RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-07-31_07:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.94 13.9244 0.327554 2 to 25 16.11 11.9666 0.197847 3 to 26 15.94 15.4216 0.434857 4 to 27 15.69 17.4210 0.573786 5 to 28 15.64 31.6807 0.983518 6 to 29 15.80 19.0643 0.675145 7 to 30 15.94 15.7761 0.460240 8 to 31 16.00 17.9623 0.608779 9 to 32 15.88 20.4776 0.749469 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.610457 Tough bday spacings test for dh-ranFile-2015-07-31_07:31: 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 35 71 110 94 74 52 35 9 8 6 (O-E)^2/E 1.1 0.1 0.1 1.6 0.1 0.2 0.0 0.9 2.3 0.3 0.9 Birthday Spacings: Sum(O-E)^2/E= 7.598, p= 0.332 RESULTS OF GCD FOR dh-ranFile-2015-07-31_07:31 Euclid's algorithm: p-value, steps to gcd: 0.801859 p-value, dist. of gcd's: 0.808224 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-07-31_07:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.155 0.940 0.044 0.561 0.954 0.473 0.418 0.762 Bits 8 to 15---> 0.995 0.542 0.060 0.921 0.279 0.145 0.123 0.776 Bits 16 to 23---> 0.171 0.905 0.481 0.192 0.366 0.839 0.306 0.738 Bits 24 to 31---> 0.504 0.051 0.099 0.293 0.704 0.843 0.368 0.635 KS test for the above 32 p values: 0.060 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-07-31_07:31, p-values for 5 runs: 0.0424, 0.9210, 0.4407, 0.6018, 0.3105 Rank test for binary matrices (31x31) for dh-ranFile-2015-07-31_07:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 211 211.4 0.001 0.001 r= 29 5223 5134.0 1.542 1.543 r= 30 23024 23103.0 0.270 1.814 r= 31 11542 11551.5 0.008 1.822 chi-square = 1.822 with df = 3; p-value = 0.390 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-07-31_07:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 212 211.4 0.002 0.002 r= 30 5015 5134.0 2.759 2.760 r= 31 23184 23103.0 0.284 3.044 r= 32 11589 11551.5 0.122 3.166 chi-square = 3.166 with df = 3; p-value = 0.633 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-07-31_07:31 b-rank test for bits 1 to 8, p=0.81308 b-rank test for bits 2 to 9, p=0.11204 b-rank test for bits 3 to 10, p=0.71290 b-rank test for bits 4 to 11, p=0.76839 b-rank test for bits 5 to 12, p=0.28179 b-rank test for bits 6 to 13, p=0.20835 b-rank test for bits 7 to 14, p=0.55510 b-rank test for bits 8 to 15, p=0.74360 b-rank test for bits 9 to 16, p=0.57064 b-rank test for bits 10 to 17, p=0.73994 b-rank test for bits 11 to 18, p=0.31292 b-rank test for bits 12 to 19, p=0.57718 b-rank test for bits 13 to 20, p=0.22718 b-rank test for bits 14 to 21, p=0.81734 b-rank test for bits 15 to 22, p=0.61247 b-rank test for bits 16 to 23, p=0.73043 b-rank test for bits 17 to 24, p=0.82909 b-rank test for bits 18 to 25, p=0.90146 b-rank test for bits 19 to 26, p=0.15202 b-rank test for bits 20 to 27, p=0.60835 b-rank test for bits 21 to 28, p=0.24714 b-rank test for bits 22 to 29, p=0.87508 b-rank test for bits 23 to 30, p=0.65222 b-rank test for bits 24 to 31, p=0.51551 b-rank test for bits 25 to 32, p=0.89377 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 = 0.157631 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-07-31_07:31 (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 142298 0.91 0.818089 2 141812 -0.23 0.410054 3 142035 0.29 0.615476 4 141851 -0.14 0.445798 5 141891 -0.04 0.482920 6 142329 0.98 0.836590 7 142063 0.36 0.640218 8 141955 0.11 0.542489 9 141507 -0.94 0.173603 10 142471 1.31 0.905293 11 141837 -0.17 0.432900 12 141186 -1.69 0.045512 13 142083 0.41 0.657545 14 141711 -0.46 0.321543 15 142191 0.66 0.744765 16 142140 0.54 0.705039 17 142036 0.30 0.616369 18 141925 0.04 0.514603 19 141908 -0.00 0.498760 20 142594 1.60 0.945167 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-07-31_07:31 Bits used No. missing words z-score p-value 23 to 32 141972 0.2161 0.585547 22 to 31 142134 0.7747 0.780749 21 to 30 141533 -1.2977 0.097197 20 to 29 141954 0.1540 0.561209 19 to 28 142344 1.4989 0.933045 18 to 27 141693 -0.7460 0.227844 17 to 26 141534 -1.2942 0.097791 16 to 25 142207 1.0264 0.847660 15 to 24 141752 -0.5425 0.293731 14 to 23 141659 -0.8632 0.194012 13 to 22 141453 -1.5736 0.057796 12 to 21 142033 0.4264 0.665109 11 to 20 141803 -0.3667 0.356938 10 to 19 141893 -0.0563 0.477547 9 to 18 141829 -0.2770 0.390890 8 to 17 141528 -1.3149 0.094267 7 to 16 141253 -2.2632 0.011811 6 to 15 142038 0.4437 0.671367 5 to 14 141401 -1.7529 0.039813 4 to 13 141225 -2.3598 0.009143 3 to 12 141930 0.0713 0.528411 2 to 11 142060 0.5196 0.698312 1 to 10 141996 0.2989 0.617477 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-07-31_07:31 Bits used No. missing words z-score p-value 28 to 32 141547 -1.2282 0.109679 27 to 31 141835 -0.2520 0.400534 26 to 30 141964 0.1853 0.573512 25 to 29 142622 2.4158 0.992150 24 to 28 141867 -0.1435 0.442951 23 to 27 142227 1.0768 0.859226 22 to 26 142031 0.4124 0.659992 21 to 25 141631 -0.9435 0.172715 20 to 24 141857 -0.1774 0.429601 19 to 23 142142 0.7887 0.784860 18 to 22 142245 1.1379 0.872411 17 to 21 141550 -1.2181 0.111599 16 to 20 141872 -0.1265 0.449651 15 to 19 141677 -0.7876 0.215477 14 to 18 141587 -1.0926 0.137275 13 to 17 142196 0.9718 0.834416 12 to 16 141292 -2.0926 0.018190 11 to 15 142027 0.3989 0.655010 10 to 14 142023 0.3853 0.650001 9 to 13 142175 0.9006 0.816093 8 to 12 141994 0.2870 0.612950 7 to 11 141352 -1.8893 0.029429 6 to 10 141008 -3.0554 0.001124 5 to 9 141642 -0.9062 0.182414 4 to 8 141768 -0.4791 0.315939 3 to 7 141388 -1.7672 0.038596 2 to 6 142108 0.6735 0.749672 1 to 5 142150 0.8158 0.792702 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-07-31_07:31 Bits used No. missing words z-score p-value 31 to 32 142224 0.9282 0.823356 30 to 31 141564 -1.0187 0.154179 29 to 30 141733 -0.5201 0.301480 28 to 29 142787 2.5890 0.995187 27 to 28 141813 -0.2842 0.388144 26 to 27 141517 -1.1573 0.123572 25 to 26 142107 0.5831 0.720086 24 to 25 141878 -0.0924 0.463183 23 to 24 141685 -0.6617 0.254069 22 to 23 141682 -0.6706 0.251241 21 to 22 141447 -1.3638 0.086314 20 to 21 141947 0.1111 0.544240 19 to 20 141879 -0.0895 0.464355 18 to 19 142039 0.3825 0.648958 17 to 18 141925 0.0462 0.518434 16 to 17 142065 0.4592 0.676956 15 to 16 141705 -0.6027 0.273340 14 to 15 142322 1.2173 0.888258 13 to 14 142002 0.2734 0.607713 12 to 13 141558 -1.0364 0.150014 11 to 12 142081 0.5064 0.693713 10 to 11 141516 -1.1603 0.122970 9 to 10 141948 0.1141 0.545409 8 to 9 141653 -0.7561 0.224784 7 to 8 142465 1.6391 0.949408 6 to 7 141416 -1.4553 0.072800 5 to 6 141658 -0.7414 0.229230 4 to 5 141918 0.0256 0.510202 3 to 4 141384 -1.5496 0.060613 2 to 3 142369 1.3560 0.912444 1 to 2 141878 -0.0924 0.463183 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-07-31_07:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2446.65 -0.754 0.225277 Test results for specific bytes for dh-ranFile-2015-07-31_07:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2476.41 -0.334 0.369338 2 to 9 2501.19 0.017 0.506723 3 to 10 2437.57 -0.883 0.188629 4 to 11 2555.11 0.779 0.782106 5 to 12 2519.37 0.274 0.607906 6 to 13 2474.38 -0.362 0.358546 7 to 14 2596.78 1.369 0.914452 8 to 15 2414.04 -1.216 0.112057 9 to 16 2511.26 0.159 0.563261 10 to 17 2408.79 -1.290 0.098542 11 to 18 2361.36 -1.961 0.024961 12 to 19 2563.81 0.902 0.816564 13 to 20 2474.86 -0.356 0.361080 14 to 21 2488.90 -0.157 0.437623 15 to 22 2504.15 0.059 0.523427 16 to 23 2444.13 -0.790 0.214729 17 to 24 2435.31 -0.915 0.180150 18 to 25 2514.36 0.203 0.580464 19 to 26 2503.05 0.043 0.517218 20 to 27 2403.63 -1.363 0.086465 21 to 28 2514.11 0.200 0.579084 22 to 29 2407.52 -1.308 0.095455 23 to 30 2350.92 -2.108 0.017503 24 to 31 2507.23 0.102 0.540719 25 to 32 2533.67 0.476 0.683007 CDPARK for dh-ranFile-2015-07-31_07:31: 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 3492 -1.4155 0.078457 3511 -0.5479 0.291865 3529 0.2740 0.607947 3515 -0.3653 0.357445 3513 -0.4566 0.323972 3514 -0.4110 0.340551 3566 1.9635 0.975204 3497 -1.1872 0.117571 3527 0.1826 0.572463 Square side=100, avg. no. parked=3516.60 sample std.=19.90 p-value of the KSTEST for those 10 p-values: 0.267546 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-07-31_07:31 0.3799,0.8379,0.6269,0.0546,0.7417,0.6417,0.8887,0.1971,0.0956,0.4854, The KS test for those 10 p-values: 0.988886 The 3DSPHERES test for dh-ranFile-2015-07-31_07:31 sample no r^3 equiv. uni. 1 12.213 0.334432 2 69.981 0.902968 3 26.946 0.592700 4 52.277 0.824928 5 12.213 0.334424 6 7.874 0.230854 7 79.793 0.930035 8 12.975 0.351121 9 27.229 0.596522 10 0.181 0.006031 11 64.774 0.884576 12 28.338 0.611163 13 59.298 0.861461 14 27.566 0.601034 15 34.434 0.682664 16 7.844 0.230075 17 10.374 0.292354 18 2.064 0.066472 19 31.351 0.648315 20 18.572 0.461555 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.865402 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-07-31_07:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 0.1 0.6 1.6 -0.4 -0.2 -0.6 0.2 0.5 -0.6 -0.6 1.0 1.3 -0.5 -0.0 1.0 -2.5 0.4 -0.3 -0.6 -0.1 1.2 0.6 -0.7 0.1 -0.7 -1.4 1.4 0.2 0.4 0.1 1.2 -0.0 0.0 2.7 -0.5 0.3 1.5 1.7 0.4 0.1 -1.0 -0.1 Chi-square with 42 degrees of freedom:38.428580 z-score=-0.389674, p-value=0.371473 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-07-31_07:31 Test no p-value 1 0.312972 2 0.125682 3 0.936287 4 0.214656 5 0.269412 6 0.071980 7 0.050750 8 0.440314 9 0.620627 10 0.855489 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.355466 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-07-31_07:31: (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 66529 0.28 66842 0.46 3 25000.00 25099 0.39 24869 0.69 4 6666.67 6725 0.51 6618 0.36 5 1388.89 1399 0.07 1379 0.07 6 238.10 212 2.86 253 0.93 7 34.72 29 0.94 38 0.31 8 4.96 6 0.22 0 4.96 p=0.49166 p=0.74504 Number of rngs required: 687531, p-value: 0.156 RESULTS OF CRAPS TEST for dh-ranFile-2015-07-31_07:31 No. of wins: Observed Expected 98959 98585.9 z-score= 1.669, pvalue=0.95243 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66996 66666.7 1.627 1.627 2 37621 37654.3 0.029 1.656 3 26800 26954.7 0.888 2.545 4 19407 19313.5 0.453 2.998 5 13829 13851.4 0.036 3.034 6 9790 9943.5 2.371 5.405 7 7078 7145.0 0.629 6.034 8 5124 5139.1 0.044 6.078 9 3751 3699.9 0.707 6.785 10 2620 2666.3 0.804 7.588 11 1952 1923.3 0.427 8.016 12 1428 1388.7 1.110 9.126 13 1007 1003.7 0.011 9.136 14 736 726.1 0.134 9.270 15 488 525.8 2.722 11.993 16 372 381.2 0.220 12.212 17 274 276.5 0.023 12.236 18 217 200.8 1.302 13.538 19 136 146.0 0.683 14.221 20 89 106.2 2.790 17.011 21 285 287.1 0.016 17.026 Chisq= 17.03 for 20 degrees of freedom, p= 0.34874 SUMMARY of craptest p-value for no. of wins: 0.952432 p-value for throws/game: 0.348741 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-07-31_07:31 No. of wins: Observed Expected 98376 98585.9 z-score=-0.939, pvalue=0.17397 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66516 66666.7 0.341 0.341 2 37904 37654.3 1.656 1.996 3 27076 26954.7 0.546 2.542 4 19560 19313.5 3.147 5.689 5 13784 13851.4 0.328 6.017 6 9861 9943.5 0.685 6.702 7 6922 7145.0 6.962 13.664 8 5167 5139.1 0.152 13.815 9 3732 3699.9 0.279 14.095 10 2599 2666.3 1.699 15.793 11 1880 1923.3 0.976 16.769 12 1306 1388.7 4.930 21.699 13 1016 1003.7 0.150 21.849 14 740 726.1 0.265 22.114 15 501 525.8 1.173 23.287 16 413 381.2 2.661 25.948 17 269 276.5 0.206 26.154 18 225 200.8 2.909 29.063 19 138 146.0 0.437 29.499 20 95 106.2 1.184 30.683 21 296 287.1 0.275 30.959 Chisq= 30.96 for 20 degrees of freedom, p= 0.94426 SUMMARY of craptest p-value for no. of wins: 0.173966 p-value for throws/game: 0.944259 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0011,0.0060,0.0091,0.0118,0.0175,0.0182,0.0250,0.0294,0.0386,0.0398, 0.0424,0.0441,0.0455,0.0507,0.0513,0.0546,0.0578,0.0602,0.0603,0.0606, 0.0665,0.0720,0.0728,0.0785,0.0863,0.0865,0.0943,0.0955,0.0956,0.0972, 0.0978,0.0985,0.0993,0.1097,0.1116,0.1120,0.1121,0.1176,0.1226,0.1230, 0.1236,0.1257,0.1373,0.1450,0.1500,0.1520,0.1542,0.1548,0.1561,0.1576, 0.1688,0.1708,0.1727,0.1736,0.1740,0.1801,0.1824,0.1886,0.1923,0.1940, 0.1971,0.1978,0.2084,0.2147,0.2147,0.2155,0.2248,0.2253,0.2272,0.2278, 0.2292,0.2301,0.2309,0.2471,0.2512,0.2541,0.2675,0.2694,0.2733,0.2794, 0.2818,0.2919,0.2924,0.2931,0.2937,0.3015,0.3058,0.3105,0.3129,0.3130, 0.3159,0.3215,0.3240,0.3276,0.3320,0.3344,0.3344,0.3406,0.3487,0.3511, 0.3555,0.3569,0.3574,0.3585,0.3611,0.3657,0.3679,0.3693,0.3715,0.3799, 0.3881,0.3898,0.3909,0.4005,0.4101,0.4184,0.4296,0.4329,0.4349,0.4376, 0.4403,0.4407,0.4430,0.4458,0.4497,0.4602,0.4616,0.4632,0.4632,0.4644, 0.4728,0.4775,0.4813,0.4829,0.4854,0.4917,0.4988,0.5043,0.5067,0.5102, 0.5146,0.5155,0.5172,0.5184,0.5234,0.5284,0.5407,0.5424,0.5425,0.5442, 0.5454,0.5551,0.5605,0.5612,0.5633,0.5706,0.5725,0.5735,0.5738,0.5772, 0.5791,0.5805,0.5855,0.5927,0.5965,0.6010,0.6018,0.6077,0.6079,0.6079, 0.6083,0.6088,0.6105,0.6112,0.6125,0.6130,0.6155,0.6164,0.6175,0.6206, 0.6269,0.6332,0.6352,0.6402,0.6417,0.6483,0.6490,0.6500,0.6522,0.6550, 0.6575,0.6600,0.6651,0.6714,0.6751,0.6770,0.6827,0.6830,0.6937,0.6983, 0.7041,0.7050,0.7129,0.7201,0.7304,0.7384,0.7399,0.7417,0.7436,0.7448, 0.7450,0.7495,0.7497,0.7621,0.7684,0.7763,0.7807,0.7821,0.7849,0.7927, 0.8019,0.8082,0.8131,0.8161,0.8166,0.8173,0.8181,0.8234,0.8249,0.8291, 0.8344,0.8366,0.8379,0.8391,0.8430,0.8477,0.8555,0.8592,0.8615,0.8654, 0.8724,0.8751,0.8846,0.8883,0.8887,0.8938,0.9015,0.9030,0.9052,0.9053, 0.9124,0.9145,0.9209,0.9210,0.9300,0.9330,0.9363,0.9403,0.9443,0.9452, 0.9494,0.9524,0.9540,0.9752,0.9835,0.9889,0.9922,0.9952,0.9954, Overall p-value after applying KStest on 269 p-values = 0.405768 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.