RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-07-26_13:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.87 13.7460 0.315007 2 to 25 15.95 17.8761 0.603303 3 to 26 15.75 14.9112 0.398122 4 to 27 15.74 24.6545 0.897284 5 to 28 15.76 15.2332 0.421309 6 to 29 15.80 20.4405 0.747681 7 to 30 15.71 15.3158 0.427252 8 to 31 15.96 16.5937 0.517795 9 to 32 16.13 17.5204 0.580320 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.366860 Tough bday spacings test for dh-ranFile-2016-07-26_13:31: 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 11 18 82 109 93 78 51 30 14 8 6 (O-E)^2/E 0.4 9.5 1.0 1.3 0.2 0.0 0.0 0.0 0.1 0.3 0.9 Birthday Spacings: Sum(O-E)^2/E= 13.712, p= 0.813 RESULTS OF GCD FOR dh-ranFile-2016-07-26_13:31 Euclid's algorithm: p-value, steps to gcd: 0.113735 p-value, dist. of gcd's: 0.625319 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-07-26_13:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.609 0.025 0.263 0.810 0.581 0.026 0.020 0.907 Bits 8 to 15---> 0.847 0.313 0.262 0.045 0.312 0.457 0.627 0.358 Bits 16 to 23---> 0.863 0.308 0.052 0.877 0.802 0.705 0.801 0.730 Bits 24 to 31---> 0.762 0.452 0.822 0.672 0.275 0.408 0.042 0.244 KS test for the above 32 p values: 0.582 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-07-26_13:31, p-values for 5 runs: 0.7183, 0.1800, 0.4985, 0.3910, 0.2199 Rank test for binary matrices (31x31) for dh-ranFile-2016-07-26_13:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 199 211.4 0.729 0.729 r= 29 5110 5134.0 0.112 0.842 r= 30 23099 23103.0 0.001 0.842 r= 31 11592 11551.5 0.142 0.984 chi-square = 0.984 with df = 3; p-value = 0.195 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-07-26_13:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 197 211.4 0.983 0.983 r= 30 5076 5134.0 0.655 1.639 r= 31 23101 23103.0 0.000 1.639 r= 32 11626 11551.5 0.480 2.119 chi-square = 2.119 with df = 3; p-value = 0.452 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-07-26_13:31 b-rank test for bits 1 to 8, p=0.73344 b-rank test for bits 2 to 9, p=0.42511 b-rank test for bits 3 to 10, p=0.43242 b-rank test for bits 4 to 11, p=0.42706 b-rank test for bits 5 to 12, p=0.37862 b-rank test for bits 6 to 13, p=0.37615 b-rank test for bits 7 to 14, p=0.24420 b-rank test for bits 8 to 15, p=0.90235 b-rank test for bits 9 to 16, p=0.57361 b-rank test for bits 10 to 17, p=0.45138 b-rank test for bits 11 to 18, p=0.40397 b-rank test for bits 12 to 19, p=0.92585 b-rank test for bits 13 to 20, p=0.36950 b-rank test for bits 14 to 21, p=0.95331 b-rank test for bits 15 to 22, p=0.96695 b-rank test for bits 16 to 23, p=0.16632 b-rank test for bits 17 to 24, p=0.27534 b-rank test for bits 18 to 25, p=0.00994 b-rank test for bits 19 to 26, p=0.96557 b-rank test for bits 20 to 27, p=0.51566 b-rank test for bits 21 to 28, p=0.34937 b-rank test for bits 22 to 29, p=0.43080 b-rank test for bits 23 to 30, p=0.92283 b-rank test for bits 24 to 31, p=0.43232 b-rank test for bits 25 to 32, p=0.26246 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 = 0.208094 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-07-26_13:31 (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 142471 1.31 0.905293 2 142205 0.69 0.755160 3 141677 -0.54 0.293624 4 141983 0.17 0.568331 5 142197 0.67 0.749248 6 142353 1.04 0.850042 7 141976 0.16 0.561893 8 141464 -1.04 0.149056 9 142027 0.27 0.608315 10 142211 0.70 0.759544 11 141461 -1.05 0.147435 12 142066 0.37 0.642837 13 141739 -0.40 0.345327 14 142408 1.17 0.878014 15 143095 2.77 0.997199 16 142476 1.32 0.907248 17 142664 1.76 0.961071 18 142484 1.34 0.910313 19 142157 0.58 0.718594 20 142467 1.30 0.903707 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-07-26_13:31 Bits used No. missing words z-score p-value 23 to 32 142465 1.9161 0.972324 22 to 31 141432 -1.6460 0.049885 21 to 30 141757 -0.5253 0.299696 20 to 29 141935 0.0885 0.535267 19 to 28 141767 -0.4908 0.311786 18 to 27 142204 1.0161 0.845210 17 to 26 141859 -0.1736 0.431109 16 to 25 141896 -0.0460 0.481669 15 to 24 141367 -1.8701 0.030735 14 to 23 142154 0.8437 0.800579 13 to 22 141857 -0.1804 0.428400 12 to 21 141837 -0.2494 0.401520 11 to 20 141573 -1.1598 0.123074 10 to 19 141945 0.1230 0.548947 9 to 18 141705 -0.7046 0.240534 8 to 17 141794 -0.3977 0.345430 7 to 16 141535 -1.2908 0.098388 6 to 15 141943 0.1161 0.546215 5 to 14 141907 -0.0080 0.496795 4 to 13 142379 1.6196 0.947336 3 to 12 141805 -0.3598 0.359514 2 to 11 141965 0.1920 0.576115 1 to 10 141982 0.2506 0.598933 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-07-26_13:31 Bits used No. missing words z-score p-value 28 to 32 141732 -0.6011 0.273881 27 to 31 141846 -0.2147 0.415009 26 to 30 141990 0.2735 0.607749 25 to 29 141538 -1.2587 0.104061 24 to 28 142119 0.7107 0.761379 23 to 27 141990 0.2735 0.607749 22 to 26 142062 0.5175 0.697605 21 to 25 141702 -0.7028 0.241086 20 to 24 142161 0.8531 0.803203 19 to 23 141905 -0.0147 0.494145 18 to 22 142729 2.7785 0.997270 17 to 21 141612 -1.0079 0.156752 16 to 20 141154 -2.5604 0.005227 15 to 19 142091 0.6158 0.730997 14 to 18 141908 -0.0045 0.498201 13 to 17 142031 0.4124 0.659992 12 to 16 142458 1.8599 0.968550 11 to 15 142021 0.3785 0.647486 10 to 14 141671 -0.8079 0.209575 9 to 13 141959 0.1684 0.566855 8 to 12 142108 0.6735 0.749672 7 to 11 141966 0.1921 0.576169 6 to 10 142237 1.1107 0.866661 5 to 9 141777 -0.4486 0.326869 4 to 8 142006 0.3277 0.628429 3 to 7 141886 -0.0791 0.468483 2 to 6 141722 -0.6350 0.262709 1 to 5 141631 -0.9435 0.172715 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-07-26_13:31 Bits used No. missing words z-score p-value 31 to 32 142116 0.6096 0.728952 30 to 31 141431 -1.4110 0.079122 29 to 30 142520 1.8014 0.964179 28 to 29 141881 -0.0836 0.466699 27 to 28 141585 -0.9567 0.169353 26 to 27 141629 -0.8269 0.204138 25 to 26 142039 0.3825 0.648958 24 to 25 141449 -1.3579 0.087247 23 to 24 141747 -0.4788 0.316023 22 to 23 142200 0.8574 0.804397 21 to 22 142171 0.7719 0.779910 20 to 21 142032 0.3619 0.641271 19 to 20 141659 -0.7384 0.230125 18 to 19 141935 0.0757 0.530180 17 to 18 141743 -0.4906 0.311837 16 to 17 142194 0.8397 0.799471 15 to 16 142231 0.9489 0.828659 14 to 15 141609 -0.8859 0.187828 13 to 14 141733 -0.5201 0.301480 12 to 13 141788 -0.3579 0.360207 11 to 12 142271 1.0669 0.856985 10 to 11 141887 -0.0659 0.473741 9 to 10 140978 -2.7473 0.003005 8 to 9 142159 0.7365 0.769284 7 to 8 141674 -0.6942 0.243782 6 to 7 141541 -1.0865 0.138625 5 to 6 141648 -0.7709 0.220388 4 to 5 142226 0.9341 0.824882 3 to 4 142461 1.6273 0.948168 2 to 3 142375 1.3737 0.915226 1 to 2 141409 -1.4759 0.069985 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-07-26_13:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2557.90 0.819 0.793575 Test results for specific bytes for dh-ranFile-2016-07-26_13:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2407.72 -1.305 0.095929 2 to 9 2494.53 -0.077 0.469196 3 to 10 2310.00 -2.687 0.003605 4 to 11 2374.17 -1.780 0.037576 5 to 12 2472.04 -0.395 0.346257 6 to 13 2509.39 0.133 0.552796 7 to 14 2465.27 -0.491 0.311666 8 to 15 2558.51 0.828 0.796023 9 to 16 2509.38 0.133 0.552741 10 to 17 2514.66 0.207 0.582102 11 to 18 2519.39 0.274 0.608014 12 to 19 2411.02 -1.258 0.104140 13 to 20 2507.46 0.106 0.542025 14 to 21 2518.92 0.268 0.605475 15 to 22 2461.32 -0.547 0.292191 16 to 23 2379.00 -1.711 0.043517 17 to 24 2454.94 -0.637 0.261964 18 to 25 2469.49 -0.431 0.333056 19 to 26 2559.67 0.844 0.800631 20 to 27 2567.88 0.960 0.831469 21 to 28 2559.55 0.842 0.800148 22 to 29 2529.11 0.412 0.659718 23 to 30 2429.95 -0.991 0.160911 24 to 31 2502.70 0.038 0.515242 25 to 32 2467.92 -0.454 0.325040 CDPARK for dh-ranFile-2016-07-26_13:31: 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 3519 -0.1826 0.427537 3525 0.0913 0.536383 3501 -1.0046 0.157553 3521 -0.0913 0.463617 3499 -1.0959 0.136563 3521 -0.0913 0.463617 3530 0.3196 0.625377 3517 -0.2740 0.392053 3514 -0.4110 0.340551 3550 1.2329 0.891189 Square side=100, avg. no. parked=3519.70 sample std.=13.69 p-value of the KSTEST for those 10 p-values: 0.438793 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-07-26_13:31 0.5598,0.3036,0.4092,0.1440,0.1321,0.3115,0.0407,0.3913,0.1197,0.5061, The KS test for those 10 p-values: 0.032616 The 3DSPHERES test for dh-ranFile-2016-07-26_13:31 sample no r^3 equiv. uni. 1 12.594 0.342814 2 53.561 0.832267 3 17.465 0.441307 4 10.864 0.303817 5 12.508 0.340940 6 20.230 0.490509 7 163.864 0.995756 8 7.733 0.227213 9 19.091 0.470795 10 28.724 0.616133 11 57.310 0.851969 12 8.800 0.254236 13 26.274 0.583469 14 5.585 0.169860 15 38.026 0.718475 16 3.804 0.119103 17 99.434 0.963646 18 63.172 0.878245 19 37.392 0.712460 20 71.554 0.907923 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.541888 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-07-26_13:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 0.5 1.8 -0.4 0.5 -0.7 0.8 -0.5 0.4 0.2 -0.3 1.2 1.7 -1.5 1.2 1.6 -0.5 -0.0 -0.2 -0.2 -1.0 0.1 -0.9 -0.3 0.1 -0.6 -1.8 -1.1 -0.6 1.2 0.3 -1.3 0.0 -0.2 -0.4 2.9 0.3 1.5 0.5 1.0 0.1 -1.0 -0.1 Chi-square with 42 degrees of freedom:40.237595 z-score=-0.192294, p-value=0.451460 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-07-26_13:31 Test no p-value 1 0.163546 2 0.006952 3 0.076326 4 0.358756 5 0.067033 6 0.041148 7 0.450648 8 0.088090 9 0.100156 10 0.421846 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000251 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-07-26_13:31: (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 66441 0.76 66444 0.74 3 25000.00 25120 0.58 25041 0.07 4 6666.67 6766 1.48 6746 0.94 5 1388.89 1385 0.01 1463 3.95 6 238.10 251 0.70 264 2.82 7 34.72 31 0.40 35 0.00 8 4.96 5 0.00 6 0.22 p=0.31373 p=0.81176 Number of rngs required: 692526, p-value: 1.000 RESULTS OF CRAPS TEST for dh-ranFile-2016-07-26_13:31 No. of wins: Observed Expected 98681 98585.9 z-score= 0.426, pvalue=0.66477 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66792 66666.7 0.236 0.236 2 37326 37654.3 2.863 3.098 3 27013 26954.7 0.126 3.224 4 19343 19313.5 0.045 3.270 5 13857 13851.4 0.002 3.272 6 9849 9943.5 0.899 4.171 7 7080 7145.0 0.592 4.762 8 5242 5139.1 2.061 6.824 9 3796 3699.9 2.498 9.322 10 2708 2666.3 0.652 9.974 11 1924 1923.3 0.000 9.974 12 1359 1388.7 0.637 10.611 13 1038 1003.7 1.171 11.782 14 771 726.1 2.771 14.554 15 537 525.8 0.237 14.791 16 391 381.2 0.255 15.045 17 279 276.5 0.022 15.067 18 183 200.8 1.583 16.650 19 116 146.0 6.159 22.809 20 95 106.2 1.184 23.993 21 301 287.1 0.672 24.664 Chisq= 24.66 for 20 degrees of freedom, p= 0.78543 SUMMARY of craptest p-value for no. of wins: 0.664774 p-value for throws/game: 0.785430 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-07-26_13:31 No. of wins: Observed Expected 98593 98585.9 z-score= 0.032, pvalue=0.51274 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66667 66666.7 0.000 0.000 2 37922 37654.3 1.903 1.903 3 26646 26954.7 3.536 5.439 4 19290 19313.5 0.029 5.468 5 14013 13851.4 1.885 7.352 6 9938 9943.5 0.003 7.355 7 7211 7145.0 0.609 7.965 8 5084 5139.1 0.590 8.555 9 3655 3699.9 0.544 9.099 10 2714 2666.3 0.853 9.952 11 1812 1923.3 6.444 16.396 12 1391 1388.7 0.004 16.400 13 1016 1003.7 0.150 16.550 14 701 726.1 0.870 17.421 15 516 525.8 0.184 17.605 16 401 381.2 1.034 18.639 17 292 276.5 0.864 19.503 18 192 200.8 0.388 19.891 19 153 146.0 0.337 20.228 20 101 106.2 0.256 20.484 21 285 287.1 0.016 20.500 Chisq= 20.50 for 20 degrees of freedom, p= 0.57293 SUMMARY of craptest p-value for no. of wins: 0.512740 p-value for throws/game: 0.572930 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0003,0.0030,0.0036,0.0052,0.0070,0.0099,0.0196,0.0246,0.0257,0.0307, 0.0326,0.0376,0.0407,0.0411,0.0423,0.0435,0.0449,0.0499,0.0524,0.0670, 0.0700,0.0763,0.0791,0.0872,0.0881,0.0959,0.0984,0.1002,0.1041,0.1041, 0.1137,0.1191,0.1197,0.1231,0.1321,0.1366,0.1386,0.1440,0.1474,0.1491, 0.1568,0.1576,0.1609,0.1635,0.1663,0.1694,0.1699,0.1727,0.1800,0.1878, 0.1949,0.2041,0.2081,0.2096,0.2199,0.2204,0.2272,0.2301,0.2405,0.2411, 0.2438,0.2442,0.2443,0.2542,0.2620,0.2622,0.2625,0.2627,0.2632,0.2739, 0.2751,0.2753,0.2922,0.2936,0.2997,0.3015,0.3036,0.3038,0.3080,0.3115, 0.3117,0.3118,0.3118,0.3124,0.3126,0.3137,0.3150,0.3160,0.3250,0.3269, 0.3331,0.3406,0.3409,0.3428,0.3453,0.3454,0.3463,0.3494,0.3582,0.3588, 0.3595,0.3602,0.3669,0.3695,0.3762,0.3786,0.3910,0.3913,0.3921,0.3981, 0.4015,0.4040,0.4076,0.4092,0.4150,0.4213,0.4218,0.4251,0.4271,0.4273, 0.4275,0.4284,0.4308,0.4311,0.4323,0.4324,0.4388,0.4413,0.4506,0.4514, 0.4515,0.4515,0.4519,0.4565,0.4636,0.4636,0.4667,0.4685,0.4692,0.4708, 0.4737,0.4817,0.4905,0.4941,0.4968,0.4982,0.4985,0.5061,0.5127,0.5152, 0.5157,0.5178,0.5302,0.5353,0.5364,0.5419,0.5420,0.5462,0.5489,0.5527, 0.5528,0.5598,0.5619,0.5669,0.5683,0.5729,0.5736,0.5761,0.5762,0.5803, 0.5812,0.5821,0.5822,0.5835,0.5989,0.6033,0.6055,0.6077,0.6077,0.6080, 0.6083,0.6086,0.6161,0.6253,0.6254,0.6271,0.6284,0.6413,0.6428,0.6475, 0.6490,0.6597,0.6600,0.6648,0.6719,0.6976,0.7049,0.7125,0.7183,0.7185, 0.7186,0.7290,0.7298,0.7310,0.7334,0.7477,0.7492,0.7497,0.7552,0.7595, 0.7614,0.7624,0.7693,0.7799,0.7854,0.7936,0.7960,0.7995,0.8001,0.8006, 0.8006,0.8014,0.8020,0.8032,0.8044,0.8099,0.8118,0.8134,0.8222,0.8249, 0.8287,0.8315,0.8323,0.8452,0.8472,0.8500,0.8520,0.8570,0.8629,0.8667, 0.8767,0.8780,0.8782,0.8912,0.8973,0.9024,0.9037,0.9053,0.9069,0.9072, 0.9079,0.9103,0.9152,0.9228,0.9259,0.9473,0.9482,0.9533,0.9611,0.9636, 0.9642,0.9656,0.9670,0.9686,0.9723,0.9958,0.9972,0.9973,1.0000, Overall p-value after applying KStest on 269 p-values = 0.304369 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.