RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-02-25_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 16.01 8.6824 0.050298 2 to 25 15.84 21.2042 0.782709 3 to 26 15.81 15.1956 0.418605 4 to 27 15.99 11.3945 0.164666 5 to 28 15.83 16.8173 0.533189 6 to 29 15.72 23.3171 0.860792 7 to 30 15.76 22.2697 0.825431 8 to 31 15.94 25.2250 0.910214 9 to 32 15.43 20.5216 0.751577 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.493687 Tough bday spacings test for dh-ranFile-2016-02-25_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 8 35 79 96 106 85 40 30 16 5 0 (O-E)^2/E 0.1 0.1 0.4 0.0 0.7 0.6 2.8 0.0 0.1 0.4 4.1 Birthday Spacings: Sum(O-E)^2/E= 9.362, p= 0.502 RESULTS OF GCD FOR dh-ranFile-2016-02-25_11:31 Euclid's algorithm: p-value, steps to gcd: 0.425946 p-value, dist. of gcd's: 0.290849 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-02-25_11:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.514 0.596 0.949 0.088 0.734 0.630 0.805 0.188 Bits 8 to 15---> 0.791 0.043 0.108 0.563 0.975 0.762 0.268 0.948 Bits 16 to 23---> 0.917 0.629 0.225 0.724 0.954 0.821 0.726 0.669 Bits 24 to 31---> 0.458 0.362 0.326 0.575 0.635 0.225 0.587 0.856 KS test for the above 32 p values: 0.832 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-02-25_11:31, p-values for 5 runs: 0.9689, 0.2067, 0.0684, 0.6100, 0.3399 Rank test for binary matrices (31x31) for dh-ranFile-2016-02-25_11:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 195 211.4 1.275 1.275 r= 29 5191 5134.0 0.633 1.908 r= 30 23067 23103.0 0.056 1.964 r= 31 11547 11551.5 0.002 1.966 chi-square = 1.966 with df = 3; p-value = 0.420 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-02-25_11:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 207 211.4 0.092 0.092 r= 30 5081 5134.0 0.547 0.640 r= 31 23268 23103.0 1.178 1.817 r= 32 11444 11551.5 1.001 2.818 chi-square = 2.818 with df = 3; p-value = 0.579 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-02-25_11:31 b-rank test for bits 1 to 8, p=0.67855 b-rank test for bits 2 to 9, p=0.61707 b-rank test for bits 3 to 10, p=0.47574 b-rank test for bits 4 to 11, p=0.55287 b-rank test for bits 5 to 12, p=0.81318 b-rank test for bits 6 to 13, p=0.70345 b-rank test for bits 7 to 14, p=0.19742 b-rank test for bits 8 to 15, p=0.38691 b-rank test for bits 9 to 16, p=0.47102 b-rank test for bits 10 to 17, p=0.22120 b-rank test for bits 11 to 18, p=0.61959 b-rank test for bits 12 to 19, p=0.87921 b-rank test for bits 13 to 20, p=0.84988 b-rank test for bits 14 to 21, p=0.65005 b-rank test for bits 15 to 22, p=0.05584 b-rank test for bits 16 to 23, p=0.91874 b-rank test for bits 17 to 24, p=0.77814 b-rank test for bits 18 to 25, p=0.99704 b-rank test for bits 19 to 26, p=0.68530 b-rank test for bits 20 to 27, p=0.39917 b-rank test for bits 21 to 28, p=0.73268 b-rank test for bits 22 to 29, p=0.01308 b-rank test for bits 23 to 30, p=0.73721 b-rank test for bits 24 to 31, p=0.93889 b-rank test for bits 25 to 32, p=0.76391 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 = 0.089507 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-02-25_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 142323 0.97 0.833108 2 141613 -0.69 0.244356 3 142422 1.20 0.884508 4 141665 -0.57 0.284046 5 142519 1.42 0.922844 6 141336 -1.34 0.090195 7 142421 1.20 0.884052 8 142294 0.90 0.815610 9 142461 1.29 0.901292 10 141904 -0.01 0.495032 11 141699 -0.49 0.311563 12 142615 1.65 0.950402 13 141876 -0.08 0.468964 14 142317 0.95 0.829578 15 142220 0.73 0.766039 16 140814 -2.56 0.005246 17 141650 -0.61 0.272287 18 142401 1.15 0.874673 19 141519 -0.91 0.180888 20 142080 0.40 0.654966 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-02-25_11:31 Bits used No. missing words z-score p-value 23 to 32 141597 -1.0770 0.140740 22 to 31 142745 2.8816 0.998022 21 to 30 142109 0.6885 0.754436 20 to 29 141619 -1.0011 0.158380 19 to 28 141858 -0.1770 0.429754 18 to 27 141277 -2.1804 0.014612 17 to 26 141761 -0.5115 0.304507 16 to 25 141843 -0.2287 0.409542 15 to 24 141389 -1.7942 0.036387 14 to 23 142151 0.8333 0.797675 13 to 22 141870 -0.1356 0.446061 12 to 21 141705 -0.7046 0.240534 11 to 20 141518 -1.3494 0.088602 10 to 19 142328 1.4437 0.925587 9 to 18 141856 -0.1839 0.427047 8 to 17 141765 -0.4977 0.309351 7 to 16 141771 -0.4770 0.316681 6 to 15 142293 1.3230 0.907082 5 to 14 142054 0.4989 0.691062 4 to 13 142028 0.4092 0.658806 3 to 12 141933 0.0816 0.532526 2 to 11 141882 -0.0942 0.462459 1 to 10 141799 -0.3804 0.351806 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-02-25_11:31 Bits used No. missing words z-score p-value 28 to 32 141702 -0.7028 0.241086 27 to 31 142197 0.9752 0.835258 26 to 30 141652 -0.8723 0.191521 25 to 29 142000 0.3074 0.620714 24 to 28 142473 1.9107 0.971981 23 to 27 142099 0.6429 0.739872 22 to 26 141978 0.2328 0.592034 21 to 25 141786 -0.4181 0.337949 20 to 24 141815 -0.3198 0.374574 19 to 23 142185 0.9345 0.824970 18 to 22 141679 -0.7808 0.217466 17 to 21 141891 -0.0621 0.475227 16 to 20 141598 -1.0554 0.145631 15 to 19 141703 -0.6994 0.242144 14 to 18 141897 -0.0418 0.483330 13 to 17 141689 -0.7469 0.227568 12 to 16 141936 0.0904 0.536018 11 to 15 142193 0.9616 0.831873 10 to 14 141790 -0.4045 0.342919 9 to 13 141620 -0.9808 0.163351 8 to 12 142518 2.0633 0.980457 7 to 11 142303 1.3345 0.908976 6 to 10 142153 0.8260 0.795598 5 to 9 141936 0.0904 0.536018 4 to 8 142470 1.9006 0.971321 3 to 7 142240 1.1209 0.868838 2 to 6 141674 -0.7977 0.212514 1 to 5 141869 -0.1367 0.445629 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-02-25_11:31 Bits used No. missing words z-score p-value 31 to 32 142521 1.8043 0.964411 30 to 31 141910 0.0020 0.500789 29 to 30 141805 -0.3078 0.379133 28 to 29 141787 -0.3609 0.359104 27 to 28 141728 -0.5349 0.296361 26 to 27 141947 0.1111 0.544240 25 to 26 142069 0.4710 0.681181 24 to 25 142129 0.6480 0.741506 23 to 24 142448 1.5890 0.943969 22 to 23 141971 0.1819 0.572176 21 to 22 141629 -0.8269 0.204138 20 to 21 142067 0.4651 0.679071 19 to 20 142279 1.0905 0.862247 18 to 19 141787 -0.3609 0.359104 17 to 18 141665 -0.7207 0.235536 16 to 17 141744 -0.4877 0.312882 15 to 16 142443 1.5742 0.942285 14 to 15 142168 0.7630 0.777280 13 to 14 142356 1.3176 0.906183 12 to 13 142171 0.7719 0.779910 11 to 12 141196 -2.1042 0.017680 10 to 11 141709 -0.5909 0.277279 9 to 10 141747 -0.4788 0.316023 8 to 9 141501 -1.2045 0.114196 7 to 8 142043 0.3943 0.653323 6 to 7 141394 -1.5201 0.064237 5 to 6 141388 -1.5378 0.062043 4 to 5 141986 0.2262 0.589464 3 to 4 141663 -0.7266 0.233724 2 to 3 142024 0.3383 0.632416 1 to 2 142587 1.9990 0.977197 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-02-25_11:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2428.78 -1.007 0.156925 Test results for specific bytes for dh-ranFile-2016-02-25_11:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2519.84 0.281 0.610465 2 to 9 2452.36 -0.674 0.250220 3 to 10 2533.43 0.473 0.681837 4 to 11 2425.57 -1.053 0.146269 5 to 12 2486.13 -0.196 0.422220 6 to 13 2544.98 0.636 0.737672 7 to 14 2546.86 0.663 0.746256 8 to 15 2499.46 -0.008 0.496954 9 to 16 2456.95 -0.609 0.271341 10 to 17 2604.33 1.475 0.929959 11 to 18 2545.41 0.642 0.739631 12 to 19 2529.32 0.415 0.660777 13 to 20 2464.70 -0.499 0.308828 14 to 21 2504.75 0.067 0.526800 15 to 22 2597.39 1.377 0.915784 16 to 23 2542.84 0.606 0.727702 17 to 24 2544.53 0.630 0.735577 18 to 25 2574.73 1.057 0.854718 19 to 26 2607.72 1.523 0.936167 20 to 27 2433.84 -0.936 0.174712 21 to 28 2457.89 -0.595 0.275770 22 to 29 2438.55 -0.869 0.192400 23 to 30 2384.53 -1.633 0.051234 24 to 31 2493.32 -0.095 0.462340 25 to 32 2486.89 -0.185 0.426439 CDPARK for dh-ranFile-2016-02-25_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 3533 0.4566 0.676028 3554 1.4155 0.921543 3533 0.4566 0.676028 3522 -0.0457 0.481790 3508 -0.6849 0.246694 3528 0.2283 0.590298 3538 0.6849 0.753306 3497 -1.1872 0.117571 3513 -0.4566 0.323972 3540 0.7763 0.781201 Square side=100, avg. no. parked=3526.60 sample std.=16.04 p-value of the KSTEST for those 10 p-values: 0.768389 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-02-25_11:31 0.3465,0.2567,0.3644,0.3106,0.2874,0.4249,0.1468,0.9662,0.0447,0.5615, The KS test for those 10 p-values: 0.173045 The 3DSPHERES test for dh-ranFile-2016-02-25_11:31 sample no r^3 equiv. uni. 1 30.481 0.637973 2 28.695 0.615765 3 78.000 0.925727 4 15.077 0.395017 5 11.993 0.329516 6 6.500 0.194800 7 64.064 0.881812 8 23.459 0.542491 9 2.786 0.088677 10 4.030 0.125692 11 8.922 0.257254 12 16.257 0.418362 13 42.028 0.753631 14 38.892 0.726484 15 8.049 0.235328 16 51.039 0.817551 17 11.228 0.312205 18 34.635 0.684786 19 12.630 0.343602 20 4.241 0.131830 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.842117 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-02-25_11:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 -0.7 0.3 -1.1 1.1 -0.5 -0.1 -0.3 0.1 -1.2 2.6 0.3 -0.5 1.0 0.6 -0.2 -1.2 -1.1 0.3 1.1 0.8 0.3 -2.3 -0.9 0.1 1.0 0.2 0.0 0.1 -0.4 -0.0 -0.5 -0.4 -0.4 -0.2 -1.6 -0.2 2.1 0.9 1.5 2.4 1.0 -1.1 Chi-square with 42 degrees of freedom:44.551973 z-score=0.278443, p-value=0.635124 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-02-25_11:31 Test no p-value 1 0.279191 2 0.627331 3 0.955049 4 0.022151 5 0.979443 6 0.643862 7 0.324660 8 0.289921 9 0.444580 10 0.833287 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.775397 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-02-25_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 66577 0.12 66900 0.82 3 25000.00 25046 0.08 24823 1.25 4 6666.67 6684 0.05 6594 0.79 5 1388.89 1411 0.35 1422 0.79 6 238.10 231 0.21 223 0.96 7 34.72 45 3.04 33 0.09 8 4.96 5 0.00 4 0.19 p=0.30408 p=0.44062 Number of rngs required: 688392, p-value: 0.495 RESULTS OF CRAPS TEST for dh-ranFile-2016-02-25_11:31 No. of wins: Observed Expected 98452 98585.9 z-score=-0.599, pvalue=0.27469 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66640 66666.7 0.011 0.011 2 37959 37654.3 2.465 2.476 3 27132 26954.7 1.166 3.642 4 19164 19313.5 1.157 4.798 5 13698 13851.4 1.699 6.498 6 9923 9943.5 0.042 6.540 7 7118 7145.0 0.102 6.642 8 5181 5139.1 0.342 6.984 9 3675 3699.9 0.167 7.152 10 2647 2666.3 0.140 7.291 11 1906 1923.3 0.156 7.447 12 1388 1388.7 0.000 7.448 13 967 1003.7 1.343 8.791 14 728 726.1 0.005 8.796 15 500 525.8 1.269 10.065 16 383 381.2 0.009 10.074 17 273 276.5 0.045 10.119 18 177 200.8 2.828 12.947 19 147 146.0 0.007 12.954 20 100 106.2 0.364 13.318 21 294 287.1 0.165 13.483 Chisq= 13.48 for 20 degrees of freedom, p= 0.14427 SUMMARY of craptest p-value for no. of wins: 0.274689 p-value for throws/game: 0.144272 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-02-25_11:31 No. of wins: Observed Expected 98488 98585.9 z-score=-0.438, pvalue=0.33081 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66643 66666.7 0.008 0.008 2 38066 37654.3 4.501 4.509 3 26848 26954.7 0.423 4.932 4 18979 19313.5 5.792 10.724 5 13885 13851.4 0.081 10.805 6 9916 9943.5 0.076 10.882 7 7192 7145.0 0.309 11.191 8 5196 5139.1 0.631 11.821 9 3703 3699.9 0.003 11.824 10 2705 2666.3 0.562 12.386 11 1852 1923.3 2.645 15.031 12 1392 1388.7 0.008 15.039 13 999 1003.7 0.022 15.061 14 700 726.1 0.941 16.002 15 529 525.8 0.019 16.021 16 388 381.2 0.123 16.144 17 270 276.5 0.155 16.299 18 186 200.8 1.095 17.394 19 170 146.0 3.951 21.344 20 105 106.2 0.014 21.358 21 276 287.1 0.430 21.789 Chisq= 21.79 for 20 degrees of freedom, p= 0.64791 SUMMARY of craptest p-value for no. of wins: 0.330809 p-value for throws/game: 0.647905 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0052,0.0131,0.0146,0.0177,0.0222,0.0364,0.0427,0.0447,0.0503,0.0512, 0.0558,0.0620,0.0642,0.0684,0.0884,0.0886,0.0887,0.0895,0.0902,0.1084, 0.1142,0.1176,0.1257,0.1318,0.1407,0.1443,0.1456,0.1463,0.1468,0.1569, 0.1584,0.1634,0.1647,0.1730,0.1747,0.1809,0.1885,0.1915,0.1924,0.1948, 0.1974,0.2041,0.2067,0.2125,0.2175,0.2212,0.2246,0.2250,0.2276,0.2337, 0.2353,0.2355,0.2405,0.2411,0.2421,0.2444,0.2467,0.2502,0.2567,0.2573, 0.2684,0.2713,0.2723,0.2747,0.2758,0.2773,0.2792,0.2840,0.2874,0.2899, 0.2908,0.2964,0.3041,0.3045,0.3088,0.3094,0.3106,0.3116,0.3122,0.3129, 0.3160,0.3167,0.3240,0.3247,0.3262,0.3295,0.3308,0.3379,0.3399,0.3429, 0.3436,0.3465,0.3518,0.3591,0.3591,0.3624,0.3644,0.3746,0.3791,0.3869, 0.3950,0.3992,0.4095,0.4184,0.4186,0.4204,0.4222,0.4249,0.4259,0.4264, 0.4270,0.4298,0.4406,0.4446,0.4456,0.4461,0.4584,0.4623,0.4625,0.4690, 0.4710,0.4752,0.4757,0.4818,0.4833,0.4937,0.4950,0.4950,0.4970,0.5008, 0.5018,0.5138,0.5268,0.5325,0.5332,0.5360,0.5360,0.5425,0.5442,0.5529, 0.5615,0.5630,0.5722,0.5748,0.5795,0.5871,0.5895,0.5903,0.5920,0.5958, 0.6100,0.6105,0.6158,0.6171,0.6196,0.6207,0.6273,0.6290,0.6305,0.6324, 0.6351,0.6351,0.6380,0.6439,0.6479,0.6500,0.6533,0.6550,0.6588,0.6608, 0.6692,0.6760,0.6760,0.6786,0.6791,0.6812,0.6818,0.6848,0.6853,0.6911, 0.7035,0.7240,0.7257,0.7265,0.7277,0.7327,0.7344,0.7356,0.7372,0.7377, 0.7396,0.7399,0.7415,0.7463,0.7516,0.7533,0.7536,0.7544,0.7621,0.7639, 0.7660,0.7684,0.7754,0.7773,0.7781,0.7799,0.7812,0.7827,0.7914,0.7956, 0.7977,0.8052,0.8132,0.8156,0.8176,0.8208,0.8250,0.8254,0.8296,0.8319, 0.8323,0.8331,0.8333,0.8353,0.8421,0.8499,0.8547,0.8556,0.8608,0.8622, 0.8688,0.8747,0.8792,0.8818,0.8841,0.8845,0.9013,0.9062,0.9071,0.9090, 0.9102,0.9158,0.9173,0.9187,0.9215,0.9228,0.9256,0.9257,0.9300,0.9362, 0.9389,0.9423,0.9440,0.9483,0.9489,0.9504,0.9543,0.9550,0.9644,0.9662, 0.9689,0.9713,0.9720,0.9753,0.9772,0.9794,0.9805,0.9970,0.9980, Overall p-value after applying KStest on 269 p-values = 0.185485 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.