RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-06-12_19:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.87 15.9439 0.472187 2 to 25 15.76 13.6469 0.308079 3 to 26 15.94 12.0577 0.203368 4 to 27 15.72 10.9773 0.142256 5 to 28 16.11 12.3232 0.219819 6 to 29 15.90 22.8104 0.844475 7 to 30 15.72 21.2599 0.785119 8 to 31 15.86 14.8819 0.396014 9 to 32 15.91 18.2638 0.627617 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.756401 Tough bday spacings test for dh-ranFile-2015-06-12_19:31: 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 7 30 80 103 87 78 61 29 9 10 6 (O-E)^2/E 0.5 1.2 0.6 0.3 1.2 0.0 1.5 0.0 2.3 1.7 0.9 Birthday Spacings: Sum(O-E)^2/E= 10.306, p= 0.586 RESULTS OF GCD FOR dh-ranFile-2015-06-12_19:31 Euclid's algorithm: p-value, steps to gcd: 0.704013 p-value, dist. of gcd's: 0.937175 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-06-12_19:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.780 0.821 0.057 0.565 0.248 0.913 0.904 0.947 Bits 8 to 15---> 0.577 0.375 0.411 0.906 0.773 0.077 0.166 0.240 Bits 16 to 23---> 0.047 0.068 0.170 0.379 0.832 0.264 0.003 0.378 Bits 24 to 31---> 0.562 0.425 0.348 0.522 0.823 0.969 0.265 0.519 KS test for the above 32 p values: 0.195 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-06-12_19:31, p-values for 5 runs: 0.8575, 0.8598, 0.0502, 0.8192, 0.2388 Rank test for binary matrices (31x31) for dh-ranFile-2015-06-12_19:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 207 211.4 0.092 0.092 r= 29 5141 5134.0 0.010 0.102 r= 30 23108 23103.0 0.001 0.103 r= 31 11544 11551.5 0.005 0.108 chi-square = 0.108 with df = 3; p-value = 0.009 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-06-12_19:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 226 211.4 1.006 1.006 r= 30 5118 5134.0 0.050 1.056 r= 31 23168 23103.0 0.183 1.238 r= 32 11488 11551.5 0.349 1.588 chi-square = 1.588 with df = 3; p-value = 0.338 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-06-12_19:31 b-rank test for bits 1 to 8, p=0.53349 b-rank test for bits 2 to 9, p=0.27842 b-rank test for bits 3 to 10, p=0.75484 b-rank test for bits 4 to 11, p=0.40281 b-rank test for bits 5 to 12, p=0.18678 b-rank test for bits 6 to 13, p=0.27275 b-rank test for bits 7 to 14, p=0.70604 b-rank test for bits 8 to 15, p=0.23236 b-rank test for bits 9 to 16, p=0.16489 b-rank test for bits 10 to 17, p=0.15104 b-rank test for bits 11 to 18, p=0.35886 b-rank test for bits 12 to 19, p=0.01891 b-rank test for bits 13 to 20, p=0.03784 b-rank test for bits 14 to 21, p=0.19395 b-rank test for bits 15 to 22, p=0.80057 b-rank test for bits 16 to 23, p=0.67424 b-rank test for bits 17 to 24, p=0.93555 b-rank test for bits 18 to 25, p=0.05903 b-rank test for bits 19 to 26, p=0.13384 b-rank test for bits 20 to 27, p=0.05962 b-rank test for bits 21 to 28, p=0.96851 b-rank test for bits 22 to 29, p=0.05619 b-rank test for bits 23 to 30, p=0.66479 b-rank test for bits 24 to 31, p=0.95764 b-rank test for bits 25 to 32, p=0.00005 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 = 0.021606 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-06-12_19:31 (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 142105 0.46 0.676227 2 142030 0.28 0.611005 3 141957 0.11 0.544342 4 140759 -2.69 0.003597 5 141812 -0.23 0.410054 6 142004 0.22 0.587528 7 141217 -1.62 0.052875 8 142169 0.61 0.727977 9 142024 0.27 0.605620 10 141998 0.21 0.582063 11 142111 0.47 0.681248 12 142260 0.82 0.793699 13 142667 1.77 0.961658 14 141306 -1.41 0.079322 15 141468 -1.03 0.151236 16 141783 -0.30 0.383935 17 142473 1.32 0.906078 18 141831 -0.18 0.427394 19 142010 0.24 0.592977 20 142871 2.25 0.987677 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-06-12_19:31 Bits used No. missing words z-score p-value 23 to 32 142250 1.1747 0.879947 22 to 31 142268 1.2368 0.891918 21 to 30 142044 0.4644 0.678812 20 to 29 141822 -0.3011 0.381655 19 to 28 141616 -1.0115 0.155893 18 to 27 142268 1.2368 0.891918 17 to 26 141853 -0.1942 0.422994 16 to 25 142264 1.2230 0.889335 15 to 24 141988 0.2713 0.606911 14 to 23 141902 -0.0253 0.489918 13 to 22 142130 0.7609 0.776651 12 to 21 142232 1.1127 0.867072 11 to 20 142024 0.3954 0.653731 10 to 19 142051 0.4885 0.687408 9 to 18 141840 -0.2391 0.405526 8 to 17 141550 -1.2391 0.107660 7 to 16 141982 0.2506 0.598933 6 to 15 141964 0.1885 0.574764 5 to 14 141734 -0.6046 0.272727 4 to 13 141751 -0.5460 0.292545 3 to 12 141444 -1.6046 0.054292 2 to 11 141697 -0.7322 0.232032 1 to 10 142027 0.4058 0.657540 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-06-12_19:31 Bits used No. missing words z-score p-value 28 to 32 141060 -2.8791 0.001994 27 to 31 142032 0.4158 0.661233 26 to 30 141459 -1.5265 0.063437 25 to 29 141836 -0.2486 0.401844 24 to 28 141513 -1.3435 0.089556 23 to 27 142083 0.5887 0.721973 22 to 26 142425 1.7480 0.959771 21 to 25 142642 2.4836 0.993497 20 to 24 142135 0.7650 0.777859 19 to 23 141970 0.2057 0.581472 18 to 22 141413 -1.6825 0.046238 17 to 21 141903 -0.0215 0.491440 16 to 20 141741 -0.5706 0.284132 15 to 19 141727 -0.6181 0.268265 14 to 18 141728 -0.6147 0.269384 13 to 17 142419 1.7277 0.957979 12 to 16 141576 -1.1299 0.129252 11 to 15 142345 1.4768 0.930142 10 to 14 141877 -0.1096 0.456366 9 to 13 142330 1.4260 0.923066 8 to 12 141540 -1.2520 0.105291 7 to 11 142159 0.8463 0.801318 6 to 10 141679 -0.7808 0.217466 5 to 9 141687 -0.7537 0.225526 4 to 8 141685 -0.7604 0.223496 3 to 7 141617 -0.9909 0.160855 2 to 6 141560 -1.1842 0.118173 1 to 5 141802 -0.3638 0.357992 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-06-12_19:31 Bits used No. missing words z-score p-value 31 to 32 141862 -0.1396 0.444482 30 to 31 141962 0.1554 0.561735 29 to 30 142088 0.5271 0.700921 28 to 29 141814 -0.2812 0.389275 27 to 28 141992 0.2439 0.596332 26 to 27 141550 -1.0600 0.144579 25 to 26 141885 -0.0718 0.471393 24 to 25 142132 0.6568 0.744359 23 to 24 141803 -0.3137 0.376891 22 to 23 141494 -1.2252 0.110257 21 to 22 141492 -1.2311 0.109150 20 to 21 141833 -0.2252 0.410927 19 to 20 141876 -0.0983 0.460840 18 to 19 141173 -2.1721 0.014925 17 to 18 141809 -0.2960 0.383631 16 to 17 141970 0.1790 0.571018 15 to 16 141948 0.1141 0.545409 14 to 15 141680 -0.6765 0.249365 13 to 14 142395 1.4327 0.924022 12 to 13 142070 0.4740 0.682233 11 to 12 142548 1.8840 0.970216 10 to 11 142167 0.7601 0.776399 9 to 10 141959 0.1465 0.558244 8 to 9 140940 -2.8594 0.002122 7 to 8 141732 -0.5231 0.300453 6 to 7 141879 -0.0895 0.464355 5 to 6 141812 -0.2871 0.387014 4 to 5 142386 1.4061 0.920154 3 to 4 142002 0.2734 0.607713 2 to 3 142173 0.7778 0.781653 1 to 2 142396 1.4356 0.924443 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-06-12_19:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2591.77 1.298 0.902836 Test results for specific bytes for dh-ranFile-2015-06-12_19:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2602.97 1.456 0.927325 2 to 9 2572.03 1.019 0.845823 3 to 10 2466.60 -0.472 0.318328 4 to 11 2447.02 -0.749 0.226845 5 to 12 2414.69 -1.206 0.113829 6 to 13 2560.92 0.862 0.805531 7 to 14 2581.15 1.148 0.874432 8 to 15 2434.27 -0.930 0.176293 9 to 16 2449.47 -0.715 0.237410 10 to 17 2488.51 -0.163 0.435433 11 to 18 2366.88 -1.883 0.029874 12 to 19 2531.35 0.443 0.671250 13 to 20 2442.40 -0.815 0.207647 14 to 21 2445.54 -0.770 0.220594 15 to 22 2496.68 -0.047 0.481271 16 to 23 2576.57 1.083 0.860569 17 to 24 2481.81 -0.257 0.398474 18 to 25 2437.47 -0.884 0.188248 19 to 26 2555.81 0.789 0.785010 20 to 27 2493.33 -0.094 0.462430 21 to 28 2526.34 0.372 0.645232 22 to 29 2663.10 2.307 0.989460 23 to 30 2558.25 0.824 0.794974 24 to 31 2625.37 1.773 0.961880 25 to 32 2434.38 -0.928 0.176711 CDPARK for dh-ranFile-2015-06-12_19:31: 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 3538 0.6849 0.753306 3551 1.2785 0.899470 3531 0.3653 0.642555 3535 0.5479 0.708135 3538 0.6849 0.753306 3541 0.8219 0.794438 3503 -0.9132 0.180558 3504 -0.8676 0.192812 3540 0.7763 0.781201 3559 1.6438 0.949895 Square side=100, avg. no. parked=3534.00 sample std.=17.04 p-value of the KSTEST for those 10 p-values: 0.074478 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-06-12_19:31 0.0588,0.8590,0.0650,0.3658,0.0411,0.2425,0.3939,0.7159,0.4657,0.5899, The KS test for those 10 p-values: 0.285748 The 3DSPHERES test for dh-ranFile-2015-06-12_19:31 sample no r^3 equiv. uni. 1 31.236 0.646974 2 7.445 0.219766 3 131.628 0.987570 4 45.604 0.781317 5 20.774 0.499655 6 2.170 0.069790 7 58.090 0.855770 8 1.146 0.037475 9 15.825 0.409928 10 3.984 0.124356 11 1.506 0.048962 12 4.148 0.129136 13 2.089 0.067264 14 37.924 0.717519 15 18.751 0.464752 16 43.160 0.762754 17 63.109 0.877986 18 2.417 0.077411 19 5.284 0.161505 20 22.202 0.522920 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.180969 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-06-12_19:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.1 2.0 -0.3 0.5 -1.5 0.4 0.1 0.1 0.4 1.2 -0.6 -0.3 1.9 -0.5 -0.1 -2.2 0.1 0.7 -1.0 0.7 -1.1 1.0 0.2 1.3 -0.6 -0.9 -0.2 -0.0 -0.1 0.1 0.2 -0.5 0.8 0.9 0.8 -0.5 1.8 0.5 0.4 1.6 1.0 -1.1 Chi-square with 42 degrees of freedom:35.451127 z-score=-0.714541, p-value=0.247726 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-06-12_19:31 Test no p-value 1 0.009813 2 0.020188 3 0.002722 4 0.334688 5 0.808426 6 0.916777 7 0.176587 8 0.402813 9 0.337575 10 0.146548 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.015900 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-06-12_19:31: (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 66636 0.01 66634 0.02 3 25000.00 25093 0.35 24948 0.11 4 6666.67 6597 0.73 6735 0.70 5 1388.89 1386 0.01 1427 1.05 6 238.10 247 0.33 225 0.72 7 34.72 37 0.15 28 1.30 8 4.96 3 0.77 2 1.77 p=0.11529 p=0.53738 Number of rngs required: 688812, p-value: 0.681 RESULTS OF CRAPS TEST for dh-ranFile-2015-06-12_19:31 No. of wins: Observed Expected 98779 98585.9 z-score= 0.864, pvalue=0.80616 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66727 66666.7 0.055 0.055 2 37754 37654.3 0.264 0.318 3 27006 26954.7 0.098 0.416 4 19312 19313.5 0.000 0.416 5 13639 13851.4 3.258 3.674 6 9990 9943.5 0.217 3.891 7 7032 7145.0 1.788 5.679 8 5106 5139.1 0.213 5.891 9 3693 3699.9 0.013 5.904 10 2638 2666.3 0.300 6.205 11 1979 1923.3 1.611 7.816 12 1366 1388.7 0.372 8.188 13 1040 1003.7 1.312 9.500 14 745 726.1 0.490 9.990 15 510 525.8 0.477 10.467 16 369 381.2 0.387 10.854 17 328 276.5 9.576 20.430 18 215 200.8 1.000 21.430 19 155 146.0 0.557 21.987 20 126 106.2 3.685 25.672 21 270 287.1 1.020 26.692 Chisq= 26.69 for 20 degrees of freedom, p= 0.85586 SUMMARY of craptest p-value for no. of wins: 0.806162 p-value for throws/game: 0.855855 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-06-12_19:31 No. of wins: Observed Expected 98735 98585.9 z-score= 0.667, pvalue=0.74763 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66653 66666.7 0.003 0.003 2 37827 37654.3 0.792 0.795 3 27129 26954.7 1.127 1.921 4 18989 19313.5 5.451 7.372 5 13801 13851.4 0.184 7.556 6 9907 9943.5 0.134 7.690 7 7197 7145.0 0.378 8.068 8 5227 5139.1 1.504 9.573 9 3726 3699.9 0.185 9.757 10 2659 2666.3 0.020 9.777 11 1798 1923.3 8.167 17.944 12 1377 1388.7 0.099 18.043 13 1025 1003.7 0.451 18.495 14 701 726.1 0.870 19.365 15 529 525.8 0.019 19.384 16 387 381.2 0.090 19.474 17 293 276.5 0.980 20.454 18 196 200.8 0.116 20.570 19 166 146.0 2.744 23.314 20 103 106.2 0.097 23.411 21 310 287.1 1.824 25.236 Chisq= 25.24 for 20 degrees of freedom, p= 0.80743 SUMMARY of craptest p-value for no. of wins: 0.747629 p-value for throws/game: 0.807434 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0000,0.0020,0.0021,0.0026,0.0027,0.0036,0.0091,0.0098,0.0149,0.0159, 0.0189,0.0202,0.0216,0.0299,0.0375,0.0378,0.0411,0.0462,0.0471,0.0490, 0.0502,0.0529,0.0543,0.0562,0.0572,0.0588,0.0590,0.0596,0.0634,0.0650, 0.0673,0.0678,0.0698,0.0745,0.0771,0.0774,0.0793,0.0896,0.1053,0.1077, 0.1091,0.1103,0.1138,0.1153,0.1182,0.1244,0.1291,0.1293,0.1338,0.1423, 0.1446,0.1465,0.1510,0.1512,0.1559,0.1609,0.1615,0.1649,0.1656,0.1697, 0.1763,0.1766,0.1767,0.1806,0.1810,0.1868,0.1882,0.1928,0.1940,0.1952, 0.2034,0.2076,0.2175,0.2198,0.2198,0.2206,0.2235,0.2255,0.2268,0.2320, 0.2324,0.2374,0.2388,0.2397,0.2425,0.2477,0.2479,0.2494,0.2636,0.2649, 0.2683,0.2694,0.2727,0.2727,0.2784,0.2841,0.2857,0.2925,0.3005,0.3081, 0.3183,0.3347,0.3376,0.3378,0.3481,0.3580,0.3589,0.3658,0.3754,0.3769, 0.3783,0.3789,0.3817,0.3836,0.3839,0.3870,0.3893,0.3939,0.3960,0.3985, 0.4018,0.4028,0.4028,0.4055,0.4099,0.4101,0.4109,0.4111,0.4230,0.4246, 0.4274,0.4354,0.4445,0.4564,0.4608,0.4624,0.4644,0.4648,0.4657,0.4714, 0.4722,0.4813,0.4899,0.4914,0.4997,0.5188,0.5220,0.5229,0.5335,0.5374, 0.5443,0.5454,0.5582,0.5617,0.5622,0.5654,0.5710,0.5748,0.5770,0.5815, 0.5821,0.5859,0.5875,0.5899,0.5930,0.5963,0.5989,0.6056,0.6069,0.6077, 0.6110,0.6276,0.6426,0.6452,0.6470,0.6537,0.6575,0.6612,0.6648,0.6713, 0.6742,0.6762,0.6788,0.6812,0.6813,0.6822,0.6874,0.7009,0.7040,0.7060, 0.7081,0.7159,0.7175,0.7220,0.7280,0.7444,0.7476,0.7533,0.7533,0.7548, 0.7564,0.7628,0.7733,0.7764,0.7767,0.7779,0.7803,0.7812,0.7813,0.7817, 0.7850,0.7851,0.7937,0.7944,0.7950,0.8006,0.8013,0.8055,0.8062,0.8074, 0.8084,0.8192,0.8214,0.8232,0.8321,0.8445,0.8458,0.8558,0.8559,0.8575, 0.8590,0.8598,0.8606,0.8671,0.8744,0.8780,0.8799,0.8893,0.8919,0.8919, 0.8995,0.9028,0.9040,0.9057,0.9061,0.9129,0.9168,0.9202,0.9231,0.9240, 0.9244,0.9273,0.9301,0.9355,0.9372,0.9469,0.9499,0.9576,0.9580,0.9598, 0.9617,0.9619,0.9685,0.9693,0.9702,0.9876,0.9877,0.9895,0.9935, Overall p-value after applying KStest on 269 p-values = 0.051239 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.