RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-10-05_11:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.74 10.4407 0.115879 2 to 25 15.91 17.3597 0.569735 3 to 26 15.92 25.0067 0.905441 4 to 27 15.76 13.9293 0.327900 5 to 28 15.93 19.2528 0.685784 6 to 29 15.67 25.0506 0.906416 7 to 30 15.73 11.0745 0.147338 8 to 31 15.77 23.9322 0.878711 9 to 32 15.85 13.6363 0.307341 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.806737 Tough bday spacings test for dh-ranFile-2015-10-05_11:31: 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 68 93 96 78 70 28 6 9 5 (O-E)^2/E 0.1 0.0 0.4 0.2 0.0 0.0 6.2 0.1 5.3 0.9 0.2 Birthday Spacings: Sum(O-E)^2/E= 13.347, p= 0.795 RESULTS OF GCD FOR dh-ranFile-2015-10-05_11:31 Euclid's algorithm: p-value, steps to gcd: 0.747495 p-value, dist. of gcd's: 0.745482 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-10-05_11:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.303 0.704 0.063 0.088 0.468 0.736 0.890 0.736 Bits 8 to 15---> 0.194 0.321 0.249 0.016 0.376 0.875 0.518 0.294 Bits 16 to 23---> 0.170 0.236 0.608 0.353 0.871 0.135 0.793 0.105 Bits 24 to 31---> 0.897 0.202 0.544 0.228 0.532 0.130 0.677 0.335 KS test for the above 32 p values: 0.768 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-10-05_11:31, p-values for 5 runs: 0.0024, 0.2632, 0.5289, 0.3500, 0.9219 Rank test for binary matrices (31x31) for dh-ranFile-2015-10-05_11:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 219 211.4 0.272 0.272 r= 29 5004 5134.0 3.292 3.564 r= 30 23215 23103.0 0.542 4.107 r= 31 11562 11551.5 0.010 4.116 chi-square = 4.116 with df = 3; p-value = 0.751 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-10-05_11:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 227 211.4 1.148 1.148 r= 30 5241 5134.0 2.230 3.378 r= 31 23065 23103.0 0.063 3.441 r= 32 11467 11551.5 0.618 4.059 chi-square = 4.059 with df = 3; p-value = 0.745 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-10-05_11:31 b-rank test for bits 1 to 8, p=0.25190 b-rank test for bits 2 to 9, p=0.30368 b-rank test for bits 3 to 10, p=0.57035 b-rank test for bits 4 to 11, p=0.58440 b-rank test for bits 5 to 12, p=0.29575 b-rank test for bits 6 to 13, p=0.23713 b-rank test for bits 7 to 14, p=0.63294 b-rank test for bits 8 to 15, p=0.85646 b-rank test for bits 9 to 16, p=0.26011 b-rank test for bits 10 to 17, p=0.11055 b-rank test for bits 11 to 18, p=0.76584 b-rank test for bits 12 to 19, p=0.61380 b-rank test for bits 13 to 20, p=0.04982 b-rank test for bits 14 to 21, p=0.20647 b-rank test for bits 15 to 22, p=0.54284 b-rank test for bits 16 to 23, p=0.22046 b-rank test for bits 17 to 24, p=0.55932 b-rank test for bits 18 to 25, p=0.01083 b-rank test for bits 19 to 26, p=0.42587 b-rank test for bits 20 to 27, p=0.97394 b-rank test for bits 21 to 28, p=0.83867 b-rank test for bits 22 to 29, p=0.58712 b-rank test for bits 23 to 30, p=0.75454 b-rank test for bits 24 to 31, p=0.14623 b-rank test for bits 25 to 32, p=0.43503 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 = 0.595510 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-10-05_11:31 (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 141651 -0.60 0.273063 2 142027 0.27 0.608315 3 142313 0.94 0.827199 4 142197 0.67 0.749248 5 141793 -0.27 0.392888 6 141726 -0.43 0.334201 7 141648 -0.61 0.270738 8 141118 -1.85 0.032236 9 142330 0.98 0.837165 10 141650 -0.61 0.272287 11 141639 -0.63 0.263820 12 141818 -0.21 0.415512 13 142439 1.24 0.892058 14 141623 -0.67 0.251749 15 141608 -0.70 0.240703 16 142175 0.62 0.732610 17 140921 -2.31 0.010467 18 141829 -0.19 0.425561 19 141487 -0.99 0.161882 20 141927 0.04 0.516466 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-10-05_11:31 Bits used No. missing words z-score p-value 23 to 32 141928 0.0644 0.525666 22 to 31 142593 2.3575 0.990800 21 to 30 142070 0.5540 0.710222 20 to 29 141964 0.1885 0.574764 19 to 28 141409 -1.7253 0.042239 18 to 27 141547 -1.2494 0.105757 17 to 26 141577 -1.1460 0.125905 16 to 25 141470 -1.5149 0.064895 15 to 24 142143 0.8058 0.789809 14 to 23 142283 1.2885 0.901217 13 to 22 142248 1.1678 0.878562 12 to 21 141513 -1.3667 0.085867 11 to 20 141850 -0.2046 0.418948 10 to 19 142110 0.6920 0.755521 9 to 18 141900 -0.0322 0.487167 8 to 17 142434 1.8092 0.964791 7 to 16 142206 1.0230 0.846846 6 to 15 141654 -0.8804 0.189308 5 to 14 142140 0.7954 0.786814 4 to 13 142381 1.6264 0.948073 3 to 12 141951 0.1437 0.557127 2 to 11 141673 -0.8149 0.207556 1 to 10 141674 -0.8115 0.208544 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-10-05_11:31 Bits used No. missing words z-score p-value 28 to 32 141875 -0.1164 0.453679 27 to 31 142273 1.2328 0.891171 26 to 30 141575 -1.1333 0.128540 25 to 29 142051 0.4802 0.684471 24 to 28 141545 -1.2350 0.108412 23 to 27 142102 0.6531 0.743160 22 to 26 141830 -0.2689 0.393998 21 to 25 142186 0.9379 0.825843 20 to 24 141502 -1.3808 0.083673 19 to 23 141683 -0.7672 0.221475 18 to 22 142062 0.5175 0.697605 17 to 21 142206 1.0057 0.842711 16 to 20 141848 -0.2079 0.417654 15 to 19 141826 -0.2825 0.388790 14 to 18 141642 -0.9062 0.182414 13 to 17 142018 0.3684 0.643702 12 to 16 142107 0.6701 0.748593 11 to 15 141995 0.2904 0.614248 10 to 14 141632 -0.9401 0.173583 9 to 13 141512 -1.3469 0.089009 8 to 12 141606 -1.0282 0.151919 7 to 11 142086 0.5989 0.725374 6 to 10 141947 0.1277 0.550805 5 to 9 141685 -0.7604 0.223496 4 to 8 141829 -0.2723 0.392694 3 to 7 142313 1.3684 0.914402 2 to 6 141865 -0.1503 0.440275 1 to 5 142571 2.2429 0.987550 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-10-05_11:31 Bits used No. missing words z-score p-value 31 to 32 142045 0.4002 0.655498 30 to 31 141693 -0.6381 0.261691 29 to 30 141586 -0.9538 0.170099 28 to 29 142382 1.3943 0.918388 27 to 28 141802 -0.3166 0.375771 26 to 27 141800 -0.3225 0.373534 25 to 26 141997 0.2586 0.602033 24 to 25 141913 0.0108 0.504319 23 to 24 141836 -0.2163 0.414372 22 to 23 141763 -0.4317 0.332997 21 to 22 142301 1.1554 0.876030 20 to 21 141448 -1.3609 0.086780 19 to 20 141432 -1.4081 0.079558 18 to 19 142006 0.2852 0.612240 17 to 18 141883 -0.0777 0.469045 16 to 17 141829 -0.2370 0.406343 15 to 16 142177 0.7896 0.785116 14 to 15 142172 0.7748 0.780782 13 to 14 141969 0.1760 0.569860 12 to 13 142006 0.2852 0.612240 11 to 12 141975 0.1937 0.576801 10 to 11 142088 0.5271 0.700921 9 to 10 141690 -0.6470 0.258819 8 to 9 142102 0.5683 0.715101 7 to 8 142236 0.9636 0.832384 6 to 7 142004 0.2793 0.609978 5 to 6 141656 -0.7473 0.227445 4 to 5 141480 -1.2665 0.102674 3 to 4 142221 0.9194 0.821052 2 to 3 142091 0.5359 0.703986 1 to 2 142463 1.6332 0.948791 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-10-05_11:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2612.78 1.595 0.944640 Test results for specific bytes for dh-ranFile-2015-10-05_11:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2507.41 0.105 0.541730 2 to 9 2486.04 -0.197 0.421775 3 to 10 2599.26 1.404 0.919798 4 to 11 2511.56 0.164 0.564946 5 to 12 2536.19 0.512 0.695585 6 to 13 2554.67 0.773 0.780285 7 to 14 2531.97 0.452 0.674436 8 to 15 2470.51 -0.417 0.338314 9 to 16 2496.91 -0.044 0.482585 10 to 17 2492.48 -0.106 0.457625 11 to 18 2509.37 0.133 0.552728 12 to 19 2621.30 1.715 0.956871 13 to 20 2663.15 2.307 0.989479 14 to 21 2485.65 -0.203 0.419605 15 to 22 2506.82 0.096 0.538411 16 to 23 2579.79 1.128 0.870412 17 to 24 2478.50 -0.304 0.380556 18 to 25 2419.33 -1.141 0.126963 19 to 26 2516.69 0.236 0.593318 20 to 27 2470.43 -0.418 0.337908 21 to 28 2546.03 0.651 0.742487 22 to 29 2337.86 -2.293 0.010924 23 to 30 2438.62 -0.868 0.192697 24 to 31 2531.53 0.446 0.672181 25 to 32 2429.39 -0.999 0.158987 CDPARK for dh-ranFile-2015-10-05_11:31: 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 3526 0.1370 0.554479 3527 0.1826 0.572463 3509 -0.6393 0.261324 3502 -0.9589 0.168804 3544 0.9589 0.831196 3550 1.2329 0.891189 3495 -1.2785 0.100530 3554 1.4155 0.921543 3538 0.6849 0.753306 3545 1.0046 0.842447 Square side=100, avg. no. parked=3529.00 sample std.=19.81 p-value of the KSTEST for those 10 p-values: 0.470883 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-10-05_11:31 0.6635,0.4758,0.6314,0.5447,0.2094,0.2618,0.3036,0.7397,0.7749,0.8337, The KS test for those 10 p-values: 0.591033 The 3DSPHERES test for dh-ranFile-2015-10-05_11:31 sample no r^3 equiv. uni. 1 133.835 0.988451 2 102.568 0.967252 3 22.130 0.521777 4 11.208 0.311755 5 36.920 0.707903 6 126.141 0.985075 7 8.418 0.244677 8 60.355 0.866255 9 47.416 0.794133 10 4.087 0.127349 11 12.841 0.348203 12 72.199 0.909882 13 25.888 0.578077 14 3.223 0.101849 15 15.647 0.406410 16 15.801 0.409443 17 11.387 0.315836 18 19.470 0.477433 19 59.688 0.863251 20 27.147 0.595422 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.287433 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-10-05_11:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 0.1 1.5 -2.0 0.2 -0.8 0.5 0.1 0.4 -0.8 0.6 1.0 -1.3 1.0 -0.7 1.4 -0.1 -0.9 -1.9 1.1 -3.1 1.0 0.2 1.0 2.1 0.6 -1.0 0.5 1.3 -0.7 -1.2 0.3 1.9 0.9 -1.2 -0.7 -1.2 0.8 -0.4 1.0 1.6 -1.0 0.8 Chi-square with 42 degrees of freedom:56.337481 z-score=1.564347, p-value=0.931366 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-10-05_11:31 Test no p-value 1 0.578982 2 0.017295 3 0.409912 4 0.316964 5 0.882083 6 0.355199 7 0.175675 8 0.148084 9 0.682122 10 0.801307 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.858673 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-10-05_11:31: (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 66394 1.12 66639 0.01 3 25000.00 25236 2.23 24902 0.38 4 6666.67 6706 0.23 6801 2.71 5 1388.89 1380 0.06 1392 0.01 6 238.10 245 0.20 229 0.35 7 34.72 30 0.64 32 0.21 8 4.96 8 1.86 4 0.19 p=0.61350 p=0.30379 Number of rngs required: 688741, p-value: 0.651 RESULTS OF CRAPS TEST for dh-ranFile-2015-10-05_11:31 No. of wins: Observed Expected 98734 98585.9 z-score= 0.663, pvalue=0.74620 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66401 66666.7 1.059 1.059 2 37790 37654.3 0.489 1.548 3 27260 26954.7 3.457 5.005 4 19334 19313.5 0.022 5.027 5 13718 13851.4 1.285 6.312 6 10011 9943.5 0.458 6.769 7 7055 7145.0 1.134 7.904 8 5019 5139.1 2.805 10.709 9 3734 3699.9 0.315 11.024 10 2709 2666.3 0.684 11.708 11 1888 1923.3 0.649 12.357 12 1384 1388.7 0.016 12.373 13 1001 1003.7 0.007 12.380 14 756 726.1 1.228 13.608 15 527 525.8 0.003 13.611 16 397 381.2 0.659 14.270 17 280 276.5 0.043 14.313 18 205 200.8 0.087 14.400 19 127 146.0 2.469 16.869 20 105 106.2 0.014 16.883 21 299 287.1 0.492 17.375 Chisq= 17.37 for 20 degrees of freedom, p= 0.37147 SUMMARY of craptest p-value for no. of wins: 0.746199 p-value for throws/game: 0.371466 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-10-05_11:31 No. of wins: Observed Expected 98490 98585.9 z-score=-0.429, pvalue=0.33406 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66523 66666.7 0.310 0.310 2 37786 37654.3 0.460 0.770 3 27085 26954.7 0.630 1.400 4 19333 19313.5 0.020 1.419 5 13782 13851.4 0.348 1.767 6 9881 9943.5 0.393 2.161 7 7080 7145.0 0.592 2.753 8 5156 5139.1 0.056 2.808 9 3733 3699.9 0.297 3.105 10 2663 2666.3 0.004 3.109 11 1893 1923.3 0.478 3.587 12 1458 1388.7 3.454 7.041 13 1022 1003.7 0.333 7.375 14 707 726.1 0.505 7.879 15 520 525.8 0.065 7.944 16 387 381.2 0.090 8.034 17 241 276.5 4.567 12.601 18 193 200.8 0.305 12.906 19 149 146.0 0.062 12.969 20 119 106.2 1.539 14.507 21 289 287.1 0.012 14.520 Chisq= 14.52 for 20 degrees of freedom, p= 0.19681 SUMMARY of craptest p-value for no. of wins: 0.334058 p-value for throws/game: 0.196808 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0024,0.0105,0.0108,0.0109,0.0159,0.0173,0.0322,0.0422,0.0498,0.0632, 0.0649,0.0796,0.0837,0.0859,0.0868,0.0876,0.0890,0.1005,0.1018,0.1027, 0.1050,0.1058,0.1084,0.1105,0.1159,0.1259,0.1270,0.1273,0.1285,0.1302, 0.1352,0.1462,0.1473,0.1481,0.1519,0.1590,0.1619,0.1688,0.1699,0.1701, 0.1736,0.1757,0.1824,0.1893,0.1927,0.1939,0.1968,0.2018,0.2065,0.2076, 0.2085,0.2094,0.2205,0.2215,0.2235,0.2274,0.2279,0.2357,0.2371,0.2407, 0.2447,0.2488,0.2517,0.2519,0.2588,0.2601,0.2613,0.2617,0.2618,0.2632, 0.2638,0.2707,0.2723,0.2731,0.2874,0.2942,0.2958,0.3027,0.3036,0.3037, 0.3038,0.3073,0.3118,0.3158,0.3170,0.3210,0.3279,0.3330,0.3341,0.3342, 0.3352,0.3379,0.3383,0.3482,0.3500,0.3532,0.3552,0.3715,0.3735,0.3758, 0.3758,0.3806,0.3888,0.3927,0.3929,0.3940,0.4063,0.4064,0.4094,0.4099, 0.4144,0.4155,0.4177,0.4189,0.4196,0.4218,0.4256,0.4259,0.4350,0.4403, 0.4537,0.4576,0.4680,0.4690,0.4709,0.4758,0.4774,0.4826,0.4872,0.5043, 0.5165,0.5184,0.5218,0.5257,0.5289,0.5317,0.5384,0.5417,0.5428,0.5436, 0.5447,0.5508,0.5527,0.5545,0.5571,0.5593,0.5649,0.5697,0.5699,0.5704, 0.5725,0.5748,0.5768,0.5781,0.5790,0.5844,0.5871,0.5910,0.5933,0.5954, 0.5955,0.6020,0.6080,0.6083,0.6100,0.6122,0.6122,0.6135,0.6138,0.6142, 0.6314,0.6329,0.6437,0.6514,0.6555,0.6635,0.6722,0.6744,0.6765,0.6821, 0.6845,0.6858,0.6956,0.6976,0.7009,0.7040,0.7043,0.7079,0.7102,0.7151, 0.7254,0.7326,0.7359,0.7364,0.7397,0.7425,0.7432,0.7449,0.7455,0.7462, 0.7475,0.7486,0.7492,0.7508,0.7533,0.7545,0.7555,0.7658,0.7678,0.7749, 0.7803,0.7808,0.7851,0.7868,0.7898,0.7928,0.7941,0.7951,0.8013,0.8067, 0.8211,0.8258,0.8272,0.8312,0.8324,0.8337,0.8372,0.8387,0.8424,0.8427, 0.8468,0.8565,0.8587,0.8633,0.8663,0.8704,0.8714,0.8746,0.8760,0.8786, 0.8787,0.8821,0.8897,0.8912,0.8912,0.8921,0.8972,0.9012,0.9054,0.9064, 0.9099,0.9144,0.9184,0.9198,0.9215,0.9219,0.9314,0.9446,0.9481,0.9488, 0.9569,0.9648,0.9673,0.9739,0.9851,0.9875,0.9885,0.9895,0.9908, Overall p-value after applying KStest on 269 p-values = 0.620460 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.