RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-12-11_08:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.81 15.4170 0.434530 2 to 25 15.69 22.1449 0.820791 3 to 26 15.65 22.8023 0.844202 4 to 27 15.66 18.8962 0.665479 5 to 28 15.71 11.5156 0.171459 6 to 29 15.91 12.9777 0.262319 7 to 30 15.41 39.9850 0.998699 8 to 31 15.65 35.3194 0.994353 9 to 32 15.63 28.5864 0.961464 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.018089 Tough bday spacings test for dh-ranFile-2015-12-11_08:31: 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 35 67 97 121 80 46 23 9 5 5 (O-E)^2/E 0.9 0.1 0.5 0.0 5.6 0.0 0.7 1.5 2.3 0.4 0.2 Birthday Spacings: Sum(O-E)^2/E= 12.294, p= 0.734 RESULTS OF GCD FOR dh-ranFile-2015-12-11_08:31 Euclid's algorithm: p-value, steps to gcd: 0.108117 p-value, dist. of gcd's: 0.843818 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-12-11_08:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.654 0.415 0.854 0.330 0.952 0.701 0.843 0.817 Bits 8 to 15---> 0.509 0.765 0.484 0.750 0.572 0.596 0.154 0.578 Bits 16 to 23---> 0.502 0.308 0.932 0.984 0.459 0.545 0.692 0.681 Bits 24 to 31---> 0.464 0.227 0.961 0.961 0.290 0.870 0.488 0.554 KS test for the above 32 p values: 0.980 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-12-11_08:31, p-values for 5 runs: 0.5132, 0.9867, 0.2597, 0.8579, 0.8091 Rank test for binary matrices (31x31) for dh-ranFile-2015-12-11_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 207 211.4 0.092 0.092 r= 29 5151 5134.0 0.056 0.149 r= 30 22991 23103.0 0.543 0.692 r= 31 11651 11551.5 0.857 1.549 chi-square = 1.549 with df = 3; p-value = 0.329 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-12-11_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 200 211.4 0.617 0.617 r= 30 5063 5134.0 0.982 1.599 r= 31 23198 23103.0 0.390 1.989 r= 32 11539 11551.5 0.014 2.003 chi-square = 2.003 with df = 3; p-value = 0.428 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-12-11_08:31 b-rank test for bits 1 to 8, p=0.72731 b-rank test for bits 2 to 9, p=0.57513 b-rank test for bits 3 to 10, p=0.75163 b-rank test for bits 4 to 11, p=0.68871 b-rank test for bits 5 to 12, p=0.93820 b-rank test for bits 6 to 13, p=0.99893 b-rank test for bits 7 to 14, p=0.31784 b-rank test for bits 8 to 15, p=0.03400 b-rank test for bits 9 to 16, p=0.84748 b-rank test for bits 10 to 17, p=0.22333 b-rank test for bits 11 to 18, p=0.28820 b-rank test for bits 12 to 19, p=0.68447 b-rank test for bits 13 to 20, p=0.43525 b-rank test for bits 14 to 21, p=0.20943 b-rank test for bits 15 to 22, p=0.65589 b-rank test for bits 16 to 23, p=0.31533 b-rank test for bits 17 to 24, p=0.62885 b-rank test for bits 18 to 25, p=0.71290 b-rank test for bits 19 to 26, p=0.13889 b-rank test for bits 20 to 27, p=0.84619 b-rank test for bits 21 to 28, p=0.07726 b-rank test for bits 22 to 29, p=0.14705 b-rank test for bits 23 to 30, p=0.08588 b-rank test for bits 24 to 31, p=0.51344 b-rank test for bits 25 to 32, p=0.07845 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 = 0.810434 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-12-11_08:31 (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 141413 -1.16 0.123096 2 141839 -0.16 0.434739 3 141900 -0.02 0.491304 4 142024 0.27 0.605620 5 142134 0.52 0.700184 6 141094 -1.90 0.028392 7 142505 1.39 0.918001 8 141652 -0.60 0.273841 9 142560 1.52 0.935777 10 141786 -0.29 0.386614 11 141418 -1.15 0.125491 12 141774 -0.32 0.375929 13 142260 0.82 0.793699 14 142250 0.80 0.786972 15 142170 0.61 0.728752 16 141378 -1.24 0.107224 17 142172 0.61 0.730298 18 140970 -2.19 0.014093 19 141609 -0.70 0.241431 20 142128 0.51 0.695293 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-12-11_08:31 Bits used No. missing words z-score p-value 23 to 32 142036 0.4368 0.668869 22 to 31 141585 -1.1184 0.131703 21 to 30 141774 -0.4667 0.320373 20 to 29 141838 -0.2460 0.402855 19 to 28 141730 -0.6184 0.268163 18 to 27 141874 -0.1218 0.451518 17 to 26 141503 -1.4011 0.080586 16 to 25 141604 -1.0529 0.146202 15 to 24 141430 -1.6529 0.049179 14 to 23 141650 -0.8942 0.185596 13 to 22 142429 1.7920 0.963431 12 to 21 142260 1.2092 0.886708 11 to 20 142160 0.8644 0.806310 10 to 19 141885 -0.0839 0.466569 9 to 18 142150 0.8299 0.796701 8 to 17 142324 1.4299 0.923627 7 to 16 141722 -0.6460 0.259151 6 to 15 141615 -1.0149 0.155069 5 to 14 141714 -0.6736 0.250298 4 to 13 141808 -0.3494 0.363389 3 to 12 142223 1.0816 0.860289 2 to 11 141877 -0.1115 0.455617 1 to 10 141862 -0.1632 0.435178 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-12-11_08:31 Bits used No. missing words z-score p-value 28 to 32 142262 1.1955 0.884053 27 to 31 142190 0.9514 0.829305 26 to 30 142276 1.2429 0.893057 25 to 29 142703 2.6904 0.996432 24 to 28 141606 -1.0282 0.151919 23 to 27 142177 0.9074 0.817891 22 to 26 142031 0.4124 0.659992 21 to 25 141662 -0.8384 0.200901 20 to 24 141330 -1.9638 0.024775 19 to 23 141363 -1.8520 0.032015 18 to 22 142100 0.6463 0.740970 17 to 21 141849 -0.2045 0.418978 16 to 20 141426 -1.6384 0.050668 15 to 19 142060 0.5107 0.695236 14 to 18 141965 0.1887 0.574841 13 to 17 141824 -0.2893 0.386193 12 to 16 141668 -0.8181 0.206659 11 to 15 141681 -0.7740 0.219465 10 to 14 142014 0.3548 0.638635 9 to 13 141613 -1.0045 0.157567 8 to 12 141751 -0.5367 0.295733 7 to 11 141496 -1.4011 0.080589 6 to 10 141927 0.0599 0.523882 5 to 9 141846 -0.2147 0.415009 4 to 8 141490 -1.4215 0.077592 3 to 7 141844 -0.2215 0.412368 2 to 6 141984 0.2531 0.599912 1 to 5 141801 -0.3672 0.356727 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-12-11_08:31 Bits used No. missing words z-score p-value 31 to 32 142136 0.6686 0.748138 30 to 31 142274 1.0757 0.858974 29 to 30 143151 3.6627 0.999875 28 to 29 141645 -0.7797 0.217774 27 to 28 142354 1.3117 0.905191 26 to 27 141928 0.0551 0.521960 25 to 26 141808 -0.2989 0.382505 24 to 25 141624 -0.8417 0.199983 23 to 24 141499 -1.2104 0.113060 22 to 23 141976 0.1967 0.577956 21 to 22 141931 0.0639 0.525484 20 to 21 142552 1.8958 0.971006 19 to 20 141741 -0.4965 0.309754 18 to 19 141691 -0.6440 0.259774 17 to 18 141635 -0.8092 0.209191 16 to 17 142109 0.5890 0.722068 15 to 16 142026 0.3442 0.634637 14 to 15 142301 1.1554 0.876030 13 to 14 141847 -0.1839 0.427060 12 to 13 142066 0.4622 0.678014 11 to 12 142009 0.2940 0.615626 10 to 11 142008 0.2911 0.614498 9 to 10 142214 0.8987 0.815602 8 to 9 142228 0.9400 0.826399 7 to 8 141665 -0.7207 0.235536 6 to 7 142025 0.3412 0.633527 5 to 6 142245 0.9902 0.838956 4 to 5 142073 0.4828 0.685382 3 to 4 141965 0.1642 0.565220 2 to 3 141675 -0.6912 0.244708 1 to 2 142660 2.2144 0.986598 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-12-11_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2586.90 1.229 0.890451 Test results for specific bytes for dh-ranFile-2015-12-11_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2442.79 -0.809 0.209238 2 to 9 2580.63 1.140 0.872922 3 to 10 2523.84 0.337 0.632004 4 to 11 2366.90 -1.882 0.029896 5 to 12 2566.22 0.936 0.825481 6 to 13 2430.75 -0.979 0.163700 7 to 14 2485.13 -0.210 0.416718 8 to 15 2522.88 0.324 0.626884 9 to 16 2457.97 -0.594 0.276136 10 to 17 2498.81 -0.017 0.493266 11 to 18 2474.47 -0.361 0.359016 12 to 19 2454.23 -0.647 0.258741 13 to 20 2377.59 -1.731 0.041717 14 to 21 2381.53 -1.675 0.046922 15 to 22 2442.36 -0.815 0.207507 16 to 23 2470.91 -0.411 0.340404 17 to 24 2559.95 0.848 0.801737 18 to 25 2449.27 -0.717 0.236575 19 to 26 2447.58 -0.741 0.229257 20 to 27 2637.99 1.951 0.974496 21 to 28 2468.43 -0.446 0.327628 22 to 29 2471.15 -0.408 0.341626 23 to 30 2595.06 1.344 0.910593 24 to 31 2541.42 0.586 0.720973 25 to 32 2419.46 -1.139 0.127348 CDPARK for dh-ranFile-2015-12-11_08:31: 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 3515 -0.3653 0.357445 3528 0.2283 0.590298 3563 1.8265 0.966111 3522 -0.0457 0.481790 3533 0.4566 0.676028 3512 -0.5023 0.307734 3529 0.2740 0.607947 3515 -0.3653 0.357445 3541 0.8219 0.794438 3556 1.5068 0.934075 Square side=100, avg. no. parked=3531.40 sample std.=16.49 p-value of the KSTEST for those 10 p-values: 0.338470 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-12-11_08:31 0.0560,0.7313,0.8700,0.0127,0.3732,0.8689,0.4960,0.5848,0.4176,0.3872, The KS test for those 10 p-values: 0.805559 The 3DSPHERES test for dh-ranFile-2015-12-11_08:31 sample no r^3 equiv. uni. 1 21.431 0.510491 2 39.269 0.729903 3 31.020 0.644418 4 21.399 0.509971 5 7.965 0.233173 6 3.683 0.115537 7 43.020 0.761649 8 7.861 0.230504 9 19.773 0.482683 10 20.601 0.496766 11 20.377 0.492991 12 10.089 0.285582 13 31.481 0.649837 14 22.375 0.525662 15 14.915 0.391752 16 7.718 0.226849 17 43.017 0.761624 18 27.003 0.593466 19 5.843 0.176986 20 56.651 0.848682 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.305910 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-12-11_08:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -1.6 -0.1 0.5 -0.1 -0.4 -0.2 1.2 0.9 -0.2 0.3 -0.2 -0.5 -0.8 0.7 0.1 -2.1 0.2 0.5 0.1 0.6 -1.3 -0.8 1.1 1.6 0.6 -1.6 -0.0 1.5 0.8 0.5 -0.1 1.3 0.9 -1.2 0.4 1.9 1.5 -0.8 0.4 -0.6 0.0 -0.1 Chi-square with 42 degrees of freedom:35.702960 z-score=-0.687063, p-value=0.257527 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-12-11_08:31 Test no p-value 1 0.252190 2 0.137928 3 0.700798 4 0.496961 5 0.703621 6 0.824464 7 0.790890 8 0.133475 9 0.073456 10 0.740413 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.732942 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-12-11_08:31: (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 66662 0.00 66695 0.01 3 25000.00 25076 0.23 24915 0.29 4 6666.67 6603 0.61 6741 0.83 5 1388.89 1386 0.01 1387 0.00 6 238.10 231 0.21 227 0.52 7 34.72 38 0.31 28 1.30 8 4.96 3 0.77 6 0.22 p=0.09374 p=0.21253 Number of rngs required: 687480, p-value: 0.142 RESULTS OF CRAPS TEST for dh-ranFile-2015-12-11_08:31 No. of wins: Observed Expected 98572 98585.9 z-score=-0.062, pvalue=0.47529 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66642 66666.7 0.009 0.009 2 37710 37654.3 0.082 0.091 3 27176 26954.7 1.816 1.908 4 19195 19313.5 0.727 2.634 5 13806 13851.4 0.149 2.783 6 9989 9943.5 0.208 2.991 7 6992 7145.0 3.277 6.269 8 5061 5139.1 1.186 7.455 9 3732 3699.9 0.279 7.734 10 2697 2666.3 0.354 8.087 11 1967 1923.3 0.992 9.079 12 1421 1388.7 0.749 9.828 13 1030 1003.7 0.688 10.517 14 737 726.1 0.162 10.679 15 508 525.8 0.605 11.284 16 405 381.2 1.492 12.776 17 235 276.5 6.240 19.016 18 181 200.8 1.958 20.974 19 141 146.0 0.170 21.144 20 97 106.2 0.800 21.944 21 278 287.1 0.289 22.233 Chisq= 22.23 for 20 degrees of freedom, p= 0.67199 SUMMARY of craptest p-value for no. of wins: 0.475288 p-value for throws/game: 0.671995 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-12-11_08:31 No. of wins: Observed Expected 98812 98585.9 z-score= 1.011, pvalue=0.84410 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67043 66666.7 2.124 2.124 2 37695 37654.3 0.044 2.168 3 26640 26954.7 3.675 5.843 4 19309 19313.5 0.001 5.844 5 13822 13851.4 0.062 5.907 6 10052 9943.5 1.183 7.090 7 7067 7145.0 0.852 7.942 8 5081 5139.1 0.656 8.598 9 3644 3699.9 0.844 9.442 10 2665 2666.3 0.001 9.442 11 1896 1923.3 0.388 9.831 12 1461 1388.7 3.760 13.590 13 980 1003.7 0.560 14.151 14 732 726.1 0.047 14.198 15 522 525.8 0.028 14.226 16 366 381.2 0.602 14.828 17 284 276.5 0.201 15.029 18 191 200.8 0.481 15.511 19 138 146.0 0.437 15.947 20 110 106.2 0.135 16.082 21 302 287.1 0.772 16.854 Chisq= 16.85 for 20 degrees of freedom, p= 0.33756 SUMMARY of craptest p-value for no. of wins: 0.844096 p-value for throws/game: 0.337564 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0127,0.0141,0.0181,0.0248,0.0284,0.0299,0.0320,0.0340,0.0417,0.0469, 0.0492,0.0507,0.0560,0.0735,0.0773,0.0776,0.0784,0.0806,0.0806,0.0859, 0.0937,0.1072,0.1081,0.1131,0.1155,0.1231,0.1255,0.1273,0.1317,0.1335, 0.1379,0.1389,0.1422,0.1462,0.1471,0.1519,0.1535,0.1551,0.1576,0.1637, 0.1715,0.1770,0.1856,0.2000,0.2009,0.2067,0.2075,0.2092,0.2092,0.2094, 0.2125,0.2178,0.2195,0.2233,0.2268,0.2268,0.2293,0.2305,0.2332,0.2355, 0.2366,0.2414,0.2447,0.2503,0.2522,0.2575,0.2587,0.2592,0.2597,0.2598, 0.2623,0.2682,0.2738,0.2761,0.2856,0.2882,0.2899,0.2957,0.3059,0.3075, 0.3077,0.3098,0.3153,0.3178,0.3204,0.3276,0.3289,0.3300,0.3376,0.3385, 0.3404,0.3416,0.3567,0.3574,0.3574,0.3590,0.3634,0.3732,0.3759,0.3825, 0.3862,0.3866,0.3872,0.3918,0.4029,0.4124,0.4150,0.4152,0.4167,0.4176, 0.4190,0.4271,0.4281,0.4345,0.4347,0.4352,0.4352,0.4515,0.4556,0.4587, 0.4638,0.4666,0.4753,0.4818,0.4827,0.4837,0.4878,0.4913,0.4930,0.4933, 0.4960,0.4968,0.4970,0.5018,0.5089,0.5100,0.5105,0.5132,0.5134,0.5220, 0.5239,0.5255,0.5257,0.5451,0.5543,0.5652,0.5722,0.5748,0.5751,0.5778, 0.5780,0.5848,0.5903,0.5935,0.5956,0.5999,0.6056,0.6079,0.6145,0.6156, 0.6269,0.6288,0.6320,0.6335,0.6346,0.6386,0.6444,0.6498,0.6537,0.6559, 0.6600,0.6655,0.6689,0.6720,0.6760,0.6780,0.6813,0.6845,0.6854,0.6887, 0.6920,0.6952,0.6953,0.7002,0.7008,0.7014,0.7036,0.7129,0.7210,0.7221, 0.7273,0.7288,0.7299,0.7303,0.7313,0.7329,0.7341,0.7404,0.7410,0.7481, 0.7504,0.7516,0.7616,0.7616,0.7655,0.7870,0.7909,0.7937,0.7944,0.7967, 0.8017,0.8056,0.8063,0.8091,0.8104,0.8156,0.8175,0.8179,0.8208,0.8245, 0.8255,0.8264,0.8293,0.8390,0.8426,0.8438,0.8441,0.8442,0.8462,0.8475, 0.8487,0.8541,0.8579,0.8590,0.8603,0.8689,0.8700,0.8702,0.8729,0.8760, 0.8841,0.8867,0.8905,0.8931,0.9052,0.9106,0.9180,0.9236,0.9323,0.9341, 0.9358,0.9382,0.9520,0.9612,0.9614,0.9615,0.9634,0.9661,0.9710,0.9745, 0.9805,0.9845,0.9866,0.9867,0.9944,0.9964,0.9987,0.9989,0.9999, Overall p-value after applying KStest on 269 p-values = 0.638112 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.