RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-07-31_17:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.77 13.6805 0.310427 2 to 25 15.56 18.6392 0.650370 3 to 26 15.67 20.3048 0.741064 4 to 27 15.85 15.4872 0.439568 5 to 28 15.97 14.3857 0.360362 6 to 29 15.79 14.1553 0.343920 7 to 30 15.71 25.0859 0.907196 8 to 31 15.95 15.2867 0.425164 9 to 32 15.84 15.1844 0.417795 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.408125 Tough bday spacings test for dh-ranFile-2015-07-31_17:31: 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 32 80 115 101 58 53 29 13 5 4 (O-E)^2/E 0.1 0.6 0.6 3.1 0.1 5.2 0.0 0.0 0.2 0.4 0.0 Birthday Spacings: Sum(O-E)^2/E= 10.329, p= 0.588 RESULTS OF GCD FOR dh-ranFile-2015-07-31_17:31 Euclid's algorithm: p-value, steps to gcd: 0.828199 p-value, dist. of gcd's: 0.710564 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-07-31_17:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.901 0.559 0.152 0.474 0.319 0.707 0.177 0.753 Bits 8 to 15---> 0.473 0.176 0.850 0.607 0.729 0.443 0.963 0.971 Bits 16 to 23---> 0.113 0.860 0.051 0.604 0.261 0.679 0.352 0.115 Bits 24 to 31---> 0.590 0.680 0.108 0.591 0.437 0.201 0.930 0.959 KS test for the above 32 p values: 0.114 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-07-31_17:31, p-values for 5 runs: 0.5233, 0.3129, 0.7167, 0.7381, 0.6353 Rank test for binary matrices (31x31) for dh-ranFile-2015-07-31_17:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 214 211.4 0.032 0.032 r= 29 5108 5134.0 0.132 0.163 r= 30 23229 23103.0 0.687 0.850 r= 31 11449 11551.5 0.910 1.760 chi-square = 1.760 with df = 3; p-value = 0.376 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-07-31_17:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 235 211.4 2.630 2.630 r= 30 5056 5134.0 1.185 3.816 r= 31 23025 23103.0 0.264 4.079 r= 32 11684 11551.5 1.519 5.599 chi-square = 5.599 with df = 3; p-value = 0.867 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-07-31_17:31 b-rank test for bits 1 to 8, p=0.37115 b-rank test for bits 2 to 9, p=0.31768 b-rank test for bits 3 to 10, p=0.73989 b-rank test for bits 4 to 11, p=0.35758 b-rank test for bits 5 to 12, p=0.37793 b-rank test for bits 6 to 13, p=0.24075 b-rank test for bits 7 to 14, p=0.32137 b-rank test for bits 8 to 15, p=0.56917 b-rank test for bits 9 to 16, p=0.98835 b-rank test for bits 10 to 17, p=0.85639 b-rank test for bits 11 to 18, p=0.34763 b-rank test for bits 12 to 19, p=0.95145 b-rank test for bits 13 to 20, p=0.74774 b-rank test for bits 14 to 21, p=0.79798 b-rank test for bits 15 to 22, p=0.50735 b-rank test for bits 16 to 23, p=0.07076 b-rank test for bits 17 to 24, p=0.68597 b-rank test for bits 18 to 25, p=0.98286 b-rank test for bits 19 to 26, p=0.22261 b-rank test for bits 20 to 27, p=0.03230 b-rank test for bits 21 to 28, p=0.32761 b-rank test for bits 22 to 29, p=0.18156 b-rank test for bits 23 to 30, p=0.25711 b-rank test for bits 24 to 31, p=0.54348 b-rank test for bits 25 to 32, p=0.58480 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 = 0.774510 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-07-31_17:31 (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 142299 0.91 0.818706 2 142493 1.36 0.913671 3 141641 -0.63 0.265350 4 141749 -0.37 0.353978 5 142258 0.81 0.792364 6 142723 1.90 0.971355 7 142296 0.90 0.816852 8 142018 0.25 0.600214 9 142356 1.04 0.851670 10 142189 0.65 0.743262 11 142437 1.23 0.891189 12 142280 0.87 0.806769 13 142359 1.05 0.853286 14 141804 -0.25 0.402803 15 142622 1.67 0.952055 16 141647 -0.61 0.269964 17 141657 -0.59 0.277744 18 142496 1.37 0.914770 19 141740 -0.40 0.346189 20 142174 0.62 0.731840 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-07-31_17:31 Bits used No. missing words z-score p-value 23 to 32 141882 -0.0942 0.462459 22 to 31 141983 0.2540 0.600266 21 to 30 142012 0.3540 0.638344 20 to 29 141821 -0.3046 0.380341 19 to 28 141574 -1.1563 0.123777 18 to 27 141568 -1.1770 0.119598 17 to 26 141901 -0.0287 0.488542 16 to 25 142325 1.4333 0.924120 15 to 24 141993 0.2885 0.613525 14 to 23 141728 -0.6253 0.265895 13 to 22 141821 -0.3046 0.380341 12 to 21 141537 -1.2839 0.099589 11 to 20 142279 1.2747 0.898797 10 to 19 141828 -0.2804 0.389567 9 to 18 142034 0.4299 0.666365 8 to 17 141720 -0.6529 0.256923 7 to 16 141718 -0.6598 0.254704 6 to 15 141885 -0.0839 0.466569 5 to 14 141904 -0.0184 0.492668 4 to 13 142134 0.7747 0.780749 3 to 12 141835 -0.2563 0.398856 2 to 11 141630 -0.9632 0.167722 1 to 10 142425 1.7782 0.962312 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-07-31_17:31 Bits used No. missing words z-score p-value 28 to 32 142180 0.9175 0.820566 27 to 31 141494 -1.4079 0.079581 26 to 30 141799 -0.3740 0.354202 25 to 29 141414 -1.6791 0.046568 24 to 28 142021 0.3785 0.647486 23 to 27 141822 -0.2960 0.383602 22 to 26 141670 -0.8113 0.208600 21 to 25 142255 1.1718 0.879354 20 to 24 141458 -1.5299 0.063017 19 to 23 142013 0.3514 0.637365 18 to 22 141973 0.2158 0.585440 17 to 21 142082 0.5853 0.720834 16 to 20 141698 -0.7164 0.236881 15 to 19 142226 1.0735 0.858467 14 to 18 141976 0.2260 0.589399 13 to 17 142521 2.0735 0.980935 12 to 16 141774 -0.4587 0.323208 11 to 15 141441 -1.5876 0.056193 10 to 14 142321 1.3955 0.918566 9 to 13 141714 -0.6621 0.253942 8 to 12 141851 -0.1977 0.421629 7 to 11 141935 0.0870 0.534671 6 to 10 141496 -1.4011 0.080589 5 to 9 141622 -0.9740 0.165028 4 to 8 141379 -1.7977 0.036110 3 to 7 141399 -1.7299 0.041821 2 to 6 142307 1.3480 0.911176 1 to 5 141991 0.2768 0.609051 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-07-31_17:31 Bits used No. missing words z-score p-value 31 to 32 142214 0.8987 0.815602 30 to 31 141845 -0.1898 0.424747 29 to 30 142253 1.0138 0.844655 28 to 29 142648 2.1790 0.985333 27 to 28 141694 -0.6352 0.262652 26 to 27 141777 -0.3904 0.348137 25 to 26 142087 0.5241 0.699896 24 to 25 141735 -0.5142 0.303539 23 to 24 141571 -0.9980 0.159134 22 to 23 142400 1.4474 0.926108 21 to 22 141489 -1.2399 0.107504 20 to 21 141704 -0.6057 0.272359 19 to 20 141940 0.0905 0.536044 18 to 19 141637 -0.8033 0.210891 17 to 18 141875 -0.1013 0.459669 16 to 17 142041 0.3884 0.651143 15 to 16 142224 0.9282 0.823356 14 to 15 142239 0.9725 0.834594 13 to 14 142185 0.8132 0.791944 12 to 13 141814 -0.2812 0.389275 11 to 12 142011 0.2999 0.617878 10 to 11 142144 0.6922 0.755607 9 to 10 141946 0.1082 0.543070 8 to 9 141784 -0.3697 0.355801 7 to 8 142301 1.1554 0.876030 6 to 7 142300 1.1524 0.875426 5 to 6 141821 -0.2606 0.397216 4 to 5 141287 -1.8358 0.033195 3 to 4 142218 0.9105 0.818729 2 to 3 141653 -0.7561 0.224784 1 to 2 142004 0.2793 0.609978 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-07-31_17:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2582.30 1.164 0.877772 Test results for specific bytes for dh-ranFile-2015-07-31_17:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2445.02 -0.778 0.218428 2 to 9 2496.34 -0.052 0.479377 3 to 10 2452.86 -0.667 0.252488 4 to 11 2517.78 0.251 0.599249 5 to 12 2450.41 -0.701 0.241538 6 to 13 2437.90 -0.878 0.189904 7 to 14 2466.50 -0.474 0.317831 8 to 15 2526.42 0.374 0.645670 9 to 16 2483.76 -0.230 0.409168 10 to 17 2451.85 -0.681 0.247971 11 to 18 2491.83 -0.116 0.453983 12 to 19 2476.30 -0.335 0.368730 13 to 20 2528.88 0.408 0.658498 14 to 21 2426.69 -1.037 0.149919 15 to 22 2372.82 -1.799 0.036044 16 to 23 2518.69 0.264 0.604248 17 to 24 2449.63 -0.712 0.238131 18 to 25 2499.13 -0.012 0.495066 19 to 26 2573.92 1.045 0.852082 20 to 27 2481.20 -0.266 0.395194 21 to 28 2594.32 1.334 0.908888 22 to 29 2589.75 1.269 0.897822 23 to 30 2549.23 0.696 0.756843 24 to 31 2420.78 -1.120 0.131283 25 to 32 2566.18 0.936 0.825337 CDPARK for dh-ranFile-2015-07-31_17:31: 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 3544 0.9589 0.831196 3522 -0.0457 0.481790 3564 1.8721 0.969407 3515 -0.3653 0.357445 3510 -0.5936 0.276387 3526 0.1370 0.554479 3479 -2.0091 0.022262 3550 1.2329 0.891189 3510 -0.5936 0.276387 Square side=100, avg. no. parked=3524.20 sample std.=22.77 p-value of the KSTEST for those 10 p-values: 0.917363 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-07-31_17:31 0.1062,0.7464,0.9476,0.8827,0.9073,0.5746,0.4935,0.5231,0.1921,0.0165, The KS test for those 10 p-values: 0.766140 The 3DSPHERES test for dh-ranFile-2015-07-31_17:31 sample no r^3 equiv. uni. 1 14.622 0.385776 2 36.745 0.706197 3 49.754 0.809567 4 68.130 0.896792 5 11.628 0.321313 6 7.399 0.218574 7 86.915 0.944821 8 5.727 0.173783 9 91.976 0.953387 10 0.900 0.029568 11 17.730 0.446231 12 2.742 0.087362 13 11.247 0.312650 14 41.167 0.746461 15 35.376 0.692478 16 37.883 0.717132 17 55.317 0.841803 18 3.185 0.100729 19 29.600 0.627177 20 68.222 0.897107 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.680086 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-07-31_17:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 1.3 -1.6 1.1 -0.8 -1.3 1.8 0.3 0.3 -1.9 -0.6 -0.8 1.3 -1.2 -1.1 0.4 -0.6 -0.3 0.3 0.5 -0.2 1.3 0.4 0.2 1.0 0.1 -0.8 1.2 -0.8 0.4 0.1 -0.9 1.6 0.7 0.2 -1.5 -0.5 -0.2 0.5 -0.8 -1.3 0.1 2.0 -0.1 Chi-square with 42 degrees of freedom:39.776260 z-score=-0.242630, p-value=0.430970 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-07-31_17:31 Test no p-value 1 0.050822 2 0.297835 3 0.677765 4 0.092262 5 0.292650 6 0.085467 7 0.119946 8 0.663708 9 0.452085 10 0.005458 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.014116 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-07-31_17:31: (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 66993 1.60 66855 0.53 3 25000.00 24753 2.44 25009 0.00 4 6666.67 6565 1.55 6477 5.40 5 1388.89 1416 0.53 1372 0.21 6 238.10 222 1.09 245 0.20 7 34.72 46 3.66 35 0.00 8 4.96 4 0.19 6 0.22 p=0.91334 p=0.63628 Number of rngs required: 686592, p-value: 0.016 RESULTS OF CRAPS TEST for dh-ranFile-2015-07-31_17:31 No. of wins: Observed Expected 98560 98585.9 z-score=-0.116, pvalue=0.45396 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66336 66666.7 1.640 1.640 2 37650 37654.3 0.000 1.641 3 27016 26954.7 0.139 1.780 4 19343 19313.5 0.045 1.825 5 13969 13851.4 0.998 2.823 6 9924 9943.5 0.038 2.862 7 7227 7145.0 0.940 3.802 8 5168 5139.1 0.163 3.965 9 3683 3699.9 0.077 4.042 10 2720 2666.3 1.082 5.123 11 1908 1923.3 0.122 5.246 12 1425 1388.7 0.947 6.192 13 1024 1003.7 0.410 6.602 14 709 726.1 0.405 7.007 15 521 525.8 0.044 7.051 16 361 381.2 1.065 8.117 17 279 276.5 0.022 8.139 18 203 200.8 0.023 8.162 19 150 146.0 0.110 8.272 20 88 106.2 3.124 11.396 21 296 287.1 0.275 11.671 Chisq= 11.67 for 20 degrees of freedom, p= 0.07307 SUMMARY of craptest p-value for no. of wins: 0.453963 p-value for throws/game: 0.073073 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-07-31_17:31 No. of wins: Observed Expected 98760 98585.9 z-score= 0.779, pvalue=0.78197 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66636 66666.7 0.014 0.014 2 37824 37654.3 0.765 0.779 3 27103 26954.7 0.816 1.594 4 19247 19313.5 0.229 1.823 5 13918 13851.4 0.320 2.143 6 9941 9943.5 0.001 2.144 7 7050 7145.0 1.264 3.407 8 5127 5139.1 0.028 3.436 9 3635 3699.9 1.137 4.573 10 2647 2666.3 0.140 4.713 11 1882 1923.3 0.888 5.601 12 1333 1388.7 2.237 7.838 13 1003 1003.7 0.001 7.839 14 732 726.1 0.047 7.886 15 518 525.8 0.117 8.003 16 407 381.2 1.753 9.756 17 283 276.5 0.151 9.907 18 208 200.8 0.256 10.163 19 153 146.0 0.337 10.500 20 94 106.2 1.405 11.905 21 259 287.1 2.753 14.657 Chisq= 14.66 for 20 degrees of freedom, p= 0.20434 SUMMARY of craptest p-value for no. of wins: 0.781969 p-value for throws/game: 0.204340 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0055,0.0141,0.0160,0.0165,0.0223,0.0296,0.0323,0.0332,0.0360,0.0361, 0.0418,0.0466,0.0508,0.0511,0.0562,0.0630,0.0708,0.0731,0.0796,0.0806, 0.0855,0.0874,0.0923,0.0996,0.1007,0.1062,0.1075,0.1081,0.1127,0.1145, 0.1147,0.1196,0.1199,0.1238,0.1313,0.1499,0.1520,0.1591,0.1650,0.1677, 0.1738,0.1755,0.1770,0.1816,0.1899,0.1921,0.2006,0.2043,0.2086,0.2109, 0.2184,0.2186,0.2226,0.2248,0.2369,0.2381,0.2408,0.2415,0.2480,0.2525, 0.2539,0.2547,0.2569,0.2571,0.2609,0.2627,0.2653,0.2659,0.2700,0.2724, 0.2764,0.2764,0.2777,0.2927,0.2978,0.3035,0.3104,0.3127,0.3129,0.3177, 0.3178,0.3189,0.3213,0.3214,0.3232,0.3276,0.3439,0.3462,0.3476,0.3481, 0.3524,0.3540,0.3542,0.3558,0.3574,0.3576,0.3604,0.3687,0.3711,0.3763, 0.3779,0.3803,0.3803,0.3836,0.3858,0.3893,0.3896,0.3952,0.3972,0.3989, 0.4028,0.4081,0.4092,0.4178,0.4216,0.4247,0.4252,0.4310,0.4374,0.4396, 0.4429,0.4462,0.4521,0.4540,0.4540,0.4597,0.4625,0.4666,0.4734,0.4736, 0.4794,0.4818,0.4818,0.4885,0.4927,0.4935,0.4951,0.5074,0.5231,0.5233, 0.5347,0.5360,0.5431,0.5435,0.5545,0.5595,0.5692,0.5746,0.5848,0.5854, 0.5879,0.5894,0.5905,0.5913,0.5992,0.6002,0.6003,0.6039,0.6042,0.6072, 0.6091,0.6100,0.6135,0.6179,0.6272,0.6353,0.6363,0.6374,0.6383,0.6457, 0.6475,0.6504,0.6511,0.6585,0.6637,0.6664,0.6778,0.6792,0.6800,0.6801, 0.6860,0.6925,0.6999,0.7062,0.7067,0.7106,0.7167,0.7171,0.7208,0.7291, 0.7318,0.7381,0.7399,0.7411,0.7433,0.7464,0.7465,0.7477,0.7531,0.7556, 0.7568,0.7661,0.7745,0.7807,0.7820,0.7919,0.7924,0.7980,0.8068,0.8096, 0.8156,0.8169,0.8187,0.8187,0.8206,0.8234,0.8253,0.8282,0.8312,0.8346, 0.8418,0.8447,0.8497,0.8517,0.8521,0.8533,0.8564,0.8585,0.8597,0.8671, 0.8754,0.8760,0.8778,0.8794,0.8827,0.8912,0.8912,0.8968,0.8971,0.8978, 0.8988,0.9008,0.9072,0.9073,0.9089,0.9112,0.9133,0.9137,0.9148,0.9174, 0.9186,0.9241,0.9261,0.9299,0.9448,0.9476,0.9515,0.9521,0.9534,0.9588, 0.9623,0.9627,0.9694,0.9707,0.9714,0.9809,0.9829,0.9853,0.9883, Overall p-value after applying KStest on 269 p-values = 0.763813 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.