RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-11-04_12:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.96 12.8362 0.252917 2 to 25 15.79 17.1512 0.555830 3 to 26 16.06 11.9315 0.195732 4 to 27 15.46 35.1385 0.994034 5 to 28 15.54 23.0292 0.851698 6 to 29 15.74 35.0818 0.993931 7 to 30 15.76 13.8748 0.324057 8 to 31 15.80 20.1421 0.732972 9 to 32 15.57 28.5218 0.960802 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.041964 Tough bday spacings test for dh-ranFile-2015-11-04_12:31: 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 85 102 91 79 47 24 15 5 7 (O-E)^2/E 0.0 0.0 1.9 0.2 0.5 0.0 0.5 1.1 0.0 0.4 2.1 Birthday Spacings: Sum(O-E)^2/E= 6.681, p= 0.245 RESULTS OF GCD FOR dh-ranFile-2015-11-04_12:31 Euclid's algorithm: p-value, steps to gcd: 0.799639 p-value, dist. of gcd's: 0.336996 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-11-04_12:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.123 0.641 0.944 0.302 0.294 0.068 0.479 0.929 Bits 8 to 15---> 0.458 0.919 0.534 0.576 0.689 0.767 0.113 0.743 Bits 16 to 23---> 0.536 0.463 0.481 0.859 0.325 0.081 0.409 0.437 Bits 24 to 31---> 0.058 0.348 0.401 0.425 0.999 0.925 0.652 0.964 KS test for the above 32 p values: 0.421 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-11-04_12:31, p-values for 5 runs: 0.1918, 0.8056, 0.4823, 0.4055, 0.9159 Rank test for binary matrices (31x31) for dh-ranFile-2015-11-04_12:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 213 211.4 0.012 0.012 r= 29 5161 5134.0 0.142 0.154 r= 30 23193 23103.0 0.350 0.504 r= 31 11433 11551.5 1.216 1.720 chi-square = 1.720 with df = 3; p-value = 0.368 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-11-04_12:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 198 211.4 0.852 0.852 r= 30 5043 5134.0 1.613 2.465 r= 31 23131 23103.0 0.034 2.499 r= 32 11628 11551.5 0.506 3.005 chi-square = 3.005 with df = 3; p-value = 0.609 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-11-04_12:31 b-rank test for bits 1 to 8, p=0.60529 b-rank test for bits 2 to 9, p=0.27910 b-rank test for bits 3 to 10, p=0.45257 b-rank test for bits 4 to 11, p=0.76535 b-rank test for bits 5 to 12, p=0.67736 b-rank test for bits 6 to 13, p=0.19193 b-rank test for bits 7 to 14, p=0.34024 b-rank test for bits 8 to 15, p=0.72057 b-rank test for bits 9 to 16, p=0.23367 b-rank test for bits 10 to 17, p=0.59532 b-rank test for bits 11 to 18, p=0.92544 b-rank test for bits 12 to 19, p=0.67621 b-rank test for bits 13 to 20, p=0.54469 b-rank test for bits 14 to 21, p=0.09690 b-rank test for bits 15 to 22, p=0.21435 b-rank test for bits 16 to 23, p=0.42253 b-rank test for bits 17 to 24, p=0.24173 b-rank test for bits 18 to 25, p=0.94198 b-rank test for bits 19 to 26, p=0.21548 b-rank test for bits 20 to 27, p=0.15992 b-rank test for bits 21 to 28, p=0.98421 b-rank test for bits 22 to 29, p=0.99669 b-rank test for bits 23 to 30, p=0.97482 b-rank test for bits 24 to 31, p=0.70797 b-rank test for bits 25 to 32, p=0.97899 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 = 0.192865 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-11-04_12:31 (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 141697 -0.50 0.309913 2 140769 -2.66 0.003857 3 142060 0.35 0.637593 4 142263 0.83 0.795692 5 141997 0.20 0.581150 6 141704 -0.48 0.315705 7 141760 -0.35 0.363582 8 141561 -0.81 0.207864 9 141796 -0.26 0.395586 10 142061 0.35 0.638469 11 141313 -1.39 0.081765 12 141850 -0.14 0.444875 13 141513 -0.93 0.177222 14 141638 -0.63 0.263057 15 142233 0.76 0.775247 16 141222 -1.61 0.054147 17 141835 -0.17 0.431063 18 142032 0.29 0.612795 19 142697 1.84 0.967142 20 141344 -1.32 0.093273 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-11-04_12:31 Bits used No. missing words z-score p-value 23 to 32 142207 1.0264 0.847660 22 to 31 142069 0.5506 0.709041 21 to 30 141860 -0.1701 0.432464 20 to 29 141829 -0.2770 0.390890 19 to 28 141376 -1.8391 0.032953 18 to 27 141634 -0.9494 0.171205 17 to 26 141784 -0.4322 0.332808 16 to 25 141667 -0.8356 0.201684 15 to 24 141434 -1.6391 0.050599 14 to 23 141488 -1.4529 0.073131 13 to 22 141691 -0.7529 0.225766 12 to 21 141158 -2.5908 0.004788 11 to 20 141747 -0.5598 0.287822 10 to 19 141172 -2.5425 0.005503 9 to 18 141799 -0.3804 0.351806 8 to 17 141603 -1.0563 0.145413 7 to 16 141794 -0.3977 0.345430 6 to 15 141962 0.1816 0.572060 5 to 14 142054 0.4989 0.691062 4 to 13 141807 -0.3529 0.362096 3 to 12 142297 1.3368 0.909355 2 to 11 141976 0.2299 0.590914 1 to 10 141717 -0.6632 0.253599 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-11-04_12:31 Bits used No. missing words z-score p-value 28 to 32 141993 0.2836 0.611652 27 to 31 141665 -0.8282 0.203768 26 to 30 142423 1.7413 0.959181 25 to 29 141733 -0.5977 0.275010 24 to 28 141999 0.3040 0.619423 23 to 27 142154 0.8294 0.796558 22 to 26 142270 1.2226 0.889262 21 to 25 141888 -0.0723 0.471180 20 to 24 141844 -0.2215 0.412368 19 to 23 142090 0.6124 0.729877 18 to 22 142265 1.2057 0.886026 17 to 21 142282 1.2633 0.896757 16 to 20 141782 -0.4316 0.333006 15 to 19 141559 -1.1876 0.117504 14 to 18 142004 0.3209 0.625863 13 to 17 141717 -0.6520 0.257212 12 to 16 141735 -0.5909 0.277277 11 to 15 141844 -0.2215 0.412368 10 to 14 141195 -2.4215 0.007729 9 to 13 141853 -0.1909 0.424283 8 to 12 141193 -2.4282 0.007586 7 to 11 141678 -0.7842 0.216470 6 to 10 142233 1.0972 0.863720 5 to 9 141780 -0.4384 0.330546 4 to 8 141640 -0.9130 0.180626 3 to 7 141478 -1.4621 0.071852 2 to 6 140970 -3.1842 0.000726 1 to 5 141758 -0.5130 0.303982 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-11-04_12:31 Bits used No. missing words z-score p-value 31 to 32 141664 -0.7237 0.234629 30 to 31 141850 -0.1750 0.430534 29 to 30 141787 -0.3609 0.359104 28 to 29 141826 -0.2458 0.402914 27 to 28 141745 -0.4847 0.313927 26 to 27 142240 0.9754 0.835326 25 to 26 141867 -0.1249 0.450314 24 to 25 141970 0.1790 0.571018 23 to 24 141883 -0.0777 0.469045 22 to 23 142226 0.9341 0.824882 21 to 22 141843 -0.1957 0.422437 20 to 21 141440 -1.3845 0.083110 19 to 20 141953 0.1288 0.551250 18 to 19 142231 0.9489 0.828659 17 to 18 142090 0.5329 0.702966 16 to 17 142098 0.5565 0.711082 15 to 16 142422 1.5123 0.934771 14 to 15 142576 1.9666 0.975384 13 to 14 142290 1.1229 0.869264 12 to 13 141717 -0.5673 0.285240 11 to 12 141962 0.1554 0.561735 10 to 11 141826 -0.2458 0.402914 9 to 10 142761 2.5123 0.994003 8 to 9 141689 -0.6499 0.257865 7 to 8 142168 0.7630 0.777280 6 to 7 142053 0.4238 0.664146 5 to 6 142104 0.5742 0.717100 4 to 5 141960 0.1495 0.559408 3 to 4 141686 -0.6588 0.255015 2 to 3 141374 -1.5791 0.057151 1 to 2 142148 0.7040 0.759297 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-11-04_12:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2525.27 0.357 0.639578 Test results for specific bytes for dh-ranFile-2015-11-04_12:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2486.80 -0.187 0.425960 2 to 9 2478.52 -0.304 0.380675 3 to 10 2420.41 -1.126 0.130184 4 to 11 2553.93 0.763 0.777184 5 to 12 2409.47 -1.280 0.100226 6 to 13 2462.01 -0.537 0.295565 7 to 14 2459.75 -0.569 0.284592 8 to 15 2518.92 0.268 0.605470 9 to 16 2571.96 1.018 0.845580 10 to 17 2457.27 -0.604 0.272815 11 to 18 2506.76 0.096 0.538057 12 to 19 2587.86 1.243 0.892990 13 to 20 2472.63 -0.387 0.349347 14 to 21 2539.30 0.556 0.710800 15 to 22 2394.53 -1.492 0.067900 16 to 23 2580.74 1.142 0.873249 17 to 24 2607.27 1.517 0.935372 18 to 25 2512.60 0.178 0.570687 19 to 26 2471.43 -0.404 0.343066 20 to 27 2527.68 0.391 0.652281 21 to 28 2538.09 0.539 0.704942 22 to 29 2449.75 -0.711 0.238650 23 to 30 2561.39 0.868 0.807341 24 to 31 2433.72 -0.937 0.174293 25 to 32 2608.11 1.529 0.936848 CDPARK for dh-ranFile-2015-11-04_12:31: 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 3501 -1.0046 0.157553 3541 0.8219 0.794438 3487 -1.6438 0.050105 3532 0.4110 0.659449 3531 0.3653 0.642555 3535 0.5479 0.708135 3515 -0.3653 0.357445 3535 0.5479 0.708135 3550 1.2329 0.891189 3533 0.4566 0.676028 Square side=100, avg. no. parked=3526.00 sample std.=18.28 p-value of the KSTEST for those 10 p-values: 0.464636 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-11-04_12:31 0.4286,0.6212,0.6577,0.9848,0.9951,0.4880,0.6817,0.4752,0.7821,0.3637, The KS test for those 10 p-values: 0.085948 The 3DSPHERES test for dh-ranFile-2015-11-04_12:31 sample no r^3 equiv. uni. 1 12.830 0.347966 2 8.757 0.253167 3 16.893 0.430554 4 114.834 0.978243 5 60.850 0.868445 6 54.555 0.837729 7 27.327 0.597841 8 60.763 0.868063 9 0.917 0.030104 10 47.832 0.796967 11 45.114 0.777713 12 4.830 0.148713 13 22.088 0.521100 14 28.885 0.618185 15 2.807 0.089337 16 39.914 0.735650 17 68.298 0.897367 18 50.074 0.811593 19 52.541 0.826461 20 43.780 0.767612 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.099116 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-11-04_12:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.5 0.3 0.2 -1.1 1.3 0.7 -0.8 -0.8 -0.7 -0.4 -1.5 -0.8 -0.7 -0.7 1.5 0.3 -0.8 1.0 -0.2 0.5 1.6 0.6 -0.8 0.2 1.0 -0.1 0.1 -0.3 0.5 -0.5 -1.7 -0.1 0.3 1.2 -0.5 1.0 0.5 0.5 1.5 -1.3 -1.0 1.8 Chi-square with 42 degrees of freedom:33.429725 z-score=-0.935094, p-value=0.175306 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-11-04_12:31 Test no p-value 1 0.648172 2 0.105096 3 0.499108 4 0.090874 5 0.045880 6 0.447667 7 0.958756 8 0.752312 9 0.936299 10 0.387591 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.856465 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-11-04_12:31: (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 66664 0.00 66429 0.85 3 25000.00 24938 0.15 25320 4.10 4 6666.67 6671 0.00 6586 0.98 5 1388.89 1441 1.96 1379 0.07 6 238.10 246 0.26 253 0.93 7 34.72 33 0.09 28 1.30 8 4.96 6 0.22 4 0.19 p=0.15190 p=0.79038 Number of rngs required: 687733, p-value: 0.219 RESULTS OF CRAPS TEST for dh-ranFile-2015-11-04_12:31 No. of wins: Observed Expected 98739 98585.9 z-score= 0.685, pvalue=0.75331 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66718 66666.7 0.040 0.040 2 37572 37654.3 0.180 0.219 3 26925 26954.7 0.033 0.252 4 19245 19313.5 0.243 0.495 5 13731 13851.4 1.047 1.542 6 9991 9943.5 0.226 1.768 7 7252 7145.0 1.602 3.370 8 5234 5139.1 1.753 5.123 9 3725 3699.9 0.171 5.294 10 2678 2666.3 0.051 5.346 11 1890 1923.3 0.578 5.923 12 1360 1388.7 0.595 6.518 13 1037 1003.7 1.104 7.622 14 730 726.1 0.021 7.642 15 518 525.8 0.117 7.759 16 412 381.2 2.497 10.256 17 292 276.5 0.864 11.120 18 188 200.8 0.820 11.940 19 137 146.0 0.553 12.493 20 92 106.2 1.902 14.395 21 273 287.1 0.694 15.089 Chisq= 15.09 for 20 degrees of freedom, p= 0.22871 SUMMARY of craptest p-value for no. of wins: 0.753308 p-value for throws/game: 0.228712 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-11-04_12:31 No. of wins: Observed Expected 98440 98585.9 z-score=-0.652, pvalue=0.25708 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66414 66666.7 0.958 0.958 2 37763 37654.3 0.314 1.271 3 26984 26954.7 0.032 1.303 4 19291 19313.5 0.026 1.329 5 13907 13851.4 0.223 1.552 6 9970 9943.5 0.070 1.623 7 7215 7145.0 0.685 2.308 8 5141 5139.1 0.001 2.309 9 3687 3699.9 0.045 2.353 10 2658 2666.3 0.026 2.379 11 1935 1923.3 0.071 2.450 12 1363 1388.7 0.477 2.927 13 966 1003.7 1.417 4.344 14 731 726.1 0.033 4.377 15 553 525.8 1.403 5.780 16 411 381.2 2.338 8.118 17 255 276.5 1.678 9.795 18 175 200.8 3.322 13.117 19 147 146.0 0.007 13.125 20 105 106.2 0.014 13.138 21 329 287.1 6.111 19.249 Chisq= 19.25 for 20 degrees of freedom, p= 0.49431 SUMMARY of craptest p-value for no. of wins: 0.257083 p-value for throws/game: 0.494305 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0007,0.0039,0.0048,0.0055,0.0076,0.0077,0.0301,0.0330,0.0420,0.0459, 0.0501,0.0506,0.0541,0.0572,0.0582,0.0679,0.0679,0.0719,0.0731,0.0813, 0.0818,0.0831,0.0859,0.0893,0.0909,0.0933,0.0969,0.0991,0.1002,0.1051, 0.1133,0.1175,0.1235,0.1302,0.1454,0.1487,0.1519,0.1576,0.1599,0.1712, 0.1743,0.1753,0.1772,0.1806,0.1918,0.1919,0.1929,0.1957,0.2017,0.2038, 0.2079,0.2143,0.2155,0.2165,0.2194,0.2258,0.2287,0.2337,0.2346,0.2386, 0.2417,0.2448,0.2529,0.2532,0.2536,0.2550,0.2571,0.2572,0.2579,0.2631, 0.2728,0.2750,0.2773,0.2791,0.2846,0.2852,0.2878,0.2943,0.2956,0.3021, 0.3040,0.3099,0.3139,0.3157,0.3241,0.3250,0.3305,0.3328,0.3330,0.3370, 0.3402,0.3431,0.3454,0.3480,0.3484,0.3493,0.3518,0.3574,0.3591,0.3621, 0.3636,0.3637,0.3675,0.3807,0.3876,0.3909,0.3956,0.4007,0.4029,0.4029, 0.4055,0.4089,0.4124,0.4124,0.4209,0.4224,0.4225,0.4243,0.4251,0.4260, 0.4286,0.4305,0.4306,0.4311,0.4325,0.4370,0.4449,0.4477,0.4503,0.4526, 0.4577,0.4630,0.4646,0.4690,0.4712,0.4752,0.4787,0.4809,0.4823,0.4880, 0.4943,0.4991,0.5211,0.5336,0.5360,0.5381,0.5447,0.5513,0.5558,0.5594, 0.5617,0.5707,0.5710,0.5721,0.5762,0.5812,0.5909,0.5953,0.5978,0.6053, 0.6055,0.6092,0.6117,0.6128,0.6182,0.6194,0.6212,0.6259,0.6376,0.6385, 0.6396,0.6414,0.6426,0.6482,0.6519,0.6523,0.6577,0.6594,0.6641,0.6760, 0.6762,0.6774,0.6817,0.6893,0.6911,0.7030,0.7049,0.7080,0.7081,0.7081, 0.7090,0.7108,0.7111,0.7171,0.7206,0.7299,0.7330,0.7357,0.7432,0.7523, 0.7533,0.7593,0.7653,0.7672,0.7676,0.7752,0.7772,0.7773,0.7777,0.7821, 0.7904,0.7944,0.7957,0.7966,0.7970,0.7996,0.8056,0.8073,0.8116,0.8249, 0.8265,0.8287,0.8353,0.8377,0.8456,0.8477,0.8517,0.8565,0.8587,0.8637, 0.8681,0.8684,0.8693,0.8732,0.8860,0.8893,0.8912,0.8930,0.8968,0.8974, 0.9094,0.9159,0.9191,0.9249,0.9254,0.9285,0.9348,0.9354,0.9363,0.9368, 0.9420,0.9438,0.9588,0.9592,0.9608,0.9642,0.9671,0.9748,0.9754,0.9782, 0.9790,0.9842,0.9848,0.9939,0.9940,0.9940,0.9951,0.9967,0.9992, Overall p-value after applying KStest on 269 p-values = 0.840486 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.