RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-01-30_17:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.45 24.2949 0.888358 2 to 25 15.73 18.4449 0.638692 3 to 26 15.80 25.4810 0.915551 4 to 27 15.88 17.0449 0.548675 5 to 28 15.40 21.6410 0.801076 6 to 29 15.48 24.0491 0.881893 7 to 30 15.61 14.6413 0.378702 8 to 31 15.67 36.3533 0.995887 9 to 32 15.77 23.8248 0.875725 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.005516 Tough bday spacings test for dh-ranFile-2017-01-30_17:31: 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 6 36 69 104 97 81 49 30 18 5 5 (O-E)^2/E 1.1 0.0 0.2 0.4 0.0 0.1 0.2 0.0 0.7 0.4 0.2 Birthday Spacings: Sum(O-E)^2/E= 3.312, p= 0.027 RESULTS OF GCD FOR dh-ranFile-2017-01-30_17:31 Euclid's algorithm: p-value, steps to gcd: 0.659330 p-value, dist. of gcd's: 0.213427 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-01-30_17:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.216 0.806 0.860 0.206 0.819 0.195 0.583 0.441 Bits 8 to 15---> 0.644 0.335 0.420 0.019 0.532 0.960 0.909 0.314 Bits 16 to 23---> 0.753 0.731 0.027 0.400 0.691 0.109 0.026 0.476 Bits 24 to 31---> 0.305 0.394 0.639 0.474 0.198 0.862 0.607 0.925 KS test for the above 32 p values: 0.013 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-01-30_17:31, p-values for 5 runs: 0.9126, 0.6383, 0.4418, 0.6679, 0.1816 Rank test for binary matrices (31x31) for dh-ranFile-2017-01-30_17:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 217 211.4 0.147 0.147 r= 29 5175 5134.0 0.327 0.475 r= 30 23037 23103.0 0.189 0.663 r= 31 11571 11551.5 0.033 0.696 chi-square = 0.696 with df = 3; p-value = 0.126 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2017-01-30_17:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 192 211.4 1.783 1.783 r= 30 5168 5134.0 0.225 2.009 r= 31 23141 23103.0 0.062 2.071 r= 32 11499 11551.5 0.239 2.310 chi-square = 2.310 with df = 3; p-value = 0.489 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2017-01-30_17:31 b-rank test for bits 1 to 8, p=0.84428 b-rank test for bits 2 to 9, p=0.06487 b-rank test for bits 3 to 10, p=0.39931 b-rank test for bits 4 to 11, p=0.05299 b-rank test for bits 5 to 12, p=0.23089 b-rank test for bits 6 to 13, p=0.82732 b-rank test for bits 7 to 14, p=0.05824 b-rank test for bits 8 to 15, p=0.97339 b-rank test for bits 9 to 16, p=0.92356 b-rank test for bits 10 to 17, p=0.21248 b-rank test for bits 11 to 18, p=0.16691 b-rank test for bits 12 to 19, p=0.07750 b-rank test for bits 13 to 20, p=0.16961 b-rank test for bits 14 to 21, p=0.46923 b-rank test for bits 15 to 22, p=0.28158 b-rank test for bits 16 to 23, p=0.60289 b-rank test for bits 17 to 24, p=0.97688 b-rank test for bits 18 to 25, p=0.54384 b-rank test for bits 19 to 26, p=0.48730 b-rank test for bits 20 to 27, p=0.33636 b-rank test for bits 21 to 28, p=0.92261 b-rank test for bits 22 to 29, p=0.26662 b-rank test for bits 23 to 30, p=0.49195 b-rank test for bits 24 to 31, p=0.01960 b-rank test for bits 25 to 32, p=0.57250 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 = 0.305693 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-01-30_17:31 (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 141686 -0.52 0.300905 2 141528 -0.89 0.186476 3 141690 -0.51 0.304167 4 141890 -0.05 0.481989 5 141794 -0.27 0.393787 6 141845 -0.15 0.440263 7 142771 2.01 0.977956 8 142703 1.85 0.968157 9 141120 -1.84 0.032575 10 142032 0.29 0.612795 11 142468 1.31 0.904105 12 141237 -1.57 0.058107 13 142321 0.96 0.831936 14 141355 -1.30 0.097632 15 141451 -1.07 0.142115 16 141643 -0.62 0.266883 17 141857 -0.12 0.451344 18 142273 0.85 0.802253 19 142009 0.23 0.592070 20 142573 1.55 0.939505 ---------------------------------------------------------------- OPSO test for dh-ranFile-2017-01-30_17:31 Bits used No. missing words z-score p-value 23 to 32 142455 1.8816 0.970056 22 to 31 142204 1.0161 0.845210 21 to 30 142235 1.1230 0.869281 20 to 29 142904 3.4299 0.999698 19 to 28 142350 1.5196 0.935688 18 to 27 141979 0.2402 0.594928 17 to 26 142134 0.7747 0.780749 16 to 25 141648 -0.9011 0.183758 15 to 24 141765 -0.4977 0.309351 14 to 23 141245 -2.2908 0.010988 13 to 22 141783 -0.4356 0.331556 12 to 21 141944 0.1196 0.547581 11 to 20 142103 0.6678 0.747878 10 to 19 140909 -3.4494 0.000281 9 to 18 141535 -1.2908 0.098388 8 to 17 141808 -0.3494 0.363389 7 to 16 142185 0.9506 0.829093 6 to 15 141400 -1.7563 0.039518 5 to 14 141192 -2.4736 0.006689 4 to 13 141286 -2.1494 0.015801 3 to 12 141371 -1.8563 0.031705 2 to 11 141894 -0.0529 0.478921 1 to 10 142067 0.5437 0.706673 ----------------------------------------------------------------- OQSO test for dh-ranFile-2017-01-30_17:31 Bits used No. missing words z-score p-value 28 to 32 141976 0.2260 0.589399 27 to 31 141916 0.0226 0.509019 26 to 30 141989 0.2701 0.606446 25 to 29 141437 -1.6011 0.054675 24 to 28 141650 -0.8791 0.189678 23 to 27 141912 0.0091 0.503611 22 to 26 141881 -0.0960 0.461747 21 to 25 141475 -1.4723 0.070469 20 to 24 142417 1.7209 0.957367 19 to 23 141106 -2.7232 0.003233 18 to 22 141715 -0.6587 0.255030 17 to 21 141894 -0.0520 0.479278 16 to 20 141747 -0.5503 0.291067 15 to 19 141629 -0.9503 0.170987 14 to 18 141917 0.0260 0.510371 13 to 17 141565 -1.1672 0.121561 12 to 16 141753 -0.5299 0.298080 11 to 15 141382 -1.7876 0.036924 10 to 14 142017 0.3650 0.642438 9 to 13 141949 0.1345 0.553486 8 to 12 142056 0.4972 0.690471 7 to 11 141890 -0.0655 0.473878 6 to 10 141633 -0.9367 0.174453 5 to 9 141715 -0.6587 0.255030 4 to 8 141703 -0.6994 0.242144 3 to 7 141878 -0.1062 0.457711 2 to 6 142174 0.8972 0.815190 1 to 5 142363 1.5379 0.937959 ----------------------------------------------------------------- DNA test for dh-ranFile-2017-01-30_17:31 Bits used No. missing words z-score p-value 31 to 32 142255 1.0197 0.846059 30 to 31 141325 -1.7237 0.042382 29 to 30 142313 1.1908 0.883127 28 to 29 141895 -0.0423 0.483141 27 to 28 141928 0.0551 0.521960 26 to 27 141407 -1.4818 0.069197 25 to 26 142269 1.0610 0.855649 24 to 25 142072 0.4799 0.684334 23 to 24 141789 -0.3550 0.361311 22 to 23 141812 -0.2871 0.387014 21 to 22 141681 -0.6735 0.250302 20 to 21 142276 1.0816 0.860290 19 to 20 142516 1.7896 0.963240 18 to 19 142489 1.7099 0.956362 17 to 18 141892 -0.0511 0.479615 16 to 17 141738 -0.5054 0.306640 15 to 16 141889 -0.0600 0.476090 14 to 15 142231 0.9489 0.828659 13 to 14 142168 0.7630 0.777280 12 to 13 141833 -0.2252 0.410927 11 to 12 141576 -0.9833 0.162736 10 to 11 142332 1.2468 0.893767 9 to 10 142047 0.4061 0.657668 8 to 9 141799 -0.3255 0.372418 7 to 8 141622 -0.8476 0.198336 6 to 7 141572 -0.9951 0.159850 5 to 6 141790 -0.3520 0.362417 4 to 5 141685 -0.6617 0.254069 3 to 4 141820 -0.2635 0.396079 2 to 3 141447 -1.3638 0.086314 1 to 2 142210 0.8869 0.812442 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2017-01-30_17:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2490.22 -0.138 0.444975 Test results for specific bytes for dh-ranFile-2017-01-30_17:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2586.69 1.226 0.889889 2 to 9 2483.34 -0.236 0.406841 3 to 10 2466.49 -0.474 0.317806 4 to 11 2425.84 -1.049 0.147126 5 to 12 2518.40 0.260 0.602669 6 to 13 2466.27 -0.477 0.316668 7 to 14 2482.50 -0.248 0.402240 8 to 15 2375.66 -1.758 0.039336 9 to 16 2589.22 1.262 0.896489 10 to 17 2521.68 0.307 0.620450 11 to 18 2571.27 1.008 0.843251 12 to 19 2543.90 0.621 0.732632 13 to 20 2465.32 -0.491 0.311887 14 to 21 2569.17 0.978 0.836003 15 to 22 2430.07 -0.989 0.161334 16 to 23 2377.65 -1.730 0.041793 17 to 24 2665.63 2.342 0.990418 18 to 25 2502.02 0.029 0.511401 19 to 26 2381.93 -1.670 0.047480 20 to 27 2417.34 -1.169 0.121204 21 to 28 2595.97 1.357 0.912651 22 to 29 2484.31 -0.222 0.412175 23 to 30 2446.53 -0.756 0.224773 24 to 31 2509.14 0.129 0.551414 25 to 32 2581.91 1.158 0.876652 CDPARK for dh-ranFile-2017-01-30_17:31: 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 3526 0.1370 0.554479 3528 0.2283 0.590298 3546 1.0502 0.853193 3549 1.1872 0.882429 3565 1.9178 0.972432 3531 0.3653 0.642555 3533 0.4566 0.676028 3534 0.5023 0.692266 3540 0.7763 0.781201 3558 1.5982 0.944998 Square side=100, avg. no. parked=3541.00 sample std.=12.50 p-value of the KSTEST for those 10 p-values: 0.006767 Results for the MINIMUM DISTANCE test for dh-ranFile-2017-01-30_17:31 0.4250,0.9135,0.3791,0.4740,0.8408,0.8593,0.7292,0.8668,0.1992,0.7907, The KS test for those 10 p-values: 0.140130 The 3DSPHERES test for dh-ranFile-2017-01-30_17:31 sample no r^3 equiv. uni. 1 1.921 0.062020 2 31.848 0.654103 3 7.487 0.220871 4 137.116 0.989648 5 45.986 0.784086 6 24.345 0.555803 7 11.761 0.324326 8 30.299 0.635767 9 8.354 0.243067 10 17.481 0.441602 11 4.951 0.152130 12 12.639 0.343802 13 20.972 0.502954 14 8.574 0.248584 15 65.120 0.885899 16 46.916 0.790674 17 38.795 0.725597 18 45.958 0.783886 19 14.169 0.376434 20 8.065 0.235722 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.911420 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-01-30_17:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -0.7 0.8 1.5 -0.5 0.3 0.3 -1.2 2.6 0.2 -1.5 0.4 -0.4 -0.5 1.1 0.2 -0.8 -0.1 0.4 1.1 -1.4 -0.3 -0.7 0.8 -0.5 -0.1 -0.7 0.4 1.5 -0.0 1.1 0.5 0.4 -1.2 0.3 0.1 -0.7 0.2 0.5 1.0 1.6 -1.0 1.8 Chi-square with 42 degrees of freedom:36.537490 z-score=-0.596009, p-value=0.291034 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2017-01-30_17:31 Test no p-value 1 0.091659 2 0.920507 3 0.907974 4 0.004062 5 0.281800 6 0.104594 7 0.024787 8 0.032662 9 0.027967 10 0.474241 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.001800 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-01-30_17:31: (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 66984 1.51 66676 0.00 3 25000.00 24858 0.81 25092 0.34 4 6666.67 6450 7.04 6669 0.00 5 1388.89 1434 1.47 1318 3.62 6 238.10 231 0.21 205 4.60 7 34.72 35 0.00 32 0.21 8 4.96 7 0.84 7 0.84 p=0.93523 p=0.85800 Number of rngs required: 688969, p-value: 0.743 RESULTS OF CRAPS TEST for dh-ranFile-2017-01-30_17:31 No. of wins: Observed Expected 98184 98585.9 z-score=-1.797, pvalue=0.03614 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66285 66666.7 2.185 2.185 2 37895 37654.3 1.538 3.723 3 26767 26954.7 1.308 5.031 4 19447 19313.5 0.923 5.954 5 14075 13851.4 3.609 9.563 6 9787 9943.5 2.464 12.028 7 7205 7145.0 0.503 12.531 8 5276 5139.1 3.648 16.179 9 3715 3699.9 0.062 16.241 10 2714 2666.3 0.853 17.095 11 1843 1923.3 3.355 20.450 12 1349 1388.7 1.137 21.587 13 947 1003.7 3.205 24.792 14 743 726.1 0.391 25.183 15 521 525.8 0.044 25.228 16 383 381.2 0.009 25.237 17 300 276.5 1.990 27.227 18 200 200.8 0.003 27.230 19 137 146.0 0.553 27.783 20 93 106.2 1.644 29.427 21 318 287.1 3.323 32.750 Chisq= 32.75 for 20 degrees of freedom, p= 0.96407 SUMMARY of craptest p-value for no. of wins: 0.036140 p-value for throws/game: 0.964066 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2017-01-30_17:31 No. of wins: Observed Expected 98776 98585.9 z-score= 0.850, pvalue=0.80246 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66904 66666.7 0.845 0.845 2 37543 37654.3 0.329 1.174 3 26951 26954.7 0.001 1.175 4 19148 19313.5 1.418 2.592 5 13885 13851.4 0.081 2.673 6 9974 9943.5 0.093 2.767 7 7098 7145.0 0.310 3.076 8 5106 5139.1 0.213 3.289 9 3737 3699.9 0.373 3.662 10 2624 2666.3 0.671 4.333 11 1880 1923.3 0.976 5.309 12 1501 1388.7 9.075 14.384 13 1005 1003.7 0.002 14.385 14 711 726.1 0.316 14.701 15 528 525.8 0.009 14.710 16 379 381.2 0.012 14.722 17 284 276.5 0.201 14.923 18 227 200.8 3.410 18.333 19 144 146.0 0.027 18.360 20 85 106.2 4.237 22.598 21 286 287.1 0.004 22.602 Chisq= 22.60 for 20 degrees of freedom, p= 0.69125 SUMMARY of craptest p-value for no. of wins: 0.802455 p-value for throws/game: 0.691253 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0003,0.0018,0.0032,0.0041,0.0055,0.0067,0.0068,0.0110,0.0131,0.0158, 0.0194,0.0196,0.0248,0.0257,0.0266,0.0269,0.0280,0.0317,0.0326,0.0327, 0.0361,0.0369,0.0393,0.0395,0.0418,0.0424,0.0475,0.0530,0.0547,0.0581, 0.0582,0.0620,0.0649,0.0692,0.0705,0.0775,0.0863,0.0917,0.0976,0.0984, 0.1046,0.1088,0.1212,0.1216,0.1259,0.1401,0.1421,0.1471,0.1521,0.1599, 0.1613,0.1627,0.1669,0.1696,0.1710,0.1745,0.1816,0.1838,0.1865,0.1897, 0.1949,0.1983,0.1983,0.1992,0.2064,0.2125,0.2134,0.2160,0.2209,0.2248, 0.2309,0.2357,0.2421,0.2431,0.2486,0.2503,0.2541,0.2550,0.2550,0.2666, 0.2669,0.2816,0.2818,0.2910,0.2911,0.2981,0.3009,0.3042,0.3053,0.3057, 0.3066,0.3094,0.3119,0.3139,0.3167,0.3178,0.3243,0.3316,0.3351,0.3364, 0.3438,0.3613,0.3624,0.3634,0.3724,0.3764,0.3787,0.3791,0.3870,0.3938, 0.3938,0.3961,0.3993,0.4001,0.4022,0.4068,0.4109,0.4122,0.4201,0.4250, 0.4403,0.4405,0.4416,0.4418,0.4450,0.4513,0.4577,0.4617,0.4692,0.4739, 0.4740,0.4742,0.4744,0.4761,0.4762,0.4789,0.4793,0.4796,0.4820,0.4831, 0.4873,0.4893,0.4919,0.5030,0.5036,0.5090,0.5104,0.5114,0.5220,0.5319, 0.5438,0.5476,0.5487,0.5514,0.5535,0.5545,0.5558,0.5725,0.5825,0.5894, 0.5903,0.5921,0.5949,0.6027,0.6029,0.6064,0.6065,0.6128,0.6205,0.6358, 0.6383,0.6387,0.6388,0.6424,0.6426,0.6438,0.6541,0.6577,0.6593,0.6679, 0.6760,0.6843,0.6905,0.6911,0.6913,0.6923,0.7067,0.7256,0.7292,0.7307, 0.7326,0.7432,0.7479,0.7531,0.7773,0.7807,0.7812,0.7839,0.7841,0.7907, 0.7907,0.8011,0.8023,0.8025,0.8062,0.8124,0.8152,0.8191,0.8273,0.8287, 0.8291,0.8319,0.8360,0.8408,0.8433,0.8443,0.8452,0.8461,0.8532,0.8556, 0.8580,0.8593,0.8596,0.8603,0.8623,0.8668,0.8693,0.8757,0.8767,0.8819, 0.8824,0.8831,0.8859,0.8884,0.8899,0.8938,0.8965,0.9041,0.9080,0.9094, 0.9114,0.9126,0.9127,0.9135,0.9156,0.9205,0.9226,0.9236,0.9246,0.9352, 0.9357,0.9380,0.9395,0.9450,0.9564,0.9574,0.9600,0.9632,0.9641,0.9682, 0.9701,0.9724,0.9734,0.9769,0.9780,0.9896,0.9904,0.9959,0.9997, Overall p-value after applying KStest on 269 p-values = 0.073212 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.