RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-04-23_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 15.81 17.5025 0.579148 2 to 25 15.78 19.9210 0.721710 3 to 26 15.66 13.7664 0.316434 4 to 27 15.65 10.6279 0.124758 5 to 28 15.52 27.3935 0.947457 6 to 29 15.67 16.6994 0.525096 7 to 30 15.63 22.3043 0.826702 8 to 31 15.69 24.4085 0.891245 9 to 32 15.63 14.0173 0.334124 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.723790 Tough bday spacings test for dh-ranFile-2016-04-23_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 10 33 73 94 116 72 57 30 8 4 3 (O-E)^2/E 0.1 0.4 0.0 0.1 3.4 0.5 0.5 0.0 3.2 1.0 0.3 Birthday Spacings: Sum(O-E)^2/E= 9.457, p= 0.511 RESULTS OF GCD FOR dh-ranFile-2016-04-23_12:31 Euclid's algorithm: p-value, steps to gcd: 0.877324 p-value, dist. of gcd's: 0.327056 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-04-23_12:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.108 0.932 0.444 0.200 0.242 0.910 0.821 0.777 Bits 8 to 15---> 0.498 0.105 0.390 0.512 0.320 0.800 0.128 0.873 Bits 16 to 23---> 0.143 0.029 0.420 0.442 0.934 0.507 0.359 0.526 Bits 24 to 31---> 0.846 0.702 0.810 0.946 0.228 0.979 0.765 0.378 KS test for the above 32 p values: 0.297 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-04-23_12:31, p-values for 5 runs: 0.6801, 0.9827, 0.2857, 0.1934, 0.8867 Rank test for binary matrices (31x31) for dh-ranFile-2016-04-23_12:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 216 211.4 0.099 0.099 r= 29 5088 5134.0 0.412 0.512 r= 30 23161 23103.0 0.145 0.657 r= 31 11535 11551.5 0.024 0.681 chi-square = 0.681 with df = 3; p-value = 0.122 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-04-23_12:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 204 211.4 0.260 0.260 r= 30 5285 5134.0 4.441 4.701 r= 31 23007 23103.0 0.399 5.100 r= 32 11504 11551.5 0.196 5.296 chi-square = 5.296 with df = 3; p-value = 0.849 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-04-23_12:31 b-rank test for bits 1 to 8, p=0.75346 b-rank test for bits 2 to 9, p=0.92500 b-rank test for bits 3 to 10, p=0.24950 b-rank test for bits 4 to 11, p=0.44389 b-rank test for bits 5 to 12, p=0.46979 b-rank test for bits 6 to 13, p=0.85230 b-rank test for bits 7 to 14, p=0.75550 b-rank test for bits 8 to 15, p=0.97127 b-rank test for bits 9 to 16, p=0.60714 b-rank test for bits 10 to 17, p=0.44084 b-rank test for bits 11 to 18, p=0.28851 b-rank test for bits 12 to 19, p=0.24081 b-rank test for bits 13 to 20, p=0.16608 b-rank test for bits 14 to 21, p=0.32990 b-rank test for bits 15 to 22, p=0.23065 b-rank test for bits 16 to 23, p=0.55002 b-rank test for bits 17 to 24, p=0.20730 b-rank test for bits 18 to 25, p=0.50879 b-rank test for bits 19 to 26, p=0.38874 b-rank test for bits 20 to 27, p=0.51110 b-rank test for bits 21 to 28, p=0.32407 b-rank test for bits 22 to 29, p=0.97383 b-rank test for bits 23 to 30, p=0.08913 b-rank test for bits 24 to 31, p=0.14017 b-rank test for bits 25 to 32, p=0.36226 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 = 0.483358 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-04-23_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 141340 -1.33 0.091725 2 142218 0.72 0.764604 3 141631 -0.65 0.257748 4 142966 2.47 0.993223 5 141860 -0.12 0.454121 6 141780 -0.30 0.381260 7 141826 -0.19 0.422815 8 141376 -1.25 0.106364 9 141284 -1.46 0.072001 10 141711 -0.46 0.321543 11 141728 -0.42 0.335904 12 140945 -2.25 0.012126 13 142169 0.61 0.727977 14 141033 -2.05 0.020305 15 141983 0.17 0.568331 16 141843 -0.15 0.438420 17 141843 -0.15 0.438420 18 141928 0.04 0.517397 19 142398 1.14 0.873222 20 142045 0.32 0.624373 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-04-23_12:31 Bits used No. missing words z-score p-value 23 to 32 141890 -0.0667 0.473428 22 to 31 142164 0.8782 0.810075 21 to 30 142110 0.6920 0.755521 20 to 29 141744 -0.5701 0.284304 19 to 28 141891 -0.0632 0.474801 18 to 27 142055 0.5023 0.692275 17 to 26 141967 0.1989 0.578815 16 to 25 141965 0.1920 0.576115 15 to 24 141890 -0.0667 0.473428 14 to 23 142220 1.0713 0.857977 13 to 22 141999 0.3092 0.621418 12 to 21 141696 -0.7356 0.230981 11 to 20 142156 0.8506 0.802500 10 to 19 142061 0.5230 0.699513 9 to 18 141586 -1.1149 0.132440 8 to 17 141893 -0.0563 0.477547 7 to 16 142070 0.5540 0.710222 6 to 15 141752 -0.5425 0.293731 5 to 14 142140 0.7954 0.786814 4 to 13 142326 1.4368 0.924612 3 to 12 141887 -0.0770 0.469312 2 to 11 141870 -0.1356 0.446061 1 to 10 142241 1.1437 0.873624 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-04-23_12:31 Bits used No. missing words z-score p-value 28 to 32 141634 -0.9333 0.175327 27 to 31 142289 1.2870 0.900956 26 to 30 141474 -1.4757 0.070013 25 to 29 142266 1.2091 0.886678 24 to 28 141681 -0.7740 0.219465 23 to 27 142004 0.3209 0.625863 22 to 26 142052 0.4836 0.685675 21 to 25 142403 1.6735 0.952881 20 to 24 141889 -0.0689 0.472529 19 to 23 141824 -0.2893 0.386193 18 to 22 141881 -0.0960 0.461747 17 to 21 141640 -0.9130 0.180626 16 to 20 142150 0.8158 0.792702 15 to 19 142121 0.7175 0.763475 14 to 18 141619 -0.9842 0.162516 13 to 17 142146 0.8023 0.788802 12 to 16 142181 0.9209 0.821453 11 to 15 141848 -0.2079 0.417654 10 to 14 142327 1.4158 0.921587 9 to 13 141574 -1.1367 0.127829 8 to 12 141907 -0.0079 0.496849 7 to 11 141739 -0.5774 0.281838 6 to 10 142016 0.3616 0.641172 5 to 9 142067 0.5345 0.703493 4 to 8 141837 -0.2452 0.403156 3 to 7 141756 -0.5198 0.301615 2 to 6 141431 -1.6215 0.052460 1 to 5 142017 0.3650 0.642438 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-04-23_12:31 Bits used No. missing words z-score p-value 31 to 32 142263 1.0433 0.851589 30 to 31 141689 -0.6499 0.257865 29 to 30 142078 0.4976 0.690600 28 to 29 142282 1.0993 0.864186 27 to 28 141866 -0.1278 0.449147 26 to 27 141468 -1.3019 0.096482 25 to 26 141768 -0.4169 0.338375 24 to 25 142196 0.8456 0.801122 23 to 24 142004 0.2793 0.609978 22 to 23 141641 -0.7915 0.214316 21 to 22 142942 3.0462 0.998841 20 to 21 142234 0.9577 0.830900 19 to 20 141962 0.1554 0.561735 18 to 19 141571 -0.9980 0.159134 17 to 18 141344 -1.6676 0.047694 16 to 17 141870 -0.1160 0.453819 15 to 16 141760 -0.4405 0.329787 14 to 15 142109 0.5890 0.722068 13 to 14 141832 -0.2281 0.409780 12 to 13 142026 0.3442 0.634637 11 to 12 141959 0.1465 0.558244 10 to 11 141428 -1.4199 0.077825 9 to 10 142129 0.6480 0.741506 8 to 9 141829 -0.2370 0.406343 7 to 8 142413 1.4858 0.931328 6 to 7 142015 0.3117 0.622370 5 to 6 141665 -0.7207 0.235536 4 to 5 142008 0.2911 0.614498 3 to 4 141688 -0.6529 0.256913 2 to 3 142397 1.4386 0.924862 1 to 2 141870 -0.1160 0.453819 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-04-23_12:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2376.40 -1.748 0.040230 Test results for specific bytes for dh-ranFile-2016-04-23_12:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2523.83 0.337 0.631929 2 to 9 2474.48 -0.361 0.359105 3 to 10 2575.15 1.063 0.856061 4 to 11 2493.48 -0.092 0.463279 5 to 12 2542.56 0.602 0.726399 6 to 13 2397.46 -1.450 0.073520 7 to 14 2539.72 0.562 0.712869 8 to 15 2488.27 -0.166 0.434140 9 to 16 2528.58 0.404 0.656968 10 to 17 2494.61 -0.076 0.469623 11 to 18 2492.47 -0.106 0.457596 12 to 19 2402.91 -1.373 0.084871 13 to 20 2453.25 -0.661 0.254246 14 to 21 2511.65 0.165 0.565438 15 to 22 2531.85 0.450 0.673817 16 to 23 2395.68 -1.475 0.070071 17 to 24 2447.85 -0.737 0.230411 18 to 25 2471.21 -0.407 0.341933 19 to 26 2334.47 -2.341 0.009616 20 to 27 2399.70 -1.419 0.078021 21 to 28 2569.19 0.979 0.836095 22 to 29 2451.84 -0.681 0.247898 23 to 30 2451.64 -0.684 0.247011 24 to 31 2450.66 -0.698 0.242663 25 to 32 2433.40 -0.942 0.173136 CDPARK for dh-ranFile-2016-04-23_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 3536 0.5936 0.723613 3515 -0.3653 0.357445 3563 1.8265 0.966111 3544 0.9589 0.831196 3523 0.0000 0.500000 3522 -0.0457 0.481790 3539 0.7306 0.767486 3507 -0.7306 0.232514 3551 1.2785 0.899470 3544 0.9589 0.831196 Square side=100, avg. no. parked=3534.40 sample std.=16.47 p-value of the KSTEST for those 10 p-values: 0.138214 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-04-23_12:31 0.2747,0.5698,0.1411,0.7412,0.0242,0.5490,0.6881,0.0845,0.5445,0.1074, The KS test for those 10 p-values: 0.217021 The 3DSPHERES test for dh-ranFile-2016-04-23_12:31 sample no r^3 equiv. uni. 1 20.545 0.495834 2 10.566 0.296871 3 66.234 0.890056 4 33.593 0.673641 5 10.107 0.286028 6 42.355 0.756303 7 13.962 0.372115 8 15.375 0.401002 9 156.788 0.994627 10 3.248 0.102612 11 34.740 0.685885 12 30.348 0.636368 13 91.139 0.952068 14 22.124 0.521674 15 26.211 0.582593 16 57.398 0.852401 17 36.922 0.707924 18 6.788 0.202492 19 18.889 0.467216 20 56.251 0.846648 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.308351 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-04-23_12:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 1.3 -0.7 1.3 1.1 -1.3 -0.7 -1.3 -0.1 -0.3 0.8 1.0 -0.3 1.2 0.3 1.2 -0.8 -0.1 -0.1 0.0 0.3 -0.3 -0.1 -1.3 0.0 -0.6 -0.0 1.6 -0.3 -0.9 0.3 -1.1 -0.7 -0.1 -0.9 0.2 -0.3 -0.7 -0.1 -1.2 1.0 -0.6 -1.0 -1.1 Chi-square with 42 degrees of freedom:27.970611 z-score=-1.530732, p-value=0.047490 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-04-23_12:31 Test no p-value 1 0.877787 2 0.624155 3 0.012211 4 0.247574 5 0.146136 6 0.381335 7 0.290657 8 0.618687 9 0.319518 10 0.024749 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.154662 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-04-23_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 66862 0.57 66543 0.23 3 25000.00 24907 0.35 25196 1.54 4 6666.67 6511 3.63 6684 0.05 5 1388.89 1444 2.19 1299 5.82 6 238.10 240 0.02 240 0.02 7 34.72 32 0.21 34 0.01 8 4.96 3 0.77 3 0.77 p=0.74244 p=0.79197 Number of rngs required: 689465, p-value: 0.892 RESULTS OF CRAPS TEST for dh-ranFile-2016-04-23_12:31 No. of wins: Observed Expected 98453 98585.9 z-score=-0.594, pvalue=0.27618 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66343 66666.7 1.571 1.571 2 37910 37654.3 1.736 3.308 3 27041 26954.7 0.276 3.584 4 19421 19313.5 0.599 4.182 5 13869 13851.4 0.022 4.205 6 9916 9943.5 0.076 4.281 7 6976 7145.0 3.999 8.280 8 5107 5139.1 0.200 8.480 9 3795 3699.9 2.446 10.926 10 2687 2666.3 0.161 11.087 11 1998 1923.3 2.899 13.986 12 1364 1388.7 0.441 14.426 13 997 1003.7 0.045 14.471 14 693 726.1 1.513 15.984 15 557 525.8 1.847 17.831 16 347 381.2 3.060 20.891 17 275 276.5 0.009 20.899 18 203 200.8 0.023 20.923 19 134 146.0 0.984 21.907 20 101 106.2 0.256 22.163 21 266 287.1 1.553 23.715 Chisq= 23.72 for 20 degrees of freedom, p= 0.74495 SUMMARY of craptest p-value for no. of wins: 0.276182 p-value for throws/game: 0.744950 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-04-23_12:31 No. of wins: Observed Expected 98495 98585.9 z-score=-0.406, pvalue=0.34223 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66604 66666.7 0.059 0.059 2 37929 37654.3 2.004 2.063 3 26947 26954.7 0.002 2.065 4 19200 19313.5 0.667 2.731 5 13771 13851.4 0.467 3.198 6 9749 9943.5 3.806 7.005 7 7255 7145.0 1.693 8.697 8 5013 5139.1 3.093 11.790 9 3801 3699.9 2.765 14.555 10 2688 2666.3 0.177 14.731 11 1937 1923.3 0.097 14.828 12 1401 1388.7 0.108 14.937 13 1003 1003.7 0.001 14.937 14 733 726.1 0.065 15.002 15 580 525.8 5.579 20.581 16 377 381.2 0.045 20.626 17 251 276.5 2.359 22.985 18 212 200.8 0.621 23.606 19 144 146.0 0.027 23.633 20 132 106.2 6.260 29.893 21 273 287.1 0.694 30.587 Chisq= 30.59 for 20 degrees of freedom, p= 0.93911 SUMMARY of craptest p-value for no. of wins: 0.342234 p-value for throws/game: 0.939109 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0096,0.0121,0.0122,0.0203,0.0242,0.0247,0.0290,0.0402,0.0475,0.0477, 0.0525,0.0700,0.0701,0.0720,0.0735,0.0778,0.0780,0.0845,0.0849,0.0891, 0.0917,0.0965,0.1026,0.1049,0.1064,0.1074,0.1082,0.1223,0.1248,0.1278, 0.1281,0.1324,0.1382,0.1402,0.1411,0.1431,0.1461,0.1547,0.1591,0.1625, 0.1661,0.1731,0.1753,0.1806,0.1934,0.1997,0.2025,0.2073,0.2143,0.2170, 0.2195,0.2280,0.2304,0.2306,0.2310,0.2325,0.2355,0.2408,0.2417,0.2427, 0.2470,0.2476,0.2479,0.2495,0.2542,0.2569,0.2577,0.2579,0.2747,0.2762, 0.2818,0.2843,0.2857,0.2860,0.2885,0.2907,0.2937,0.2969,0.2970,0.3016, 0.3084,0.3164,0.3195,0.3197,0.3215,0.3241,0.3271,0.3298,0.3299,0.3341, 0.3359,0.3384,0.3419,0.3422,0.3574,0.3591,0.3592,0.3623,0.3721,0.3780, 0.3813,0.3813,0.3862,0.3887,0.3904,0.4010,0.4032,0.4063,0.4098,0.4177, 0.4204,0.4228,0.4341,0.4384,0.4384,0.4408,0.4418,0.4439,0.4439,0.4461, 0.4491,0.4538,0.4538,0.4541,0.4576,0.4617,0.4633,0.4672,0.4693,0.4696, 0.4698,0.4725,0.4734,0.4734,0.4748,0.4775,0.4818,0.4834,0.4958,0.4968, 0.4985,0.5000,0.5065,0.5088,0.5106,0.5111,0.5118,0.5174,0.5217,0.5251, 0.5261,0.5445,0.5490,0.5500,0.5582,0.5617,0.5654,0.5683,0.5698,0.5761, 0.5788,0.5791,0.5826,0.6071,0.6100,0.6145,0.6187,0.6214,0.6224,0.6242, 0.6244,0.6259,0.6319,0.6346,0.6364,0.6412,0.6424,0.6570,0.6736,0.6738, 0.6801,0.6857,0.6859,0.6881,0.6906,0.6923,0.6995,0.7015,0.7035,0.7079, 0.7102,0.7129,0.7217,0.7221,0.7236,0.7238,0.7264,0.7280,0.7412,0.7415, 0.7424,0.7449,0.7535,0.7555,0.7555,0.7563,0.7635,0.7646,0.7649,0.7675, 0.7771,0.7868,0.7888,0.7920,0.7927,0.7999,0.8011,0.8025,0.8101,0.8105, 0.8206,0.8215,0.8267,0.8309,0.8312,0.8312,0.8361,0.8463,0.8466,0.8486, 0.8516,0.8523,0.8524,0.8561,0.8580,0.8642,0.8729,0.8732,0.8736,0.8773, 0.8778,0.8867,0.8867,0.8901,0.8912,0.8916,0.8995,0.9010,0.9096,0.9216, 0.9246,0.9249,0.9250,0.9313,0.9317,0.9337,0.9391,0.9462,0.9475,0.9521, 0.9529,0.9661,0.9713,0.9738,0.9792,0.9827,0.9932,0.9946,0.9988, Overall p-value after applying KStest on 269 p-values = 0.803079 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.