RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-11-10_13:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.92 10.9921 0.143028 2 to 25 15.53 19.3192 0.689480 3 to 26 16.11 25.9615 0.924835 4 to 27 15.97 14.6229 0.377374 5 to 28 15.78 20.1513 0.733436 6 to 29 15.78 11.7668 0.185950 7 to 30 15.75 19.0331 0.673367 8 to 31 15.84 21.5371 0.796817 9 to 32 15.73 23.8051 0.875172 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.463115 Tough bday spacings test for dh-ranFile-2015-11-10_13:31: 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 29 72 103 100 83 52 22 16 5 7 (O-E)^2/E 0.4 1.6 0.0 0.3 0.1 0.3 0.0 2.0 0.1 0.4 2.1 Birthday Spacings: Sum(O-E)^2/E= 7.251, p= 0.298 RESULTS OF GCD FOR dh-ranFile-2015-11-10_13:31 Euclid's algorithm: p-value, steps to gcd: 0.124977 p-value, dist. of gcd's: 0.683216 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-11-10_13:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.944 0.466 0.602 0.514 0.822 0.888 0.084 0.773 Bits 8 to 15---> 0.850 0.254 0.182 0.660 0.102 0.487 0.104 0.311 Bits 16 to 23---> 0.585 0.778 0.645 0.839 0.592 0.918 0.984 0.635 Bits 24 to 31---> 0.011 0.057 0.973 0.609 0.521 0.669 0.347 0.933 KS test for the above 32 p values: 0.718 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-11-10_13:31, p-values for 5 runs: 0.3187, 0.5160, 0.7423, 0.6703, 0.8310 Rank test for binary matrices (31x31) for dh-ranFile-2015-11-10_13:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 234 211.4 2.412 2.412 r= 29 5231 5134.0 1.832 4.244 r= 30 22903 23103.0 1.732 5.977 r= 31 11632 11551.5 0.561 6.537 chi-square = 6.537 with df = 3; p-value = 0.912 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-11-10_13:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 214 211.4 0.032 0.032 r= 30 5089 5134.0 0.395 0.426 r= 31 23109 23103.0 0.002 0.428 r= 32 11588 11551.5 0.115 0.543 chi-square = 0.543 with df = 3; p-value = 0.091 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-11-10_13:31 b-rank test for bits 1 to 8, p=0.12351 b-rank test for bits 2 to 9, p=0.53627 b-rank test for bits 3 to 10, p=0.35289 b-rank test for bits 4 to 11, p=0.12995 b-rank test for bits 5 to 12, p=0.06158 b-rank test for bits 6 to 13, p=0.16139 b-rank test for bits 7 to 14, p=0.43705 b-rank test for bits 8 to 15, p=0.49944 b-rank test for bits 9 to 16, p=0.09672 b-rank test for bits 10 to 17, p=0.44926 b-rank test for bits 11 to 18, p=0.14734 b-rank test for bits 12 to 19, p=0.10292 b-rank test for bits 13 to 20, p=0.11756 b-rank test for bits 14 to 21, p=0.48645 b-rank test for bits 15 to 22, p=0.34634 b-rank test for bits 16 to 23, p=0.24352 b-rank test for bits 17 to 24, p=0.25343 b-rank test for bits 18 to 25, p=0.67263 b-rank test for bits 19 to 26, p=0.37518 b-rank test for bits 20 to 27, p=0.15555 b-rank test for bits 21 to 28, p=0.05091 b-rank test for bits 22 to 29, p=0.15516 b-rank test for bits 23 to 30, p=0.49949 b-rank test for bits 24 to 31, p=0.39711 b-rank test for bits 25 to 32, p=0.09533 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 = 0.000122 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-11-10_13:31 (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 142184 0.64 0.739483 2 141574 -0.78 0.216672 3 141654 -0.60 0.275399 4 141723 -0.44 0.331654 5 141778 -0.31 0.379480 6 141807 -0.24 0.405518 7 142400 1.15 0.874190 8 141923 0.03 0.512740 9 141744 -0.39 0.349643 10 141301 -1.42 0.077610 11 141566 -0.80 0.211227 12 141927 0.04 0.516466 13 141573 -0.79 0.215987 14 142770 2.01 0.977833 15 142353 1.04 0.850042 16 142044 0.31 0.623486 17 141931 0.05 0.520190 18 142256 0.81 0.791023 19 141990 0.19 0.574750 20 141768 -0.33 0.370621 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-11-10_13:31 Bits used No. missing words z-score p-value 23 to 32 141360 -1.8942 0.029096 22 to 31 141773 -0.4701 0.319141 21 to 30 141993 0.2885 0.613525 20 to 29 142207 1.0264 0.847660 19 to 28 142207 1.0264 0.847660 18 to 27 142203 1.0127 0.844388 17 to 26 141493 -1.4356 0.075555 16 to 25 141717 -0.6632 0.253599 15 to 24 141515 -1.3598 0.086953 14 to 23 142088 0.6161 0.731087 13 to 22 142457 1.8885 0.970522 12 to 21 141729 -0.6218 0.267028 11 to 20 141932 0.0782 0.531155 10 to 19 141844 -0.2253 0.410882 9 to 18 142205 1.0196 0.846029 8 to 17 141867 -0.1460 0.441974 7 to 16 142007 0.3368 0.631864 6 to 15 142085 0.6058 0.727663 5 to 14 141808 -0.3494 0.363389 4 to 13 142258 1.2023 0.885378 3 to 12 142262 1.2161 0.888027 2 to 11 141805 -0.3598 0.359514 1 to 10 141943 0.1161 0.546215 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-11-10_13:31 Bits used No. missing words z-score p-value 28 to 32 142010 0.3413 0.633544 27 to 31 141858 -0.1740 0.430933 26 to 30 141618 -0.9876 0.161684 25 to 29 141754 -0.5265 0.299256 24 to 28 141869 -0.1367 0.445629 23 to 27 142340 1.4599 0.927841 22 to 26 142312 1.3650 0.913871 21 to 25 141410 -1.6926 0.045262 20 to 24 142078 0.5718 0.716259 19 to 23 141923 0.0463 0.518480 18 to 22 141714 -0.6621 0.253942 17 to 21 141906 -0.0113 0.495497 16 to 20 142251 1.1582 0.876610 15 to 19 141936 0.0904 0.536018 14 to 18 141926 0.0565 0.522532 13 to 17 141728 -0.6147 0.269384 12 to 16 141808 -0.3435 0.365614 11 to 15 142126 0.7345 0.768670 10 to 14 142683 2.6226 0.995637 9 to 13 142248 1.1480 0.874523 8 to 12 142293 1.3006 0.903298 7 to 11 141406 -1.7062 0.043985 6 to 10 142181 0.9209 0.821453 5 to 9 141897 -0.0418 0.483330 4 to 8 141999 0.3040 0.619423 3 to 7 142176 0.9040 0.816993 2 to 6 141759 -0.5096 0.305168 1 to 5 141612 -1.0079 0.156752 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-11-10_13:31 Bits used No. missing words z-score p-value 31 to 32 142346 1.2881 0.901147 30 to 31 142192 0.8338 0.797813 29 to 30 141486 -1.2488 0.105876 28 to 29 141855 -0.1603 0.436336 27 to 28 141435 -1.3992 0.080876 26 to 27 142021 0.3294 0.629077 25 to 26 141775 -0.3963 0.345959 24 to 25 141989 0.2350 0.592901 23 to 24 142096 0.5506 0.709063 22 to 23 142267 1.0551 0.854304 21 to 22 142068 0.4681 0.680127 20 to 21 141518 -1.1544 0.124175 19 to 20 141013 -2.6440 0.004096 18 to 19 142633 2.1347 0.983608 17 to 18 141638 -0.8004 0.211744 16 to 17 141896 -0.0393 0.484317 15 to 16 141996 0.2557 0.600895 14 to 15 141951 0.1229 0.548915 13 to 14 141591 -0.9390 0.173859 12 to 13 142513 1.7807 0.962522 11 to 12 141879 -0.0895 0.464355 10 to 11 141616 -0.8653 0.193443 9 to 10 142513 1.7807 0.962522 8 to 9 141735 -0.5142 0.303539 7 to 8 141750 -0.4700 0.319178 6 to 7 142176 0.7866 0.784253 5 to 6 141770 -0.4110 0.340535 4 to 5 141624 -0.8417 0.199983 3 to 4 142193 0.8368 0.798643 2 to 3 141323 -1.7296 0.041852 1 to 2 141685 -0.6617 0.254069 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-11-10_13:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2530.54 0.432 0.667095 Test results for specific bytes for dh-ranFile-2015-11-10_13:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2623.65 1.749 0.959825 2 to 9 2567.04 0.948 0.828459 3 to 10 2450.92 -0.694 0.243831 4 to 11 2661.83 2.289 0.988951 5 to 12 2558.78 0.831 0.797071 6 to 13 2552.78 0.746 0.772298 7 to 14 2394.05 -1.498 0.067011 8 to 15 2472.86 -0.384 0.350565 9 to 16 2626.05 1.783 0.962672 10 to 17 2525.97 0.367 0.643288 11 to 18 2503.54 0.050 0.519979 12 to 19 2571.65 1.013 0.844522 13 to 20 2494.46 -0.078 0.468781 14 to 21 2465.47 -0.488 0.312680 15 to 22 2474.44 -0.362 0.358849 16 to 23 2535.31 0.499 0.691247 17 to 24 2436.59 -0.897 0.184943 18 to 25 2494.61 -0.076 0.469617 19 to 26 2481.05 -0.268 0.394371 20 to 27 2553.89 0.762 0.777012 21 to 28 2401.22 -1.397 0.081207 22 to 29 2427.21 -1.029 0.151648 23 to 30 2444.83 -0.780 0.217645 24 to 31 2522.94 0.324 0.627176 25 to 32 2620.82 1.709 0.956240 CDPARK for dh-ranFile-2015-11-10_13:31: 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 3509 -0.6393 0.261324 3528 0.2283 0.590298 3512 -0.5023 0.307734 3530 0.3196 0.625377 3496 -1.2329 0.108811 3514 -0.4110 0.340551 3557 1.5525 0.939730 3511 -0.5479 0.291865 3526 0.1370 0.554479 3546 1.0502 0.853193 Square side=100, avg. no. parked=3522.90 sample std.=17.43 p-value of the KSTEST for those 10 p-values: 0.898288 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-11-10_13:31 0.5775,0.1761,0.7227,0.7050,0.4598,0.2970,0.6032,0.6668,0.5263,0.5305, The KS test for those 10 p-values: 0.272441 The 3DSPHERES test for dh-ranFile-2015-11-10_13:31 sample no r^3 equiv. uni. 1 8.185 0.238784 2 55.803 0.844342 3 34.968 0.688265 4 49.203 0.806042 5 22.538 0.528236 6 12.904 0.349585 7 2.216 0.071191 8 1.405 0.045766 9 23.179 0.538205 10 44.495 0.773080 11 39.647 0.733283 12 6.502 0.194846 13 1.439 0.046832 14 29.332 0.623833 15 67.004 0.892844 16 2.299 0.073771 17 87.556 0.945987 18 15.776 0.408961 19 37.025 0.708919 20 7.574 0.223118 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.878681 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-11-10_13:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 1.3 1.8 0.8 -0.1 0.3 0.3 1.3 2.5 0.5 0.1 1.4 1.7 0.1 0.2 -0.5 -0.6 0.2 0.2 0.3 -0.4 -2.2 -0.7 -0.9 0.7 -1.3 1.3 -2.1 0.2 0.6 0.5 0.3 -1.1 2.0 0.8 -0.8 -0.1 1.4 0.8 -0.4 -1.3 -0.6 3.0 -0.1 Chi-square with 42 degrees of freedom:55.018670 z-score=1.420453, p-value=0.914140 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-11-10_13:31 Test no p-value 1 0.399469 2 0.132395 3 0.067019 4 0.340020 5 0.289116 6 0.870262 7 0.168206 8 0.742428 9 0.169780 10 0.052433 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.070109 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-11-10_13:31: (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 66683 0.00 66652 0.00 3 25000.00 25017 0.01 24831 1.14 4 6666.67 6609 0.50 6786 2.14 5 1388.89 1426 0.99 1434 1.47 6 238.10 223 0.96 259 1.84 7 34.72 34 0.01 33 0.09 8 4.96 7 0.84 4 0.19 p=0.23186 p=0.66536 Number of rngs required: 688836, p-value: 0.691 RESULTS OF CRAPS TEST for dh-ranFile-2015-11-10_13:31 No. of wins: Observed Expected 98521 98585.9 z-score=-0.290, pvalue=0.38588 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66542 66666.7 0.233 0.233 2 37583 37654.3 0.135 0.368 3 26899 26954.7 0.115 0.483 4 19543 19313.5 2.728 3.211 5 13752 13851.4 0.714 3.925 6 9925 9943.5 0.035 3.960 7 7296 7145.0 3.190 7.150 8 5059 5139.1 1.248 8.397 9 3668 3699.9 0.274 8.672 10 2682 2666.3 0.092 8.764 11 1914 1923.3 0.045 8.810 12 1360 1388.7 0.595 9.404 13 993 1003.7 0.114 9.519 14 748 726.1 0.658 10.177 15 559 525.8 2.092 12.268 16 417 381.2 3.372 15.640 17 295 276.5 1.232 16.873 18 188 200.8 0.820 17.692 19 158 146.0 0.989 18.681 20 122 106.2 2.346 21.027 21 297 287.1 0.340 21.367 Chisq= 21.37 for 20 degrees of freedom, p= 0.62420 SUMMARY of craptest p-value for no. of wins: 0.385875 p-value for throws/game: 0.624199 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-11-10_13:31 No. of wins: Observed Expected 98913 98585.9 z-score= 1.463, pvalue=0.92829 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66512 66666.7 0.359 0.359 2 37570 37654.3 0.189 0.548 3 27166 26954.7 1.656 2.204 4 19449 19313.5 0.951 3.155 5 13795 13851.4 0.230 3.385 6 10060 9943.5 1.364 4.748 7 7032 7145.0 1.788 6.536 8 5095 5139.1 0.378 6.914 9 3710 3699.9 0.028 6.942 10 2649 2666.3 0.112 7.054 11 1909 1923.3 0.107 7.161 12 1343 1388.7 1.507 8.668 13 1046 1003.7 1.781 10.449 14 724 726.1 0.006 10.455 15 526 525.8 0.000 10.455 16 341 381.2 4.229 14.685 17 316 276.5 5.631 20.316 18 202 200.8 0.007 20.322 19 156 146.0 0.687 21.010 20 107 106.2 0.006 21.015 21 292 287.1 0.083 21.099 Chisq= 21.10 for 20 degrees of freedom, p= 0.60865 SUMMARY of craptest p-value for no. of wins: 0.928289 p-value for throws/game: 0.608646 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0001,0.0041,0.0110,0.0291,0.0419,0.0440,0.0453,0.0458,0.0468,0.0509, 0.0524,0.0568,0.0616,0.0670,0.0670,0.0701,0.0712,0.0738,0.0756,0.0776, 0.0809,0.0812,0.0836,0.0870,0.0906,0.0953,0.0967,0.1024,0.1029,0.1038, 0.1059,0.1088,0.1176,0.1235,0.1242,0.1250,0.1299,0.1324,0.1430,0.1473, 0.1516,0.1552,0.1556,0.1568,0.1614,0.1617,0.1682,0.1698,0.1739,0.1761, 0.1817,0.1849,0.1860,0.1934,0.1948,0.2000,0.2112,0.2117,0.2160,0.2167, 0.2176,0.2231,0.2319,0.2388,0.2435,0.2438,0.2534,0.2536,0.2539,0.2541, 0.2543,0.2613,0.2670,0.2694,0.2724,0.2754,0.2891,0.2919,0.2970,0.2985, 0.2993,0.3035,0.3052,0.3077,0.3113,0.3127,0.3187,0.3191,0.3192,0.3317, 0.3400,0.3405,0.3406,0.3460,0.3463,0.3470,0.3496,0.3496,0.3506,0.3529, 0.3588,0.3595,0.3634,0.3656,0.3706,0.3752,0.3774,0.3795,0.3859,0.3944, 0.3971,0.3995,0.4055,0.4090,0.4109,0.4309,0.4363,0.4370,0.4420,0.4456, 0.4493,0.4598,0.4631,0.4644,0.4656,0.4688,0.4696,0.4833,0.4843,0.4865, 0.4865,0.4955,0.4994,0.4995,0.5127,0.5139,0.5160,0.5165,0.5185,0.5200, 0.5202,0.5212,0.5225,0.5263,0.5282,0.5305,0.5312,0.5360,0.5363,0.5382, 0.5462,0.5489,0.5545,0.5748,0.5775,0.5849,0.5903,0.5920,0.5929,0.6009, 0.6018,0.6032,0.6086,0.6092,0.6135,0.6194,0.6235,0.6238,0.6242,0.6254, 0.6272,0.6291,0.6319,0.6335,0.6352,0.6433,0.6449,0.6604,0.6654,0.6668, 0.6671,0.6686,0.6703,0.6726,0.6734,0.6801,0.6832,0.6883,0.6895,0.6911, 0.6912,0.7050,0.7089,0.7091,0.7163,0.7183,0.7227,0.7277,0.7311,0.7333, 0.7334,0.7395,0.7423,0.7424,0.7687,0.7723,0.7730,0.7731,0.7770,0.7777, 0.7843,0.7910,0.7968,0.7971,0.7978,0.7986,0.8060,0.8170,0.8215,0.8218, 0.8285,0.8310,0.8394,0.8443,0.8444,0.8445,0.8460,0.8477,0.8477,0.8500, 0.8500,0.8532,0.8543,0.8703,0.8742,0.8745,0.8752,0.8766,0.8787,0.8854, 0.8880,0.8884,0.8928,0.8983,0.9011,0.9033,0.9118,0.9139,0.9141,0.9182, 0.9248,0.9278,0.9283,0.9330,0.9397,0.9440,0.9460,0.9562,0.9598,0.9625, 0.9625,0.9627,0.9705,0.9729,0.9778,0.9836,0.9838,0.9890,0.9956, Overall p-value after applying KStest on 269 p-values = 0.984106 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.