RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-01-13_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 15.99 11.9260 0.195406 2 to 25 16.01 9.0053 0.059905 3 to 26 15.65 22.1213 0.819901 4 to 27 15.67 19.5102 0.699953 5 to 28 15.82 11.8231 0.189270 6 to 29 15.82 13.2323 0.279499 7 to 30 16.02 16.2575 0.494339 8 to 31 15.95 15.0993 0.411673 9 to 32 15.67 16.8535 0.535668 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.605565 Tough bday spacings test for dh-ranFile-2017-01-13_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 11 39 78 99 90 86 45 21 18 6 7 (O-E)^2/E 0.4 0.2 0.3 0.0 0.6 0.8 1.0 2.6 0.7 0.1 2.1 Birthday Spacings: Sum(O-E)^2/E= 8.618, p= 0.431 RESULTS OF GCD FOR dh-ranFile-2017-01-13_20:31 Euclid's algorithm: p-value, steps to gcd: 0.595089 p-value, dist. of gcd's: 0.239833 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-01-13_20:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.415 0.092 0.727 0.934 0.884 0.274 0.237 0.481 Bits 8 to 15---> 0.693 0.857 0.724 0.960 0.982 0.740 0.849 0.973 Bits 16 to 23---> 0.062 0.413 0.119 0.626 0.628 0.049 0.632 0.612 Bits 24 to 31---> 0.717 0.750 0.492 0.936 0.844 0.905 0.962 0.408 KS test for the above 32 p values: 0.982 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-01-13_20:31, p-values for 5 runs: 0.4248, 0.3495, 0.0905, 0.0400, 0.8096 Rank test for binary matrices (31x31) for dh-ranFile-2017-01-13_20:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 199 211.4 0.729 0.729 r= 29 5161 5134.0 0.142 0.871 r= 30 23157 23103.0 0.126 0.997 r= 31 11483 11551.5 0.406 1.404 chi-square = 1.404 with df = 3; p-value = 0.295 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2017-01-13_20:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 219 211.4 0.272 0.272 r= 30 5143 5134.0 0.016 0.288 r= 31 23158 23103.0 0.131 0.418 r= 32 11480 11551.5 0.443 0.861 chi-square = 0.861 with df = 3; p-value = 0.165 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2017-01-13_20:31 b-rank test for bits 1 to 8, p=0.90888 b-rank test for bits 2 to 9, p=0.92144 b-rank test for bits 3 to 10, p=0.92899 b-rank test for bits 4 to 11, p=0.15979 b-rank test for bits 5 to 12, p=0.85675 b-rank test for bits 6 to 13, p=0.71904 b-rank test for bits 7 to 14, p=0.06558 b-rank test for bits 8 to 15, p=0.06843 b-rank test for bits 9 to 16, p=0.08074 b-rank test for bits 10 to 17, p=0.16129 b-rank test for bits 11 to 18, p=0.00546 b-rank test for bits 12 to 19, p=0.85207 b-rank test for bits 13 to 20, p=0.36182 b-rank test for bits 14 to 21, p=0.09419 b-rank test for bits 15 to 22, p=0.93211 b-rank test for bits 16 to 23, p=0.46306 b-rank test for bits 17 to 24, p=0.41545 b-rank test for bits 18 to 25, p=0.52468 b-rank test for bits 19 to 26, p=0.07848 b-rank test for bits 20 to 27, p=0.64399 b-rank test for bits 21 to 28, p=0.74140 b-rank test for bits 22 to 29, p=0.07930 b-rank test for bits 23 to 30, p=0.02390 b-rank test for bits 24 to 31, p=0.41215 b-rank test for bits 25 to 32, p=0.71325 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 = 0.117605 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-01-13_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 142726 1.91 0.971811 2 142481 1.34 0.909173 3 141539 -0.87 0.193449 4 142659 1.75 0.960076 5 142213 0.71 0.760996 6 142118 0.49 0.687065 7 142187 0.65 0.741754 8 141510 -0.93 0.175406 9 141454 -1.06 0.143697 10 142537 1.47 0.928746 11 142290 0.89 0.813110 12 142751 1.97 0.975381 13 141686 -0.52 0.300905 14 141641 -0.63 0.265350 15 141434 -1.11 0.133374 16 142219 0.72 0.765322 17 141576 -0.78 0.218046 18 142031 0.28 0.611900 19 142338 1.00 0.841723 20 141996 0.20 0.580237 ---------------------------------------------------------------- OPSO test for dh-ranFile-2017-01-13_20:31 Bits used No. missing words z-score p-value 23 to 32 142087 0.6127 0.729948 22 to 31 142553 2.2196 0.986775 21 to 30 141684 -0.7770 0.218579 20 to 29 142106 0.6782 0.751169 19 to 28 141772 -0.4736 0.317910 18 to 27 141753 -0.5391 0.294920 17 to 26 141440 -1.6184 0.052790 16 to 25 141408 -1.7287 0.041929 15 to 24 141577 -1.1460 0.125905 14 to 23 141803 -0.3667 0.356938 13 to 22 141711 -0.6839 0.247020 12 to 21 141154 -2.6046 0.004599 11 to 20 141302 -2.0942 0.018119 10 to 19 142017 0.3713 0.644784 9 to 18 141921 0.0402 0.516050 8 to 17 142056 0.5058 0.693487 7 to 16 141668 -0.8322 0.202656 6 to 15 141316 -2.0460 0.020380 5 to 14 141670 -0.8253 0.204608 4 to 13 141718 -0.6598 0.254704 3 to 12 141908 -0.0046 0.498170 2 to 11 142145 0.8127 0.791792 1 to 10 142337 1.4747 0.929857 ----------------------------------------------------------------- OQSO test for dh-ranFile-2017-01-13_20:31 Bits used No. missing words z-score p-value 28 to 32 141191 -2.4350 0.007446 27 to 31 142084 0.5921 0.723109 26 to 30 142240 1.1209 0.868838 25 to 29 142253 1.1650 0.877987 24 to 28 142051 0.4802 0.684471 23 to 27 142168 0.8768 0.809715 22 to 26 141913 0.0124 0.504963 21 to 25 142031 0.4124 0.659992 20 to 24 141778 -0.4452 0.328093 19 to 23 142097 0.6362 0.737667 18 to 22 141946 0.1243 0.549463 17 to 21 142387 1.6192 0.947300 16 to 20 141851 -0.1977 0.421629 15 to 19 141896 -0.0452 0.481979 14 to 18 142320 1.3921 0.918054 13 to 17 141636 -0.9265 0.177082 12 to 16 141987 0.2633 0.603836 11 to 15 141408 -1.6994 0.044620 10 to 14 141871 -0.1299 0.448310 9 to 13 141727 -0.6181 0.268265 8 to 12 141544 -1.2384 0.107783 7 to 11 141831 -0.2655 0.395302 6 to 10 142363 1.5379 0.937959 5 to 9 141627 -0.9571 0.169271 4 to 8 141968 0.1989 0.578822 3 to 7 142248 1.1480 0.874523 2 to 6 141586 -1.0960 0.136532 1 to 5 142204 0.9989 0.841074 ----------------------------------------------------------------- DNA test for dh-ranFile-2017-01-13_20:31 Bits used No. missing words z-score p-value 31 to 32 141946 0.1082 0.543070 30 to 31 142019 0.3235 0.626846 29 to 30 141551 -1.0570 0.145251 28 to 29 141861 -0.1426 0.443316 27 to 28 142119 0.6185 0.731876 26 to 27 141642 -0.7886 0.215178 25 to 26 141501 -1.2045 0.114196 24 to 25 142355 1.3147 0.905688 23 to 24 141712 -0.5821 0.280252 22 to 23 142394 1.4297 0.923599 21 to 22 141340 -1.6794 0.046533 20 to 21 142670 2.2439 0.987579 19 to 20 141946 0.1082 0.543070 18 to 19 141859 -0.1485 0.440988 17 to 18 141331 -1.7060 0.044005 16 to 17 141732 -0.5231 0.300453 15 to 16 142196 0.8456 0.801122 14 to 15 141646 -0.7768 0.218643 13 to 14 142295 1.1377 0.872371 12 to 13 141431 -1.4110 0.079122 11 to 12 141580 -0.9715 0.165656 10 to 11 142225 0.9312 0.824120 9 to 10 141873 -0.1072 0.457328 8 to 9 141543 -1.0806 0.139933 7 to 8 142245 0.9902 0.838956 6 to 7 141608 -0.8889 0.187034 5 to 6 142008 0.2911 0.614498 4 to 5 141857 -0.1544 0.438661 3 to 4 141496 -1.2193 0.111372 2 to 3 142195 0.8427 0.800298 1 to 2 141487 -1.2458 0.106417 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2017-01-13_20:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2582.79 1.171 0.879173 Test results for specific bytes for dh-ranFile-2017-01-13_20:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2509.08 0.128 0.551104 2 to 9 2456.75 -0.612 0.270401 3 to 10 2343.53 -2.213 0.013456 4 to 11 2484.60 -0.218 0.413816 5 to 12 2447.23 -0.746 0.227741 6 to 13 2486.91 -0.185 0.426572 7 to 14 2557.85 0.818 0.793342 8 to 15 2498.61 -0.020 0.492142 9 to 16 2475.56 -0.346 0.364828 10 to 17 2433.90 -0.935 0.174935 11 to 18 2499.95 -0.001 0.499717 12 to 19 2490.45 -0.135 0.446292 13 to 20 2542.57 0.602 0.726422 14 to 21 2537.08 0.524 0.700015 15 to 22 2571.38 1.009 0.843628 16 to 23 2618.86 1.681 0.953616 17 to 24 2453.53 -0.657 0.255513 18 to 25 2452.82 -0.667 0.252322 19 to 26 2607.39 1.519 0.935591 20 to 27 2544.11 0.624 0.733639 21 to 28 2503.97 0.056 0.522406 22 to 29 2480.09 -0.282 0.389148 23 to 30 2477.39 -0.320 0.374551 24 to 31 2346.25 -2.174 0.014839 25 to 32 2508.83 0.125 0.549695 CDPARK for dh-ranFile-2017-01-13_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 3502 -0.9589 0.168804 3483 -1.8265 0.033889 3525 0.0913 0.536383 3529 0.2740 0.607947 3500 -1.0502 0.146807 3541 0.8219 0.794438 3511 -0.5479 0.291865 3567 2.0091 0.977738 3511 -0.5479 0.291865 3488 -1.5982 0.055002 Square side=100, avg. no. parked=3515.70 sample std.=24.19 p-value of the KSTEST for those 10 p-values: 0.328037 Results for the MINIMUM DISTANCE test for dh-ranFile-2017-01-13_20:31 0.3242,0.1332,0.5507,0.4062,0.3337,0.3338,0.7169,0.8650,0.1477,0.9121, The KS test for those 10 p-values: 0.857490 The 3DSPHERES test for dh-ranFile-2017-01-13_20:31 sample no r^3 equiv. uni. 1 14.140 0.375825 2 23.508 0.543248 3 26.811 0.590858 4 12.378 0.338078 5 13.652 0.365597 6 37.015 0.708825 7 15.061 0.394701 8 49.351 0.806993 9 17.630 0.444381 10 2.041 0.065782 11 62.506 0.875508 12 12.829 0.347942 13 19.204 0.472784 14 2.949 0.093611 15 2.229 0.071612 16 58.766 0.858980 17 3.406 0.107340 18 23.447 0.542306 19 5.970 0.180454 20 21.165 0.506137 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.374801 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-01-13_20:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.5 1.5 0.8 0.6 -0.1 0.1 0.2 -0.0 -1.6 0.9 0.8 1.4 -0.4 0.9 -0.2 0.1 0.3 -0.8 -0.2 -0.1 -0.4 -0.3 0.5 -0.9 -0.9 0.2 0.3 0.8 -0.0 -1.7 -1.5 0.2 -0.3 0.1 0.2 1.4 -1.3 0.5 0.4 1.6 0.0 0.8 Chi-square with 42 degrees of freedom:27.360011 z-score=-1.597354, p-value=0.039372 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2017-01-13_20:31 Test no p-value 1 0.346903 2 0.106282 3 0.154839 4 0.003457 5 0.015078 6 0.599222 7 0.859624 8 0.037441 9 0.285222 10 0.456085 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.013646 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-01-13_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 66656 0.00 66585 0.10 3 25000.00 25065 0.17 25041 0.07 4 6666.67 6643 0.08 6752 1.09 5 1388.89 1344 1.45 1344 1.45 6 238.10 253 0.93 238 0.00 7 34.72 31 0.40 34 0.01 8 4.96 7 0.84 5 0.00 p=0.30658 p=0.15759 Number of rngs required: 689505, p-value: 0.900 RESULTS OF CRAPS TEST for dh-ranFile-2017-01-13_20:31 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 66930 66666.7 1.040 1.040 2 37575 37654.3 0.167 1.207 3 26893 26954.7 0.141 1.349 4 19423 19313.5 0.621 1.970 5 13667 13851.4 2.455 4.425 6 9991 9943.5 0.226 4.652 7 7211 7145.0 0.609 5.261 8 5152 5139.1 0.033 5.293 9 3633 3699.9 1.208 6.502 10 2618 2666.3 0.875 7.377 11 1923 1923.3 0.000 7.377 12 1368 1388.7 0.310 7.687 13 1003 1003.7 0.001 7.687 14 697 726.1 1.169 8.857 15 538 525.8 0.281 9.138 16 374 381.2 0.134 9.272 17 264 276.5 0.569 9.841 18 179 200.8 2.373 12.214 19 152 146.0 0.248 12.461 20 112 106.2 0.315 12.776 21 297 287.1 0.340 13.117 Chisq= 13.12 for 20 degrees of freedom, p= 0.12769 SUMMARY of craptest p-value for no. of wins: 0.539443 p-value for throws/game: 0.127686 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2017-01-13_20:31 No. of wins: Observed Expected 98920 98585.9 z-score= 1.494, pvalue=0.93247 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66779 66666.7 0.189 0.189 2 37538 37654.3 0.359 0.549 3 27085 26954.7 0.630 1.178 4 19279 19313.5 0.061 1.240 5 13851 13851.4 0.000 1.240 6 9864 9943.5 0.636 1.876 7 7168 7145.0 0.074 1.950 8 5161 5139.1 0.094 2.043 9 3737 3699.9 0.373 2.416 10 2624 2666.3 0.671 3.087 11 1913 1923.3 0.055 3.143 12 1370 1388.7 0.253 3.395 13 1004 1003.7 0.000 3.396 14 706 726.1 0.559 3.954 15 510 525.8 0.477 4.431 16 372 381.2 0.220 4.651 17 265 276.5 0.482 5.132 18 219 200.8 1.644 6.776 19 148 146.0 0.028 6.804 20 115 106.2 0.727 7.531 21 292 287.1 0.083 7.614 Chisq= 7.61 for 20 degrees of freedom, p= 0.00587 SUMMARY of craptest p-value for no. of wins: 0.932474 p-value for throws/game: 0.005870 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0035,0.0046,0.0055,0.0059,0.0074,0.0135,0.0136,0.0148,0.0151,0.0181, 0.0204,0.0239,0.0339,0.0374,0.0394,0.0400,0.0419,0.0440,0.0446,0.0465, 0.0493,0.0528,0.0550,0.0599,0.0617,0.0656,0.0658,0.0684,0.0716,0.0785, 0.0791,0.0793,0.0807,0.0905,0.0917,0.0936,0.0942,0.1063,0.1064,0.1073, 0.1078,0.1114,0.1142,0.1176,0.1188,0.1259,0.1277,0.1332,0.1334,0.1365, 0.1399,0.1437,0.1453,0.1468,0.1477,0.1548,0.1576,0.1598,0.1613,0.1652, 0.1657,0.1688,0.1693,0.1749,0.1754,0.1771,0.1805,0.1870,0.1893,0.1934, 0.1954,0.2027,0.2046,0.2152,0.2180,0.2186,0.2186,0.2277,0.2368,0.2398, 0.2470,0.2523,0.2547,0.2555,0.2653,0.2683,0.2704,0.2738,0.2795,0.2803, 0.2852,0.2919,0.2919,0.2949,0.2953,0.3005,0.3009,0.3066,0.3179,0.3242, 0.3280,0.3281,0.3337,0.3338,0.3381,0.3469,0.3479,0.3495,0.3569,0.3618, 0.3648,0.3656,0.3746,0.3748,0.3758,0.3891,0.3947,0.3953,0.4062,0.4079, 0.4117,0.4122,0.4125,0.4138,0.4154,0.4154,0.4216,0.4248,0.4266,0.4313, 0.4387,0.4410,0.4433,0.4444,0.4463,0.4483,0.4561,0.4573,0.4631,0.4728, 0.4807,0.4820,0.4921,0.4922,0.4943,0.4982,0.4997,0.5050,0.5061,0.5160, 0.5224,0.5247,0.5357,0.5364,0.5394,0.5423,0.5431,0.5431,0.5432,0.5495, 0.5497,0.5507,0.5511,0.5788,0.5802,0.5909,0.5951,0.5992,0.6038,0.6056, 0.6079,0.6119,0.6122,0.6145,0.6256,0.6268,0.6282,0.6317,0.6440,0.6448, 0.6600,0.6845,0.6871,0.6931,0.6935,0.7000,0.7000,0.7088,0.7133,0.7166, 0.7169,0.7190,0.7231,0.7241,0.7264,0.7274,0.7299,0.7319,0.7336,0.7377, 0.7399,0.7414,0.7418,0.7505,0.7512,0.7610,0.7653,0.7918,0.7933,0.7944, 0.8003,0.8011,0.8070,0.8096,0.8097,0.8131,0.8199,0.8241,0.8390,0.8411, 0.8417,0.8436,0.8444,0.8492,0.8521,0.8567,0.8573,0.8575,0.8590,0.8596, 0.8650,0.8688,0.8724,0.8745,0.8755,0.8780,0.8792,0.8840,0.9001,0.9046, 0.9057,0.9089,0.9092,0.9121,0.9181,0.9214,0.9236,0.9287,0.9290,0.9299, 0.9321,0.9325,0.9342,0.9356,0.9364,0.9380,0.9473,0.9536,0.9601,0.9602, 0.9615,0.9718,0.9728,0.9754,0.9777,0.9819,0.9822,0.9868,0.9876, Overall p-value after applying KStest on 269 p-values = 0.070099 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.