8004 0.211744 16 to 17 142096 0.5506 0.709063 15 to 16 142354 1.3117 0.905191 14 to 15 141501 -1.2045 0.114196 13 to 14 141882 -0.0806 0.467872 12 to 13 141917 0.0226 0.509025 11 to 12 141774 -0.3992 0.344872 10 to 11 141833 -0.2252 0.410927 9 to 10 141398 -1.5083 0.065733 8 to 9 141785 -0.3668 0.356901 7 to 8 142129 0.6480 0.741506 6 to 7 142332 1.2468 0.893767 5 to 6 142675 2.2586 0.988046 4 to 5 141644 -0.7827 0.216906 3 to 4 142044 0.3973 0.654411 2 to 3 142002 0.2734 0.607713 1 to 2 141908 -0.0039 0.498435 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2017-02-14_20:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2600.99 1.428 0.923376 Test results for specific bytes for dh-ranFile-2017-02-14_20:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2453.97 -0.651 0.257513 2 to 9 2521.50 0.304 0.619474 3 to 10 2521.48 0.304 0.619324 4 to 11 2388.67 -1.575 0.057685 5 to 12 2514.35 0.203 0.580426 6 to 13 2600.59 1.422 0.922558 7 to 14 2464.58 -0.501 0.308240 8 to 15 2619.59 1.691 0.954604 9 to 16 2516.11 0.228 0.590135 10 to 17 2520.12 0.285 0.611987 11 to 18 2370.95 -1.825 0.033995 12 to 19 2451.04 -0.692 0.244353 13 to 20 2540.58 0.574 0.717000 14 to 21 2509.96 0.141 0.556001 15 to 22 2501.63 0.023 0.509219 16 to 23 2485.44 -0.206 0.418444 17 to 24 2474.89 -0.355 0.361235 18 to 25 2436.18 -0.902 0.183400 19 to 26 2395.63 -1.476 0.069977 20 to 27 2447.17 -0.747 0.227509 21 to 28 2563.79 0.902 0.816501 22 to 29 2481.81 -0.257 0.398506 23 to 30 2477.41 -0.319 0.374678 24 to 31 2500.15 0.002 0.500821 25 to 32 2519.22 0.272 0.607128 CDPARK for dh-ranFile-2017-02-14_20:31: 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 3534 0.5023 0.692266 3530 0.3196 0.625377 3536 0.5936 0.723613 3484 -1.7808 0.037471 3509 -0.6393 0.261324 3562 1.7808 0.962529 3533 0.4566 0.676028 3513 -0.4566 0.323972 3562 1.7808 0.962529 3508 -0.6849 0.246694 Square side=100, avg. no. parked=3527.10 sample std.=23.14 p-value of the KSTEST for those 10 p-values: 0.690720 Results for the MINIMUM DISTANCE test for dh-ranFile-2017-02-14_20:31 0.1384,0.8807,0.3673,0.7495,0.3923,0.3398,0.6412,0.0972,0.1414,0.8811, The KS test for those 10 p-values: 0.862705 The 3DSPHERES test for dh-ranFile-2017-02-14_20:31 sample no r^3 equiv. uni. 1 15.308 0.399667 2 30.612 0.639547 3 17.948 0.450240 4 13.100 0.353805 5 29.140 0.621423 6 26.630 0.588385 7 30.981 0.643959 8 16.380 0.420747 9 2.638 0.084164 10 7.592 0.223571 11 20.088 0.488085 12 62.013 0.873449 13 17.099 0.434449 14 120.900 0.982225 15 13.472 0.361777 16 59.048 0.860301 17 9.886 0.280739 18 51.455 0.820068 19 76.694 0.922421 20 61.559 0.871518 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.394369 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-02-14_20:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 1.3 0.8 -0.8 -0.2 -0.1 -0.6 -0.9 0.3 -0.4 1.0 0.7 -0.9 0.1 -1.0 1.0 0.4 -0.8 0.2 -0.1 -0.2 0.5 1.0 -0.9 -2.4 0.6 0.2 0.0 1.6 0.7 1.8 -0.3 -0.4 -1.4 0.9 0.6 0.3 -0.1 0.1 -0.1 0.9 0.0 1.8 Chi-square with 42 degrees of freedom:32.124498 z-score=-1.077506, p-value=0.135340 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2017-02-14_20:31 Test no p-value 1 0.235720 2 0.814305 3 0.464313 4 0.948248 5 0.277379 6 0.967028 7 0.570189 8 0.784516 9 0.401745 10 0.501272 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.442531 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-02-14_20:31: (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 66464 0.62 66483 0.51 3 25000.00 25188 1.41 24996 0.00 4 6666.67 6643 0.08 6828 3.90 5 1388.89 1412 0.38 1393 0.01 6 238.10 252 0.81 256 1.35 7 34.72 36 0.05 40 0.80 8 4.96 4 0.19 3 0.77 p=0.26183 p=0.71004 Number of rngs required: 689934, p-value: 0.964 RESULTS OF CRAPS TEST for dh-ranFile-2017-02-14_20:31 No. of wins: Observed Expected 98289 98585.9 z-score=-1.328, pvalue=0.09213 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66499 66666.7 0.422 0.422 2 37885 37654.3 1.413 1.835 3 27067 26954.7 0.468 2.302 4 19166 19313.5 1.126 3.428 5 13979 13851.4 1.175 4.603 6 9758 9943.5 3.462 8.066 7 7201 7145.0 0.439 8.504 8 5097 5139.1 0.344 8.849 9 3718 3699.9 0.089 8.937 10 2621 2666.3 0.770 9.707 11 2003 1923.3 3.300 13.007 12 1384 1388.7 0.016 13.023 13 997 1003.7 0.045 13.068 14 744 726.1 0.439 13.508 15 500 525.8 1.269 14.777 16 353 381.2 2.079 16.856 17 291 276.5 0.756 17.612 18 194 200.8 0.232 17.845 19 152 146.0 0.248 18.092 20 108 106.2 0.030 18.122 21 283 287.1 0.059 18.181 Chisq= 18.18 for 20 degrees of freedom, p= 0.42454 SUMMARY of craptest p-value for no. of wins: 0.092135 p-value for throws/game: 0.424539 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2017-02-14_20:31 No. of wins: Observed Expected 98746 98585.9 z-score= 0.716, pvalue=0.76308 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66648 66666.7 0.005 0.005 2 37526 37654.3 0.437 0.443 3 26920 26954.7 0.045 0.487 4 19269 19313.5 0.102 0.590 5 13936 13851.4 0.516 1.106 6 9849 9943.5 0.899 2.005 7 7242 7145.0 1.316 3.321 8 5163 5139.1 0.111 3.433 9 3678 3699.9 0.129 3.562 10 2700 2666.3 0.426 3.988 11 1944 1923.3 0.222 4.210 12 1416 1388.7 0.535 4.745 13 1038 1003.7 1.171 5.916 14 770 726.1 2.649 8.565 15 506 525.8 0.748 9.314 16 354 381.2 1.934 11.248 17 264 276.5 0.569 11.816 18 191 200.8 0.481 12.297 19 148 146.0 0.028 12.325 20 115 106.2 0.727 13.052 21 323 287.1 4.485 17.537 Chisq= 17.54 for 20 degrees of freedom, p= 0.38212 SUMMARY of craptest p-value for no. of wins: 0.763080 p-value for throws/game: 0.382125 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0032,0.0109,0.0161,0.0223,0.0279,0.0340,0.0375,0.0535,0.0539,0.0577, 0.0655,0.0657,0.0700,0.0797,0.0835,0.0842,0.0921,0.0927,0.0948,0.0972, 0.0992,0.1035,0.1115,0.1142,0.1148,0.1220,0.1230,0.1273,0.1353,0.1384, 0.1392,0.1414,0.1419,0.1491,0.1588,0.1625,0.1677,0.1746,0.1754,0.1754, 0.1765,0.1821,0.1834,0.1840,0.1917,0.2085,0.2096,0.2117,0.2166,0.2169, 0.2236,0.2239,0.2265,0.2275,0.2351,0.2357,0.2444,0.2451,0.2467,0.2575, 0.2591,0.2613,0.2618,0.2655,0.2669,0.2768,0.2774,0.2807,0.2831,0.2856, 0.2887,0.2912,0.2947,0.2953,0.3054,0.3064,0.3082,0.3083,0.3108,0.3171, 0.3240,0.3273,0.3303,0.3398,0.3449,0.3464,0.3538,0.3567,0.3569,0.3594, 0.3612,0.3618,0.3656,0.3673,0.3733,0.3747,0.3821,0.3862,0.3923,0.3944, 0.3985,0.3986,0.3997,0.4017,0.4109,0.4139,0.4162,0.4184,0.4207,0.4245, 0.4308,0.4311,0.4344,0.4425,0.4450,0.4502,0.4515,0.4587,0.4615,0.4643, 0.4649,0.4679,0.4752,0.4779,0.4823,0.4844,0.4881,0.4910,0.4982,0.4984, 0.5008,0.5013,0.5034,0.5050,0.5090,0.5092,0.5121,0.5155,0.5157,0.5158, 0.5160,0.5229,0.5231,0.5295,0.5417,0.5441,0.5508,0.5560,0.5610,0.5653, 0.5702,0.5722,0.5784,0.5804,0.5884,0.5901,0.5924,0.5936,0.6051,0.6071, 0.6077,0.6120,0.6137,0.6193,0.6195,0.6201,0.6214,0.6243,0.6254,0.6352, 0.6367,0.6395,0.6412,0.6437,0.6440,0.6482,0.6502,0.6544,0.6563,0.6610, 0.6735,0.6760,0.6762,0.6828,0.6907,0.6918,0.6923,0.7091,0.7100,0.7100, 0.7102,0.7141,0.7170,0.7178,0.7220,0.7236,0.7310,0.7390,0.7415,0.7495, 0.7498,0.7597,0.7631,0.7687,0.7710,0.7718,0.7718,0.7773,0.7776,0.7808, 0.7845,0.7888,0.7917,0.8051,0.8124,0.8143,0.8165,0.8201,0.8241,0.8244, 0.8275,0.8348,0.8359,0.8418,0.8418,0.8489,0.8603,0.8627,0.8715,0.8734, 0.8764,0.8780,0.8807,0.8808,0.8811,0.8839,0.8871,0.8893,0.8932,0.8938, 0.8966,0.8974,0.9006,0.9052,0.9057,0.9097,0.9203,0.9221,0.9224,0.9226, 0.9234,0.9257,0.9274,0.9346,0.9368,0.9414,0.9450,0.9482,0.9546,0.9573, 0.9625,0.9625,0.9640,0.9667,0.9670,0.9707,0.9822,0.9880,0.9889, Overall p-value after applying KStest on 269 p-values = 0.522544 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.