RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-08-25_07:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.86 23.6510 0.870767 2 to 25 15.39 26.7219 0.937725 3 to 26 15.67 16.3528 0.501020 4 to 27 15.72 21.3796 0.790232 5 to 28 15.49 20.1923 0.735489 6 to 29 15.55 17.2724 0.563938 7 to 30 15.59 21.8194 0.808236 8 to 31 15.73 14.1149 0.341048 9 to 32 15.40 30.6282 0.977846 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.032459 Tough bday spacings test for dh-ranFile-2016-08-25_07:31: 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 7 31 73 98 109 75 49 31 20 2 5 (O-E)^2/E 0.5 0.9 0.0 0.0 1.3 0.1 0.2 0.1 1.8 3.2 0.2 Birthday Spacings: Sum(O-E)^2/E= 8.241, p= 0.395 RESULTS OF GCD FOR dh-ranFile-2016-08-25_07:31 Euclid's algorithm: p-value, steps to gcd: 0.440993 p-value, dist. of gcd's: 0.042943 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-08-25_07:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.318 0.573 0.021 0.474 0.148 0.417 0.090 0.280 Bits 8 to 15---> 0.705 0.612 0.838 0.215 0.866 0.424 0.101 0.161 Bits 16 to 23---> 0.440 0.910 0.589 0.521 0.170 0.148 0.317 0.479 Bits 24 to 31---> 0.799 0.265 0.783 0.849 0.994 0.368 0.006 0.506 KS test for the above 32 p values: 0.415 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-08-25_07:31, p-values for 5 runs: 0.8160, 0.7065, 0.4433, 0.4054, 0.3633 Rank test for binary matrices (31x31) for dh-ranFile-2016-08-25_07:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 207 211.4 0.092 0.092 r= 29 5041 5134.0 1.685 1.777 r= 30 23017 23103.0 0.320 2.098 r= 31 11735 11551.5 2.914 5.012 chi-square = 5.012 with df = 3; p-value = 0.829 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-08-25_07:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 196 211.4 1.124 1.124 r= 30 5083 5134.0 0.507 1.631 r= 31 23123 23103.0 0.017 1.648 r= 32 11598 11551.5 0.187 1.835 chi-square = 1.835 with df = 3; p-value = 0.393 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-08-25_07:31 b-rank test for bits 1 to 8, p=0.98206 b-rank test for bits 2 to 9, p=0.62261 b-rank test for bits 3 to 10, p=0.45858 b-rank test for bits 4 to 11, p=0.01760 b-rank test for bits 5 to 12, p=0.72608 b-rank test for bits 6 to 13, p=0.23645 b-rank test for bits 7 to 14, p=0.11112 b-rank test for bits 8 to 15, p=0.69550 b-rank test for bits 9 to 16, p=0.06930 b-rank test for bits 10 to 17, p=0.35263 b-rank test for bits 11 to 18, p=0.65357 b-rank test for bits 12 to 19, p=0.01187 b-rank test for bits 13 to 20, p=0.04231 b-rank test for bits 14 to 21, p=0.09269 b-rank test for bits 15 to 22, p=0.55257 b-rank test for bits 16 to 23, p=0.99418 b-rank test for bits 17 to 24, p=0.36906 b-rank test for bits 18 to 25, p=0.70203 b-rank test for bits 19 to 26, p=0.88871 b-rank test for bits 20 to 27, p=0.92018 b-rank test for bits 21 to 28, p=0.70653 b-rank test for bits 22 to 29, p=0.71018 b-rank test for bits 23 to 30, p=0.55822 b-rank test for bits 24 to 31, p=0.22827 b-rank test for bits 25 to 32, p=0.33178 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 = 0.607140 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-08-25_07:31 (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 141805 -0.24 0.403708 2 141475 -1.01 0.155103 3 141417 -1.15 0.125009 4 142193 0.66 0.746264 5 141478 -1.01 0.156780 6 142268 0.84 0.798989 7 142544 1.48 0.930946 8 141983 0.17 0.568331 9 141595 -0.73 0.231348 10 141598 -0.73 0.233489 11 141747 -0.38 0.352242 12 142394 1.13 0.871268 13 142100 0.45 0.672017 14 142054 0.34 0.632324 15 142194 0.67 0.747012 16 141914 0.01 0.504353 17 141710 -0.47 0.320706 18 142137 0.53 0.702616 19 142050 0.33 0.628797 20 142317 0.95 0.829578 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-08-25_07:31 Bits used No. missing words z-score p-value 23 to 32 142294 1.3264 0.907654 22 to 31 141846 -0.2184 0.413567 21 to 30 141512 -1.3701 0.085327 20 to 29 141742 -0.5770 0.281970 19 to 28 142027 0.4058 0.657540 18 to 27 141733 -0.6080 0.271582 17 to 26 141755 -0.5322 0.297303 16 to 25 141839 -0.2425 0.404190 15 to 24 141692 -0.7494 0.226804 14 to 23 141720 -0.6529 0.256923 13 to 22 141945 0.1230 0.548947 12 to 21 141767 -0.4908 0.311786 11 to 20 142372 1.5954 0.944690 10 to 19 141476 -1.4942 0.067556 9 to 18 142442 1.8368 0.966880 8 to 17 142222 1.0782 0.859522 7 to 16 141786 -0.4253 0.335318 6 to 15 142233 1.1161 0.867811 5 to 14 142241 1.1437 0.873624 4 to 13 142265 1.2264 0.889985 3 to 12 141838 -0.2460 0.402855 2 to 11 142000 0.3127 0.622729 1 to 10 141875 -0.1184 0.452884 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-08-25_07:31 Bits used No. missing words z-score p-value 28 to 32 141711 -0.6723 0.250695 27 to 31 142034 0.4226 0.663710 26 to 30 142138 0.7752 0.780875 25 to 29 142163 0.8599 0.805077 24 to 28 141879 -0.1028 0.459056 23 to 27 142135 0.7650 0.777859 22 to 26 141499 -1.3909 0.082120 21 to 25 141432 -1.6181 0.052824 20 to 24 141953 0.1480 0.558842 19 to 23 141972 0.2124 0.584118 18 to 22 142411 1.7006 0.955489 17 to 21 142042 0.4497 0.673547 16 to 20 141692 -0.7367 0.230649 15 to 19 141586 -1.0960 0.136532 14 to 18 141749 -0.5435 0.293396 13 to 17 142328 1.4192 0.922083 12 to 16 142702 2.6870 0.996395 11 to 15 141918 0.0294 0.511723 10 to 14 141976 0.2260 0.589399 9 to 13 141707 -0.6859 0.246399 8 to 12 141907 -0.0079 0.496849 7 to 11 141452 -1.5503 0.060538 6 to 10 142159 0.8463 0.801318 5 to 9 141614 -1.0011 0.158385 4 to 8 142095 0.6294 0.735453 3 to 7 142002 0.3141 0.623291 2 to 6 141862 -0.1604 0.436267 1 to 5 141833 -0.2587 0.397916 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-08-25_07:31 Bits used No. missing words z-score p-value 31 to 32 142683 2.2822 0.988762 30 to 31 141445 -1.3697 0.085390 29 to 30 142006 0.2852 0.612240 28 to 29 141434 -1.4022 0.080435 27 to 28 141904 -0.0157 0.493728 26 to 27 141922 0.0374 0.514907 25 to 26 142579 1.9754 0.975890 24 to 25 141739 -0.5024 0.307676 23 to 24 141968 0.1731 0.568701 22 to 23 142467 1.6450 0.950020 21 to 22 141445 -1.3697 0.085390 20 to 21 142465 1.6391 0.949408 19 to 20 141260 -1.9154 0.027719 18 to 19 141265 -1.9007 0.028672 17 to 18 141966 0.1672 0.566381 16 to 17 141882 -0.0806 0.467872 15 to 16 142173 0.7778 0.781653 14 to 15 142320 1.2114 0.887132 13 to 14 141459 -1.3284 0.092022 12 to 13 142224 0.9282 0.823356 11 to 12 142368 1.3530 0.911974 10 to 11 141841 -0.2016 0.420129 9 to 10 141511 -1.1750 0.119994 8 to 9 142008 0.2911 0.614498 7 to 8 142370 1.3589 0.912912 6 to 7 142083 0.5123 0.695780 5 to 6 142194 0.8397 0.799471 4 to 5 141893 -0.0482 0.480790 3 to 4 142078 0.4976 0.690600 2 to 3 141750 -0.4700 0.319178 1 to 2 142553 1.8987 0.971200 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-08-25_07:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2465.66 -0.486 0.313625 Test results for specific bytes for dh-ranFile-2016-08-25_07:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2471.01 -0.410 0.340915 2 to 9 2539.56 0.560 0.712091 3 to 10 2575.65 1.070 0.857665 4 to 11 2585.97 1.216 0.887958 5 to 12 2610.58 1.564 0.941070 6 to 13 2420.09 -1.130 0.129207 7 to 14 2443.93 -0.793 0.213919 8 to 15 2540.95 0.579 0.718748 9 to 16 2499.26 -0.010 0.495831 10 to 17 2470.19 -0.422 0.336680 11 to 18 2499.89 -0.002 0.499379 12 to 19 2406.38 -1.324 0.092759 13 to 20 2716.55 3.062 0.998902 14 to 21 2510.17 0.144 0.557189 15 to 22 2438.64 -0.868 0.192774 16 to 23 2489.77 -0.145 0.442501 17 to 24 2542.60 0.602 0.726572 18 to 25 2476.41 -0.334 0.369341 19 to 26 2518.68 0.264 0.604192 20 to 27 2413.15 -1.228 0.109675 21 to 28 2513.71 0.194 0.576878 22 to 29 2551.17 0.724 0.765352 23 to 30 2648.34 2.098 0.982043 24 to 31 2540.02 0.566 0.714272 25 to 32 2489.09 -0.154 0.438686 CDPARK for dh-ranFile-2016-08-25_07:31: 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 3511 -0.5479 0.291865 3479 -2.0091 0.022262 3510 -0.5936 0.276387 3515 -0.3653 0.357445 3553 1.3699 0.914635 3537 0.6393 0.738676 3528 0.2283 0.590298 3540 0.7763 0.781201 3494 -1.3242 0.092718 3544 0.9589 0.831196 Square side=100, avg. no. parked=3521.10 sample std.=22.29 p-value of the KSTEST for those 10 p-values: 0.962876 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-08-25_07:31 0.4294,0.3101,0.2925,0.4918,0.5800,0.3245,0.6433,0.0577,0.5367,0.0136, The KS test for those 10 p-values: 0.160490 The 3DSPHERES test for dh-ranFile-2016-08-25_07:31 sample no r^3 equiv. uni. 1 18.623 0.462474 2 81.327 0.933522 3 5.373 0.163990 4 22.759 0.531691 5 43.823 0.767939 6 65.268 0.886459 7 19.593 0.479567 8 10.428 0.293609 9 34.756 0.686056 10 34.222 0.680412 11 104.231 0.969018 12 35.996 0.698762 13 24.365 0.556098 14 28.534 0.613694 15 44.889 0.776044 16 3.565 0.112040 17 3.773 0.118188 18 2.385 0.076422 19 96.490 0.959899 20 16.897 0.430637 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.604235 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-08-25_07:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.5 0.6 -0.7 -0.1 -0.1 0.1 -1.7 0.7 0.9 0.6 0.7 0.3 0.4 0.1 -0.9 -0.4 -1.2 0.1 0.8 0.2 0.7 -0.8 -1.8 1.8 0.0 0.9 -1.5 0.0 -0.4 0.5 0.4 -1.6 0.9 1.0 0.2 0.0 0.2 -0.8 -0.7 3.9 -1.0 -1.1 Chi-square with 42 degrees of freedom:43.289107 z-score=0.140653, p-value=0.583898 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-08-25_07:31 Test no p-value 1 0.234763 2 0.574393 3 0.338953 4 0.051200 5 0.459068 6 0.006973 7 0.744676 8 0.518615 9 0.788956 10 0.951190 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.868933 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-08-25_07:31: (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 66528 0.29 66480 0.52 3 25000.00 24921 0.25 24987 0.01 4 6666.67 6828 3.90 6790 2.28 5 1388.89 1439 1.81 1448 2.52 6 238.10 248 0.41 248 0.41 7 34.72 30 0.64 40 0.80 8 4.96 5 0.00 6 0.22 p=0.70637 p=0.65636 Number of rngs required: 690621, p-value: 0.996 RESULTS OF CRAPS TEST for dh-ranFile-2016-08-25_07:31 No. of wins: Observed Expected 98714 98585.9 z-score= 0.573, pvalue=0.71672 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66868 66666.7 0.608 0.608 2 37742 37654.3 0.204 0.812 3 27055 26954.7 0.373 1.185 4 19200 19313.5 0.667 1.852 5 13779 13851.4 0.379 2.230 6 9912 9943.5 0.100 2.330 7 7035 7145.0 1.694 4.025 8 5180 5139.1 0.326 4.351 9 3680 3699.9 0.107 4.457 10 2621 2666.3 0.770 5.227 11 1924 1923.3 0.000 5.227 12 1378 1388.7 0.083 5.310 13 1012 1003.7 0.068 5.379 14 720 726.1 0.052 5.430 15 538 525.8 0.281 5.712 16 371 381.2 0.270 5.982 17 264 276.5 0.569 6.551 18 180 200.8 2.160 8.711 19 150 146.0 0.110 8.822 20 110 106.2 0.135 8.957 21 281 287.1 0.130 9.087 Chisq= 9.09 for 20 degrees of freedom, p= 0.01812 SUMMARY of craptest p-value for no. of wins: 0.716719 p-value for throws/game: 0.018120 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-08-25_07:31 No. of wins: Observed Expected 98314 98585.9 z-score=-1.216, pvalue=0.11201 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66572 66666.7 0.134 0.134 2 37590 37654.3 0.110 0.244 3 27140 26954.7 1.273 1.518 4 19427 19313.5 0.667 2.185 5 13977 13851.4 1.139 3.324 6 9979 9943.5 0.126 3.450 7 7022 7145.0 2.118 5.568 8 5151 5139.1 0.028 5.596 9 3556 3699.9 5.594 11.190 10 2658 2666.3 0.026 11.216 11 1990 1923.3 2.311 13.527 12 1398 1388.7 0.062 13.589 13 962 1003.7 1.734 15.322 14 694 726.1 1.423 16.745 15 525 525.8 0.001 16.746 16 344 381.2 3.621 20.367 17 280 276.5 0.043 20.411 18 208 200.8 0.256 20.667 19 139 146.0 0.334 21.001 20 100 106.2 0.364 21.365 21 288 287.1 0.003 21.367 Chisq= 21.37 for 20 degrees of freedom, p= 0.62420 SUMMARY of craptest p-value for no. of wins: 0.112010 p-value for throws/game: 0.624200 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0065,0.0070,0.0119,0.0136,0.0176,0.0181,0.0205,0.0223,0.0277,0.0287, 0.0325,0.0423,0.0429,0.0512,0.0528,0.0577,0.0605,0.0676,0.0693,0.0764, 0.0804,0.0821,0.0853,0.0854,0.0854,0.0905,0.0920,0.0927,0.0927,0.0928, 0.1012,0.1097,0.1111,0.1120,0.1120,0.1182,0.1200,0.1250,0.1292,0.1365, 0.1478,0.1479,0.1551,0.1568,0.1584,0.1605,0.1607,0.1640,0.1698,0.1928, 0.2139,0.2155,0.2268,0.2283,0.2306,0.2313,0.2335,0.2348,0.2364,0.2464, 0.2507,0.2569,0.2654,0.2716,0.2764,0.2800,0.2820,0.2919,0.2925,0.2934, 0.2936,0.2973,0.3077,0.3101,0.3118,0.3136,0.3174,0.3184,0.3192,0.3207, 0.3245,0.3318,0.3353,0.3367,0.3390,0.3409,0.3410,0.3522,0.3526,0.3574, 0.3633,0.3683,0.3691,0.3693,0.3927,0.3947,0.3979,0.4029,0.4037,0.4042, 0.4054,0.4136,0.4147,0.4170,0.4201,0.4236,0.4294,0.4306,0.4363,0.4387, 0.4399,0.4410,0.4425,0.4433,0.4529,0.4586,0.4591,0.4591,0.4625,0.4679, 0.4742,0.4786,0.4796,0.4808,0.4918,0.4937,0.4958,0.4968,0.4994,0.5010, 0.5044,0.5060,0.5117,0.5149,0.5186,0.5214,0.5317,0.5367,0.5489,0.5526, 0.5561,0.5572,0.5582,0.5588,0.5639,0.5664,0.5683,0.5687,0.5731,0.5744, 0.5769,0.5800,0.5839,0.5841,0.5887,0.5894,0.5903,0.6042,0.6042,0.6071, 0.6117,0.6122,0.6137,0.6145,0.6226,0.6227,0.6233,0.6242,0.6288,0.6323, 0.6433,0.6536,0.6564,0.6575,0.6637,0.6720,0.6735,0.6804,0.6861,0.6906, 0.6955,0.6958,0.6988,0.7020,0.7026,0.7047,0.7064,0.7065,0.7065,0.7102, 0.7121,0.7143,0.7167,0.7187,0.7261,0.7266,0.7355,0.7355,0.7387,0.7447, 0.7463,0.7470,0.7654,0.7679,0.7760,0.7779,0.7809,0.7812,0.7817,0.7835, 0.7890,0.7902,0.7990,0.7993,0.7995,0.8013,0.8051,0.8082,0.8160,0.8234, 0.8291,0.8296,0.8312,0.8385,0.8488,0.8577,0.8595,0.8658,0.8678,0.8689, 0.8708,0.8713,0.8736,0.8865,0.8871,0.8880,0.8887,0.8900,0.9077,0.9103, 0.9120,0.9129,0.9146,0.9202,0.9221,0.9309,0.9335,0.9377,0.9411,0.9447, 0.9494,0.9500,0.9512,0.9555,0.9599,0.9629,0.9669,0.9690,0.9712,0.9759, 0.9778,0.9820,0.9821,0.9888,0.9942,0.9943,0.9960,0.9964,0.9989, Overall p-value after applying KStest on 269 p-values = 0.622580 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.