RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-10-25_22:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.56 18.8069 0.660273 2 to 25 15.52 19.8295 0.716956 3 to 26 15.82 17.0623 0.549844 4 to 27 15.65 30.7712 0.978709 5 to 28 15.62 28.6567 0.962174 6 to 29 15.76 18.0199 0.612411 7 to 30 16.01 8.8616 0.055496 8 to 31 16.07 20.3135 0.741493 9 to 32 15.88 19.3864 0.693189 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.093116 Tough bday spacings test for dh-ranFile-2016-10-25_22:31: 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 10 37 76 93 92 80 56 28 18 8 2 (O-E)^2/E 0.1 0.0 0.1 0.2 0.3 0.0 0.3 0.1 0.7 0.3 1.0 Birthday Spacings: Sum(O-E)^2/E= 3.172, p= 0.023 RESULTS OF GCD FOR dh-ranFile-2016-10-25_22:31 Euclid's algorithm: p-value, steps to gcd: 0.020020 p-value, dist. of gcd's: 0.544409 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-10-25_22:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.688 0.252 0.706 0.780 0.826 0.066 0.492 0.775 Bits 8 to 15---> 0.092 0.741 0.261 0.071 0.951 0.814 0.461 0.200 Bits 16 to 23---> 0.785 0.149 0.585 0.653 0.452 0.756 0.453 0.143 Bits 24 to 31---> 0.596 0.781 0.944 0.408 0.780 0.893 0.368 0.864 KS test for the above 32 p values: 0.671 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-10-25_22:31, p-values for 5 runs: 0.2878, 0.7861, 0.3336, 0.9098, 0.8789 Rank test for binary matrices (31x31) for dh-ranFile-2016-10-25_22:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 206 211.4 0.139 0.139 r= 29 5031 5134.0 2.067 2.206 r= 30 23053 23103.0 0.108 2.314 r= 31 11710 11551.5 2.174 4.488 chi-square = 4.488 with df = 3; p-value = 0.787 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-10-25_22:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 205 211.4 0.195 0.195 r= 30 5118 5134.0 0.050 0.245 r= 31 23127 23103.0 0.025 0.270 r= 32 11550 11551.5 0.000 0.270 chi-square = 0.270 with df = 3; p-value = 0.034 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-10-25_22:31 b-rank test for bits 1 to 8, p=0.42891 b-rank test for bits 2 to 9, p=0.92304 b-rank test for bits 3 to 10, p=0.75602 b-rank test for bits 4 to 11, p=0.68187 b-rank test for bits 5 to 12, p=0.22470 b-rank test for bits 6 to 13, p=0.19906 b-rank test for bits 7 to 14, p=0.29692 b-rank test for bits 8 to 15, p=0.79086 b-rank test for bits 9 to 16, p=0.21563 b-rank test for bits 10 to 17, p=0.35675 b-rank test for bits 11 to 18, p=0.01547 b-rank test for bits 12 to 19, p=0.69525 b-rank test for bits 13 to 20, p=0.73299 b-rank test for bits 14 to 21, p=0.38712 b-rank test for bits 15 to 22, p=0.84110 b-rank test for bits 16 to 23, p=0.20715 b-rank test for bits 17 to 24, p=0.37519 b-rank test for bits 18 to 25, p=0.10005 b-rank test for bits 19 to 26, p=0.22741 b-rank test for bits 20 to 27, p=0.42788 b-rank test for bits 21 to 28, p=0.68981 b-rank test for bits 22 to 29, p=0.77039 b-rank test for bits 23 to 30, p=0.09060 b-rank test for bits 24 to 31, p=0.66454 b-rank test for bits 25 to 32, p=0.07195 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 = 0.488821 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-10-25_22:31 (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 141792 -0.27 0.391990 2 141488 -0.98 0.162456 3 141792 -0.27 0.391990 4 142212 0.71 0.760271 5 141818 -0.21 0.415512 6 141940 0.07 0.528563 7 142745 1.95 0.974561 8 142215 0.71 0.762443 9 141841 -0.16 0.436579 10 141324 -1.37 0.085720 11 141705 -0.48 0.316536 12 141482 -1.00 0.159034 13 142201 0.68 0.752214 14 141804 -0.25 0.402803 15 141557 -0.82 0.205197 16 141833 -0.18 0.429228 17 142420 1.19 0.883596 18 141756 -0.36 0.360079 19 141501 -0.95 0.170031 20 142436 1.23 0.890752 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-10-25_22:31 Bits used No. missing words z-score p-value 23 to 32 142078 0.5816 0.719589 22 to 31 142363 1.5644 0.941136 21 to 30 142273 1.2540 0.895085 20 to 29 142027 0.4058 0.657540 19 to 28 141774 -0.4667 0.320373 18 to 27 141848 -0.2115 0.416255 17 to 26 142062 0.5264 0.700712 16 to 25 141600 -1.0667 0.143064 15 to 24 141623 -0.9873 0.161737 14 to 23 141695 -0.7391 0.229933 13 to 22 142075 0.5713 0.716094 12 to 21 141365 -1.8770 0.030259 11 to 20 141602 -1.0598 0.144627 10 to 19 141631 -0.9598 0.168588 9 to 18 141797 -0.3873 0.349251 8 to 17 142382 1.6299 0.948438 7 to 16 141786 -0.4253 0.335318 6 to 15 141404 -1.7425 0.040709 5 to 14 142030 0.4161 0.661333 4 to 13 142093 0.6333 0.736746 3 to 12 142043 0.4609 0.677576 2 to 11 141532 -1.3011 0.096606 1 to 10 141744 -0.5701 0.284304 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-10-25_22:31 Bits used No. missing words z-score p-value 28 to 32 141804 -0.3571 0.360527 27 to 31 142109 0.6768 0.750749 26 to 30 141891 -0.0621 0.475227 25 to 29 141810 -0.3367 0.368167 24 to 28 141972 0.2124 0.584118 23 to 27 141881 -0.0960 0.461747 22 to 26 142356 1.5141 0.935004 21 to 25 141879 -0.1028 0.459056 20 to 24 142200 0.9853 0.837767 19 to 23 141670 -0.8113 0.208600 18 to 22 141738 -0.5808 0.280695 17 to 21 141733 -0.5977 0.275010 16 to 20 141889 -0.0689 0.472529 15 to 19 142486 1.9548 0.974697 14 to 18 141878 -0.1062 0.457711 13 to 17 142218 1.0463 0.852298 12 to 16 142120 0.7141 0.762428 11 to 15 141678 -0.7842 0.216470 10 to 14 142275 1.2396 0.892431 9 to 13 141850 -0.2011 0.420303 8 to 12 141778 -0.4452 0.328093 7 to 11 142076 0.5650 0.713957 6 to 10 141758 -0.5130 0.303982 5 to 9 142160 0.8497 0.802262 4 to 8 141837 -0.2452 0.403156 3 to 7 141758 -0.5130 0.303982 2 to 6 141875 -0.1164 0.453679 1 to 5 141900 -0.0316 0.487385 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-10-25_22:31 Bits used No. missing words z-score p-value 31 to 32 141989 0.2350 0.592901 30 to 31 141385 -1.5467 0.060968 29 to 30 141822 -0.2576 0.398354 28 to 29 141535 -1.1042 0.134749 27 to 28 141638 -0.8004 0.211744 26 to 27 141464 -1.3137 0.094481 25 to 26 142568 1.9430 0.973991 24 to 25 141921 0.0344 0.513731 23 to 24 141929 0.0580 0.523135 22 to 23 141600 -0.9125 0.180759 21 to 22 141960 0.1495 0.559408 20 to 21 141909 -0.0010 0.499612 19 to 20 141566 -1.0128 0.155584 18 to 19 141374 -1.5791 0.057151 17 to 18 141824 -0.2517 0.400632 16 to 17 141314 -1.7561 0.039533 15 to 16 141783 -0.3727 0.354703 14 to 15 141994 0.2498 0.598615 13 to 14 141902 -0.0216 0.491375 12 to 13 141849 -0.1780 0.429375 11 to 12 142319 1.2085 0.886566 10 to 11 141928 0.0551 0.521960 9 to 10 142627 2.1170 0.982871 8 to 9 141984 0.2203 0.587168 7 to 8 141869 -0.1190 0.452651 6 to 7 141342 -1.6735 0.047111 5 to 6 141831 -0.2311 0.408633 4 to 5 141562 -1.0246 0.152783 3 to 4 141966 0.1672 0.566381 2 to 3 142249 1.0020 0.841823 1 to 2 141948 0.1141 0.545409 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-10-25_22:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2384.67 -1.631 0.051449 Test results for specific bytes for dh-ranFile-2016-10-25_22:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2517.97 0.254 0.600326 2 to 9 2514.34 0.203 0.580351 3 to 10 2403.45 -1.365 0.086054 4 to 11 2499.20 -0.011 0.495464 5 to 12 2420.86 -1.119 0.131539 6 to 13 2583.19 1.176 0.880299 7 to 14 2424.68 -1.065 0.143409 8 to 15 2409.92 -1.274 0.101350 9 to 16 2536.74 0.520 0.698339 10 to 17 2432.00 -0.962 0.168107 11 to 18 2566.13 0.935 0.825169 12 to 19 2553.24 0.753 0.774270 13 to 20 2506.85 0.097 0.538598 14 to 21 2566.84 0.945 0.827737 15 to 22 2530.85 0.436 0.668672 16 to 23 2439.58 -0.854 0.196418 17 to 24 2474.66 -0.358 0.360015 18 to 25 2466.67 -0.471 0.318670 19 to 26 2445.61 -0.769 0.220887 20 to 27 2560.88 0.861 0.805382 21 to 28 2537.06 0.524 0.699901 22 to 29 2503.74 0.053 0.521090 23 to 30 2519.52 0.276 0.608762 24 to 31 2438.90 -0.864 0.193780 25 to 32 2578.90 1.116 0.867743 CDPARK for dh-ranFile-2016-10-25_22:31: 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 3503 -0.9132 0.180558 3519 -0.1826 0.427537 3553 1.3699 0.914635 3513 -0.4566 0.323972 3549 1.1872 0.882429 3520 -0.1370 0.445521 3507 -0.7306 0.232514 3546 1.0502 0.853193 3512 -0.5023 0.307734 3554 1.4155 0.921543 Square side=100, avg. no. parked=3527.60 sample std.=19.38 p-value of the KSTEST for those 10 p-values: 0.494501 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-10-25_22:31 0.7101,0.0549,0.2243,0.6204,0.2624,0.5162,0.6641,0.4480,0.4474,0.5981, The KS test for those 10 p-values: 0.482042 The 3DSPHERES test for dh-ranFile-2016-10-25_22:31 sample no r^3 equiv. uni. 1 4.400 0.136432 2 6.464 0.193827 3 23.465 0.542579 4 16.937 0.431391 5 82.452 0.935970 6 4.661 0.143888 7 21.772 0.516037 8 19.932 0.485422 9 16.182 0.416892 10 4.676 0.144339 11 77.153 0.923599 12 39.606 0.732919 13 92.827 0.954690 14 34.266 0.680879 15 134.032 0.988527 16 16.815 0.429069 17 27.331 0.597887 18 79.957 0.930417 19 102.558 0.967242 20 56.962 0.850242 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.107393 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-10-25_22:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 1.3 0.1 0.6 -2.6 -2.1 -0.0 1.5 -2.6 1.6 0.3 -0.7 -1.2 1.4 -1.1 -1.0 1.4 0.1 -0.4 0.2 0.8 0.1 0.9 -1.6 0.5 0.8 1.4 -2.4 1.4 0.1 0.8 0.2 -1.8 -0.9 -0.8 1.9 -1.2 -0.1 -1.2 -1.3 1.6 0.0 -0.1 Chi-square with 42 degrees of freedom:63.500943 z-score=2.345945, p-value=0.982334 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-10-25_22:31 Test no p-value 1 0.994523 2 0.325314 3 0.455315 4 0.162456 5 0.102009 6 0.053625 7 0.145571 8 0.274355 9 0.340673 10 0.786675 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.143997 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-10-25_22:31: (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 66481 0.52 66829 0.40 3 25000.00 25201 1.62 24884 0.54 4 6666.67 6655 0.02 6645 0.07 5 1388.89 1407 0.24 1388 0.00 6 238.10 224 0.83 214 2.44 7 34.72 29 0.94 35 0.00 8 4.96 2 1.77 4 0.19 p=0.56926 p=0.27353 Number of rngs required: 690526, p-value: 0.994 RESULTS OF CRAPS TEST for dh-ranFile-2016-10-25_22:31 No. of wins: Observed Expected 98820 98585.9 z-score= 1.047, pvalue=0.85250 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66641 66666.7 0.010 0.010 2 37706 37654.3 0.071 0.081 3 27140 26954.7 1.273 1.354 4 19407 19313.5 0.453 1.807 5 13745 13851.4 0.818 2.625 6 9963 9943.5 0.038 2.663 7 7197 7145.0 0.378 3.041 8 5097 5139.1 0.344 3.385 9 3590 3699.9 3.262 6.648 10 2539 2666.3 6.078 12.725 11 1963 1923.3 0.818 13.544 12 1434 1388.7 1.475 15.019 13 1017 1003.7 0.176 15.194 14 715 726.1 0.171 15.365 15 515 525.8 0.223 15.589 16 370 381.2 0.326 15.915 17 256 276.5 1.526 17.440 18 207 200.8 0.190 17.630 19 123 146.0 3.619 21.249 20 84 106.2 4.646 25.895 21 291 287.1 0.053 25.948 Chisq= 25.95 for 20 degrees of freedom, p= 0.83246 SUMMARY of craptest p-value for no. of wins: 0.852500 p-value for throws/game: 0.832455 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-10-25_22:31 No. of wins: Observed Expected 98084 98585.9 z-score=-2.245, pvalue=0.01240 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66154 66666.7 3.942 3.942 2 37457 37654.3 1.034 4.976 3 27412 26954.7 7.757 12.734 4 19361 19313.5 0.117 12.851 5 13867 13851.4 0.018 12.868 6 9987 9943.5 0.190 13.058 7 7230 7145.0 1.011 14.069 8 5150 5139.1 0.023 14.092 9 3728 3699.9 0.214 14.306 10 2667 2666.3 0.000 14.306 11 1944 1923.3 0.222 14.528 12 1397 1388.7 0.049 14.577 13 1008 1003.7 0.018 14.596 14 754 726.1 1.069 15.664 15 520 525.8 0.065 15.729 16 367 381.2 0.525 16.255 17 261 276.5 0.873 17.128 18 196 200.8 0.116 17.244 19 138 146.0 0.437 17.681 20 106 106.2 0.000 17.681 21 296 287.1 0.275 17.956 Chisq= 17.96 for 20 degrees of freedom, p= 0.40970 SUMMARY of craptest p-value for no. of wins: 0.012397 p-value for throws/game: 0.409702 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0124,0.0155,0.0200,0.0229,0.0303,0.0344,0.0395,0.0407,0.0471,0.0514, 0.0536,0.0549,0.0555,0.0572,0.0610,0.0658,0.0714,0.0719,0.0857,0.0861, 0.0906,0.0918,0.0931,0.0945,0.0966,0.1001,0.1014,0.1020,0.1074,0.1315, 0.1347,0.1364,0.1426,0.1431,0.1434,0.1439,0.1440,0.1443,0.1446,0.1456, 0.1491,0.1528,0.1556,0.1590,0.1617,0.1625,0.1625,0.1681,0.1686,0.1700, 0.1806,0.1808,0.1938,0.1938,0.1964,0.1991,0.1999,0.2052,0.2072,0.2086, 0.2117,0.2156,0.2165,0.2209,0.2243,0.2247,0.2274,0.2299,0.2325,0.2515, 0.2611,0.2624,0.2735,0.2744,0.2750,0.2807,0.2843,0.2878,0.2969,0.3040, 0.3040,0.3077,0.3165,0.3187,0.3204,0.3240,0.3253,0.3281,0.3336,0.3353, 0.3407,0.3493,0.3547,0.3567,0.3600,0.3601,0.3605,0.3680,0.3682,0.3752, 0.3871,0.3920,0.3920,0.3984,0.4006,0.4028,0.4032,0.4080,0.4086,0.4097, 0.4155,0.4163,0.4169,0.4203,0.4275,0.4279,0.4289,0.4291,0.4292,0.4294, 0.4314,0.4366,0.4455,0.4474,0.4480,0.4525,0.4526,0.4527,0.4537,0.4553, 0.4577,0.4591,0.4609,0.4617,0.4725,0.4752,0.4820,0.4854,0.4874,0.4888, 0.4914,0.4917,0.4945,0.4955,0.4996,0.5137,0.5160,0.5162,0.5211,0.5220, 0.5231,0.5286,0.5386,0.5426,0.5444,0.5454,0.5498,0.5594,0.5664,0.5693, 0.5804,0.5841,0.5851,0.5872,0.5929,0.5956,0.5979,0.5981,0.5986,0.6003, 0.6088,0.6124,0.6204,0.6532,0.6575,0.6603,0.6613,0.6641,0.6645,0.6687, 0.6706,0.6776,0.6809,0.6819,0.6885,0.6898,0.6932,0.6952,0.6983,0.6999, 0.7007,0.7057,0.7101,0.7140,0.7161,0.7170,0.7196,0.7329,0.7330,0.7367, 0.7415,0.7415,0.7507,0.7522,0.7560,0.7562,0.7603,0.7624,0.7624,0.7704, 0.7743,0.7746,0.7798,0.7803,0.7807,0.7852,0.7861,0.7867,0.7867,0.7909, 0.8023,0.8054,0.8135,0.8252,0.8259,0.8277,0.8325,0.8378,0.8411,0.8418, 0.8502,0.8523,0.8525,0.8532,0.8644,0.8677,0.8789,0.8803,0.8824,0.8836, 0.8866,0.8908,0.8924,0.8932,0.8951,0.9098,0.9146,0.9215,0.9230,0.9236, 0.9304,0.9350,0.9360,0.9411,0.9439,0.9484,0.9506,0.9547,0.9622,0.9672, 0.9740,0.9746,0.9747,0.9787,0.9823,0.9829,0.9885,0.9944,0.9945, Overall p-value after applying KStest on 269 p-values = 0.877004 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.