RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-06-23_18:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.62 19.0351 0.673482 2 to 25 15.87 22.0673 0.817857 3 to 26 15.79 12.4301 0.226575 4 to 27 15.82 26.0975 0.927298 5 to 28 16.00 10.7231 0.129407 6 to 29 16.02 10.4217 0.114997 7 to 30 15.63 16.0851 0.482191 8 to 31 15.80 16.3555 0.501212 9 to 32 15.60 21.1588 0.780732 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.980596 Tough bday spacings test for dh-ranFile-2016-06-23_18:31: 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 14 28 68 107 115 64 59 26 13 4 2 (O-E)^2/E 2.6 2.0 0.4 0.9 3.1 2.6 0.9 0.5 0.2 1.0 1.0 Birthday Spacings: Sum(O-E)^2/E= 15.206, p= 0.875 RESULTS OF GCD FOR dh-ranFile-2016-06-23_18:31 Euclid's algorithm: p-value, steps to gcd: 0.419748 p-value, dist. of gcd's: 0.807795 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-06-23_18:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.796 0.276 0.816 0.620 0.510 0.670 0.937 0.858 Bits 8 to 15---> 0.851 0.123 0.526 0.265 0.191 0.696 0.622 0.114 Bits 16 to 23---> 0.424 0.507 0.495 0.199 0.336 0.134 0.770 0.079 Bits 24 to 31---> 0.762 0.459 0.065 0.325 0.935 0.832 0.154 0.537 KS test for the above 32 p values: 0.053 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-06-23_18:31, p-values for 5 runs: 0.5664, 0.2052, 0.4779, 0.4603, 0.2477 Rank test for binary matrices (31x31) for dh-ranFile-2016-06-23_18:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 217 211.4 0.147 0.147 r= 29 5181 5134.0 0.430 0.577 r= 30 23024 23103.0 0.270 0.848 r= 31 11578 11551.5 0.061 0.909 chi-square = 0.909 with df = 3; p-value = 0.177 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-06-23_18:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 229 211.4 1.462 1.462 r= 30 5190 5134.0 0.611 2.073 r= 31 23076 23103.0 0.032 2.104 r= 32 11505 11551.5 0.187 2.292 chi-square = 2.292 with df = 3; p-value = 0.486 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-06-23_18:31 b-rank test for bits 1 to 8, p=0.88251 b-rank test for bits 2 to 9, p=0.25817 b-rank test for bits 3 to 10, p=0.17632 b-rank test for bits 4 to 11, p=0.93090 b-rank test for bits 5 to 12, p=0.85442 b-rank test for bits 6 to 13, p=0.39251 b-rank test for bits 7 to 14, p=0.95266 b-rank test for bits 8 to 15, p=0.35798 b-rank test for bits 9 to 16, p=0.33278 b-rank test for bits 10 to 17, p=0.36639 b-rank test for bits 11 to 18, p=0.12035 b-rank test for bits 12 to 19, p=0.34131 b-rank test for bits 13 to 20, p=0.73485 b-rank test for bits 14 to 21, p=0.85821 b-rank test for bits 15 to 22, p=0.67595 b-rank test for bits 16 to 23, p=0.22929 b-rank test for bits 17 to 24, p=0.02162 b-rank test for bits 18 to 25, p=0.93618 b-rank test for bits 19 to 26, p=0.46243 b-rank test for bits 20 to 27, p=0.83998 b-rank test for bits 21 to 28, p=0.66346 b-rank test for bits 22 to 29, p=0.55722 b-rank test for bits 23 to 30, p=0.43642 b-rank test for bits 24 to 31, p=0.44012 b-rank test for bits 25 to 32, p=0.61489 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 = 0.741828 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-06-23_18:31 (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 141908 -0.00 0.498760 2 141707 -0.47 0.318202 3 142362 1.06 0.854890 4 142730 1.92 0.972410 5 142320 0.96 0.831349 6 141601 -0.72 0.235640 7 142431 1.22 0.888550 8 142123 0.50 0.691191 9 141828 -0.19 0.424645 10 142170 0.61 0.728752 11 142119 0.49 0.687892 12 141844 -0.15 0.439341 13 142928 2.38 0.991345 14 140612 -3.03 0.001218 15 143189 2.99 0.998605 16 141263 -1.51 0.065507 17 142126 0.51 0.693655 18 142774 2.02 0.978322 19 142006 0.23 0.589347 20 142194 0.67 0.747012 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-06-23_18:31 Bits used No. missing words z-score p-value 23 to 32 142348 1.5127 0.934816 22 to 31 142201 1.0058 0.842734 21 to 30 141672 -0.8184 0.206570 20 to 29 141696 -0.7356 0.230981 19 to 28 141861 -0.1667 0.433821 18 to 27 142063 0.5299 0.701908 17 to 26 141856 -0.1839 0.427047 16 to 25 141415 -1.7046 0.044136 15 to 24 142196 0.9885 0.838550 14 to 23 142119 0.7230 0.765160 13 to 22 141756 -0.5287 0.298498 12 to 21 142112 0.6989 0.757681 11 to 20 142165 0.8816 0.811009 10 to 19 142179 0.9299 0.823788 9 to 18 141881 -0.0977 0.461089 8 to 17 141657 -0.8701 0.192122 7 to 16 141642 -0.9218 0.178309 6 to 15 141936 0.0920 0.536637 5 to 14 141599 -1.0701 0.142286 4 to 13 141993 0.2885 0.613525 3 to 12 141644 -0.9149 0.180114 2 to 11 141828 -0.2804 0.389567 1 to 10 141897 -0.0425 0.483043 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-06-23_18:31 Bits used No. missing words z-score p-value 28 to 32 142189 0.9480 0.828444 27 to 31 141923 0.0463 0.518480 26 to 30 141560 -1.1842 0.118173 25 to 29 142723 2.7582 0.997094 24 to 28 141879 -0.1028 0.459056 23 to 27 141976 0.2260 0.589399 22 to 26 142146 0.8023 0.788802 21 to 25 142148 0.8091 0.790757 20 to 24 141536 -1.2655 0.102842 19 to 23 142413 1.7074 0.956122 18 to 22 142030 0.4091 0.658749 17 to 21 141919 0.0328 0.513075 16 to 20 142209 1.0158 0.845145 15 to 19 142479 1.9311 0.973264 14 to 18 142154 0.8294 0.796558 13 to 17 141556 -1.1977 0.115511 12 to 16 142083 0.5887 0.721973 11 to 15 141886 -0.0791 0.468483 10 to 14 141688 -0.7503 0.226546 9 to 13 141764 -0.4926 0.311132 8 to 12 141762 -0.4994 0.308741 7 to 11 141967 0.1955 0.577496 6 to 10 141915 0.0192 0.507667 5 to 9 142062 0.5175 0.697605 4 to 8 141712 -0.6689 0.251775 3 to 7 141850 -0.2011 0.420303 2 to 6 141743 -0.5638 0.286435 1 to 5 141474 -1.4757 0.070013 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-06-23_18:31 Bits used No. missing words z-score p-value 31 to 32 142105 0.5772 0.718097 30 to 31 142260 1.0344 0.849531 29 to 30 141834 -0.2222 0.412074 28 to 29 142503 1.7512 0.960048 27 to 28 141802 -0.3166 0.375771 26 to 27 142092 0.5388 0.705005 25 to 26 142555 1.9046 0.971586 24 to 25 142111 0.5949 0.724044 23 to 24 142428 1.5300 0.936992 22 to 23 142259 1.0315 0.848841 21 to 22 141998 0.2616 0.603171 20 to 21 142054 0.4268 0.665221 19 to 20 142115 0.6067 0.727974 18 to 19 142087 0.5241 0.699896 17 to 18 142341 1.2734 0.898555 16 to 17 141543 -1.0806 0.139933 15 to 16 142330 1.2409 0.892681 14 to 15 142127 0.6421 0.739594 13 to 14 142423 1.5153 0.935146 12 to 13 141846 -0.1868 0.425903 11 to 12 142798 2.6214 0.995622 10 to 11 141943 0.0993 0.539559 9 to 10 142063 0.4533 0.674835 8 to 9 142135 0.6657 0.747196 7 to 8 141432 -1.4081 0.079558 6 to 7 141674 -0.6942 0.243782 5 to 6 141789 -0.3550 0.361311 4 to 5 141885 -0.0718 0.471393 3 to 4 142026 0.3442 0.634637 2 to 3 142031 0.3589 0.640168 1 to 2 142103 0.5713 0.716101 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-06-23_18:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2505.04 0.071 0.528426 Test results for specific bytes for dh-ranFile-2016-06-23_18:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2521.09 0.298 0.617268 2 to 9 2452.98 -0.665 0.253033 3 to 10 2509.49 0.134 0.553362 4 to 11 2634.64 1.904 0.971553 5 to 12 2600.73 1.425 0.922855 6 to 13 2549.51 0.700 0.758100 7 to 14 2562.63 0.886 0.812130 8 to 15 2564.94 0.918 0.820786 9 to 16 2550.73 0.717 0.763445 10 to 17 2468.94 -0.439 0.330243 11 to 18 2415.43 -1.196 0.115836 12 to 19 2591.09 1.288 0.901175 13 to 20 2582.47 1.166 0.878253 14 to 21 2501.48 0.021 0.508330 15 to 22 2528.91 0.409 0.658686 16 to 23 2544.96 0.636 0.737578 17 to 24 2536.94 0.522 0.699291 18 to 25 2559.11 0.836 0.798415 19 to 26 2453.66 -0.655 0.256117 20 to 27 2611.62 1.578 0.942772 21 to 28 2545.98 0.650 0.742253 22 to 29 2455.67 -0.627 0.265355 23 to 30 2644.89 2.049 0.979774 24 to 31 2554.74 0.774 0.780586 25 to 32 2627.96 1.810 0.964821 CDPARK for dh-ranFile-2016-06-23_18:31: 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 3509 -0.6393 0.261324 3513 -0.4566 0.323972 3523 0.0000 0.500000 3540 0.7763 0.781201 3496 -1.2329 0.108811 3490 -1.5068 0.065925 3512 -0.5023 0.307734 3505 -0.8219 0.205562 3515 -0.3653 0.357445 3553 1.3699 0.914635 Square side=100, avg. no. parked=3515.60 sample std.=18.07 p-value of the KSTEST for those 10 p-values: 0.302485 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-06-23_18:31 0.6810,0.2175,0.3594,0.0451,0.6855,0.1875,0.7646,0.7027,0.7406,0.7598, The KS test for those 10 p-values: 0.542329 The 3DSPHERES test for dh-ranFile-2016-06-23_18:31 sample no r^3 equiv. uni. 1 12.558 0.342041 2 17.843 0.448311 3 28.565 0.614091 4 10.076 0.285275 5 6.042 0.182406 6 24.887 0.563756 7 46.512 0.787834 8 21.487 0.511413 9 14.935 0.392163 10 9.448 0.270174 11 1.223 0.039950 12 84.512 0.940220 13 156.058 0.994494 14 19.085 0.470685 15 45.600 0.781286 16 5.419 0.165256 17 47.706 0.796114 18 1.688 0.054715 19 8.125 0.237253 20 6.885 0.205073 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.737283 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-06-23_18:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 0.5 0.6 0.3 -0.7 -0.8 0.1 0.8 2.1 -1.3 1.1 2.2 0.2 0.2 -0.8 0.5 0.3 -1.8 0.6 0.7 -0.4 -1.4 0.3 0.1 -1.5 0.3 -1.5 0.9 -0.4 0.9 -1.3 -0.1 1.4 -0.8 0.6 1.0 -1.4 -0.4 1.3 -0.7 -0.6 0.0 -0.1 Chi-square with 42 degrees of freedom:39.679485 z-score=-0.253189, p-value=0.426674 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-06-23_18:31 Test no p-value 1 0.723119 2 0.937667 3 0.094698 4 0.733232 5 0.425441 6 0.139462 7 0.007018 8 0.210434 9 0.002475 10 0.317509 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.069251 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-06-23_18:31: (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 66693 0.01 66606 0.06 3 25000.00 24997 0.00 25073 0.21 4 6666.67 6721 0.44 6681 0.03 5 1388.89 1332 2.33 1393 0.01 6 238.10 230 0.28 215 2.24 7 34.72 22 4.66 23 3.96 8 4.96 4 0.19 8 1.86 p=0.75485 p=0.78783 Number of rngs required: 688696, p-value: 0.632 RESULTS OF CRAPS TEST for dh-ranFile-2016-06-23_18:31 No. of wins: Observed Expected 98486 98585.9 z-score=-0.447, pvalue=0.32757 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66623 66666.7 0.029 0.029 2 38090 37654.3 5.041 5.070 3 26798 26954.7 0.911 5.981 4 19331 19313.5 0.016 5.997 5 13651 13851.4 2.900 8.897 6 9938 9943.5 0.003 8.900 7 7151 7145.0 0.005 8.905 8 5110 5139.1 0.164 9.069 9 3779 3699.9 1.693 10.762 10 2644 2666.3 0.186 10.948 11 1842 1923.3 3.439 14.387 12 1390 1388.7 0.001 14.389 13 1015 1003.7 0.127 14.516 14 738 726.1 0.194 14.709 15 520 525.8 0.065 14.774 16 347 381.2 3.060 17.834 17 271 276.5 0.111 17.945 18 224 200.8 2.673 20.618 19 143 146.0 0.061 20.679 20 117 106.2 1.095 21.774 21 278 287.1 0.289 22.063 Chisq= 22.06 for 20 degrees of freedom, p= 0.66292 SUMMARY of craptest p-value for no. of wins: 0.327573 p-value for throws/game: 0.662915 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-06-23_18:31 No. of wins: Observed Expected 98608 98585.9 z-score= 0.099, pvalue=0.53944 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66413 66666.7 0.965 0.965 2 37521 37654.3 0.472 1.437 3 27032 26954.7 0.221 1.659 4 19542 19313.5 2.704 4.363 5 13972 13851.4 1.050 5.413 6 10025 9943.5 0.667 6.080 7 7093 7145.0 0.379 6.459 8 5167 5139.1 0.152 6.611 9 3741 3699.9 0.457 7.068 10 2645 2666.3 0.170 7.238 11 1829 1923.3 4.626 11.864 12 1343 1388.7 1.507 13.371 13 945 1003.7 3.435 16.806 14 760 726.1 1.579 18.384 15 563 525.8 2.627 21.011 16 398 381.2 0.745 21.756 17 304 276.5 2.727 24.483 18 205 200.8 0.087 24.569 19 127 146.0 2.469 27.038 20 118 106.2 1.308 28.346 21 257 287.1 3.159 31.504 Chisq= 31.50 for 20 degrees of freedom, p= 0.95112 SUMMARY of craptest p-value for no. of wins: 0.539443 p-value for throws/game: 0.951124 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0012,0.0025,0.0070,0.0216,0.0400,0.0441,0.0451,0.0534,0.0547,0.0655, 0.0655,0.0659,0.0693,0.0700,0.0794,0.0796,0.0947,0.1028,0.1088,0.1137, 0.1150,0.1155,0.1158,0.1182,0.1203,0.1226,0.1294,0.1338,0.1395,0.1399, 0.1423,0.1540,0.1653,0.1763,0.1766,0.1783,0.1801,0.1824,0.1875,0.1911, 0.1921,0.1987,0.2051,0.2052,0.2056,0.2066,0.2104,0.2175,0.2265,0.2266, 0.2293,0.2310,0.2356,0.2373,0.2438,0.2477,0.2518,0.2530,0.2561,0.2582, 0.2613,0.2648,0.2654,0.2702,0.2761,0.2853,0.2864,0.2985,0.3025,0.3077, 0.3087,0.3111,0.3175,0.3182,0.3240,0.3253,0.3276,0.3302,0.3328,0.3355, 0.3413,0.3420,0.3574,0.3580,0.3594,0.3613,0.3664,0.3758,0.3896,0.3922, 0.3925,0.4121,0.4197,0.4203,0.4242,0.4246,0.4254,0.4259,0.4267,0.4270, 0.4338,0.4364,0.4393,0.4401,0.4483,0.4587,0.4591,0.4603,0.4611,0.4624, 0.4685,0.4707,0.4714,0.4779,0.4822,0.4830,0.4859,0.4951,0.4988,0.5000, 0.5012,0.5071,0.5077,0.5083,0.5096,0.5114,0.5131,0.5185,0.5255,0.5284, 0.5366,0.5375,0.5394,0.5396,0.5423,0.5534,0.5572,0.5638,0.5664,0.5775, 0.5893,0.5894,0.6032,0.6135,0.6141,0.6149,0.6173,0.6202,0.6221,0.6321, 0.6346,0.6402,0.6587,0.6587,0.6629,0.6635,0.6652,0.6696,0.6735,0.6748, 0.6760,0.6810,0.6855,0.6879,0.6912,0.6937,0.6958,0.6976,0.6993,0.6999, 0.7019,0.7027,0.7050,0.7161,0.7181,0.7220,0.7231,0.7240,0.7280,0.7288, 0.7332,0.7349,0.7373,0.7376,0.7396,0.7406,0.7418,0.7423,0.7470,0.7472, 0.7548,0.7577,0.7581,0.7598,0.7623,0.7634,0.7646,0.7652,0.7699,0.7806, 0.7807,0.7812,0.7813,0.7878,0.7878,0.7888,0.7908,0.7961,0.7964,0.7966, 0.7984,0.8078,0.8110,0.8121,0.8164,0.8179,0.8208,0.8238,0.8284,0.8313, 0.8323,0.8386,0.8400,0.8427,0.8451,0.8488,0.8495,0.8511,0.8544,0.8549, 0.8581,0.8582,0.8753,0.8783,0.8825,0.8886,0.8927,0.8986,0.9012,0.9146, 0.9229,0.9273,0.9309,0.9348,0.9351,0.9353,0.9362,0.9370,0.9373,0.9377, 0.9402,0.9428,0.9511,0.9527,0.9561,0.9600,0.9648,0.9716,0.9716,0.9724, 0.9733,0.9783,0.9798,0.9806,0.9913,0.9945,0.9956,0.9971,0.9986, Overall p-value after applying KStest on 269 p-values = 0.025557 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.