RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-12-20_23:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.84 19.3021 0.688527 2 to 25 15.53 17.3336 0.568005 3 to 26 15.78 15.9700 0.474036 4 to 27 16.00 12.6719 0.242140 5 to 28 15.98 15.6663 0.452398 6 to 29 15.90 19.9306 0.722205 7 to 30 15.66 11.6284 0.177901 8 to 31 15.55 24.0611 0.882217 9 to 32 15.76 18.8231 0.661221 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.690106 Tough bday spacings test for dh-ranFile-2015-12-20_23:31: 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 13 26 63 104 105 72 58 30 22 4 3 (O-E)^2/E 1.6 3.1 1.4 0.4 0.5 0.5 0.7 0.0 3.4 1.0 0.3 Birthday Spacings: Sum(O-E)^2/E= 12.960, p= 0.774 RESULTS OF GCD FOR dh-ranFile-2015-12-20_23:31 Euclid's algorithm: p-value, steps to gcd: 0.715651 p-value, dist. of gcd's: 0.267662 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-12-20_23:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.231 0.916 0.334 0.266 0.005 0.751 0.582 0.533 Bits 8 to 15---> 0.755 0.360 0.630 0.083 0.477 0.015 0.332 0.650 Bits 16 to 23---> 0.341 0.496 0.234 0.347 0.395 0.181 0.285 0.734 Bits 24 to 31---> 0.252 0.943 0.539 0.637 0.614 0.674 0.915 0.532 KS test for the above 32 p values: 0.544 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-12-20_23:31, p-values for 5 runs: 0.6749, 0.2883, 0.5537, 0.8708, 0.9031 Rank test for binary matrices (31x31) for dh-ranFile-2015-12-20_23:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 203 211.4 0.335 0.335 r= 29 5170 5134.0 0.252 0.587 r= 30 23108 23103.0 0.001 0.589 r= 31 11519 11551.5 0.092 0.680 chi-square = 0.680 with df = 3; p-value = 0.122 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-12-20_23:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 188 211.4 2.594 2.594 r= 30 5042 5134.0 1.649 4.243 r= 31 23032 23103.0 0.218 4.461 r= 32 11738 11551.5 3.010 7.472 chi-square = 7.472 with df = 3; p-value = 0.942 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-12-20_23:31 b-rank test for bits 1 to 8, p=0.39522 b-rank test for bits 2 to 9, p=0.24667 b-rank test for bits 3 to 10, p=0.15463 b-rank test for bits 4 to 11, p=0.93284 b-rank test for bits 5 to 12, p=0.24507 b-rank test for bits 6 to 13, p=0.30919 b-rank test for bits 7 to 14, p=0.59228 b-rank test for bits 8 to 15, p=0.73948 b-rank test for bits 9 to 16, p=0.70692 b-rank test for bits 10 to 17, p=0.96890 b-rank test for bits 11 to 18, p=0.43831 b-rank test for bits 12 to 19, p=0.39944 b-rank test for bits 13 to 20, p=0.85834 b-rank test for bits 14 to 21, p=0.44061 b-rank test for bits 15 to 22, p=0.62452 b-rank test for bits 16 to 23, p=0.85324 b-rank test for bits 17 to 24, p=0.32850 b-rank test for bits 18 to 25, p=0.97103 b-rank test for bits 19 to 26, p=0.37675 b-rank test for bits 20 to 27, p=0.52541 b-rank test for bits 21 to 28, p=0.92639 b-rank test for bits 22 to 29, p=0.23244 b-rank test for bits 23 to 30, p=0.16313 b-rank test for bits 24 to 31, p=0.35635 b-rank test for bits 25 to 32, p=0.08379 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 = 0.682318 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-12-20_23:31 (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 142093 0.43 0.666088 2 141936 0.06 0.524843 3 141828 -0.19 0.424645 4 142723 1.90 0.971355 5 141858 -0.12 0.452269 6 142329 0.98 0.836590 7 141566 -0.80 0.211227 8 142019 0.26 0.601117 9 141273 -1.49 0.068540 10 141474 -1.02 0.154547 11 142513 1.41 0.920796 12 142572 1.55 0.939224 13 142194 0.67 0.747012 14 141560 -0.82 0.207195 15 142179 0.63 0.735676 16 141666 -0.57 0.284838 17 141709 -0.47 0.319871 18 142725 1.91 0.971660 19 141514 -0.92 0.177830 20 141459 -1.05 0.146360 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-12-20_23:31 Bits used No. missing words z-score p-value 23 to 32 141846 -0.2184 0.413567 22 to 31 141960 0.1747 0.569352 21 to 30 142075 0.5713 0.716094 20 to 29 141896 -0.0460 0.481669 19 to 28 142317 1.4058 0.920102 18 to 27 141478 -1.4873 0.068462 17 to 26 142154 0.8437 0.800579 16 to 25 141681 -0.7873 0.215540 15 to 24 141407 -1.7322 0.041621 14 to 23 141786 -0.4253 0.335318 13 to 22 141899 -0.0356 0.485792 12 to 21 142158 0.8575 0.804411 11 to 20 142442 1.8368 0.966880 10 to 19 142202 1.0092 0.843562 9 to 18 141793 -0.4011 0.344159 8 to 17 141783 -0.4356 0.331556 7 to 16 141730 -0.6184 0.268163 6 to 15 141479 -1.4839 0.068918 5 to 14 141825 -0.2908 0.385605 4 to 13 142032 0.4230 0.663852 3 to 12 141849 -0.2080 0.417601 2 to 11 141937 0.0954 0.538007 1 to 10 141506 -1.3908 0.082144 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-12-20_23:31 Bits used No. missing words z-score p-value 28 to 32 142091 0.6158 0.730997 27 to 31 142265 1.2057 0.886026 26 to 30 141609 -1.0181 0.154323 25 to 29 141392 -1.7537 0.039744 24 to 28 141750 -0.5401 0.294564 23 to 27 141764 -0.4926 0.311132 22 to 26 141420 -1.6587 0.048584 21 to 25 142145 0.7989 0.787820 20 to 24 141730 -0.6079 0.271628 19 to 23 141963 0.1819 0.572182 18 to 22 141795 -0.3876 0.349171 17 to 21 141734 -0.5943 0.276143 16 to 20 142326 1.4124 0.921090 15 to 19 141735 -0.5909 0.277277 14 to 18 142051 0.4802 0.684471 13 to 17 142942 3.5006 0.999768 12 to 16 141908 -0.0045 0.498201 11 to 15 141739 -0.5774 0.281838 10 to 14 141611 -1.0113 0.155939 9 to 13 142008 0.3345 0.630989 8 to 12 141887 -0.0757 0.469831 7 to 11 141604 -1.0350 0.150331 6 to 10 141753 -0.5299 0.298080 5 to 9 142240 1.1209 0.868838 4 to 8 142131 0.7514 0.773801 3 to 7 141643 -0.9028 0.183312 2 to 6 141896 -0.0452 0.481979 1 to 5 142197 0.9752 0.835258 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-12-20_23:31 Bits used No. missing words z-score p-value 31 to 32 142613 2.0757 0.981040 30 to 31 141715 -0.5732 0.283240 29 to 30 141753 -0.4612 0.322345 28 to 29 141922 0.0374 0.514907 27 to 28 141668 -0.7119 0.238267 26 to 27 142339 1.2675 0.897505 25 to 26 142444 1.5772 0.942625 24 to 25 142012 0.3029 0.619002 23 to 24 141574 -0.9892 0.161289 22 to 23 141757 -0.4494 0.326589 21 to 22 141967 0.1701 0.567541 20 to 21 141889 -0.0600 0.476090 19 to 20 141917 0.0226 0.509025 18 to 19 141707 -0.5968 0.275306 17 to 18 141997 0.2586 0.602033 16 to 17 141795 -0.3373 0.367962 15 to 16 142152 0.7158 0.762955 14 to 15 141473 -1.2871 0.099028 13 to 14 142468 1.6480 0.950323 12 to 13 142075 0.4887 0.687474 11 to 12 141813 -0.2842 0.388144 10 to 11 142276 1.0816 0.860290 9 to 10 141616 -0.8653 0.193443 8 to 9 142035 0.3707 0.644573 7 to 8 141969 0.1760 0.569860 6 to 7 141896 -0.0393 0.484317 5 to 6 141917 0.0226 0.509025 4 to 5 141730 -0.5290 0.298404 3 to 4 141508 -1.1839 0.118233 2 to 3 142055 0.4297 0.666295 1 to 2 141978 0.2026 0.580263 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-12-20_23:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2446.48 -0.757 0.224566 Test results for specific bytes for dh-ranFile-2015-12-20_23:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2529.97 0.424 0.664135 2 to 9 2573.69 1.042 0.851340 3 to 10 2550.54 0.715 0.762602 4 to 11 2556.45 0.798 0.787658 5 to 12 2572.26 1.022 0.846596 6 to 13 2550.22 0.710 0.761224 7 to 14 2541.08 0.581 0.719355 8 to 15 2436.20 -0.902 0.183446 9 to 16 2537.42 0.529 0.701661 10 to 17 2548.36 0.684 0.752965 11 to 18 2513.42 0.190 0.575258 12 to 19 2374.63 -1.773 0.038118 13 to 20 2757.85 3.647 0.999867 14 to 21 2639.41 1.972 0.975672 15 to 22 2523.10 0.327 0.628050 16 to 23 2549.57 0.701 0.758360 17 to 24 2432.77 -0.951 0.170873 18 to 25 2497.40 -0.037 0.485308 19 to 26 2570.49 0.997 0.840602 20 to 27 2526.81 0.379 0.647716 21 to 28 2472.19 -0.393 0.347033 22 to 29 2552.91 0.748 0.772852 23 to 30 2469.26 -0.435 0.331874 24 to 31 2473.38 -0.376 0.353283 25 to 32 2520.03 0.283 0.611534 CDPARK for dh-ranFile-2015-12-20_23:31: 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 3540 0.7763 0.781201 3503 -0.9132 0.180558 3536 0.5936 0.723613 3537 0.6393 0.738676 3562 1.7808 0.962529 3579 2.5571 0.994722 3505 -0.8219 0.205562 3482 -1.8721 0.030593 3510 -0.5936 0.276387 3508 -0.6849 0.246694 Square side=100, avg. no. parked=3526.20 sample std.=28.30 p-value of the KSTEST for those 10 p-values: 0.467891 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-12-20_23:31 0.7853,0.4303,0.5646,0.6873,0.0231,0.5057,0.9544,0.5089,0.6648,0.2922, The KS test for those 10 p-values: 0.732970 The 3DSPHERES test for dh-ranFile-2015-12-20_23:31 sample no r^3 equiv. uni. 1 17.279 0.437838 2 41.336 0.747883 3 43.066 0.762011 4 0.978 0.032069 5 12.916 0.349829 6 7.701 0.226404 7 43.240 0.763385 8 16.339 0.419948 9 86.539 0.944125 10 76.338 0.921496 11 72.097 0.909574 12 105.762 0.970560 13 9.954 0.282357 14 18.942 0.468162 15 59.007 0.860110 16 18.626 0.462519 17 15.934 0.412062 18 17.512 0.442180 19 140.262 0.990678 20 4.785 0.147421 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.250618 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-12-20_23:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 0.9 0.1 -0.3 -1.4 -0.1 0.0 -1.5 -1.9 -2.1 -0.9 0.5 0.8 1.0 -0.0 0.8 1.2 1.2 -0.9 -0.8 0.9 -0.1 0.5 -0.4 -0.9 -0.5 -0.3 -0.6 0.2 0.0 -0.3 -0.1 0.8 0.8 -0.8 -1.2 1.0 -0.4 -1.2 -0.7 0.1 2.0 -1.1 Chi-square with 42 degrees of freedom:35.678628 z-score=-0.689718, p-value=0.256574 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-12-20_23:31 Test no p-value 1 0.272127 2 0.042740 3 0.188463 4 0.106413 5 0.004330 6 0.285408 7 0.010440 8 0.345678 9 0.430033 10 0.050494 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000202 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-12-20_23:31: (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 66723 0.05 66724 0.05 3 25000.00 24928 0.21 25004 0.00 4 6666.67 6650 0.04 6599 0.69 5 1388.89 1423 0.84 1421 0.74 6 238.10 232 0.16 219 1.53 7 34.72 37 0.15 27 1.72 8 4.96 6 0.22 5 0.00 p=0.05170 p=0.42079 Number of rngs required: 687381, p-value: 0.118 RESULTS OF CRAPS TEST for dh-ranFile-2015-12-20_23:31 No. of wins: Observed Expected 98532 98585.9 z-score=-0.241, pvalue=0.40482 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66822 66666.7 0.362 0.362 2 37671 37654.3 0.007 0.369 3 26936 26954.7 0.013 0.382 4 19131 19313.5 1.724 2.106 5 13775 13851.4 0.422 2.528 6 10111 9943.5 2.820 5.348 7 7082 7145.0 0.556 5.904 8 5133 5139.1 0.007 5.911 9 3666 3699.9 0.310 6.221 10 2673 2666.3 0.017 6.238 11 1926 1923.3 0.004 6.241 12 1406 1388.7 0.215 6.456 13 988 1003.7 0.246 6.702 14 719 726.1 0.070 6.772 15 564 525.8 2.770 9.542 16 389 381.2 0.162 9.704 17 288 276.5 0.475 10.179 18 209 200.8 0.332 10.511 19 153 146.0 0.337 10.848 20 92 106.2 1.902 12.751 21 266 287.1 1.553 14.303 Chisq= 14.30 for 20 degrees of freedom, p= 0.18522 SUMMARY of craptest p-value for no. of wins: 0.404821 p-value for throws/game: 0.185217 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-12-20_23:31 No. of wins: Observed Expected 98657 98585.9 z-score= 0.318, pvalue=0.62483 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66746 66666.7 0.094 0.094 2 37698 37654.3 0.051 0.145 3 26805 26954.7 0.832 0.977 4 19231 19313.5 0.352 1.329 5 13776 13851.4 0.411 1.740 6 10031 9943.5 0.769 2.509 7 7031 7145.0 1.820 4.328 8 5250 5139.1 2.394 6.723 9 3768 3699.9 1.255 7.978 10 2643 2666.3 0.204 8.181 11 1947 1923.3 0.291 8.473 12 1394 1388.7 0.020 8.492 13 1081 1003.7 5.951 14.443 14 679 726.1 3.060 17.504 15 536 525.8 0.196 17.700 16 395 381.2 0.503 18.203 17 284 276.5 0.201 18.405 18 196 200.8 0.116 18.521 19 140 146.0 0.245 18.766 20 92 106.2 1.902 20.669 21 277 287.1 0.356 21.025 Chisq= 21.02 for 20 degrees of freedom, p= 0.60433 SUMMARY of craptest p-value for no. of wins: 0.624828 p-value for throws/game: 0.604329 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0002,0.0043,0.0053,0.0104,0.0154,0.0231,0.0306,0.0321,0.0381,0.0397, 0.0416,0.0427,0.0486,0.0505,0.0517,0.0685,0.0685,0.0689,0.0821,0.0826, 0.0838,0.0990,0.1064,0.1175,0.1182,0.1221,0.1464,0.1474,0.1503,0.1543, 0.1545,0.1546,0.1559,0.1613,0.1631,0.1709,0.1778,0.1779,0.1806,0.1810, 0.1833,0.1834,0.1852,0.1885,0.1934,0.2056,0.2072,0.2112,0.2155,0.2246, 0.2264,0.2313,0.2324,0.2340,0.2383,0.2421,0.2451,0.2467,0.2467,0.2506, 0.2515,0.2566,0.2659,0.2677,0.2682,0.2716,0.2721,0.2753,0.2761,0.2764, 0.2773,0.2818,0.2824,0.2832,0.2848,0.2854,0.2855,0.2883,0.2922,0.2946, 0.2981,0.2984,0.3092,0.3111,0.3199,0.3223,0.3266,0.3285,0.3316,0.3319, 0.3324,0.3337,0.3353,0.3405,0.3442,0.3457,0.3470,0.3473,0.3492,0.3498, 0.3533,0.3564,0.3598,0.3680,0.3767,0.3856,0.3881,0.3952,0.3954,0.3994, 0.4048,0.4121,0.4136,0.4176,0.4199,0.4208,0.4246,0.4300,0.4303,0.4378, 0.4383,0.4406,0.4422,0.4523,0.4524,0.4625,0.4679,0.4682,0.4698,0.4740, 0.4761,0.4766,0.4817,0.4820,0.4843,0.4853,0.4858,0.4958,0.4982,0.5057, 0.5089,0.5090,0.5090,0.5149,0.5248,0.5254,0.5322,0.5330,0.5380,0.5390, 0.5442,0.5537,0.5646,0.5675,0.5680,0.5694,0.5699,0.5722,0.5753,0.5803, 0.5818,0.5923,0.6011,0.6020,0.6043,0.6115,0.6135,0.6190,0.6245,0.6248, 0.6281,0.6304,0.6310,0.6370,0.6446,0.6477,0.6505,0.6612,0.6639,0.6641, 0.6648,0.6661,0.6663,0.6741,0.6749,0.6823,0.6845,0.6873,0.6875,0.6885, 0.6901,0.7017,0.7069,0.7157,0.7161,0.7194,0.7222,0.7236,0.7310,0.7330, 0.7336,0.7357,0.7387,0.7395,0.7470,0.7479,0.7515,0.7530,0.7547,0.7584, 0.7612,0.7620,0.7626,0.7630,0.7634,0.7729,0.7738,0.7741,0.7812,0.7853, 0.7877,0.7878,0.8006,0.8044,0.8353,0.8366,0.8406,0.8436,0.8466,0.8513, 0.8532,0.8583,0.8601,0.8603,0.8688,0.8708,0.8822,0.8860,0.8975,0.9031, 0.9096,0.9150,0.9155,0.9201,0.9208,0.9211,0.9215,0.9264,0.9328,0.9392, 0.9417,0.9426,0.9431,0.9441,0.9503,0.9544,0.9625,0.9669,0.9689,0.9706, 0.9710,0.9714,0.9717,0.9757,0.9810,0.9907,0.9947,0.9998,0.9999, Overall p-value after applying KStest on 269 p-values = 0.609294 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.