RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-08-10_00:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.57 17.0323 0.547821 2 to 25 15.60 17.3247 0.567416 3 to 26 15.83 16.1433 0.486298 4 to 27 15.82 13.0127 0.264663 5 to 28 15.97 15.1424 0.414774 6 to 29 15.83 10.0571 0.098802 7 to 30 15.94 7.6177 0.025947 8 to 31 15.90 16.0689 0.481046 9 to 32 15.65 15.8316 0.464196 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.162505 Tough bday spacings test for dh-ranFile-2015-08-10_00:31: 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 6 45 77 96 85 93 40 28 17 8 5 (O-E)^2/E 1.1 1.9 0.2 0.0 1.6 2.8 2.8 0.1 0.3 0.3 0.2 Birthday Spacings: Sum(O-E)^2/E= 11.410, p= 0.673 RESULTS OF GCD FOR dh-ranFile-2015-08-10_00:31 Euclid's algorithm: p-value, steps to gcd: 0.168552 p-value, dist. of gcd's: 0.348152 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-08-10_00:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.921 0.598 0.376 0.555 0.632 0.302 0.944 0.280 Bits 8 to 15---> 0.313 0.364 0.056 0.811 0.840 0.855 0.866 0.658 Bits 16 to 23---> 0.142 0.309 0.831 0.133 0.740 0.446 0.667 0.727 Bits 24 to 31---> 0.644 0.924 0.164 0.103 0.721 0.061 0.541 0.533 KS test for the above 32 p values: 0.215 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-08-10_00:31, p-values for 5 runs: 0.7772, 0.5493, 0.2417, 0.7237, 0.3751 Rank test for binary matrices (31x31) for dh-ranFile-2015-08-10_00:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 225 211.4 0.873 0.873 r= 29 5155 5134.0 0.086 0.958 r= 30 23043 23103.0 0.156 1.114 r= 31 11577 11551.5 0.056 1.171 chi-square = 1.171 with df = 3; p-value = 0.240 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-08-10_00:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 202 211.4 0.420 0.420 r= 30 5055 5134.0 1.216 1.635 r= 31 23194 23103.0 0.358 1.994 r= 32 11549 11551.5 0.001 1.994 chi-square = 1.994 with df = 3; p-value = 0.426 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-08-10_00:31 b-rank test for bits 1 to 8, p=0.64753 b-rank test for bits 2 to 9, p=0.00172 b-rank test for bits 3 to 10, p=0.22842 b-rank test for bits 4 to 11, p=0.60205 b-rank test for bits 5 to 12, p=0.25865 b-rank test for bits 6 to 13, p=0.85439 b-rank test for bits 7 to 14, p=0.48823 b-rank test for bits 8 to 15, p=0.74932 b-rank test for bits 9 to 16, p=0.85706 b-rank test for bits 10 to 17, p=0.10365 b-rank test for bits 11 to 18, p=0.45650 b-rank test for bits 12 to 19, p=0.82527 b-rank test for bits 13 to 20, p=0.36308 b-rank test for bits 14 to 21, p=0.52959 b-rank test for bits 15 to 22, p=0.12670 b-rank test for bits 16 to 23, p=0.11628 b-rank test for bits 17 to 24, p=0.73354 b-rank test for bits 18 to 25, p=0.92349 b-rank test for bits 19 to 26, p=0.29750 b-rank test for bits 20 to 27, p=0.79525 b-rank test for bits 21 to 28, p=0.69731 b-rank test for bits 22 to 29, p=0.43755 b-rank test for bits 23 to 30, p=0.22909 b-rank test for bits 24 to 31, p=0.99939 b-rank test for bits 25 to 32, p=0.48239 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 = 0.932747 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-08-10_00:31 (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 142599 1.61 0.946451 2 142506 1.39 0.918355 3 142013 0.24 0.595695 4 142021 0.26 0.602920 5 142195 0.67 0.747759 6 141434 -1.11 0.133374 7 142405 1.16 0.876590 8 141605 -0.71 0.238526 9 142214 0.71 0.761720 10 141589 -0.75 0.227099 11 142136 0.53 0.701806 12 141569 -0.80 0.213259 13 142201 0.68 0.752214 14 142027 0.27 0.608315 15 141784 -0.29 0.384827 16 141881 -0.07 0.473613 17 141455 -1.06 0.144227 18 142999 2.55 0.994551 19 141862 -0.11 0.455973 20 141590 -0.75 0.227804 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-08-10_00:31 Bits used No. missing words z-score p-value 23 to 32 141748 -0.5563 0.288999 22 to 31 141670 -0.8253 0.204608 21 to 30 141975 0.2264 0.589574 20 to 29 141213 -2.4011 0.008172 19 to 28 141963 0.1851 0.573413 18 to 27 142064 0.5333 0.703103 17 to 26 141647 -0.9046 0.182842 16 to 25 142108 0.6851 0.753350 15 to 24 142016 0.3678 0.643499 14 to 23 141930 0.0713 0.528411 13 to 22 141984 0.2575 0.601597 12 to 21 142086 0.6092 0.728806 11 to 20 142004 0.3264 0.627957 10 to 19 141975 0.2264 0.589574 9 to 18 142004 0.3264 0.627957 8 to 17 141979 0.2402 0.594928 7 to 16 141661 -0.8563 0.195913 6 to 15 141632 -0.9563 0.169458 5 to 14 142180 0.9333 0.824679 4 to 13 141490 -1.4460 0.074093 3 to 12 142119 0.7230 0.765160 2 to 11 142186 0.9540 0.829967 1 to 10 141829 -0.2770 0.390890 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-08-10_00:31 Bits used No. missing words z-score p-value 28 to 32 141633 -0.9367 0.174453 27 to 31 141519 -1.3232 0.092892 26 to 30 142124 0.7277 0.766600 25 to 29 141437 -1.6011 0.054675 24 to 28 141617 -0.9909 0.160855 23 to 27 142198 0.9785 0.836097 22 to 26 141939 0.1006 0.540057 21 to 25 141658 -0.8520 0.197116 20 to 24 142257 1.1785 0.880710 19 to 23 141345 -1.9130 0.027875 18 to 22 141944 0.1175 0.546778 17 to 21 142340 1.4599 0.927841 16 to 20 141542 -1.2452 0.106532 15 to 19 141554 -1.2045 0.114197 14 to 18 142034 0.4226 0.663710 13 to 17 141627 -0.9571 0.169271 12 to 16 141602 -1.0418 0.148753 11 to 15 142546 2.1582 0.984544 10 to 14 142506 2.0226 0.978443 9 to 13 142314 1.3718 0.914931 8 to 12 142007 0.3311 0.629710 7 to 11 141486 -1.4350 0.075641 6 to 10 142113 0.6904 0.755031 5 to 9 142032 0.4158 0.661233 4 to 8 141987 0.2633 0.603836 3 to 7 141932 0.0768 0.530628 2 to 6 141977 0.2294 0.590717 1 to 5 142040 0.4429 0.671099 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-08-10_00:31 Bits used No. missing words z-score p-value 31 to 32 141926 0.0492 0.519610 30 to 31 142162 0.7453 0.771967 29 to 30 142692 2.3088 0.989522 28 to 29 141986 0.2262 0.589464 27 to 28 141505 -1.1927 0.116491 26 to 27 141939 0.0875 0.534872 25 to 26 141712 -0.5821 0.280252 24 to 25 141982 0.2144 0.584869 23 to 24 141773 -0.4022 0.343786 22 to 23 141503 -1.1986 0.115339 21 to 22 141665 -0.7207 0.235536 20 to 21 142367 1.3501 0.911501 19 to 20 142369 1.3560 0.912444 18 to 19 141404 -1.4906 0.068027 17 to 18 142190 0.8279 0.796146 16 to 17 143346 4.2380 0.999989 15 to 16 141301 -1.7945 0.036368 14 to 15 141660 -0.7355 0.231022 13 to 14 141930 0.0610 0.524310 12 to 13 142334 1.2527 0.894845 11 to 12 142546 1.8781 0.969815 10 to 11 141964 0.1613 0.564059 9 to 10 141853 -0.1662 0.434014 8 to 9 142191 0.8309 0.796981 7 to 8 142133 0.6598 0.745307 6 to 7 142045 0.4002 0.655498 5 to 6 141595 -0.9272 0.176904 4 to 5 142420 1.5064 0.934018 3 to 4 141927 0.0521 0.520785 2 to 3 141946 0.1082 0.543070 1 to 2 142061 0.4474 0.672708 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-08-10_00:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2355.97 -2.037 0.020827 Test results for specific bytes for dh-ranFile-2015-08-10_00:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2458.44 -0.588 0.278328 2 to 9 2507.04 0.100 0.539649 3 to 10 2558.46 0.827 0.795813 4 to 11 2623.84 1.751 0.960062 5 to 12 2464.90 -0.496 0.309804 6 to 13 2360.67 -1.970 0.024394 7 to 14 2622.57 1.733 0.958485 8 to 15 2442.19 -0.818 0.206819 9 to 16 2444.25 -0.788 0.215223 10 to 17 2490.21 -0.138 0.444969 11 to 18 2583.61 1.182 0.881484 12 to 19 2509.36 0.132 0.552664 13 to 20 2528.55 0.404 0.656811 14 to 21 2474.68 -0.358 0.360129 15 to 22 2502.48 0.035 0.513992 16 to 23 2554.64 0.773 0.780168 17 to 24 2428.66 -1.009 0.156507 18 to 25 2458.95 -0.580 0.280793 19 to 26 2523.12 0.327 0.628164 20 to 27 2567.72 0.958 0.830878 21 to 28 2604.40 1.476 0.930089 22 to 29 2525.48 0.360 0.640695 23 to 30 2399.79 -1.417 0.078206 24 to 31 2507.08 0.100 0.539887 25 to 32 2523.86 0.337 0.632092 CDPARK for dh-ranFile-2015-08-10_00:31: 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 3522 -0.0457 0.481790 3510 -0.5936 0.276387 3539 0.7306 0.767486 3533 0.4566 0.676028 3502 -0.9589 0.168804 3537 0.6393 0.738676 3497 -1.1872 0.117571 3534 0.5023 0.692266 3520 -0.1370 0.445521 3526 0.1370 0.554479 Square side=100, avg. no. parked=3522.00 sample std.=14.03 p-value of the KSTEST for those 10 p-values: 0.724077 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-08-10_00:31 0.1536,0.2714,0.4907,0.6116,0.1530,0.2378,0.4906,0.9920,0.3355,0.3666, The KS test for those 10 p-values: 0.280510 The 3DSPHERES test for dh-ranFile-2015-08-10_00:31 sample no r^3 equiv. uni. 1 5.244 0.160382 2 46.630 0.788669 3 14.604 0.385405 4 12.612 0.343224 5 19.135 0.471556 6 0.726 0.023915 7 9.491 0.271211 8 37.032 0.708995 9 8.845 0.255351 10 16.495 0.422951 11 10.737 0.300847 12 23.322 0.540399 13 32.556 0.662163 14 21.932 0.518604 15 4.267 0.132594 16 15.016 0.393788 17 26.469 0.586173 18 42.809 0.759960 19 33.872 0.676668 20 47.734 0.796303 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.418382 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-08-10_00:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 0.1 -0.4 0.0 -0.5 -0.4 0.2 -0.7 0.1 -0.9 1.2 -0.6 0.1 -0.3 1.2 1.0 -1.2 -0.8 -0.0 0.9 1.0 0.1 0.3 -0.1 -0.7 -0.9 0.6 0.9 -2.4 -1.1 1.3 -3.2 0.9 0.4 -0.1 0.4 -1.6 0.5 0.9 -0.7 -0.6 2.0 0.8 Chi-square with 42 degrees of freedom:43.135435 z-score=0.123886, p-value=0.577478 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-08-10_00:31 Test no p-value 1 0.113391 2 0.658406 3 0.155014 4 0.642194 5 0.087811 6 0.014416 7 0.014368 8 0.000466 9 0.000009 10 0.033210 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000001 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-08-10_00:31: (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 66925 1.00 66739 0.08 3 25000.00 24835 1.09 25022 0.02 4 6666.67 6623 0.29 6586 0.98 5 1388.89 1364 0.45 1384 0.02 6 238.10 224 0.83 235 0.04 7 34.72 24 3.31 29 0.94 8 4.96 4 0.19 4 0.19 p=0.69300 p=0.10566 Number of rngs required: 689129, p-value: 0.799 RESULTS OF CRAPS TEST for dh-ranFile-2015-08-10_00:31 No. of wins: Observed Expected 98318 98585.9 z-score=-1.198, pvalue=0.11545 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66539 66666.7 0.244 0.244 2 37456 37654.3 1.045 1.289 3 27073 26954.7 0.519 1.808 4 19545 19313.5 2.776 4.584 5 13888 13851.4 0.097 4.680 6 9942 9943.5 0.000 4.681 7 7109 7145.0 0.182 4.862 8 5120 5139.1 0.071 4.933 9 3727 3699.9 0.199 5.132 10 2671 2666.3 0.008 5.140 11 1861 1923.3 2.020 7.160 12 1424 1388.7 0.895 8.055 13 1035 1003.7 0.975 9.031 14 722 726.1 0.024 9.054 15 531 525.8 0.051 9.105 16 373 381.2 0.174 9.279 17 279 276.5 0.022 9.301 18 190 200.8 0.584 9.885 19 141 146.0 0.170 10.055 20 94 106.2 1.405 11.460 21 280 287.1 0.176 11.636 Chisq= 11.64 for 20 degrees of freedom, p= 0.07197 SUMMARY of craptest p-value for no. of wins: 0.115455 p-value for throws/game: 0.071974 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-08-10_00:31 No. of wins: Observed Expected 98474 98585.9 z-score=-0.500, pvalue=0.30843 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66645 66666.7 0.007 0.007 2 37664 37654.3 0.002 0.010 3 26929 26954.7 0.025 0.034 4 19492 19313.5 1.650 1.685 5 13687 13851.4 1.952 3.636 6 9824 9943.5 1.437 5.073 7 7132 7145.0 0.024 5.097 8 5260 5139.1 2.846 7.943 9 3673 3699.9 0.195 8.138 10 2691 2666.3 0.229 8.367 11 1956 1923.3 0.555 8.922 12 1460 1388.7 3.657 12.578 13 938 1003.7 4.302 16.881 14 736 726.1 0.134 17.014 15 502 525.8 1.080 18.095 16 404 381.2 1.370 19.465 17 281 276.5 0.072 19.537 18 207 200.8 0.190 19.726 19 141 146.0 0.170 19.896 20 106 106.2 0.000 19.897 21 272 287.1 0.796 20.692 Chisq= 20.69 for 20 degrees of freedom, p= 0.58457 SUMMARY of craptest p-value for no. of wins: 0.308433 p-value for throws/game: 0.584573 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0000,0.0000,0.0005,0.0017,0.0082,0.0144,0.0144,0.0208,0.0239,0.0244, 0.0259,0.0279,0.0332,0.0364,0.0547,0.0555,0.0605,0.0680,0.0720,0.0741, 0.0756,0.0782,0.0878,0.0929,0.0988,0.1028,0.1036,0.1057,0.1065,0.1134, 0.1142,0.1153,0.1155,0.1163,0.1165,0.1176,0.1267,0.1326,0.1334,0.1334, 0.1418,0.1442,0.1488,0.1530,0.1536,0.1550,0.1565,0.1604,0.1609,0.1625, 0.1635,0.1686,0.1688,0.1693,0.1695,0.1745,0.1769,0.1828,0.1959,0.1971, 0.2046,0.2068,0.2133,0.2152,0.2152,0.2271,0.2278,0.2284,0.2291,0.2310, 0.2355,0.2378,0.2385,0.2399,0.2417,0.2554,0.2586,0.2647,0.2712,0.2714, 0.2764,0.2783,0.2798,0.2803,0.2805,0.2808,0.2890,0.2975,0.3008,0.3022, 0.3084,0.3091,0.3098,0.3130,0.3355,0.3432,0.3438,0.3482,0.3601,0.3631, 0.3642,0.3666,0.3751,0.3758,0.3848,0.3854,0.3909,0.3938,0.4148,0.4184, 0.4230,0.4264,0.4340,0.4376,0.4450,0.4455,0.4465,0.4560,0.4565,0.4642, 0.4716,0.4736,0.4810,0.4818,0.4824,0.4863,0.4882,0.4906,0.4907,0.5140, 0.5186,0.5196,0.5208,0.5243,0.5284,0.5296,0.5306,0.5332,0.5349,0.5396, 0.5399,0.5401,0.5404,0.5410,0.5431,0.5468,0.5478,0.5493,0.5527,0.5545, 0.5551,0.5641,0.5674,0.5734,0.5775,0.5846,0.5849,0.5862,0.5895,0.5896, 0.5896,0.5907,0.5949,0.5957,0.5985,0.6016,0.6021,0.6029,0.6038,0.6083, 0.6116,0.6280,0.6280,0.6282,0.6297,0.6315,0.6321,0.6407,0.6422,0.6435, 0.6445,0.6475,0.6555,0.6568,0.6582,0.6584,0.6612,0.6622,0.6637,0.6668, 0.6711,0.6727,0.6735,0.6760,0.6767,0.6923,0.6930,0.6973,0.7018,0.7031, 0.7090,0.7212,0.7237,0.7241,0.7265,0.7288,0.7335,0.7387,0.7396,0.7453, 0.7478,0.7493,0.7522,0.7533,0.7550,0.7600,0.7617,0.7652,0.7666,0.7675, 0.7720,0.7772,0.7802,0.7887,0.7953,0.7958,0.7961,0.7963,0.7970,0.7994, 0.8108,0.8247,0.8253,0.8300,0.8307,0.8309,0.8361,0.8396,0.8544,0.8552, 0.8571,0.8664,0.8766,0.8807,0.8815,0.8948,0.9115,0.9124,0.9149,0.9184, 0.9212,0.9235,0.9235,0.9278,0.9301,0.9327,0.9340,0.9438,0.9465,0.9585, 0.9601,0.9698,0.9784,0.9845,0.9895,0.9920,0.9946,0.9994,1.0000, Overall p-value after applying KStest on 269 p-values = 0.280254 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.