RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-02-05_15:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 16.07 15.4670 0.438118 2 to 25 15.93 18.8314 0.661708 3 to 26 15.99 13.5501 0.301346 4 to 27 15.81 15.7427 0.457857 5 to 28 15.48 19.6547 0.707727 6 to 29 15.82 12.0418 0.202399 7 to 30 16.02 11.0649 0.146830 8 to 31 15.91 15.5490 0.444000 9 to 32 15.79 17.7698 0.596497 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.431226 Tough bday spacings test for dh-ranFile-2017-02-05_15:31: 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 8 31 79 91 105 83 52 29 13 7 2 (O-E)^2/E 0.1 0.9 0.4 0.5 0.5 0.3 0.0 0.0 0.2 0.0 1.0 Birthday Spacings: Sum(O-E)^2/E= 4.099, p= 0.057 RESULTS OF GCD FOR dh-ranFile-2017-02-05_15:31 Euclid's algorithm: p-value, steps to gcd: 0.347284 p-value, dist. of gcd's: 0.442599 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-02-05_15:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.251 0.578 0.641 0.926 0.264 0.142 0.938 0.469 Bits 8 to 15---> 0.925 0.261 0.506 0.586 0.357 0.613 0.145 0.148 Bits 16 to 23---> 0.242 0.933 0.494 0.178 0.225 0.674 0.828 0.908 Bits 24 to 31---> 0.431 0.426 0.444 0.290 0.904 0.933 0.449 0.594 KS test for the above 32 p values: 0.601 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-02-05_15:31, p-values for 5 runs: 0.4772, 0.7973, 0.2063, 0.5760, 0.4751 Rank test for binary matrices (31x31) for dh-ranFile-2017-02-05_15:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 191 211.4 1.972 1.972 r= 29 5206 5134.0 1.009 2.981 r= 30 23178 23103.0 0.243 3.225 r= 31 11425 11551.5 1.386 4.610 chi-square = 4.610 with df = 3; p-value = 0.797 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2017-02-05_15:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 198 211.4 0.852 0.852 r= 30 5154 5134.0 0.078 0.929 r= 31 23041 23103.0 0.167 1.096 r= 32 11607 11551.5 0.266 1.362 chi-square = 1.362 with df = 3; p-value = 0.286 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2017-02-05_15:31 b-rank test for bits 1 to 8, p=0.51873 b-rank test for bits 2 to 9, p=0.97698 b-rank test for bits 3 to 10, p=0.93765 b-rank test for bits 4 to 11, p=0.37987 b-rank test for bits 5 to 12, p=0.97106 b-rank test for bits 6 to 13, p=0.22793 b-rank test for bits 7 to 14, p=0.81032 b-rank test for bits 8 to 15, p=0.46052 b-rank test for bits 9 to 16, p=0.82648 b-rank test for bits 10 to 17, p=0.03424 b-rank test for bits 11 to 18, p=0.94308 b-rank test for bits 12 to 19, p=0.01416 b-rank test for bits 13 to 20, p=0.29015 b-rank test for bits 14 to 21, p=0.66347 b-rank test for bits 15 to 22, p=0.63520 b-rank test for bits 16 to 23, p=0.91095 b-rank test for bits 17 to 24, p=0.56487 b-rank test for bits 18 to 25, p=0.36804 b-rank test for bits 19 to 26, p=0.92249 b-rank test for bits 20 to 27, p=0.94086 b-rank test for bits 21 to 28, p=0.75924 b-rank test for bits 22 to 29, p=0.54554 b-rank test for bits 23 to 30, p=0.81608 b-rank test for bits 24 to 31, p=0.02771 b-rank test for bits 25 to 32, p=0.79393 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 = 0.036766 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-02-05_15:31 (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 141910 0.00 0.500625 2 141718 -0.45 0.327426 3 142417 1.19 0.882217 4 142106 0.46 0.677066 5 142242 0.78 0.781499 6 141544 -0.85 0.196670 7 141953 0.10 0.540635 8 141862 -0.11 0.455973 9 141331 -1.35 0.088310 10 142429 1.21 0.887661 11 141935 0.06 0.523913 12 142478 1.33 0.908021 13 142029 0.28 0.610109 14 141928 0.04 0.517397 15 140908 -2.34 0.009653 16 141999 0.21 0.582975 17 141972 0.15 0.558207 18 141863 -0.11 0.456900 19 141859 -0.12 0.453195 20 142086 0.41 0.660116 ---------------------------------------------------------------- OPSO test for dh-ranFile-2017-02-05_15:31 Bits used No. missing words z-score p-value 23 to 32 141730 -0.6184 0.268163 22 to 31 141530 -1.3080 0.095431 21 to 30 142088 0.6161 0.731087 20 to 29 141812 -0.3356 0.368579 19 to 28 141971 0.2127 0.584202 18 to 27 141731 -0.6149 0.269300 17 to 26 141757 -0.5253 0.299696 16 to 25 142012 0.3540 0.638344 15 to 24 141674 -0.8115 0.208544 14 to 23 142136 0.7816 0.782781 13 to 22 142060 0.5196 0.698312 12 to 21 141831 -0.2701 0.393540 11 to 20 141899 -0.0356 0.485792 10 to 19 141877 -0.1115 0.455617 9 to 18 142065 0.5368 0.704295 8 to 17 142307 1.3713 0.914856 7 to 16 142334 1.4644 0.928455 6 to 15 141863 -0.1598 0.436536 5 to 14 141893 -0.0563 0.477547 4 to 13 142147 0.8196 0.793764 3 to 12 142028 0.4092 0.658806 2 to 11 141490 -1.4460 0.074093 1 to 10 141919 0.0333 0.513300 ----------------------------------------------------------------- OQSO test for dh-ranFile-2017-02-05_15:31 Bits used No. missing words z-score p-value 28 to 32 141992 0.2802 0.610352 27 to 31 142141 0.7853 0.783868 26 to 30 141899 -0.0350 0.486033 25 to 29 141639 -0.9164 0.179736 24 to 28 141989 0.2701 0.606446 23 to 27 141976 0.2260 0.589399 22 to 26 141705 -0.6926 0.244267 21 to 25 141616 -0.9943 0.160029 20 to 24 141796 -0.3842 0.350426 19 to 23 141723 -0.6316 0.263815 18 to 22 141567 -1.1604 0.122935 17 to 21 141905 -0.0147 0.494145 16 to 20 141585 -1.0994 0.135792 15 to 19 142195 0.9684 0.833571 14 to 18 142445 1.8158 0.965302 13 to 17 141440 -1.5909 0.055811 12 to 16 141718 -0.6486 0.258306 11 to 15 142451 1.8362 0.966834 10 to 14 141742 -0.5672 0.285282 9 to 13 141823 -0.2926 0.384897 8 to 12 141837 -0.2452 0.403156 7 to 11 142010 0.3413 0.633544 6 to 10 142123 0.7243 0.765561 5 to 9 141481 -1.4520 0.073256 4 to 8 141616 -0.9943 0.160029 3 to 7 142009 0.3379 0.632267 2 to 6 141926 0.0565 0.522532 1 to 5 141442 -1.5842 0.056578 ----------------------------------------------------------------- DNA test for dh-ranFile-2017-02-05_15:31 Bits used No. missing words z-score p-value 31 to 32 141633 -0.8151 0.207498 30 to 31 141383 -1.5526 0.060260 29 to 30 142563 1.9282 0.973087 28 to 29 142207 0.8781 0.810051 27 to 28 141888 -0.0629 0.474915 26 to 27 141922 0.0374 0.514907 25 to 26 141471 -1.2930 0.098004 24 to 25 141938 0.0846 0.533699 23 to 24 142371 1.3619 0.913379 22 to 23 142052 0.4209 0.663070 21 to 22 142078 0.4976 0.690600 20 to 21 141305 -1.7827 0.037319 19 to 20 141898 -0.0334 0.486669 18 to 19 142076 0.4917 0.688517 17 to 18 142134 0.6627 0.746253 16 to 17 141892 -0.0511 0.479615 15 to 16 141978 0.2026 0.580263 14 to 15 141845 -0.1898 0.424747 13 to 14 141549 -1.0629 0.143909 12 to 13 141471 -1.2930 0.098004 11 to 12 142345 1.2852 0.900632 10 to 11 141840 -0.2045 0.418976 9 to 10 141643 -0.7856 0.216041 8 to 9 142394 1.4297 0.923599 7 to 8 141823 -0.2547 0.399493 6 to 7 142234 0.9577 0.830900 5 to 6 141752 -0.4641 0.321288 4 to 5 141881 -0.0836 0.466699 3 to 4 141639 -0.7974 0.212600 2 to 3 141846 -0.1868 0.425903 1 to 2 141636 -0.8063 0.210040 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2017-02-05_15:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2390.70 -1.546 0.061086 Test results for specific bytes for dh-ranFile-2017-02-05_15:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2489.94 -0.142 0.443414 2 to 9 2445.35 -0.773 0.219820 3 to 10 2398.77 -1.432 0.076121 4 to 11 2493.02 -0.099 0.460664 5 to 12 2402.49 -1.379 0.083941 6 to 13 2468.90 -0.440 0.330044 7 to 14 2547.25 0.668 0.747993 8 to 15 2489.41 -0.150 0.440459 9 to 16 2402.58 -1.378 0.084142 10 to 17 2472.65 -0.387 0.349483 11 to 18 2433.65 -0.938 0.174043 12 to 19 2549.99 0.707 0.760195 13 to 20 2408.19 -1.298 0.097077 14 to 21 2653.33 2.168 0.984938 15 to 22 2507.59 0.107 0.542723 16 to 23 2467.07 -0.466 0.320729 17 to 24 2538.97 0.551 0.709206 18 to 25 2390.77 -1.545 0.061195 19 to 26 2523.96 0.339 0.632646 20 to 27 2508.29 0.117 0.546643 21 to 28 2619.46 1.689 0.954427 22 to 29 2628.29 1.814 0.965187 23 to 30 2601.60 1.437 0.924628 24 to 31 2457.10 -0.607 0.272038 25 to 32 2427.83 -1.021 0.153697 CDPARK for dh-ranFile-2017-02-05_15:31: 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 3518 -0.2283 0.409702 3544 0.9589 0.831196 3550 1.2329 0.891189 3502 -0.9589 0.168804 3484 -1.7808 0.037471 3519 -0.1826 0.427537 3548 1.1416 0.873180 3527 0.1826 0.572463 3517 -0.2740 0.392053 3554 1.4155 0.921543 Square side=100, avg. no. parked=3526.30 sample std.=21.68 p-value of the KSTEST for those 10 p-values: 0.723556 Results for the MINIMUM DISTANCE test for dh-ranFile-2017-02-05_15:31 0.3711,0.3379,0.1372,0.8078,0.8845,0.8589,0.6289,0.4945,0.1896,0.2613, The KS test for those 10 p-values: 0.949921 The 3DSPHERES test for dh-ranFile-2017-02-05_15:31 sample no r^3 equiv. uni. 1 22.734 0.531298 2 49.431 0.807506 3 33.021 0.667361 4 6.198 0.186654 5 2.170 0.069790 6 9.432 0.269776 7 48.235 0.799678 8 26.944 0.592666 9 9.507 0.271600 10 10.178 0.287711 11 15.905 0.411492 12 3.599 0.113045 13 42.923 0.760873 14 3.553 0.111690 15 38.710 0.724826 16 68.746 0.898888 17 4.731 0.145885 18 16.563 0.424262 19 9.743 0.277298 20 17.589 0.443612 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.523679 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-02-05_15:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 2.2 -0.8 -1.0 -2.7 -0.2 -2.2 0.5 -0.3 -1.6 -0.7 -1.3 0.6 -1.8 0.3 0.1 -1.8 -0.4 1.0 0.5 3.1 0.4 0.8 0.7 -0.5 -0.7 0.4 0.2 0.6 1.4 1.2 -0.7 0.3 -1.4 0.6 1.1 -0.5 0.5 1.7 0.4 0.9 1.0 -0.1 Chi-square with 42 degrees of freedom:57.611086 z-score=1.703309, p-value=0.945155 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2017-02-05_15:31 Test no p-value 1 0.001654 2 0.667913 3 0.466298 4 0.013656 5 0.340670 6 0.413299 7 0.606567 8 0.660290 9 0.137827 10 0.663797 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.150934 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-02-05_15:31: (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 66613 0.04 66664 0.00 3 25000.00 25123 0.61 24938 0.15 4 6666.67 6634 0.16 6713 0.32 5 1388.89 1382 0.03 1404 0.16 6 238.10 208 3.80 243 0.10 7 34.72 36 0.05 32 0.21 8 4.96 3 0.77 5 0.00 p=0.51471 p=0.01273 Number of rngs required: 687707, p-value: 0.211 RESULTS OF CRAPS TEST for dh-ranFile-2017-02-05_15:31 No. of wins: Observed Expected 98759 98585.9 z-score= 0.774, pvalue=0.78065 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66318 66666.7 1.824 1.824 2 37862 37654.3 1.145 2.969 3 27134 26954.7 1.192 4.161 4 19265 19313.5 0.122 4.283 5 13985 13851.4 1.288 5.571 6 9802 9943.5 2.015 7.586 7 7109 7145.0 0.182 7.767 8 5197 5139.1 0.653 8.420 9 3643 3699.9 0.874 9.294 10 2713 2666.3 0.818 10.112 11 1947 1923.3 0.291 10.404 12 1351 1388.7 1.026 11.429 13 1036 1003.7 1.038 12.468 14 672 726.1 4.037 16.505 15 543 525.8 0.560 17.065 16 399 381.2 0.836 17.901 17 253 276.5 2.004 19.904 18 213 200.8 0.737 20.642 19 152 146.0 0.248 20.890 20 102 106.2 0.167 21.057 21 304 287.1 0.993 22.050 Chisq= 22.05 for 20 degrees of freedom, p= 0.66221 SUMMARY of craptest p-value for no. of wins: 0.780650 p-value for throws/game: 0.662209 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2017-02-05_15:31 No. of wins: Observed Expected 98798 98585.9 z-score= 0.949, pvalue=0.82864 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66808 66666.7 0.300 0.300 2 38010 37654.3 3.360 3.659 3 26718 26954.7 2.079 5.738 4 19240 19313.5 0.279 6.018 5 13829 13851.4 0.036 6.054 6 9855 9943.5 0.788 6.843 7 7177 7145.0 0.143 6.986 8 5162 5139.1 0.102 7.088 9 3771 3699.9 1.368 8.456 10 2682 2666.3 0.092 8.548 11 1869 1923.3 1.535 10.083 12 1333 1388.7 2.237 12.320 13 1002 1003.7 0.003 12.323 14 687 726.1 2.110 14.433 15 517 525.8 0.148 14.581 16 365 381.2 0.684 15.266 17 280 276.5 0.043 15.309 18 198 200.8 0.040 15.349 19 133 146.0 1.155 16.504 20 100 106.2 0.364 16.867 21 264 287.1 1.861 18.728 Chisq= 18.73 for 20 degrees of freedom, p= 0.46044 SUMMARY of craptest p-value for no. of wins: 0.828644 p-value for throws/game: 0.460444 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0017,0.0097,0.0127,0.0137,0.0142,0.0277,0.0342,0.0368,0.0373,0.0375, 0.0558,0.0566,0.0572,0.0603,0.0611,0.0612,0.0698,0.0733,0.0741,0.0761, 0.0839,0.0841,0.0883,0.0954,0.0971,0.0980,0.0980,0.1117,0.1130,0.1229, 0.1358,0.1372,0.1378,0.1425,0.1439,0.1450,0.1459,0.1468,0.1477,0.1509, 0.1537,0.1600,0.1600,0.1688,0.1740,0.1784,0.1797,0.1867,0.1896,0.1967, 0.2024,0.2063,0.2075,0.2085,0.2100,0.2106,0.2126,0.2160,0.2198,0.2245, 0.2279,0.2425,0.2443,0.2514,0.2583,0.2613,0.2614,0.2638,0.2638,0.2682, 0.2693,0.2698,0.2716,0.2720,0.2773,0.2853,0.2856,0.2877,0.2901,0.2905, 0.2997,0.3013,0.3207,0.3213,0.3274,0.3300,0.3379,0.3407,0.3473,0.3495, 0.3504,0.3570,0.3680,0.3686,0.3711,0.3799,0.3849,0.3921,0.3935,0.3995, 0.4032,0.4097,0.4115,0.4133,0.4190,0.4243,0.4247,0.4256,0.4259,0.4275, 0.4311,0.4312,0.4365,0.4381,0.4405,0.4426,0.4434,0.4436,0.4437,0.4440, 0.4494,0.4532,0.4556,0.4560,0.4569,0.4579,0.4604,0.4605,0.4607,0.4663, 0.4667,0.4685,0.4749,0.4751,0.4772,0.4775,0.4796,0.4858,0.4860,0.4867, 0.4941,0.4942,0.4945,0.5006,0.5058,0.5133,0.5147,0.5149,0.5174,0.5187, 0.5225,0.5237,0.5239,0.5313,0.5337,0.5406,0.5427,0.5455,0.5466,0.5582, 0.5649,0.5725,0.5760,0.5784,0.5803,0.5830,0.5842,0.5864,0.5894,0.5927, 0.5940,0.5965,0.6010,0.6064,0.6066,0.6101,0.6104,0.6131,0.6289,0.6323, 0.6326,0.6335,0.6352,0.6383,0.6410,0.6588,0.6601,0.6603,0.6617,0.6622, 0.6631,0.6635,0.6638,0.6674,0.6679,0.6745,0.6771,0.6885,0.6906,0.6983, 0.7043,0.7077,0.7092,0.7236,0.7248,0.7311,0.7463,0.7480,0.7592,0.7602, 0.7609,0.7656,0.7806,0.7815,0.7828,0.7839,0.7938,0.7939,0.7973,0.7973, 0.7997,0.8075,0.8078,0.8101,0.8103,0.8161,0.8265,0.8279,0.8286,0.8309, 0.8312,0.8336,0.8589,0.8732,0.8822,0.8845,0.8877,0.8912,0.8989,0.9006, 0.9039,0.9076,0.9080,0.9110,0.9134,0.9149,0.9215,0.9225,0.9236,0.9246, 0.9247,0.9263,0.9285,0.9325,0.9331,0.9377,0.9382,0.9409,0.9431,0.9452, 0.9499,0.9544,0.9652,0.9653,0.9668,0.9711,0.9731,0.9770,0.9849, Overall p-value after applying KStest on 269 p-values = 0.452564 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.