RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-12-05_02:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.71 21.2569 0.784989 2 to 25 15.59 16.0611 0.480489 3 to 26 15.78 21.7617 0.805943 4 to 27 16.21 15.5797 0.446196 5 to 28 15.69 11.8414 0.190356 6 to 29 15.89 10.5993 0.123378 7 to 30 15.83 24.3901 0.890784 8 to 31 15.56 24.6752 0.897782 9 to 32 15.85 13.2038 0.277562 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.841312 Tough bday spacings test for dh-ranFile-2015-12-05_02:31: 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 8 29 82 96 87 90 57 31 13 3 4 (O-E)^2/E 0.1 1.6 1.0 0.0 1.2 1.8 0.5 0.1 0.2 2.0 0.0 Birthday Spacings: Sum(O-E)^2/E= 8.501, p= 0.420 RESULTS OF GCD FOR dh-ranFile-2015-12-05_02:31 Euclid's algorithm: p-value, steps to gcd: 0.926508 p-value, dist. of gcd's: 0.674179 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-12-05_02:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.424 0.566 0.599 0.771 0.765 0.224 0.701 0.870 Bits 8 to 15---> 0.610 0.157 0.819 0.501 0.502 0.351 0.421 0.637 Bits 16 to 23---> 0.606 0.859 0.717 0.794 0.794 0.340 0.220 0.701 Bits 24 to 31---> 0.893 0.536 0.313 0.387 0.331 0.055 0.204 0.845 KS test for the above 32 p values: 0.766 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-12-05_02:31, p-values for 5 runs: 0.2152, 0.4907, 0.6183, 0.4073, 0.3828 Rank test for binary matrices (31x31) for dh-ranFile-2015-12-05_02:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 218 211.4 0.205 0.205 r= 29 5158 5134.0 0.112 0.317 r= 30 23081 23103.0 0.021 0.338 r= 31 11543 11551.5 0.006 0.344 chi-square = 0.344 with df = 3; p-value = 0.049 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-12-05_02:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 223 211.4 0.634 0.634 r= 30 5116 5134.0 0.063 0.698 r= 31 23117 23103.0 0.008 0.706 r= 32 11544 11551.5 0.005 0.711 chi-square = 0.711 with df = 3; p-value = 0.129 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-12-05_02:31 b-rank test for bits 1 to 8, p=0.06545 b-rank test for bits 2 to 9, p=0.08560 b-rank test for bits 3 to 10, p=0.44641 b-rank test for bits 4 to 11, p=0.42529 b-rank test for bits 5 to 12, p=0.42095 b-rank test for bits 6 to 13, p=0.53712 b-rank test for bits 7 to 14, p=0.15037 b-rank test for bits 8 to 15, p=0.83522 b-rank test for bits 9 to 16, p=0.85881 b-rank test for bits 10 to 17, p=0.57845 b-rank test for bits 11 to 18, p=0.79671 b-rank test for bits 12 to 19, p=0.13400 b-rank test for bits 13 to 20, p=0.38453 b-rank test for bits 14 to 21, p=0.25118 b-rank test for bits 15 to 22, p=0.16447 b-rank test for bits 16 to 23, p=0.65726 b-rank test for bits 17 to 24, p=0.64143 b-rank test for bits 18 to 25, p=0.97100 b-rank test for bits 19 to 26, p=0.87573 b-rank test for bits 20 to 27, p=0.81471 b-rank test for bits 21 to 28, p=0.71236 b-rank test for bits 22 to 29, p=0.11398 b-rank test for bits 23 to 30, p=0.69284 b-rank test for bits 24 to 31, p=0.68955 b-rank test for bits 25 to 32, p=0.53624 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 = 0.916097 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-12-05_02:31 (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 142387 1.12 0.867800 2 141050 -2.01 0.022333 3 142200 0.68 0.751474 4 142177 0.63 0.734145 5 142059 0.35 0.636717 6 141237 -1.57 0.058107 7 142486 1.35 0.911068 8 142251 0.80 0.787650 9 141908 -0.00 0.498760 10 141912 0.01 0.502489 11 142495 1.37 0.914405 12 141255 -1.53 0.063156 13 141372 -1.26 0.104659 14 142127 0.51 0.694475 15 142267 0.84 0.798332 16 142472 1.31 0.905686 17 142201 0.68 0.752214 18 142372 1.08 0.860153 19 142379 1.10 0.863758 20 141652 -0.60 0.273841 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-12-05_02:31 Bits used No. missing words z-score p-value 23 to 32 142100 0.6575 0.744565 22 to 31 142031 0.4196 0.662594 21 to 30 141850 -0.2046 0.418948 20 to 29 142145 0.8127 0.791792 19 to 28 141384 -1.8115 0.035033 18 to 27 141488 -1.4529 0.073131 17 to 26 142114 0.7058 0.759831 16 to 25 141970 0.2092 0.582857 15 to 24 141547 -1.2494 0.105757 14 to 23 141131 -2.6839 0.003638 13 to 22 141680 -0.7908 0.214532 12 to 21 141612 -1.0253 0.152617 11 to 20 141568 -1.1770 0.119598 10 to 19 141974 0.2230 0.588232 9 to 18 141959 0.1713 0.567997 8 to 17 142140 0.7954 0.786814 7 to 16 142251 1.1782 0.880636 6 to 15 142200 1.0023 0.841903 5 to 14 142011 0.3506 0.637051 4 to 13 142177 0.9230 0.821996 3 to 12 141890 -0.0667 0.473428 2 to 11 142355 1.5368 0.937828 1 to 10 142090 0.6230 0.733358 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-12-05_02:31 Bits used No. missing words z-score p-value 28 to 32 142108 0.6735 0.749672 27 to 31 141875 -0.1164 0.453679 26 to 30 142076 0.5650 0.713957 25 to 29 141810 -0.3367 0.368167 24 to 28 141781 -0.4350 0.331775 23 to 27 141978 0.2328 0.592034 22 to 26 141615 -0.9977 0.159205 21 to 25 142035 0.4260 0.664946 20 to 24 142101 0.6497 0.742066 19 to 23 141299 -2.0689 0.019277 18 to 22 142225 1.0701 0.857706 17 to 21 141996 0.2938 0.615543 16 to 20 141951 0.1413 0.556166 15 to 19 141941 0.1074 0.542747 14 to 18 142199 0.9819 0.836933 13 to 17 140905 -3.4045 0.000331 12 to 16 141446 -1.5706 0.058137 11 to 15 141560 -1.1842 0.118173 10 to 14 141216 -2.3503 0.009380 9 to 13 141536 -1.2655 0.102842 8 to 12 142233 1.0972 0.863720 7 to 11 142144 0.7955 0.786836 6 to 10 141538 -1.2587 0.104061 5 to 9 142220 1.0531 0.853857 4 to 8 141645 -0.8960 0.185117 3 to 7 142332 1.4328 0.924040 2 to 6 141811 -0.3333 0.369446 1 to 5 141941 0.1074 0.542747 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-12-05_02:31 Bits used No. missing words z-score p-value 31 to 32 142053 0.4238 0.664146 30 to 31 141448 -1.3609 0.086780 29 to 30 142074 0.4858 0.686429 28 to 29 141533 -1.1101 0.133474 27 to 28 142211 0.8899 0.813235 26 to 27 142127 0.6421 0.739594 25 to 26 142232 0.9518 0.829408 24 to 25 141977 0.1996 0.579110 23 to 24 141825 -0.2488 0.401773 22 to 23 141946 0.1082 0.543070 21 to 22 142430 1.5359 0.937719 20 to 21 142098 0.5565 0.711082 19 to 20 141576 -0.9833 0.162736 18 to 19 141277 -1.8653 0.031071 17 to 18 141456 -1.3373 0.090569 16 to 17 142136 0.6686 0.748138 15 to 16 141976 0.1967 0.577956 14 to 15 141585 -0.9567 0.169353 13 to 14 142386 1.4061 0.920154 12 to 13 141362 -1.6145 0.053205 11 to 12 141879 -0.0895 0.464355 10 to 11 141437 -1.3933 0.081764 9 to 10 142179 0.7955 0.786835 8 to 9 142397 1.4386 0.924862 7 to 8 141710 -0.5880 0.278268 6 to 7 142773 2.5477 0.994578 5 to 6 142345 1.2852 0.900632 4 to 5 141868 -0.1219 0.451482 3 to 4 141454 -1.3432 0.089611 2 to 3 141911 0.0049 0.501965 1 to 2 142172 0.7748 0.780782 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-12-05_02:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2415.34 -1.197 0.115588 Test results for specific bytes for dh-ranFile-2015-12-05_02:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2503.83 0.054 0.521570 2 to 9 2385.42 -1.620 0.052568 3 to 10 2467.15 -0.465 0.321127 4 to 11 2405.04 -1.343 0.089656 5 to 12 2500.40 0.006 0.502256 6 to 13 2578.42 1.109 0.866292 7 to 14 2519.58 0.277 0.609056 8 to 15 2527.08 0.383 0.649138 9 to 16 2515.91 0.225 0.589022 10 to 17 2562.47 0.883 0.811489 11 to 18 2503.43 0.048 0.519328 12 to 19 2531.77 0.449 0.673372 13 to 20 2452.34 -0.674 0.250146 14 to 21 2425.92 -1.048 0.147398 15 to 22 2520.48 0.290 0.613957 16 to 23 2497.21 -0.039 0.484284 17 to 24 2460.52 -0.558 0.288308 18 to 25 2596.63 1.367 0.914112 19 to 26 2544.48 0.629 0.735343 20 to 27 2598.59 1.394 0.918373 21 to 28 2651.06 2.136 0.983672 22 to 29 2519.58 0.277 0.609069 23 to 30 2461.26 -0.548 0.291891 24 to 31 2383.98 -1.641 0.050423 25 to 32 2541.48 0.587 0.721292 CDPARK for dh-ranFile-2015-12-05_02:31: 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 3529 0.2740 0.607947 3544 0.9589 0.831196 3522 -0.0457 0.481790 3533 0.4566 0.676028 3495 -1.2785 0.100530 3552 1.3242 0.907282 3518 -0.2283 0.409702 3534 0.5023 0.692266 3505 -0.8219 0.205562 3523 0.0000 0.500000 Square side=100, avg. no. parked=3525.50 sample std.=16.16 p-value of the KSTEST for those 10 p-values: 0.862971 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-12-05_02:31 0.7599,0.2160,0.4182,0.7438,0.7045,0.8518,0.0689,0.0006,0.2111,0.4078, The KS test for those 10 p-values: 0.454661 The 3DSPHERES test for dh-ranFile-2015-12-05_02:31 sample no r^3 equiv. uni. 1 10.871 0.303976 2 31.462 0.649619 3 46.267 0.786096 4 27.397 0.598781 5 18.359 0.457723 6 84.900 0.940987 7 24.610 0.559711 8 42.369 0.756417 9 54.551 0.837708 10 8.297 0.241613 11 8.387 0.243880 12 13.741 0.367470 13 4.304 0.133653 14 3.232 0.102145 15 28.887 0.618211 16 37.200 0.710620 17 14.883 0.391104 18 27.690 0.602679 19 20.490 0.494909 20 34.053 0.678610 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.574419 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-12-05_02:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 0.1 0.3 0.6 0.1 -0.7 0.0 -0.0 -1.0 -0.1 -0.5 -0.1 0.8 -1.2 -0.4 0.8 0.7 1.3 -2.2 0.8 -0.2 -0.1 0.2 2.6 -0.9 -1.7 1.2 -0.3 0.4 0.3 -0.8 -0.7 0.8 -1.1 -0.4 -1.7 -1.6 -1.0 -1.2 1.0 0.9 2.0 -1.1 Chi-square with 42 degrees of freedom:44.246252 z-score=0.245086, p-value=0.622993 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-12-05_02:31 Test no p-value 1 0.925503 2 0.010798 3 0.331691 4 0.660069 5 0.256290 6 0.022547 7 0.300098 8 0.223329 9 0.016503 10 0.311061 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.019103 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-12-05_02:31: (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 66822 0.36 66722 0.05 3 25000.00 24832 1.13 24994 0.00 4 6666.67 6714 0.34 6590 0.88 5 1388.89 1366 0.38 1374 0.16 6 238.10 226 0.61 273 5.12 7 34.72 34 0.01 39 0.53 8 4.96 5 0.00 7 0.84 p=0.17060 p=0.72887 Number of rngs required: 688724, p-value: 0.644 RESULTS OF CRAPS TEST for dh-ranFile-2015-12-05_02:31 No. of wins: Observed Expected 98511 98585.9 z-score=-0.335, pvalue=0.36888 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66719 66666.7 0.041 0.041 2 37568 37654.3 0.198 0.239 3 26903 26954.7 0.099 0.338 4 19280 19313.5 0.058 0.396 5 13819 13851.4 0.076 0.472 6 9994 9943.5 0.256 0.728 7 7180 7145.0 0.171 0.899 8 5097 5139.1 0.344 1.244 9 3743 3699.9 0.503 1.747 10 2674 2666.3 0.022 1.769 11 1986 1923.3 2.042 3.811 12 1366 1388.7 0.372 4.183 13 1027 1003.7 0.540 4.724 14 746 726.1 0.543 5.267 15 543 525.8 0.560 5.827 16 339 381.2 4.661 10.488 17 263 276.5 0.663 11.151 18 201 200.8 0.000 11.151 19 157 146.0 0.831 11.983 20 109 106.2 0.073 12.056 21 286 287.1 0.004 12.060 Chisq= 12.06 for 20 degrees of freedom, p= 0.08600 SUMMARY of craptest p-value for no. of wins: 0.368884 p-value for throws/game: 0.086002 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-12-05_02:31 No. of wins: Observed Expected 98221 98585.9 z-score=-1.632, pvalue=0.05135 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66592 66666.7 0.084 0.084 2 37755 37654.3 0.269 0.353 3 26802 26954.7 0.865 1.218 4 19627 19313.5 5.090 6.308 5 13722 13851.4 1.209 7.517 6 10081 9943.5 1.900 9.418 7 7002 7145.0 2.863 12.281 8 5113 5139.1 0.132 12.413 9 3750 3699.9 0.679 13.092 10 2623 2666.3 0.703 13.795 11 1907 1923.3 0.139 13.934 12 1409 1388.7 0.296 14.230 13 1065 1003.7 3.742 17.972 14 707 726.1 0.505 18.476 15 509 525.8 0.539 19.015 16 357 381.2 1.530 20.545 17 266 276.5 0.402 20.947 18 184 200.8 1.410 22.357 19 128 146.0 2.216 24.573 20 106 106.2 0.000 24.573 21 295 287.1 0.217 24.790 Chisq= 24.79 for 20 degrees of freedom, p= 0.79042 SUMMARY of craptest p-value for no. of wins: 0.051354 p-value for throws/game: 0.790417 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0003,0.0006,0.0036,0.0094,0.0108,0.0165,0.0191,0.0193,0.0223,0.0225, 0.0311,0.0350,0.0485,0.0504,0.0514,0.0526,0.0532,0.0546,0.0581,0.0581, 0.0632,0.0655,0.0689,0.0731,0.0818,0.0856,0.0860,0.0868,0.0896,0.0897, 0.0906,0.1005,0.1021,0.1028,0.1041,0.1047,0.1058,0.1140,0.1156,0.1182, 0.1196,0.1234,0.1294,0.1335,0.1337,0.1340,0.1474,0.1504,0.1526,0.1571, 0.1592,0.1627,0.1645,0.1694,0.1706,0.1851,0.1904,0.2044,0.2056,0.2111, 0.2145,0.2152,0.2160,0.2203,0.2233,0.2244,0.2416,0.2439,0.2501,0.2512, 0.2563,0.2738,0.2776,0.2783,0.2883,0.2919,0.3001,0.3040,0.3111,0.3130, 0.3211,0.3306,0.3317,0.3318,0.3397,0.3511,0.3675,0.3682,0.3689,0.3694, 0.3828,0.3845,0.3869,0.3911,0.4018,0.4073,0.4078,0.4097,0.4182,0.4189, 0.4200,0.4206,0.4210,0.4244,0.4253,0.4462,0.4464,0.4515,0.4537,0.4547, 0.4577,0.4644,0.4734,0.4805,0.4818,0.4843,0.4907,0.4949,0.4988,0.5000, 0.5013,0.5020,0.5020,0.5023,0.5025,0.5193,0.5216,0.5357,0.5362,0.5371, 0.5427,0.5427,0.5431,0.5562,0.5597,0.5656,0.5680,0.5744,0.5780,0.5785, 0.5791,0.5829,0.5882,0.5890,0.5920,0.5988,0.5988,0.6027,0.6059,0.6079, 0.6091,0.6091,0.6100,0.6140,0.6155,0.6182,0.6183,0.6230,0.6367,0.6371, 0.6375,0.6414,0.6442,0.6491,0.6496,0.6573,0.6601,0.6626,0.6641,0.6649, 0.6734,0.6742,0.6760,0.6786,0.6864,0.6895,0.6923,0.6928,0.6945,0.7008, 0.7008,0.7045,0.7106,0.7111,0.7124,0.7140,0.7171,0.7213,0.7289,0.7334, 0.7341,0.7353,0.7396,0.7421,0.7438,0.7446,0.7481,0.7497,0.7515,0.7522, 0.7564,0.7598,0.7599,0.7649,0.7660,0.7709,0.7808,0.7850,0.7861,0.7868, 0.7868,0.7868,0.7877,0.7904,0.7918,0.7937,0.7945,0.7967,0.7983,0.8059, 0.8115,0.8132,0.8147,0.8187,0.8220,0.8294,0.8312,0.8352,0.8369,0.8377, 0.8413,0.8419,0.8450,0.8518,0.8539,0.8577,0.8587,0.8588,0.8602,0.8630, 0.8637,0.8638,0.8663,0.8678,0.8705,0.8757,0.8806,0.8908,0.8928,0.8978, 0.9006,0.9057,0.9073,0.9111,0.9141,0.9144,0.9161,0.9184,0.9202,0.9240, 0.9249,0.9255,0.9265,0.9377,0.9378,0.9410,0.9710,0.9837,0.9946, Overall p-value after applying KStest on 269 p-values = 0.101487 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.