RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-12-19_19:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.84 17.0006 0.545677 2 to 25 15.55 21.5788 0.798534 3 to 26 15.75 17.9456 0.607721 4 to 27 15.96 10.5506 0.121048 5 to 28 15.92 9.6476 0.082267 6 to 29 15.69 20.4945 0.750280 7 to 30 15.59 21.9918 0.814966 8 to 31 15.80 23.3374 0.861414 9 to 32 15.60 25.1918 0.909501 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.288094 Tough bday spacings test for dh-ranFile-2015-12-19_19:31: 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 12 37 76 81 104 75 43 34 21 11 6 (O-E)^2/E 0.9 0.0 0.1 2.8 0.4 0.1 1.6 0.6 2.5 2.9 0.9 Birthday Spacings: Sum(O-E)^2/E= 12.900, p= 0.771 RESULTS OF GCD FOR dh-ranFile-2015-12-19_19:31 Euclid's algorithm: p-value, steps to gcd: 0.642129 p-value, dist. of gcd's: 0.270223 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-12-19_19:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.591 0.146 0.786 0.514 0.332 0.897 0.363 0.592 Bits 8 to 15---> 0.978 0.416 0.023 0.309 0.350 0.780 0.310 0.482 Bits 16 to 23---> 0.603 0.738 0.452 0.494 0.252 0.695 0.020 0.256 Bits 24 to 31---> 0.880 0.823 0.504 0.087 0.657 0.444 0.197 0.845 KS test for the above 32 p values: 0.119 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-12-19_19:31, p-values for 5 runs: 0.5127, 0.1400, 0.8471, 0.7788, 0.2955 Rank test for binary matrices (31x31) for dh-ranFile-2015-12-19_19:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 188 211.4 2.594 2.594 r= 29 5079 5134.0 0.589 3.183 r= 30 23109 23103.0 0.002 3.185 r= 31 11624 11551.5 0.455 3.640 chi-square = 3.640 with df = 3; p-value = 0.697 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-12-19_19:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 175 211.4 6.273 6.273 r= 30 5054 5134.0 1.247 7.520 r= 31 23013 23103.0 0.351 7.871 r= 32 11758 11551.5 3.691 11.562 chi-square = 11.562 with df = 3; p-value = 0.991 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-12-19_19:31 b-rank test for bits 1 to 8, p=0.79022 b-rank test for bits 2 to 9, p=0.17613 b-rank test for bits 3 to 10, p=0.52599 b-rank test for bits 4 to 11, p=0.21514 b-rank test for bits 5 to 12, p=0.07754 b-rank test for bits 6 to 13, p=0.80684 b-rank test for bits 7 to 14, p=0.62678 b-rank test for bits 8 to 15, p=0.17518 b-rank test for bits 9 to 16, p=0.27098 b-rank test for bits 10 to 17, p=0.72138 b-rank test for bits 11 to 18, p=0.43642 b-rank test for bits 12 to 19, p=0.43416 b-rank test for bits 13 to 20, p=0.47400 b-rank test for bits 14 to 21, p=0.85271 b-rank test for bits 15 to 22, p=0.58747 b-rank test for bits 16 to 23, p=0.10355 b-rank test for bits 17 to 24, p=0.78634 b-rank test for bits 18 to 25, p=0.78687 b-rank test for bits 19 to 26, p=0.15920 b-rank test for bits 20 to 27, p=0.59296 b-rank test for bits 21 to 28, p=0.48201 b-rank test for bits 22 to 29, p=0.69924 b-rank test for bits 23 to 30, p=0.65927 b-rank test for bits 24 to 31, p=0.29965 b-rank test for bits 25 to 32, p=0.28121 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 = 0.559484 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-12-19_19:31 (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 141368 -1.26 0.102973 2 142904 2.32 0.989937 3 142043 0.31 0.622599 4 141329 -1.36 0.087564 5 141834 -0.18 0.430145 6 141588 -0.75 0.226395 7 142525 1.44 0.924851 8 142175 0.62 0.732610 9 141802 -0.25 0.400996 10 141574 -0.78 0.216672 11 142152 0.57 0.714638 12 142034 0.29 0.614583 13 141600 -0.72 0.234922 14 142213 0.71 0.760996 15 142126 0.51 0.693655 16 141843 -0.15 0.438420 17 142463 1.29 0.902102 18 141736 -0.40 0.342747 19 142561 1.52 0.936070 20 141517 -0.92 0.179661 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-12-19_19:31 Bits used No. missing words z-score p-value 23 to 32 141428 -1.6598 0.048482 22 to 31 141800 -0.3770 0.353087 21 to 30 140972 -3.2322 0.000614 20 to 29 141265 -2.2218 0.013147 19 to 28 141718 -0.6598 0.254704 18 to 27 142048 0.4782 0.683736 17 to 26 141935 0.0885 0.535267 16 to 25 141903 -0.0218 0.491293 15 to 24 141397 -1.7667 0.038643 14 to 23 141894 -0.0529 0.478921 13 to 22 141858 -0.1770 0.429754 12 to 21 141854 -0.1908 0.424344 11 to 20 141749 -0.5529 0.290179 10 to 19 142227 1.0954 0.863332 9 to 18 141765 -0.4977 0.309351 8 to 17 141965 0.1920 0.576115 7 to 16 142105 0.6747 0.750075 6 to 15 141627 -0.9736 0.165140 5 to 14 142404 1.7058 0.955973 4 to 13 141767 -0.4908 0.311786 3 to 12 142170 0.8989 0.815637 2 to 11 141787 -0.4218 0.336575 1 to 10 141654 -0.8804 0.189308 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-12-19_19:31 Bits used No. missing words z-score p-value 28 to 32 142479 1.9311 0.973264 27 to 31 142041 0.4463 0.672324 26 to 30 142036 0.4294 0.666180 25 to 29 142048 0.4701 0.680847 24 to 28 141957 0.1616 0.564187 23 to 27 142330 1.4260 0.923066 22 to 26 141525 -1.3028 0.096319 21 to 25 141771 -0.4689 0.319565 20 to 24 141471 -1.4859 0.068658 19 to 23 141652 -0.8723 0.191521 18 to 22 142193 0.9616 0.831873 17 to 21 142479 1.9311 0.973264 16 to 20 142008 0.3345 0.630989 15 to 19 142556 2.1921 0.985814 14 to 18 141668 -0.8181 0.206659 13 to 17 142206 1.0057 0.842711 12 to 16 141482 -1.4486 0.073728 11 to 15 141496 -1.4011 0.080589 10 to 14 141853 -0.1909 0.424283 9 to 13 141851 -0.1977 0.421629 8 to 12 141801 -0.3672 0.356727 7 to 11 141714 -0.6621 0.253942 6 to 10 141784 -0.4248 0.335474 5 to 9 141396 -1.7401 0.040921 4 to 8 141824 -0.2893 0.386193 3 to 7 141935 0.0870 0.534671 2 to 6 141916 0.0226 0.509019 1 to 5 141585 -1.0994 0.135792 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-12-19_19:31 Bits used No. missing words z-score p-value 31 to 32 142364 1.3412 0.910074 30 to 31 141621 -0.8505 0.197515 29 to 30 141787 -0.3609 0.359104 28 to 29 141018 -2.6293 0.004278 27 to 28 141760 -0.4405 0.329787 26 to 27 142548 1.8840 0.970216 25 to 26 141951 0.1229 0.548915 24 to 25 142005 0.2822 0.611110 23 to 24 141831 -0.2311 0.408633 22 to 23 142125 0.6362 0.737675 21 to 22 141757 -0.4494 0.326589 20 to 21 141734 -0.5172 0.302509 19 to 20 142079 0.5005 0.691639 18 to 19 141869 -0.1190 0.452651 17 to 18 141751 -0.4671 0.320232 16 to 17 141637 -0.8033 0.210891 15 to 16 141425 -1.4287 0.076545 14 to 15 141349 -1.6529 0.049177 13 to 14 142257 1.0256 0.847454 12 to 13 141081 -2.4435 0.007274 11 to 12 141220 -2.0334 0.021005 10 to 11 142084 0.5153 0.696811 9 to 10 141386 -1.5437 0.061325 8 to 9 141760 -0.4405 0.329787 7 to 8 141872 -0.1101 0.456158 6 to 7 141777 -0.3904 0.348137 5 to 6 142224 0.9282 0.823356 4 to 5 141652 -0.7591 0.223901 3 to 4 141738 -0.5054 0.306640 2 to 3 141810 -0.2930 0.384758 1 to 2 140962 -2.7945 0.002599 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-12-19_19:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2604.36 1.476 0.930018 Test results for specific bytes for dh-ranFile-2015-12-19_19:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2458.67 -0.585 0.279432 2 to 9 2445.12 -0.776 0.218837 3 to 10 2491.72 -0.117 0.453398 4 to 11 2488.38 -0.164 0.434709 5 to 12 2451.69 -0.683 0.247241 6 to 13 2541.31 0.584 0.720438 7 to 14 2455.01 -0.636 0.262302 8 to 15 2465.82 -0.483 0.314433 9 to 16 2330.37 -2.399 0.008220 10 to 17 2512.19 0.172 0.568434 11 to 18 2482.96 -0.241 0.404789 12 to 19 2463.04 -0.523 0.300616 13 to 20 2467.13 -0.465 0.321042 14 to 21 2390.04 -1.555 0.059962 15 to 22 2506.56 0.093 0.536980 16 to 23 2624.45 1.760 0.960791 17 to 24 2502.59 0.037 0.514608 18 to 25 2580.10 1.133 0.871346 19 to 26 2469.69 -0.429 0.334099 20 to 27 2561.88 0.875 0.809263 21 to 28 2472.38 -0.391 0.348053 22 to 29 2511.28 0.159 0.563359 23 to 30 2416.85 -1.176 0.119806 24 to 31 2463.71 -0.513 0.303892 25 to 32 2463.40 -0.518 0.302359 CDPARK for dh-ranFile-2015-12-19_19:31: 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 3534 0.5023 0.692266 3533 0.4566 0.676028 3523 0.0000 0.500000 3506 -0.7763 0.218799 3550 1.2329 0.891189 3585 2.8311 0.997680 3530 0.3196 0.625377 3518 -0.2283 0.409702 3547 1.0959 0.863437 3500 -1.0502 0.146807 Square side=100, avg. no. parked=3532.60 sample std.=23.11 p-value of the KSTEST for those 10 p-values: 0.395502 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-12-19_19:31 0.0886,0.9232,0.0393,0.8726,0.2803,0.3162,0.2177,0.2247,0.6020,0.3673, The KS test for those 10 p-values: 0.352533 The 3DSPHERES test for dh-ranFile-2015-12-19_19:31 sample no r^3 equiv. uni. 1 15.063 0.394743 2 36.993 0.708615 3 108.832 0.973424 4 28.976 0.619342 5 16.062 0.414573 6 3.507 0.110327 7 16.635 0.425635 8 21.013 0.503628 9 11.119 0.309713 10 27.674 0.602462 11 7.571 0.223034 12 81.332 0.933533 13 100.722 0.965174 14 24.323 0.555481 15 49.116 0.805473 16 9.415 0.269358 17 41.903 0.752607 18 10.525 0.295902 19 101.335 0.965878 20 1.923 0.062078 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.642355 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-12-19_19:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 1.3 0.5 0.6 0.8 0.8 -1.7 0.6 0.2 1.1 0.8 -1.0 -0.8 -0.6 0.7 -1.3 0.3 0.1 -2.0 0.5 2.3 0.0 1.8 -0.8 -0.1 0.2 0.8 -1.3 -0.8 -0.8 -0.9 -0.0 0.6 -0.6 -0.6 1.6 0.1 1.0 1.1 0.1 1.5 0.9 3.0 -0.1 Chi-square with 42 degrees of freedom:48.585210 z-score=0.718505, p-value=0.775167 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-12-19_19:31 Test no p-value 1 0.452276 2 0.336007 3 0.741026 4 0.758388 5 0.968279 6 0.012682 7 0.000197 8 0.853191 9 0.261238 10 0.655849 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.300288 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-12-19_19:31: (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 66587 0.10 66489 0.47 3 25000.00 25077 0.24 25221 1.95 4 6666.67 6661 0.00 6673 0.01 5 1388.89 1399 0.07 1379 0.07 6 238.10 225 0.72 210 3.32 7 34.72 43 1.97 23 3.96 8 4.96 7 0.84 4 0.19 p=0.31583 p=0.87369 Number of rngs required: 689635, p-value: 0.925 RESULTS OF CRAPS TEST for dh-ranFile-2015-12-19_19:31 No. of wins: Observed Expected 98633 98585.9 z-score= 0.211, pvalue=0.58350 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66950 66666.7 1.204 1.204 2 37634 37654.3 0.011 1.215 3 26747 26954.7 1.601 2.816 4 19311 19313.5 0.000 2.816 5 13908 13851.4 0.231 3.047 6 10073 9943.5 1.685 4.733 7 7043 7145.0 1.457 6.190 8 5071 5139.1 0.902 7.091 9 3717 3699.9 0.079 7.171 10 2639 2666.3 0.279 7.450 11 1877 1923.3 1.116 8.566 12 1457 1388.7 3.355 11.921 13 1010 1003.7 0.039 11.961 14 711 726.1 0.316 12.276 15 495 525.8 1.808 14.085 16 371 381.2 0.270 14.355 17 255 276.5 1.678 16.033 18 201 200.8 0.000 16.033 19 154 146.0 0.440 16.473 20 104 106.2 0.046 16.519 21 272 287.1 0.796 17.315 Chisq= 17.31 for 20 degrees of freedom, p= 0.36755 SUMMARY of craptest p-value for no. of wins: 0.583495 p-value for throws/game: 0.367551 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-12-19_19:31 No. of wins: Observed Expected 98434 98585.9 z-score=-0.679, pvalue=0.24851 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66909 66666.7 0.881 0.881 2 37775 37654.3 0.387 1.268 3 26703 26954.7 2.351 3.619 4 19210 19313.5 0.554 4.173 5 13832 13851.4 0.027 4.200 6 9964 9943.5 0.042 4.242 7 7090 7145.0 0.424 4.666 8 5245 5139.1 2.183 6.849 9 3641 3699.9 0.937 7.786 10 2703 2666.3 0.505 8.291 11 1907 1923.3 0.139 8.430 12 1349 1388.7 1.137 9.567 13 1039 1003.7 1.240 10.807 14 775 726.1 3.288 14.095 15 529 525.8 0.019 14.114 16 385 381.2 0.039 14.153 17 257 276.5 1.381 15.533 18 182 200.8 1.765 17.299 19 145 146.0 0.007 17.306 20 91 106.2 2.180 19.485 21 269 287.1 1.143 20.628 Chisq= 20.63 for 20 degrees of freedom, p= 0.58069 SUMMARY of craptest p-value for no. of wins: 0.248506 p-value for throws/game: 0.580687 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0002,0.0006,0.0026,0.0043,0.0073,0.0082,0.0127,0.0131,0.0198,0.0210, 0.0233,0.0386,0.0393,0.0409,0.0485,0.0492,0.0600,0.0613,0.0621,0.0687, 0.0737,0.0765,0.0775,0.0806,0.0823,0.0870,0.0876,0.0886,0.0963,0.1030, 0.1035,0.1103,0.1193,0.1198,0.1210,0.1358,0.1400,0.1455,0.1468,0.1592, 0.1651,0.1752,0.1761,0.1797,0.1893,0.1915,0.1966,0.1975,0.2067,0.2109, 0.2151,0.2167,0.2177,0.2188,0.2188,0.2230,0.2239,0.2247,0.2264,0.2349, 0.2472,0.2485,0.2515,0.2539,0.2547,0.2557,0.2612,0.2623,0.2694,0.2702, 0.2710,0.2794,0.2803,0.2812,0.2881,0.2902,0.2955,0.2959,0.2997,0.3003, 0.3006,0.3024,0.3025,0.3039,0.3066,0.3094,0.3095,0.3097,0.3104,0.3118, 0.3144,0.3158,0.3162,0.3196,0.3202,0.3210,0.3266,0.3298,0.3298,0.3325, 0.3341,0.3355,0.3360,0.3366,0.3427,0.3481,0.3481,0.3503,0.3525,0.3531, 0.3567,0.3591,0.3634,0.3673,0.3676,0.3848,0.3862,0.3947,0.3955,0.4010, 0.4048,0.4086,0.4097,0.4146,0.4157,0.4216,0.4243,0.4243,0.4256,0.4298, 0.4301,0.4342,0.4347,0.4364,0.4384,0.4439,0.4517,0.4523,0.4527,0.4534, 0.4562,0.4740,0.4789,0.4820,0.4825,0.4913,0.4943,0.5000,0.5036,0.5043, 0.5090,0.5127,0.5139,0.5146,0.5260,0.5347,0.5353,0.5370,0.5457,0.5489, 0.5555,0.5595,0.5634,0.5642,0.5684,0.5761,0.5807,0.5835,0.5875,0.5907, 0.5922,0.5930,0.6020,0.6025,0.6030,0.6077,0.6111,0.6146,0.6193,0.6226, 0.6254,0.6268,0.6310,0.6421,0.6424,0.6558,0.6574,0.6593,0.6662,0.6723, 0.6760,0.6808,0.6837,0.6916,0.6923,0.6937,0.6947,0.6968,0.6969,0.6992, 0.7086,0.7146,0.7204,0.7214,0.7326,0.7377,0.7383,0.7410,0.7501,0.7503, 0.7526,0.7584,0.7610,0.7707,0.7752,0.7788,0.7801,0.7860,0.7863,0.7869, 0.7902,0.7985,0.8055,0.8068,0.8093,0.8150,0.8156,0.8225,0.8234,0.8319, 0.8427,0.8453,0.8471,0.8475,0.8527,0.8532,0.8614,0.8633,0.8634,0.8713, 0.8726,0.8737,0.8802,0.8912,0.8972,0.9021,0.9095,0.9101,0.9231,0.9232, 0.9247,0.9249,0.9300,0.9335,0.9361,0.9560,0.9608,0.9652,0.9659,0.9683, 0.9702,0.9733,0.9733,0.9734,0.9782,0.9858,0.9899,0.9910,0.9977, Overall p-value after applying KStest on 269 p-values = 0.211394 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.