RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-04-15_07:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.44 36.7999 0.996418 2 to 25 15.53 19.9393 0.722653 3 to 26 15.69 15.6954 0.454478 4 to 27 15.93 12.5276 0.232808 5 to 28 15.82 11.9498 0.196835 6 to 29 15.88 10.0456 0.098312 7 to 30 15.93 23.3715 0.862458 8 to 31 15.82 7.0231 0.016752 9 to 32 15.73 13.7553 0.315657 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.481802 Tough bday spacings test for dh-ranFile-2018-04-15_07:31: 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 41 79 97 108 79 40 31 12 7 3 (O-E)^2/E 4.1 0.5 0.4 0.0 1.1 0.0 2.8 0.1 0.6 0.0 0.3 Birthday Spacings: Sum(O-E)^2/E= 9.936, p= 0.554 RESULTS OF GCD FOR dh-ranFile-2018-04-15_07:31 Euclid's algorithm: p-value, steps to gcd: 0.287342 p-value, dist. of gcd's: 0.869785 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-04-15_07:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.459 0.540 0.588 0.271 0.234 0.120 0.689 0.981 Bits 8 to 15---> 0.678 0.055 0.585 0.776 0.196 0.181 0.864 0.359 Bits 16 to 23---> 0.021 0.381 0.788 0.851 0.250 0.839 0.163 0.800 Bits 24 to 31---> 0.663 0.635 0.487 0.195 0.192 0.189 0.836 0.621 KS test for the above 32 p values: 0.170 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-04-15_07:31, p-values for 5 runs: 0.4000, 0.4123, 0.1643, 0.5496, 0.8984 Rank test for binary matrices (31x31) for dh-ranFile-2018-04-15_07:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 225 211.4 0.873 0.873 r= 29 5197 5134.0 0.773 1.645 r= 30 23036 23103.0 0.195 1.840 r= 31 11542 11551.5 0.008 1.848 chi-square = 1.848 with df = 3; p-value = 0.395 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-04-15_07:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 204 211.4 0.260 0.260 r= 30 5048 5134.0 1.441 1.701 r= 31 23140 23103.0 0.059 1.760 r= 32 11608 11551.5 0.276 2.036 chi-square = 2.036 with df = 3; p-value = 0.435 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-04-15_07:31 b-rank test for bits 1 to 8, p=0.72062 b-rank test for bits 2 to 9, p=0.21714 b-rank test for bits 3 to 10, p=0.53476 b-rank test for bits 4 to 11, p=0.08594 b-rank test for bits 5 to 12, p=0.34208 b-rank test for bits 6 to 13, p=0.06494 b-rank test for bits 7 to 14, p=0.47333 b-rank test for bits 8 to 15, p=0.40831 b-rank test for bits 9 to 16, p=0.40194 b-rank test for bits 10 to 17, p=0.85457 b-rank test for bits 11 to 18, p=0.20676 b-rank test for bits 12 to 19, p=0.98805 b-rank test for bits 13 to 20, p=0.11387 b-rank test for bits 14 to 21, p=0.21552 b-rank test for bits 15 to 22, p=0.22597 b-rank test for bits 16 to 23, p=0.58864 b-rank test for bits 17 to 24, p=0.01273 b-rank test for bits 18 to 25, p=0.22815 b-rank test for bits 19 to 26, p=0.11412 b-rank test for bits 20 to 27, p=0.01264 b-rank test for bits 21 to 28, p=0.76858 b-rank test for bits 22 to 29, p=0.59174 b-rank test for bits 23 to 30, p=0.96815 b-rank test for bits 24 to 31, p=0.20807 b-rank test for bits 25 to 32, p=0.67214 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 = 0.111505 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-04-15_07:31 (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 141447 -1.08 0.140024 2 141643 -0.62 0.266883 3 142125 0.50 0.692835 4 141815 -0.22 0.412781 5 141609 -0.70 0.241431 6 142383 1.11 0.865789 7 142014 0.24 0.596600 8 141594 -0.74 0.230637 9 141434 -1.11 0.133374 10 141689 -0.51 0.303350 11 141938 0.07 0.526704 12 141918 0.02 0.508081 13 142129 0.51 0.696111 14 143023 2.60 0.995366 15 141048 -2.01 0.022086 16 141329 -1.36 0.087564 17 142373 1.08 0.860672 18 141337 -1.34 0.090575 19 140962 -2.21 0.013435 20 141662 -0.58 0.281675 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-04-15_07:31 Bits used No. missing words z-score p-value 23 to 32 141759 -0.5184 0.302097 22 to 31 141462 -1.5425 0.061474 21 to 30 141816 -0.3218 0.373792 20 to 29 142276 1.2644 0.896953 19 to 28 141788 -0.4184 0.337835 18 to 27 142082 0.5954 0.724217 17 to 26 141904 -0.0184 0.492668 16 to 25 141429 -1.6563 0.048830 15 to 24 142160 0.8644 0.806310 14 to 23 141882 -0.0942 0.462459 13 to 22 142551 2.2127 0.986539 12 to 21 141927 0.0609 0.524293 11 to 20 141987 0.2678 0.605584 10 to 19 142450 1.8644 0.968866 9 to 18 142605 2.3989 0.991777 8 to 17 142074 0.5678 0.714924 7 to 16 141751 -0.5460 0.292545 6 to 15 141833 -0.2632 0.396196 5 to 14 142008 0.3402 0.633163 4 to 13 141634 -0.9494 0.171205 3 to 12 142471 1.9368 0.973615 2 to 11 142149 0.8264 0.795725 1 to 10 142238 1.1333 0.871465 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-04-15_07:31 Bits used No. missing words z-score p-value 28 to 32 142175 0.9006 0.816093 27 to 31 141403 -1.7164 0.043047 26 to 30 141797 -0.3808 0.351683 25 to 29 141911 0.0057 0.502258 24 to 28 141844 -0.2215 0.412368 23 to 27 141791 -0.4011 0.344166 22 to 26 141921 0.0396 0.515778 21 to 25 141642 -0.9062 0.182414 20 to 24 142017 0.3650 0.642438 19 to 23 142074 0.5582 0.711647 18 to 22 141742 -0.5672 0.285282 17 to 21 141912 0.0091 0.503611 16 to 20 142668 2.5718 0.994941 15 to 19 141891 -0.0621 0.475227 14 to 18 141864 -0.1537 0.438939 13 to 17 141900 -0.0316 0.487385 12 to 16 142033 0.4192 0.662473 11 to 15 141813 -0.3265 0.372007 10 to 14 141903 -0.0215 0.491440 9 to 13 141977 0.2294 0.590717 8 to 12 142089 0.6091 0.728755 7 to 11 142035 0.4260 0.664946 6 to 10 141425 -1.6418 0.050316 5 to 9 141823 -0.2926 0.384897 4 to 8 141927 0.0599 0.523882 3 to 7 142185 0.9345 0.824970 2 to 6 141698 -0.7164 0.236881 1 to 5 141573 -1.1401 0.127122 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-04-15_07:31 Bits used No. missing words z-score p-value 31 to 32 142200 0.8574 0.804397 30 to 31 141872 -0.1101 0.456158 29 to 30 142283 1.1023 0.864828 28 to 29 142313 1.1908 0.883127 27 to 28 142293 1.1318 0.871134 26 to 27 141836 -0.2163 0.414372 25 to 26 141760 -0.4405 0.329787 24 to 25 141955 0.1347 0.553583 23 to 24 141753 -0.4612 0.322345 22 to 23 141643 -0.7856 0.216041 21 to 22 141537 -1.0983 0.136033 20 to 21 141929 0.0580 0.523135 19 to 20 141498 -1.2134 0.112496 18 to 19 141891 -0.0541 0.478439 17 to 18 141786 -0.3638 0.358002 16 to 17 141710 -0.5880 0.278268 15 to 16 141766 -0.4228 0.336220 14 to 15 142233 0.9548 0.830155 13 to 14 142100 0.5624 0.713095 12 to 13 142313 1.1908 0.883127 11 to 12 142571 1.9518 0.974521 10 to 11 141530 -1.1190 0.131577 9 to 10 141561 -1.0275 0.152087 8 to 9 142329 1.2380 0.892135 7 to 8 141704 -0.6057 0.272359 6 to 7 142027 0.3471 0.635745 5 to 6 141672 -0.7001 0.241936 4 to 5 141850 -0.1750 0.430534 3 to 4 141968 0.1731 0.568701 2 to 3 142305 1.1672 0.878429 1 to 2 141891 -0.0541 0.478439 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-04-15_07:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2485.38 -0.207 0.418105 Test results for specific bytes for dh-ranFile-2018-04-15_07:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2478.29 -0.307 0.379435 2 to 9 2389.40 -1.564 0.058903 3 to 10 2499.95 -0.001 0.499705 4 to 11 2496.42 -0.051 0.479828 5 to 12 2430.88 -0.977 0.164165 6 to 13 2564.96 0.919 0.820885 7 to 14 2477.02 -0.325 0.372582 8 to 15 2419.95 -1.132 0.128812 9 to 16 2490.37 -0.136 0.445857 10 to 17 2474.81 -0.356 0.360817 11 to 18 2460.84 -0.554 0.289855 12 to 19 2478.71 -0.301 0.381692 13 to 20 2429.40 -0.998 0.159032 14 to 21 2561.13 0.864 0.806339 15 to 22 2585.33 1.207 0.886235 16 to 23 2655.09 2.193 0.985857 17 to 24 2566.19 0.936 0.825372 18 to 25 2565.45 0.926 0.822682 19 to 26 2455.29 -0.632 0.263589 20 to 27 2505.89 0.083 0.533175 21 to 28 2518.28 0.258 0.601973 22 to 29 2569.07 0.977 0.835658 23 to 30 2525.31 0.358 0.639810 24 to 31 2456.00 -0.622 0.266894 25 to 32 2552.25 0.739 0.770011 CDPARK for dh-ranFile-2018-04-15_07:31: 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 3494 -1.3242 0.092718 3518 -0.2283 0.409702 3536 0.5936 0.723613 3563 1.8265 0.966111 3546 1.0502 0.853193 3510 -0.5936 0.276387 3540 0.7763 0.781201 3498 -1.1416 0.126820 3526 0.1370 0.554479 3514 -0.4110 0.340551 Square side=100, avg. no. parked=3524.50 sample std.=20.77 p-value of the KSTEST for those 10 p-values: 0.998112 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-04-15_07:31 0.2324,0.0716,0.1900,0.9641,0.3751,0.6535,0.7199,0.0664,0.1172,0.8964, The KS test for those 10 p-values: 0.471694 The 3DSPHERES test for dh-ranFile-2018-04-15_07:31 sample no r^3 equiv. uni. 1 42.755 0.759529 2 3.945 0.123221 3 1.563 0.050757 4 24.914 0.564149 5 10.243 0.289246 6 5.142 0.157527 7 22.131 0.521790 8 6.775 0.202140 9 4.791 0.147611 10 18.267 0.456053 11 28.298 0.610649 12 88.065 0.946896 13 39.409 0.731155 14 101.295 0.965833 15 70.536 0.904745 16 31.151 0.645970 17 11.901 0.327470 18 47.606 0.795437 19 9.601 0.273872 20 28.099 0.608050 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.996905 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-04-15_07:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -2.0 -0.4 -0.8 -1.5 1.7 1.7 1.2 -0.4 -0.6 -0.4 -0.2 -1.7 -0.1 -0.2 -0.4 -1.2 -0.2 1.4 -0.8 2.0 -0.4 0.5 -0.9 1.7 0.8 1.0 1.6 -0.2 -1.6 0.6 -1.2 0.0 -1.4 -0.2 -0.5 -1.2 -0.1 -0.8 -0.1 0.1 0.0 -0.1 Chi-square with 42 degrees of freedom:43.857037 z-score=0.202619, p-value=0.607291 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-04-15_07:31 Test no p-value 1 0.161462 2 0.036266 3 0.298867 4 0.018964 5 0.044786 6 0.032202 7 0.460748 8 0.026656 9 0.221339 10 0.185545 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000034 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-04-15_07:31: (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 66954 1.24 66821 0.36 3 25000.00 24811 1.43 24818 1.32 4 6666.67 6573 1.32 6646 0.06 5 1388.89 1363 0.48 1450 2.69 6 238.10 254 1.06 225 0.72 7 34.72 38 0.31 31 0.40 8 4.96 6 0.22 8 1.86 p=0.58309 p=0.71601 Number of rngs required: 687008, p-value: 0.051 RESULTS OF CRAPS TEST for dh-ranFile-2018-04-15_07:31 No. of wins: Observed Expected 98506 98585.9 z-score=-0.357, pvalue=0.36048 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66489 66666.7 0.473 0.473 2 37775 37654.3 0.387 0.860 3 26961 26954.7 0.001 0.862 4 19382 19313.5 0.243 1.105 5 14045 13851.4 2.705 3.810 6 9820 9943.5 1.535 5.345 7 7109 7145.0 0.182 5.527 8 5057 5139.1 1.311 6.838 9 3646 3699.9 0.784 7.622 10 2638 2666.3 0.300 7.922 11 1987 1923.3 2.108 10.030 12 1414 1388.7 0.459 10.489 13 1028 1003.7 0.588 11.077 14 748 726.1 0.658 11.735 15 510 525.8 0.477 12.212 16 384 381.2 0.021 12.233 17 279 276.5 0.022 12.255 18 204 200.8 0.050 12.305 19 135 146.0 0.827 13.132 20 110 106.2 0.135 13.266 21 279 287.1 0.229 13.496 Chisq= 13.50 for 20 degrees of freedom, p= 0.14489 SUMMARY of craptest p-value for no. of wins: 0.360481 p-value for throws/game: 0.144887 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-04-15_07:31 No. of wins: Observed Expected 98844 98585.9 z-score= 1.155, pvalue=0.87586 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66753 66666.7 0.112 0.112 2 37611 37654.3 0.050 0.162 3 26854 26954.7 0.376 0.538 4 19410 19313.5 0.483 1.021 5 13788 13851.4 0.290 1.311 6 9938 9943.5 0.003 1.314 7 7061 7145.0 0.988 2.302 8 5168 5139.1 0.163 2.465 9 3764 3699.9 1.112 3.577 10 2648 2666.3 0.126 3.702 11 1960 1923.3 0.699 4.402 12 1361 1388.7 0.554 4.956 13 1017 1003.7 0.176 5.132 14 766 726.1 2.188 7.319 15 495 525.8 1.808 9.128 16 396 381.2 0.579 9.706 17 271 276.5 0.111 9.817 18 203 200.8 0.023 9.841 19 143 146.0 0.061 9.902 20 102 106.2 0.167 10.069 21 291 287.1 0.053 10.122 Chisq= 10.12 for 20 degrees of freedom, p= 0.03409 SUMMARY of craptest p-value for no. of wins: 0.875864 p-value for throws/game: 0.034087 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0000,0.0126,0.0127,0.0134,0.0168,0.0190,0.0213,0.0221,0.0267,0.0322, 0.0341,0.0363,0.0430,0.0448,0.0488,0.0503,0.0508,0.0511,0.0550,0.0589, 0.0615,0.0649,0.0664,0.0716,0.0859,0.0876,0.0906,0.0927,0.0983,0.1115, 0.1125,0.1139,0.1141,0.1172,0.1204,0.1232,0.1268,0.1271,0.1288,0.1316, 0.1334,0.1360,0.1400,0.1449,0.1476,0.1521,0.1575,0.1590,0.1615,0.1632, 0.1642,0.1643,0.1696,0.1712,0.1815,0.1824,0.1855,0.1889,0.1900,0.1916, 0.1950,0.1957,0.1968,0.2021,0.2068,0.2081,0.2155,0.2160,0.2171,0.2213, 0.2260,0.2281,0.2306,0.2324,0.2328,0.2340,0.2369,0.2414,0.2419,0.2501, 0.2636,0.2669,0.2669,0.2707,0.2724,0.2739,0.2764,0.2783,0.2817,0.2853, 0.2873,0.2892,0.2899,0.2925,0.2989,0.3021,0.3034,0.3157,0.3223,0.3275, 0.3298,0.3362,0.3378,0.3406,0.3421,0.3442,0.3517,0.3580,0.3586,0.3605, 0.3608,0.3720,0.3726,0.3738,0.3751,0.3794,0.3805,0.3817,0.3849,0.3954, 0.3962,0.4000,0.4019,0.4083,0.4097,0.4123,0.4124,0.4128,0.4144,0.4181, 0.4305,0.4351,0.4389,0.4459,0.4545,0.4561,0.4562,0.4586,0.4607,0.4625, 0.4717,0.4733,0.4752,0.4784,0.4784,0.4798,0.4818,0.4866,0.4874,0.4914, 0.4927,0.4997,0.5023,0.5036,0.5081,0.5158,0.5218,0.5231,0.5239,0.5243, 0.5267,0.5332,0.5348,0.5397,0.5496,0.5536,0.5539,0.5545,0.5641,0.5687, 0.5831,0.5846,0.5882,0.5886,0.5907,0.5917,0.5966,0.6020,0.6056,0.6073, 0.6080,0.6106,0.6210,0.6332,0.6354,0.6357,0.6398,0.6424,0.6460,0.6535, 0.6625,0.6632,0.6649,0.6721,0.6784,0.6894,0.6928,0.6961,0.7116,0.7131, 0.7149,0.7160,0.7199,0.7206,0.7227,0.7236,0.7242,0.7288,0.7312,0.7595, 0.7686,0.7700,0.7761,0.7812,0.7879,0.7954,0.7957,0.8003,0.8044,0.8063, 0.8063,0.8161,0.8209,0.8227,0.8250,0.8254,0.8302,0.8357,0.8359,0.8386, 0.8515,0.8532,0.8546,0.8607,0.8625,0.8643,0.8648,0.8658,0.8698,0.8711, 0.8715,0.8759,0.8784,0.8831,0.8831,0.8862,0.8921,0.8964,0.8970,0.8984, 0.9047,0.9469,0.9641,0.9658,0.9661,0.9681,0.9689,0.9736,0.9745,0.9805, 0.9859,0.9865,0.9881,0.9918,0.9949,0.9954,0.9964,0.9969,0.9981, Overall p-value after applying KStest on 269 p-values = 0.078983 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.