RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-02-21_11:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.68 19.4703 0.697787 2 to 25 15.50 19.0511 0.674393 3 to 26 15.85 22.0689 0.817916 4 to 27 15.88 10.7949 0.132974 5 to 28 15.87 14.6826 0.381666 6 to 29 15.88 18.5836 0.647051 7 to 30 15.53 19.5871 0.704110 8 to 31 15.78 23.2695 0.859321 9 to 32 15.90 23.8521 0.876491 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.154830 Tough bday spacings test for dh-ranFile-2016-02-21_11:31: 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 5 29 59 104 109 90 53 25 12 6 8 (O-E)^2/E 1.9 1.6 2.8 0.4 1.3 1.8 0.0 0.8 0.6 0.1 3.8 Birthday Spacings: Sum(O-E)^2/E= 14.974, p= 0.867 RESULTS OF GCD FOR dh-ranFile-2016-02-21_11:31 Euclid's algorithm: p-value, steps to gcd: 0.251491 p-value, dist. of gcd's: 0.529486 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-02-21_11:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.703 0.527 0.801 0.808 0.249 0.121 0.804 0.332 Bits 8 to 15---> 0.366 0.479 0.018 0.800 0.071 0.336 0.039 0.961 Bits 16 to 23---> 0.714 0.787 0.463 0.871 0.544 0.586 0.447 0.919 Bits 24 to 31---> 0.673 0.186 0.101 0.277 0.748 0.331 0.855 0.560 KS test for the above 32 p values: 0.057 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-02-21_11:31, p-values for 5 runs: 0.1559, 0.8046, 0.6264, 0.6993, 0.4542 Rank test for binary matrices (31x31) for dh-ranFile-2016-02-21_11:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 225 211.4 0.873 0.873 r= 29 5138 5134.0 0.003 0.876 r= 30 23061 23103.0 0.077 0.952 r= 31 11576 11551.5 0.052 1.004 chi-square = 1.004 with df = 3; p-value = 0.200 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-02-21_11:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 212 211.4 0.002 0.002 r= 30 5120 5134.0 0.038 0.040 r= 31 23106 23103.0 0.000 0.040 r= 32 11562 11551.5 0.010 0.050 chi-square = 0.050 with df = 3; p-value = 0.003 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-02-21_11:31 b-rank test for bits 1 to 8, p=0.68181 b-rank test for bits 2 to 9, p=0.05860 b-rank test for bits 3 to 10, p=0.54526 b-rank test for bits 4 to 11, p=0.09333 b-rank test for bits 5 to 12, p=0.78033 b-rank test for bits 6 to 13, p=0.16608 b-rank test for bits 7 to 14, p=0.78777 b-rank test for bits 8 to 15, p=0.19771 b-rank test for bits 9 to 16, p=0.93891 b-rank test for bits 10 to 17, p=0.68783 b-rank test for bits 11 to 18, p=0.19647 b-rank test for bits 12 to 19, p=0.10782 b-rank test for bits 13 to 20, p=0.00709 b-rank test for bits 14 to 21, p=0.24345 b-rank test for bits 15 to 22, p=0.94896 b-rank test for bits 16 to 23, p=0.98926 b-rank test for bits 17 to 24, p=0.31155 b-rank test for bits 18 to 25, p=0.65253 b-rank test for bits 19 to 26, p=0.50939 b-rank test for bits 20 to 27, p=0.97735 b-rank test for bits 21 to 28, p=0.62874 b-rank test for bits 22 to 29, p=0.35763 b-rank test for bits 23 to 30, p=0.87750 b-rank test for bits 24 to 31, p=0.51649 b-rank test for bits 25 to 32, p=0.48755 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 = 0.880481 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-02-21_11:31 (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 142129 0.51 0.696111 2 141769 -0.33 0.371504 3 141217 -1.62 0.052875 4 141807 -0.24 0.405518 5 142009 0.23 0.592070 6 141587 -0.75 0.225693 7 141998 0.21 0.582063 8 142234 0.76 0.775947 9 141997 0.20 0.581150 10 141321 -1.37 0.084627 11 141285 -1.46 0.072322 12 142314 0.95 0.827796 13 141932 0.05 0.521121 14 141579 -0.77 0.220117 15 141815 -0.22 0.412781 16 141788 -0.28 0.388404 17 142072 0.38 0.648053 18 141880 -0.07 0.472683 19 141702 -0.48 0.314045 20 141300 -1.42 0.077271 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-02-21_11:31 Bits used No. missing words z-score p-value 23 to 32 141501 -1.4080 0.079560 22 to 31 141652 -0.8873 0.187447 21 to 30 141004 -3.1218 0.000899 20 to 29 141694 -0.7425 0.228887 19 to 28 142476 1.9540 0.974651 18 to 27 141864 -0.1563 0.437894 17 to 26 142084 0.6023 0.726516 16 to 25 141950 0.1402 0.555765 15 to 24 142215 1.0540 0.854066 14 to 23 142149 0.8264 0.795725 13 to 22 142223 1.0816 0.860289 12 to 21 142193 0.9782 0.836006 11 to 20 141836 -0.2529 0.400187 10 to 19 142382 1.6299 0.948438 9 to 18 141927 0.0609 0.524293 8 to 17 141724 -0.6391 0.261389 7 to 16 142328 1.4437 0.925587 6 to 15 141890 -0.0667 0.473428 5 to 14 141499 -1.4149 0.078544 4 to 13 142493 2.0127 0.977925 3 to 12 141785 -0.4287 0.334062 2 to 11 141940 0.1058 0.542113 1 to 10 142227 1.0954 0.863332 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-02-21_11:31 Bits used No. missing words z-score p-value 28 to 32 142216 1.0396 0.850728 27 to 31 142000 0.3074 0.620714 26 to 30 142127 0.7379 0.769702 25 to 29 141455 -1.5401 0.061768 24 to 28 141861 -0.1638 0.434932 23 to 27 142236 1.1074 0.865930 22 to 26 141527 -1.2960 0.097482 21 to 25 141610 -1.0147 0.155130 20 to 24 141952 0.1446 0.557504 19 to 23 142003 0.3175 0.624578 18 to 22 142167 0.8735 0.808793 17 to 21 142041 0.4463 0.672324 16 to 20 141426 -1.6384 0.050668 15 to 19 141747 -0.5503 0.291067 14 to 18 141716 -0.6554 0.256119 13 to 17 141888 -0.0723 0.471180 12 to 16 142389 1.6260 0.948025 11 to 15 141798 -0.3774 0.352942 10 to 14 142350 1.4938 0.932386 9 to 13 141875 -0.1164 0.453679 8 to 12 141746 -0.5537 0.289905 7 to 11 141957 0.1616 0.564187 6 to 10 141416 -1.6723 0.047232 5 to 9 141446 -1.5706 0.058137 4 to 8 142311 1.3616 0.913337 3 to 7 141949 0.1345 0.553486 2 to 6 141355 -1.8791 0.030116 1 to 5 142131 0.7514 0.773801 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-02-21_11:31 Bits used No. missing words z-score p-value 31 to 32 141660 -0.7355 0.231022 30 to 31 142075 0.4887 0.687474 29 to 30 141366 -1.6027 0.054496 28 to 29 141946 0.1082 0.543070 27 to 28 141898 -0.0334 0.486669 26 to 27 141740 -0.4995 0.308714 25 to 26 141948 0.1141 0.545409 24 to 25 141575 -0.9862 0.162012 23 to 24 142073 0.4828 0.685382 22 to 23 141746 -0.4818 0.314974 21 to 22 141677 -0.6853 0.246565 20 to 21 141887 -0.0659 0.473741 19 to 20 141738 -0.5054 0.306640 18 to 19 141760 -0.4405 0.329787 17 to 18 141782 -0.3756 0.353605 16 to 17 141949 0.1170 0.546578 15 to 16 141740 -0.4995 0.308714 14 to 15 142088 0.5271 0.700921 13 to 14 142212 0.8928 0.814026 12 to 13 142062 0.4504 0.673772 11 to 12 141813 -0.2842 0.388144 10 to 11 142018 0.3206 0.625728 9 to 10 142305 1.1672 0.878429 8 to 9 141683 -0.6676 0.252182 7 to 8 143159 3.6863 0.999886 6 to 7 141683 -0.6676 0.252182 5 to 6 141861 -0.1426 0.443316 4 to 5 141951 0.1229 0.548915 3 to 4 142375 1.3737 0.915226 2 to 3 142027 0.3471 0.635745 1 to 2 141945 0.1052 0.541900 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-02-21_11:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2499.57 -0.006 0.497566 Test results for specific bytes for dh-ranFile-2016-02-21_11:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2449.07 -0.720 0.235671 2 to 9 2593.39 1.321 0.906703 3 to 10 2438.86 -0.865 0.193605 4 to 11 2355.75 -2.040 0.020675 5 to 12 2498.87 -0.016 0.493605 6 to 13 2439.07 -0.862 0.194413 7 to 14 2487.99 -0.170 0.432593 8 to 15 2455.60 -0.628 0.265042 9 to 16 2556.43 0.798 0.787589 10 to 17 2459.31 -0.575 0.282508 11 to 18 2455.77 -0.625 0.265832 12 to 19 2526.74 0.378 0.647351 13 to 20 2514.97 0.212 0.583847 14 to 21 2415.54 -1.194 0.116151 15 to 22 2565.82 0.931 0.824016 16 to 23 2511.84 0.167 0.566486 17 to 24 2431.22 -0.973 0.165350 18 to 25 2542.58 0.602 0.726493 19 to 26 2542.16 0.596 0.724508 20 to 27 2508.49 0.120 0.547785 21 to 28 2457.28 -0.604 0.272892 22 to 29 2489.84 -0.144 0.442889 23 to 30 2441.17 -0.832 0.202717 24 to 31 2472.82 -0.384 0.350358 25 to 32 2520.67 0.292 0.614963 CDPARK for dh-ranFile-2016-02-21_11:31: 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 3502 -0.9589 0.168804 3518 -0.2283 0.409702 3499 -1.0959 0.136563 3522 -0.0457 0.481790 3557 1.5525 0.939730 3524 0.0457 0.518210 3520 -0.1370 0.445521 3503 -0.9132 0.180558 3501 -1.0046 0.157553 3511 -0.5479 0.291865 Square side=100, avg. no. parked=3515.70 sample std.=16.44 p-value of the KSTEST for those 10 p-values: 0.172742 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-02-21_11:31 0.0133,0.4587,0.4672,0.3902,0.8686,0.8238,0.7418,0.8803,0.9951,0.6507, The KS test for those 10 p-values: 0.196234 The 3DSPHERES test for dh-ranFile-2016-02-21_11:31 sample no r^3 equiv. uni. 1 22.629 0.529664 2 6.737 0.201148 3 20.317 0.491977 4 49.911 0.810565 5 17.681 0.445316 6 58.038 0.855516 7 3.993 0.124637 8 49.003 0.804739 9 33.707 0.674879 10 0.917 0.030107 11 44.428 0.772576 12 78.853 0.927808 13 4.480 0.138707 14 8.320 0.242198 15 29.227 0.622519 16 12.358 0.337636 17 84.106 0.939405 18 44.655 0.774286 19 22.446 0.526782 20 1.681 0.054497 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.973653 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-02-21_11:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -1.2 1.1 -0.5 -1.4 -0.8 -0.1 -0.1 0.2 0.0 0.4 0.5 -0.0 -0.0 -0.3 -1.6 -0.6 -0.4 1.3 -0.3 -1.0 0.1 2.0 1.3 0.2 0.2 -0.1 0.2 -0.2 -0.7 0.9 0.0 -0.4 -1.3 0.1 1.1 0.3 -0.1 0.1 0.4 2.4 0.0 0.8 Chi-square with 42 degrees of freedom:29.267924 z-score=-1.389183, p-value=0.068592 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-02-21_11:31 Test no p-value 1 0.297205 2 0.982863 3 0.010096 4 0.459093 5 0.918465 6 0.128991 7 0.143413 8 0.677603 9 0.914543 10 0.392063 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.613723 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-02-21_11:31: (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 66671 0.00 66552 0.20 3 25000.00 24949 0.10 25095 0.36 4 6666.67 6718 0.40 6748 0.99 5 1388.89 1399 0.07 1344 1.45 6 238.10 219 1.53 219 1.53 7 34.72 38 0.31 32 0.21 8 4.96 5 0.00 9 3.29 p=0.12212 p=0.76456 Number of rngs required: 688191, p-value: 0.404 RESULTS OF CRAPS TEST for dh-ranFile-2016-02-21_11:31 No. of wins: Observed Expected 98429 98585.9 z-score=-0.702, pvalue=0.24148 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66766 66666.7 0.148 0.148 2 37735 37654.3 0.173 0.321 3 27000 26954.7 0.076 0.397 4 19228 19313.5 0.378 0.775 5 14027 13851.4 2.226 3.001 6 9758 9943.5 3.462 6.463 7 7152 7145.0 0.007 6.470 8 5146 5139.1 0.009 6.479 9 3754 3699.9 0.792 7.271 10 2645 2666.3 0.170 7.441 11 1787 1923.3 9.663 17.104 12 1348 1388.7 1.195 18.300 13 1062 1003.7 3.385 21.684 14 740 726.1 0.265 21.949 15 506 525.8 0.748 22.697 16 377 381.2 0.045 22.742 17 258 276.5 1.243 23.985 18 179 200.8 2.373 26.358 19 138 146.0 0.437 26.795 20 113 106.2 0.433 27.228 21 281 287.1 0.130 27.358 Chisq= 27.36 for 20 degrees of freedom, p= 0.87452 SUMMARY of craptest p-value for no. of wins: 0.241476 p-value for throws/game: 0.874518 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-02-21_11:31 No. of wins: Observed Expected 98567 98585.9 z-score=-0.084, pvalue=0.46639 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66478 66666.7 0.534 0.534 2 37832 37654.3 0.838 1.372 3 27024 26954.7 0.178 1.550 4 19202 19313.5 0.643 2.194 5 13903 13851.4 0.192 2.386 6 9943 9943.5 0.000 2.386 7 7206 7145.0 0.520 2.906 8 5059 5139.1 1.248 4.154 9 3695 3699.9 0.006 4.160 10 2713 2666.3 0.818 4.978 11 1880 1923.3 0.976 5.954 12 1426 1388.7 1.000 6.954 13 1020 1003.7 0.264 7.218 14 733 726.1 0.065 7.283 15 481 525.8 3.823 11.106 16 368 381.2 0.454 11.560 17 258 276.5 1.243 12.803 18 197 200.8 0.073 12.876 19 139 146.0 0.334 13.210 20 117 106.2 1.095 14.305 21 326 287.1 5.267 19.571 Chisq= 19.57 for 20 degrees of freedom, p= 0.51499 SUMMARY of craptest p-value for no. of wins: 0.466390 p-value for throws/game: 0.514988 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0009,0.0029,0.0071,0.0101,0.0133,0.0180,0.0207,0.0301,0.0301,0.0385, 0.0472,0.0507,0.0529,0.0545,0.0545,0.0573,0.0581,0.0586,0.0618,0.0686, 0.0709,0.0723,0.0773,0.0785,0.0796,0.0846,0.0933,0.0975,0.1005,0.1078, 0.1162,0.1211,0.1221,0.1246,0.1290,0.1330,0.1366,0.1387,0.1434,0.1548, 0.1551,0.1559,0.1576,0.1620,0.1653,0.1661,0.1688,0.1727,0.1806,0.1858, 0.1874,0.1936,0.1944,0.1962,0.1965,0.1977,0.1997,0.2011,0.2027,0.2201, 0.2257,0.2289,0.2310,0.2357,0.2415,0.2422,0.2434,0.2466,0.2491,0.2515, 0.2522,0.2522,0.2561,0.2614,0.2650,0.2658,0.2729,0.2769,0.2825,0.2899, 0.2911,0.2919,0.2972,0.3066,0.3087,0.3087,0.3115,0.3140,0.3150,0.3298, 0.3312,0.3320,0.3341,0.3362,0.3376,0.3504,0.3529,0.3536,0.3576,0.3661, 0.3715,0.3817,0.3881,0.3884,0.3902,0.3921,0.4002,0.4036,0.4055,0.4097, 0.4128,0.4326,0.4349,0.4379,0.4429,0.4433,0.4453,0.4455,0.4474,0.4537, 0.4542,0.4587,0.4591,0.4626,0.4664,0.4672,0.4712,0.4727,0.4734,0.4737, 0.4786,0.4818,0.4867,0.4875,0.4920,0.4936,0.4976,0.5094,0.5150,0.5165, 0.5182,0.5211,0.5243,0.5268,0.5269,0.5295,0.5297,0.5419,0.5421,0.5431, 0.5435,0.5453,0.5454,0.5466,0.5478,0.5489,0.5535,0.5558,0.5575,0.5602, 0.5642,0.5665,0.5812,0.5821,0.5838,0.5861,0.5921,0.6137,0.6150,0.6207, 0.6225,0.6246,0.6257,0.6264,0.6287,0.6357,0.6471,0.6474,0.6481,0.6507, 0.6525,0.6723,0.6726,0.6738,0.6744,0.6749,0.6776,0.6818,0.6854,0.6875, 0.6878,0.6961,0.6978,0.6993,0.7009,0.7027,0.7041,0.7140,0.7245,0.7265, 0.7265,0.7418,0.7480,0.7646,0.7697,0.7726,0.7738,0.7743,0.7759,0.7803, 0.7867,0.7876,0.7878,0.7957,0.8001,0.8009,0.8038,0.8046,0.8047,0.8084, 0.8088,0.8106,0.8140,0.8179,0.8238,0.8240,0.8278,0.8360,0.8507,0.8541, 0.8552,0.8555,0.8593,0.8603,0.8633,0.8659,0.8670,0.8686,0.8711,0.8745, 0.8765,0.8775,0.8784,0.8803,0.8805,0.9067,0.9133,0.9145,0.9152,0.9185, 0.9186,0.9256,0.9278,0.9324,0.9389,0.9394,0.9397,0.9480,0.9484,0.9490, 0.9609,0.9737,0.9747,0.9774,0.9779,0.9829,0.9893,0.9951,0.9999, Overall p-value after applying KStest on 269 p-values = 0.976245 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.