RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-01-02_14:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.58 14.8334 0.392520 2 to 25 15.80 30.8935 0.979424 3 to 26 15.72 15.2157 0.420049 4 to 27 15.85 12.6818 0.242784 5 to 28 15.95 14.6462 0.379054 6 to 29 15.96 17.8430 0.601193 7 to 30 15.84 12.9024 0.257307 8 to 31 15.82 20.3291 0.742257 9 to 32 16.07 15.9139 0.470051 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.568372 Tough bday spacings test for dh-ranFile-2016-01-02_14:31: 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 7 35 75 88 97 92 58 22 14 7 5 (O-E)^2/E 0.5 0.1 0.0 1.0 0.0 2.5 0.7 2.0 0.1 0.0 0.2 Birthday Spacings: Sum(O-E)^2/E= 7.029, p= 0.277 RESULTS OF GCD FOR dh-ranFile-2016-01-02_14:31 Euclid's algorithm: p-value, steps to gcd: 0.644134 p-value, dist. of gcd's: 0.210191 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-01-02_14:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.560 0.976 0.176 0.911 0.298 0.200 0.458 0.891 Bits 8 to 15---> 0.249 0.108 0.630 0.313 0.856 0.432 0.411 0.241 Bits 16 to 23---> 0.702 0.411 0.371 0.628 0.046 0.229 0.960 0.721 Bits 24 to 31---> 0.337 0.771 0.751 0.063 0.205 0.505 0.290 0.582 KS test for the above 32 p values: 0.154 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-01-02_14:31, p-values for 5 runs: 0.3474, 0.2310, 0.4423, 0.2241, 0.4813 Rank test for binary matrices (31x31) for dh-ranFile-2016-01-02_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 209 211.4 0.028 0.028 r= 29 5172 5134.0 0.281 0.309 r= 30 22998 23103.0 0.478 0.786 r= 31 11621 11551.5 0.418 1.204 chi-square = 1.204 with df = 3; p-value = 0.248 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-01-02_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 210 211.4 0.010 0.010 r= 30 5077 5134.0 0.633 0.643 r= 31 23240 23103.0 0.812 1.454 r= 32 11473 11551.5 0.534 1.988 chi-square = 1.988 with df = 3; p-value = 0.425 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-01-02_14:31 b-rank test for bits 1 to 8, p=0.89186 b-rank test for bits 2 to 9, p=0.23103 b-rank test for bits 3 to 10, p=0.67475 b-rank test for bits 4 to 11, p=0.57873 b-rank test for bits 5 to 12, p=0.23950 b-rank test for bits 6 to 13, p=0.15164 b-rank test for bits 7 to 14, p=0.26695 b-rank test for bits 8 to 15, p=0.29771 b-rank test for bits 9 to 16, p=0.28865 b-rank test for bits 10 to 17, p=0.35616 b-rank test for bits 11 to 18, p=0.13543 b-rank test for bits 12 to 19, p=0.40277 b-rank test for bits 13 to 20, p=0.73234 b-rank test for bits 14 to 21, p=0.53747 b-rank test for bits 15 to 22, p=0.25752 b-rank test for bits 16 to 23, p=0.15766 b-rank test for bits 17 to 24, p=0.04741 b-rank test for bits 18 to 25, p=0.36791 b-rank test for bits 19 to 26, p=0.45058 b-rank test for bits 20 to 27, p=0.42165 b-rank test for bits 21 to 28, p=0.50250 b-rank test for bits 22 to 29, p=0.00048 b-rank test for bits 23 to 30, p=0.08199 b-rank test for bits 24 to 31, p=0.64172 b-rank test for bits 25 to 32, p=0.29429 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 = 0.017853 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-01-02_14:31 (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 141634 -0.64 0.260017 2 141967 0.13 0.553593 3 141862 -0.11 0.455973 4 141557 -0.82 0.205197 5 141012 -2.10 0.018016 6 142004 0.22 0.587528 7 141483 -1.00 0.159601 8 141672 -0.55 0.289615 9 141352 -1.30 0.096429 10 142068 0.37 0.644579 11 140810 -2.57 0.005107 12 141706 -0.48 0.317369 13 142580 1.57 0.941441 14 142258 0.81 0.792364 15 142107 0.46 0.677904 16 141788 -0.28 0.388404 17 142210 0.70 0.758816 18 142825 2.14 0.983799 19 142107 0.46 0.677904 20 141733 -0.41 0.340175 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-01-02_14:31 Bits used No. missing words z-score p-value 23 to 32 142444 1.8437 0.967386 22 to 31 141686 -0.7701 0.220619 21 to 30 142057 0.5092 0.694696 20 to 29 141957 0.1644 0.565284 19 to 28 141945 0.1230 0.548947 18 to 27 141794 -0.3977 0.345430 17 to 26 141591 -1.0977 0.136170 16 to 25 141677 -0.8011 0.211526 15 to 24 141616 -1.0115 0.155893 14 to 23 141671 -0.8218 0.205588 13 to 22 141881 -0.0977 0.461089 12 to 21 142105 0.6747 0.750075 11 to 20 142384 1.6368 0.949163 10 to 19 141786 -0.4253 0.335318 9 to 18 141492 -1.4391 0.075066 8 to 17 141868 -0.1425 0.443336 7 to 16 141765 -0.4977 0.309351 6 to 15 141992 0.2851 0.612204 5 to 14 142135 0.7782 0.781766 4 to 13 141887 -0.0770 0.469312 3 to 12 141550 -1.2391 0.107660 2 to 11 141969 0.2058 0.581510 1 to 10 141880 -0.1011 0.459721 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-01-02_14:31 Bits used No. missing words z-score p-value 28 to 32 141604 -1.0350 0.150331 27 to 31 141858 -0.1740 0.430933 26 to 30 141867 -0.1435 0.442951 25 to 29 142105 0.6633 0.746427 24 to 28 142225 1.0701 0.857706 23 to 27 141737 -0.5842 0.279553 22 to 26 141604 -1.0350 0.150331 21 to 25 142647 2.5006 0.993800 20 to 24 141353 -1.8859 0.029657 19 to 23 141641 -0.9096 0.181519 18 to 22 141506 -1.3672 0.085778 17 to 21 141900 -0.0316 0.487385 16 to 20 142302 1.3311 0.908419 15 to 19 141862 -0.1604 0.436267 14 to 18 141946 0.1243 0.549463 13 to 17 141422 -1.6520 0.049271 12 to 16 142420 1.7311 0.958282 11 to 15 141672 -0.8045 0.210552 10 to 14 141699 -0.7130 0.237928 9 to 13 141954 0.1514 0.560179 8 to 12 142057 0.5006 0.691665 7 to 11 141265 -2.1842 0.014475 6 to 10 141791 -0.4011 0.344166 5 to 9 142072 0.5514 0.709328 4 to 8 142002 0.3141 0.623291 3 to 7 142009 0.3379 0.632267 2 to 6 141732 -0.6011 0.273881 1 to 5 142178 0.9107 0.818785 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-01-02_14:31 Bits used No. missing words z-score p-value 31 to 32 142284 1.1052 0.865468 30 to 31 142218 0.9105 0.818729 29 to 30 142220 0.9164 0.820280 28 to 29 141995 0.2527 0.599755 27 to 28 141520 -1.1485 0.125388 26 to 27 142134 0.6627 0.746253 25 to 26 142372 1.3648 0.913843 24 to 25 141906 -0.0098 0.496081 23 to 24 142001 0.2704 0.606579 22 to 23 141784 -0.3697 0.355801 21 to 22 142031 0.3589 0.640168 20 to 21 141624 -0.8417 0.199983 19 to 20 142090 0.5329 0.702966 18 to 19 141808 -0.2989 0.382505 17 to 18 141738 -0.5054 0.306640 16 to 17 141998 0.2616 0.603171 15 to 16 141311 -1.7650 0.038783 14 to 15 142444 1.5772 0.942625 13 to 14 142336 1.2586 0.895915 12 to 13 142234 0.9577 0.830900 11 to 12 142345 1.2852 0.900632 10 to 11 142545 1.8751 0.969613 9 to 10 142264 1.0462 0.852271 8 to 9 142228 0.9400 0.826399 7 to 8 142074 0.4858 0.686429 6 to 7 141941 0.0934 0.537216 5 to 6 142420 1.5064 0.934018 4 to 5 142440 1.5654 0.941255 3 to 4 142012 0.3029 0.619002 2 to 3 141835 -0.2193 0.413223 1 to 2 142270 1.0639 0.856318 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-01-02_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2553.88 0.762 0.776974 Test results for specific bytes for dh-ranFile-2016-01-02_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2472.19 -0.393 0.347045 2 to 9 2584.02 1.188 0.882635 3 to 10 2508.05 0.114 0.545298 4 to 11 2651.91 2.148 0.984158 5 to 12 2482.10 -0.253 0.400060 6 to 13 2437.92 -0.878 0.189993 7 to 14 2576.60 1.083 0.860672 8 to 15 2455.78 -0.625 0.265859 9 to 16 2451.69 -0.683 0.247231 10 to 17 2469.60 -0.430 0.333636 11 to 18 2541.31 0.584 0.720441 12 to 19 2453.18 -0.662 0.253942 13 to 20 2367.63 -1.872 0.030602 14 to 21 2472.40 -0.390 0.348127 15 to 22 2458.15 -0.592 0.276995 16 to 23 2538.18 0.540 0.705401 17 to 24 2499.84 -0.002 0.499102 18 to 25 2328.64 -2.423 0.007689 19 to 26 2405.37 -1.338 0.090397 20 to 27 2454.14 -0.649 0.258305 21 to 28 2590.08 1.274 0.898665 22 to 29 2360.48 -1.973 0.024245 23 to 30 2762.98 3.719 0.999900 24 to 31 2589.70 1.269 0.897698 25 to 32 2527.27 0.386 0.650117 CDPARK for dh-ranFile-2016-01-02_14:31: 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 3503 -0.9132 0.180558 3470 -2.4201 0.007758 3511 -0.5479 0.291865 3499 -1.0959 0.136563 3550 1.2329 0.891189 3513 -0.4566 0.323972 3523 0.0000 0.500000 3548 1.1416 0.873180 3499 -1.0959 0.136563 3547 1.0959 0.863437 Square side=100, avg. no. parked=3516.30 sample std.=24.67 p-value of the KSTEST for those 10 p-values: 0.360730 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-01-02_14:31 0.8615,0.3503,0.0278,0.0432,0.1482,0.9323,0.9978,0.1706,0.7308,0.3097, The KS test for those 10 p-values: 0.270872 The 3DSPHERES test for dh-ranFile-2016-01-02_14:31 sample no r^3 equiv. uni. 1 18.698 0.463812 2 11.557 0.319710 3 41.872 0.752346 4 52.139 0.824122 5 6.651 0.198833 6 2.375 0.076104 7 10.575 0.297070 8 20.945 0.502501 9 88.273 0.947263 10 0.728 0.023982 11 18.554 0.461231 12 14.875 0.390934 13 8.072 0.235911 14 107.039 0.971786 15 2.485 0.079504 16 9.836 0.279540 17 5.955 0.180045 18 8.672 0.251026 19 17.906 0.449463 20 32.747 0.664306 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.318682 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-01-02_14:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -0.3 -0.8 -0.5 0.1 1.4 0.7 0.5 0.4 0.2 -0.1 -0.1 1.2 -0.7 -0.3 1.7 -0.1 -0.1 -0.1 -1.3 -0.7 0.3 -0.8 1.4 -1.2 0.0 0.5 -0.1 0.2 -0.8 0.2 0.8 -0.6 -0.8 0.1 -0.7 2.8 -0.7 -0.8 -0.7 0.1 -1.0 -1.1 Chi-square with 42 degrees of freedom:30.767431 z-score=-1.225574, p-value=0.100047 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-01-02_14:31 Test no p-value 1 0.000209 2 0.091715 3 0.293323 4 0.511977 5 0.371291 6 0.119682 7 0.114321 8 0.538448 9 0.542348 10 0.266996 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.018475 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-01-02_14:31: (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 66749 0.10 66644 0.01 3 25000.00 24999 0.00 25044 0.08 4 6666.67 6598 0.71 6686 0.06 5 1388.89 1376 0.12 1324 3.03 6 238.10 241 0.04 254 1.06 7 34.72 35 0.00 46 3.66 8 4.96 1 3.16 1 3.16 p=0.34064 p=0.91351 Number of rngs required: 687546, p-value: 0.160 RESULTS OF CRAPS TEST for dh-ranFile-2016-01-02_14:31 No. of wins: Observed Expected 99003 98585.9 z-score= 1.866, pvalue=0.96896 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66712 66666.7 0.031 0.031 2 37708 37654.3 0.077 0.107 3 27119 26954.7 1.001 1.108 4 19162 19313.5 1.188 2.296 5 13816 13851.4 0.091 2.387 6 9756 9943.5 3.537 5.924 7 7171 7145.0 0.094 6.018 8 5179 5139.1 0.310 6.329 9 3737 3699.9 0.373 6.701 10 2735 2666.3 1.770 8.472 11 1897 1923.3 0.360 8.832 12 1393 1388.7 0.013 8.845 13 993 1003.7 0.114 8.960 14 741 726.1 0.304 9.264 15 500 525.8 1.269 10.533 16 383 381.2 0.009 10.542 17 275 276.5 0.009 10.551 18 209 200.8 0.332 10.883 19 124 146.0 3.311 14.194 20 112 106.2 0.315 14.509 21 278 287.1 0.289 14.798 Chisq= 14.80 for 20 degrees of freedom, p= 0.21215 SUMMARY of craptest p-value for no. of wins: 0.968958 p-value for throws/game: 0.212153 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-01-02_14:31 No. of wins: Observed Expected 98684 98585.9 z-score= 0.439, pvalue=0.66965 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66887 66666.7 0.728 0.728 2 37691 37654.3 0.036 0.764 3 27083 26954.7 0.610 1.374 4 19024 19313.5 4.338 5.713 5 13965 13851.4 0.931 6.644 6 9729 9943.5 4.629 11.273 7 7172 7145.0 0.102 11.375 8 5138 5139.1 0.000 11.375 9 3640 3699.9 0.969 12.344 10 2595 2666.3 1.907 14.250 11 1974 1923.3 1.335 15.585 12 1373 1388.7 0.178 15.764 13 1034 1003.7 0.914 16.677 14 716 726.1 0.142 16.819 15 557 525.8 1.847 18.666 16 396 381.2 0.579 19.244 17 286 276.5 0.324 19.568 18 208 200.8 0.256 19.824 19 141 146.0 0.170 19.994 20 95 106.2 1.184 21.178 21 296 287.1 0.275 21.453 Chisq= 21.45 for 20 degrees of freedom, p= 0.62911 SUMMARY of craptest p-value for no. of wins: 0.669650 p-value for throws/game: 0.629113 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0002,0.0005,0.0051,0.0077,0.0078,0.0145,0.0179,0.0180,0.0185,0.0240, 0.0242,0.0278,0.0297,0.0306,0.0388,0.0432,0.0456,0.0474,0.0493,0.0629, 0.0751,0.0761,0.0795,0.0820,0.0858,0.0904,0.0917,0.0964,0.1000,0.1077, 0.1083,0.1143,0.1197,0.1254,0.1354,0.1362,0.1366,0.1366,0.1482,0.1503, 0.1503,0.1516,0.1542,0.1559,0.1577,0.1596,0.1604,0.1706,0.1761,0.1800, 0.1806,0.1815,0.1900,0.1988,0.1999,0.2000,0.2049,0.2052,0.2056,0.2102, 0.2106,0.2115,0.2122,0.2206,0.2241,0.2288,0.2310,0.2310,0.2359,0.2379, 0.2395,0.2406,0.2428,0.2472,0.2480,0.2487,0.2510,0.2539,0.2573,0.2575, 0.2583,0.2600,0.2659,0.2670,0.2670,0.2709,0.2739,0.2770,0.2773,0.2795, 0.2796,0.2887,0.2896,0.2901,0.2919,0.2933,0.2943,0.2971,0.2977,0.2984, 0.3066,0.3094,0.3097,0.3126,0.3174,0.3187,0.3197,0.3240,0.3336,0.3353, 0.3372,0.3402,0.3406,0.3442,0.3454,0.3470,0.3474,0.3481,0.3503,0.3558, 0.3562,0.3607,0.3679,0.3713,0.3713,0.3791,0.3825,0.3884,0.3909,0.3925, 0.4001,0.4028,0.4109,0.4110,0.4132,0.4200,0.4216,0.4251,0.4309,0.4317, 0.4363,0.4423,0.4430,0.4433,0.4495,0.4506,0.4560,0.4577,0.4597,0.4611, 0.4612,0.4638,0.4693,0.4701,0.4813,0.4874,0.4961,0.4991,0.5000,0.5025, 0.5025,0.5052,0.5120,0.5372,0.5375,0.5384,0.5423,0.5453,0.5489,0.5495, 0.5536,0.5599,0.5602,0.5653,0.5684,0.5787,0.5815,0.5823,0.5875,0.5998, 0.6012,0.6032,0.6066,0.6122,0.6190,0.6233,0.6277,0.6291,0.6302,0.6323, 0.6402,0.6417,0.6441,0.6446,0.6501,0.6643,0.6696,0.6748,0.6779,0.6779, 0.6864,0.6917,0.6947,0.7015,0.7030,0.7054,0.7093,0.7204,0.7206,0.7308, 0.7323,0.7423,0.7463,0.7464,0.7501,0.7509,0.7523,0.7588,0.7706,0.7770, 0.7818,0.7924,0.8187,0.8188,0.8203,0.8241,0.8264,0.8309,0.8523,0.8562, 0.8563,0.8577,0.8607,0.8615,0.8634,0.8655,0.8732,0.8826,0.8909,0.8912, 0.8919,0.8959,0.8977,0.8987,0.9006,0.9084,0.9107,0.9135,0.9138,0.9323, 0.9340,0.9413,0.9414,0.9426,0.9473,0.9492,0.9583,0.9598,0.9674,0.9690, 0.9696,0.9718,0.9760,0.9794,0.9838,0.9842,0.9938,0.9978,0.9999, Overall p-value after applying KStest on 269 p-values = 0.014528 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.