RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-10-27_19:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.83 19.8017 0.715502 2 to 25 15.88 12.8382 0.253050 3 to 26 15.44 22.3119 0.826982 4 to 27 15.61 15.2296 0.421052 5 to 28 15.91 23.7791 0.874439 6 to 29 15.67 19.7369 0.712090 7 to 30 15.74 11.5213 0.171780 8 to 31 15.85 21.6154 0.800033 9 to 32 15.64 12.9893 0.263096 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.654580 Tough bday spacings test for dh-ranFile-2015-10-27_19:31: 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 38 70 100 85 88 64 25 13 5 6 (O-E)^2/E 1.1 0.1 0.1 0.1 1.6 1.2 2.7 0.8 0.2 0.4 0.9 Birthday Spacings: Sum(O-E)^2/E= 9.266, p= 0.493 RESULTS OF GCD FOR dh-ranFile-2015-10-27_19:31 Euclid's algorithm: p-value, steps to gcd: 0.463113 p-value, dist. of gcd's: 0.454956 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-10-27_19:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.567 0.275 0.034 0.789 0.304 0.459 0.880 0.367 Bits 8 to 15---> 0.978 0.715 0.704 0.766 0.577 0.480 0.435 0.049 Bits 16 to 23---> 0.539 0.326 0.870 0.315 0.433 0.075 0.006 0.650 Bits 24 to 31---> 0.511 0.775 0.842 0.159 0.396 0.978 0.279 0.251 KS test for the above 32 p values: 0.043 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-10-27_19:31, p-values for 5 runs: 0.6093, 0.6231, 0.8926, 0.2779, 0.5848 Rank test for binary matrices (31x31) for dh-ranFile-2015-10-27_19:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 221 211.4 0.434 0.434 r= 29 5126 5134.0 0.012 0.447 r= 30 23073 23103.0 0.039 0.486 r= 31 11580 11551.5 0.070 0.556 chi-square = 0.556 with df = 3; p-value = 0.094 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-10-27_19:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 209 211.4 0.028 0.028 r= 30 5120 5134.0 0.038 0.066 r= 31 23143 23103.0 0.069 0.135 r= 32 11528 11551.5 0.048 0.183 chi-square = 0.183 with df = 3; p-value = 0.020 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-10-27_19:31 b-rank test for bits 1 to 8, p=0.58954 b-rank test for bits 2 to 9, p=0.74796 b-rank test for bits 3 to 10, p=0.25453 b-rank test for bits 4 to 11, p=0.29302 b-rank test for bits 5 to 12, p=0.11073 b-rank test for bits 6 to 13, p=0.63424 b-rank test for bits 7 to 14, p=0.15161 b-rank test for bits 8 to 15, p=0.15275 b-rank test for bits 9 to 16, p=0.85439 b-rank test for bits 10 to 17, p=0.23367 b-rank test for bits 11 to 18, p=0.40780 b-rank test for bits 12 to 19, p=0.31430 b-rank test for bits 13 to 20, p=0.17334 b-rank test for bits 14 to 21, p=0.81734 b-rank test for bits 15 to 22, p=0.52802 b-rank test for bits 16 to 23, p=0.19329 b-rank test for bits 17 to 24, p=0.25242 b-rank test for bits 18 to 25, p=0.75000 b-rank test for bits 19 to 26, p=0.60577 b-rank test for bits 20 to 27, p=0.48467 b-rank test for bits 21 to 28, p=0.77907 b-rank test for bits 22 to 29, p=0.71236 b-rank test for bits 23 to 30, p=0.07574 b-rank test for bits 24 to 31, p=0.66251 b-rank test for bits 25 to 32, p=0.14675 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 = 0.280922 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-10-27_19:31 (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 141141 -1.80 0.036314 2 141929 0.05 0.518328 3 141316 -1.39 0.082830 4 141726 -0.43 0.334201 5 141843 -0.15 0.438420 6 142034 0.29 0.614583 7 142341 1.01 0.843411 8 142091 0.42 0.664386 9 142119 0.49 0.687892 10 141977 0.16 0.562814 11 142408 1.17 0.878014 12 141910 0.00 0.500625 13 141768 -0.33 0.370621 14 142235 0.76 0.776645 15 142436 1.23 0.890752 16 141812 -0.23 0.410054 17 141859 -0.12 0.453195 18 142760 1.99 0.976569 19 142194 0.67 0.747012 20 142340 1.01 0.842850 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-10-27_19:31 Bits used No. missing words z-score p-value 23 to 32 142114 0.7058 0.759831 22 to 31 141293 -2.1253 0.016782 21 to 30 142004 0.3264 0.627957 20 to 29 141638 -0.9356 0.174734 19 to 28 141767 -0.4908 0.311786 18 to 27 142156 0.8506 0.802500 17 to 26 141967 0.1989 0.578815 16 to 25 141976 0.2299 0.590914 15 to 24 141740 -0.5839 0.279645 14 to 23 142516 2.0920 0.981779 13 to 22 141564 -1.1908 0.116867 12 to 21 141669 -0.8287 0.203630 11 to 20 141616 -1.0115 0.155893 10 to 19 141972 0.2161 0.585547 9 to 18 141707 -0.6977 0.242686 8 to 17 141837 -0.2494 0.401520 7 to 16 141725 -0.6356 0.262512 6 to 15 141574 -1.1563 0.123777 5 to 14 141232 -2.3356 0.009756 4 to 13 142463 1.9092 0.971882 3 to 12 142461 1.9023 0.971435 2 to 11 141893 -0.0563 0.477547 1 to 10 141923 0.0471 0.518798 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-10-27_19:31 Bits used No. missing words z-score p-value 28 to 32 141392 -1.7537 0.039744 27 to 31 141798 -0.3774 0.352942 26 to 30 141774 -0.4587 0.323208 25 to 29 141984 0.2531 0.599912 24 to 28 142291 1.2938 0.902132 23 to 27 141970 0.2057 0.581472 22 to 26 141568 -1.1571 0.123626 21 to 25 142163 0.8599 0.805077 20 to 24 141502 -1.3808 0.083673 19 to 23 142193 0.9616 0.831873 18 to 22 142291 1.2938 0.902132 17 to 21 142042 0.4497 0.673547 16 to 20 141703 -0.6994 0.242144 15 to 19 141919 0.0328 0.513075 14 to 18 142295 1.3074 0.904454 13 to 17 141982 0.2463 0.597290 12 to 16 142012 0.3480 0.636093 11 to 15 141989 0.2701 0.606446 10 to 14 141898 -0.0384 0.484682 9 to 13 141760 -0.5062 0.306357 8 to 12 141970 0.2057 0.581472 7 to 11 141449 -1.5604 0.059328 6 to 10 142260 1.1887 0.882723 5 to 9 141573 -1.1401 0.127122 4 to 8 142313 1.3684 0.914402 3 to 7 141836 -0.2486 0.401844 2 to 6 142032 0.4158 0.661233 1 to 5 142337 1.4497 0.926433 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-10-27_19:31 Bits used No. missing words z-score p-value 31 to 32 141960 0.1495 0.559408 30 to 31 141935 0.0757 0.530180 29 to 30 141897 -0.0364 0.485493 28 to 29 141831 -0.2311 0.408633 27 to 28 141366 -1.6027 0.054496 26 to 27 141697 -0.6263 0.265545 25 to 26 142496 1.7306 0.958238 24 to 25 141855 -0.1603 0.436336 23 to 24 141916 0.0197 0.507849 22 to 23 141344 -1.6676 0.047694 21 to 22 142118 0.6155 0.730903 20 to 21 142076 0.4917 0.688517 19 to 20 142078 0.4976 0.690600 18 to 19 142237 0.9666 0.833123 17 to 18 142126 0.6391 0.738636 16 to 17 141965 0.1642 0.565220 15 to 16 142173 0.7778 0.781653 14 to 15 141633 -0.8151 0.207498 13 to 14 141705 -0.6027 0.273340 12 to 13 141931 0.0639 0.525484 11 to 12 141684 -0.6647 0.253124 10 to 11 141319 -1.7414 0.040808 9 to 10 141931 0.0639 0.525484 8 to 9 142556 1.9076 0.971777 7 to 8 142238 0.9695 0.833859 6 to 7 141880 -0.0865 0.465527 5 to 6 142178 0.7925 0.785976 4 to 5 141199 -2.0954 0.018069 3 to 4 141956 0.1377 0.554749 2 to 3 141917 0.0226 0.509025 1 to 2 141786 -0.3638 0.358002 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-10-27_19:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2512.62 0.178 0.570824 Test results for specific bytes for dh-ranFile-2015-10-27_19:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2569.77 0.987 0.838121 2 to 9 2624.11 1.755 0.960380 3 to 10 2523.70 0.335 0.631253 4 to 11 2433.56 -0.940 0.173697 5 to 12 2539.89 0.564 0.713690 6 to 13 2487.81 -0.172 0.431542 7 to 14 2459.28 -0.576 0.282351 8 to 15 2580.74 1.142 0.873243 9 to 16 2444.63 -0.783 0.216791 10 to 17 2457.63 -0.599 0.274538 11 to 18 2513.74 0.194 0.577007 12 to 19 2540.58 0.574 0.716968 13 to 20 2460.71 -0.556 0.289217 14 to 21 2395.78 -1.474 0.070263 15 to 22 2563.97 0.905 0.817178 16 to 23 2550.29 0.711 0.761512 17 to 24 2562.93 0.890 0.813274 18 to 25 2506.68 0.094 0.537633 19 to 26 2450.78 -0.696 0.243198 20 to 27 2363.96 -1.924 0.027185 21 to 28 2413.24 -1.227 0.109907 22 to 29 2605.86 1.497 0.932816 23 to 30 2518.20 0.257 0.601549 24 to 31 2565.63 0.928 0.823351 25 to 32 2489.73 -0.145 0.442269 CDPARK for dh-ranFile-2015-10-27_19:31: 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 3552 1.3242 0.907282 3544 0.9589 0.831196 3488 -1.5982 0.055002 3485 -1.7352 0.041356 3531 0.3653 0.642555 3513 -0.4566 0.323972 3464 -2.6941 0.003529 3484 -1.7808 0.037471 3565 1.9178 0.972432 3539 0.7306 0.767486 Square side=100, avg. no. parked=3516.50 sample std.=32.73 p-value of the KSTEST for those 10 p-values: 0.084933 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-10-27_19:31 0.8720,0.1600,0.4447,0.6277,0.1072,0.9642,0.5048,0.9027,0.4947,0.4992, The KS test for those 10 p-values: 0.717809 The 3DSPHERES test for dh-ranFile-2015-10-27_19:31 sample no r^3 equiv. uni. 1 17.367 0.439488 2 30.982 0.643969 3 32.092 0.656895 4 44.526 0.773317 5 40.657 0.742113 6 27.828 0.604497 7 16.133 0.415948 8 18.736 0.464495 9 43.515 0.765546 10 11.720 0.323387 11 77.996 0.925717 12 35.279 0.691477 13 0.171 0.005682 14 45.974 0.783999 15 0.494 0.016316 16 47.042 0.791554 17 10.663 0.299120 18 7.451 0.219916 19 10.967 0.306205 20 36.832 0.707048 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.429881 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-10-27_19:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 3.0 1.3 1.5 0.1 1.9 0.8 -1.4 -0.0 -1.3 -1.5 -0.8 0.7 -0.9 1.3 1.0 -0.4 -0.8 0.4 0.5 0.5 -0.9 0.3 -0.6 2.2 -2.0 -0.3 1.1 -0.4 -0.9 -1.1 1.5 1.3 1.8 0.3 1.1 0.0 -0.4 0.5 2.1 0.1 1.0 -0.1 Chi-square with 42 degrees of freedom:59.301260 z-score=1.887722, p-value=0.959749 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-10-27_19:31 Test no p-value 1 0.400911 2 0.063685 3 0.579785 4 0.151661 5 0.544818 6 0.240673 7 0.090001 8 0.181583 9 0.453353 10 0.307668 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.045746 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-10-27_19:31: (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 66892 0.76 66671 0.00 3 25000.00 24844 0.97 24919 0.26 4 6666.67 6548 2.11 6728 0.56 5 1388.89 1402 0.12 1376 0.12 6 238.10 273 5.12 266 3.27 7 34.72 33 0.09 37 0.15 8 4.96 7 0.84 2 1.77 p=0.87587 p=0.59156 Number of rngs required: 688658, p-value: 0.615 RESULTS OF CRAPS TEST for dh-ranFile-2015-10-27_19:31 No. of wins: Observed Expected 98522 98585.9 z-score=-0.286, pvalue=0.38759 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66695 66666.7 0.012 0.012 2 37691 37654.3 0.036 0.048 3 26964 26954.7 0.003 0.051 4 19188 19313.5 0.815 0.866 5 14068 13851.4 3.386 4.252 6 9802 9943.5 2.015 6.267 7 7151 7145.0 0.005 6.272 8 5190 5139.1 0.505 6.777 9 3754 3699.9 0.792 7.569 10 2530 2666.3 6.967 14.536 11 1932 1923.3 0.039 14.575 12 1430 1388.7 1.226 15.801 13 994 1003.7 0.094 15.895 14 689 726.1 1.900 17.795 15 506 525.8 0.748 18.543 16 382 381.2 0.002 18.545 17 272 276.5 0.075 18.620 18 192 200.8 0.388 19.008 19 141 146.0 0.170 19.178 20 118 106.2 1.308 20.486 21 311 287.1 1.987 22.473 Chisq= 22.47 for 20 degrees of freedom, p= 0.68458 SUMMARY of craptest p-value for no. of wins: 0.387587 p-value for throws/game: 0.684580 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-10-27_19:31 No. of wins: Observed Expected 98218 98585.9 z-score=-1.645, pvalue=0.04996 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66705 66666.7 0.022 0.022 2 37672 37654.3 0.008 0.030 3 27109 26954.7 0.883 0.913 4 19120 19313.5 1.938 2.851 5 13885 13851.4 0.081 2.933 6 9993 9943.5 0.246 3.179 7 7122 7145.0 0.074 3.253 8 5208 5139.1 0.924 4.177 9 3676 3699.9 0.154 4.331 10 2626 2666.3 0.609 4.940 11 1881 1923.3 0.932 5.872 12 1345 1388.7 1.378 7.249 13 991 1003.7 0.161 7.411 14 745 726.1 0.490 7.900 15 520 525.8 0.065 7.965 16 361 381.2 1.065 9.030 17 279 276.5 0.022 9.052 18 206 200.8 0.133 9.185 19 147 146.0 0.007 9.193 20 125 106.2 3.322 12.515 21 284 287.1 0.034 12.548 Chisq= 12.55 for 20 degrees of freedom, p= 0.10409 SUMMARY of craptest p-value for no. of wins: 0.049956 p-value for throws/game: 0.104094 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0035,0.0057,0.0059,0.0098,0.0163,0.0168,0.0181,0.0197,0.0272,0.0335, 0.0363,0.0375,0.0397,0.0408,0.0414,0.0427,0.0457,0.0477,0.0488,0.0500, 0.0545,0.0550,0.0593,0.0637,0.0703,0.0747,0.0757,0.0828,0.0837,0.0849, 0.0900,0.0936,0.1041,0.1072,0.1099,0.1107,0.1169,0.1236,0.1238,0.1271, 0.1468,0.1516,0.1517,0.1528,0.1559,0.1586,0.1600,0.1718,0.1733,0.1737, 0.1747,0.1816,0.1933,0.2036,0.2075,0.2168,0.2199,0.2337,0.2407,0.2421, 0.2427,0.2432,0.2508,0.2524,0.2530,0.2531,0.2545,0.2625,0.2631,0.2655, 0.2733,0.2745,0.2752,0.2779,0.2788,0.2796,0.2809,0.2824,0.2892,0.2930, 0.2991,0.3035,0.3062,0.3064,0.3077,0.3118,0.3143,0.3147,0.3232,0.3234, 0.3240,0.3265,0.3342,0.3529,0.3580,0.3674,0.3706,0.3876,0.3964,0.4009, 0.4015,0.4018,0.4078,0.4086,0.4101,0.4159,0.4211,0.4299,0.4315,0.4332, 0.4349,0.4363,0.4384,0.4395,0.4423,0.4447,0.4532,0.4534,0.4550,0.4591, 0.4631,0.4645,0.4655,0.4775,0.4802,0.4847,0.4847,0.4855,0.4929,0.4947, 0.4992,0.5006,0.5048,0.5078,0.5090,0.5113,0.5131,0.5183,0.5188,0.5255, 0.5255,0.5280,0.5302,0.5376,0.5395,0.5448,0.5547,0.5594,0.5628,0.5652, 0.5666,0.5708,0.5770,0.5772,0.5788,0.5798,0.5815,0.5815,0.5848,0.5855, 0.5895,0.5909,0.5916,0.5973,0.5999,0.6015,0.6045,0.6058,0.6064,0.6093, 0.6146,0.6154,0.6231,0.6277,0.6280,0.6313,0.6342,0.6361,0.6426,0.6440, 0.6496,0.6546,0.6569,0.6612,0.6625,0.6644,0.6735,0.6846,0.6879,0.6885, 0.6906,0.6915,0.7036,0.7070,0.7121,0.7124,0.7137,0.7147,0.7155,0.7170, 0.7178,0.7309,0.7386,0.7421,0.7470,0.7480,0.7500,0.7598,0.7615,0.7655, 0.7662,0.7675,0.7733,0.7748,0.7766,0.7791,0.7817,0.7840,0.7860,0.7890, 0.7916,0.8000,0.8025,0.8051,0.8133,0.8172,0.8173,0.8234,0.8270,0.8312, 0.8319,0.8331,0.8339,0.8381,0.8420,0.8428,0.8434,0.8544,0.8702,0.8720, 0.8732,0.8744,0.8759,0.8780,0.8799,0.8827,0.8908,0.8926,0.9021,0.9021, 0.9027,0.9045,0.9073,0.9144,0.9257,0.9264,0.9328,0.9582,0.9597,0.9604, 0.9642,0.9714,0.9718,0.9719,0.9724,0.9766,0.9778,0.9783,0.9818, Overall p-value after applying KStest on 269 p-values = 0.576805 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.