RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-12-21_03:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.96 24.7688 0.899995 2 to 25 15.71 17.3941 0.572012 3 to 26 15.80 23.3524 0.861873 4 to 27 15.67 19.6909 0.709655 5 to 28 15.80 18.1940 0.623295 6 to 29 15.60 24.6492 0.897160 7 to 30 15.61 20.7802 0.763724 8 to 31 16.06 16.7118 0.525946 9 to 32 15.87 9.7742 0.087190 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.128366 Tough bday spacings test for dh-ranFile-2015-12-21_03:31: 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 9 37 90 88 91 65 55 29 26 4 6 (O-E)^2/E 0.0 0.0 3.8 1.0 0.5 2.2 0.2 0.0 8.3 1.0 0.9 Birthday Spacings: Sum(O-E)^2/E= 17.894, p= 0.943 RESULTS OF GCD FOR dh-ranFile-2015-12-21_03:31 Euclid's algorithm: p-value, steps to gcd: 0.240012 p-value, dist. of gcd's: 0.916281 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-12-21_03:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.750 0.164 0.323 0.336 0.177 0.218 0.062 0.251 Bits 8 to 15---> 0.183 0.487 0.404 0.992 0.844 0.520 0.834 0.251 Bits 16 to 23---> 0.340 0.466 0.076 0.343 0.007 0.677 0.021 0.820 Bits 24 to 31---> 0.706 0.000 0.602 0.413 0.566 0.333 0.713 0.873 KS test for the above 32 p values: 0.776 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-12-21_03:31, p-values for 5 runs: 0.4649, 0.2984, 0.2906, 0.8338, 0.1875 Rank test for binary matrices (31x31) for dh-ranFile-2015-12-21_03:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 214 211.4 0.032 0.032 r= 29 5077 5134.0 0.633 0.665 r= 30 23083 23103.0 0.017 0.682 r= 31 11626 11551.5 0.480 1.162 chi-square = 1.162 with df = 3; p-value = 0.238 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-12-21_03:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 218 211.4 0.205 0.205 r= 30 5020 5134.0 2.532 2.737 r= 31 23185 23103.0 0.291 3.027 r= 32 11577 11551.5 0.056 3.084 chi-square = 3.084 with df = 3; p-value = 0.621 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-12-21_03:31 b-rank test for bits 1 to 8, p=0.15743 b-rank test for bits 2 to 9, p=0.42798 b-rank test for bits 3 to 10, p=0.19317 b-rank test for bits 4 to 11, p=0.25898 b-rank test for bits 5 to 12, p=0.79536 b-rank test for bits 6 to 13, p=0.60890 b-rank test for bits 7 to 14, p=0.04687 b-rank test for bits 8 to 15, p=0.96649 b-rank test for bits 9 to 16, p=0.26936 b-rank test for bits 10 to 17, p=0.61202 b-rank test for bits 11 to 18, p=0.41931 b-rank test for bits 12 to 19, p=0.49692 b-rank test for bits 13 to 20, p=0.21407 b-rank test for bits 14 to 21, p=0.56973 b-rank test for bits 15 to 22, p=0.88332 b-rank test for bits 16 to 23, p=0.74542 b-rank test for bits 17 to 24, p=0.84057 b-rank test for bits 18 to 25, p=0.32021 b-rank test for bits 19 to 26, p=0.68752 b-rank test for bits 20 to 27, p=0.43849 b-rank test for bits 21 to 28, p=0.79163 b-rank test for bits 22 to 29, p=0.58077 b-rank test for bits 23 to 30, p=0.31061 b-rank test for bits 24 to 31, p=0.19557 b-rank test for bits 25 to 32, p=0.94907 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 = 0.942884 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-12-21_03:31 (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 142003 0.22 0.586619 2 141875 -0.08 0.468035 3 141990 0.19 0.574750 4 141147 -1.78 0.037444 5 141913 0.01 0.503421 6 141787 -0.29 0.387509 7 142505 1.39 0.918001 8 141620 -0.68 0.249519 9 141394 -1.20 0.114287 10 141761 -0.35 0.364459 11 142466 1.30 0.903308 12 141969 0.14 0.555439 13 141927 0.04 0.516466 14 141494 -0.97 0.165924 15 142570 1.54 0.938660 16 141863 -0.11 0.456900 17 142788 2.05 0.979962 18 142045 0.32 0.624373 19 142430 1.22 0.888106 20 142226 0.74 0.770315 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-12-21_03:31 Bits used No. missing words z-score p-value 23 to 32 142014 0.3609 0.640925 22 to 31 142546 2.1954 0.985933 21 to 30 141663 -0.8494 0.197826 20 to 29 141668 -0.8322 0.202656 19 to 28 142060 0.5196 0.698312 18 to 27 141795 -0.3942 0.346701 17 to 26 141902 -0.0253 0.489918 16 to 25 141577 -1.1460 0.125905 15 to 24 141384 -1.8115 0.035033 14 to 23 141809 -0.3460 0.364684 13 to 22 141772 -0.4736 0.317910 12 to 21 141526 -1.3218 0.093113 11 to 20 142191 0.9713 0.834295 10 to 19 142105 0.6747 0.750075 9 to 18 142126 0.7471 0.772510 8 to 17 142018 0.3747 0.646067 7 to 16 141366 -1.8736 0.030496 6 to 15 142064 0.5333 0.703103 5 to 14 141917 0.0264 0.510550 4 to 13 141579 -1.1391 0.127337 3 to 12 141557 -1.2149 0.112196 2 to 11 142306 1.3678 0.914317 1 to 10 142207 1.0264 0.847660 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-12-21_03:31 Bits used No. missing words z-score p-value 28 to 32 141662 -0.8384 0.200901 27 to 31 142323 1.4023 0.919583 26 to 30 142088 0.6057 0.727630 25 to 29 141898 -0.0384 0.484682 24 to 28 142122 0.7209 0.764519 23 to 27 142613 2.3853 0.991468 22 to 26 141999 0.3040 0.619423 21 to 25 141677 -0.7876 0.215477 20 to 24 142053 0.4870 0.686877 19 to 23 142185 0.9345 0.824970 18 to 22 141737 -0.5842 0.279553 17 to 21 141684 -0.7638 0.222484 16 to 20 141997 0.2972 0.616838 15 to 19 141740 -0.5740 0.282984 14 to 18 142117 0.7040 0.759273 13 to 17 142064 0.5243 0.699967 12 to 16 141698 -0.7164 0.236881 11 to 15 141906 -0.0113 0.495497 10 to 14 141900 -0.0316 0.487385 9 to 13 141641 -0.9096 0.181519 8 to 12 141536 -1.2655 0.102842 7 to 11 141571 -1.1469 0.125715 6 to 10 141682 -0.7706 0.220469 5 to 9 142364 1.5413 0.938373 4 to 8 141621 -0.9774 0.164188 3 to 7 141766 -0.4859 0.313532 2 to 6 141613 -1.0045 0.157567 1 to 5 141805 -0.3537 0.361797 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-12-21_03:31 Bits used No. missing words z-score p-value 31 to 32 142201 0.8604 0.805211 30 to 31 141935 0.0757 0.530180 29 to 30 142068 0.4681 0.680127 28 to 29 142588 2.0020 0.977356 27 to 28 141870 -0.1160 0.453819 26 to 27 141687 -0.6558 0.255963 25 to 26 142212 0.8928 0.814026 24 to 25 142225 0.9312 0.824120 23 to 24 141656 -0.7473 0.227445 22 to 23 141900 -0.0275 0.489022 21 to 22 142351 1.3029 0.903689 20 to 21 141699 -0.6204 0.267483 19 to 20 141647 -0.7738 0.219514 18 to 19 141440 -1.3845 0.083110 17 to 18 142349 1.2970 0.902678 16 to 17 141808 -0.2989 0.382505 15 to 16 142125 0.6362 0.737675 14 to 15 141587 -0.9508 0.170846 13 to 14 141619 -0.8564 0.195880 12 to 13 141995 0.2527 0.599755 11 to 12 141330 -1.7089 0.043731 10 to 11 141580 -0.9715 0.165656 9 to 10 141728 -0.5349 0.296361 8 to 9 141630 -0.8240 0.204975 7 to 8 141622 -0.8476 0.198336 6 to 7 142171 0.7719 0.779910 5 to 6 141532 -1.1131 0.132840 4 to 5 141714 -0.5762 0.282242 3 to 4 142539 1.8574 0.968375 2 to 3 142206 0.8751 0.809249 1 to 2 141802 -0.3166 0.375771 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-12-21_03:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2412.87 -1.232 0.108927 Test results for specific bytes for dh-ranFile-2015-12-21_03:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2566.73 0.944 0.827342 2 to 9 2464.67 -0.500 0.308651 3 to 10 2528.55 0.404 0.656807 4 to 11 2517.91 0.253 0.599991 5 to 12 2489.82 -0.144 0.442760 6 to 13 2430.84 -0.978 0.164025 7 to 14 2509.05 0.128 0.550914 8 to 15 2445.29 -0.774 0.219566 9 to 16 2418.92 -1.147 0.125759 10 to 17 2506.18 0.087 0.534831 11 to 18 2573.12 1.034 0.849446 12 to 19 2566.61 0.942 0.826897 13 to 20 2497.64 -0.033 0.486667 14 to 21 2522.83 0.323 0.626597 15 to 22 2512.12 0.171 0.568048 16 to 23 2559.90 0.847 0.801532 17 to 24 2576.80 1.086 0.861277 18 to 25 2453.00 -0.665 0.253129 19 to 26 2482.82 -0.243 0.403994 20 to 27 2470.70 -0.414 0.339295 21 to 28 2606.77 1.510 0.934478 22 to 29 2538.81 0.549 0.708459 23 to 30 2417.30 -1.170 0.121101 24 to 31 2489.76 -0.145 0.442412 25 to 32 2504.72 0.067 0.526598 CDPARK for dh-ranFile-2015-12-21_03:31: 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 3579 2.5571 0.994722 3482 -1.8721 0.030593 3536 0.5936 0.723613 3557 1.5525 0.939730 3523 0.0000 0.500000 3570 2.1461 0.984068 3544 0.9589 0.831196 3508 -0.6849 0.246694 3503 -0.9132 0.180558 3544 0.9589 0.831196 Square side=100, avg. no. parked=3534.60 sample std.=29.18 p-value of the KSTEST for those 10 p-values: 0.084312 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-12-21_03:31 0.8279,0.3780,0.4563,0.9372,0.9611,0.4118,0.1561,0.6251,0.9513,0.0669, The KS test for those 10 p-values: 0.424431 The 3DSPHERES test for dh-ranFile-2015-12-21_03:31 sample no r^3 equiv. uni. 1 0.839 0.027586 2 4.213 0.131008 3 1.603 0.052043 4 29.239 0.622667 5 132.723 0.988015 6 28.655 0.615251 7 16.867 0.430072 8 78.824 0.927738 9 13.630 0.365122 10 16.896 0.430617 11 6.665 0.199208 12 37.879 0.717091 13 59.098 0.860534 14 5.487 0.167141 15 2.537 0.081086 16 1.870 0.060415 17 108.659 0.973270 18 10.438 0.293847 19 227.273 0.999487 20 0.814 0.026773 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.101438 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-12-21_03:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 0.9 -0.6 -0.3 0.3 1.7 -0.8 -1.6 0.1 0.5 -0.4 -0.6 2.3 -1.5 -0.6 1.0 0.2 -0.7 0.4 0.2 0.6 -0.8 0.9 -1.7 -0.1 -0.1 -0.7 0.2 0.6 1.0 0.5 0.4 2.1 -1.1 -0.2 -0.5 -0.2 0.2 -0.8 0.4 -0.6 0.0 -1.1 Chi-square with 42 degrees of freedom:33.797011 z-score=-0.895019, p-value=0.187564 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-12-21_03:31 Test no p-value 1 0.344892 2 0.984977 3 0.156795 4 0.292502 5 0.241784 6 0.377720 7 0.360962 8 0.975138 9 0.159988 10 0.756487 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.326980 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-12-21_03:31: (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 66700 0.02 66444 0.74 3 25000.00 25048 0.09 25153 0.94 4 6666.67 6627 0.24 6646 0.06 5 1388.89 1355 0.83 1448 2.52 6 238.10 236 0.02 270 4.28 7 34.72 30 0.64 36 0.05 8 4.96 3 0.77 2 1.77 p=0.14363 p=0.88929 Number of rngs required: 687554, p-value: 0.163 RESULTS OF CRAPS TEST for dh-ranFile-2015-12-21_03:31 No. of wins: Observed Expected 98432 98585.9 z-score=-0.688, pvalue=0.24568 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66686 66666.7 0.006 0.006 2 37655 37654.3 0.000 0.006 3 26867 26954.7 0.286 0.291 4 19430 19313.5 0.703 0.994 5 13820 13851.4 0.071 1.066 6 9788 9943.5 2.433 3.499 7 7193 7145.0 0.322 3.821 8 5206 5139.1 0.872 4.692 9 3725 3699.9 0.171 4.863 10 2620 2666.3 0.804 5.667 11 2021 1923.3 4.960 10.627 12 1371 1388.7 0.227 10.854 13 999 1003.7 0.022 10.876 14 717 726.1 0.115 10.991 15 521 525.8 0.044 11.035 16 353 381.2 2.079 13.115 17 272 276.5 0.075 13.189 18 196 200.8 0.116 13.305 19 154 146.0 0.440 13.745 20 120 106.2 1.789 15.534 21 286 287.1 0.004 15.539 Chisq= 15.54 for 20 degrees of freedom, p= 0.25520 SUMMARY of craptest p-value for no. of wins: 0.245681 p-value for throws/game: 0.255197 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-12-21_03:31 No. of wins: Observed Expected 98406 98585.9 z-score=-0.804, pvalue=0.21057 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66552 66666.7 0.197 0.197 2 38099 37654.3 5.251 5.449 3 26842 26954.7 0.471 5.920 4 19247 19313.5 0.229 6.149 5 13728 13851.4 1.100 7.249 6 9883 9943.5 0.369 7.617 7 7231 7145.0 1.035 8.652 8 5138 5139.1 0.000 8.652 9 3638 3699.9 1.034 9.686 10 2609 2666.3 1.231 10.918 11 1924 1923.3 0.000 10.918 12 1442 1388.7 2.043 12.960 13 961 1003.7 1.818 14.778 14 742 726.1 0.346 15.125 15 530 525.8 0.033 15.158 16 384 381.2 0.021 15.179 17 285 276.5 0.259 15.438 18 209 200.8 0.332 15.770 19 160 146.0 1.346 17.116 20 109 106.2 0.073 17.189 21 287 287.1 0.000 17.189 Chisq= 17.19 for 20 degrees of freedom, p= 0.35932 SUMMARY of craptest p-value for no. of wins: 0.210574 p-value for throws/game: 0.359319 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0003,0.0075,0.0208,0.0268,0.0276,0.0305,0.0306,0.0350,0.0374,0.0437, 0.0469,0.0520,0.0604,0.0622,0.0669,0.0764,0.0811,0.0831,0.0843,0.0872, 0.0931,0.1014,0.1028,0.1089,0.1122,0.1143,0.1211,0.1257,0.1258,0.1259, 0.1273,0.1284,0.1310,0.1328,0.1436,0.1561,0.1568,0.1574,0.1576,0.1600, 0.1627,0.1636,0.1640,0.1642,0.1657,0.1659,0.1671,0.1708,0.1773,0.1806, 0.1815,0.1825,0.1875,0.1876,0.1932,0.1956,0.1959,0.1978,0.1983,0.1992, 0.2009,0.2027,0.2050,0.2106,0.2141,0.2155,0.2183,0.2195,0.2196,0.2205, 0.2225,0.2274,0.2369,0.2379,0.2400,0.2418,0.2457,0.2467,0.2495,0.2507, 0.2507,0.2531,0.2552,0.2560,0.2590,0.2675,0.2694,0.2796,0.2822,0.2830, 0.2906,0.2925,0.2938,0.2964,0.2984,0.3087,0.3106,0.3135,0.3179,0.3202, 0.3230,0.3270,0.3334,0.3362,0.3393,0.3404,0.3432,0.3449,0.3467,0.3593, 0.3610,0.3618,0.3645,0.3647,0.3651,0.3758,0.3777,0.3780,0.3825,0.3875, 0.4036,0.4040,0.4118,0.4126,0.4193,0.4244,0.4280,0.4301,0.4306,0.4385, 0.4424,0.4428,0.4538,0.4563,0.4569,0.4649,0.4664,0.4680,0.4847,0.4867, 0.4872,0.4874,0.4890,0.4899,0.4955,0.4969,0.5000,0.5034,0.5106,0.5165, 0.5200,0.5259,0.5266,0.5302,0.5348,0.5509,0.5554,0.5657,0.5680,0.5697, 0.5720,0.5748,0.5808,0.5866,0.5998,0.6000,0.6017,0.6089,0.6120,0.6153, 0.6168,0.6194,0.6211,0.6227,0.6233,0.6244,0.6251,0.6266,0.6409,0.6461, 0.6568,0.6772,0.6801,0.6869,0.6875,0.6983,0.7000,0.7031,0.7060,0.7085, 0.7097,0.7126,0.7171,0.7236,0.7276,0.7377,0.7454,0.7498,0.7501,0.7565, 0.7593,0.7637,0.7645,0.7703,0.7725,0.7765,0.7799,0.7916,0.7954,0.8015, 0.8052,0.8092,0.8140,0.8197,0.8241,0.8250,0.8269,0.8273,0.8279,0.8312, 0.8312,0.8338,0.8342,0.8343,0.8406,0.8441,0.8477,0.8494,0.8605,0.8613, 0.8619,0.8732,0.8833,0.8881,0.8893,0.8972,0.9000,0.9027,0.9033,0.9037, 0.9143,0.9163,0.9180,0.9196,0.9277,0.9345,0.9372,0.9384,0.9387,0.9397, 0.9429,0.9432,0.9491,0.9513,0.9611,0.9665,0.9684,0.9733,0.9751,0.9774, 0.9800,0.9841,0.9850,0.9859,0.9880,0.9915,0.9922,0.9947,0.9995, Overall p-value after applying KStest on 269 p-values = 0.242108 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.