RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-12-11_01:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 16.04 23.6824 0.871676 2 to 25 15.98 17.4474 0.575522 3 to 26 15.79 16.8087 0.532604 4 to 27 15.82 16.0304 0.478321 5 to 28 15.90 13.6632 0.309218 6 to 29 15.87 15.5364 0.443098 7 to 30 15.68 13.7541 0.315575 8 to 31 15.90 17.4823 0.577818 9 to 32 15.60 12.6180 0.238641 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.394971 Tough bday spacings test for dh-ranFile-2015-12-11_01:31: 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 34 66 92 99 78 49 33 27 7 5 (O-E)^2/E 0.1 0.2 0.7 0.3 0.0 0.0 0.2 0.4 9.9 0.0 0.2 Birthday Spacings: Sum(O-E)^2/E= 11.967, p= 0.713 RESULTS OF GCD FOR dh-ranFile-2015-12-11_01:31 Euclid's algorithm: p-value, steps to gcd: 0.742438 p-value, dist. of gcd's: 0.744287 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-12-11_01:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.283 0.361 0.858 0.192 0.576 0.932 0.295 0.343 Bits 8 to 15---> 0.859 0.497 0.369 0.589 0.917 0.590 0.487 0.904 Bits 16 to 23---> 0.514 0.476 0.492 0.096 0.727 0.514 0.633 0.864 Bits 24 to 31---> 0.126 0.797 0.484 0.905 0.087 0.910 0.899 0.370 KS test for the above 32 p values: 0.773 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-12-11_01:31, p-values for 5 runs: 0.6936, 0.1896, 0.7901, 0.0001, 0.9929 Rank test for binary matrices (31x31) for dh-ranFile-2015-12-11_01:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 189 211.4 2.377 2.377 r= 29 5225 5134.0 1.613 3.990 r= 30 23348 23103.0 2.597 6.587 r= 31 11238 11551.5 8.509 15.096 chi-square = 15.096 with df = 3; p-value = 0.998 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-12-11_01:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 213 211.4 0.012 0.012 r= 30 5065 5134.0 0.928 0.939 r= 31 23131 23103.0 0.034 0.973 r= 32 11591 11551.5 0.135 1.108 chi-square = 1.108 with df = 3; p-value = 0.225 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-12-11_01:31 b-rank test for bits 1 to 8, p=0.51035 b-rank test for bits 2 to 9, p=0.95072 b-rank test for bits 3 to 10, p=0.59942 b-rank test for bits 4 to 11, p=0.51047 b-rank test for bits 5 to 12, p=0.95977 b-rank test for bits 6 to 13, p=0.25615 b-rank test for bits 7 to 14, p=0.83838 b-rank test for bits 8 to 15, p=0.02428 b-rank test for bits 9 to 16, p=0.25569 b-rank test for bits 10 to 17, p=0.41877 b-rank test for bits 11 to 18, p=0.07399 b-rank test for bits 12 to 19, p=0.61231 b-rank test for bits 13 to 20, p=0.34220 b-rank test for bits 14 to 21, p=0.84110 b-rank test for bits 15 to 22, p=0.84618 b-rank test for bits 16 to 23, p=0.67160 b-rank test for bits 17 to 24, p=0.82999 b-rank test for bits 18 to 25, p=0.76391 b-rank test for bits 19 to 26, p=0.29057 b-rank test for bits 20 to 27, p=0.35594 b-rank test for bits 21 to 28, p=0.22676 b-rank test for bits 22 to 29, p=0.40170 b-rank test for bits 23 to 30, p=0.53530 b-rank test for bits 24 to 31, p=0.48987 b-rank test for bits 25 to 32, p=0.25090 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 = 0.872836 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-12-11_01:31 (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 141327 -1.36 0.086823 2 141918 0.02 0.508081 3 142530 1.45 0.926494 4 142347 1.02 0.846750 5 141582 -0.76 0.222198 6 141855 -0.13 0.449494 7 142088 0.42 0.661827 8 141770 -0.33 0.372387 9 141809 -0.23 0.407331 10 141105 -1.88 0.030103 11 141545 -0.85 0.197319 12 141560 -0.82 0.207195 13 142860 2.22 0.986831 14 141301 -1.42 0.077610 15 141952 0.10 0.539707 16 142164 0.60 0.724086 17 142167 0.60 0.726424 18 142303 0.92 0.821159 19 141121 -1.84 0.032745 20 141367 -1.27 0.102555 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-12-11_01:31 Bits used No. missing words z-score p-value 23 to 32 141872 -0.1287 0.448788 22 to 31 141909 -0.0011 0.499546 21 to 30 141662 -0.8529 0.196868 20 to 29 141638 -0.9356 0.174734 19 to 28 141403 -1.7460 0.040408 18 to 27 141858 -0.1770 0.429754 17 to 26 142074 0.5678 0.714924 16 to 25 142060 0.5196 0.698312 15 to 24 142384 1.6368 0.949163 14 to 23 142104 0.6713 0.748978 13 to 22 142532 2.1471 0.984109 12 to 21 142251 1.1782 0.880636 11 to 20 142341 1.4885 0.931693 10 to 19 141823 -0.2977 0.382970 9 to 18 142049 0.4816 0.684962 8 to 17 141747 -0.5598 0.287822 7 to 16 141546 -1.2529 0.105128 6 to 15 141771 -0.4770 0.316681 5 to 14 141701 -0.7184 0.236262 4 to 13 141711 -0.6839 0.247020 3 to 12 141462 -1.5425 0.061474 2 to 11 141773 -0.4701 0.319141 1 to 10 141883 -0.0908 0.463829 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-12-11_01:31 Bits used No. missing words z-score p-value 28 to 32 141964 0.1853 0.573512 27 to 31 142165 0.8667 0.806941 26 to 30 141798 -0.3774 0.352942 25 to 29 141700 -0.7096 0.238978 24 to 28 141904 -0.0181 0.492792 23 to 27 142205 1.0023 0.841894 22 to 26 141395 -1.7435 0.040624 21 to 25 141900 -0.0316 0.487385 20 to 24 142182 0.9243 0.822336 19 to 23 141870 -0.1333 0.446969 18 to 22 141873 -0.1232 0.450993 17 to 21 141720 -0.6418 0.260503 16 to 20 142077 0.5684 0.715109 15 to 19 142171 0.8870 0.812465 14 to 18 141941 0.1074 0.542747 13 to 17 141575 -1.1333 0.128540 12 to 16 142186 0.9379 0.825843 11 to 15 142250 1.1548 0.875917 10 to 14 142084 0.5921 0.723109 9 to 13 141688 -0.7503 0.226546 8 to 12 141958 0.1650 0.565521 7 to 11 142040 0.4429 0.671099 6 to 10 142278 1.2497 0.894301 5 to 9 141640 -0.9130 0.180626 4 to 8 142351 1.4972 0.932828 3 to 7 142259 1.1853 0.882055 2 to 6 142258 1.1819 0.881384 1 to 5 142067 0.5345 0.703493 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-12-11_01:31 Bits used No. missing words z-score p-value 31 to 32 141620 -0.8535 0.196696 30 to 31 141513 -1.1691 0.121179 29 to 30 142533 1.8397 0.967096 28 to 29 142349 1.2970 0.902678 27 to 28 142317 1.2026 0.885428 26 to 27 141819 -0.2665 0.394942 25 to 26 141537 -1.0983 0.136033 24 to 25 141244 -1.9626 0.024845 23 to 24 141707 -0.5968 0.275306 22 to 23 141903 -0.0187 0.492551 21 to 22 141956 0.1377 0.554749 20 to 21 142345 1.2852 0.900632 19 to 20 141866 -0.1278 0.449147 18 to 19 141340 -1.6794 0.046533 17 to 18 141885 -0.0718 0.471393 16 to 17 141563 -1.0216 0.153480 15 to 16 142437 1.5565 0.940211 14 to 15 142507 1.7630 0.961053 13 to 14 142051 0.4179 0.661992 12 to 13 141964 0.1613 0.564059 11 to 12 141049 -2.5378 0.005577 10 to 11 142122 0.6273 0.734784 9 to 10 142094 0.5447 0.707037 8 to 9 141985 0.2232 0.588316 7 to 8 141348 -1.6558 0.048877 6 to 7 141765 -0.4258 0.335144 5 to 6 141070 -2.4759 0.006645 4 to 5 142434 1.5477 0.939153 3 to 4 142065 0.4592 0.676956 2 to 3 142284 1.1052 0.865468 1 to 2 141951 0.1229 0.548915 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-12-11_01:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2375.09 -1.767 0.038656 Test results for specific bytes for dh-ranFile-2015-12-11_01:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2439.93 -0.850 0.197793 2 to 9 2577.49 1.096 0.863424 3 to 10 2459.54 -0.572 0.283597 4 to 11 2624.22 1.757 0.960523 5 to 12 2449.67 -0.712 0.238317 6 to 13 2574.20 1.049 0.852990 7 to 14 2484.69 -0.217 0.414285 8 to 15 2661.70 2.287 0.988896 9 to 16 2500.29 0.004 0.501636 10 to 17 2549.93 0.706 0.759923 11 to 18 2563.76 0.902 0.816375 12 to 19 2457.97 -0.594 0.276119 13 to 20 2537.23 0.527 0.700758 14 to 21 2406.86 -1.317 0.093895 15 to 22 2374.87 -1.770 0.038391 16 to 23 2443.03 -0.806 0.210225 17 to 24 2469.99 -0.424 0.335635 18 to 25 2546.87 0.663 0.746303 19 to 26 2489.15 -0.153 0.439043 20 to 27 2422.90 -1.090 0.137783 21 to 28 2482.77 -0.244 0.403720 22 to 29 2452.84 -0.667 0.252419 23 to 30 2416.69 -1.178 0.119365 24 to 31 2376.88 -1.741 0.040829 25 to 32 2498.54 -0.021 0.491742 CDPARK for dh-ranFile-2015-12-11_01:31: 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 3540 0.7763 0.781201 3530 0.3196 0.625377 3503 -0.9132 0.180558 3535 0.5479 0.708135 3518 -0.2283 0.409702 3532 0.4110 0.659449 3525 0.0913 0.536383 3550 1.2329 0.891189 3534 0.5023 0.692266 3521 -0.0913 0.463617 Square side=100, avg. no. parked=3528.80 sample std.=12.29 p-value of the KSTEST for those 10 p-values: 0.287195 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-12-11_01:31 0.7386,0.4001,0.6223,0.5201,0.9429,0.1828,0.2545,0.7661,0.0588,0.4393, The KS test for those 10 p-values: 0.998681 The 3DSPHERES test for dh-ranFile-2015-12-11_01:31 sample no r^3 equiv. uni. 1 116.671 0.979535 2 29.337 0.623905 3 53.503 0.831940 4 2.335 0.074867 5 9.711 0.276529 6 21.205 0.506789 7 44.249 0.771212 8 32.175 0.657847 9 109.014 0.973584 10 75.435 0.919097 11 34.192 0.680093 12 5.588 0.169954 13 27.267 0.597032 14 3.359 0.105937 15 123.686 0.983802 16 30.954 0.643631 17 52.849 0.828238 18 55.362 0.842040 19 16.736 0.427568 20 33.068 0.667888 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.060200 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-12-11_01:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 0.9 -0.4 -0.8 -0.9 0.9 -0.6 0.1 1.6 -2.4 -1.7 -0.4 -0.3 -0.2 0.2 1.7 -0.3 -0.8 1.5 0.9 0.2 1.1 -0.4 -0.1 -0.4 -0.6 -0.9 -0.3 -1.2 -0.2 0.7 1.0 -1.4 -0.6 -1.0 0.6 -0.9 -1.3 0.9 0.4 0.9 0.0 0.8 Chi-square with 42 degrees of freedom:37.045790 z-score=-0.540549, p-value=0.312124 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-12-11_01:31 Test no p-value 1 0.028415 2 0.345019 3 0.166350 4 0.054590 5 0.325350 6 0.055389 7 0.611238 8 0.858697 9 0.548906 10 0.861531 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.241375 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-12-11_01:31: (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 66445 0.74 66691 0.01 3 25000.00 24978 0.02 24916 0.28 4 6666.67 6833 4.15 6733 0.66 5 1388.89 1461 3.74 1367 0.35 6 238.10 232 0.16 248 0.41 7 34.72 42 1.53 41 1.14 8 4.96 8 1.86 3 0.77 p=0.94226 p=0.27186 Number of rngs required: 688268, p-value: 0.438 RESULTS OF CRAPS TEST for dh-ranFile-2015-12-11_01:31 No. of wins: Observed Expected 98426 98585.9 z-score=-0.715, pvalue=0.23731 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66682 66666.7 0.004 0.004 2 37599 37654.3 0.081 0.085 3 26681 26954.7 2.780 2.865 4 19351 19313.5 0.073 2.938 5 13844 13851.4 0.004 2.942 6 9981 9943.5 0.141 3.083 7 7344 7145.0 5.541 8.624 8 5157 5139.1 0.063 8.686 9 3775 3699.9 1.526 10.212 10 2657 2666.3 0.032 10.244 11 2009 1923.3 3.816 14.061 12 1319 1388.7 3.502 17.563 13 974 1003.7 0.880 18.442 14 683 726.1 2.563 21.005 15 545 525.8 0.698 21.704 16 388 381.2 0.123 21.827 17 273 276.5 0.045 21.872 18 185 200.8 1.248 23.120 19 129 146.0 1.976 25.096 20 125 106.2 3.322 28.418 21 299 287.1 0.492 28.910 Chisq= 28.91 for 20 degrees of freedom, p= 0.91046 SUMMARY of craptest p-value for no. of wins: 0.237310 p-value for throws/game: 0.910460 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-12-11_01:31 No. of wins: Observed Expected 98348 98585.9 z-score=-1.064, pvalue=0.14370 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67049 66666.7 2.193 2.193 2 37499 37654.3 0.641 2.833 3 26837 26954.7 0.514 3.348 4 19356 19313.5 0.094 3.441 5 13729 13851.4 1.082 4.523 6 9862 9943.5 0.669 5.192 7 7111 7145.0 0.162 5.354 8 5137 5139.1 0.001 5.355 9 3679 3699.9 0.118 5.472 10 2737 2666.3 1.875 7.347 11 1968 1923.3 1.038 8.385 12 1416 1388.7 0.535 8.920 13 987 1003.7 0.278 9.198 14 727 726.1 0.001 9.199 15 511 525.8 0.419 9.618 16 374 381.2 0.134 9.752 17 274 276.5 0.023 9.775 18 200 200.8 0.003 9.779 19 147 146.0 0.007 9.786 20 111 106.2 0.216 10.001 21 289 287.1 0.012 10.014 Chisq= 10.01 for 20 degrees of freedom, p= 0.03208 SUMMARY of craptest p-value for no. of wins: 0.143700 p-value for throws/game: 0.032078 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0001,0.0056,0.0066,0.0243,0.0248,0.0284,0.0301,0.0321,0.0327,0.0384, 0.0387,0.0404,0.0406,0.0408,0.0465,0.0489,0.0546,0.0554,0.0588,0.0602, 0.0615,0.0740,0.0749,0.0776,0.0868,0.0871,0.0939,0.0958,0.1026,0.1051, 0.1059,0.1194,0.1212,0.1262,0.1285,0.1360,0.1378,0.1437,0.1535,0.1664, 0.1700,0.1747,0.1806,0.1806,0.1828,0.1896,0.1922,0.1967,0.1969,0.1973, 0.1978,0.2072,0.2102,0.2222,0.2249,0.2265,0.2268,0.2363,0.2373,0.2383, 0.2386,0.2390,0.2414,0.2470,0.2509,0.2524,0.2545,0.2557,0.2562,0.2605, 0.2719,0.2753,0.2761,0.2765,0.2826,0.2836,0.2872,0.2878,0.2906,0.2949, 0.3092,0.3121,0.3156,0.3167,0.3191,0.3253,0.3351,0.3356,0.3422,0.3434, 0.3450,0.3529,0.3559,0.3605,0.3686,0.3699,0.3724,0.3830,0.3949,0.3950, 0.4001,0.4017,0.4037,0.4073,0.4097,0.4143,0.4188,0.4276,0.4298,0.4383, 0.4390,0.4393,0.4431,0.4470,0.4488,0.4491,0.4495,0.4510,0.4636,0.4638, 0.4714,0.4764,0.4783,0.4840,0.4874,0.4875,0.4899,0.4917,0.4924,0.4926, 0.4928,0.4973,0.4995,0.5016,0.5068,0.5081,0.5103,0.5105,0.5140,0.5144, 0.5201,0.5326,0.5353,0.5364,0.5397,0.5427,0.5489,0.5489,0.5547,0.5641, 0.5655,0.5735,0.5755,0.5756,0.5778,0.5883,0.5887,0.5903,0.5970,0.5994, 0.6112,0.6123,0.6223,0.6239,0.6254,0.6325,0.6436,0.6578,0.6594,0.6618, 0.6620,0.6679,0.6711,0.6716,0.6770,0.6801,0.6850,0.6923,0.6936,0.6983, 0.7008,0.7035,0.7070,0.7081,0.7127,0.7149,0.7151,0.7231,0.7241,0.7264, 0.7273,0.7348,0.7386,0.7424,0.7443,0.7463,0.7490,0.7599,0.7639,0.7661, 0.7712,0.7732,0.7812,0.7901,0.7967,0.8069,0.8125,0.8164,0.8212,0.8223, 0.8258,0.8282,0.8300,0.8319,0.8384,0.8411,0.8419,0.8420,0.8462,0.8467, 0.8530,0.8580,0.8586,0.8587,0.8615,0.8634,0.8637,0.8655,0.8717,0.8728, 0.8759,0.8806,0.8814,0.8821,0.8854,0.8912,0.8943,0.8994,0.9006,0.9027, 0.9040,0.9050,0.9096,0.9105,0.9171,0.9191,0.9265,0.9317,0.9320,0.9328, 0.9392,0.9402,0.9423,0.9429,0.9492,0.9507,0.9598,0.9605,0.9611,0.9671, 0.9736,0.9795,0.9838,0.9841,0.9868,0.9889,0.9929,0.9983,0.9987, Overall p-value after applying KStest on 269 p-values = 0.637581 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.