RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-27_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 15.99 18.2256 0.625256 2 to 25 15.79 13.5029 0.298080 3 to 26 15.83 26.2185 0.929429 4 to 27 15.97 12.4052 0.224994 5 to 28 15.93 12.8827 0.256001 6 to 29 15.93 18.6497 0.650993 7 to 30 15.92 22.8177 0.844720 8 to 31 15.68 14.1302 0.342138 9 to 32 15.64 13.8881 0.324993 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.745876 Tough bday spacings test for dh-ranFile-2018-06-27_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 9 36 62 102 103 80 61 27 10 8 2 (O-E)^2/E 0.0 0.0 1.7 0.2 0.3 0.0 1.5 0.3 1.6 0.3 1.0 Birthday Spacings: Sum(O-E)^2/E= 6.991, p= 0.274 RESULTS OF GCD FOR dh-ranFile-2018-06-27_13:31 Euclid's algorithm: p-value, steps to gcd: 0.493297 p-value, dist. of gcd's: 0.676011 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-27_13:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.480 0.454 0.563 0.024 0.562 0.925 0.578 0.965 Bits 8 to 15---> 0.859 0.321 0.725 0.214 0.379 0.522 0.248 0.584 Bits 16 to 23---> 0.061 0.799 0.671 0.490 0.542 0.301 0.893 0.045 Bits 24 to 31---> 0.197 0.877 0.440 0.135 0.748 0.177 0.101 0.380 KS test for the above 32 p values: 0.045 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-27_13:31, p-values for 5 runs: 0.0000, 0.9541, 0.0041, 0.5097, 0.2195 Rank test for binary matrices (31x31) for dh-ranFile-2018-06-27_13:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 220 211.4 0.348 0.348 r= 29 5124 5134.0 0.020 0.368 r= 30 22903 23103.0 1.732 2.100 r= 31 11753 11551.5 3.514 5.614 chi-square = 5.614 with df = 3; p-value = 0.868 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-06-27_13:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 221 211.4 0.434 0.434 r= 30 5157 5134.0 0.103 0.537 r= 31 23077 23103.0 0.029 0.567 r= 32 11545 11551.5 0.004 0.570 chi-square = 0.570 with df = 3; p-value = 0.097 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-06-27_13:31 b-rank test for bits 1 to 8, p=0.68337 b-rank test for bits 2 to 9, p=0.03788 b-rank test for bits 3 to 10, p=0.06832 b-rank test for bits 4 to 11, p=0.82246 b-rank test for bits 5 to 12, p=0.96898 b-rank test for bits 6 to 13, p=0.66956 b-rank test for bits 7 to 14, p=0.67585 b-rank test for bits 8 to 15, p=0.51615 b-rank test for bits 9 to 16, p=0.50384 b-rank test for bits 10 to 17, p=0.54117 b-rank test for bits 11 to 18, p=0.13906 b-rank test for bits 12 to 19, p=0.35408 b-rank test for bits 13 to 20, p=0.75158 b-rank test for bits 14 to 21, p=0.58322 b-rank test for bits 15 to 22, p=0.41261 b-rank test for bits 16 to 23, p=0.59005 b-rank test for bits 17 to 24, p=0.75319 b-rank test for bits 18 to 25, p=0.04950 b-rank test for bits 19 to 26, p=0.20350 b-rank test for bits 20 to 27, p=0.30598 b-rank test for bits 21 to 28, p=0.41765 b-rank test for bits 22 to 29, p=0.57628 b-rank test for bits 23 to 30, p=0.71611 b-rank test for bits 24 to 31, p=0.71944 b-rank test for bits 25 to 32, p=0.79361 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 = 0.542388 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-27_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 141903 -0.01 0.494100 2 141985 0.18 0.570167 3 142045 0.32 0.624373 4 142875 2.26 0.987972 5 142218 0.72 0.764604 6 142312 0.94 0.826601 7 142014 0.24 0.596600 8 141865 -0.10 0.458753 9 141297 -1.43 0.076261 10 141895 -0.03 0.486645 11 142344 1.02 0.845086 12 142240 0.77 0.780119 13 142631 1.69 0.954116 14 142422 1.20 0.884508 15 141596 -0.73 0.232060 16 141604 -0.71 0.237803 17 142451 1.27 0.897169 18 141771 -0.32 0.373272 19 141156 -1.76 0.039194 20 142484 1.34 0.910313 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-06-27_13:31 Bits used No. missing words z-score p-value 23 to 32 141925 0.0540 0.521546 22 to 31 142384 1.6368 0.949163 21 to 30 142510 2.0713 0.980833 20 to 29 141763 -0.5046 0.306925 19 to 28 141924 0.0506 0.520172 18 to 27 142048 0.4782 0.683736 17 to 26 142148 0.8230 0.794746 16 to 25 141879 -0.1046 0.458352 15 to 24 141827 -0.2839 0.388245 14 to 23 141612 -1.0253 0.152617 13 to 22 141826 -0.2873 0.386924 12 to 21 142101 0.6609 0.745672 11 to 20 141787 -0.4218 0.336575 10 to 19 141982 0.2506 0.598933 9 to 18 141717 -0.6632 0.253599 8 to 17 141493 -1.4356 0.075555 7 to 16 141951 0.1437 0.557127 6 to 15 141559 -1.2080 0.113517 5 to 14 142082 0.5954 0.724217 4 to 13 142073 0.5644 0.713752 3 to 12 141790 -0.4115 0.340359 2 to 11 141710 -0.6873 0.245933 1 to 10 141620 -0.9977 0.159215 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-06-27_13:31 Bits used No. missing words z-score p-value 28 to 32 142003 0.3175 0.624578 27 to 31 142099 0.6429 0.739872 26 to 30 141812 -0.3299 0.370726 25 to 29 141643 -0.9028 0.183312 24 to 28 142339 1.4565 0.927374 23 to 27 141813 -0.3265 0.372007 22 to 26 141820 -0.3028 0.381016 21 to 25 141921 0.0396 0.515778 20 to 24 141884 -0.0859 0.465787 19 to 23 141370 -1.8282 0.033757 18 to 22 141958 0.1650 0.565521 17 to 21 141913 0.0124 0.504963 16 to 20 141712 -0.6689 0.251775 15 to 19 141538 -1.2587 0.104061 14 to 18 142055 0.4938 0.689275 13 to 17 141207 -2.3808 0.008638 12 to 16 141932 0.0768 0.530628 11 to 15 141681 -0.7740 0.219465 10 to 14 142277 1.2463 0.893680 9 to 13 141547 -1.2282 0.109679 8 to 12 142239 1.1175 0.868115 7 to 11 142082 0.5853 0.720834 6 to 10 142253 1.1650 0.877987 5 to 9 141663 -0.8350 0.201854 4 to 8 141719 -0.6452 0.259403 3 to 7 141602 -1.0418 0.148753 2 to 6 142130 0.7480 0.772780 1 to 5 141838 -0.2418 0.404469 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-06-27_13:31 Bits used No. missing words z-score p-value 31 to 32 142116 0.6096 0.728952 30 to 31 141936 0.0787 0.531354 29 to 30 141734 -0.5172 0.302509 28 to 29 142142 0.6863 0.753751 27 to 28 142079 0.5005 0.691639 26 to 27 141936 0.0787 0.531354 25 to 26 142506 1.7601 0.960804 24 to 25 142534 1.8427 0.967312 23 to 24 141703 -0.6086 0.271381 22 to 23 142104 0.5742 0.717100 21 to 22 141959 0.1465 0.558244 20 to 21 142166 0.7571 0.775517 19 to 20 141733 -0.5201 0.301480 18 to 19 141545 -1.0747 0.141250 17 to 18 142021 0.3294 0.629077 16 to 17 142347 1.2911 0.901659 15 to 16 141151 -2.2370 0.012644 14 to 15 141575 -0.9862 0.162012 13 to 14 141824 -0.2517 0.400632 12 to 13 141880 -0.0865 0.465527 11 to 12 142596 2.0256 0.978596 10 to 11 141754 -0.4582 0.323404 9 to 10 142633 2.1347 0.983608 8 to 9 142079 0.5005 0.691639 7 to 8 142224 0.9282 0.823356 6 to 7 141560 -1.0305 0.151394 5 to 6 142056 0.4327 0.667367 4 to 5 141530 -1.1190 0.131577 3 to 4 141935 0.0757 0.530180 2 to 3 141878 -0.0924 0.463183 1 to 2 141853 -0.1662 0.434014 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-27_13:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2639.96 1.979 0.976112 Test results for specific bytes for dh-ranFile-2018-06-27_13:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2571.14 1.006 0.842813 2 to 9 2548.75 0.689 0.754702 3 to 10 2505.55 0.079 0.531295 4 to 11 2640.36 1.985 0.976431 5 to 12 2543.94 0.621 0.732819 6 to 13 2470.48 -0.417 0.338172 7 to 14 2568.23 0.965 0.832701 8 to 15 2467.69 -0.457 0.323855 9 to 16 2566.84 0.945 0.827740 10 to 17 2334.53 -2.340 0.009640 11 to 18 2455.55 -0.629 0.264813 12 to 19 2582.10 1.161 0.877196 13 to 20 2649.90 2.120 0.982995 14 to 21 2479.74 -0.287 0.387230 15 to 22 2591.48 1.294 0.902126 16 to 23 2450.36 -0.702 0.241322 17 to 24 2540.60 0.574 0.717067 18 to 25 2386.90 -1.600 0.054850 19 to 26 2537.70 0.533 0.703031 20 to 27 2397.38 -1.451 0.073354 21 to 28 2416.29 -1.184 0.118238 22 to 29 2611.63 1.579 0.942799 23 to 30 2403.24 -1.368 0.085595 24 to 31 2567.12 0.949 0.828744 25 to 32 2521.43 0.303 0.619080 CDPARK for dh-ranFile-2018-06-27_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 3510 -0.5936 0.276387 3520 -0.1370 0.445521 3526 0.1370 0.554479 3524 0.0457 0.518210 3558 1.5982 0.944998 3493 -1.3699 0.085365 3536 0.5936 0.723613 3524 0.0457 0.518210 3535 0.5479 0.708135 3525 0.0913 0.536383 Square side=100, avg. no. parked=3525.10 sample std.=16.08 p-value of the KSTEST for those 10 p-values: 0.628405 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-27_13:31 0.3585,0.1951,0.1348,0.7745,0.0649,0.4064,0.2941,0.4061,0.3134,0.8938, The KS test for those 10 p-values: 0.286150 The 3DSPHERES test for dh-ranFile-2018-06-27_13:31 sample no r^3 equiv. uni. 1 72.168 0.909790 2 23.715 0.546377 3 19.532 0.478517 4 78.966 0.928080 5 19.954 0.485796 6 24.722 0.561355 7 79.680 0.929772 8 21.325 0.508761 9 15.997 0.413290 10 9.182 0.263672 11 9.746 0.277383 12 69.862 0.902582 13 78.241 0.926322 14 20.437 0.494002 15 44.777 0.775206 16 17.438 0.440802 17 8.482 0.246284 18 5.235 0.160137 19 60.559 0.867165 20 3.573 0.112266 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.325187 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-27_13:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.1 0.6 1.1 -0.6 0.7 -1.2 -0.5 0.3 -0.4 1.2 0.4 0.5 -0.2 -2.1 0.9 -0.6 0.2 0.1 -0.9 -1.1 0.5 1.5 1.6 0.4 -1.6 -0.7 1.3 0.7 1.5 0.6 -0.5 -0.3 -1.3 0.3 -0.7 -1.2 0.5 0.5 -1.3 0.1 0.0 -1.1 Chi-square with 42 degrees of freedom:33.771147 z-score=-0.897841, p-value=0.186686 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-06-27_13:31 Test no p-value 1 0.400639 2 0.670448 3 0.020318 4 0.010374 5 0.002208 6 0.466955 7 0.010752 8 0.210646 9 0.679261 10 0.289917 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.002214 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-27_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 66751 0.11 66583 0.11 3 25000.00 24864 0.74 25079 0.25 4 6666.67 6695 0.12 6616 0.39 5 1388.89 1416 0.53 1443 2.11 6 238.10 237 0.01 235 0.04 7 34.72 32 0.21 38 0.31 8 4.96 4 0.19 5 0.00 p=0.07134 p=0.21642 Number of rngs required: 689422, p-value: 0.882 RESULTS OF CRAPS TEST for dh-ranFile-2018-06-27_13:31 No. of wins: Observed Expected 98482 98585.9 z-score=-0.465, pvalue=0.32114 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66567 66666.7 0.149 0.149 2 37606 37654.3 0.062 0.211 3 27030 26954.7 0.210 0.421 4 19415 19313.5 0.534 0.955 5 13992 13851.4 1.427 2.382 6 9978 9943.5 0.119 2.501 7 7237 7145.0 1.184 3.685 8 5061 5139.1 1.186 4.871 9 3680 3699.9 0.107 4.978 10 2528 2666.3 7.173 12.151 11 1879 1923.3 1.022 13.173 12 1384 1388.7 0.016 13.189 13 1003 1003.7 0.001 13.190 14 770 726.1 2.649 15.839 15 473 525.8 5.309 21.148 16 406 381.2 1.620 22.768 17 266 276.5 0.402 23.169 18 198 200.8 0.040 23.209 19 139 146.0 0.334 23.543 20 97 106.2 0.800 24.343 21 291 287.1 0.053 24.395 Chisq= 24.40 for 20 degrees of freedom, p= 0.77446 SUMMARY of craptest p-value for no. of wins: 0.321139 p-value for throws/game: 0.774457 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-27_13:31 No. of wins: Observed Expected 98668 98585.9 z-score= 0.367, pvalue=0.64333 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66917 66666.7 0.940 0.940 2 37455 37654.3 1.055 1.995 3 26925 26954.7 0.033 2.028 4 19328 19313.5 0.011 2.039 5 13805 13851.4 0.156 2.194 6 10082 9943.5 1.928 4.122 7 7232 7145.0 1.059 5.181 8 5059 5139.1 1.248 6.429 9 3609 3699.9 2.232 8.660 10 2607 2666.3 1.319 9.979 11 1985 1923.3 1.977 11.956 12 1409 1388.7 0.296 12.252 13 982 1003.7 0.470 12.722 14 718 726.1 0.091 12.813 15 519 525.8 0.089 12.902 16 374 381.2 0.134 13.036 17 252 276.5 2.178 15.214 18 200 200.8 0.003 15.217 19 142 146.0 0.109 15.326 20 128 106.2 4.468 19.794 21 272 287.1 0.796 20.589 Chisq= 20.59 for 20 degrees of freedom, p= 0.57836 SUMMARY of craptest p-value for no. of wins: 0.643334 p-value for throws/game: 0.578360 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0000,0.0022,0.0022,0.0041,0.0086,0.0096,0.0104,0.0108,0.0126,0.0203, 0.0241,0.0338,0.0379,0.0392,0.0446,0.0451,0.0495,0.0549,0.0608,0.0649, 0.0683,0.0713,0.0734,0.0756,0.0763,0.0854,0.0856,0.0968,0.1008,0.1041, 0.1097,0.1123,0.1135,0.1182,0.1316,0.1348,0.1349,0.1391,0.1413,0.1488, 0.1514,0.1526,0.1592,0.1601,0.1620,0.1766,0.1833,0.1867,0.1951,0.1968, 0.2019,0.2035,0.2106,0.2139,0.2164,0.2195,0.2195,0.2250,0.2321,0.2378, 0.2413,0.2459,0.2463,0.2481,0.2518,0.2536,0.2560,0.2594,0.2637,0.2648, 0.2714,0.2737,0.2764,0.2774,0.2861,0.2899,0.2941,0.2981,0.3008,0.3015, 0.3025,0.3060,0.3069,0.3134,0.3211,0.3212,0.3234,0.3239,0.3250,0.3252, 0.3366,0.3382,0.3404,0.3421,0.3541,0.3585,0.3707,0.3720,0.3733,0.3787, 0.3800,0.3810,0.3869,0.3872,0.3882,0.4006,0.4006,0.4045,0.4061,0.4064, 0.4126,0.4133,0.4177,0.4340,0.4403,0.4408,0.4455,0.4544,0.4584,0.4588, 0.4632,0.4655,0.4658,0.4670,0.4785,0.4795,0.4858,0.4866,0.4903,0.4933, 0.4940,0.4941,0.5038,0.5050,0.5088,0.5097,0.5158,0.5161,0.5182,0.5182, 0.5202,0.5215,0.5218,0.5302,0.5306,0.5313,0.5314,0.5314,0.5364,0.5412, 0.5420,0.5424,0.5464,0.5545,0.5571,0.5582,0.5614,0.5619,0.5635,0.5655, 0.5702,0.5763,0.5780,0.5784,0.5832,0.5842,0.5900,0.5966,0.5989,0.6191, 0.6244,0.6246,0.6253,0.6284,0.6291,0.6433,0.6510,0.6674,0.6696,0.6704, 0.6706,0.6758,0.6760,0.6793,0.6834,0.6837,0.6893,0.6916,0.6916,0.7030, 0.7081,0.7138,0.7161,0.7171,0.7171,0.7194,0.7208,0.7236,0.7242,0.7253, 0.7290,0.7328,0.7399,0.7457,0.7459,0.7477,0.7516,0.7532,0.7538,0.7547, 0.7646,0.7728,0.7745,0.7745,0.7752,0.7755,0.7801,0.7936,0.7947,0.7993, 0.8225,0.8234,0.8266,0.8277,0.8287,0.8327,0.8428,0.8447,0.8451,0.8591, 0.8672,0.8680,0.8681,0.8771,0.8772,0.8780,0.8818,0.8845,0.8927,0.8937, 0.8938,0.8972,0.9017,0.9021,0.9026,0.9098,0.9103,0.9246,0.9263,0.9274, 0.9281,0.9294,0.9298,0.9428,0.9450,0.9492,0.9541,0.9541,0.9608,0.9647, 0.9673,0.9690,0.9761,0.9764,0.9786,0.9808,0.9830,0.9836,0.9880, Overall p-value after applying KStest on 269 p-values = 0.897501 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.