RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-09-19_07:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.76 14.8387 0.392900 2 to 25 15.67 19.2546 0.685887 3 to 26 15.55 23.2339 0.858211 4 to 27 16.04 15.9615 0.473431 5 to 28 15.87 5.1575 0.002710 6 to 29 15.80 14.6898 0.382184 7 to 30 15.74 19.6241 0.706093 8 to 31 15.73 17.0802 0.551057 9 to 32 15.75 11.2748 0.158074 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.693998 Tough bday spacings test for dh-ranFile-2015-09-19_07:31: 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 7 38 63 101 106 73 57 29 15 8 3 (O-E)^2/E 0.5 0.1 1.4 0.1 0.7 0.3 0.5 0.0 0.0 0.3 0.3 Birthday Spacings: Sum(O-E)^2/E= 4.208, p= 0.063 RESULTS OF GCD FOR dh-ranFile-2015-09-19_07:31 Euclid's algorithm: p-value, steps to gcd: 0.369001 p-value, dist. of gcd's: 0.114153 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-09-19_07:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.437 0.297 0.429 0.897 0.288 0.691 0.541 0.692 Bits 8 to 15---> 0.929 0.769 0.776 0.053 0.422 0.255 0.407 0.867 Bits 16 to 23---> 0.655 0.659 0.895 0.520 0.440 0.532 0.006 0.688 Bits 24 to 31---> 0.545 0.894 0.257 0.334 0.428 0.585 0.599 0.037 KS test for the above 32 p values: 0.565 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-09-19_07:31, p-values for 5 runs: 0.3458, 0.5823, 0.1056, 0.9186, 0.9730 Rank test for binary matrices (31x31) for dh-ranFile-2015-09-19_07:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 238 211.4 3.342 3.342 r= 29 5077 5134.0 0.633 3.975 r= 30 23057 23103.0 0.092 4.067 r= 31 11628 11551.5 0.506 4.573 chi-square = 4.573 with df = 3; p-value = 0.794 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-09-19_07:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 221 211.4 0.434 0.434 r= 30 5050 5134.0 1.375 1.809 r= 31 23144 23103.0 0.073 1.882 r= 32 11585 11551.5 0.097 1.979 chi-square = 1.979 with df = 3; p-value = 0.423 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-09-19_07:31 b-rank test for bits 1 to 8, p=0.54233 b-rank test for bits 2 to 9, p=0.25148 b-rank test for bits 3 to 10, p=0.63421 b-rank test for bits 4 to 11, p=0.81385 b-rank test for bits 5 to 12, p=0.47951 b-rank test for bits 6 to 13, p=0.87335 b-rank test for bits 7 to 14, p=0.21228 b-rank test for bits 8 to 15, p=0.12822 b-rank test for bits 9 to 16, p=0.80816 b-rank test for bits 10 to 17, p=0.60135 b-rank test for bits 11 to 18, p=0.40117 b-rank test for bits 12 to 19, p=0.97845 b-rank test for bits 13 to 20, p=0.94370 b-rank test for bits 14 to 21, p=0.29472 b-rank test for bits 15 to 22, p=0.00467 b-rank test for bits 16 to 23, p=0.94424 b-rank test for bits 17 to 24, p=0.22250 b-rank test for bits 18 to 25, p=0.82635 b-rank test for bits 19 to 26, p=0.71852 b-rank test for bits 20 to 27, p=0.65645 b-rank test for bits 21 to 28, p=0.90981 b-rank test for bits 22 to 29, p=0.75522 b-rank test for bits 23 to 30, p=0.36818 b-rank test for bits 24 to 31, p=0.72612 b-rank test for bits 25 to 32, p=0.34440 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 = 0.322961 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-09-19_07:31 (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 142001 0.21 0.584798 2 141695 -0.50 0.308266 3 141903 -0.01 0.494100 4 141971 0.14 0.557285 5 142154 0.57 0.716223 6 141495 -0.97 0.166507 7 141222 -1.61 0.054147 8 142198 0.67 0.749991 9 141151 -1.77 0.038214 10 141696 -0.50 0.309089 11 142121 0.49 0.689543 12 141668 -0.56 0.286426 13 142393 1.13 0.870777 14 141854 -0.13 0.448570 15 141866 -0.10 0.459681 16 141390 -1.21 0.112491 17 141522 -0.90 0.182739 18 141906 -0.01 0.496896 19 142634 1.69 0.954787 20 141628 -0.66 0.255490 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-09-19_07:31 Bits used No. missing words z-score p-value 23 to 32 142203 1.0127 0.844388 22 to 31 141418 -1.6942 0.045110 21 to 30 141956 0.1609 0.563926 20 to 29 141583 -1.1253 0.130236 19 to 28 142662 2.5954 0.995276 18 to 27 142156 0.8506 0.802500 17 to 26 141981 0.2471 0.597599 16 to 25 141600 -1.0667 0.143064 15 to 24 142265 1.2264 0.889985 14 to 23 141842 -0.2322 0.408202 13 to 22 142224 1.0851 0.861054 12 to 21 141687 -0.7667 0.221643 11 to 20 141930 0.0713 0.528411 10 to 19 141761 -0.5115 0.304507 9 to 18 141817 -0.3184 0.375099 8 to 17 141556 -1.2184 0.111540 7 to 16 141967 0.1989 0.578815 6 to 15 141527 -1.3184 0.093688 5 to 14 142164 0.8782 0.810075 4 to 13 141466 -1.5287 0.063166 3 to 12 142125 0.7437 0.771468 2 to 11 142098 0.6506 0.742343 1 to 10 141651 -0.8908 0.186520 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-09-19_07:31 Bits used No. missing words z-score p-value 28 to 32 142074 0.5582 0.711647 27 to 31 142057 0.5006 0.691665 26 to 30 142090 0.6124 0.729877 25 to 29 141790 -0.4045 0.342919 24 to 28 141652 -0.8723 0.191521 23 to 27 141453 -1.5469 0.060946 22 to 26 141809 -0.3401 0.366890 21 to 25 141627 -0.9571 0.169271 20 to 24 142061 0.5141 0.696421 19 to 23 141779 -0.4418 0.329318 18 to 22 141990 0.2735 0.607749 17 to 21 142042 0.4497 0.673547 16 to 20 141771 -0.4689 0.319565 15 to 19 142683 2.6226 0.995637 14 to 18 142538 2.1311 0.983459 13 to 17 141278 -2.1401 0.016173 12 to 16 141737 -0.5842 0.279553 11 to 15 141883 -0.0893 0.464440 10 to 14 141421 -1.6554 0.048926 9 to 13 142338 1.4531 0.926905 8 to 12 142105 0.6633 0.746427 7 to 11 142028 0.4023 0.656258 6 to 10 142361 1.5311 0.937126 5 to 9 141909 -0.0011 0.499554 4 to 8 141457 -1.5333 0.062598 3 to 7 141892 -0.0587 0.476577 2 to 6 141731 -0.6045 0.272753 1 to 5 142517 2.0599 0.980296 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-09-19_07:31 Bits used No. missing words z-score p-value 31 to 32 141717 -0.5673 0.285240 30 to 31 141687 -0.6558 0.255963 29 to 30 142275 1.0787 0.859633 28 to 29 142337 1.2616 0.896447 27 to 28 142509 1.7689 0.961548 26 to 27 142103 0.5713 0.716101 25 to 26 141625 -0.8387 0.200810 24 to 25 142076 0.4917 0.688517 23 to 24 141655 -0.7502 0.226556 22 to 23 142552 1.8958 0.971006 21 to 22 141585 -0.9567 0.169353 20 to 21 141714 -0.5762 0.282242 19 to 20 141972 0.1849 0.573333 18 to 19 141952 0.1259 0.550083 17 to 18 142501 1.7453 0.959537 16 to 17 141718 -0.5644 0.286243 15 to 16 142023 0.3353 0.631304 14 to 15 141931 0.0639 0.525484 13 to 14 142441 1.5683 0.941600 12 to 13 141735 -0.5142 0.303539 11 to 12 142402 1.4533 0.926930 10 to 11 142298 1.1465 0.874210 9 to 10 142053 0.4238 0.664146 8 to 9 141683 -0.6676 0.252182 7 to 8 142108 0.5860 0.721078 6 to 7 142340 1.2704 0.898031 5 to 6 142443 1.5742 0.942285 4 to 5 142242 0.9813 0.836784 3 to 4 141598 -0.9184 0.179211 2 to 3 141241 -1.9715 0.024335 1 to 2 142367 1.3501 0.911501 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-09-19_07:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2377.22 -1.736 0.041253 Test results for specific bytes for dh-ranFile-2015-09-19_07:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2382.32 -1.664 0.048029 2 to 9 2511.40 0.161 0.564036 3 to 10 2523.39 0.331 0.629574 4 to 11 2536.32 0.514 0.696252 5 to 12 2616.70 1.650 0.950563 6 to 13 2492.92 -0.100 0.460120 7 to 14 2404.93 -1.345 0.089385 8 to 15 2447.28 -0.746 0.227945 9 to 16 2645.17 2.053 0.979961 10 to 17 2538.72 0.548 0.708035 11 to 18 2382.32 -1.664 0.048032 12 to 19 2542.34 0.599 0.725342 13 to 20 2491.34 -0.122 0.451272 14 to 21 2372.98 -1.796 0.036219 15 to 22 2506.18 0.087 0.534799 16 to 23 2370.43 -1.832 0.033445 17 to 24 2435.71 -0.909 0.181617 18 to 25 2416.48 -1.181 0.118770 19 to 26 2560.25 0.852 0.802927 20 to 27 2501.45 0.021 0.508205 21 to 28 2463.96 -0.510 0.305160 22 to 29 2360.72 -1.970 0.024436 23 to 30 2514.67 0.207 0.582182 24 to 31 2584.04 1.188 0.882677 25 to 32 2476.84 -0.328 0.371628 CDPARK for dh-ranFile-2015-09-19_07:31: 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 3550 1.2329 0.891189 3560 1.6895 0.954438 3545 1.0046 0.842447 3515 -0.3653 0.357445 3511 -0.5479 0.291865 3488 -1.5982 0.055002 3495 -1.2785 0.100530 3516 -0.3196 0.374623 3518 -0.2283 0.409702 3561 1.7352 0.958644 Square side=100, avg. no. parked=3525.90 sample std.=24.97 p-value of the KSTEST for those 10 p-values: 0.515041 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-09-19_07:31 0.8167,0.5568,0.8067,0.6452,0.5732,0.2758,0.2466,0.2854,0.8398,0.2335, The KS test for those 10 p-values: 0.645689 The 3DSPHERES test for dh-ranFile-2015-09-19_07:31 sample no r^3 equiv. uni. 1 50.047 0.811423 2 59.461 0.862212 3 31.340 0.648188 4 40.535 0.741059 5 21.396 0.509929 6 2.230 0.071646 7 7.068 0.209915 8 20.301 0.491703 9 54.366 0.836707 10 4.458 0.138090 11 42.229 0.755278 12 70.311 0.904029 13 11.518 0.318829 14 2.901 0.092180 15 41.771 0.751512 16 24.369 0.556171 17 15.671 0.406882 18 0.489 0.016183 19 35.583 0.694592 20 4.457 0.138071 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.863706 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-09-19_07:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 0.5 0.8 -0.1 0.1 -0.6 0.8 -1.4 -0.6 -0.4 -1.0 -0.0 -1.7 2.0 0.3 0.6 -0.1 -0.8 -0.4 1.4 -0.3 1.0 0.1 0.1 -0.2 0.0 -1.7 -0.5 1.2 0.1 -0.4 0.6 -0.6 -0.5 0.1 -0.7 0.0 -0.1 1.3 -0.1 1.6 -1.0 0.8 Chi-square with 42 degrees of freedom:29.613332 z-score=-1.351496, p-value=0.075147 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-09-19_07:31 Test no p-value 1 0.162953 2 0.499398 3 0.552557 4 0.003496 5 0.440332 6 0.167768 7 0.011327 8 0.487181 9 0.228030 10 0.796057 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.065610 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-09-19_07:31: (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 66634 0.02 66637 0.01 3 25000.00 24980 0.02 25092 0.34 4 6666.67 6639 0.11 6598 0.71 5 1388.89 1457 3.34 1390 0.00 6 238.10 237 0.01 242 0.06 7 34.72 50 6.72 35 0.00 8 4.96 2 1.77 5 0.00 p=0.93765 p=0.01965 Number of rngs required: 689436, p-value: 0.885 RESULTS OF CRAPS TEST for dh-ranFile-2015-09-19_07:31 No. of wins: Observed Expected 98724 98585.9 z-score= 0.618, pvalue=0.73166 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66629 66666.7 0.021 0.021 2 37756 37654.3 0.275 0.296 3 27174 26954.7 1.784 2.080 4 19139 19313.5 1.576 3.655 5 13689 13851.4 1.905 5.560 6 9965 9943.5 0.046 5.606 7 7201 7145.0 0.439 6.045 8 5199 5139.1 0.699 6.744 9 3654 3699.9 0.569 7.312 10 2651 2666.3 0.088 7.400 11 1860 1923.3 2.085 9.485 12 1414 1388.7 0.459 9.945 13 1019 1003.7 0.233 10.177 14 736 726.1 0.134 10.311 15 540 525.8 0.382 10.693 16 369 381.2 0.387 11.080 17 273 276.5 0.045 11.125 18 192 200.8 0.388 11.514 19 139 146.0 0.334 11.848 20 116 106.2 0.901 12.749 21 285 287.1 0.016 12.765 Chisq= 12.76 for 20 degrees of freedom, p= 0.11275 SUMMARY of craptest p-value for no. of wins: 0.731663 p-value for throws/game: 0.112753 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-09-19_07:31 No. of wins: Observed Expected 98329 98585.9 z-score=-1.149, pvalue=0.12531 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66486 66666.7 0.490 0.490 2 38031 37654.3 3.768 4.258 3 26839 26954.7 0.497 4.755 4 19431 19313.5 0.715 5.470 5 13744 13851.4 0.833 6.303 6 9897 9943.5 0.218 6.521 7 7279 7145.0 2.512 9.033 8 5151 5139.1 0.028 9.061 9 3569 3699.9 4.629 13.689 10 2661 2666.3 0.011 13.700 11 1978 1923.3 1.554 15.254 12 1327 1388.7 2.745 17.999 13 965 1003.7 1.493 19.492 14 715 726.1 0.171 19.663 15 557 525.8 1.847 21.510 16 387 381.2 0.090 21.600 17 263 276.5 0.663 22.263 18 176 200.8 3.070 25.333 19 134 146.0 0.984 26.316 20 111 106.2 0.216 26.532 21 299 287.1 0.492 27.024 Chisq= 27.02 for 20 degrees of freedom, p= 0.86541 SUMMARY of craptest p-value for no. of wins: 0.125315 p-value for throws/game: 0.865410 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0027,0.0035,0.0047,0.0063,0.0113,0.0162,0.0162,0.0196,0.0243,0.0244, 0.0334,0.0362,0.0369,0.0382,0.0413,0.0451,0.0480,0.0480,0.0489,0.0532, 0.0541,0.0550,0.0609,0.0625,0.0626,0.0632,0.0656,0.0716,0.0751,0.0894, 0.0922,0.0937,0.1005,0.1056,0.1115,0.1125,0.1128,0.1142,0.1188,0.1253, 0.1282,0.1302,0.1381,0.1381,0.1431,0.1581,0.1630,0.1665,0.1678,0.1693, 0.1694,0.1792,0.1816,0.1827,0.1865,0.1915,0.2008,0.2099,0.2123,0.2216, 0.2225,0.2266,0.2279,0.2280,0.2335,0.2466,0.2515,0.2522,0.2551,0.2555, 0.2560,0.2570,0.2728,0.2758,0.2796,0.2822,0.2852,0.2854,0.2862,0.2864, 0.2878,0.2919,0.2947,0.2974,0.3035,0.3045,0.3052,0.3083,0.3091,0.3188, 0.3196,0.3230,0.3293,0.3345,0.3429,0.3444,0.3458,0.3574,0.3669,0.3682, 0.3690,0.3716,0.3746,0.3751,0.3822,0.3929,0.4012,0.4069,0.4069,0.4082, 0.4097,0.4221,0.4231,0.4283,0.4289,0.4367,0.4397,0.4403,0.4486,0.4513, 0.4597,0.4601,0.4644,0.4734,0.4766,0.4795,0.4872,0.4917,0.4941,0.4969, 0.4994,0.4996,0.5082,0.5099,0.5150,0.5197,0.5255,0.5284,0.5318,0.5348, 0.5408,0.5423,0.5446,0.5501,0.5511,0.5526,0.5562,0.5568,0.5573,0.5639, 0.5640,0.5653,0.5732,0.5733,0.5788,0.5822,0.5823,0.5846,0.5848,0.5976, 0.5993,0.6014,0.6077,0.6296,0.6313,0.6342,0.6452,0.6457,0.6482,0.6547, 0.6563,0.6564,0.6589,0.6641,0.6735,0.6859,0.6876,0.6885,0.6895,0.6907, 0.6917,0.6918,0.6940,0.6946,0.6963,0.6964,0.7061,0.7080,0.7116,0.7161, 0.7162,0.7185,0.7211,0.7253,0.7261,0.7299,0.7317,0.7411,0.7423,0.7464, 0.7500,0.7515,0.7552,0.7553,0.7693,0.7715,0.7764,0.7942,0.7961,0.8025, 0.8029,0.8067,0.8082,0.8101,0.8114,0.8139,0.8167,0.8263,0.8367,0.8368, 0.8398,0.8424,0.8444,0.8582,0.8596,0.8611,0.8622,0.8637,0.8654,0.8674, 0.8708,0.8734,0.8742,0.8827,0.8850,0.8900,0.8912,0.8935,0.8951,0.8964, 0.8974,0.8980,0.9040,0.9098,0.9115,0.9186,0.9269,0.9269,0.9289,0.9371, 0.9377,0.9416,0.9423,0.9437,0.9442,0.9506,0.9544,0.9548,0.9586,0.9595, 0.9615,0.9710,0.9730,0.9785,0.9800,0.9803,0.9835,0.9953,0.9956, Overall p-value after applying KStest on 269 p-values = 0.791344 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.