RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-07-23_14:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.87 17.0828 0.551228 2 to 25 15.88 28.2117 0.957476 3 to 26 16.03 7.5668 0.025046 4 to 27 15.71 17.8200 0.599718 5 to 28 15.87 15.5594 0.444743 6 to 29 15.74 32.3087 0.986228 7 to 30 15.49 16.6228 0.519809 8 to 31 15.84 22.1618 0.821423 9 to 32 15.54 24.1016 0.883300 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.158123 Tough bday spacings test for dh-ranFile-2015-07-23_14:31: 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 27 53 116 103 63 51 52 9 9 5 (O-E)^2/E 0.9 2.5 5.6 3.4 0.3 2.9 0.0 16.6 2.3 0.9 0.2 Birthday Spacings: Sum(O-E)^2/E= 35.701, p= 1.000 RESULTS OF GCD FOR dh-ranFile-2015-07-23_14:31 Euclid's algorithm: p-value, steps to gcd: 0.970275 p-value, dist. of gcd's: 0.478053 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-07-23_14:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.591 0.201 0.349 0.729 0.128 0.441 0.606 0.483 Bits 8 to 15---> 0.826 0.939 0.161 0.529 0.398 0.358 0.424 0.833 Bits 16 to 23---> 0.140 0.193 0.985 0.180 0.499 0.616 0.464 0.840 Bits 24 to 31---> 0.046 0.692 0.899 0.316 0.924 0.451 0.406 0.420 KS test for the above 32 p values: 0.251 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-07-23_14:31, p-values for 5 runs: 0.4550, 0.1646, 0.5761, 0.0000, 0.3743 Rank test for binary matrices (31x31) for dh-ranFile-2015-07-23_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 233 211.4 2.203 2.203 r= 29 5087 5134.0 0.430 2.634 r= 30 23282 23103.0 1.386 4.020 r= 31 11398 11551.5 2.040 6.060 chi-square = 6.060 with df = 3; p-value = 0.891 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-07-23_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 255 211.4 8.984 8.984 r= 30 5149 5134.0 0.044 9.028 r= 31 23167 23103.0 0.177 9.205 r= 32 11429 11551.5 1.300 10.504 chi-square = 10.504 with df = 3; p-value = 0.985 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-07-23_14:31 b-rank test for bits 1 to 8, p=0.09367 b-rank test for bits 2 to 9, p=0.12368 b-rank test for bits 3 to 10, p=0.15712 b-rank test for bits 4 to 11, p=0.93084 b-rank test for bits 5 to 12, p=0.82144 b-rank test for bits 6 to 13, p=0.52464 b-rank test for bits 7 to 14, p=0.59898 b-rank test for bits 8 to 15, p=0.63748 b-rank test for bits 9 to 16, p=0.36437 b-rank test for bits 10 to 17, p=0.65184 b-rank test for bits 11 to 18, p=0.19894 b-rank test for bits 12 to 19, p=0.79930 b-rank test for bits 13 to 20, p=0.37647 b-rank test for bits 14 to 21, p=0.85639 b-rank test for bits 15 to 22, p=0.94844 b-rank test for bits 16 to 23, p=0.83667 b-rank test for bits 17 to 24, p=0.70649 b-rank test for bits 18 to 25, p=0.52971 b-rank test for bits 19 to 26, p=0.61584 b-rank test for bits 20 to 27, p=0.34086 b-rank test for bits 21 to 28, p=0.85021 b-rank test for bits 22 to 29, p=0.68815 b-rank test for bits 23 to 30, p=0.58987 b-rank test for bits 24 to 31, p=0.01366 b-rank test for bits 25 to 32, p=0.69871 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 = 0.441169 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-07-23_14:31 (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 141952 0.10 0.539707 2 142020 0.26 0.602018 3 142133 0.52 0.699371 4 141388 -1.22 0.111600 5 142048 0.32 0.627029 6 141452 -1.07 0.142641 7 141828 -0.19 0.424645 8 141918 0.02 0.508081 9 141792 -0.27 0.391990 10 142335 0.99 0.840024 11 142619 1.66 0.951352 12 141967 0.13 0.553593 13 141210 -1.63 0.051135 14 141551 -0.84 0.201235 15 141876 -0.08 0.468964 16 141077 -1.94 0.025906 17 141772 -0.32 0.374157 18 141483 -1.00 0.159601 19 141307 -1.41 0.079667 20 141555 -0.83 0.203871 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-07-23_14:31 Bits used No. missing words z-score p-value 23 to 32 142247 1.1644 0.877865 22 to 31 142064 0.5333 0.703103 21 to 30 141907 -0.0080 0.496795 20 to 29 142188 0.9609 0.831707 19 to 28 142011 0.3506 0.637051 18 to 27 141271 -2.2011 0.013863 17 to 26 141887 -0.0770 0.469312 16 to 25 142226 1.0920 0.862576 15 to 24 141804 -0.3632 0.358225 14 to 23 141981 0.2471 0.597599 13 to 22 142107 0.6816 0.752261 12 to 21 142081 0.5920 0.723063 11 to 20 142056 0.5058 0.693487 10 to 19 141876 -0.1149 0.454250 9 to 18 141808 -0.3494 0.363389 8 to 17 141739 -0.5873 0.278486 7 to 16 142044 0.4644 0.678812 6 to 15 142091 0.6264 0.734490 5 to 14 141909 -0.0011 0.499546 4 to 13 141836 -0.2529 0.400187 3 to 12 141943 0.1161 0.546215 2 to 11 141449 -1.5873 0.056217 1 to 10 141816 -0.3218 0.373792 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-07-23_14:31 Bits used No. missing words z-score p-value 28 to 32 142042 0.4497 0.673547 27 to 31 142240 1.1209 0.868838 26 to 30 141829 -0.2723 0.392694 25 to 29 142289 1.2870 0.900956 24 to 28 141553 -1.2079 0.113543 23 to 27 141968 0.1989 0.578822 22 to 26 142185 0.9345 0.824970 21 to 25 141760 -0.5062 0.306357 20 to 24 141967 0.1955 0.577496 19 to 23 142297 1.3141 0.905600 18 to 22 142047 0.4667 0.679635 17 to 21 142108 0.6735 0.749672 16 to 20 142426 1.7514 0.960064 15 to 19 141687 -0.7537 0.225526 14 to 18 141638 -0.9198 0.178848 13 to 17 141782 -0.4316 0.333006 12 to 16 142202 0.9921 0.839426 11 to 15 141821 -0.2994 0.382308 10 to 14 142020 0.3752 0.646227 9 to 13 141834 -0.2554 0.399224 8 to 12 142113 0.6904 0.755031 7 to 11 142613 2.3853 0.991468 6 to 10 142068 0.5379 0.704665 5 to 9 141847 -0.2113 0.416331 4 to 8 142053 0.4870 0.686877 3 to 7 141569 -1.1537 0.124320 2 to 6 141887 -0.0757 0.469831 1 to 5 142334 1.4396 0.925004 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-07-23_14:31 Bits used No. missing words z-score p-value 31 to 32 141549 -1.0629 0.143909 30 to 31 141115 -2.3432 0.009561 29 to 30 141863 -0.1367 0.445647 28 to 29 142163 0.7483 0.772857 27 to 28 142006 0.2852 0.612240 26 to 27 142274 1.0757 0.858974 25 to 26 141888 -0.0629 0.474915 24 to 25 142631 2.1288 0.983365 23 to 24 142549 1.8869 0.970415 22 to 23 141666 -0.7178 0.236444 21 to 22 142046 0.4032 0.656583 20 to 21 141718 -0.5644 0.286243 19 to 20 142166 0.7571 0.775517 18 to 19 141772 -0.4051 0.342701 17 to 18 142084 0.5153 0.696811 16 to 17 141532 -1.1131 0.132840 15 to 16 142245 0.9902 0.838956 14 to 15 141651 -0.7620 0.223019 13 to 14 141943 0.0993 0.539559 12 to 13 141717 -0.5673 0.285240 11 to 12 141721 -0.5555 0.289261 10 to 11 142274 1.0757 0.858974 9 to 10 142240 0.9754 0.835326 8 to 9 141917 0.0226 0.509025 7 to 8 141941 0.0934 0.537216 6 to 7 141753 -0.4612 0.322345 5 to 6 141491 -1.2340 0.108599 4 to 5 142252 1.0108 0.843950 3 to 4 142092 0.5388 0.705005 2 to 3 141928 0.0551 0.521960 1 to 2 141572 -0.9951 0.159850 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-07-23_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2421.03 -1.117 0.132035 Test results for specific bytes for dh-ranFile-2015-07-23_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2371.09 -1.823 0.034150 2 to 9 2326.59 -2.452 0.007095 3 to 10 2525.33 0.358 0.639923 4 to 11 2485.02 -0.212 0.416131 5 to 12 2548.83 0.691 0.755090 6 to 13 2459.89 -0.567 0.285268 7 to 14 2595.33 1.348 0.911199 8 to 15 2592.56 1.309 0.904742 9 to 16 2506.28 0.089 0.535361 10 to 17 2337.52 -2.298 0.010787 11 to 18 2419.24 -1.142 0.126690 12 to 19 2372.77 -1.799 0.035980 13 to 20 2456.49 -0.615 0.269187 14 to 21 2415.91 -1.189 0.117173 15 to 22 2562.82 0.888 0.812842 16 to 23 2518.64 0.264 0.603954 17 to 24 2582.97 1.173 0.879668 18 to 25 2488.76 -0.159 0.436848 19 to 26 2452.88 -0.666 0.252562 20 to 27 2516.45 0.233 0.591975 21 to 28 2470.81 -0.413 0.339881 22 to 29 2488.95 -0.156 0.437919 23 to 30 2471.91 -0.397 0.345614 24 to 31 2687.04 2.645 0.995917 25 to 32 2512.56 0.178 0.570512 CDPARK for dh-ranFile-2015-07-23_14:31: 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 3508 -0.6849 0.246694 3543 0.9132 0.819442 3551 1.2785 0.899470 3538 0.6849 0.753306 3518 -0.2283 0.409702 3534 0.5023 0.692266 3510 -0.5936 0.276387 3507 -0.7306 0.232514 3523 0.0000 0.500000 3495 -1.2785 0.100530 Square side=100, avg. no. parked=3522.70 sample std.=17.29 p-value of the KSTEST for those 10 p-values: 0.973417 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-07-23_14:31 0.9398,0.3628,0.0484,0.1826,0.5695,0.4017,0.9607,0.3547,0.7554,0.5839, The KS test for those 10 p-values: 0.958136 The 3DSPHERES test for dh-ranFile-2015-07-23_14:31 sample no r^3 equiv. uni. 1 3.704 0.116150 2 67.106 0.893208 3 131.569 0.987545 4 22.032 0.520201 5 33.216 0.669516 6 52.690 0.827322 7 15.155 0.396587 8 14.627 0.385873 9 5.347 0.163267 10 20.359 0.492698 11 23.738 0.546725 12 37.606 0.714510 13 31.792 0.653457 14 1.609 0.052216 15 8.183 0.238739 16 41.745 0.751298 17 16.274 0.418689 18 54.719 0.838618 19 16.206 0.417362 20 10.603 0.297729 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.958169 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-07-23_14:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 -0.7 1.5 1.2 0.1 0.8 -0.8 -0.0 -0.6 -0.3 -0.3 -0.4 0.0 0.3 -0.5 1.1 -1.4 -1.4 -0.5 1.1 0.8 0.4 1.3 1.0 0.1 -0.8 0.4 0.2 -1.8 -1.0 1.0 2.0 -0.5 0.0 -1.2 0.4 -1.2 -0.4 1.7 0.4 0.1 -1.0 -1.1 Chi-square with 42 degrees of freedom:37.911961 z-score=-0.446042, p-value=0.349019 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-07-23_14:31 Test no p-value 1 0.251494 2 0.600209 3 0.133971 4 0.181236 5 0.042024 6 0.736359 7 0.413204 8 0.091024 9 0.794995 10 0.180709 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.125718 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-07-23_14:31: (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 66665 0.00 66755 0.12 3 25000.00 24928 0.21 24863 0.75 4 6666.67 6760 1.31 6727 0.55 5 1388.89 1387 0.00 1354 0.88 6 238.10 213 2.65 260 2.02 7 34.72 41 1.14 36 0.05 8 4.96 5 0.00 4 0.19 p=0.49378 p=0.39578 Number of rngs required: 688704, p-value: 0.636 RESULTS OF CRAPS TEST for dh-ranFile-2015-07-23_14:31 No. of wins: Observed Expected 98771 98585.9 z-score= 0.828, pvalue=0.79618 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66749 66666.7 0.102 0.102 2 37760 37654.3 0.297 0.398 3 27037 26954.7 0.251 0.649 4 19278 19313.5 0.065 0.714 5 13826 13851.4 0.047 0.761 6 10070 9943.5 1.608 2.369 7 7051 7145.0 1.237 3.607 8 5090 5139.1 0.469 4.075 9 3570 3699.9 4.558 8.634 10 2621 2666.3 0.770 9.403 11 1861 1923.3 2.020 11.423 12 1378 1388.7 0.083 11.506 13 1038 1003.7 1.171 12.677 14 708 726.1 0.453 13.130 15 538 525.8 0.281 13.412 16 401 381.2 1.034 14.445 17 283 276.5 0.151 14.596 18 203 200.8 0.023 14.620 19 138 146.0 0.437 15.056 20 104 106.2 0.046 15.103 21 296 287.1 0.275 15.378 Chisq= 15.38 for 20 degrees of freedom, p= 0.24560 SUMMARY of craptest p-value for no. of wins: 0.796182 p-value for throws/game: 0.245597 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-07-23_14:31 No. of wins: Observed Expected 98755 98585.9 z-score= 0.756, pvalue=0.77532 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66622 66666.7 0.030 0.030 2 37424 37654.3 1.409 1.439 3 26807 26954.7 0.810 2.248 4 19307 19313.5 0.002 2.251 5 14010 13851.4 1.816 4.066 6 10026 9943.5 0.684 4.750 7 7175 7145.0 0.126 4.876 8 5200 5139.1 0.722 5.598 9 3680 3699.9 0.107 5.705 10 2705 2666.3 0.562 6.266 11 1956 1923.3 0.555 6.821 12 1392 1388.7 0.008 6.829 13 994 1003.7 0.094 6.923 14 721 726.1 0.036 6.959 15 564 525.8 2.770 9.729 16 375 381.2 0.099 9.829 17 270 276.5 0.155 9.983 18 193 200.8 0.305 10.289 19 162 146.0 1.757 12.046 20 111 106.2 0.216 12.261 21 306 287.1 1.242 13.503 Chisq= 13.50 for 20 degrees of freedom, p= 0.14524 SUMMARY of craptest p-value for no. of wins: 0.775325 p-value for throws/game: 0.145243 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0000,0.0071,0.0096,0.0108,0.0137,0.0139,0.0250,0.0259,0.0342,0.0360, 0.0420,0.0457,0.0484,0.0511,0.0522,0.0562,0.0797,0.0910,0.0937,0.1005, 0.1086,0.1116,0.1135,0.1162,0.1172,0.1237,0.1243,0.1257,0.1267,0.1282, 0.1320,0.1328,0.1340,0.1404,0.1426,0.1439,0.1452,0.1571,0.1581,0.1596, 0.1599,0.1606,0.1633,0.1646,0.1788,0.1797,0.1807,0.1812,0.1826,0.1927, 0.1989,0.2010,0.2012,0.2039,0.2230,0.2255,0.2325,0.2364,0.2387,0.2456, 0.2467,0.2507,0.2515,0.2526,0.2692,0.2764,0.2785,0.2852,0.2853,0.2862, 0.2893,0.2977,0.3064,0.3158,0.3223,0.3330,0.3399,0.3409,0.3427,0.3456, 0.3488,0.3490,0.3547,0.3582,0.3583,0.3628,0.3634,0.3644,0.3738,0.3742, 0.3743,0.3765,0.3823,0.3859,0.3920,0.3927,0.3958,0.3966,0.3985,0.3992, 0.4002,0.4017,0.4064,0.4097,0.4132,0.4161,0.4163,0.4174,0.4187,0.4201, 0.4235,0.4246,0.4368,0.4379,0.4408,0.4412,0.4447,0.4456,0.4509,0.4542, 0.4550,0.4638,0.4690,0.4693,0.4698,0.4749,0.4781,0.4827,0.4927,0.4938, 0.4968,0.4990,0.4995,0.5000,0.5081,0.5090,0.5198,0.5202,0.5220,0.5246, 0.5294,0.5297,0.5354,0.5372,0.5396,0.5397,0.5462,0.5467,0.5512,0.5536, 0.5695,0.5705,0.5761,0.5775,0.5788,0.5839,0.5899,0.5908,0.5920,0.5976, 0.5990,0.5997,0.6002,0.6020,0.6040,0.6063,0.6122,0.6157,0.6158,0.6270, 0.6355,0.6371,0.6375,0.6399,0.6462,0.6518,0.6535,0.6566,0.6695,0.6735, 0.6788,0.6796,0.6869,0.6882,0.6915,0.6923,0.6935,0.6968,0.6987,0.6994, 0.7031,0.7047,0.7050,0.7065,0.7145,0.7231,0.7289,0.7345,0.7364,0.7497, 0.7513,0.7523,0.7533,0.7550,0.7551,0.7554,0.7729,0.7753,0.7755,0.7950, 0.7962,0.7993,0.8128,0.8194,0.8214,0.8214,0.8250,0.8262,0.8273,0.8317, 0.8329,0.8353,0.8367,0.8386,0.8390,0.8394,0.8395,0.8400,0.8440,0.8502, 0.8564,0.8590,0.8590,0.8626,0.8688,0.8779,0.8797,0.8833,0.8913,0.8932, 0.8995,0.8995,0.9010,0.9047,0.9056,0.9112,0.9241,0.9250,0.9308,0.9392, 0.9398,0.9484,0.9514,0.9575,0.9581,0.9582,0.9601,0.9607,0.9703,0.9704, 0.9734,0.9834,0.9851,0.9853,0.9862,0.9875,0.9915,0.9959,0.9999, Overall p-value after applying KStest on 269 p-values = 0.662977 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.