RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-07_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 15.83 15.7892 0.461173 2 to 25 15.93 18.5346 0.644112 3 to 26 15.85 12.4197 0.225915 4 to 27 16.06 10.8712 0.136820 5 to 28 15.87 22.5125 0.834197 6 to 29 15.89 6.7140 0.013041 7 to 30 15.49 23.0585 0.852643 8 to 31 15.62 14.6868 0.381974 9 to 32 15.78 22.0401 0.816818 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.912325 Tough bday spacings test for dh-ranFile-2018-07-07_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 12 45 67 115 107 70 43 25 9 3 4 (O-E)^2/E 0.9 1.9 0.5 3.1 0.9 0.8 1.6 0.8 2.3 2.0 0.0 Birthday Spacings: Sum(O-E)^2/E= 14.794, p= 0.860 RESULTS OF GCD FOR dh-ranFile-2018-07-07_03:31 Euclid's algorithm: p-value, steps to gcd: 0.232380 p-value, dist. of gcd's: 0.688104 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-07_03:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.097 0.913 0.804 0.236 0.003 0.723 0.181 0.343 Bits 8 to 15---> 0.476 0.810 0.263 0.824 0.187 0.726 0.597 0.218 Bits 16 to 23---> 0.094 0.783 0.587 0.125 0.373 0.784 0.472 0.384 Bits 24 to 31---> 0.317 0.959 0.118 0.774 0.552 0.421 0.847 0.267 KS test for the above 32 p values: 0.164 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-07_03:31, p-values for 5 runs: 0.4541, 0.6927, 0.7032, 0.4365, 0.9780 Rank test for binary matrices (31x31) for dh-ranFile-2018-07-07_03:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 226 211.4 1.006 1.006 r= 29 5148 5134.0 0.038 1.044 r= 30 22941 23103.0 1.137 2.180 r= 31 11685 11551.5 1.542 3.723 chi-square = 3.723 with df = 3; p-value = 0.707 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-07-07_03:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 191 211.4 1.972 1.972 r= 30 5068 5134.0 0.849 2.821 r= 31 23276 23103.0 1.295 4.115 r= 32 11465 11551.5 0.648 4.763 chi-square = 4.763 with df = 3; p-value = 0.810 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-07-07_03:31 b-rank test for bits 1 to 8, p=0.77724 b-rank test for bits 2 to 9, p=0.20221 b-rank test for bits 3 to 10, p=0.15714 b-rank test for bits 4 to 11, p=0.48298 b-rank test for bits 5 to 12, p=0.16618 b-rank test for bits 6 to 13, p=0.49828 b-rank test for bits 7 to 14, p=0.57003 b-rank test for bits 8 to 15, p=0.12520 b-rank test for bits 9 to 16, p=0.01938 b-rank test for bits 10 to 17, p=0.46463 b-rank test for bits 11 to 18, p=0.11330 b-rank test for bits 12 to 19, p=0.58271 b-rank test for bits 13 to 20, p=0.84941 b-rank test for bits 14 to 21, p=0.38219 b-rank test for bits 15 to 22, p=0.34367 b-rank test for bits 16 to 23, p=0.24103 b-rank test for bits 17 to 24, p=0.84907 b-rank test for bits 18 to 25, p=0.49068 b-rank test for bits 19 to 26, p=0.62449 b-rank test for bits 20 to 27, p=0.11283 b-rank test for bits 21 to 28, p=0.01026 b-rank test for bits 22 to 29, p=0.53616 b-rank test for bits 23 to 30, p=0.01814 b-rank test for bits 24 to 31, p=0.83238 b-rank test for bits 25 to 32, p=0.15579 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 = 0.056291 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-07_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 142106 0.46 0.677066 2 142435 1.23 0.890314 3 142624 1.67 0.952520 4 141557 -0.82 0.205197 5 141141 -1.80 0.036314 6 142710 1.87 0.969308 7 142586 1.58 0.943062 8 142280 0.87 0.806769 9 141746 -0.38 0.351375 10 141599 -0.73 0.234205 11 141382 -1.23 0.108960 12 141729 -0.42 0.336756 13 141486 -0.99 0.161310 14 142156 0.58 0.717805 15 142044 0.31 0.623486 16 142169 0.61 0.727977 17 141603 -0.72 0.237081 18 141875 -0.08 0.468035 19 142018 0.25 0.600214 20 142316 0.95 0.828985 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-07-07_03:31 Bits used No. missing words z-score p-value 23 to 32 141703 -0.7115 0.238393 22 to 31 142388 1.6506 0.950588 21 to 30 142022 0.3885 0.651183 20 to 29 141535 -1.2908 0.098388 19 to 28 142109 0.6885 0.754436 18 to 27 142229 1.1023 0.864837 17 to 26 141740 -0.5839 0.279645 16 to 25 141974 0.2230 0.588232 15 to 24 141977 0.2333 0.592253 14 to 23 141874 -0.1218 0.451518 13 to 22 141691 -0.7529 0.225766 12 to 21 142578 2.3058 0.989438 11 to 20 142397 1.6816 0.953679 10 to 19 142114 0.7058 0.759831 9 to 18 141946 0.1264 0.550312 8 to 17 142024 0.3954 0.653731 7 to 16 141709 -0.6908 0.244848 6 to 15 141824 -0.2942 0.384287 5 to 14 141737 -0.5942 0.276175 4 to 13 141994 0.2920 0.614844 3 to 12 142157 0.8540 0.803457 2 to 11 141687 -0.7667 0.221643 1 to 10 141624 -0.9839 0.162583 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-07-07_03:31 Bits used No. missing words z-score p-value 28 to 32 142247 1.1446 0.873822 27 to 31 141783 -0.4282 0.334239 26 to 30 141692 -0.7367 0.230649 25 to 29 141669 -0.8147 0.207628 24 to 28 142082 0.5853 0.720834 23 to 27 141705 -0.6926 0.244267 22 to 26 141931 0.0735 0.529279 21 to 25 141595 -1.0655 0.143319 20 to 24 142231 1.0904 0.862233 19 to 23 141558 -1.1909 0.116837 18 to 22 141815 -0.3198 0.374574 17 to 21 141893 -0.0554 0.477928 16 to 20 141746 -0.5537 0.289905 15 to 19 141825 -0.2859 0.387491 14 to 18 141968 0.1989 0.578822 13 to 17 141567 -1.1604 0.122935 12 to 16 141575 -1.1333 0.128540 11 to 15 141360 -1.8621 0.031292 10 to 14 142630 2.4429 0.992716 9 to 13 141511 -1.3503 0.088465 8 to 12 141608 -1.0215 0.153519 7 to 11 141846 -0.2147 0.415009 6 to 10 141906 -0.0113 0.495497 5 to 9 141780 -0.4384 0.330546 4 to 8 141899 -0.0350 0.486033 3 to 7 141795 -0.3876 0.349171 2 to 6 141995 0.2904 0.614248 1 to 5 141408 -1.6994 0.044620 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-07-07_03:31 Bits used No. missing words z-score p-value 31 to 32 141936 0.0787 0.531354 30 to 31 141502 -1.2016 0.114766 29 to 30 141344 -1.6676 0.047694 28 to 29 141906 -0.0098 0.496081 27 to 28 142009 0.2940 0.615626 26 to 27 141726 -0.5408 0.294324 25 to 26 141947 0.1111 0.544240 24 to 25 141526 -1.1308 0.129077 23 to 24 141792 -0.3461 0.364632 22 to 23 141985 0.2232 0.588316 21 to 22 141536 -1.1013 0.135390 20 to 21 142188 0.8220 0.794472 19 to 20 141718 -0.5644 0.286243 18 to 19 142174 0.7807 0.782522 17 to 18 142187 0.8191 0.793631 16 to 17 141754 -0.4582 0.323404 15 to 16 141918 0.0256 0.510202 14 to 15 142239 0.9725 0.834594 13 to 14 142341 1.2734 0.898555 12 to 13 141789 -0.3550 0.361311 11 to 12 141396 -1.5142 0.064982 10 to 11 141570 -1.0010 0.158420 9 to 10 142056 0.4327 0.667367 8 to 9 141966 0.1672 0.566381 7 to 8 142166 0.7571 0.775517 6 to 7 141602 -0.9066 0.182315 5 to 6 141646 -0.7768 0.218643 4 to 5 141481 -1.2635 0.103203 3 to 4 141554 -1.0482 0.147280 2 to 3 142261 1.0374 0.850219 1 to 2 142322 1.2173 0.888258 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-07_03:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2514.48 0.205 0.581132 Test results for specific bytes for dh-ranFile-2018-07-07_03:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2462.96 -0.524 0.300184 2 to 9 2532.37 0.458 0.676429 3 to 10 2558.54 0.828 0.796128 4 to 11 2513.60 0.192 0.576279 5 to 12 2529.16 0.412 0.659989 6 to 13 2513.68 0.193 0.576696 7 to 14 2475.01 -0.353 0.361878 8 to 15 2418.86 -1.148 0.125578 9 to 16 2405.20 -1.341 0.090011 10 to 17 2547.66 0.674 0.749861 11 to 18 2515.84 0.224 0.588621 12 to 19 2418.76 -1.149 0.125304 13 to 20 2501.01 0.014 0.505705 14 to 21 2594.98 1.343 0.910391 15 to 22 2549.58 0.701 0.758416 16 to 23 2516.37 0.231 0.591514 17 to 24 2450.41 -0.701 0.241554 18 to 25 2405.49 -1.337 0.090674 19 to 26 2460.47 -0.559 0.288059 20 to 27 2399.25 -1.425 0.077108 21 to 28 2433.85 -0.936 0.174749 22 to 29 2483.59 -0.232 0.408218 23 to 30 2502.53 0.036 0.514244 24 to 31 2470.11 -0.423 0.336273 25 to 32 2529.06 0.411 0.659449 CDPARK for dh-ranFile-2018-07-07_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 3559 1.6438 0.949895 3541 0.8219 0.794438 3547 1.0959 0.863437 3527 0.1826 0.572463 3491 -1.4612 0.071982 3533 0.4566 0.676028 3516 -0.3196 0.374623 3518 -0.2283 0.409702 3550 1.2329 0.891189 3529 0.2740 0.607947 Square side=100, avg. no. parked=3531.10 sample std.=18.76 p-value of the KSTEST for those 10 p-values: 0.340263 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-07_03:31 0.5836,0.1092,0.9251,0.3456,0.9056,0.0548,0.7050,0.7395,0.4343,0.3713, The KS test for those 10 p-values: 0.990761 The 3DSPHERES test for dh-ranFile-2018-07-07_03:31 sample no r^3 equiv. uni. 1 58.994 0.860051 2 41.206 0.746786 3 6.785 0.202419 4 1.307 0.042639 5 3.278 0.103521 6 12.909 0.349683 7 69.499 0.901395 8 4.231 0.131549 9 0.513 0.016962 10 47.028 0.791456 11 5.220 0.159709 12 54.454 0.837182 13 17.005 0.432680 14 19.746 0.482216 15 80.130 0.930816 16 13.364 0.359482 17 11.170 0.310874 18 6.634 0.198403 19 4.425 0.137138 20 24.819 0.562772 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.366076 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-07_03:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 -0.3 1.1 -0.1 0.4 -2.4 0.5 0.8 0.3 -0.2 -0.8 0.5 -1.2 3.3 0.2 0.2 -0.9 -0.6 0.9 -0.2 0.5 -0.6 -1.0 0.9 -1.0 -0.8 -0.9 -1.0 1.4 -0.3 1.0 0.3 -0.1 -1.3 0.1 1.3 0.7 0.5 -1.2 -1.8 -1.3 0.0 -1.1 Chi-square with 42 degrees of freedom:44.494051 z-score=0.272123, p-value=0.632840 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-07-07_03:31 Test no p-value 1 0.140047 2 0.331149 3 0.836202 4 0.735260 5 0.091970 6 0.032770 7 0.028301 8 0.855855 9 0.086541 10 0.543530 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.095769 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-07_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 66638 0.01 66894 0.78 3 25000.00 25154 0.95 24646 5.01 4 6666.67 6560 1.71 6755 1.17 5 1388.89 1403 0.14 1421 0.74 6 238.10 207 4.06 246 0.26 7 34.72 36 0.05 32 0.21 8 4.96 1 3.16 5 0.00 p=0.87871 p=0.77453 Number of rngs required: 688630, p-value: 0.603 RESULTS OF CRAPS TEST for dh-ranFile-2018-07-07_03:31 No. of wins: Observed Expected 98762 98585.9 z-score= 0.788, pvalue=0.78460 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66470 66666.7 0.580 0.580 2 37563 37654.3 0.221 0.802 3 27169 26954.7 1.703 2.505 4 19263 19313.5 0.132 2.637 5 13823 13851.4 0.058 2.695 6 10155 9943.5 4.497 7.192 7 7106 7145.0 0.213 7.405 8 5129 5139.1 0.020 7.425 9 3614 3699.9 1.993 9.417 10 2714 2666.3 0.853 10.271 11 1942 1923.3 0.181 10.452 12 1370 1388.7 0.253 10.705 13 1005 1003.7 0.002 10.707 14 698 726.1 1.091 11.797 15 528 525.8 0.009 11.806 16 398 381.2 0.745 12.551 17 294 276.5 1.102 13.653 18 207 200.8 0.190 13.843 19 139 146.0 0.334 14.177 20 113 106.2 0.433 14.611 21 300 287.1 0.578 15.189 Chisq= 15.19 for 20 degrees of freedom, p= 0.23450 SUMMARY of craptest p-value for no. of wins: 0.784595 p-value for throws/game: 0.234501 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-07_03:31 No. of wins: Observed Expected 98760 98585.9 z-score= 0.779, pvalue=0.78197 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66465 66666.7 0.610 0.610 2 37507 37654.3 0.576 1.186 3 27188 26954.7 2.019 3.205 4 19229 19313.5 0.369 3.575 5 13979 13851.4 1.175 4.750 6 10018 9943.5 0.558 5.307 7 6987 7145.0 3.495 8.802 8 5207 5139.1 0.898 9.700 9 3768 3699.9 1.255 10.955 10 2637 2666.3 0.322 11.277 11 1953 1923.3 0.458 11.734 12 1445 1388.7 2.279 14.014 13 980 1003.7 0.560 14.574 14 707 726.1 0.505 15.078 15 547 525.8 0.852 15.930 16 367 381.2 0.525 16.456 17 287 276.5 0.396 16.851 18 175 200.8 3.322 20.173 19 127 146.0 2.469 22.642 20 123 106.2 2.652 25.295 21 304 287.1 0.993 26.288 Chisq= 26.29 for 20 degrees of freedom, p= 0.84348 SUMMARY of craptest p-value for no. of wins: 0.781969 p-value for throws/game: 0.843484 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0028,0.0103,0.0130,0.0170,0.0181,0.0194,0.0283,0.0313,0.0328,0.0363, 0.0426,0.0446,0.0477,0.0548,0.0563,0.0650,0.0720,0.0771,0.0865,0.0885, 0.0900,0.0907,0.0920,0.0941,0.0958,0.0967,0.0984,0.1032,0.1035,0.1090, 0.1092,0.1128,0.1133,0.1148,0.1168,0.1185,0.1229,0.1250,0.1252,0.1253, 0.1256,0.1285,0.1291,0.1315,0.1354,0.1368,0.1371,0.1400,0.1433,0.1473, 0.1535,0.1558,0.1571,0.1584,0.1597,0.1613,0.1626,0.1641,0.1662,0.1747, 0.1805,0.1823,0.1874,0.1984,0.2022,0.2024,0.2052,0.2076,0.2181,0.2186, 0.2216,0.2258,0.2259,0.2306,0.2324,0.2342,0.2345,0.2364,0.2371,0.2384, 0.2410,0.2416,0.2443,0.2448,0.2627,0.2669,0.2762,0.2796,0.2862,0.2881, 0.2899,0.2943,0.3002,0.3109,0.3174,0.3234,0.3305,0.3311,0.3342,0.3363, 0.3368,0.3403,0.3431,0.3437,0.3456,0.3492,0.3497,0.3514,0.3595,0.3613, 0.3619,0.3646,0.3661,0.3713,0.3731,0.3746,0.3746,0.3820,0.3822,0.3843, 0.3843,0.3875,0.4082,0.4097,0.4150,0.4212,0.4327,0.4343,0.4365,0.4515, 0.4541,0.4612,0.4646,0.4680,0.4722,0.4761,0.4779,0.4822,0.4830,0.4860, 0.4907,0.4955,0.4961,0.4983,0.5057,0.5102,0.5142,0.5293,0.5314,0.5362, 0.5435,0.5442,0.5503,0.5517,0.5628,0.5664,0.5700,0.5725,0.5763,0.5767, 0.5788,0.5811,0.5827,0.5836,0.5871,0.5882,0.5883,0.5886,0.5915,0.5923, 0.5973,0.6002,0.6030,0.6079,0.6142,0.6148,0.6156,0.6235,0.6245,0.6328, 0.6441,0.6512,0.6537,0.6594,0.6600,0.6674,0.6760,0.6764,0.6771,0.6881, 0.6927,0.7032,0.7050,0.7070,0.7178,0.7208,0.7228,0.7256,0.7280,0.7353, 0.7395,0.7468,0.7499,0.7544,0.7584,0.7598,0.7742,0.7745,0.7755,0.7772, 0.7820,0.7825,0.7832,0.7842,0.7846,0.7915,0.7936,0.7944,0.7945,0.7961, 0.8035,0.8039,0.8068,0.8100,0.8101,0.8168,0.8237,0.8290,0.8324,0.8342, 0.8346,0.8362,0.8372,0.8435,0.8474,0.8491,0.8494,0.8502,0.8526,0.8559, 0.8601,0.8602,0.8622,0.8634,0.8648,0.8738,0.8787,0.8883,0.8903,0.8912, 0.8986,0.9014,0.9056,0.9104,0.9123,0.9127,0.9251,0.9308,0.9431,0.9499, 0.9506,0.9525,0.9537,0.9587,0.9693,0.9780,0.9894,0.9908,0.9927, Overall p-value after applying KStest on 269 p-values = 0.151115 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.