RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-03-20_13:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.88 7.7484 0.028366 2 to 25 15.60 20.2709 0.739391 3 to 26 15.30 28.7115 0.962719 4 to 27 15.65 16.8142 0.532975 5 to 28 15.82 24.3686 0.890238 6 to 29 15.69 16.9826 0.544454 7 to 30 15.84 23.3589 0.862073 8 to 31 15.83 22.9146 0.847948 9 to 32 15.80 11.8993 0.193804 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.254465 Tough bday spacings test for dh-ranFile-2016-03-20_13:31: 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 11 31 80 104 86 77 53 26 22 6 4 (O-E)^2/E 0.4 0.9 0.6 0.4 1.4 0.0 0.0 0.5 3.4 0.1 0.0 Birthday Spacings: Sum(O-E)^2/E= 7.631, p= 0.335 RESULTS OF GCD FOR dh-ranFile-2016-03-20_13:31 Euclid's algorithm: p-value, steps to gcd: 0.958368 p-value, dist. of gcd's: 0.045614 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-03-20_13:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.180 0.604 0.909 0.934 0.370 0.354 0.509 0.011 Bits 8 to 15---> 0.967 0.462 0.293 0.727 0.793 0.915 0.852 0.153 Bits 16 to 23---> 0.136 0.591 0.300 0.860 0.326 0.630 0.104 0.945 Bits 24 to 31---> 0.655 0.987 0.609 0.576 0.534 0.232 0.084 0.725 KS test for the above 32 p values: 0.271 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-03-20_13:31, p-values for 5 runs: 0.2255, 0.8245, 0.7417, 0.8465, 0.9360 Rank test for binary matrices (31x31) for dh-ranFile-2016-03-20_13:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 212 211.4 0.002 0.002 r= 29 5061 5134.0 1.038 1.040 r= 30 23118 23103.0 0.010 1.050 r= 31 11609 11551.5 0.286 1.336 chi-square = 1.336 with df = 3; p-value = 0.279 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-03-20_13:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 199 211.4 0.729 0.729 r= 30 5200 5134.0 0.848 1.578 r= 31 23095 23103.0 0.003 1.580 r= 32 11506 11551.5 0.179 1.760 chi-square = 1.760 with df = 3; p-value = 0.376 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-03-20_13:31 b-rank test for bits 1 to 8, p=0.39384 b-rank test for bits 2 to 9, p=0.50943 b-rank test for bits 3 to 10, p=0.11860 b-rank test for bits 4 to 11, p=0.17025 b-rank test for bits 5 to 12, p=0.02104 b-rank test for bits 6 to 13, p=0.14916 b-rank test for bits 7 to 14, p=0.86136 b-rank test for bits 8 to 15, p=0.20389 b-rank test for bits 9 to 16, p=0.45554 b-rank test for bits 10 to 17, p=0.22065 b-rank test for bits 11 to 18, p=0.73672 b-rank test for bits 12 to 19, p=0.56087 b-rank test for bits 13 to 20, p=0.05937 b-rank test for bits 14 to 21, p=0.17209 b-rank test for bits 15 to 22, p=0.01746 b-rank test for bits 16 to 23, p=0.28977 b-rank test for bits 17 to 24, p=0.38324 b-rank test for bits 18 to 25, p=0.40203 b-rank test for bits 19 to 26, p=0.42611 b-rank test for bits 20 to 27, p=0.91346 b-rank test for bits 21 to 28, p=0.26563 b-rank test for bits 22 to 29, p=0.15527 b-rank test for bits 23 to 30, p=0.95291 b-rank test for bits 24 to 31, p=0.59304 b-rank test for bits 25 to 32, p=0.87774 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 = 0.106532 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-03-20_13:31 (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 142064 0.36 0.641092 2 142184 0.64 0.739483 3 141700 -0.49 0.312389 4 141780 -0.30 0.381260 5 141432 -1.12 0.132370 6 142073 0.38 0.648920 7 141605 -0.71 0.238526 8 141548 -0.84 0.199271 9 142544 1.48 0.930946 10 142420 1.19 0.883596 11 142145 0.55 0.709057 12 141457 -1.06 0.145291 13 141806 -0.24 0.404613 14 141246 -1.55 0.060590 15 141717 -0.45 0.326583 16 141076 -1.95 0.025765 17 141935 0.06 0.523913 18 142186 0.65 0.740998 19 142823 2.13 0.983609 20 142693 1.83 0.966450 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-03-20_13:31 Bits used No. missing words z-score p-value 23 to 32 142243 1.1506 0.875049 22 to 31 141698 -0.7287 0.233085 21 to 30 141667 -0.8356 0.201684 20 to 29 141778 -0.4529 0.325324 19 to 28 142029 0.4127 0.660070 18 to 27 141822 -0.3011 0.381655 17 to 26 142278 1.2713 0.898185 16 to 25 141636 -0.9425 0.172964 15 to 24 142170 0.8989 0.815637 14 to 23 142119 0.7230 0.765160 13 to 22 141583 -1.1253 0.130236 12 to 21 142251 1.1782 0.880636 11 to 20 141933 0.0816 0.532526 10 to 19 142287 1.3023 0.903595 9 to 18 141645 -0.9115 0.181021 8 to 17 141754 -0.5356 0.296110 7 to 16 141829 -0.2770 0.390890 6 to 15 141711 -0.6839 0.247020 5 to 14 141847 -0.2149 0.414911 4 to 13 142314 1.3954 0.918554 3 to 12 141866 -0.1494 0.440614 2 to 11 141848 -0.2115 0.416255 1 to 10 141696 -0.7356 0.230981 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-03-20_13:31 Bits used No. missing words z-score p-value 28 to 32 141694 -0.7299 0.232716 27 to 31 142069 0.5413 0.705834 26 to 30 141828 -0.2757 0.391391 25 to 29 141757 -0.5164 0.302797 24 to 28 142319 1.3887 0.917540 23 to 27 142386 1.6158 0.946935 22 to 26 142197 0.9752 0.835258 21 to 25 141692 -0.7367 0.230649 20 to 24 141703 -0.6994 0.242144 19 to 23 142105 0.6633 0.746427 18 to 22 141912 0.0091 0.503611 17 to 21 141824 -0.2893 0.386193 16 to 20 142446 1.8192 0.965561 15 to 19 141963 0.1819 0.572182 14 to 18 141616 -0.9943 0.160029 13 to 17 141432 -1.6181 0.052824 12 to 16 141512 -1.3469 0.089009 11 to 15 141976 0.2260 0.589399 10 to 14 141552 -1.2113 0.112893 9 to 13 142021 0.3785 0.647486 8 to 12 142046 0.4633 0.678421 7 to 11 142052 0.4836 0.685675 6 to 10 141840 -0.2350 0.407098 5 to 9 142261 1.1921 0.883389 4 to 8 141653 -0.8689 0.192447 3 to 7 141246 -2.2486 0.012270 2 to 6 141655 -0.8621 0.194306 1 to 5 142169 0.8802 0.810635 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-03-20_13:31 Bits used No. missing words z-score p-value 31 to 32 141910 0.0020 0.500789 30 to 31 141504 -1.1957 0.115914 29 to 30 141907 -0.0069 0.497258 28 to 29 142284 1.1052 0.865468 27 to 28 141411 -1.4700 0.070781 26 to 27 142169 0.7660 0.778158 25 to 26 142673 2.2527 0.987861 24 to 25 142244 0.9872 0.838234 23 to 24 141415 -1.4582 0.072393 22 to 23 142510 1.7719 0.961793 21 to 22 141876 -0.0983 0.460840 20 to 21 141920 0.0315 0.512555 19 to 20 141893 -0.0482 0.480790 18 to 19 141672 -0.7001 0.241936 17 to 18 141452 -1.3491 0.088660 16 to 17 141968 0.1731 0.568701 15 to 16 142448 1.5890 0.943969 14 to 15 142178 0.7925 0.785976 13 to 14 141770 -0.4110 0.340535 12 to 13 141992 0.2439 0.596332 11 to 12 141729 -0.5319 0.297381 10 to 11 141441 -1.3815 0.083562 9 to 10 141642 -0.7886 0.215178 8 to 9 141466 -1.3078 0.095478 7 to 8 141948 0.1141 0.545409 6 to 7 142035 0.3707 0.644573 5 to 6 141706 -0.5998 0.274322 4 to 5 141981 0.2114 0.583719 3 to 4 142233 0.9548 0.830155 2 to 3 141339 -1.6824 0.046247 1 to 2 141949 0.1170 0.546578 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-03-20_13:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2454.86 -0.638 0.261631 Test results for specific bytes for dh-ranFile-2016-03-20_13:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2517.00 0.240 0.594983 2 to 9 2483.45 -0.234 0.407490 3 to 10 2509.43 0.133 0.553043 4 to 11 2409.90 -1.274 0.101300 5 to 12 2522.70 0.321 0.625927 6 to 13 2585.20 1.205 0.885874 7 to 14 2407.56 -1.307 0.095565 8 to 15 2514.11 0.200 0.579108 9 to 16 2361.82 -1.954 0.025340 10 to 17 2505.77 0.082 0.532500 11 to 18 2469.06 -0.438 0.330859 12 to 19 2436.32 -0.901 0.183915 13 to 20 2473.48 -0.375 0.353823 14 to 21 2474.80 -0.356 0.360802 15 to 22 2380.42 -1.691 0.045404 16 to 23 2465.41 -0.489 0.312337 17 to 24 2491.36 -0.122 0.451349 18 to 25 2597.38 1.377 0.915765 19 to 26 2626.83 1.794 0.963567 20 to 27 2519.39 0.274 0.608025 21 to 28 2541.59 0.588 0.721769 22 to 29 2439.81 -0.851 0.197309 23 to 30 2395.04 -1.484 0.068860 24 to 31 2520.95 0.296 0.616494 25 to 32 2503.05 0.043 0.517204 CDPARK for dh-ranFile-2016-03-20_13:31: 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 3526 0.1370 0.554479 3563 1.8265 0.966111 3536 0.5936 0.723613 3523 0.0000 0.500000 3538 0.6849 0.753306 3522 -0.0457 0.481790 3568 2.0548 0.980051 3504 -0.8676 0.192812 3515 -0.3653 0.357445 3524 0.0457 0.518210 Square side=100, avg. no. parked=3531.90 sample std.=19.14 p-value of the KSTEST for those 10 p-values: 0.313188 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-03-20_13:31 0.1586,0.7052,0.1063,0.5365,0.0950,0.6908,0.0618,0.2712,0.8497,0.4008, The KS test for those 10 p-values: 0.348879 The 3DSPHERES test for dh-ranFile-2016-03-20_13:31 sample no r^3 equiv. uni. 1 31.438 0.649342 2 17.033 0.433205 3 40.372 0.739649 4 1.120 0.036651 5 137.532 0.989790 6 57.260 0.851723 7 19.848 0.483968 8 22.460 0.526997 9 22.044 0.520402 10 16.074 0.414791 11 27.393 0.598728 12 86.414 0.943892 13 6.559 0.196394 14 17.489 0.441766 15 15.939 0.412154 16 29.016 0.619858 17 14.229 0.377687 18 17.834 0.448142 19 28.399 0.611958 20 14.699 0.387358 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.257097 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-03-20_13:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -2.0 -0.8 -1.0 0.6 0.9 0.7 -0.9 -0.3 -0.1 1.6 0.5 0.0 0.7 -1.0 -0.5 1.8 -0.9 0.5 0.8 -0.4 -0.4 -2.0 0.5 0.3 -0.1 -0.1 -0.8 -0.4 -0.4 -0.7 -0.1 0.6 0.9 -0.9 -1.2 -0.9 1.1 -1.6 -0.1 -0.6 -1.0 0.8 Chi-square with 42 degrees of freedom:34.834568 z-score=-0.781813, p-value=0.224407 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-03-20_13:31 Test no p-value 1 0.210553 2 0.225502 3 0.316384 4 0.637417 5 0.093862 6 0.172971 7 0.993164 8 0.461267 9 0.267915 10 0.490619 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.218450 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-03-20_13:31: (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 66718 0.04 66860 0.56 3 25000.00 24819 1.31 24940 0.14 4 6666.67 6747 0.97 6610 0.48 5 1388.89 1432 1.34 1309 4.60 6 238.10 240 0.02 236 0.02 7 34.72 37 0.15 41 1.14 8 4.96 6 0.22 3 0.77 p=0.32860 p=0.73992 Number of rngs required: 688644, p-value: 0.609 RESULTS OF CRAPS TEST for dh-ranFile-2016-03-20_13:31 No. of wins: Observed Expected 99073 98585.9 z-score= 2.179, pvalue=0.98533 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66673 66666.7 0.001 0.001 2 37587 37654.3 0.120 0.121 3 26818 26954.7 0.694 0.815 4 19501 19313.5 1.821 2.636 5 13964 13851.4 0.915 3.551 6 10003 9943.5 0.356 3.906 7 7139 7145.0 0.005 3.911 8 5142 5139.1 0.002 3.913 9 3667 3699.9 0.292 4.205 10 2516 2666.3 8.472 12.677 11 2004 1923.3 3.384 16.061 12 1354 1388.7 0.869 16.930 13 1003 1003.7 0.001 16.930 14 746 726.1 0.543 17.473 15 471 525.8 5.718 23.192 16 393 381.2 0.368 23.560 17 277 276.5 0.001 23.561 18 193 200.8 0.305 23.866 19 150 146.0 0.110 23.977 20 105 106.2 0.014 23.991 21 294 287.1 0.165 24.156 Chisq= 24.16 for 20 degrees of freedom, p= 0.76434 SUMMARY of craptest p-value for no. of wins: 0.985326 p-value for throws/game: 0.764342 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-03-20_13:31 No. of wins: Observed Expected 98935 98585.9 z-score= 1.562, pvalue=0.94080 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67119 66666.7 3.069 3.069 2 37462 37654.3 0.982 4.051 3 26814 26954.7 0.735 4.786 4 19344 19313.5 0.048 4.834 5 13940 13851.4 0.566 5.401 6 9693 9943.5 6.313 11.714 7 7208 7145.0 0.555 12.269 8 5052 5139.1 1.475 13.744 9 3782 3699.9 1.823 15.567 10 2605 2666.3 1.409 16.977 11 1889 1923.3 0.613 17.589 12 1402 1388.7 0.127 17.716 13 982 1003.7 0.470 18.186 14 706 726.1 0.559 18.744 15 551 525.8 1.204 19.949 16 411 381.2 2.338 22.286 17 290 276.5 0.655 22.941 18 199 200.8 0.017 22.958 19 159 146.0 1.160 24.119 20 110 106.2 0.135 24.253 21 282 287.1 0.091 24.344 Chisq= 24.34 for 20 degrees of freedom, p= 0.77233 SUMMARY of craptest p-value for no. of wins: 0.940805 p-value for throws/game: 0.772332 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0111,0.0123,0.0175,0.0210,0.0253,0.0258,0.0284,0.0367,0.0454,0.0456, 0.0462,0.0528,0.0594,0.0606,0.0618,0.0689,0.0708,0.0724,0.0836,0.0837, 0.0887,0.0890,0.0939,0.0950,0.0955,0.0956,0.1013,0.1043,0.1063,0.1065, 0.1129,0.1159,0.1186,0.1302,0.1324,0.1360,0.1453,0.1492,0.1530,0.1553, 0.1586,0.1600,0.1703,0.1721,0.1730,0.1730,0.1800,0.1810,0.1839,0.1924, 0.1928,0.1938,0.1943,0.1964,0.1973,0.1993,0.2017,0.2039,0.2106,0.2152, 0.2184,0.2207,0.2244,0.2255,0.2255,0.2306,0.2310,0.2320,0.2327,0.2331, 0.2385,0.2419,0.2421,0.2470,0.2545,0.2571,0.2616,0.2656,0.2679,0.2712, 0.2713,0.2743,0.2793,0.2898,0.2934,0.2961,0.2974,0.2999,0.3028,0.3123, 0.3124,0.3132,0.3164,0.3253,0.3261,0.3266,0.3286,0.3309,0.3352,0.3405, 0.3489,0.3538,0.3544,0.3574,0.3608,0.3704,0.3763,0.3777,0.3813,0.3817, 0.3832,0.3862,0.3874,0.3909,0.3914,0.3938,0.4008,0.4020,0.4046,0.4071, 0.4075,0.4122,0.4148,0.4149,0.4163,0.4261,0.4332,0.4406,0.4418,0.4481, 0.4513,0.4555,0.4608,0.4613,0.4624,0.4808,0.4818,0.4840,0.4906,0.4973, 0.5000,0.5008,0.5036,0.5094,0.5095,0.5126,0.5172,0.5182,0.5204,0.5239, 0.5270,0.5325,0.5325,0.5330,0.5342,0.5365,0.5445,0.5454,0.5466,0.5530, 0.5545,0.5609,0.5687,0.5722,0.5761,0.5791,0.5837,0.5894,0.5910,0.5930, 0.5950,0.5963,0.5987,0.6041,0.6080,0.6093,0.6093,0.6120,0.6165,0.6199, 0.6259,0.6302,0.6374,0.6411,0.6446,0.6475,0.6489,0.6493,0.6547,0.6601, 0.6784,0.6857,0.6908,0.7052,0.7058,0.7091,0.7218,0.7236,0.7254,0.7273, 0.7367,0.7394,0.7395,0.7396,0.7399,0.7410,0.7417,0.7464,0.7533,0.7643, 0.7652,0.7723,0.7782,0.7860,0.7935,0.8106,0.8156,0.8245,0.8302,0.8353, 0.8382,0.8465,0.8479,0.8497,0.8517,0.8523,0.8599,0.8614,0.8621,0.8655, 0.8750,0.8777,0.8806,0.8834,0.8836,0.8859,0.8902,0.8982,0.9036,0.9086, 0.9135,0.9153,0.9158,0.9175,0.9186,0.9309,0.9338,0.9360,0.9408,0.9439, 0.9440,0.9447,0.9469,0.9529,0.9584,0.9618,0.9627,0.9636,0.9656,0.9661, 0.9665,0.9672,0.9801,0.9836,0.9853,0.9868,0.9879,0.9898,0.9932, Overall p-value after applying KStest on 269 p-values = 0.461568 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.