RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-05-21_16:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 16.12 22.8337 0.845258 2 to 25 15.70 12.3764 0.223169 3 to 26 15.89 16.8161 0.533106 4 to 27 15.85 21.6068 0.799685 5 to 28 15.82 15.7523 0.458545 6 to 29 15.42 26.5865 0.935583 7 to 30 15.67 20.4039 0.745907 8 to 31 15.90 15.0394 0.407355 9 to 32 15.62 14.9867 0.403558 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.494357 Tough bday spacings test for dh-ranFile-2016-05-21_16:31: 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 4 30 79 98 100 79 60 35 8 4 3 (O-E)^2/E 2.9 1.2 0.4 0.0 0.1 0.0 1.2 0.9 3.2 1.0 0.3 Birthday Spacings: Sum(O-E)^2/E= 11.236, p= 0.661 RESULTS OF GCD FOR dh-ranFile-2016-05-21_16:31 Euclid's algorithm: p-value, steps to gcd: 0.184573 p-value, dist. of gcd's: 0.145163 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-05-21_16:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.875 0.203 0.691 0.902 0.028 0.471 0.402 0.744 Bits 8 to 15---> 0.483 0.207 0.390 0.090 0.102 0.275 0.063 0.561 Bits 16 to 23---> 0.572 0.927 0.280 0.520 0.030 0.811 0.061 0.901 Bits 24 to 31---> 0.148 0.864 1.000 0.860 0.522 0.539 0.544 0.712 KS test for the above 32 p values: 0.183 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-05-21_16:31, p-values for 5 runs: 0.7549, 0.0237, 0.8059, 0.6104, 0.5764 Rank test for binary matrices (31x31) for dh-ranFile-2016-05-21_16:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 185 211.4 3.301 3.301 r= 29 5173 5134.0 0.296 3.597 r= 30 23115 23103.0 0.006 3.603 r= 31 11527 11551.5 0.052 3.655 chi-square = 3.655 with df = 3; p-value = 0.699 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-05-21_16:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 208 211.4 0.055 0.055 r= 30 5231 5134.0 1.832 1.888 r= 31 23092 23103.0 0.005 1.893 r= 32 11469 11551.5 0.590 2.482 chi-square = 2.482 with df = 3; p-value = 0.522 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-05-21_16:31 b-rank test for bits 1 to 8, p=0.73940 b-rank test for bits 2 to 9, p=0.45487 b-rank test for bits 3 to 10, p=0.54767 b-rank test for bits 4 to 11, p=0.06465 b-rank test for bits 5 to 12, p=0.57651 b-rank test for bits 6 to 13, p=0.38289 b-rank test for bits 7 to 14, p=0.02929 b-rank test for bits 8 to 15, p=0.04463 b-rank test for bits 9 to 16, p=0.87713 b-rank test for bits 10 to 17, p=0.09150 b-rank test for bits 11 to 18, p=0.42964 b-rank test for bits 12 to 19, p=0.94372 b-rank test for bits 13 to 20, p=0.08825 b-rank test for bits 14 to 21, p=0.16233 b-rank test for bits 15 to 22, p=0.62282 b-rank test for bits 16 to 23, p=0.28080 b-rank test for bits 17 to 24, p=0.51521 b-rank test for bits 18 to 25, p=0.21655 b-rank test for bits 19 to 26, p=0.47230 b-rank test for bits 20 to 27, p=0.07374 b-rank test for bits 21 to 28, p=0.75707 b-rank test for bits 22 to 29, p=0.30008 b-rank test for bits 23 to 30, p=0.45381 b-rank test for bits 24 to 31, p=0.86790 b-rank test for bits 25 to 32, p=0.04415 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 = 0.114811 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-05-21_16:31 (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 142179 0.63 0.735676 2 141614 -0.69 0.245090 3 142038 0.30 0.618152 4 142788 2.05 0.979962 5 141532 -0.88 0.188993 6 141871 -0.09 0.464320 7 141607 -0.71 0.239976 8 141345 -1.32 0.093663 9 142236 0.76 0.777342 10 141786 -0.29 0.386614 11 142343 1.01 0.844529 12 141369 -1.26 0.103393 13 141765 -0.34 0.367976 14 140990 -2.15 0.015858 15 142265 0.83 0.797015 16 141119 -1.85 0.032405 17 141638 -0.63 0.263057 18 141691 -0.51 0.304985 19 142264 0.83 0.796354 20 141972 0.15 0.558207 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-05-21_16:31 Bits used No. missing words z-score p-value 23 to 32 141940 0.1058 0.542113 22 to 31 141833 -0.2632 0.396196 21 to 30 141781 -0.4425 0.329058 20 to 29 141650 -0.8942 0.185596 19 to 28 142022 0.3885 0.651183 18 to 27 141912 0.0092 0.503673 17 to 26 141909 -0.0011 0.499546 16 to 25 142096 0.6437 0.740112 15 to 24 141566 -1.1839 0.118227 14 to 23 142433 1.8058 0.964522 13 to 22 141884 -0.0873 0.465199 12 to 21 142031 0.4196 0.662594 11 to 20 141507 -1.3873 0.082668 10 to 19 141634 -0.9494 0.171205 9 to 18 142176 0.9196 0.821097 8 to 17 142055 0.5023 0.692275 7 to 16 142108 0.6851 0.753350 6 to 15 141659 -0.8632 0.194012 5 to 14 141808 -0.3494 0.363389 4 to 13 141327 -2.0080 0.022320 3 to 12 141965 0.1920 0.576115 2 to 11 141929 0.0678 0.527039 1 to 10 141394 -1.7770 0.037784 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-05-21_16:31 Bits used No. missing words z-score p-value 28 to 32 142134 0.7616 0.776849 27 to 31 142189 0.9480 0.828444 26 to 30 141880 -0.0994 0.460401 25 to 29 141445 -1.5740 0.057744 24 to 28 141977 0.2294 0.590717 23 to 27 141844 -0.2215 0.412368 22 to 26 141908 -0.0045 0.498201 21 to 25 141465 -1.5062 0.066008 20 to 24 141492 -1.4147 0.078581 19 to 23 141737 -0.5842 0.279553 18 to 22 141962 0.1785 0.570852 17 to 21 141629 -0.9503 0.170987 16 to 20 141903 -0.0215 0.491440 15 to 19 141664 -0.8316 0.202810 14 to 18 141953 0.1480 0.558842 13 to 17 141969 0.2023 0.580148 12 to 16 141820 -0.3028 0.381016 11 to 15 142073 0.5548 0.710489 10 to 14 142023 0.3853 0.650001 9 to 13 141784 -0.4248 0.335474 8 to 12 141618 -0.9876 0.161684 7 to 11 141909 -0.0011 0.499554 6 to 10 141623 -0.9706 0.165871 5 to 9 141611 -1.0113 0.155939 4 to 8 142156 0.8362 0.798470 3 to 7 141670 -0.8113 0.208600 2 to 6 141295 -2.0825 0.018650 1 to 5 141758 -0.5130 0.303982 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-05-21_16:31 Bits used No. missing words z-score p-value 31 to 32 142576 1.9666 0.975384 30 to 31 142187 0.8191 0.793631 29 to 30 142263 1.0433 0.851589 28 to 29 141495 -1.2222 0.110814 27 to 28 142358 1.3235 0.907167 26 to 27 141740 -0.4995 0.308714 25 to 26 142396 1.4356 0.924443 24 to 25 142025 0.3412 0.633527 23 to 24 141501 -1.2045 0.114196 22 to 23 141855 -0.1603 0.436336 21 to 22 142153 0.7188 0.763865 20 to 21 141401 -1.4995 0.066872 19 to 20 141869 -0.1190 0.452651 18 to 19 141993 0.2468 0.597474 17 to 18 141994 0.2498 0.598615 16 to 17 141358 -1.6263 0.051938 15 to 16 141985 0.2232 0.588316 14 to 15 141904 -0.0157 0.493728 13 to 14 141731 -0.5260 0.299428 12 to 13 142322 1.2173 0.888258 11 to 12 141281 -1.8535 0.031907 10 to 11 141600 -0.9125 0.180759 9 to 10 141953 0.1288 0.551250 8 to 9 142410 1.4769 0.930149 7 to 8 142171 0.7719 0.779910 6 to 7 141908 -0.0039 0.498435 5 to 6 141591 -0.9390 0.173859 4 to 5 141887 -0.0659 0.473741 3 to 4 141198 -2.0983 0.017939 2 to 3 141907 -0.0069 0.497258 1 to 2 142021 0.3294 0.629077 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-05-21_16:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2597.31 1.376 0.915608 Test results for specific bytes for dh-ranFile-2016-05-21_16:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2548.74 0.689 0.754700 2 to 9 2497.86 -0.030 0.487934 3 to 10 2660.58 2.271 0.988426 4 to 11 2526.38 0.373 0.645447 5 to 12 2417.52 -1.167 0.121706 6 to 13 2468.77 -0.442 0.329378 7 to 14 2562.46 0.883 0.811454 8 to 15 2579.96 1.131 0.870917 9 to 16 2488.11 -0.168 0.433227 10 to 17 2489.01 -0.155 0.438219 11 to 18 2428.56 -1.010 0.156177 12 to 19 2634.23 1.898 0.971168 13 to 20 2569.80 0.987 0.838211 14 to 21 2578.29 1.107 0.865903 15 to 22 2564.46 0.912 0.819000 16 to 23 2442.37 -0.815 0.207532 17 to 24 2404.90 -1.345 0.089319 18 to 25 2652.48 2.156 0.984471 19 to 26 2556.20 0.795 0.786617 20 to 27 2497.71 -0.032 0.487109 21 to 28 2487.57 -0.176 0.430233 22 to 29 2474.97 -0.354 0.361660 23 to 30 2446.59 -0.755 0.225017 24 to 31 2414.56 -1.208 0.113453 25 to 32 2514.90 0.211 0.583473 CDPARK for dh-ranFile-2016-05-21_16:31: 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 3492 -1.4155 0.078457 3499 -1.0959 0.136563 3556 1.5068 0.934075 3517 -0.2740 0.392053 3551 1.2785 0.899470 3503 -0.9132 0.180558 3497 -1.1872 0.117571 3512 -0.5023 0.307734 3516 -0.3196 0.374623 Square side=100, avg. no. parked=3515.30 sample std.=20.66 p-value of the KSTEST for those 10 p-values: 0.152700 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-05-21_16:31 0.2479,0.6892,0.8471,0.9705,0.3635,0.0292,0.6646,0.0724,0.5893,0.8028, The KS test for those 10 p-values: 0.913466 The 3DSPHERES test for dh-ranFile-2016-05-21_16:31 sample no r^3 equiv. uni. 1 66.469 0.890916 2 25.520 0.572874 3 12.970 0.351015 4 47.482 0.794589 5 23.125 0.537376 6 68.361 0.897582 7 11.165 0.310768 8 9.439 0.269939 9 19.848 0.483977 10 11.058 0.308288 11 44.799 0.775372 12 13.555 0.363535 13 7.828 0.229660 14 11.297 0.313794 15 6.611 0.197782 16 3.335 0.105210 17 15.918 0.411753 18 19.521 0.478328 19 12.352 0.337498 20 19.032 0.469739 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.224403 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-05-21_16:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 0.5 -0.6 0.3 -0.9 2.6 0.8 -1.2 1.3 -1.5 0.2 -1.0 1.4 1.5 0.4 0.2 -3.4 1.8 -1.7 -1.1 1.1 -1.7 1.4 0.7 1.1 0.4 1.0 -1.4 -0.6 -0.3 2.4 -0.1 -0.5 -0.5 -0.4 0.6 2.6 -0.7 -0.4 -1.3 -1.3 -1.0 0.8 Chi-square with 42 degrees of freedom:69.773269 z-score=3.030312, p-value=0.995474 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-05-21_16:31 Test no p-value 1 0.120654 2 0.104127 3 0.842640 4 0.427894 5 0.444773 6 0.005535 7 0.216872 8 0.116494 9 0.375362 10 0.126049 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.016501 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-05-21_16:31: (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 66520 0.32 66463 0.62 3 25000.00 25087 0.30 25058 0.13 4 6666.67 6577 1.21 6777 1.83 5 1388.89 1510 10.56 1415 0.49 6 238.10 259 1.84 248 0.41 7 34.72 41 1.14 31 0.40 8 4.96 5 0.00 7 0.84 p=0.98239 p=0.42022 Number of rngs required: 689117, p-value: 0.795 RESULTS OF CRAPS TEST for dh-ranFile-2016-05-21_16:31 No. of wins: Observed Expected 98718 98585.9 z-score= 0.591, pvalue=0.72274 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66789 66666.7 0.224 0.224 2 37612 37654.3 0.048 0.272 3 26972 26954.7 0.011 0.283 4 19343 19313.5 0.045 0.328 5 13843 13851.4 0.005 0.333 6 9890 9943.5 0.288 0.622 7 7071 7145.0 0.767 1.389 8 5063 5139.1 1.126 2.515 9 3656 3699.9 0.520 3.035 10 2730 2666.3 1.522 4.557 11 1956 1923.3 0.555 5.112 12 1450 1388.7 2.702 7.814 13 968 1003.7 1.271 9.085 14 707 726.1 0.505 9.589 15 543 525.8 0.560 10.150 16 394 381.2 0.433 10.583 17 266 276.5 0.402 10.984 18 210 200.8 0.419 11.403 19 159 146.0 1.160 12.564 20 106 106.2 0.000 12.564 21 272 287.1 0.796 13.360 Chisq= 13.36 for 20 degrees of freedom, p= 0.13858 SUMMARY of craptest p-value for no. of wins: 0.722744 p-value for throws/game: 0.138577 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-05-21_16:31 No. of wins: Observed Expected 98587 98585.9 z-score= 0.005, pvalue=0.50204 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66514 66666.7 0.350 0.350 2 37827 37654.3 0.792 1.141 3 26911 26954.7 0.071 1.212 4 19308 19313.5 0.002 1.214 5 13838 13851.4 0.013 1.227 6 9911 9943.5 0.107 1.334 7 7241 7145.0 1.289 2.623 8 5172 5139.1 0.211 2.834 9 3713 3699.9 0.047 2.880 10 2628 2666.3 0.550 3.430 11 1933 1923.3 0.049 3.479 12 1355 1388.7 0.820 4.299 13 965 1003.7 1.493 5.792 14 730 726.1 0.021 5.813 15 526 525.8 0.000 5.813 16 375 381.2 0.099 5.912 17 268 276.5 0.264 6.176 18 225 200.8 2.909 9.084 19 172 146.0 4.636 13.721 20 92 106.2 1.902 15.623 21 296 287.1 0.275 15.898 Chisq= 15.90 for 20 degrees of freedom, p= 0.27708 SUMMARY of craptest p-value for no. of wins: 0.502037 p-value for throws/game: 0.277077 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0055,0.0159,0.0165,0.0179,0.0186,0.0223,0.0237,0.0282,0.0292,0.0293, 0.0302,0.0319,0.0324,0.0378,0.0442,0.0446,0.0519,0.0577,0.0609,0.0630, 0.0646,0.0660,0.0669,0.0724,0.0737,0.0785,0.0786,0.0827,0.0882,0.0893, 0.0898,0.0915,0.0937,0.1017,0.1034,0.1041,0.1052,0.1108,0.1135,0.1142, 0.1148,0.1165,0.1176,0.1182,0.1207,0.1217,0.1260,0.1366,0.1386,0.1452, 0.1482,0.1527,0.1559,0.1562,0.1617,0.1623,0.1659,0.1710,0.1712,0.1739, 0.1806,0.1808,0.1827,0.1846,0.1856,0.1890,0.1940,0.1978,0.2028,0.2035, 0.2072,0.2075,0.2086,0.2166,0.2169,0.2232,0.2244,0.2250,0.2297,0.2400, 0.2451,0.2479,0.2631,0.2699,0.2750,0.2764,0.2771,0.2796,0.2797,0.2808, 0.2994,0.3001,0.3040,0.3050,0.3077,0.3083,0.3087,0.3108,0.3138,0.3291, 0.3294,0.3355,0.3375,0.3510,0.3617,0.3634,0.3635,0.3635,0.3680,0.3746, 0.3754,0.3810,0.3829,0.3866,0.3900,0.3921,0.3962,0.4018,0.4036,0.4074, 0.4118,0.4124,0.4202,0.4279,0.4296,0.4302,0.4332,0.4363,0.4382,0.4448, 0.4527,0.4538,0.4549,0.4585,0.4604,0.4643,0.4652,0.4697,0.4706,0.4723, 0.4737,0.4783,0.4827,0.4840,0.4871,0.4879,0.4914,0.4937,0.4944,0.4973, 0.4982,0.4984,0.4995,0.4996,0.5020,0.5037,0.5152,0.5196,0.5215,0.5224, 0.5270,0.5331,0.5374,0.5393,0.5421,0.5442,0.5477,0.5513,0.5582,0.5588, 0.5607,0.5709,0.5718,0.5729,0.5761,0.5764,0.5765,0.5801,0.5835,0.5883, 0.5893,0.5907,0.5975,0.5986,0.6104,0.6182,0.6228,0.6291,0.6335,0.6454, 0.6500,0.6512,0.6605,0.6626,0.6646,0.6892,0.6909,0.6923,0.6988,0.7105, 0.7117,0.7227,0.7357,0.7394,0.7401,0.7437,0.7459,0.7533,0.7547,0.7549, 0.7571,0.7639,0.7754,0.7768,0.7773,0.7799,0.7866,0.7936,0.7946,0.7954, 0.7964,0.7970,0.7985,0.7997,0.8028,0.8059,0.8105,0.8115,0.8190,0.8211, 0.8284,0.8382,0.8426,0.8445,0.8453,0.8471,0.8516,0.8601,0.8643,0.8659, 0.8679,0.8709,0.8747,0.8771,0.8883,0.8909,0.8976,0.8995,0.9012,0.9024, 0.9072,0.9135,0.9156,0.9244,0.9269,0.9301,0.9341,0.9356,0.9437,0.9645, 0.9705,0.9712,0.9754,0.9800,0.9824,0.9845,0.9884,0.9955,0.9996, Overall p-value after applying KStest on 269 p-values = 0.044682 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.