RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-06-30_14:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.83 14.6246 0.377500 2 to 25 16.00 15.7109 0.455588 3 to 26 15.48 17.4130 0.573256 4 to 27 15.62 16.8956 0.538541 5 to 28 15.91 12.8256 0.252219 6 to 29 16.08 19.2755 0.687049 7 to 30 15.87 9.3439 0.071147 8 to 31 16.10 10.2716 0.108163 9 to 32 15.66 18.2818 0.628724 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.440873 Tough bday spacings test for dh-ranFile-2016-06-30_14:31: 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 37 68 98 100 76 55 39 9 2 5 (O-E)^2/E 0.4 0.0 0.4 0.0 0.1 0.1 0.2 2.9 2.3 3.2 0.2 Birthday Spacings: Sum(O-E)^2/E= 9.652, p= 0.528 RESULTS OF GCD FOR dh-ranFile-2016-06-30_14:31 Euclid's algorithm: p-value, steps to gcd: 0.346383 p-value, dist. of gcd's: 0.779086 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-06-30_14:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.378 0.368 0.987 0.261 0.474 0.174 0.894 0.145 Bits 8 to 15---> 0.127 0.720 0.966 0.398 0.945 0.360 0.448 0.258 Bits 16 to 23---> 0.921 0.460 0.884 0.967 0.313 0.253 0.094 0.937 Bits 24 to 31---> 0.765 0.568 0.636 0.093 0.263 0.981 0.760 0.238 KS test for the above 32 p values: 0.769 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-06-30_14:31, p-values for 5 runs: 0.9284, 0.6177, 0.3784, 0.4406, 0.2137 Rank test for binary matrices (31x31) for dh-ranFile-2016-06-30_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 231 211.4 1.814 1.814 r= 29 4981 5134.0 4.560 6.374 r= 30 23121 23103.0 0.014 6.388 r= 31 11667 11551.5 1.154 7.542 chi-square = 7.542 with df = 3; p-value = 0.944 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-06-30_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 200 211.4 0.617 0.617 r= 30 5120 5134.0 0.038 0.655 r= 31 23093 23103.0 0.004 0.659 r= 32 11587 11551.5 0.109 0.768 chi-square = 0.768 with df = 3; p-value = 0.143 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-06-30_14:31 b-rank test for bits 1 to 8, p=0.79961 b-rank test for bits 2 to 9, p=0.50904 b-rank test for bits 3 to 10, p=0.36345 b-rank test for bits 4 to 11, p=0.96905 b-rank test for bits 5 to 12, p=0.92921 b-rank test for bits 6 to 13, p=0.71922 b-rank test for bits 7 to 14, p=0.70142 b-rank test for bits 8 to 15, p=0.79748 b-rank test for bits 9 to 16, p=0.68526 b-rank test for bits 10 to 17, p=0.68472 b-rank test for bits 11 to 18, p=0.41009 b-rank test for bits 12 to 19, p=0.88165 b-rank test for bits 13 to 20, p=0.38158 b-rank test for bits 14 to 21, p=0.79019 b-rank test for bits 15 to 22, p=0.33363 b-rank test for bits 16 to 23, p=0.20606 b-rank test for bits 17 to 24, p=0.07728 b-rank test for bits 18 to 25, p=0.91266 b-rank test for bits 19 to 26, p=0.89494 b-rank test for bits 20 to 27, p=0.42318 b-rank test for bits 21 to 28, p=0.86620 b-rank test for bits 22 to 29, p=0.88580 b-rank test for bits 23 to 30, p=0.48330 b-rank test for bits 24 to 31, p=0.96431 b-rank test for bits 25 to 32, p=0.98923 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 = 0.005216 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-06-30_14:31 (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 141465 -1.04 0.149599 2 142030 0.28 0.611005 3 141934 0.06 0.522982 4 142001 0.21 0.584798 5 142212 0.71 0.760271 6 142111 0.47 0.681248 7 141987 0.18 0.572001 8 142147 0.56 0.710657 9 141855 -0.13 0.449494 10 142026 0.27 0.607417 11 141743 -0.39 0.348778 12 142454 1.27 0.898419 13 141756 -0.36 0.360079 14 141169 -1.73 0.041838 15 141764 -0.34 0.367095 16 142026 0.27 0.607417 17 141799 -0.26 0.398288 18 142317 0.95 0.829578 19 141688 -0.52 0.302534 20 141533 -0.88 0.189626 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-06-30_14:31 Bits used No. missing words z-score p-value 23 to 32 142360 1.5540 0.939912 22 to 31 142076 0.5747 0.717261 21 to 30 141811 -0.3391 0.367279 20 to 29 141782 -0.4391 0.330306 19 to 28 142078 0.5816 0.719589 18 to 27 141569 -1.1736 0.120287 17 to 26 141526 -1.3218 0.093113 16 to 25 142130 0.7609 0.776651 15 to 24 141918 0.0299 0.511925 14 to 23 141675 -0.8080 0.209535 13 to 22 142495 2.0196 0.978285 12 to 21 142126 0.7471 0.772510 11 to 20 141967 0.1989 0.578815 10 to 19 142132 0.7678 0.778705 9 to 18 142145 0.8127 0.791792 8 to 17 142339 1.4816 0.930779 7 to 16 141915 0.0196 0.507800 6 to 15 142086 0.6092 0.728806 5 to 14 142013 0.3575 0.639635 4 to 13 141918 0.0299 0.511925 3 to 12 141899 -0.0356 0.485792 2 to 11 141903 -0.0218 0.491293 1 to 10 142315 1.3989 0.919073 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-06-30_14:31 Bits used No. missing words z-score p-value 28 to 32 142609 2.3718 0.991148 27 to 31 141785 -0.4215 0.336711 26 to 30 142103 0.6565 0.744252 25 to 29 142076 0.5650 0.713957 24 to 28 141982 0.2463 0.597290 23 to 27 141003 -3.0723 0.001062 22 to 26 142093 0.6226 0.733230 21 to 25 141859 -0.1706 0.432265 20 to 24 142253 1.1650 0.877987 19 to 23 141708 -0.6825 0.247470 18 to 22 141774 -0.4587 0.323208 17 to 21 141478 -1.4621 0.071852 16 to 20 141976 0.2260 0.589399 15 to 19 141970 0.2057 0.581472 14 to 18 142152 0.8226 0.794635 13 to 17 142087 0.6023 0.726503 12 to 16 141763 -0.4960 0.309935 11 to 15 141307 -2.0418 0.020586 10 to 14 141431 -1.6215 0.052460 9 to 13 141823 -0.2926 0.384897 8 to 12 141544 -1.2384 0.107783 7 to 11 141593 -1.0723 0.141792 6 to 10 142465 1.8836 0.970192 5 to 9 142531 2.1074 0.982457 4 to 8 141901 -0.0282 0.488737 3 to 7 141713 -0.6655 0.252857 2 to 6 142048 0.4701 0.680847 1 to 5 142095 0.6294 0.735453 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-06-30_14:31 Bits used No. missing words z-score p-value 31 to 32 142000 0.2675 0.605444 30 to 31 142495 1.7276 0.957974 29 to 30 141039 -2.5673 0.005124 28 to 29 142360 1.3294 0.908144 27 to 28 142193 0.8368 0.798643 26 to 27 141775 -0.3963 0.345959 25 to 26 141941 0.0934 0.537216 24 to 25 142039 0.3825 0.648958 23 to 24 141635 -0.8092 0.209191 22 to 23 142072 0.4799 0.684334 21 to 22 141792 -0.3461 0.364632 20 to 21 141675 -0.6912 0.244708 19 to 20 142375 1.3737 0.915226 18 to 19 141907 -0.0069 0.497258 17 to 18 142001 0.2704 0.606579 16 to 17 142193 0.8368 0.798643 15 to 16 141516 -1.1603 0.122970 14 to 15 141752 -0.4641 0.321288 13 to 14 141836 -0.2163 0.414372 12 to 13 142158 0.7335 0.768385 11 to 12 142311 1.1849 0.881965 10 to 11 141674 -0.6942 0.243782 9 to 10 142080 0.5035 0.692677 8 to 9 141863 -0.1367 0.445647 7 to 8 141600 -0.9125 0.180759 6 to 7 141872 -0.1101 0.456158 5 to 6 141626 -0.8358 0.201639 4 to 5 141935 0.0757 0.530180 3 to 4 141198 -2.0983 0.017939 2 to 3 142221 0.9194 0.821052 1 to 2 141920 0.0315 0.512555 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-06-30_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2487.31 -0.179 0.428794 Test results for specific bytes for dh-ranFile-2016-06-30_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2515.41 0.218 0.586270 2 to 9 2584.47 1.195 0.883869 3 to 10 2417.39 -1.168 0.121355 4 to 11 2472.35 -0.391 0.347899 5 to 12 2448.31 -0.731 0.232366 6 to 13 2448.53 -0.728 0.233332 7 to 14 2488.89 -0.157 0.437593 8 to 15 2418.46 -1.153 0.124436 9 to 16 2488.87 -0.157 0.437459 10 to 17 2606.89 1.512 0.934685 11 to 18 2620.20 1.700 0.955423 12 to 19 2403.73 -1.361 0.086681 13 to 20 2500.63 0.009 0.503577 14 to 21 2462.25 -0.534 0.296709 15 to 22 2451.77 -0.682 0.247595 16 to 23 2491.13 -0.125 0.450074 17 to 24 2511.80 0.167 0.566257 18 to 25 2411.66 -1.249 0.105784 19 to 26 2495.48 -0.064 0.474519 20 to 27 2507.70 0.109 0.543362 21 to 28 2568.18 0.964 0.832522 22 to 29 2521.44 0.303 0.619149 23 to 30 2521.03 0.297 0.616926 24 to 31 2361.28 -1.962 0.024894 25 to 32 2407.74 -1.305 0.095996 CDPARK for dh-ranFile-2016-06-30_14:31: 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 3499 -1.0959 0.136563 3517 -0.2740 0.392053 3528 0.2283 0.590298 3512 -0.5023 0.307734 3536 0.5936 0.723613 3479 -2.0091 0.022262 3514 -0.4110 0.340551 3555 1.4612 0.928018 3494 -1.3242 0.092718 3518 -0.2283 0.409702 Square side=100, avg. no. parked=3515.20 sample std.=20.56 p-value of the KSTEST for those 10 p-values: 0.457758 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-06-30_14:31 0.9896,0.8761,0.5091,0.4475,0.6172,0.8695,0.8355,0.9748,0.1821,0.6467, The KS test for those 10 p-values: 0.042585 The 3DSPHERES test for dh-ranFile-2016-06-30_14:31 sample no r^3 equiv. uni. 1 109.371 0.973897 2 23.607 0.544739 3 7.416 0.219009 4 33.759 0.675440 5 10.880 0.304186 6 16.431 0.421719 7 3.531 0.111023 8 27.326 0.597830 9 6.817 0.203275 10 27.256 0.596885 11 16.862 0.429966 12 14.705 0.387485 13 19.620 0.480045 14 104.978 0.969781 15 24.008 0.550787 16 3.306 0.104343 17 20.333 0.492258 18 88.664 0.947946 19 4.103 0.127831 20 41.986 0.753285 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.724931 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-06-30_14:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -0.3 -1.1 0.9 -0.5 0.9 1.2 0.8 -0.6 0.5 0.7 -1.2 1.0 -2.4 1.2 1.6 0.4 -0.1 0.8 -0.5 0.2 -1.0 -0.6 -2.4 0.2 0.3 -0.1 0.8 -1.9 2.1 -0.5 -0.5 -0.0 -0.1 1.2 1.0 1.0 0.8 1.7 0.4 -0.6 -1.0 -1.1 Chi-square with 42 degrees of freedom:45.418696 z-score=0.373010, p-value=0.668468 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-06-30_14:31 Test no p-value 1 0.602862 2 0.142135 3 0.955303 4 0.135807 5 0.338232 6 0.251079 7 0.878505 8 0.376243 9 0.361595 10 0.912744 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.757593 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-06-30_14:31: (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 66709 0.03 66832 0.41 3 25000.00 24940 0.14 24779 1.95 4 6666.67 6677 0.02 6723 0.48 5 1388.89 1396 0.04 1365 0.41 6 238.10 245 0.20 253 0.93 7 34.72 28 1.30 42 1.53 8 4.96 4 0.19 5 0.00 p=0.07221 p=0.54359 Number of rngs required: 689142, p-value: 0.804 RESULTS OF CRAPS TEST for dh-ranFile-2016-06-30_14:31 No. of wins: Observed Expected 98744 98585.9 z-score= 0.707, pvalue=0.76031 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66688 66666.7 0.007 0.007 2 37720 37654.3 0.115 0.121 3 26988 26954.7 0.041 0.162 4 19174 19313.5 1.007 1.169 5 13872 13851.4 0.031 1.200 6 9886 9943.5 0.333 1.533 7 7188 7145.0 0.258 1.792 8 5241 5139.1 2.022 3.813 9 3630 3699.9 1.319 5.132 10 2675 2666.3 0.028 5.161 11 1902 1923.3 0.237 5.397 12 1380 1388.7 0.055 5.452 13 977 1003.7 0.711 6.163 14 717 726.1 0.115 6.279 15 542 525.8 0.497 6.775 16 408 381.2 1.891 8.667 17 282 276.5 0.108 8.775 18 197 200.8 0.073 8.848 19 147 146.0 0.007 8.855 20 113 106.2 0.433 9.288 21 273 287.1 0.694 9.982 Chisq= 9.98 for 20 degrees of freedom, p= 0.03150 SUMMARY of craptest p-value for no. of wins: 0.760310 p-value for throws/game: 0.031501 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-06-30_14:31 No. of wins: Observed Expected 98534 98585.9 z-score=-0.232, pvalue=0.40829 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66329 66666.7 1.710 1.710 2 37875 37654.3 1.293 3.004 3 26852 26954.7 0.392 3.395 4 19239 19313.5 0.287 3.682 5 13929 13851.4 0.435 4.117 6 9953 9943.5 0.009 4.126 7 7378 7145.0 7.596 11.722 8 5064 5139.1 1.097 12.819 9 3725 3699.9 0.171 12.990 10 2692 2666.3 0.248 13.237 11 1924 1923.3 0.000 13.238 12 1412 1388.7 0.390 13.627 13 980 1003.7 0.560 14.188 14 725 726.1 0.002 14.189 15 505 525.8 0.826 15.015 16 391 381.2 0.255 15.269 17 271 276.5 0.111 15.380 18 205 200.8 0.087 15.467 19 145 146.0 0.007 15.474 20 110 106.2 0.135 15.609 21 296 287.1 0.275 15.884 Chisq= 15.88 for 20 degrees of freedom, p= 0.27618 SUMMARY of craptest p-value for no. of wins: 0.408292 p-value for throws/game: 0.276177 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0011,0.0051,0.0052,0.0179,0.0206,0.0223,0.0249,0.0315,0.0418,0.0426, 0.0525,0.0711,0.0719,0.0722,0.0773,0.0867,0.0927,0.0927,0.0931,0.0943, 0.0960,0.1043,0.1058,0.1078,0.1082,0.1110,0.1203,0.1214,0.1230,0.1244, 0.1270,0.1278,0.1358,0.1366,0.1418,0.1421,0.1429,0.1447,0.1496,0.1740, 0.1808,0.1821,0.1896,0.2016,0.2033,0.2061,0.2092,0.2095,0.2137,0.2190, 0.2324,0.2333,0.2381,0.2438,0.2447,0.2475,0.2476,0.2511,0.2522,0.2528, 0.2529,0.2578,0.2611,0.2630,0.2762,0.2967,0.3025,0.3042,0.3077,0.3099, 0.3126,0.3213,0.3232,0.3303,0.3336,0.3367,0.3382,0.3406,0.3460,0.3464, 0.3479,0.3488,0.3599,0.3601,0.3616,0.3635,0.3646,0.3671,0.3673,0.3680, 0.3762,0.3775,0.3777,0.3784,0.3816,0.3849,0.3875,0.3921,0.3975,0.3983, 0.4083,0.4097,0.4101,0.4144,0.4217,0.4232,0.4288,0.4300,0.4323,0.4375, 0.4376,0.4406,0.4409,0.4456,0.4475,0.4483,0.4495,0.4501,0.4556,0.4562, 0.4578,0.4600,0.4735,0.4745,0.4800,0.4833,0.4858,0.4887,0.4913,0.4923, 0.4973,0.5036,0.5078,0.5090,0.5091,0.5119,0.5119,0.5126,0.5230,0.5285, 0.5302,0.5372,0.5385,0.5434,0.5436,0.5447,0.5508,0.5663,0.5684,0.5720, 0.5733,0.5788,0.5815,0.5848,0.5863,0.5894,0.5903,0.5969,0.5973,0.5978, 0.6029,0.6054,0.6066,0.6074,0.6074,0.6110,0.6169,0.6172,0.6177,0.6191, 0.6287,0.6360,0.6396,0.6467,0.6490,0.6685,0.6754,0.6808,0.6812,0.6843, 0.6847,0.6853,0.6870,0.6927,0.7014,0.7107,0.7140,0.7173,0.7192,0.7196, 0.7199,0.7236,0.7249,0.7265,0.7288,0.7332,0.7355,0.7443,0.7533,0.7576, 0.7603,0.7603,0.7604,0.7648,0.7684,0.7694,0.7725,0.7767,0.7787,0.7791, 0.7902,0.7918,0.7946,0.7975,0.7986,0.7986,0.7996,0.8036,0.8211,0.8296, 0.8325,0.8355,0.8662,0.8695,0.8761,0.8780,0.8785,0.8817,0.8820,0.8837, 0.8839,0.8858,0.8944,0.8949,0.8984,0.9081,0.9127,0.9127,0.9152,0.9191, 0.9206,0.9280,0.9284,0.9292,0.9308,0.9347,0.9368,0.9399,0.9435,0.9449, 0.9479,0.9553,0.9554,0.9580,0.9643,0.9664,0.9672,0.9690,0.9698,0.9702, 0.9739,0.9748,0.9783,0.9812,0.9825,0.9873,0.9892,0.9896,0.9911, Overall p-value after applying KStest on 269 p-values = 0.290361 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.