RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-10-26_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 15.77 6.6343 0.012191 2 to 25 15.93 10.7352 0.130004 3 to 26 15.77 15.4087 0.433928 4 to 27 15.74 21.3841 0.790422 5 to 28 15.54 21.1169 0.778894 6 to 29 15.94 9.8195 0.088994 7 to 30 15.87 16.6645 0.522690 8 to 31 15.93 29.3054 0.968189 9 to 32 15.74 18.3974 0.635805 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.810507 Tough bday spacings test for dh-ranFile-2015-10-26_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 37 63 96 103 76 51 29 19 10 6 (O-E)^2/E 0.1 0.0 1.4 0.0 0.3 0.1 0.0 0.0 1.1 1.7 0.9 Birthday Spacings: Sum(O-E)^2/E= 5.728, p= 0.162 RESULTS OF GCD FOR dh-ranFile-2015-10-26_03:31 Euclid's algorithm: p-value, steps to gcd: 0.855659 p-value, dist. of gcd's: 0.630611 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-10-26_03:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.131 0.007 0.476 0.691 0.191 0.926 0.857 0.788 Bits 8 to 15---> 0.892 0.206 0.584 0.989 0.129 0.129 0.057 0.317 Bits 16 to 23---> 0.606 0.419 0.697 0.703 0.737 0.205 0.538 0.593 Bits 24 to 31---> 0.477 0.202 0.229 0.403 0.480 0.252 0.051 0.119 KS test for the above 32 p values: 0.575 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-10-26_03:31, p-values for 5 runs: 0.1221, 0.2305, 0.8787, 0.3977, 0.2278 Rank test for binary matrices (31x31) for dh-ranFile-2015-10-26_03:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 204 211.4 0.260 0.260 r= 29 5167 5134.0 0.212 0.472 r= 30 23284 23103.0 1.417 1.890 r= 31 11345 11551.5 3.692 5.582 chi-square = 5.582 with df = 3; p-value = 0.866 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-10-26_03:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 239 211.4 3.598 3.598 r= 30 5132 5134.0 0.001 3.599 r= 31 23216 23103.0 0.552 4.151 r= 32 11413 11551.5 1.661 5.813 chi-square = 5.813 with df = 3; p-value = 0.879 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-10-26_03:31 b-rank test for bits 1 to 8, p=0.53860 b-rank test for bits 2 to 9, p=0.98979 b-rank test for bits 3 to 10, p=0.97294 b-rank test for bits 4 to 11, p=0.84206 b-rank test for bits 5 to 12, p=0.23748 b-rank test for bits 6 to 13, p=0.42502 b-rank test for bits 7 to 14, p=0.44447 b-rank test for bits 8 to 15, p=0.63984 b-rank test for bits 9 to 16, p=0.23576 b-rank test for bits 10 to 17, p=0.89913 b-rank test for bits 11 to 18, p=0.40159 b-rank test for bits 12 to 19, p=0.01903 b-rank test for bits 13 to 20, p=0.82875 b-rank test for bits 14 to 21, p=0.02342 b-rank test for bits 15 to 22, p=0.21875 b-rank test for bits 16 to 23, p=0.14412 b-rank test for bits 17 to 24, p=0.77116 b-rank test for bits 18 to 25, p=0.82133 b-rank test for bits 19 to 26, p=0.73117 b-rank test for bits 20 to 27, p=0.45312 b-rank test for bits 21 to 28, p=0.83544 b-rank test for bits 22 to 29, p=0.21853 b-rank test for bits 23 to 30, p=0.06209 b-rank test for bits 24 to 31, p=0.37810 b-rank test for bits 25 to 32, p=0.79604 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 = 0.810563 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-10-26_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 141680 -0.54 0.296042 2 142086 0.41 0.660116 3 142297 0.91 0.817471 4 141765 -0.34 0.367976 5 142969 2.48 0.993354 6 141844 -0.15 0.439341 7 141711 -0.46 0.321543 8 141454 -1.06 0.143697 9 142303 0.92 0.821159 10 142278 0.86 0.805485 11 142121 0.49 0.689543 12 141312 -1.40 0.081413 13 141847 -0.15 0.442106 14 142014 0.24 0.596600 15 142537 1.47 0.928746 16 141348 -1.31 0.094841 17 141999 0.21 0.582975 18 141315 -1.39 0.082474 19 143001 2.55 0.994624 20 142284 0.88 0.809321 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-10-26_03:31 Bits used No. missing words z-score p-value 23 to 32 142298 1.3402 0.909917 22 to 31 141986 0.2644 0.604256 21 to 30 141708 -0.6942 0.243765 20 to 29 142316 1.4023 0.919589 19 to 28 141363 -1.8839 0.029789 18 to 27 142054 0.4989 0.691062 17 to 26 142047 0.4747 0.682508 16 to 25 142144 0.8092 0.790802 15 to 24 142370 1.5885 0.943915 14 to 23 142038 0.4437 0.671367 13 to 22 141797 -0.3873 0.349251 12 to 21 141471 -1.5115 0.065333 11 to 20 142258 1.2023 0.885378 10 to 19 141828 -0.2804 0.389567 9 to 18 141918 0.0299 0.511925 8 to 17 142226 1.0920 0.862576 7 to 16 142035 0.4333 0.667618 6 to 15 142056 0.5058 0.693487 5 to 14 141856 -0.1839 0.427047 4 to 13 142061 0.5230 0.699513 3 to 12 141497 -1.4218 0.077538 2 to 11 141898 -0.0391 0.484418 1 to 10 141675 -0.8080 0.209535 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-10-26_03:31 Bits used No. missing words z-score p-value 28 to 32 142481 1.9379 0.973680 27 to 31 142043 0.4531 0.674768 26 to 30 141849 -0.2045 0.418978 25 to 29 141689 -0.7469 0.227568 24 to 28 141565 -1.1672 0.121561 23 to 27 141966 0.1921 0.576169 22 to 26 141562 -1.1774 0.119520 21 to 25 141680 -0.7774 0.218464 20 to 24 141955 0.1548 0.561516 19 to 23 142127 0.7379 0.769702 18 to 22 142026 0.3955 0.653760 17 to 21 142316 1.3785 0.915982 16 to 20 141746 -0.5537 0.289905 15 to 19 142170 0.8836 0.811551 14 to 18 141996 0.2938 0.615543 13 to 17 142343 1.4701 0.929228 12 to 16 141909 -0.0011 0.499554 11 to 15 142157 0.8396 0.799422 10 to 14 142261 1.1921 0.883389 9 to 13 142057 0.5006 0.691665 8 to 12 141417 -1.6689 0.047567 7 to 11 141889 -0.0689 0.472529 6 to 10 141756 -0.5198 0.301615 5 to 9 141731 -0.6045 0.272753 4 to 8 141769 -0.4757 0.317146 3 to 7 141969 0.2023 0.580148 2 to 6 141638 -0.9198 0.178848 1 to 5 141381 -1.7909 0.036651 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-10-26_03:31 Bits used No. missing words z-score p-value 31 to 32 141041 -2.5614 0.005212 30 to 31 141623 -0.8446 0.199158 29 to 30 142228 0.9400 0.826399 28 to 29 141872 -0.1101 0.456158 27 to 28 142161 0.7424 0.771074 26 to 27 141789 -0.3550 0.361311 25 to 26 142421 1.5094 0.934395 24 to 25 141826 -0.2458 0.402914 23 to 24 141127 -2.3078 0.010506 22 to 23 142000 0.2675 0.605444 21 to 22 141714 -0.5762 0.282242 20 to 21 141755 -0.4553 0.324464 19 to 20 142045 0.4002 0.655498 18 to 19 141478 -1.2724 0.101623 17 to 18 142096 0.5506 0.709063 16 to 17 141983 0.2173 0.586019 15 to 16 141512 -1.1721 0.120586 14 to 15 141964 0.1613 0.564059 13 to 14 141765 -0.4258 0.335144 12 to 13 141982 0.2144 0.584869 11 to 12 141872 -0.1101 0.456158 10 to 11 141712 -0.5821 0.280252 9 to 10 141977 0.1996 0.579110 8 to 9 141805 -0.3078 0.379133 7 to 8 142221 0.9194 0.821052 6 to 7 141705 -0.6027 0.273340 5 to 6 142180 0.7984 0.787691 4 to 5 142366 1.3471 0.911027 3 to 4 141384 -1.5496 0.060613 2 to 3 141579 -0.9744 0.164923 1 to 2 141714 -0.5762 0.282242 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-10-26_03:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2381.54 -1.675 0.046937 Test results for specific bytes for dh-ranFile-2015-10-26_03:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2531.43 0.444 0.671657 2 to 9 2554.89 0.776 0.781213 3 to 10 2469.45 -0.432 0.332835 4 to 11 2482.53 -0.247 0.402422 5 to 12 2431.90 -0.963 0.167751 6 to 13 2467.75 -0.456 0.324189 7 to 14 2600.06 1.415 0.921481 8 to 15 2493.39 -0.093 0.462789 9 to 16 2447.67 -0.740 0.229638 10 to 17 2544.13 0.624 0.733717 11 to 18 2503.56 0.050 0.520076 12 to 19 2574.17 1.049 0.852894 13 to 20 2423.66 -1.080 0.140165 14 to 21 2492.32 -0.109 0.456763 15 to 22 2368.94 -1.854 0.031903 16 to 23 2330.61 -2.396 0.008298 17 to 24 2521.39 0.303 0.618874 18 to 25 2511.24 0.159 0.563121 19 to 26 2448.14 -0.733 0.231648 20 to 27 2454.75 -0.640 0.261093 21 to 28 2453.32 -0.660 0.254595 22 to 29 2610.67 1.565 0.941221 23 to 30 2429.84 -0.992 0.160535 24 to 31 2579.04 1.118 0.868158 25 to 32 2395.88 -1.473 0.070442 CDPARK for dh-ranFile-2015-10-26_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 3516 -0.3196 0.374623 3514 -0.4110 0.340551 3496 -1.2329 0.108811 3512 -0.5023 0.307734 3530 0.3196 0.625377 3550 1.2329 0.891189 3521 -0.0913 0.463617 3508 -0.6849 0.246694 3536 0.5936 0.723613 3535 0.5479 0.708135 Square side=100, avg. no. parked=3521.80 sample std.=15.12 p-value of the KSTEST for those 10 p-values: 0.856710 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-10-26_03:31 0.0661,0.4110,0.8056,0.2440,0.9951,0.9648,0.5325,0.3159,0.5866,0.9627, The KS test for those 10 p-values: 0.240171 The 3DSPHERES test for dh-ranFile-2015-10-26_03:31 sample no r^3 equiv. uni. 1 39.972 0.736155 2 41.844 0.752118 3 12.573 0.342353 4 26.818 0.590953 5 12.701 0.345153 6 24.675 0.560668 7 51.928 0.822880 8 22.454 0.526906 9 90.596 0.951193 10 7.579 0.223252 11 81.347 0.933568 12 3.525 0.110858 13 89.849 0.949962 14 2.457 0.078634 15 3.168 0.100226 16 32.033 0.656226 17 4.307 0.133734 18 88.388 0.947464 19 3.437 0.108252 20 2.106 0.067787 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.514204 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-10-26_03:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 0.9 0.6 1.2 -0.1 0.8 -0.2 0.1 -1.1 1.0 0.8 -0.0 0.3 1.0 -1.4 0.4 -1.2 -0.3 1.6 -0.5 -1.2 0.5 0.8 0.5 -2.3 0.9 -1.5 -0.4 1.9 -0.4 -0.3 0.4 0.5 1.2 0.6 0.2 0.0 -1.3 -0.4 2.6 -1.3 -1.0 0.8 Chi-square with 42 degrees of freedom:43.576363 z-score=0.171995, p-value=0.595798 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-10-26_03:31 Test no p-value 1 0.335216 2 0.186731 3 0.748181 4 0.003640 5 0.332747 6 0.336242 7 0.172423 8 0.078800 9 0.003565 10 0.959652 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.019405 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-10-26_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 66578 0.12 66740 0.08 3 25000.00 25044 0.08 25015 0.01 4 6666.67 6710 0.28 6604 0.59 5 1388.89 1390 0.00 1339 1.79 6 238.10 234 0.07 261 2.20 7 34.72 42 1.53 36 0.05 8 4.96 1 3.16 4 0.19 p=0.48613 p=0.44425 Number of rngs required: 687811, p-value: 0.247 RESULTS OF CRAPS TEST for dh-ranFile-2015-10-26_03:31 No. of wins: Observed Expected 98656 98585.9 z-score= 0.314, pvalue=0.62313 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66658 66666.7 0.001 0.001 2 37464 37654.3 0.962 0.963 3 27192 26954.7 2.089 3.052 4 19262 19313.5 0.137 3.189 5 13987 13851.4 1.327 4.516 6 9959 9943.5 0.024 4.540 7 7103 7145.0 0.247 4.787 8 5115 5139.1 0.113 4.900 9 3684 3699.9 0.068 4.968 10 2628 2666.3 0.550 5.518 11 1905 1923.3 0.175 5.693 12 1418 1388.7 0.616 6.309 13 998 1003.7 0.033 6.342 14 715 726.1 0.171 6.513 15 529 525.8 0.019 6.532 16 363 381.2 0.864 7.396 17 302 276.5 2.344 9.740 18 211 200.8 0.515 10.255 19 131 146.0 1.538 11.793 20 108 106.2 0.030 11.823 21 268 287.1 1.272 13.096 Chisq= 13.10 for 20 degrees of freedom, p= 0.12675 SUMMARY of craptest p-value for no. of wins: 0.623131 p-value for throws/game: 0.126753 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-10-26_03:31 No. of wins: Observed Expected 98707 98585.9 z-score= 0.542, pvalue=0.70603 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66674 66666.7 0.001 0.001 2 37709 37654.3 0.079 0.080 3 26916 26954.7 0.056 0.136 4 19123 19313.5 1.878 2.014 5 13807 13851.4 0.142 2.157 6 9998 9943.5 0.298 2.455 7 7221 7145.0 0.808 3.263 8 5130 5139.1 0.016 3.279 9 3717 3699.9 0.079 3.358 10 2679 2666.3 0.061 3.419 11 1979 1923.3 1.611 5.030 12 1402 1388.7 0.127 5.157 13 939 1003.7 4.173 9.329 14 775 726.1 3.288 12.617 15 551 525.8 1.204 13.821 16 367 381.2 0.525 14.346 17 262 276.5 0.764 15.111 18 194 200.8 0.232 15.343 19 159 146.0 1.160 16.503 20 76 106.2 8.595 25.099 21 322 287.1 4.239 29.338 Chisq= 29.34 for 20 degrees of freedom, p= 0.91868 SUMMARY of craptest p-value for no. of wins: 0.706027 p-value for throws/game: 0.918679 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0036,0.0036,0.0052,0.0069,0.0083,0.0105,0.0122,0.0190,0.0194,0.0234, 0.0298,0.0319,0.0367,0.0469,0.0476,0.0508,0.0568,0.0606,0.0621,0.0653, 0.0661,0.0678,0.0704,0.0775,0.0786,0.0788,0.0814,0.0825,0.0890,0.0948, 0.1002,0.1016,0.1083,0.1088,0.1109,0.1192,0.1195,0.1206,0.1216,0.1221, 0.1268,0.1293,0.1294,0.1300,0.1311,0.1337,0.1402,0.1437,0.1441,0.1605, 0.1624,0.1649,0.1678,0.1724,0.1788,0.1867,0.1909,0.1992,0.2023,0.2050, 0.2057,0.2095,0.2185,0.2185,0.2188,0.2233,0.2276,0.2278,0.2288,0.2296, 0.2305,0.2316,0.2358,0.2375,0.2402,0.2438,0.2440,0.2467,0.2472,0.2516, 0.2546,0.2611,0.2728,0.2733,0.2803,0.2822,0.2822,0.2899,0.2960,0.3016, 0.3077,0.3159,0.3169,0.3171,0.3215,0.3242,0.3245,0.3327,0.3328,0.3351, 0.3352,0.3362,0.3406,0.3424,0.3452,0.3493,0.3613,0.3680,0.3746,0.3781, 0.3791,0.3896,0.3977,0.4016,0.4024,0.4028,0.4029,0.4110,0.4190,0.4192, 0.4250,0.4270,0.4339,0.4393,0.4421,0.4442,0.4445,0.4531,0.4562,0.4562, 0.4568,0.4628,0.4636,0.4725,0.4760,0.4767,0.4796,0.4844,0.4861,0.4996, 0.5119,0.5142,0.5201,0.5227,0.5269,0.5325,0.5377,0.5386,0.5607,0.5615, 0.5631,0.5641,0.5753,0.5762,0.5791,0.5801,0.5830,0.5837,0.5849,0.5860, 0.5866,0.5910,0.5927,0.5958,0.5966,0.6043,0.6054,0.6059,0.6155,0.6189, 0.6231,0.6254,0.6306,0.6358,0.6398,0.6538,0.6555,0.6562,0.6601,0.6676, 0.6714,0.6717,0.6748,0.6825,0.6895,0.6911,0.6915,0.6917,0.6935,0.6974, 0.6995,0.7029,0.7060,0.7081,0.7091,0.7236,0.7312,0.7337,0.7362,0.7368, 0.7482,0.7521,0.7697,0.7711,0.7712,0.7789,0.7812,0.7877,0.7885,0.7904, 0.7908,0.7960,0.7994,0.8055,0.8056,0.8093,0.8105,0.8106,0.8116,0.8175, 0.8211,0.8212,0.8213,0.8229,0.8264,0.8288,0.8354,0.8421,0.8529,0.8557, 0.8567,0.8567,0.8626,0.8662,0.8682,0.8787,0.8789,0.8834,0.8854,0.8912, 0.8917,0.8991,0.9099,0.9110,0.9160,0.9187,0.9196,0.9215,0.9255,0.9287, 0.9292,0.9336,0.9344,0.9412,0.9439,0.9475,0.9500,0.9512,0.9597,0.9627, 0.9648,0.9682,0.9729,0.9737,0.9887,0.9898,0.9934,0.9946,0.9951, Overall p-value after applying KStest on 269 p-values = 0.628364 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.