RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-10-29_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 15.88 15.1840 0.417767 2 to 25 15.78 20.7094 0.760440 3 to 26 15.89 18.3638 0.633757 4 to 27 15.85 17.8969 0.604624 5 to 28 15.67 20.4705 0.749125 6 to 29 15.88 18.2184 0.624809 7 to 30 15.65 12.1389 0.208349 8 to 31 15.70 22.6667 0.839580 9 to 32 15.61 42.8533 0.999496 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.115957 Tough bday spacings test for dh-ranFile-2015-10-29_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 41 70 94 95 77 59 23 19 9 2 (O-E)^2/E 0.4 0.5 0.1 0.1 0.1 0.0 0.9 1.5 1.1 0.9 1.0 Birthday Spacings: Sum(O-E)^2/E= 6.767, p= 0.253 RESULTS OF GCD FOR dh-ranFile-2015-10-29_03:31 Euclid's algorithm: p-value, steps to gcd: 0.137535 p-value, dist. of gcd's: 0.638023 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-10-29_03:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.385 0.152 0.757 0.108 0.201 0.786 0.280 0.447 Bits 8 to 15---> 0.106 0.001 0.605 0.117 0.328 0.189 0.085 0.041 Bits 16 to 23---> 0.817 0.269 0.930 0.899 0.534 0.171 0.510 0.199 Bits 24 to 31---> 0.881 0.850 0.253 0.253 0.555 0.368 0.651 0.777 KS test for the above 32 p values: 0.822 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-10-29_03:31, p-values for 5 runs: 0.8894, 0.4088, 0.7087, 0.3572, 0.4321 Rank test for binary matrices (31x31) for dh-ranFile-2015-10-29_03:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 214 211.4 0.032 0.032 r= 29 5140 5134.0 0.007 0.039 r= 30 23045 23103.0 0.146 0.184 r= 31 11601 11551.5 0.212 0.396 chi-square = 0.396 with df = 3; p-value = 0.059 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-10-29_03:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 195 211.4 1.275 1.275 r= 30 5186 5134.0 0.526 1.801 r= 31 23031 23103.0 0.225 2.026 r= 32 11588 11551.5 0.115 2.141 chi-square = 2.141 with df = 3; p-value = 0.456 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-10-29_03:31 b-rank test for bits 1 to 8, p=0.04229 b-rank test for bits 2 to 9, p=0.28859 b-rank test for bits 3 to 10, p=0.98956 b-rank test for bits 4 to 11, p=0.86111 b-rank test for bits 5 to 12, p=0.89250 b-rank test for bits 6 to 13, p=0.13725 b-rank test for bits 7 to 14, p=0.83787 b-rank test for bits 8 to 15, p=0.49032 b-rank test for bits 9 to 16, p=0.25694 b-rank test for bits 10 to 17, p=0.76463 b-rank test for bits 11 to 18, p=0.64032 b-rank test for bits 12 to 19, p=0.86440 b-rank test for bits 13 to 20, p=0.40537 b-rank test for bits 14 to 21, p=0.19242 b-rank test for bits 15 to 22, p=0.02625 b-rank test for bits 16 to 23, p=0.58393 b-rank test for bits 17 to 24, p=0.24875 b-rank test for bits 18 to 25, p=0.23216 b-rank test for bits 19 to 26, p=0.76372 b-rank test for bits 20 to 27, p=0.77722 b-rank test for bits 21 to 28, p=0.42017 b-rank test for bits 22 to 29, p=0.15736 b-rank test for bits 23 to 30, p=0.65819 b-rank test for bits 24 to 31, p=0.84907 b-rank test for bits 25 to 32, p=0.60169 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 = 0.925008 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-10-29_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 141741 -0.39 0.347051 2 141452 -1.07 0.142641 3 141962 0.12 0.548971 4 142072 0.38 0.648053 5 141462 -1.05 0.147974 6 142067 0.37 0.643708 7 141793 -0.27 0.392888 8 141336 -1.34 0.090195 9 141544 -0.85 0.196670 10 141612 -0.69 0.243623 11 141679 -0.54 0.295235 12 141630 -0.65 0.256994 13 141824 -0.20 0.420987 14 142316 0.95 0.828985 15 142998 2.54 0.994515 16 141459 -1.05 0.146360 17 142048 0.32 0.627029 18 142487 1.35 0.911443 19 141834 -0.18 0.430145 20 141964 0.13 0.550820 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-10-29_03:31 Bits used No. missing words z-score p-value 23 to 32 141830 -0.2736 0.392215 22 to 31 141568 -1.1770 0.119598 21 to 30 142579 2.3092 0.989534 20 to 29 141377 -1.8356 0.033207 19 to 28 141664 -0.8460 0.198786 18 to 27 141884 -0.0873 0.465199 17 to 26 142020 0.3816 0.648629 16 to 25 141796 -0.3908 0.347975 15 to 24 142200 1.0023 0.841903 14 to 23 142210 1.0368 0.850084 13 to 22 142016 0.3678 0.643499 12 to 21 141959 0.1713 0.567997 11 to 20 142000 0.3127 0.622729 10 to 19 141596 -1.0804 0.139971 9 to 18 141705 -0.7046 0.240534 8 to 17 141996 0.2989 0.617477 7 to 16 141860 -0.1701 0.432464 6 to 15 141697 -0.7322 0.232032 5 to 14 141675 -0.8080 0.209535 4 to 13 141815 -0.3253 0.372486 3 to 12 141583 -1.1253 0.130236 2 to 11 141447 -1.5942 0.055441 1 to 10 141903 -0.0218 0.491293 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-10-29_03:31 Bits used No. missing words z-score p-value 28 to 32 141672 -0.8045 0.210552 27 to 31 142075 0.5616 0.712803 26 to 30 142055 0.4938 0.689275 25 to 29 142659 2.5413 0.994477 24 to 28 141818 -0.3096 0.378435 23 to 27 141700 -0.7096 0.238978 22 to 26 142518 2.0633 0.980457 21 to 25 141730 -0.6079 0.271628 20 to 24 141530 -1.2859 0.099245 19 to 23 141666 -0.8248 0.204729 18 to 22 141886 -0.0791 0.468483 17 to 21 141514 -1.3401 0.090106 16 to 20 142159 0.8463 0.801318 15 to 19 141720 -0.6418 0.260503 14 to 18 142017 0.3650 0.642438 13 to 17 141360 -1.8621 0.031292 12 to 16 141650 -0.8791 0.189678 11 to 15 141643 -0.9028 0.183312 10 to 14 141721 -0.6384 0.261605 9 to 13 141998 0.3006 0.618131 8 to 12 141422 -1.6520 0.049271 7 to 11 141881 -0.0960 0.461747 6 to 10 142398 1.6565 0.951191 5 to 9 141798 -0.3774 0.352942 4 to 8 141714 -0.6621 0.253942 3 to 7 142636 2.4633 0.993117 2 to 6 142138 0.7752 0.780875 1 to 5 141733 -0.5977 0.275010 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-10-29_03:31 Bits used No. missing words z-score p-value 31 to 32 141943 0.0993 0.539559 30 to 31 142494 1.7247 0.957708 29 to 30 141737 -0.5083 0.305605 28 to 29 142002 0.2734 0.607713 27 to 28 142124 0.6332 0.736713 26 to 27 142402 1.4533 0.926930 25 to 26 141713 -0.5791 0.281246 24 to 25 141694 -0.6352 0.262652 23 to 24 141935 0.0757 0.530180 22 to 23 142080 0.5035 0.692677 21 to 22 141646 -0.7768 0.218643 20 to 21 141481 -1.2635 0.103203 19 to 20 141634 -0.8122 0.208343 18 to 19 142296 1.1406 0.872986 17 to 18 141850 -0.1750 0.430534 16 to 17 141940 0.0905 0.536044 15 to 16 141529 -1.1219 0.130949 14 to 15 141908 -0.0039 0.498435 13 to 14 141977 0.1996 0.579110 12 to 13 141459 -1.3284 0.092022 11 to 12 141652 -0.7591 0.223901 10 to 11 141999 0.2645 0.604308 9 to 10 141987 0.2291 0.590610 8 to 9 142212 0.8928 0.814026 7 to 8 141439 -1.3874 0.082659 6 to 7 142243 0.9843 0.837510 5 to 6 142168 0.7630 0.777280 4 to 5 142178 0.7925 0.785976 3 to 4 142050 0.4150 0.660913 2 to 3 141597 -0.9213 0.178440 1 to 2 142145 0.6952 0.756532 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-10-29_03:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2384.01 -1.640 0.050466 Test results for specific bytes for dh-ranFile-2015-10-29_03:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2452.03 -0.678 0.248781 2 to 9 2467.00 -0.467 0.320380 3 to 10 2437.78 -0.880 0.189433 4 to 11 2440.27 -0.845 0.199141 5 to 12 2382.69 -1.659 0.048551 6 to 13 2543.80 0.619 0.732174 7 to 14 2435.94 -0.906 0.182464 8 to 15 2445.27 -0.774 0.219469 9 to 16 2615.59 1.635 0.948941 10 to 17 2444.79 -0.781 0.217443 11 to 18 2464.68 -0.499 0.308735 12 to 19 2523.28 0.329 0.629016 13 to 20 2538.65 0.547 0.707668 14 to 21 2506.53 0.092 0.536790 15 to 22 2437.24 -0.888 0.187396 16 to 23 2557.64 0.815 0.792512 17 to 24 2378.73 -1.715 0.043172 18 to 25 2359.22 -1.991 0.023247 19 to 26 2521.15 0.299 0.617548 20 to 27 2446.35 -0.759 0.224000 21 to 28 2442.71 -0.810 0.208905 22 to 29 2501.00 0.014 0.505652 23 to 30 2546.31 0.655 0.743763 24 to 31 2662.81 2.303 0.989348 25 to 32 2504.41 0.062 0.524851 CDPARK for dh-ranFile-2015-10-29_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 3517 -0.2740 0.392053 3505 -0.8219 0.205562 3523 0.0000 0.500000 3556 1.5068 0.934075 3516 -0.3196 0.374623 3528 0.2283 0.590298 3551 1.2785 0.899470 3533 0.4566 0.676028 3549 1.1872 0.882429 3472 -2.3288 0.009936 Square side=100, avg. no. parked=3525.00 sample std.=23.76 p-value of the KSTEST for those 10 p-values: 0.808994 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-10-29_03:31 0.2735,0.2436,0.9833,0.5956,0.8962,0.8370,0.8352,0.0668,0.5175,0.6881, The KS test for those 10 p-values: 0.529903 The 3DSPHERES test for dh-ranFile-2015-10-29_03:31 sample no r^3 equiv. uni. 1 29.140 0.621424 2 15.887 0.411142 3 29.692 0.628325 4 83.308 0.937771 5 33.746 0.675305 6 13.860 0.369986 7 1.346 0.043879 8 8.474 0.246069 9 29.149 0.621541 10 37.195 0.710570 11 54.179 0.835684 12 6.793 0.202636 13 3.961 0.123688 14 8.286 0.241337 15 4.697 0.144919 16 48.351 0.800449 17 4.810 0.148147 18 53.345 0.831055 19 69.027 0.899831 20 24.268 0.554661 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.966181 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-10-29_03:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -1.2 2.5 0.8 -1.2 0.3 -3.0 0.2 -0.6 1.2 -0.1 1.0 1.8 1.6 0.4 0.3 -0.0 -0.1 -1.1 1.0 -0.5 0.5 -2.1 -2.2 -0.7 0.0 0.7 0.1 -0.8 -0.7 1.2 -0.5 -0.3 -0.4 -0.4 -1.4 0.5 1.8 0.9 -0.1 -0.6 -1.0 -1.1 Chi-square with 42 degrees of freedom:52.729171 z-score=1.170649, p-value=0.875954 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-10-29_03:31 Test no p-value 1 0.340243 2 0.760564 3 0.632092 4 0.671416 5 0.151652 6 0.097761 7 0.159722 8 0.423703 9 0.320759 10 0.011742 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.198678 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-10-29_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 66413 0.97 66742 0.09 3 25000.00 25208 1.73 25024 0.02 4 6666.67 6716 0.37 6564 1.58 5 1388.89 1387 0.00 1390 0.00 6 238.10 225 0.72 237 0.01 7 34.72 45 3.04 40 0.80 8 4.96 5 0.00 2 1.77 p=0.66292 p=0.35909 Number of rngs required: 688578, p-value: 0.580 RESULTS OF CRAPS TEST for dh-ranFile-2015-10-29_03:31 No. of wins: Observed Expected 98355 98585.9 z-score=-1.033, pvalue=0.15091 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66460 66666.7 0.641 0.641 2 37859 37654.3 1.113 1.753 3 27286 26954.7 4.071 5.824 4 19202 19313.5 0.643 6.468 5 13931 13851.4 0.457 6.925 6 9771 9943.5 2.994 9.919 7 6963 7145.0 4.637 14.556 8 5066 5139.1 1.039 15.595 9 3686 3699.9 0.052 15.647 10 2785 2666.3 5.285 20.932 11 1915 1923.3 0.036 20.968 12 1441 1388.7 1.967 22.934 13 981 1003.7 0.514 23.448 14 746 726.1 0.543 23.992 15 525 525.8 0.001 23.993 16 362 381.2 0.962 24.955 17 263 276.5 0.663 25.618 18 201 200.8 0.000 25.618 19 157 146.0 0.831 26.449 20 115 106.2 0.727 27.176 21 285 287.1 0.016 27.192 Chisq= 27.19 for 20 degrees of freedom, p= 0.87004 SUMMARY of craptest p-value for no. of wins: 0.150911 p-value for throws/game: 0.870039 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-10-29_03:31 No. of wins: Observed Expected 98541 98585.9 z-score=-0.201, pvalue=0.42049 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66718 66666.7 0.040 0.040 2 37584 37654.3 0.131 0.171 3 27042 26954.7 0.283 0.453 4 19160 19313.5 1.219 1.673 5 14019 13851.4 2.027 3.700 6 9837 9943.5 1.142 4.842 7 7208 7145.0 0.555 5.397 8 5166 5139.1 0.141 5.538 9 3684 3699.9 0.068 5.606 10 2656 2666.3 0.040 5.646 11 1949 1923.3 0.343 5.988 12 1393 1388.7 0.013 6.001 13 1016 1003.7 0.150 6.152 14 722 726.1 0.024 6.175 15 492 525.8 2.177 8.353 16 363 381.2 0.864 9.217 17 271 276.5 0.111 9.328 18 195 200.8 0.169 9.497 19 131 146.0 1.538 11.035 20 126 106.2 3.685 14.721 21 268 287.1 1.272 15.993 Chisq= 15.99 for 20 degrees of freedom, p= 0.28294 SUMMARY of craptest p-value for no. of wins: 0.420492 p-value for throws/game: 0.282944 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0009,0.0099,0.0117,0.0232,0.0262,0.0313,0.0332,0.0412,0.0423,0.0432, 0.0439,0.0486,0.0493,0.0505,0.0554,0.0590,0.0668,0.0827,0.0852,0.0901, 0.0902,0.0920,0.0978,0.0992,0.1032,0.1060,0.1084,0.1160,0.1172,0.1196, 0.1237,0.1302,0.1309,0.1372,0.1375,0.1400,0.1426,0.1449,0.1464,0.1480, 0.1481,0.1509,0.1517,0.1524,0.1574,0.1597,0.1713,0.1784,0.1825,0.1833, 0.1874,0.1894,0.1894,0.1897,0.1924,0.1967,0.1987,0.1988,0.1991,0.1992, 0.2015,0.2026,0.2047,0.2056,0.2083,0.2083,0.2089,0.2095,0.2106,0.2174, 0.2186,0.2195,0.2239,0.2240,0.2320,0.2322,0.2390,0.2405,0.2413,0.2436, 0.2436,0.2461,0.2487,0.2488,0.2527,0.2528,0.2533,0.2539,0.2569,0.2570, 0.2605,0.2616,0.2627,0.2686,0.2716,0.2735,0.2750,0.2796,0.2812,0.2829, 0.2886,0.2952,0.3056,0.3087,0.3204,0.3208,0.3276,0.3402,0.3471,0.3480, 0.3529,0.3572,0.3591,0.3677,0.3700,0.3725,0.3746,0.3784,0.3853,0.3921, 0.3922,0.3929,0.4054,0.4088,0.4111,0.4178,0.4202,0.4205,0.4210,0.4237, 0.4301,0.4305,0.4321,0.4325,0.4470,0.4564,0.4617,0.4652,0.4685,0.4903, 0.4913,0.4984,0.5000,0.5057,0.5099,0.5175,0.5249,0.5299,0.5302,0.5340, 0.5360,0.5368,0.5396,0.5490,0.5508,0.5547,0.5554,0.5680,0.5791,0.5798, 0.5839,0.5903,0.5906,0.5956,0.6017,0.6043,0.6046,0.6054,0.6077,0.6175, 0.6175,0.6181,0.6214,0.6215,0.6227,0.6248,0.6270,0.6283,0.6290,0.6321, 0.6338,0.6380,0.6403,0.6424,0.6435,0.6437,0.6481,0.6486,0.6512,0.6582, 0.6609,0.6629,0.6714,0.6753,0.6760,0.6881,0.6893,0.6927,0.7077,0.7087, 0.7106,0.7128,0.7322,0.7367,0.7438,0.7491,0.7565,0.7565,0.7604,0.7606, 0.7637,0.7646,0.7772,0.7773,0.7774,0.7809,0.7860,0.7863,0.7925,0.8004, 0.8013,0.8090,0.8140,0.8167,0.8219,0.8290,0.8311,0.8352,0.8357,0.8370, 0.8375,0.8379,0.8396,0.8419,0.8491,0.8496,0.8501,0.8611,0.8644,0.8700, 0.8730,0.8760,0.8806,0.8824,0.8894,0.8925,0.8962,0.8993,0.8995,0.8998, 0.9114,0.9250,0.9269,0.9297,0.9341,0.9378,0.9489,0.9512,0.9577,0.9662, 0.9805,0.9833,0.9893,0.9895,0.9896,0.9931,0.9945,0.9945,0.9995, Overall p-value after applying KStest on 269 p-values = 0.109850 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.