RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-01-10_20:31 (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 17.4000 0.572401 2 to 25 16.12 8.1739 0.037314 3 to 26 15.77 16.7273 0.527014 4 to 27 15.59 15.7904 0.461262 5 to 28 15.86 19.9340 0.722382 6 to 29 15.78 23.6478 0.870674 7 to 30 15.89 12.6309 0.239477 8 to 31 15.67 22.8057 0.844317 9 to 32 15.89 25.4413 0.914742 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.705970 Tough bday spacings test for dh-ranFile-2017-01-10_20:31: 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 41 71 108 104 76 45 28 17 1 3 (O-E)^2/E 1.1 0.5 0.1 1.1 0.4 0.1 1.0 0.1 0.3 4.8 0.3 Birthday Spacings: Sum(O-E)^2/E= 9.656, p= 0.529 RESULTS OF GCD FOR dh-ranFile-2017-01-10_20:31 Euclid's algorithm: p-value, steps to gcd: 0.006989 p-value, dist. of gcd's: 0.706194 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-01-10_20:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.734 0.350 0.043 0.150 0.353 0.964 0.266 0.973 Bits 8 to 15---> 0.714 0.353 0.151 0.176 0.965 0.111 0.023 0.302 Bits 16 to 23---> 0.232 0.693 0.345 0.296 0.908 0.473 0.228 0.987 Bits 24 to 31---> 0.571 0.313 0.627 0.733 0.232 0.826 0.184 0.286 KS test for the above 32 p values: 0.738 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-01-10_20:31, p-values for 5 runs: 0.4306, 0.2657, 0.7058, 0.7335, 0.5588 Rank test for binary matrices (31x31) for dh-ranFile-2017-01-10_20:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 210 211.4 0.010 0.010 r= 29 5127 5134.0 0.010 0.019 r= 30 23223 23103.0 0.623 0.642 r= 31 11440 11551.5 1.077 1.719 chi-square = 1.719 with df = 3; p-value = 0.367 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2017-01-10_20:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 216 211.4 0.099 0.099 r= 30 5126 5134.0 0.012 0.112 r= 31 23085 23103.0 0.014 0.126 r= 32 11573 11551.5 0.040 0.166 chi-square = 0.166 with df = 3; p-value = 0.017 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2017-01-10_20:31 b-rank test for bits 1 to 8, p=0.45900 b-rank test for bits 2 to 9, p=0.33767 b-rank test for bits 3 to 10, p=0.24032 b-rank test for bits 4 to 11, p=0.60870 b-rank test for bits 5 to 12, p=0.44009 b-rank test for bits 6 to 13, p=0.82200 b-rank test for bits 7 to 14, p=0.98400 b-rank test for bits 8 to 15, p=0.57094 b-rank test for bits 9 to 16, p=0.79425 b-rank test for bits 10 to 17, p=0.97789 b-rank test for bits 11 to 18, p=0.60222 b-rank test for bits 12 to 19, p=0.04087 b-rank test for bits 13 to 20, p=0.51266 b-rank test for bits 14 to 21, p=0.17605 b-rank test for bits 15 to 22, p=0.91287 b-rank test for bits 16 to 23, p=0.44057 b-rank test for bits 17 to 24, p=0.33102 b-rank test for bits 18 to 25, p=0.44725 b-rank test for bits 19 to 26, p=0.70756 b-rank test for bits 20 to 27, p=0.58507 b-rank test for bits 21 to 28, p=0.52666 b-rank test for bits 22 to 29, p=0.11939 b-rank test for bits 23 to 30, p=0.70110 b-rank test for bits 24 to 31, p=0.59748 b-rank test for bits 25 to 32, p=0.01184 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 = 0.757610 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-01-10_20:31 (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 141600 -0.72 0.234922 2 141855 -0.13 0.449494 3 142366 1.07 0.857011 4 141865 -0.10 0.458753 5 141798 -0.26 0.397387 6 141362 -1.28 0.100482 7 141692 -0.51 0.305804 8 141452 -1.07 0.142641 9 141495 -0.97 0.166507 10 141999 0.21 0.582975 11 141805 -0.24 0.403708 12 141461 -1.05 0.147435 13 141670 -0.56 0.288019 14 142849 2.20 0.985936 15 141274 -1.48 0.068849 16 141537 -0.87 0.192169 17 141590 -0.75 0.227804 18 141693 -0.51 0.306624 19 141360 -1.28 0.099662 20 141523 -0.90 0.183358 ---------------------------------------------------------------- OPSO test for dh-ranFile-2017-01-10_20:31 Bits used No. missing words z-score p-value 23 to 32 142176 0.9196 0.821097 22 to 31 142645 2.5368 0.994406 21 to 30 141847 -0.2149 0.414911 20 to 29 141740 -0.5839 0.279645 19 to 28 142017 0.3713 0.644784 18 to 27 142088 0.6161 0.731087 17 to 26 141631 -0.9598 0.168588 16 to 25 141502 -1.4046 0.080072 15 to 24 141801 -0.3736 0.354369 14 to 23 142134 0.7747 0.780749 13 to 22 142147 0.8196 0.793764 12 to 21 142072 0.5609 0.712578 11 to 20 142076 0.5747 0.717261 10 to 19 141543 -1.2632 0.103257 9 to 18 141977 0.2333 0.592253 8 to 17 141874 -0.1218 0.451518 7 to 16 142008 0.3402 0.633163 6 to 15 142200 1.0023 0.841903 5 to 14 142345 1.5023 0.933492 4 to 13 141567 -1.1804 0.118911 3 to 12 141630 -0.9632 0.167722 2 to 11 142251 1.1782 0.880636 1 to 10 142012 0.3540 0.638344 ----------------------------------------------------------------- OQSO test for dh-ranFile-2017-01-10_20:31 Bits used No. missing words z-score p-value 28 to 32 142277 1.2463 0.893680 27 to 31 142182 0.9243 0.822336 26 to 30 142020 0.3752 0.646227 25 to 29 142018 0.3684 0.643702 24 to 28 142131 0.7514 0.773801 23 to 27 141990 0.2735 0.607749 22 to 26 142147 0.8057 0.789781 21 to 25 141981 0.2429 0.595978 20 to 24 142142 0.7887 0.784860 19 to 23 142537 2.1277 0.983319 18 to 22 141759 -0.5096 0.305168 17 to 21 142317 1.3819 0.916504 16 to 20 142366 1.5480 0.939193 15 to 19 142231 1.0904 0.862233 14 to 18 142155 0.8328 0.797516 13 to 17 141595 -1.0655 0.143319 12 to 16 141624 -0.9672 0.166717 11 to 15 141816 -0.3164 0.375860 10 to 14 142619 2.4057 0.991928 9 to 13 141582 -1.1096 0.133587 8 to 12 141985 0.2565 0.601221 7 to 11 141595 -1.0655 0.143319 6 to 10 141717 -0.6520 0.257212 5 to 9 142494 1.9819 0.976257 4 to 8 141792 -0.3977 0.345415 3 to 7 142036 0.4294 0.666180 2 to 6 142347 1.4836 0.931046 1 to 5 142316 1.3785 0.915982 ----------------------------------------------------------------- DNA test for dh-ranFile-2017-01-10_20:31 Bits used No. missing words z-score p-value 31 to 32 141820 -0.2635 0.396079 30 to 31 142099 0.5595 0.712089 29 to 30 142486 1.7011 0.955537 28 to 29 141366 -1.6027 0.054496 27 to 28 142469 1.6509 0.950625 26 to 27 142392 1.4238 0.922749 25 to 26 141831 -0.2311 0.408633 24 to 25 141873 -0.1072 0.457328 23 to 24 141790 -0.3520 0.362417 22 to 23 141995 0.2527 0.599755 21 to 22 142460 1.6244 0.947854 20 to 21 142377 1.3796 0.916139 19 to 20 141720 -0.5585 0.288253 18 to 19 142228 0.9400 0.826399 17 to 18 141846 -0.1868 0.425903 16 to 17 141463 -1.3166 0.093985 15 to 16 142277 1.0846 0.860944 14 to 15 141480 -1.2665 0.102674 13 to 14 142404 1.4592 0.927745 12 to 13 142158 0.7335 0.768385 11 to 12 141787 -0.3609 0.359104 10 to 11 141625 -0.8387 0.200810 9 to 10 142252 1.0108 0.843950 8 to 9 141391 -1.5290 0.063133 7 to 8 142041 0.3884 0.651143 6 to 7 142096 0.5506 0.709063 5 to 6 141905 -0.0128 0.494905 4 to 5 141934 0.0728 0.529007 3 to 4 141878 -0.0924 0.463183 2 to 3 141922 0.0374 0.514907 1 to 2 141534 -1.1072 0.134111 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2017-01-10_20:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2549.84 0.705 0.759544 Test results for specific bytes for dh-ranFile-2017-01-10_20:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2488.79 -0.159 0.437020 2 to 9 2619.15 1.685 0.954016 3 to 10 2579.96 1.131 0.870917 4 to 11 2415.09 -1.201 0.114924 5 to 12 2542.80 0.605 0.727528 6 to 13 2597.17 1.374 0.915317 7 to 14 2650.67 2.131 0.983445 8 to 15 2690.65 2.696 0.996494 9 to 16 2568.63 0.971 0.834133 10 to 17 2459.82 -0.568 0.284919 11 to 18 2595.89 1.356 0.912470 12 to 19 2547.59 0.673 0.749530 13 to 20 2526.54 0.375 0.646278 14 to 21 2463.45 -0.517 0.302614 15 to 22 2541.86 0.592 0.723083 16 to 23 2530.27 0.428 0.665726 17 to 24 2383.43 -1.649 0.049624 18 to 25 2531.33 0.443 0.671159 19 to 26 2451.69 -0.683 0.247238 20 to 27 2587.70 1.240 0.892561 21 to 28 2380.66 -1.688 0.045731 22 to 29 2581.75 1.156 0.876193 23 to 30 2409.23 -1.284 0.099637 24 to 31 2533.71 0.477 0.683242 25 to 32 2503.24 0.046 0.518281 CDPARK for dh-ranFile-2017-01-10_20:31: 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 3512 -0.5023 0.307734 3505 -0.8219 0.205562 3510 -0.5936 0.276387 3507 -0.7306 0.232514 3507 -0.7306 0.232514 3512 -0.5023 0.307734 3513 -0.4566 0.323972 3530 0.3196 0.625377 3544 0.9589 0.831196 3525 0.0913 0.536383 Square side=100, avg. no. parked=3516.50 sample std.=11.91 p-value of the KSTEST for those 10 p-values: 0.134593 Results for the MINIMUM DISTANCE test for dh-ranFile-2017-01-10_20:31 0.5421,0.0660,0.7899,0.6422,0.5477,0.1398,0.8813,0.1572,0.3644,0.4985, The KS test for those 10 p-values: 0.917500 The 3DSPHERES test for dh-ranFile-2017-01-10_20:31 sample no r^3 equiv. uni. 1 52.176 0.824340 2 89.197 0.948862 3 59.253 0.861254 4 1.857 0.060024 5 42.802 0.759912 6 29.367 0.624278 7 58.481 0.857635 8 44.731 0.774862 9 17.673 0.445176 10 2.041 0.065763 11 16.608 0.425132 12 16.874 0.430200 13 41.913 0.752687 14 23.738 0.546722 15 15.667 0.406815 16 36.344 0.702236 17 36.970 0.708387 18 17.398 0.440069 19 23.936 0.549711 20 21.416 0.510261 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.175730 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-01-10_20:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 -0.3 0.6 0.3 1.6 0.8 0.0 0.4 -1.3 1.8 0.9 0.3 -1.5 -0.6 0.9 0.5 1.3 0.2 -1.0 -0.0 -1.1 -0.3 -0.7 0.0 -0.0 -0.1 1.4 -0.6 -0.1 -1.1 -1.5 0.4 0.1 1.3 -0.5 -0.8 -1.2 -0.1 0.5 1.0 0.1 1.0 0.8 Chi-square with 42 degrees of freedom:31.080420 z-score=-1.191424, p-value=0.107609 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2017-01-10_20:31 Test no p-value 1 0.026701 2 0.334159 3 0.428797 4 0.349352 5 0.095960 6 0.663536 7 0.082053 8 0.839647 9 0.244751 10 0.067611 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.056207 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-01-10_20:31: (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 66646 0.01 66726 0.05 3 25000.00 25002 0.00 24814 1.38 4 6666.67 6723 0.48 6720 0.43 5 1388.89 1367 0.35 1465 4.17 6 238.10 218 1.70 234 0.07 7 34.72 35 0.00 35 0.00 8 4.96 8 1.86 5 0.00 p=0.37582 p=0.58869 Number of rngs required: 690009, p-value: 0.971 RESULTS OF CRAPS TEST for dh-ranFile-2017-01-10_20:31 No. of wins: Observed Expected 98460 98585.9 z-score=-0.563, pvalue=0.28675 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66579 66666.7 0.115 0.115 2 37868 37654.3 1.213 1.328 3 26879 26954.7 0.213 1.541 4 19242 19313.5 0.264 1.805 5 13782 13851.4 0.348 2.153 6 9830 9943.5 1.297 3.449 7 7243 7145.0 1.343 4.793 8 5303 5139.1 5.229 10.022 9 3659 3699.9 0.451 10.473 10 2595 2666.3 1.907 12.380 11 1927 1923.3 0.007 12.387 12 1352 1388.7 0.972 13.359 13 979 1003.7 0.609 13.967 14 782 726.1 4.297 18.264 15 548 525.8 0.934 19.199 16 364 381.2 0.772 19.970 17 307 276.5 3.355 23.326 18 193 200.8 0.305 23.631 19 172 146.0 4.636 28.267 20 107 106.2 0.006 28.273 21 289 287.1 0.012 28.285 Chisq= 28.29 for 20 degrees of freedom, p= 0.89718 SUMMARY of craptest p-value for no. of wins: 0.286747 p-value for throws/game: 0.897183 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2017-01-10_20:31 No. of wins: Observed Expected 98778 98585.9 z-score= 0.859, pvalue=0.80493 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66790 66666.7 0.228 0.228 2 37581 37654.3 0.143 0.371 3 26769 26954.7 1.280 1.651 4 19405 19313.5 0.434 2.085 5 13810 13851.4 0.124 2.208 6 10020 9943.5 0.588 2.796 7 7156 7145.0 0.017 2.813 8 5126 5139.1 0.033 2.846 9 3716 3699.9 0.070 2.917 10 2593 2666.3 2.015 4.932 11 1957 1923.3 0.589 5.521 12 1419 1388.7 0.659 6.181 13 999 1003.7 0.022 6.203 14 755 726.1 1.147 7.350 15 522 525.8 0.028 7.378 16 371 381.2 0.270 7.648 17 283 276.5 0.151 7.799 18 207 200.8 0.190 7.988 19 145 146.0 0.007 7.995 20 93 106.2 1.644 9.639 21 283 287.1 0.059 9.698 Chisq= 9.70 for 20 degrees of freedom, p= 0.02668 SUMMARY of craptest p-value for no. of wins: 0.804931 p-value for throws/game: 0.026682 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0070,0.0118,0.0171,0.0231,0.0267,0.0267,0.0373,0.0409,0.0434,0.0457, 0.0496,0.0545,0.0562,0.0600,0.0631,0.0658,0.0660,0.0676,0.0688,0.0801, 0.0821,0.0940,0.0960,0.0996,0.0997,0.1005,0.1027,0.1033,0.1076,0.1113, 0.1149,0.1189,0.1194,0.1336,0.1341,0.1346,0.1398,0.1426,0.1433,0.1433, 0.1474,0.1503,0.1507,0.1572,0.1665,0.1667,0.1677,0.1686,0.1757,0.1760, 0.1761,0.1834,0.1837,0.1922,0.2008,0.2056,0.2276,0.2278,0.2319,0.2320, 0.2325,0.2325,0.2349,0.2395,0.2403,0.2448,0.2472,0.2572,0.2657,0.2663, 0.2764,0.2796,0.2849,0.2861,0.2867,0.2880,0.2883,0.2961,0.3022,0.3026, 0.3052,0.3058,0.3066,0.3077,0.3077,0.3125,0.3240,0.3310,0.3342,0.3377, 0.3447,0.3454,0.3494,0.3495,0.3526,0.3534,0.3544,0.3591,0.3624,0.3644, 0.3672,0.3758,0.3759,0.3961,0.3974,0.4037,0.4068,0.4086,0.4149,0.4251, 0.4259,0.4288,0.4302,0.4306,0.4370,0.4401,0.4401,0.4406,0.4452,0.4472, 0.4495,0.4515,0.4573,0.4588,0.4590,0.4613,0.4632,0.4731,0.4949,0.4985, 0.5103,0.5127,0.5149,0.5183,0.5267,0.5270,0.5288,0.5290,0.5364,0.5421, 0.5467,0.5477,0.5497,0.5588,0.5709,0.5710,0.5724,0.5830,0.5851,0.5887, 0.5923,0.5960,0.5975,0.5998,0.6012,0.6022,0.6077,0.6087,0.6243,0.6254, 0.6271,0.6332,0.6383,0.6422,0.6437,0.6448,0.6462,0.6463,0.6511,0.6635, 0.6657,0.6662,0.6712,0.6832,0.6927,0.7011,0.7022,0.7058,0.7060,0.7062, 0.7076,0.7084,0.7091,0.7121,0.7126,0.7142,0.7173,0.7224,0.7231,0.7275, 0.7311,0.7327,0.7335,0.7337,0.7377,0.7495,0.7527,0.7576,0.7595,0.7599, 0.7684,0.7738,0.7749,0.7807,0.7849,0.7898,0.7899,0.7938,0.7942,0.7975, 0.8049,0.8211,0.8220,0.8223,0.8243,0.8261,0.8264,0.8312,0.8341,0.8396, 0.8419,0.8440,0.8443,0.8570,0.8576,0.8609,0.8613,0.8622,0.8707,0.8709, 0.8762,0.8806,0.8813,0.8926,0.8937,0.8972,0.9078,0.9125,0.9129,0.9147, 0.9153,0.9160,0.9161,0.9165,0.9175,0.9227,0.9277,0.9310,0.9335,0.9392, 0.9479,0.9489,0.9506,0.9540,0.9555,0.9644,0.9655,0.9707,0.9732,0.9763, 0.9779,0.9833,0.9834,0.9840,0.9859,0.9874,0.9919,0.9944,0.9965, Overall p-value after applying KStest on 269 p-values = 0.635208 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.