RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-12-27_09:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.70 15.7378 0.457506 2 to 25 15.83 28.5700 0.961297 3 to 26 15.86 8.7281 0.051593 4 to 27 15.68 31.2186 0.981217 5 to 28 15.71 19.9105 0.721169 6 to 29 15.97 19.8356 0.717275 7 to 30 16.03 21.6464 0.801296 8 to 31 15.89 25.6417 0.918759 9 to 32 15.68 23.6082 0.869521 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.019989 Tough bday spacings test for dh-ranFile-2015-12-27_09:31: 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 8 27 85 88 101 70 59 38 16 3 5 (O-E)^2/E 0.1 2.5 1.9 1.0 0.1 0.8 0.9 2.3 0.1 2.0 0.2 Birthday Spacings: Sum(O-E)^2/E= 11.945, p= 0.711 RESULTS OF GCD FOR dh-ranFile-2015-12-27_09:31 Euclid's algorithm: p-value, steps to gcd: 0.677328 p-value, dist. of gcd's: 0.604572 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-12-27_09:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.491 0.259 0.420 0.059 0.367 0.937 0.530 0.405 Bits 8 to 15---> 0.715 0.159 0.261 0.606 0.038 0.156 0.051 0.494 Bits 16 to 23---> 0.692 0.547 0.160 0.437 0.570 0.470 0.101 0.521 Bits 24 to 31---> 0.638 0.951 0.293 0.168 0.721 0.577 0.033 0.714 KS test for the above 32 p values: 0.844 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-12-27_09:31, p-values for 5 runs: 0.0321, 0.8556, 0.3091, 0.1158, 0.1856 Rank test for binary matrices (31x31) for dh-ranFile-2015-12-27_09:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 206 211.4 0.139 0.139 r= 29 5140 5134.0 0.007 0.146 r= 30 23128 23103.0 0.027 0.173 r= 31 11526 11551.5 0.056 0.229 chi-square = 0.229 with df = 3; p-value = 0.027 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-12-27_09:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 224 211.4 0.749 0.749 r= 30 5159 5134.0 0.122 0.870 r= 31 22931 23103.0 1.281 2.152 r= 32 11686 11551.5 1.565 3.717 chi-square = 3.717 with df = 3; p-value = 0.706 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-12-27_09:31 b-rank test for bits 1 to 8, p=0.29856 b-rank test for bits 2 to 9, p=0.92844 b-rank test for bits 3 to 10, p=0.04562 b-rank test for bits 4 to 11, p=0.38884 b-rank test for bits 5 to 12, p=0.18332 b-rank test for bits 6 to 13, p=0.67485 b-rank test for bits 7 to 14, p=0.14886 b-rank test for bits 8 to 15, p=0.04177 b-rank test for bits 9 to 16, p=0.28806 b-rank test for bits 10 to 17, p=0.94924 b-rank test for bits 11 to 18, p=0.52075 b-rank test for bits 12 to 19, p=0.55858 b-rank test for bits 13 to 20, p=0.84527 b-rank test for bits 14 to 21, p=0.41135 b-rank test for bits 15 to 22, p=0.27361 b-rank test for bits 16 to 23, p=0.76532 b-rank test for bits 17 to 24, p=0.30606 b-rank test for bits 18 to 25, p=0.71362 b-rank test for bits 19 to 26, p=0.22554 b-rank test for bits 20 to 27, p=0.81111 b-rank test for bits 21 to 28, p=0.53277 b-rank test for bits 22 to 29, p=0.11483 b-rank test for bits 23 to 30, p=0.07447 b-rank test for bits 24 to 31, p=0.11245 b-rank test for bits 25 to 32, p=0.18916 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 = 0.246374 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-12-27_09:31 (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 142264 0.83 0.796354 2 141569 -0.80 0.213259 3 141624 -0.67 0.252495 4 142551 1.50 0.933093 5 141796 -0.26 0.395586 6 141362 -1.28 0.100482 7 141665 -0.57 0.284046 8 141976 0.16 0.561893 9 141854 -0.13 0.448570 10 141497 -0.96 0.167676 11 141648 -0.61 0.270738 12 142042 0.31 0.621711 13 141783 -0.30 0.383935 14 142380 1.10 0.864268 15 141743 -0.39 0.348778 16 141600 -0.72 0.234922 17 141737 -0.40 0.343607 18 142011 0.24 0.593884 19 141794 -0.27 0.393787 20 141948 0.09 0.535996 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-12-27_09:31 Bits used No. missing words z-score p-value 23 to 32 141962 0.1816 0.572060 22 to 31 141958 0.1678 0.566641 21 to 30 141643 -0.9184 0.179210 20 to 29 142300 1.3471 0.911032 19 to 28 142422 1.7678 0.961455 18 to 27 142608 2.4092 0.992006 17 to 26 142023 0.3920 0.652458 16 to 25 142245 1.1575 0.876462 15 to 24 141962 0.1816 0.572060 14 to 23 141979 0.2402 0.594928 13 to 22 142357 1.5437 0.938668 12 to 21 142003 0.3230 0.626652 11 to 20 142165 0.8816 0.811009 10 to 19 141670 -0.8253 0.204608 9 to 18 142060 0.5196 0.698312 8 to 17 141817 -0.3184 0.375099 7 to 16 142040 0.4506 0.673856 6 to 15 142236 1.1264 0.870012 5 to 14 142009 0.3437 0.634460 4 to 13 141260 -2.2391 0.012576 3 to 12 142162 0.8713 0.808198 2 to 11 141878 -0.1080 0.456984 1 to 10 142197 0.9920 0.839393 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-12-27_09:31 Bits used No. missing words z-score p-value 28 to 32 142301 1.3277 0.907861 27 to 31 142135 0.7650 0.777859 26 to 30 142252 1.1616 0.877300 25 to 29 142090 0.6124 0.729877 24 to 28 141893 -0.0554 0.477928 23 to 27 141815 -0.3198 0.374574 22 to 26 141401 -1.7232 0.042430 21 to 25 141456 -1.5367 0.062182 20 to 24 142034 0.4226 0.663710 19 to 23 141649 -0.8825 0.188760 18 to 22 142642 2.4836 0.993497 17 to 21 141805 -0.3537 0.361797 16 to 20 141914 0.0158 0.506315 15 to 19 141778 -0.4452 0.328093 14 to 18 141908 -0.0045 0.498201 13 to 17 141703 -0.6994 0.242144 12 to 16 142065 0.5277 0.701145 11 to 15 141478 -1.4621 0.071852 10 to 14 141773 -0.4621 0.321992 9 to 13 141914 0.0158 0.506315 8 to 12 142030 0.4091 0.658749 7 to 11 141841 -0.2316 0.408414 6 to 10 142215 1.0362 0.849938 5 to 9 142070 0.5446 0.707001 4 to 8 141977 0.2294 0.590717 3 to 7 141739 -0.5774 0.281838 2 to 6 141869 -0.1367 0.445629 1 to 5 141793 -0.3943 0.346665 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-12-27_09:31 Bits used No. missing words z-score p-value 31 to 32 141998 0.2616 0.603171 30 to 31 142708 2.3560 0.990763 29 to 30 141646 -0.7768 0.218643 28 to 29 141448 -1.3609 0.086780 27 to 28 141773 -0.4022 0.343786 26 to 27 142125 0.6362 0.737675 25 to 26 141644 -0.7827 0.216906 24 to 25 142399 1.4445 0.925694 23 to 24 141829 -0.2370 0.406343 22 to 23 141991 0.2409 0.595189 21 to 22 141667 -0.7148 0.237355 20 to 21 142043 0.3943 0.653323 19 to 20 141504 -1.1957 0.115914 18 to 19 141933 0.0698 0.527833 17 to 18 141404 -1.4906 0.068027 16 to 17 141758 -0.4464 0.327654 15 to 16 141581 -0.9685 0.166391 14 to 15 142349 1.2970 0.902678 13 to 14 141097 -2.3963 0.008282 12 to 13 141831 -0.2311 0.408633 11 to 12 142068 0.4681 0.680127 10 to 11 141222 -2.0275 0.021305 9 to 10 142221 0.9194 0.821052 8 to 9 142509 1.7689 0.961548 7 to 8 141826 -0.2458 0.402914 6 to 7 142181 0.8014 0.788546 5 to 6 142147 0.7011 0.758377 4 to 5 141838 -0.2104 0.416673 3 to 4 141966 0.1672 0.566381 2 to 3 141995 0.2527 0.599755 1 to 2 141862 -0.1396 0.444482 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-12-27_09:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2441.01 -0.834 0.202052 Test results for specific bytes for dh-ranFile-2015-12-27_09:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2637.66 1.947 0.974218 2 to 9 2518.54 0.262 0.603388 3 to 10 2526.76 0.378 0.647428 4 to 11 2417.03 -1.173 0.120311 5 to 12 2382.62 -1.660 0.048453 6 to 13 2514.12 0.200 0.579113 7 to 14 2468.51 -0.445 0.328040 8 to 15 2521.77 0.308 0.620890 9 to 16 2557.99 0.820 0.793938 10 to 17 2415.25 -1.198 0.115365 11 to 18 2419.61 -1.137 0.127790 12 to 19 2614.48 1.619 0.947277 13 to 20 2448.92 -0.722 0.235017 14 to 21 2503.38 0.048 0.519083 15 to 22 2543.59 0.616 0.731188 16 to 23 2515.61 0.221 0.587340 17 to 24 2539.33 0.556 0.710989 18 to 25 2445.84 -0.766 0.221857 19 to 26 2512.09 0.171 0.567905 20 to 27 2581.75 1.156 0.876187 21 to 28 2593.64 1.324 0.907285 22 to 29 2436.66 -0.896 0.185173 23 to 30 2640.87 1.992 0.976827 24 to 31 2540.47 0.572 0.716447 25 to 32 2552.55 0.743 0.771327 CDPARK for dh-ranFile-2015-12-27_09:31: 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 3478 -2.0548 0.019949 3485 -1.7352 0.041356 3515 -0.3653 0.357445 3538 0.6849 0.753306 3514 -0.4110 0.340551 3521 -0.0913 0.463617 3556 1.5068 0.934075 3520 -0.1370 0.445521 3517 -0.2740 0.392053 3540 0.7763 0.781201 Square side=100, avg. no. parked=3518.40 sample std.=22.48 p-value of the KSTEST for those 10 p-values: 0.683636 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-12-27_09:31 0.9299,0.0373,0.0448,0.4157,0.4315,0.4664,0.5318,0.8871,0.5846,0.8302, The KS test for those 10 p-values: 0.773933 The 3DSPHERES test for dh-ranFile-2015-12-27_09:31 sample no r^3 equiv. uni. 1 38.617 0.723970 2 58.450 0.857486 3 29.925 0.631203 4 15.138 0.396250 5 58.216 0.856371 6 4.779 0.147258 7 11.709 0.323146 8 42.449 0.757069 9 13.130 0.354450 10 69.222 0.900480 11 15.132 0.396141 12 12.710 0.345368 13 0.285 0.009464 14 10.155 0.287159 15 77.500 0.924478 16 4.882 0.150187 17 121.572 0.982619 18 20.312 0.491892 19 45.457 0.780244 20 16.493 0.422907 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.793966 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-12-27_09:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.5 -1.3 -1.0 -0.8 0.6 0.0 -0.8 -0.7 1.1 0.6 0.3 0.8 -0.1 0.7 -0.8 -0.6 -0.7 1.1 0.1 0.9 0.1 -0.7 -0.1 0.8 -0.4 -0.9 -1.1 -0.1 -0.5 -1.0 -0.3 -1.0 -1.4 0.8 1.1 -0.5 0.5 -0.4 -1.8 -0.6 0.0 0.8 Chi-square with 42 degrees of freedom:25.920918 z-score=-1.754372, p-value=0.024321 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-12-27_09:31 Test no p-value 1 0.272666 2 0.123616 3 0.902579 4 0.074161 5 0.962688 6 0.045143 7 0.124741 8 0.171806 9 0.127807 10 0.543381 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.035253 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-12-27_09:31: (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 66474 0.56 66912 0.90 3 25000.00 25064 0.16 24835 1.09 4 6666.67 6757 1.22 6590 0.88 5 1388.89 1429 1.16 1393 0.01 6 238.10 234 0.07 230 0.28 7 34.72 36 0.05 35 0.00 8 4.96 5 0.00 4 0.19 p=0.21934 p=0.23606 Number of rngs required: 688622, p-value: 0.599 RESULTS OF CRAPS TEST for dh-ranFile-2015-12-27_09:31 No. of wins: Observed Expected 98448 98585.9 z-score=-0.617, pvalue=0.26875 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66954 66666.7 1.238 1.238 2 37630 37654.3 0.016 1.254 3 26876 26954.7 0.230 1.484 4 19307 19313.5 0.002 1.486 5 13885 13851.4 0.081 1.568 6 9937 9943.5 0.004 1.572 7 7093 7145.0 0.379 1.951 8 5013 5139.1 3.093 5.044 9 3630 3699.9 1.319 6.363 10 2600 2666.3 1.648 8.011 11 1969 1923.3 1.084 9.096 12 1386 1388.7 0.005 9.101 13 1002 1003.7 0.003 9.104 14 753 726.1 0.994 10.098 15 557 525.8 1.847 11.945 16 392 381.2 0.309 12.253 17 263 276.5 0.663 12.916 18 205 200.8 0.087 13.003 19 149 146.0 0.062 13.065 20 101 106.2 0.256 13.321 21 298 287.1 0.413 13.734 Chisq= 13.73 for 20 degrees of freedom, p= 0.15628 SUMMARY of craptest p-value for no. of wins: 0.268755 p-value for throws/game: 0.156281 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-12-27_09:31 No. of wins: Observed Expected 98766 98585.9 z-score= 0.806, pvalue=0.78979 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66829 66666.7 0.395 0.395 2 37943 37654.3 2.213 2.608 3 26797 26954.7 0.923 3.531 4 19105 19313.5 2.250 5.782 5 13999 13851.4 1.572 7.354 6 9963 9943.5 0.038 7.392 7 7223 7145.0 0.851 8.243 8 5027 5139.1 2.444 10.687 9 3634 3699.9 1.173 11.860 10 2526 2666.3 7.382 19.242 11 1912 1923.3 0.067 19.309 12 1418 1388.7 0.616 19.925 13 1028 1003.7 0.588 20.513 14 713 726.1 0.238 20.750 15 564 525.8 2.770 23.520 16 353 381.2 2.079 25.599 17 277 276.5 0.001 25.600 18 194 200.8 0.232 25.832 19 148 146.0 0.028 25.860 20 91 106.2 2.180 28.040 21 256 287.1 3.372 31.412 Chisq= 31.41 for 20 degrees of freedom, p= 0.95001 SUMMARY of craptest p-value for no. of wins: 0.789791 p-value for throws/game: 0.950014 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0083,0.0095,0.0126,0.0199,0.0200,0.0213,0.0243,0.0273,0.0321,0.0331, 0.0353,0.0373,0.0378,0.0414,0.0418,0.0424,0.0448,0.0451,0.0456,0.0485, 0.0513,0.0516,0.0588,0.0622,0.0680,0.0719,0.0742,0.0745,0.0868,0.1005, 0.1006,0.1124,0.1148,0.1154,0.1158,0.1159,0.1203,0.1236,0.1247,0.1278, 0.1278,0.1473,0.1489,0.1502,0.1563,0.1563,0.1585,0.1595,0.1664,0.1677, 0.1678,0.1718,0.1792,0.1833,0.1852,0.1856,0.1888,0.1892,0.2021,0.2046, 0.2133,0.2169,0.2186,0.2193,0.2219,0.2255,0.2349,0.2350,0.2361,0.2374, 0.2421,0.2464,0.2525,0.2589,0.2612,0.2688,0.2707,0.2727,0.2736,0.2818, 0.2840,0.2872,0.2881,0.2927,0.2986,0.3061,0.3091,0.3220,0.3231,0.3277, 0.3280,0.3281,0.3406,0.3436,0.3438,0.3454,0.3467,0.3488,0.3544,0.3574, 0.3618,0.3670,0.3746,0.3751,0.3839,0.3888,0.3921,0.3938,0.3956,0.3961, 0.3962,0.4029,0.4054,0.4063,0.4084,0.4086,0.4114,0.4157,0.4167,0.4202, 0.4229,0.4315,0.4375,0.4445,0.4455,0.4456,0.4486,0.4570,0.4575,0.4636, 0.4664,0.4698,0.4779,0.4913,0.4919,0.4937,0.4982,0.5063,0.5063,0.5191, 0.5208,0.5208,0.5278,0.5297,0.5318,0.5328,0.5360,0.5434,0.5473,0.5586, 0.5619,0.5664,0.5666,0.5679,0.5700,0.5721,0.5721,0.5770,0.5791,0.5846, 0.5873,0.5907,0.5939,0.5949,0.5952,0.5995,0.5998,0.6032,0.6034,0.6046, 0.6061,0.6209,0.6217,0.6267,0.6312,0.6345,0.6381,0.6474,0.6525,0.6533, 0.6587,0.6637,0.6739,0.6749,0.6773,0.6801,0.6836,0.6917,0.6983,0.7011, 0.7063,0.7070,0.7110,0.7112,0.7136,0.7139,0.7151,0.7164,0.7173,0.7212, 0.7215,0.7240,0.7299,0.7312,0.7377,0.7533,0.7571,0.7584,0.7653,0.7713, 0.7739,0.7779,0.7802,0.7812,0.7885,0.7898,0.7939,0.7940,0.7964,0.8013, 0.8082,0.8110,0.8111,0.8211,0.8302,0.8394,0.8436,0.8453,0.8499,0.8556, 0.8564,0.8575,0.8643,0.8695,0.8700,0.8762,0.8765,0.8773,0.8871,0.9005, 0.9026,0.9027,0.9073,0.9079,0.9110,0.9188,0.9245,0.9257,0.9284,0.9299, 0.9331,0.9341,0.9372,0.9387,0.9473,0.9492,0.9500,0.9511,0.9613,0.9615, 0.9615,0.9627,0.9742,0.9768,0.9812,0.9826,0.9908,0.9920,0.9935, Overall p-value after applying KStest on 269 p-values = 0.872923 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.