RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-07-06_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 15.58 15.9328 0.471396 2 to 25 15.51 22.8400 0.845468 3 to 26 15.83 12.4155 0.225650 4 to 27 15.76 12.9570 0.260940 5 to 28 15.74 17.1606 0.556460 6 to 29 15.46 18.6061 0.648396 7 to 30 15.41 34.8907 0.993570 8 to 31 15.77 12.8429 0.253363 9 to 32 15.88 23.7720 0.874237 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.602040 Tough bday spacings test for dh-ranFile-2015-07-06_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 11 37 76 90 94 94 50 23 12 10 3 (O-E)^2/E 0.4 0.0 0.1 0.6 0.1 3.2 0.1 1.5 0.6 1.7 0.3 Birthday Spacings: Sum(O-E)^2/E= 8.630, p= 0.432 RESULTS OF GCD FOR dh-ranFile-2015-07-06_03:31 Euclid's algorithm: p-value, steps to gcd: 0.714282 p-value, dist. of gcd's: 0.773278 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-07-06_03:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.556 0.172 0.678 0.796 0.666 0.806 0.966 0.794 Bits 8 to 15---> 0.461 0.390 0.530 0.962 0.491 0.274 0.427 0.779 Bits 16 to 23---> 0.613 0.180 0.915 0.351 0.873 0.981 0.595 0.341 Bits 24 to 31---> 0.295 0.771 0.703 0.405 0.602 0.471 0.877 0.344 KS test for the above 32 p values: 0.931 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-07-06_03:31, p-values for 5 runs: 0.2139, 0.1710, 0.4240, 0.4502, 0.3674 Rank test for binary matrices (31x31) for dh-ranFile-2015-07-06_03:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 197 211.4 0.983 0.983 r= 29 5116 5134.0 0.063 1.046 r= 30 23175 23103.0 0.224 1.271 r= 31 11512 11551.5 0.135 1.406 chi-square = 1.406 with df = 3; p-value = 0.296 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-07-06_03:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 214 211.4 0.032 0.032 r= 30 5174 5134.0 0.311 0.343 r= 31 23028 23103.0 0.244 0.587 r= 32 11584 11551.5 0.091 0.678 chi-square = 0.678 with df = 3; p-value = 0.122 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-07-06_03:31 b-rank test for bits 1 to 8, p=0.21155 b-rank test for bits 2 to 9, p=0.05656 b-rank test for bits 3 to 10, p=0.68940 b-rank test for bits 4 to 11, p=0.45135 b-rank test for bits 5 to 12, p=0.28109 b-rank test for bits 6 to 13, p=0.87332 b-rank test for bits 7 to 14, p=0.97591 b-rank test for bits 8 to 15, p=0.72754 b-rank test for bits 9 to 16, p=0.09487 b-rank test for bits 10 to 17, p=0.05744 b-rank test for bits 11 to 18, p=0.72943 b-rank test for bits 12 to 19, p=0.02402 b-rank test for bits 13 to 20, p=0.25881 b-rank test for bits 14 to 21, p=0.85403 b-rank test for bits 15 to 22, p=0.67299 b-rank test for bits 16 to 23, p=0.80744 b-rank test for bits 17 to 24, p=0.72833 b-rank test for bits 18 to 25, p=0.13215 b-rank test for bits 19 to 26, p=0.61644 b-rank test for bits 20 to 27, p=0.88425 b-rank test for bits 21 to 28, p=0.83088 b-rank test for bits 22 to 29, p=0.07123 b-rank test for bits 23 to 30, p=0.66037 b-rank test for bits 24 to 31, p=0.09265 b-rank test for bits 25 to 32, p=0.60353 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 = 0.407276 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-07-06_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 141767 -0.33 0.369738 2 141623 -0.67 0.251749 3 141995 0.20 0.579324 4 142429 1.21 0.887661 5 142351 1.03 0.848950 6 142136 0.53 0.701806 7 141714 -0.46 0.324059 8 141241 -1.56 0.059201 9 142343 1.01 0.844529 10 142382 1.10 0.865284 11 141505 -0.94 0.172407 12 141361 -1.28 0.100071 13 142300 0.91 0.819321 14 141911 0.00 0.501557 15 141714 -0.46 0.324059 16 141460 -1.05 0.146897 17 142567 1.54 0.937806 18 141984 0.17 0.569249 19 142446 1.25 0.895061 20 142489 1.35 0.912191 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-07-06_03:31 Bits used No. missing words z-score p-value 23 to 32 141867 -0.1460 0.441974 22 to 31 141501 -1.4080 0.079560 21 to 30 142041 0.4540 0.675098 20 to 29 141953 0.1506 0.559849 19 to 28 142009 0.3437 0.634460 18 to 27 141441 -1.6149 0.053163 17 to 26 141462 -1.5425 0.061474 16 to 25 141708 -0.6942 0.243765 15 to 24 141863 -0.1598 0.436536 14 to 23 141745 -0.5667 0.285474 13 to 22 141845 -0.2218 0.412224 12 to 21 141830 -0.2736 0.392215 11 to 20 142068 0.5471 0.707858 10 to 19 141768 -0.4873 0.313007 9 to 18 141911 0.0058 0.502297 8 to 17 141935 0.0885 0.535267 7 to 16 142119 0.7230 0.765160 6 to 15 142288 1.3058 0.904183 5 to 14 141841 -0.2356 0.406864 4 to 13 141997 0.3023 0.618792 3 to 12 141935 0.0885 0.535267 2 to 11 141777 -0.4563 0.324083 1 to 10 141130 -2.6873 0.003601 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-07-06_03:31 Bits used No. missing words z-score p-value 28 to 32 142287 1.2802 0.899769 27 to 31 142343 1.4701 0.929228 26 to 30 141534 -1.2723 0.101632 25 to 29 141851 -0.1977 0.421629 24 to 28 142506 2.0226 0.978443 23 to 27 141836 -0.2486 0.401844 22 to 26 141811 -0.3333 0.369446 21 to 25 142074 0.5582 0.711647 20 to 24 142082 0.5853 0.720834 19 to 23 141836 -0.2486 0.401844 18 to 22 142209 1.0158 0.845145 17 to 21 142032 0.4158 0.661233 16 to 20 141542 -1.2452 0.106532 15 to 19 141809 -0.3401 0.366890 14 to 18 141600 -1.0486 0.147187 13 to 17 142056 0.4972 0.690471 12 to 16 141827 -0.2791 0.390090 11 to 15 141960 0.1718 0.568188 10 to 14 141836 -0.2486 0.401844 9 to 13 141756 -0.5198 0.301615 8 to 12 142014 0.3548 0.638635 7 to 11 141868 -0.1401 0.444290 6 to 10 141845 -0.2181 0.413688 5 to 9 142013 0.3514 0.637365 4 to 8 142533 2.1141 0.982748 3 to 7 141591 -1.0791 0.140275 2 to 6 142169 0.8802 0.810635 1 to 5 141590 -1.0825 0.139521 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-07-06_03:31 Bits used No. missing words z-score p-value 31 to 32 141907 -0.0069 0.497258 30 to 31 142059 0.4415 0.670576 29 to 30 141622 -0.8476 0.198336 28 to 29 141908 -0.0039 0.498435 27 to 28 141656 -0.7473 0.227445 26 to 27 141814 -0.2812 0.389275 25 to 26 140743 -3.4405 0.000290 24 to 25 142277 1.0846 0.860944 23 to 24 141573 -0.9921 0.160569 22 to 23 141933 0.0698 0.527833 21 to 22 142386 1.4061 0.920154 20 to 21 142023 0.3353 0.631304 19 to 20 141673 -0.6971 0.242858 18 to 19 141510 -1.1780 0.119405 17 to 18 141523 -1.1396 0.127223 16 to 17 141779 -0.3845 0.350321 15 to 16 142367 1.3501 0.911501 14 to 15 142288 1.1170 0.868007 13 to 14 142319 1.2085 0.886566 12 to 13 141477 -1.2753 0.101100 11 to 12 142065 0.4592 0.676956 10 to 11 142340 1.2704 0.898031 9 to 10 142147 0.7011 0.758377 8 to 9 142529 1.8279 0.966220 7 to 8 141614 -0.8712 0.191828 6 to 7 142145 0.6952 0.756532 5 to 6 141445 -1.3697 0.085390 4 to 5 141252 -1.9390 0.026249 3 to 4 142184 0.8102 0.791098 2 to 3 142145 0.6952 0.756532 1 to 2 141585 -0.9567 0.169353 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-07-06_03:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2433.44 -0.941 0.173259 Test results for specific bytes for dh-ranFile-2015-07-06_03:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2487.85 -0.172 0.431775 2 to 9 2460.06 -0.565 0.286087 3 to 10 2518.96 0.268 0.605707 4 to 11 2471.89 -0.398 0.345463 5 to 12 2487.89 -0.171 0.432030 6 to 13 2436.34 -0.900 0.183999 7 to 14 2510.67 0.151 0.559974 8 to 15 2454.03 -0.650 0.257800 9 to 16 2479.30 -0.293 0.384856 10 to 17 2448.50 -0.728 0.233230 11 to 18 2385.60 -1.618 0.052851 12 to 19 2434.68 -0.924 0.177809 13 to 20 2521.23 0.300 0.617982 14 to 21 2467.67 -0.457 0.323783 15 to 22 2446.90 -0.751 0.226354 16 to 23 2468.83 -0.441 0.329658 17 to 24 2535.13 0.497 0.690361 18 to 25 2329.72 -2.408 0.008017 19 to 26 2432.24 -0.958 0.168960 20 to 27 2456.63 -0.613 0.269839 21 to 28 2487.49 -0.177 0.429808 22 to 29 2482.97 -0.241 0.404834 23 to 30 2357.70 -2.012 0.022085 24 to 31 2486.24 -0.195 0.422829 25 to 32 2561.82 0.874 0.809022 CDPARK for dh-ranFile-2015-07-06_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 3526 0.1370 0.554479 3557 1.5525 0.939730 3493 -1.3699 0.085365 3529 0.2740 0.607947 3491 -1.4612 0.071982 3494 -1.3242 0.092718 3513 -0.4566 0.323972 3569 2.1005 0.982156 3536 0.5936 0.723613 3546 1.0502 0.853193 Square side=100, avg. no. parked=3525.40 sample std.=26.12 p-value of the KSTEST for those 10 p-values: 0.609464 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-07-06_03:31 0.1820,0.1958,0.3797,0.2217,0.8332,0.4499,0.9576,0.8107,0.0582,0.8030, The KS test for those 10 p-values: 0.846764 The 3DSPHERES test for dh-ranFile-2015-07-06_03:31 sample no r^3 equiv. uni. 1 16.250 0.418215 2 21.636 0.513836 3 63.204 0.878375 4 96.160 0.959454 5 25.596 0.573949 6 57.785 0.854296 7 12.366 0.337803 8 0.742 0.024433 9 14.648 0.386318 10 9.721 0.276767 11 42.920 0.760854 12 56.040 0.845570 13 0.201 0.006687 14 30.092 0.633247 15 54.964 0.839929 16 19.084 0.470659 17 52.749 0.827665 18 32.025 0.656131 19 11.356 0.315127 20 28.872 0.618020 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.437714 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-07-06_03:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 1.3 0.1 -0.1 0.2 0.0 -1.7 2.5 0.4 -1.5 0.4 -0.4 1.0 -0.2 0.5 0.2 -3.2 -0.9 0.9 0.8 -0.5 -0.8 1.2 0.5 0.3 -1.2 2.0 0.3 1.1 -1.1 0.4 0.7 0.3 0.8 0.1 0.6 0.4 -0.9 0.5 3.0 0.4 -1.3 -1.0 -1.1 Chi-square with 42 degrees of freedom:54.043058 z-score=1.314005, p-value=0.899235 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-07-06_03:31 Test no p-value 1 0.160204 2 0.716261 3 0.888321 4 0.940230 5 0.312651 6 0.711474 7 0.123910 8 0.000750 9 0.004397 10 0.173838 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.070650 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-07-06_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 66511 0.36 66526 0.30 3 25000.00 25194 1.51 25149 0.89 4 6666.67 6626 0.25 6690 0.08 5 1388.89 1386 0.01 1353 0.93 6 238.10 245 0.20 242 0.06 7 34.72 32 0.21 33 0.09 8 4.96 5 0.00 6 0.22 p=0.13566 p=0.13845 Number of rngs required: 688561, p-value: 0.572 RESULTS OF CRAPS TEST for dh-ranFile-2015-07-06_03:31 No. of wins: Observed Expected 98618 98585.9 z-score= 0.144, pvalue=0.55715 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66557 66666.7 0.180 0.180 2 37632 37654.3 0.013 0.194 3 27138 26954.7 1.246 1.440 4 19359 19313.5 0.107 1.547 5 13851 13851.4 0.000 1.547 6 9927 9943.5 0.028 1.575 7 7158 7145.0 0.024 1.598 8 5040 5139.1 1.910 3.508 9 3714 3699.9 0.054 3.562 10 2737 2666.3 1.875 5.437 11 1922 1923.3 0.001 5.438 12 1362 1388.7 0.515 5.953 13 1019 1003.7 0.233 6.185 14 702 726.1 0.803 6.988 15 539 525.8 0.330 7.318 16 337 381.2 5.114 12.432 17 298 276.5 1.665 14.097 18 208 200.8 0.256 14.353 19 143 146.0 0.061 14.414 20 120 106.2 1.789 16.203 21 237 287.1 8.747 24.950 Chisq= 24.95 for 20 degrees of freedom, p= 0.79666 SUMMARY of craptest p-value for no. of wins: 0.557153 p-value for throws/game: 0.796662 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-07-06_03:31 No. of wins: Observed Expected 98412 98585.9 z-score=-0.778, pvalue=0.21840 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66984 66666.7 1.511 1.511 2 37400 37654.3 1.718 3.228 3 26911 26954.7 0.071 3.299 4 19354 19313.5 0.085 3.384 5 13599 13851.4 4.600 7.984 6 9993 9943.5 0.246 8.230 7 7083 7145.0 0.538 8.769 8 5230 5139.1 1.609 10.377 9 3721 3699.9 0.121 10.498 10 2678 2666.3 0.051 10.550 11 1981 1923.3 1.729 12.279 12 1408 1388.7 0.267 12.546 13 986 1003.7 0.313 12.859 14 720 726.1 0.052 12.911 15 532 525.8 0.072 12.983 16 373 381.2 0.174 13.157 17 302 276.5 2.344 15.501 18 192 200.8 0.388 15.889 19 113 146.0 7.453 23.342 20 99 106.2 0.490 23.832 21 341 287.1 10.113 33.946 Chisq= 33.95 for 20 degrees of freedom, p= 0.97350 SUMMARY of craptest p-value for no. of wins: 0.218403 p-value for throws/game: 0.973505 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0003,0.0007,0.0036,0.0044,0.0067,0.0080,0.0221,0.0240,0.0244,0.0262, 0.0529,0.0532,0.0566,0.0574,0.0582,0.0592,0.0615,0.0706,0.0712,0.0720, 0.0796,0.0854,0.0854,0.0926,0.0927,0.0949,0.1001,0.1011,0.1016,0.1065, 0.1194,0.1217,0.1239,0.1272,0.1322,0.1357,0.1384,0.1395,0.1403,0.1469, 0.1472,0.1602,0.1606,0.1690,0.1694,0.1710,0.1724,0.1724,0.1733,0.1738, 0.1778,0.1804,0.1820,0.1840,0.1918,0.1958,0.1983,0.2116,0.2139,0.2184, 0.2217,0.2256,0.2264,0.2274,0.2332,0.2429,0.2438,0.2517,0.2534,0.2578, 0.2588,0.2609,0.2698,0.2738,0.2768,0.2811,0.2855,0.2861,0.2946,0.2958, 0.3016,0.3127,0.3130,0.3151,0.3238,0.3240,0.3241,0.3241,0.3241,0.3297, 0.3378,0.3405,0.3441,0.3455,0.3503,0.3505,0.3669,0.3674,0.3694,0.3697, 0.3797,0.3849,0.3863,0.3893,0.3898,0.3901,0.3922,0.4018,0.4018,0.4018, 0.4047,0.4048,0.4069,0.4073,0.4122,0.4137,0.4182,0.4216,0.4228,0.4240, 0.4267,0.4298,0.4318,0.4320,0.4325,0.4365,0.4377,0.4420,0.4443,0.4499, 0.4502,0.4513,0.4607,0.4706,0.4707,0.4714,0.4914,0.4973,0.4984,0.5016, 0.5023,0.5138,0.5278,0.5297,0.5353,0.5353,0.5545,0.5556,0.5565,0.5572, 0.5598,0.5600,0.5682,0.5692,0.5721,0.5739,0.5793,0.5951,0.6020,0.6023, 0.6035,0.6057,0.6079,0.6095,0.6134,0.6164,0.6180,0.6180,0.6188,0.6313, 0.6332,0.6345,0.6374,0.6386,0.6484,0.6561,0.6604,0.6612,0.6659,0.6706, 0.6730,0.6751,0.6770,0.6776,0.6894,0.6904,0.6905,0.7018,0.7030,0.7079, 0.7115,0.7116,0.7143,0.7163,0.7208,0.7236,0.7275,0.7283,0.7294,0.7565, 0.7565,0.7584,0.7609,0.7652,0.7714,0.7733,0.7789,0.7911,0.7935,0.7958, 0.7967,0.8030,0.8061,0.8074,0.8090,0.8106,0.8107,0.8193,0.8277,0.8309, 0.8332,0.8399,0.8445,0.8451,0.8455,0.8456,0.8468,0.8489,0.8532,0.8540, 0.8543,0.8609,0.8653,0.8680,0.8731,0.8733,0.8742,0.8768,0.8784,0.8843, 0.8866,0.8877,0.8883,0.8951,0.8980,0.8992,0.8998,0.9042,0.9115,0.9122, 0.9146,0.9202,0.9292,0.9306,0.9378,0.9397,0.9402,0.9576,0.9595,0.9620, 0.9657,0.9662,0.9735,0.9759,0.9784,0.9808,0.9822,0.9827,0.9936, Overall p-value after applying KStest on 269 p-values = 0.960048 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.