RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-03-26_17:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 16.00 10.6943 0.127994 2 to 25 15.86 16.9163 0.539951 3 to 26 16.00 15.8922 0.468509 4 to 27 15.66 16.8454 0.535115 5 to 28 16.01 19.1880 0.682154 6 to 29 15.95 10.3745 0.112826 7 to 30 15.94 16.8857 0.537865 8 to 31 15.81 16.0205 0.477615 9 to 32 15.86 26.8691 0.939984 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.643400 Tough bday spacings test for dh-ranFile-2018-03-26_17:31: 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 6 42 77 100 101 68 58 33 10 3 2 (O-E)^2/E 1.1 0.8 0.2 0.1 0.1 1.3 0.7 0.4 1.6 2.0 1.0 Birthday Spacings: Sum(O-E)^2/E= 9.200, p= 0.487 RESULTS OF GCD FOR dh-ranFile-2018-03-26_17:31 Euclid's algorithm: p-value, steps to gcd: 0.482370 p-value, dist. of gcd's: 0.067744 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-03-26_17:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.617 0.197 0.900 0.774 0.860 0.280 0.491 0.810 Bits 8 to 15---> 0.331 0.573 0.025 0.317 0.760 0.909 0.959 0.463 Bits 16 to 23---> 0.962 0.796 0.768 0.380 0.899 0.396 0.958 0.458 Bits 24 to 31---> 0.832 0.512 0.702 0.515 0.635 0.556 0.331 0.518 KS test for the above 32 p values: 0.956 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-03-26_17:31, p-values for 5 runs: 0.8374, 0.0694, 0.2917, 0.9890, 0.7564 Rank test for binary matrices (31x31) for dh-ranFile-2018-03-26_17:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 220 211.4 0.348 0.348 r= 29 5087 5134.0 0.430 0.779 r= 30 23112 23103.0 0.003 0.782 r= 31 11581 11551.5 0.075 0.858 chi-square = 0.858 with df = 3; p-value = 0.164 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-03-26_17:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 221 211.4 0.434 0.434 r= 30 5142 5134.0 0.012 0.447 r= 31 23091 23103.0 0.006 0.453 r= 32 11546 11551.5 0.003 0.456 chi-square = 0.456 with df = 3; p-value = 0.071 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-03-26_17:31 b-rank test for bits 1 to 8, p=0.95781 b-rank test for bits 2 to 9, p=0.78226 b-rank test for bits 3 to 10, p=0.39970 b-rank test for bits 4 to 11, p=0.72796 b-rank test for bits 5 to 12, p=0.43946 b-rank test for bits 6 to 13, p=0.75279 b-rank test for bits 7 to 14, p=0.69823 b-rank test for bits 8 to 15, p=0.09272 b-rank test for bits 9 to 16, p=0.82182 b-rank test for bits 10 to 17, p=0.25409 b-rank test for bits 11 to 18, p=0.10578 b-rank test for bits 12 to 19, p=0.05365 b-rank test for bits 13 to 20, p=0.35490 b-rank test for bits 14 to 21, p=0.92984 b-rank test for bits 15 to 22, p=0.83292 b-rank test for bits 16 to 23, p=0.86815 b-rank test for bits 17 to 24, p=0.43766 b-rank test for bits 18 to 25, p=0.81776 b-rank test for bits 19 to 26, p=0.16054 b-rank test for bits 20 to 27, p=0.91796 b-rank test for bits 21 to 28, p=0.78222 b-rank test for bits 22 to 29, p=0.42319 b-rank test for bits 23 to 30, p=0.86343 b-rank test for bits 24 to 31, p=0.53268 b-rank test for bits 25 to 32, p=0.84165 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 = 0.113572 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-03-26_17:31 (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 141314 -1.39 0.082119 2 141506 -0.94 0.173004 3 141422 -1.14 0.127431 4 141688 -0.52 0.302534 5 141905 -0.01 0.495964 6 141583 -0.76 0.222895 7 141701 -0.49 0.313217 8 140999 -2.13 0.016713 9 142024 0.27 0.605620 10 141743 -0.39 0.348778 11 141640 -0.63 0.264584 12 141482 -1.00 0.159034 13 141565 -0.80 0.210551 14 142328 0.98 0.836013 15 142324 0.97 0.833691 16 141879 -0.07 0.471753 17 142660 1.75 0.960276 18 142438 1.24 0.891624 19 142682 1.81 0.964486 20 141178 -1.71 0.043752 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-03-26_17:31 Bits used No. missing words z-score p-value 23 to 32 142020 0.3816 0.648629 22 to 31 141820 -0.3080 0.379028 21 to 30 141912 0.0092 0.503673 20 to 29 141858 -0.1770 0.429754 19 to 28 141590 -1.1011 0.135418 18 to 27 141800 -0.3770 0.353087 17 to 26 142143 0.8058 0.789809 16 to 25 141824 -0.2942 0.384287 15 to 24 141772 -0.4736 0.317910 14 to 23 141950 0.1402 0.555765 13 to 22 141639 -0.9322 0.175624 12 to 21 141632 -0.9563 0.169458 11 to 20 142036 0.4368 0.668869 10 to 19 141680 -0.7908 0.214532 9 to 18 141950 0.1402 0.555765 8 to 17 142064 0.5333 0.703103 7 to 16 141800 -0.3770 0.353087 6 to 15 141694 -0.7425 0.228887 5 to 14 141802 -0.3701 0.355653 4 to 13 142152 0.8368 0.798646 3 to 12 142174 0.9127 0.819288 2 to 11 141717 -0.6632 0.253599 1 to 10 141893 -0.0563 0.477547 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-03-26_17:31 Bits used No. missing words z-score p-value 28 to 32 141766 -0.4859 0.313532 27 to 31 141483 -1.4452 0.074203 26 to 30 141871 -0.1299 0.448310 25 to 29 141816 -0.3164 0.375860 24 to 28 141393 -1.7503 0.040036 23 to 27 141687 -0.7537 0.225526 22 to 26 141923 0.0463 0.518480 21 to 25 141518 -1.3265 0.092330 20 to 24 142059 0.5074 0.694048 19 to 23 141765 -0.4893 0.312331 18 to 22 142398 1.6565 0.951191 17 to 21 142018 0.3684 0.643702 16 to 20 141602 -1.0418 0.148753 15 to 19 141860 -0.1672 0.433598 14 to 18 142403 1.6735 0.952881 13 to 17 142229 1.0836 0.860735 12 to 16 142014 0.3548 0.638635 11 to 15 142236 1.1074 0.865930 10 to 14 142004 0.3209 0.625863 9 to 13 141868 -0.1401 0.444290 8 to 12 142053 0.4870 0.686877 7 to 11 141831 -0.2655 0.395302 6 to 10 141659 -0.8486 0.198059 5 to 9 141695 -0.7265 0.233753 4 to 8 142130 0.7480 0.772780 3 to 7 141640 -0.9130 0.180626 2 to 6 142093 0.6226 0.733230 1 to 5 142170 0.8836 0.811551 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-03-26_17:31 Bits used No. missing words z-score p-value 31 to 32 142171 0.7719 0.779910 30 to 31 141682 -0.6706 0.251241 29 to 30 141281 -1.8535 0.031907 28 to 29 142240 0.9754 0.835326 27 to 28 142626 2.1141 0.982745 26 to 27 141609 -0.8859 0.187828 25 to 26 141818 -0.2694 0.393807 24 to 25 141017 -2.6322 0.004241 23 to 24 141972 0.1849 0.573333 22 to 23 141754 -0.4582 0.323404 21 to 22 141594 -0.9302 0.176140 20 to 21 142075 0.4887 0.687474 19 to 20 141553 -1.0511 0.146602 18 to 19 142511 1.7748 0.962038 17 to 18 141674 -0.6942 0.243782 16 to 17 141975 0.1937 0.576801 15 to 16 141379 -1.5644 0.058862 14 to 15 141838 -0.2104 0.416673 13 to 14 141707 -0.5968 0.275306 12 to 13 141703 -0.6086 0.271381 11 to 12 142213 0.8958 0.814815 10 to 11 142026 0.3442 0.634637 9 to 10 141966 0.1672 0.566381 8 to 9 142210 0.8869 0.812442 7 to 8 141612 -0.8771 0.190222 6 to 7 141880 -0.0865 0.465527 5 to 6 142226 0.9341 0.824882 4 to 5 141836 -0.2163 0.414372 3 to 4 141900 -0.0275 0.489022 2 to 3 142097 0.5536 0.710073 1 to 2 141940 0.0905 0.536044 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-03-26_17:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2507.09 0.100 0.539937 Test results for specific bytes for dh-ranFile-2018-03-26_17:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2552.30 0.740 0.770247 2 to 9 2583.63 1.183 0.881548 3 to 10 2474.23 -0.364 0.357774 4 to 11 2482.55 -0.247 0.402553 5 to 12 2488.93 -0.157 0.437778 6 to 13 2540.22 0.569 0.715238 7 to 14 2466.82 -0.469 0.319465 8 to 15 2565.43 0.925 0.822595 9 to 16 2418.82 -1.148 0.125468 10 to 17 2562.37 0.882 0.811124 11 to 18 2472.10 -0.395 0.346576 12 to 19 2487.46 -0.177 0.429626 13 to 20 2664.06 2.320 0.989835 14 to 21 2436.52 -0.898 0.184650 15 to 22 2455.45 -0.630 0.264346 16 to 23 2508.13 0.115 0.545788 17 to 24 2604.72 1.481 0.930686 18 to 25 2498.56 -0.020 0.491865 19 to 26 2512.94 0.183 0.572596 20 to 27 2432.93 -0.949 0.171437 21 to 28 2454.88 -0.638 0.261686 22 to 29 2678.34 2.522 0.994167 23 to 30 2417.81 -1.162 0.122556 24 to 31 2542.38 0.599 0.725523 25 to 32 2497.69 -0.033 0.486970 CDPARK for dh-ranFile-2018-03-26_17:31: 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 3502 -0.9589 0.168804 3478 -2.0548 0.019949 3527 0.1826 0.572463 3482 -1.8721 0.030593 3504 -0.8676 0.192812 3551 1.2785 0.899470 3525 0.0913 0.536383 3524 0.0457 0.518210 3549 1.1872 0.882429 3530 0.3196 0.625377 Square side=100, avg. no. parked=3517.20 sample std.=23.88 p-value of the KSTEST for those 10 p-values: 0.559621 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-03-26_17:31 0.5115,0.4520,0.9816,0.6851,0.6578,0.3824,0.6525,0.7652,0.9435,0.0065, The KS test for those 10 p-values: 0.300335 The 3DSPHERES test for dh-ranFile-2018-03-26_17:31 sample no r^3 equiv. uni. 1 8.712 0.252035 2 59.738 0.863478 3 18.909 0.467570 4 49.382 0.807194 5 15.618 0.405844 6 144.487 0.991903 7 6.039 0.182341 8 15.282 0.399150 9 10.612 0.297949 10 39.227 0.729524 11 28.657 0.615272 12 4.800 0.147848 13 63.354 0.878981 14 60.163 0.865396 15 5.090 0.156053 16 5.696 0.172933 17 111.311 0.975531 18 1.176 0.038429 19 8.405 0.244349 20 7.159 0.212288 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.588970 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-03-26_17:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.5 -0.6 0.9 -0.7 0.9 0.8 -0.6 -1.1 -0.9 0.5 -0.3 0.5 -0.6 -1.8 1.5 -1.6 0.7 0.8 -0.5 2.6 1.5 -0.7 -0.5 -0.7 -1.3 -0.5 0.5 -0.4 1.3 0.1 0.2 -0.9 -0.3 -0.9 1.0 0.0 -0.1 0.9 -0.7 0.1 0.0 0.8 Chi-square with 42 degrees of freedom:35.465976 z-score=-0.712920, p-value=0.248300 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-03-26_17:31 Test no p-value 1 0.808579 2 0.052133 3 0.820721 4 0.175376 5 0.072487 6 0.275569 7 0.142051 8 0.011632 9 0.162637 10 0.333961 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.015230 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-03-26_17:31: (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 66659 0.00 66726 0.05 3 25000.00 24982 0.01 25004 0.00 4 6666.67 6632 0.18 6588 0.93 5 1388.89 1430 1.22 1399 0.07 6 238.10 260 2.02 237 0.01 7 34.72 28 1.30 43 1.97 8 4.96 8 1.86 2 1.77 p=0.63958 p=0.43048 Number of rngs required: 687755, p-value: 0.227 RESULTS OF CRAPS TEST for dh-ranFile-2018-03-26_17:31 No. of wins: Observed Expected 98803 98585.9 z-score= 0.971, pvalue=0.83427 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67024 66666.7 1.915 1.915 2 37553 37654.3 0.273 2.188 3 26863 26954.7 0.312 2.500 4 19374 19313.5 0.190 2.690 5 13771 13851.4 0.467 3.157 6 9905 9943.5 0.149 3.306 7 7142 7145.0 0.001 3.307 8 5219 5139.1 1.243 4.551 9 3711 3699.9 0.034 4.584 10 2596 2666.3 1.853 6.438 11 1900 1923.3 0.283 6.720 12 1340 1388.7 1.711 8.431 13 1014 1003.7 0.105 8.536 14 687 726.1 2.110 10.646 15 521 525.8 0.044 10.691 16 340 381.2 4.443 15.134 17 293 276.5 0.980 16.113 18 209 200.8 0.332 16.446 19 142 146.0 0.109 16.554 20 112 106.2 0.315 16.869 21 284 287.1 0.034 16.903 Chisq= 16.90 for 20 degrees of freedom, p= 0.34075 SUMMARY of craptest p-value for no. of wins: 0.834271 p-value for throws/game: 0.340754 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-03-26_17:31 No. of wins: Observed Expected 98550 98585.9 z-score=-0.160, pvalue=0.43629 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66900 66666.7 0.817 0.817 2 37629 37654.3 0.017 0.834 3 27024 26954.7 0.178 1.012 4 19341 19313.5 0.039 1.051 5 13712 13851.4 1.403 2.454 6 9928 9943.5 0.024 2.479 7 7120 7145.0 0.088 2.566 8 5110 5139.1 0.164 2.731 9 3622 3699.9 1.639 4.369 10 2652 2666.3 0.077 4.446 11 1906 1923.3 0.156 4.602 12 1357 1388.7 0.725 5.328 13 1037 1003.7 1.104 6.431 14 716 726.1 0.142 6.573 15 530 525.8 0.033 6.606 16 388 381.2 0.123 6.729 17 274 276.5 0.023 6.752 18 212 200.8 0.621 7.374 19 141 146.0 0.170 7.544 20 105 106.2 0.014 7.558 21 296 287.1 0.275 7.833 Chisq= 7.83 for 20 degrees of freedom, p= 0.00708 SUMMARY of craptest p-value for no. of wins: 0.436291 p-value for throws/game: 0.007083 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0042,0.0065,0.0071,0.0116,0.0152,0.0167,0.0199,0.0245,0.0306,0.0319, 0.0384,0.0400,0.0438,0.0521,0.0536,0.0589,0.0677,0.0694,0.0715,0.0725, 0.0742,0.0821,0.0923,0.0927,0.1058,0.1128,0.1136,0.1226,0.1255,0.1274, 0.1280,0.1354,0.1421,0.1466,0.1478,0.1488,0.1561,0.1590,0.1605,0.1626, 0.1643,0.1688,0.1695,0.1714,0.1729,0.1730,0.1754,0.1756,0.1761,0.1806, 0.1823,0.1847,0.1878,0.1902,0.1928,0.1968,0.1981,0.2106,0.2123,0.2145, 0.2229,0.2255,0.2271,0.2289,0.2338,0.2438,0.2443,0.2483,0.2512,0.2520, 0.2536,0.2541,0.2617,0.2643,0.2646,0.2714,0.2753,0.2756,0.2797,0.2917, 0.2979,0.3003,0.3025,0.3123,0.3132,0.3135,0.3173,0.3179,0.3195,0.3234, 0.3309,0.3314,0.3340,0.3408,0.3466,0.3488,0.3531,0.3531,0.3549,0.3557, 0.3578,0.3759,0.3790,0.3800,0.3824,0.3843,0.3938,0.3953,0.3962,0.3991, 0.3997,0.4026,0.4058,0.4144,0.4167,0.4232,0.4296,0.4298,0.4305,0.4336, 0.4363,0.4377,0.4378,0.4395,0.4443,0.4483,0.4520,0.4584,0.4632,0.4655, 0.4676,0.4685,0.4718,0.4775,0.4776,0.4824,0.4867,0.4870,0.4890,0.4906, 0.4919,0.4960,0.5037,0.5115,0.5121,0.5145,0.5182,0.5182,0.5185,0.5327, 0.5351,0.5360,0.5364,0.5379,0.5399,0.5400,0.5458,0.5558,0.5558,0.5562, 0.5596,0.5664,0.5725,0.5726,0.5732,0.5733,0.5768,0.5890,0.6056,0.6153, 0.6175,0.6254,0.6259,0.6346,0.6346,0.6386,0.6396,0.6434,0.6437,0.6486, 0.6525,0.6578,0.6689,0.6822,0.6851,0.6869,0.6875,0.6940,0.6982,0.7021, 0.7031,0.7101,0.7152,0.7255,0.7280,0.7295,0.7332,0.7528,0.7564,0.7603, 0.7652,0.7682,0.7702,0.7728,0.7738,0.7799,0.7822,0.7823,0.7898,0.7964, 0.7986,0.8072,0.8086,0.8097,0.8111,0.8116,0.8124,0.8148,0.8178,0.8193, 0.8207,0.8218,0.8226,0.8249,0.8322,0.8329,0.8337,0.8343,0.8353,0.8360, 0.8374,0.8416,0.8596,0.8607,0.8634,0.8635,0.8654,0.8659,0.8682,0.8790, 0.8815,0.8824,0.8916,0.8989,0.8995,0.9003,0.9091,0.9180,0.9298,0.9307, 0.9400,0.9435,0.9512,0.9529,0.9557,0.9578,0.9582,0.9586,0.9603,0.9620, 0.9620,0.9645,0.9755,0.9816,0.9827,0.9890,0.9898,0.9919,0.9942, Overall p-value after applying KStest on 269 p-values = 0.907640 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.