RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-12-06_03:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.67 27.6080 0.950267 2 to 25 15.78 12.6447 0.240371 3 to 26 15.64 15.5617 0.444911 4 to 27 15.68 15.5233 0.442157 5 to 28 15.96 22.7284 0.841697 6 to 29 15.99 22.5431 0.835275 7 to 30 15.82 20.4454 0.747918 8 to 31 15.51 21.6448 0.801232 9 to 32 15.83 13.0657 0.268224 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.321557 Tough bday spacings test for dh-ranFile-2015-12-06_03:31: 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 30 64 103 111 62 61 28 21 6 4 (O-E)^2/E 0.1 1.2 1.2 0.3 1.8 3.3 1.5 0.1 2.5 0.1 0.0 Birthday Spacings: Sum(O-E)^2/E= 12.087, p= 0.721 RESULTS OF GCD FOR dh-ranFile-2015-12-06_03:31 Euclid's algorithm: p-value, steps to gcd: 0.690120 p-value, dist. of gcd's: 0.780134 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-12-06_03:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.165 0.640 0.939 0.711 0.096 0.059 0.319 0.441 Bits 8 to 15---> 0.686 0.721 0.075 0.208 0.359 0.904 0.948 0.110 Bits 16 to 23---> 0.867 0.951 0.190 0.559 0.725 0.384 0.389 0.894 Bits 24 to 31---> 0.933 0.096 0.540 0.649 0.787 0.082 0.886 0.206 KS test for the above 32 p values: 0.407 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-12-06_03:31, p-values for 5 runs: 0.8651, 0.5083, 0.1805, 0.4191, 0.9299 Rank test for binary matrices (31x31) for dh-ranFile-2015-12-06_03:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 229 211.4 1.462 1.462 r= 29 5175 5134.0 0.327 1.789 r= 30 23078 23103.0 0.027 1.817 r= 31 11518 11551.5 0.097 1.914 chi-square = 1.914 with df = 3; p-value = 0.410 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-12-06_03:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 209 211.4 0.028 0.028 r= 30 5176 5134.0 0.343 0.371 r= 31 23220 23103.0 0.592 0.963 r= 32 11395 11551.5 2.121 3.084 chi-square = 3.084 with df = 3; p-value = 0.621 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-12-06_03:31 b-rank test for bits 1 to 8, p=0.59578 b-rank test for bits 2 to 9, p=0.02814 b-rank test for bits 3 to 10, p=0.41995 b-rank test for bits 4 to 11, p=0.03142 b-rank test for bits 5 to 12, p=0.42115 b-rank test for bits 6 to 13, p=0.58295 b-rank test for bits 7 to 14, p=0.20315 b-rank test for bits 8 to 15, p=0.13916 b-rank test for bits 9 to 16, p=0.16537 b-rank test for bits 10 to 17, p=0.78426 b-rank test for bits 11 to 18, p=0.36279 b-rank test for bits 12 to 19, p=0.35304 b-rank test for bits 13 to 20, p=0.37243 b-rank test for bits 14 to 21, p=0.84204 b-rank test for bits 15 to 22, p=0.46194 b-rank test for bits 16 to 23, p=0.66004 b-rank test for bits 17 to 24, p=0.42793 b-rank test for bits 18 to 25, p=0.15422 b-rank test for bits 19 to 26, p=0.59255 b-rank test for bits 20 to 27, p=0.05268 b-rank test for bits 21 to 28, p=0.35401 b-rank test for bits 22 to 29, p=0.05063 b-rank test for bits 23 to 30, p=0.56693 b-rank test for bits 24 to 31, p=0.23200 b-rank test for bits 25 to 32, p=0.69962 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 = 0.053855 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-12-06_03:31 (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 141715 -0.45 0.324899 2 142389 1.12 0.868797 3 141760 -0.35 0.363582 4 142987 2.52 0.994098 5 141916 0.02 0.506217 6 142070 0.38 0.646317 7 142293 0.90 0.814987 8 141315 -1.39 0.082474 9 141728 -0.42 0.335904 10 140688 -2.85 0.002162 11 142041 0.31 0.620822 12 141156 -1.76 0.039194 13 142242 0.78 0.781499 14 142046 0.32 0.625259 15 141918 0.02 0.508081 16 141424 -1.13 0.128408 17 142175 0.62 0.732610 18 141678 -0.54 0.294429 19 142162 0.59 0.722522 20 142169 0.61 0.727977 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-12-06_03:31 Bits used No. missing words z-score p-value 23 to 32 141979 0.2402 0.594928 22 to 31 141496 -1.4253 0.077039 21 to 30 141843 -0.2287 0.409542 20 to 29 141757 -0.5253 0.299696 19 to 28 141695 -0.7391 0.229933 18 to 27 142034 0.4299 0.666365 17 to 26 142130 0.7609 0.776651 16 to 25 142009 0.3437 0.634460 15 to 24 142252 1.1816 0.881322 14 to 23 142219 1.0678 0.857201 13 to 22 141890 -0.0667 0.473428 12 to 21 141586 -1.1149 0.132440 11 to 20 141819 -0.3115 0.377717 10 to 19 141699 -0.7253 0.234141 9 to 18 141640 -0.9287 0.176516 8 to 17 141604 -1.0529 0.146202 7 to 16 142114 0.7058 0.759831 6 to 15 141906 -0.0115 0.495419 5 to 14 142272 1.2506 0.894457 4 to 13 141631 -0.9598 0.168588 3 to 12 141500 -1.4115 0.079051 2 to 11 142020 0.3816 0.648629 1 to 10 141598 -1.0736 0.141512 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-12-06_03:31 Bits used No. missing words z-score p-value 28 to 32 142075 0.5616 0.712803 27 to 31 141765 -0.4893 0.312331 26 to 30 141849 -0.2045 0.418978 25 to 29 142327 1.4158 0.921587 24 to 28 142118 0.7074 0.760327 23 to 27 142501 2.0057 0.977554 22 to 26 141536 -1.2655 0.102842 21 to 25 141781 -0.4350 0.331775 20 to 24 142044 0.4565 0.675988 19 to 23 142000 0.3074 0.620714 18 to 22 142080 0.5785 0.718551 17 to 21 141764 -0.4926 0.311132 16 to 20 141949 0.1345 0.553486 15 to 19 141755 -0.5232 0.300434 14 to 18 141758 -0.5130 0.303982 13 to 17 141560 -1.1842 0.118173 12 to 16 141900 -0.0316 0.487385 11 to 15 141769 -0.4757 0.317146 10 to 14 142031 0.4124 0.659992 9 to 13 142496 1.9887 0.976634 8 to 12 141920 0.0362 0.514426 7 to 11 141811 -0.3333 0.369446 6 to 10 142256 1.1752 0.880033 5 to 9 141978 0.2328 0.592034 4 to 8 142501 2.0057 0.977554 3 to 7 141607 -1.0248 0.152718 2 to 6 141121 -2.6723 0.003767 1 to 5 141757 -0.5164 0.302797 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-12-06_03:31 Bits used No. missing words z-score p-value 31 to 32 141394 -1.5201 0.064237 30 to 31 141987 0.2291 0.590610 29 to 30 141291 -1.8240 0.034077 28 to 29 142106 0.5801 0.719092 27 to 28 142245 0.9902 0.838956 26 to 27 142051 0.4179 0.661992 25 to 26 142250 1.0049 0.842534 24 to 25 142522 1.8073 0.964641 23 to 24 141546 -1.0718 0.141912 22 to 23 141475 -1.2812 0.100060 21 to 22 141718 -0.5644 0.286243 20 to 21 141636 -0.8063 0.210040 19 to 20 141454 -1.3432 0.089611 18 to 19 141762 -0.4346 0.331926 17 to 18 142110 0.5919 0.723057 16 to 17 140990 -2.7119 0.003345 15 to 16 141540 -1.0895 0.137974 14 to 15 141978 0.2026 0.580263 13 to 14 141703 -0.6086 0.271381 12 to 13 142103 0.5713 0.716101 11 to 12 142614 2.0787 0.981176 10 to 11 141666 -0.7178 0.236444 9 to 10 142290 1.1229 0.869264 8 to 9 142154 0.7217 0.764773 7 to 8 141965 0.1642 0.565220 6 to 7 141878 -0.0924 0.463183 5 to 6 142164 0.7512 0.773746 4 to 5 141664 -0.7237 0.234629 3 to 4 141543 -1.0806 0.139933 2 to 3 141923 0.0403 0.516083 1 to 2 141967 0.1701 0.567541 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-12-06_03:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2377.69 -1.730 0.041834 Test results for specific bytes for dh-ranFile-2015-12-06_03:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2506.12 0.087 0.534500 2 to 9 2519.69 0.279 0.609691 3 to 10 2474.94 -0.354 0.361541 4 to 11 2488.51 -0.163 0.435449 5 to 12 2513.40 0.189 0.575137 6 to 13 2486.71 -0.188 0.425442 7 to 14 2386.51 -1.605 0.054244 8 to 15 2448.41 -0.730 0.232808 9 to 16 2397.48 -1.450 0.073543 10 to 17 2322.65 -2.508 0.006070 11 to 18 2445.84 -0.766 0.221843 12 to 19 2367.40 -1.875 0.030382 13 to 20 2483.68 -0.231 0.408719 14 to 21 2445.64 -0.769 0.221027 15 to 22 2487.32 -0.179 0.428818 16 to 23 2478.55 -0.303 0.380794 17 to 24 2527.35 0.387 0.650526 18 to 25 2506.91 0.098 0.538902 19 to 26 2425.65 -1.051 0.146522 20 to 27 2560.48 0.855 0.803799 21 to 28 2485.35 -0.207 0.417916 22 to 29 2447.68 -0.740 0.229664 23 to 30 2607.63 1.522 0.936010 24 to 31 2486.61 -0.189 0.424920 25 to 32 2513.38 0.189 0.575039 CDPARK for dh-ranFile-2015-12-06_03:31: 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 3514 -0.4110 0.340551 3530 0.3196 0.625377 3528 0.2283 0.590298 3539 0.7306 0.767486 3468 -2.5114 0.006012 3509 -0.6393 0.261324 3513 -0.4566 0.323972 3523 0.0000 0.500000 3520 -0.1370 0.445521 Square side=100, avg. no. parked=3516.60 sample std.=18.25 p-value of the KSTEST for those 10 p-values: 0.345781 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-12-06_03:31 0.1875,0.6522,0.5643,0.8489,0.3116,0.4140,0.6643,0.8014,0.7774,0.6149, The KS test for those 10 p-values: 0.376792 The 3DSPHERES test for dh-ranFile-2015-12-06_03:31 sample no r^3 equiv. uni. 1 6.266 0.188502 2 6.248 0.187996 3 40.391 0.739816 4 7.164 0.212425 5 85.694 0.942528 6 10.327 0.291228 7 27.750 0.603475 8 9.490 0.271190 9 48.675 0.802596 10 8.969 0.258428 11 17.530 0.442524 12 7.078 0.210171 13 7.889 0.231244 14 33.279 0.670209 15 28.261 0.610160 16 7.182 0.212902 17 14.688 0.387119 18 38.206 0.720162 19 50.764 0.815872 20 16.597 0.424914 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.347250 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-12-06_03:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 0.9 -0.6 -0.7 -1.1 0.1 -0.5 1.7 -0.9 -0.5 -0.0 1.2 0.1 -0.4 0.7 -0.8 -0.5 0.6 1.3 -1.0 0.1 -0.4 -1.5 0.4 0.8 1.4 0.9 -1.1 -1.7 -0.4 -2.3 0.4 0.0 1.4 1.9 0.2 1.4 -1.0 1.7 2.1 -1.3 0.0 -1.1 Chi-square with 42 degrees of freedom:48.398080 z-score=0.698088, p-value=0.769571 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-12-06_03:31 Test no p-value 1 0.531046 2 0.014217 3 0.006736 4 0.070759 5 0.367966 6 0.022261 7 0.800147 8 0.000551 9 0.222071 10 0.016676 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000024 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-12-06_03:31: (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 66337 1.63 66654 0.00 3 25000.00 25253 2.56 24969 0.04 4 6666.67 6778 1.86 6640 0.11 5 1388.89 1362 0.52 1456 3.24 6 238.10 232 0.16 248 0.41 7 34.72 30 0.64 28 1.30 8 4.96 7 0.84 4 0.19 p=0.77668 p=0.49265 Number of rngs required: 687909, p-value: 0.284 RESULTS OF CRAPS TEST for dh-ranFile-2015-12-06_03:31 No. of wins: Observed Expected 98215 98585.9 z-score=-1.659, pvalue=0.04859 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66134 66666.7 4.256 4.256 2 38005 37654.3 3.266 7.522 3 26920 26954.7 0.045 7.567 4 19511 19313.5 2.020 9.587 5 13800 13851.4 0.191 9.778 6 10072 9943.5 1.659 11.437 7 7203 7145.0 0.470 11.908 8 5241 5139.1 2.022 13.929 9 3669 3699.9 0.257 14.187 10 2546 2666.3 5.428 19.615 11 1875 1923.3 1.214 20.829 12 1378 1388.7 0.083 20.912 13 1062 1003.7 3.385 24.297 14 705 726.1 0.615 24.912 15 513 525.8 0.313 25.225 16 387 381.2 0.090 25.315 17 261 276.5 0.873 26.188 18 182 200.8 1.765 27.954 19 144 146.0 0.027 27.981 20 105 106.2 0.014 27.995 21 287 287.1 0.000 27.995 Chisq= 27.99 for 20 degrees of freedom, p= 0.89048 SUMMARY of craptest p-value for no. of wins: 0.048589 p-value for throws/game: 0.890476 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-12-06_03:31 No. of wins: Observed Expected 99015 98585.9 z-score= 1.919, pvalue=0.97253 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66882 66666.7 0.696 0.696 2 37848 37654.3 0.996 1.692 3 26918 26954.7 0.050 1.742 4 19252 19313.5 0.196 1.937 5 13893 13851.4 0.125 2.062 6 9917 9943.5 0.071 2.133 7 7130 7145.0 0.032 2.165 8 5013 5139.1 3.093 5.257 9 3653 3699.9 0.594 5.851 10 2583 2666.3 2.602 8.453 11 1891 1923.3 0.543 8.997 12 1346 1388.7 1.315 10.312 13 994 1003.7 0.094 10.406 14 756 726.1 1.228 11.634 15 486 525.8 3.018 14.652 16 417 381.2 3.372 18.024 17 294 276.5 1.102 19.126 18 179 200.8 2.373 21.499 19 158 146.0 0.989 22.488 20 77 106.2 8.036 30.524 21 313 287.1 2.334 32.858 Chisq= 32.86 for 20 degrees of freedom, p= 0.96503 SUMMARY of craptest p-value for no. of wins: 0.972531 p-value for throws/game: 0.965027 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0000,0.0006,0.0022,0.0033,0.0038,0.0060,0.0061,0.0067,0.0142,0.0167, 0.0223,0.0281,0.0304,0.0314,0.0341,0.0392,0.0418,0.0486,0.0506,0.0527, 0.0539,0.0542,0.0591,0.0642,0.0708,0.0735,0.0751,0.0770,0.0791,0.0817, 0.0825,0.0896,0.0958,0.0964,0.1001,0.1028,0.1104,0.1182,0.1284,0.1324, 0.1380,0.1392,0.1399,0.1415,0.1419,0.1462,0.1465,0.1527,0.1542,0.1646, 0.1654,0.1686,0.1765,0.1805,0.1875,0.1880,0.1885,0.1902,0.2031,0.2059, 0.2081,0.2100,0.2102,0.2124,0.2129,0.2210,0.2218,0.2221,0.2297,0.2299, 0.2312,0.2320,0.2328,0.2341,0.2346,0.2364,0.2404,0.2584,0.2613,0.2682, 0.2712,0.2714,0.2845,0.2862,0.2912,0.2944,0.2997,0.3004,0.3028,0.3040, 0.3111,0.3116,0.3123,0.3171,0.3190,0.3216,0.3240,0.3249,0.3318,0.3319, 0.3359,0.3406,0.3458,0.3472,0.3530,0.3540,0.3593,0.3615,0.3628,0.3636, 0.3680,0.3694,0.3724,0.3768,0.3777,0.3808,0.3843,0.3871,0.3888,0.4066, 0.4087,0.4095,0.4095,0.4140,0.4179,0.4190,0.4191,0.4200,0.4211,0.4249, 0.4249,0.4254,0.4279,0.4288,0.4354,0.4411,0.4422,0.4425,0.4449,0.4455, 0.4619,0.4632,0.4734,0.4818,0.4874,0.4927,0.4954,0.5000,0.5062,0.5081, 0.5083,0.5144,0.5161,0.5310,0.5345,0.5389,0.5404,0.5535,0.5594,0.5643, 0.5652,0.5669,0.5675,0.5750,0.5751,0.5803,0.5830,0.5903,0.5906,0.5920, 0.5925,0.5949,0.5958,0.6035,0.6097,0.6102,0.6149,0.6207,0.6208,0.6211, 0.6253,0.6254,0.6345,0.6397,0.6463,0.6486,0.6488,0.6505,0.6522,0.6600, 0.6600,0.6620,0.6643,0.6664,0.6702,0.6760,0.6859,0.6901,0.6996,0.7109, 0.7128,0.7161,0.7186,0.7191,0.7202,0.7207,0.7214,0.7225,0.7231,0.7250, 0.7280,0.7326,0.7398,0.7479,0.7598,0.7603,0.7648,0.7675,0.7696,0.7737, 0.7767,0.7767,0.7774,0.7801,0.7815,0.7843,0.7874,0.8001,0.8012,0.8014, 0.8026,0.8038,0.8150,0.8159,0.8353,0.8390,0.8417,0.8420,0.8425,0.8489, 0.8572,0.8651,0.8670,0.8688,0.8693,0.8800,0.8813,0.8858,0.8905,0.8943, 0.8945,0.9042,0.9216,0.9299,0.9328,0.9360,0.9388,0.9425,0.9484,0.9503, 0.9505,0.9646,0.9650,0.9725,0.9766,0.9776,0.9776,0.9812,0.9941, Overall p-value after applying KStest on 269 p-values = 0.059191 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.