RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-11-21_09:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.78 12.9335 0.259371 2 to 25 15.81 14.8507 0.393762 3 to 26 15.79 30.1455 0.974686 4 to 27 15.95 12.1438 0.208646 5 to 28 15.77 9.3753 0.072253 6 to 29 15.52 25.2681 0.911132 7 to 30 15.93 22.7655 0.842958 8 to 31 15.59 26.3849 0.932272 9 to 32 15.64 23.0651 0.852857 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.170828 Tough bday spacings test for dh-ranFile-2015-11-21_09:31: 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 31 76 108 121 65 40 26 17 5 3 (O-E)^2/E 0.1 0.9 0.1 1.1 5.6 2.2 2.8 0.5 0.3 0.4 0.3 Birthday Spacings: Sum(O-E)^2/E= 14.242, p= 0.838 RESULTS OF GCD FOR dh-ranFile-2015-11-21_09:31 Euclid's algorithm: p-value, steps to gcd: 0.214538 p-value, dist. of gcd's: 0.020136 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-11-21_09:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.894 0.972 0.500 0.809 0.179 0.522 0.779 0.531 Bits 8 to 15---> 0.933 0.714 0.923 0.565 0.650 0.065 0.192 0.621 Bits 16 to 23---> 0.380 0.228 0.883 0.328 0.842 0.852 0.325 0.997 Bits 24 to 31---> 0.094 0.403 0.912 0.242 0.814 0.277 0.158 0.078 KS test for the above 32 p values: 0.581 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-11-21_09:31, p-values for 5 runs: 0.3945, 0.8162, 0.5973, 0.6003, 0.9072 Rank test for binary matrices (31x31) for dh-ranFile-2015-11-21_09:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 214 211.4 0.032 0.032 r= 29 5140 5134.0 0.007 0.039 r= 30 23105 23103.0 0.000 0.039 r= 31 11541 11551.5 0.010 0.048 chi-square = 0.048 with df = 3; p-value = 0.003 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-11-21_09:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 216 211.4 0.099 0.099 r= 30 5222 5134.0 1.508 1.607 r= 31 22968 23103.0 0.789 2.397 r= 32 11594 11551.5 0.156 2.553 chi-square = 2.553 with df = 3; p-value = 0.534 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-11-21_09:31 b-rank test for bits 1 to 8, p=0.33422 b-rank test for bits 2 to 9, p=0.62354 b-rank test for bits 3 to 10, p=0.42442 b-rank test for bits 4 to 11, p=0.94587 b-rank test for bits 5 to 12, p=0.89640 b-rank test for bits 6 to 13, p=0.49601 b-rank test for bits 7 to 14, p=0.19886 b-rank test for bits 8 to 15, p=0.20959 b-rank test for bits 9 to 16, p=0.45457 b-rank test for bits 10 to 17, p=0.73117 b-rank test for bits 11 to 18, p=0.57262 b-rank test for bits 12 to 19, p=0.14419 b-rank test for bits 13 to 20, p=0.21214 b-rank test for bits 14 to 21, p=0.51380 b-rank test for bits 15 to 22, p=0.04019 b-rank test for bits 16 to 23, p=0.11535 b-rank test for bits 17 to 24, p=0.02575 b-rank test for bits 18 to 25, p=0.91934 b-rank test for bits 19 to 26, p=0.93541 b-rank test for bits 20 to 27, p=0.87425 b-rank test for bits 21 to 28, p=0.54433 b-rank test for bits 22 to 29, p=0.90268 b-rank test for bits 23 to 30, p=0.12627 b-rank test for bits 24 to 31, p=0.03831 b-rank test for bits 25 to 32, p=0.25945 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 = 0.529388 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-11-21_09:31 (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 142321 0.96 0.831936 2 142149 0.56 0.712252 3 142683 1.81 0.964669 4 142349 1.03 0.847852 5 142104 0.45 0.675387 6 141500 -0.96 0.169441 7 142120 0.49 0.688718 8 142324 0.97 0.833691 9 141715 -0.45 0.324899 10 141595 -0.73 0.231348 11 142179 0.63 0.735676 12 142357 1.05 0.852210 13 142046 0.32 0.625259 14 141651 -0.60 0.273063 15 142301 0.92 0.819935 16 141576 -0.78 0.218046 17 141304 -1.41 0.078634 18 141876 -0.08 0.468964 19 141744 -0.39 0.349643 20 142460 1.29 0.900885 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-11-21_09:31 Bits used No. missing words z-score p-value 23 to 32 141599 -1.0701 0.142286 22 to 31 141307 -2.0770 0.018901 21 to 30 141582 -1.1287 0.129507 20 to 29 141113 -2.7460 0.003017 19 to 28 141777 -0.4563 0.324083 18 to 27 141797 -0.3873 0.349251 17 to 26 142004 0.3264 0.627957 16 to 25 141736 -0.5977 0.275024 15 to 24 141913 0.0127 0.505049 14 to 23 141517 -1.3529 0.088050 13 to 22 142207 1.0264 0.847660 12 to 21 142090 0.6230 0.733358 11 to 20 142061 0.5230 0.699513 10 to 19 141775 -0.4632 0.321608 9 to 18 141836 -0.2529 0.400187 8 to 17 141591 -1.0977 0.136170 7 to 16 142105 0.6747 0.750075 6 to 15 141292 -2.1287 0.016639 5 to 14 142429 1.7920 0.963431 4 to 13 141897 -0.0425 0.483043 3 to 12 142505 2.0540 0.980014 2 to 11 141709 -0.6908 0.244848 1 to 10 142159 0.8609 0.805362 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-11-21_09:31 Bits used No. missing words z-score p-value 28 to 32 140954 -3.2384 0.000601 27 to 31 142290 1.2904 0.901545 26 to 30 141626 -0.9604 0.168417 25 to 29 141703 -0.6994 0.242144 24 to 28 142001 0.3107 0.622003 23 to 27 141581 -1.1130 0.132858 22 to 26 142071 0.5480 0.708166 21 to 25 141959 0.1684 0.566855 20 to 24 141971 0.2091 0.582796 19 to 23 142258 1.1819 0.881384 18 to 22 141248 -2.2418 0.012487 17 to 21 142057 0.5006 0.691665 16 to 20 141727 -0.6181 0.268265 15 to 19 142266 1.2091 0.886678 14 to 18 142115 0.6972 0.757157 13 to 17 141879 -0.1028 0.459056 12 to 16 142098 0.6396 0.738770 11 to 15 141786 -0.4181 0.337949 10 to 14 141819 -0.3062 0.379725 9 to 13 141828 -0.2757 0.391391 8 to 12 142376 1.5819 0.943167 7 to 11 142398 1.6565 0.951191 6 to 10 141622 -0.9740 0.165028 5 to 9 141690 -0.7435 0.228592 4 to 8 141941 0.1074 0.542747 3 to 7 141786 -0.4181 0.337949 2 to 6 141755 -0.5232 0.300434 1 to 5 142547 2.1616 0.984675 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-11-21_09:31 Bits used No. missing words z-score p-value 31 to 32 141816 -0.2753 0.391539 30 to 31 141914 0.0138 0.505496 29 to 30 141801 -0.3196 0.374652 28 to 29 141907 -0.0069 0.497258 27 to 28 141624 -0.8417 0.199983 26 to 27 141958 0.1436 0.557080 25 to 26 141862 -0.1396 0.444482 24 to 25 141895 -0.0423 0.483141 23 to 24 142138 0.6745 0.750017 22 to 23 142099 0.5595 0.712089 21 to 22 141780 -0.3815 0.351415 20 to 21 141196 -2.1042 0.017680 19 to 20 142200 0.8574 0.804397 18 to 19 142523 1.8102 0.964870 17 to 18 142303 1.1613 0.877234 16 to 17 141298 -1.8033 0.035668 15 to 16 141345 -1.6647 0.047987 14 to 15 141857 -0.1544 0.438661 13 to 14 142046 0.4032 0.656583 12 to 13 141493 -1.2281 0.109702 11 to 12 142263 1.0433 0.851589 10 to 11 141516 -1.1603 0.122970 9 to 10 141790 -0.3520 0.362417 8 to 9 141942 0.0964 0.538387 7 to 8 141787 -0.3609 0.359104 6 to 7 141732 -0.5231 0.300453 5 to 6 142465 1.6391 0.949408 4 to 5 141264 -1.9036 0.028479 3 to 4 141864 -0.1337 0.446813 2 to 3 141931 0.0639 0.525484 1 to 2 140991 -2.7089 0.003375 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-11-21_09:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2456.12 -0.621 0.267460 Test results for specific bytes for dh-ranFile-2015-11-21_09:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2537.58 0.532 0.702464 2 to 9 2513.70 0.194 0.576821 3 to 10 2579.55 1.125 0.869708 4 to 11 2545.85 0.648 0.741656 5 to 12 2522.06 0.312 0.622471 6 to 13 2406.85 -1.317 0.093851 7 to 14 2607.64 1.522 0.936028 8 to 15 2417.84 -1.162 0.122644 9 to 16 2436.89 -0.893 0.186061 10 to 17 2295.54 -2.892 0.001917 11 to 18 2526.15 0.370 0.644238 12 to 19 2437.26 -0.887 0.187455 13 to 20 2494.70 -0.075 0.470150 14 to 21 2438.07 -0.876 0.190560 15 to 22 2506.91 0.098 0.538919 16 to 23 2353.46 -2.072 0.019117 17 to 24 2673.87 2.459 0.993032 18 to 25 2486.53 -0.190 0.424484 19 to 26 2439.46 -0.856 0.195947 20 to 27 2618.70 1.679 0.953390 21 to 28 2557.75 0.817 0.792938 22 to 29 2553.00 0.750 0.773228 23 to 30 2630.70 1.848 0.967727 24 to 31 2467.12 -0.465 0.320946 25 to 32 2448.20 -0.733 0.231928 CDPARK for dh-ranFile-2015-11-21_09:31: 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 3511 -0.5479 0.291865 3485 -1.7352 0.041356 3532 0.4110 0.659449 3524 0.0457 0.518210 3485 -1.7352 0.041356 3519 -0.1826 0.427537 3521 -0.0913 0.463617 3551 1.2785 0.899470 3524 0.0457 0.518210 3524 0.0457 0.518210 Square side=100, avg. no. parked=3517.60 sample std.=19.05 p-value of the KSTEST for those 10 p-values: 0.469612 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-11-21_09:31 0.4231,0.5118,0.0110,0.7525,0.6338,0.8833,0.3925,0.0758,0.8852,0.5605, The KS test for those 10 p-values: 0.843625 The 3DSPHERES test for dh-ranFile-2015-11-21_09:31 sample no r^3 equiv. uni. 1 26.073 0.580671 2 41.183 0.746594 3 3.528 0.110960 4 28.691 0.615716 5 24.901 0.563968 6 1.151 0.037631 7 2.435 0.077960 8 2.579 0.082378 9 14.015 0.373230 10 153.138 0.993931 11 32.848 0.665442 12 39.204 0.729315 13 2.139 0.068831 14 30.013 0.632286 15 51.378 0.819602 16 0.439 0.014522 17 10.667 0.299232 18 22.252 0.523712 19 15.636 0.406194 20 26.967 0.592984 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.343060 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-11-21_09:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.1 -0.8 -1.3 0.4 0.8 -0.4 -0.1 0.4 0.4 0.8 -0.5 -0.1 0.6 1.4 -1.3 -1.8 1.3 -0.3 -0.4 0.3 0.2 -0.8 1.5 -0.1 -1.3 -0.1 1.3 -1.2 -0.4 -0.0 1.2 0.4 -1.1 1.2 -0.5 0.5 -0.4 0.1 0.4 -0.6 0.0 0.8 Chi-square with 42 degrees of freedom:27.615891 z-score=-1.569435, p-value=0.042640 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-11-21_09:31 Test no p-value 1 0.003214 2 0.146864 3 0.005379 4 0.081444 5 0.791876 6 0.060224 7 0.329256 8 0.014146 9 0.029195 10 0.097836 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000005 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-11-21_09:31: (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 66498 0.43 66553 0.19 3 25000.00 24997 0.00 25083 0.28 4 6666.67 6755 1.17 6642 0.09 5 1388.89 1436 1.60 1429 1.16 6 238.10 268 3.76 250 0.60 7 34.72 39 0.53 34 0.01 8 4.96 6 0.22 8 1.86 p=0.73885 p=0.34934 Number of rngs required: 691524, p-value: 1.000 RESULTS OF CRAPS TEST for dh-ranFile-2015-11-21_09:31 No. of wins: Observed Expected 98690 98585.9 z-score= 0.466, pvalue=0.67931 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66780 66666.7 0.193 0.193 2 37501 37654.3 0.624 0.817 3 26623 26954.7 4.083 4.900 4 19355 19313.5 0.089 4.989 5 13827 13851.4 0.043 5.032 6 10092 9943.5 2.216 7.248 7 7341 7145.0 5.375 12.624 8 5084 5139.1 0.590 13.214 9 3604 3699.9 2.484 15.698 10 2681 2666.3 0.081 15.779 11 1910 1923.3 0.092 15.871 12 1451 1388.7 2.791 18.662 13 1022 1003.7 0.333 18.995 14 766 726.1 2.188 21.183 15 543 525.8 0.560 21.744 16 395 381.2 0.503 22.247 17 271 276.5 0.111 22.358 18 202 200.8 0.007 22.365 19 147 146.0 0.007 22.372 20 100 106.2 0.364 22.735 21 305 287.1 1.114 23.850 Chisq= 23.85 for 20 degrees of freedom, p= 0.75098 SUMMARY of craptest p-value for no. of wins: 0.679314 p-value for throws/game: 0.750980 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-11-21_09:31 No. of wins: Observed Expected 99207 98585.9 z-score= 2.778, pvalue=0.99727 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66722 66666.7 0.046 0.046 2 37487 37654.3 0.744 0.789 3 26614 26954.7 4.307 5.097 4 19499 19313.5 1.782 6.879 5 13735 13851.4 0.979 7.858 6 10176 9943.5 5.434 13.292 7 7225 7145.0 0.895 14.187 8 5233 5139.1 1.717 15.904 9 3669 3699.9 0.257 16.161 10 2728 2666.3 1.428 17.589 11 1856 1923.3 2.357 19.946 12 1356 1388.7 0.772 20.718 13 1006 1003.7 0.005 20.723 14 775 726.1 3.288 24.011 15 525 525.8 0.001 24.012 16 364 381.2 0.772 24.784 17 246 276.5 3.373 28.156 18 212 200.8 0.621 28.778 19 165 146.0 2.477 31.255 20 114 106.2 0.571 31.825 21 293 287.1 0.121 31.946 Chisq= 31.95 for 20 degrees of freedom, p= 0.95612 SUMMARY of craptest p-value for no. of wins: 0.997266 p-value for throws/game: 0.956121 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0000,0.0006,0.0019,0.0028,0.0030,0.0032,0.0034,0.0054,0.0110,0.0125, 0.0141,0.0145,0.0166,0.0177,0.0189,0.0191,0.0201,0.0258,0.0285,0.0292, 0.0357,0.0376,0.0383,0.0402,0.0414,0.0414,0.0426,0.0480,0.0602,0.0653, 0.0688,0.0723,0.0758,0.0778,0.0780,0.0786,0.0814,0.0824,0.0880,0.0939, 0.0943,0.0978,0.1097,0.1110,0.1154,0.1226,0.1230,0.1263,0.1295,0.1329, 0.1362,0.1423,0.1442,0.1469,0.1577,0.1650,0.1684,0.1694,0.1708,0.1788, 0.1861,0.1875,0.1906,0.1922,0.1959,0.1989,0.2000,0.2086,0.2096,0.2121, 0.2145,0.2180,0.2278,0.2286,0.2313,0.2319,0.2417,0.2421,0.2448,0.2594, 0.2595,0.2675,0.2683,0.2731,0.2750,0.2774,0.2919,0.2992,0.3004,0.3005, 0.3209,0.3216,0.3241,0.3249,0.3251,0.3285,0.3293,0.3342,0.3379,0.3379, 0.3431,0.3493,0.3493,0.3496,0.3514,0.3591,0.3624,0.3732,0.3747,0.3797, 0.3801,0.3914,0.3915,0.3925,0.3938,0.3945,0.4002,0.4031,0.4062,0.4231, 0.4244,0.4245,0.4275,0.4387,0.4445,0.4468,0.4546,0.4591,0.4636,0.4690, 0.4696,0.4702,0.4830,0.4831,0.4960,0.4973,0.4998,0.5050,0.5055,0.5118, 0.5138,0.5182,0.5182,0.5182,0.5218,0.5237,0.5255,0.5294,0.5309,0.5342, 0.5384,0.5389,0.5427,0.5443,0.5571,0.5605,0.5640,0.5653,0.5669,0.5726, 0.5768,0.5806,0.5807,0.5828,0.5930,0.5973,0.6003,0.6157,0.6215,0.6220, 0.6225,0.6235,0.6253,0.6280,0.6323,0.6338,0.6442,0.6504,0.6566,0.6594, 0.6654,0.6754,0.6793,0.6887,0.6917,0.6995,0.7025,0.7082,0.7121,0.7123, 0.7144,0.7293,0.7312,0.7334,0.7357,0.7388,0.7389,0.7417,0.7466,0.7500, 0.7501,0.7510,0.7525,0.7572,0.7732,0.7792,0.7919,0.7929,0.8044,0.8054, 0.8088,0.8142,0.8162,0.8196,0.8199,0.8319,0.8337,0.8378,0.8416,0.8430, 0.8436,0.8477,0.8479,0.8516,0.8521,0.8522,0.8529,0.8697,0.8743,0.8772, 0.8814,0.8826,0.8833,0.8852,0.8867,0.8939,0.8964,0.8995,0.9009,0.9015, 0.9027,0.9072,0.9111,0.9118,0.9193,0.9225,0.9323,0.9326,0.9354,0.9360, 0.9432,0.9459,0.9494,0.9512,0.9534,0.9561,0.9634,0.9647,0.9649,0.9677, 0.9715,0.9747,0.9800,0.9847,0.9930,0.9939,0.9970,0.9973,0.9999, Overall p-value after applying KStest on 269 p-values = 0.048928 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.