RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-01-19_00:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.72 19.9492 0.723165 2 to 25 15.91 18.7070 0.654390 3 to 26 15.40 39.4796 0.998468 4 to 27 15.73 21.5706 0.798200 5 to 28 15.44 26.0760 0.926912 6 to 29 15.62 15.2894 0.425352 7 to 30 15.94 18.6759 0.652552 8 to 31 15.65 11.8548 0.191151 9 to 32 15.66 13.9628 0.330268 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.219951 Tough bday spacings test for dh-ranFile-2016-01-19_00:31: 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 10 35 67 96 99 82 57 31 15 3 5 (O-E)^2/E 0.1 0.1 0.5 0.0 0.0 0.2 0.5 0.1 0.0 2.0 0.2 Birthday Spacings: Sum(O-E)^2/E= 3.626, p= 0.037 RESULTS OF GCD FOR dh-ranFile-2016-01-19_00:31 Euclid's algorithm: p-value, steps to gcd: 0.999462 p-value, dist. of gcd's: 0.032447 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-01-19_00:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.405 0.642 0.897 0.016 0.833 0.967 0.722 0.400 Bits 8 to 15---> 0.627 0.515 0.235 0.919 0.536 0.653 0.610 0.420 Bits 16 to 23---> 0.483 0.801 0.516 0.807 0.920 0.226 0.270 0.844 Bits 24 to 31---> 0.525 0.207 0.367 0.635 0.558 0.662 0.508 0.666 KS test for the above 32 p values: 0.889 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-01-19_00:31, p-values for 5 runs: 0.7072, 0.6139, 0.8502, 0.7358, 0.4305 Rank test for binary matrices (31x31) for dh-ranFile-2016-01-19_00:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 215 211.4 0.061 0.061 r= 29 5185 5134.0 0.506 0.567 r= 30 23026 23103.0 0.257 0.824 r= 31 11574 11551.5 0.044 0.868 chi-square = 0.868 with df = 3; p-value = 0.167 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-01-19_00:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 212 211.4 0.002 0.002 r= 30 5251 5134.0 2.666 2.667 r= 31 23066 23103.0 0.059 2.727 r= 32 11471 11551.5 0.561 3.288 chi-square = 3.288 with df = 3; p-value = 0.651 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-01-19_00:31 b-rank test for bits 1 to 8, p=0.65341 b-rank test for bits 2 to 9, p=0.60399 b-rank test for bits 3 to 10, p=0.73614 b-rank test for bits 4 to 11, p=0.77342 b-rank test for bits 5 to 12, p=0.28258 b-rank test for bits 6 to 13, p=0.53018 b-rank test for bits 7 to 14, p=0.33844 b-rank test for bits 8 to 15, p=0.01655 b-rank test for bits 9 to 16, p=0.00434 b-rank test for bits 10 to 17, p=0.79972 b-rank test for bits 11 to 18, p=0.55297 b-rank test for bits 12 to 19, p=0.02858 b-rank test for bits 13 to 20, p=0.08172 b-rank test for bits 14 to 21, p=0.37329 b-rank test for bits 15 to 22, p=0.58641 b-rank test for bits 16 to 23, p=0.83820 b-rank test for bits 17 to 24, p=0.35182 b-rank test for bits 18 to 25, p=0.22636 b-rank test for bits 19 to 26, p=0.24927 b-rank test for bits 20 to 27, p=0.38353 b-rank test for bits 21 to 28, p=0.17564 b-rank test for bits 22 to 29, p=0.11754 b-rank test for bits 23 to 30, p=0.46373 b-rank test for bits 24 to 31, p=0.78869 b-rank test for bits 25 to 32, p=0.56791 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 = 0.219611 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-01-19_00:31 (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 142087 0.42 0.660972 2 141858 -0.12 0.452269 3 141999 0.21 0.582975 4 141541 -0.86 0.194734 5 141785 -0.29 0.385720 6 142473 1.32 0.906078 7 141862 -0.11 0.455973 8 141594 -0.74 0.230637 9 142402 1.15 0.875154 10 141997 0.20 0.581150 11 141804 -0.25 0.402803 12 141826 -0.19 0.422815 13 141682 -0.53 0.297659 14 142090 0.42 0.663534 15 141873 -0.08 0.466177 16 141927 0.04 0.516466 17 141837 -0.17 0.432900 18 141878 -0.07 0.470823 19 141746 -0.38 0.351375 20 142770 2.01 0.977833 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-01-19_00:31 Bits used No. missing words z-score p-value 23 to 32 141750 -0.5494 0.291361 22 to 31 142488 1.9954 0.977001 21 to 30 142250 1.1747 0.879947 20 to 29 142201 1.0058 0.842734 19 to 28 142081 0.5920 0.723063 18 to 27 141646 -0.9080 0.181930 17 to 26 141837 -0.2494 0.401520 16 to 25 142163 0.8747 0.809138 15 to 24 142143 0.8058 0.789809 14 to 23 141665 -0.8425 0.199749 13 to 22 141922 0.0437 0.517424 12 to 21 141639 -0.9322 0.175624 11 to 20 141856 -0.1839 0.427047 10 to 19 142030 0.4161 0.661333 9 to 18 142088 0.6161 0.731087 8 to 17 141492 -1.4391 0.075066 7 to 16 141384 -1.8115 0.035033 6 to 15 141511 -1.3736 0.084790 5 to 14 141705 -0.7046 0.240534 4 to 13 141970 0.2092 0.582857 3 to 12 141640 -0.9287 0.176516 2 to 11 141736 -0.5977 0.275024 1 to 10 141763 -0.5046 0.306925 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-01-19_00:31 Bits used No. missing words z-score p-value 28 to 32 141731 -0.6045 0.272753 27 to 31 142018 0.3684 0.643702 26 to 30 141312 -2.0248 0.021442 25 to 29 141959 0.1684 0.566855 24 to 28 141519 -1.3232 0.092892 23 to 27 141601 -1.0452 0.147968 22 to 26 142100 0.6463 0.740970 21 to 25 142040 0.4429 0.671099 20 to 24 141987 0.2633 0.603836 19 to 23 142076 0.5650 0.713957 18 to 22 142108 0.6735 0.749672 17 to 21 142293 1.3006 0.903298 16 to 20 142002 0.3141 0.623291 15 to 19 141822 -0.2960 0.383602 14 to 18 142092 0.6192 0.732114 13 to 17 141811 -0.3333 0.369446 12 to 16 141967 0.1955 0.577496 11 to 15 142274 1.2362 0.891802 10 to 14 141338 -1.9367 0.026390 9 to 13 141882 -0.0926 0.463093 8 to 12 142052 0.4836 0.685675 7 to 11 141791 -0.4011 0.344166 6 to 10 142125 0.7311 0.767636 5 to 9 141931 0.0735 0.529279 4 to 8 141818 -0.3096 0.378435 3 to 7 142085 0.5955 0.724243 2 to 6 141577 -1.1265 0.129968 1 to 5 141743 -0.5638 0.286435 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-01-19_00:31 Bits used No. missing words z-score p-value 31 to 32 141514 -1.1662 0.121774 30 to 31 142337 1.2616 0.896447 29 to 30 142085 0.5182 0.697841 28 to 29 141991 0.2409 0.595189 27 to 28 141928 0.0551 0.521960 26 to 27 141582 -0.9656 0.167128 25 to 26 142557 1.9105 0.971968 24 to 25 141639 -0.7974 0.212600 23 to 24 142113 0.6008 0.726012 22 to 23 141619 -0.8564 0.195880 21 to 22 141902 -0.0216 0.491375 20 to 21 141831 -0.2311 0.408633 19 to 20 142251 1.0079 0.843243 18 to 19 141691 -0.6440 0.259774 17 to 18 141951 0.1229 0.548915 16 to 17 141709 -0.5909 0.277279 15 to 16 141784 -0.3697 0.355801 14 to 15 141384 -1.5496 0.060613 13 to 14 141870 -0.1160 0.453819 12 to 13 142099 0.5595 0.712089 11 to 12 141640 -0.7945 0.213457 10 to 11 142356 1.3176 0.906183 9 to 10 142172 0.7748 0.780782 8 to 9 141753 -0.4612 0.322345 7 to 8 142060 0.4445 0.671643 6 to 7 142362 1.3353 0.909113 5 to 6 142161 0.7424 0.771074 4 to 5 142429 1.5329 0.937356 3 to 4 142235 0.9607 0.831643 2 to 3 142317 1.2026 0.885428 1 to 2 141933 0.0698 0.527833 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-01-19_00:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2520.98 0.297 0.616670 Test results for specific bytes for dh-ranFile-2016-01-19_00:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2535.99 0.509 0.694603 2 to 9 2428.92 -1.005 0.157387 3 to 10 2486.92 -0.185 0.426646 4 to 11 2574.28 1.050 0.853252 5 to 12 2463.07 -0.522 0.300719 6 to 13 2579.59 1.126 0.869829 7 to 14 2519.45 0.275 0.608362 8 to 15 2589.72 1.269 0.897757 9 to 16 2358.25 -2.005 0.022504 10 to 17 2452.49 -0.672 0.250804 11 to 18 2638.27 1.955 0.974731 12 to 19 2432.97 -0.948 0.171575 13 to 20 2545.73 0.647 0.741106 14 to 21 2452.87 -0.667 0.252528 15 to 22 2492.46 -0.107 0.457535 16 to 23 2527.21 0.385 0.649835 17 to 24 2523.31 0.330 0.629143 18 to 25 2411.93 -1.245 0.106484 19 to 26 2397.41 -1.451 0.073406 20 to 27 2414.08 -1.215 0.112160 21 to 28 2428.71 -1.008 0.156686 22 to 29 2532.23 0.456 0.675715 23 to 30 2488.00 -0.170 0.432645 24 to 31 2520.22 0.286 0.612542 25 to 32 2524.24 0.343 0.634126 CDPARK for dh-ranFile-2016-01-19_00:31: 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 3510 -0.5936 0.276387 3517 -0.2740 0.392053 3519 -0.1826 0.427537 3541 0.8219 0.794438 3510 -0.5936 0.276387 3566 1.9635 0.975204 3503 -0.9132 0.180558 3520 -0.1370 0.445521 3518 -0.2283 0.409702 3514 -0.4110 0.340551 Square side=100, avg. no. parked=3521.80 sample std.=17.50 p-value of the KSTEST for those 10 p-values: 0.336444 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-01-19_00:31 0.8784,0.5058,0.0061,0.0758,0.9521,0.9691,0.1282,0.1636,0.9687,0.3846, The KS test for those 10 p-values: 0.139083 The 3DSPHERES test for dh-ranFile-2016-01-19_00:31 sample no r^3 equiv. uni. 1 0.824 0.027094 2 19.456 0.477193 3 40.920 0.744366 4 3.326 0.104928 5 25.159 0.567702 6 18.242 0.455589 7 15.770 0.408835 8 7.748 0.227603 9 27.091 0.594655 10 44.512 0.773213 11 11.284 0.313490 12 40.927 0.744422 13 35.946 0.698264 14 4.638 0.143248 15 71.368 0.907352 16 153.830 0.994070 17 16.897 0.430639 18 67.593 0.894928 19 1.555 0.050510 20 11.810 0.325422 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.997544 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-01-19_00:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 1.3 0.5 -1.6 1.2 0.2 0.8 1.8 0.8 1.0 0.2 -0.1 -0.7 0.0 -0.8 0.1 -0.3 1.1 -0.4 -1.2 0.6 -0.8 1.4 -0.5 -1.0 0.8 -1.9 0.5 -0.3 0.6 0.7 0.7 0.6 -0.1 0.5 2.4 2.2 -0.5 -0.7 1.3 1.0 0.1 1.0 1.8 Chi-square with 42 degrees of freedom:45.022129 z-score=0.329741, p-value=0.653411 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-01-19_00:31 Test no p-value 1 0.096104 2 0.078032 3 0.580242 4 0.207554 5 0.203907 6 0.322135 7 0.913077 8 0.298770 9 0.228091 10 0.213076 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.041214 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-01-19_00:31: (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 66868 0.61 66715 0.04 3 25000.00 24888 0.50 24899 0.41 4 6666.67 6604 0.59 6669 0.00 5 1388.89 1367 0.35 1424 0.89 6 238.10 233 0.11 252 0.81 7 34.72 31 0.40 28 1.30 8 4.96 8 1.86 12 9.99 p=0.37926 p=0.96339 Number of rngs required: 688759, p-value: 0.659 RESULTS OF CRAPS TEST for dh-ranFile-2016-01-19_00:31 No. of wins: Observed Expected 98670 98585.9 z-score= 0.376, pvalue=0.64666 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66856 66666.7 0.538 0.538 2 37515 37654.3 0.515 1.053 3 26594 26954.7 4.828 5.881 4 19438 19313.5 0.803 6.684 5 13944 13851.4 0.619 7.303 6 10015 9943.5 0.514 7.816 7 7233 7145.0 1.083 8.899 8 5111 5139.1 0.153 9.053 9 3589 3699.9 3.322 12.375 10 2599 2666.3 1.699 14.073 11 2002 1923.3 3.218 17.291 12 1395 1388.7 0.028 17.319 13 1031 1003.7 0.742 18.061 14 757 726.1 1.311 19.373 15 514 525.8 0.266 19.639 16 370 381.2 0.326 19.965 17 280 276.5 0.043 20.009 18 219 200.8 1.644 21.653 19 132 146.0 1.340 22.992 20 122 106.2 2.346 25.338 21 284 287.1 0.034 25.372 Chisq= 25.37 for 20 degrees of freedom, p= 0.81242 SUMMARY of craptest p-value for no. of wins: 0.646664 p-value for throws/game: 0.812421 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-01-19_00:31 No. of wins: Observed Expected 98770 98585.9 z-score= 0.824, pvalue=0.79491 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66797 66666.7 0.255 0.255 2 37719 37654.3 0.111 0.366 3 26822 26954.7 0.654 1.020 4 19150 19313.5 1.383 2.403 5 13969 13851.4 0.998 3.401 6 9830 9943.5 1.297 4.698 7 7154 7145.0 0.011 4.709 8 5216 5139.1 1.152 5.860 9 3716 3699.9 0.070 5.931 10 2686 2666.3 0.146 6.076 11 1950 1923.3 0.370 6.446 12 1398 1388.7 0.062 6.508 13 968 1003.7 1.271 7.779 14 723 726.1 0.014 7.792 15 517 525.8 0.148 7.941 16 374 381.2 0.134 8.075 17 274 276.5 0.023 8.098 18 197 200.8 0.073 8.171 19 123 146.0 3.619 11.790 20 107 106.2 0.006 11.796 21 310 287.1 1.824 13.620 Chisq= 13.62 for 20 degrees of freedom, p= 0.15078 SUMMARY of craptest p-value for no. of wins: 0.794913 p-value for throws/game: 0.150781 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0043,0.0061,0.0155,0.0165,0.0214,0.0225,0.0264,0.0271,0.0286,0.0324, 0.0350,0.0373,0.0412,0.0505,0.0606,0.0734,0.0751,0.0758,0.0780,0.0817, 0.0848,0.0929,0.0961,0.1049,0.1065,0.1122,0.1175,0.1218,0.1282,0.1300, 0.1391,0.1432,0.1480,0.1508,0.1567,0.1574,0.1636,0.1668,0.1671,0.1716, 0.1756,0.1756,0.1765,0.1806,0.1819,0.1912,0.1947,0.1959,0.1997,0.2039, 0.2072,0.2076,0.2126,0.2131,0.2135,0.2196,0.2200,0.2263,0.2264,0.2276, 0.2281,0.2306,0.2354,0.2405,0.2493,0.2508,0.2525,0.2598,0.2700,0.2728, 0.2750,0.2764,0.2764,0.2773,0.2826,0.2864,0.2914,0.2977,0.2988,0.3007, 0.3069,0.3135,0.3221,0.3223,0.3254,0.3303,0.3364,0.3384,0.3406,0.3442, 0.3514,0.3518,0.3558,0.3673,0.3694,0.3733,0.3784,0.3793,0.3835,0.3836, 0.3846,0.3857,0.3921,0.4004,0.4015,0.4028,0.4052,0.4086,0.4088,0.4097, 0.4201,0.4228,0.4254,0.4266,0.4270,0.4275,0.4305,0.4306,0.4326,0.4329, 0.4455,0.4523,0.4538,0.4556,0.4560,0.4575,0.4631,0.4637,0.4662,0.4708, 0.4772,0.4827,0.4914,0.5058,0.5079,0.5147,0.5163,0.5165,0.5174,0.5220, 0.5248,0.5278,0.5293,0.5302,0.5356,0.5489,0.5530,0.5583,0.5669,0.5677, 0.5679,0.5775,0.5802,0.5812,0.5829,0.5830,0.5864,0.5947,0.5952,0.6038, 0.6040,0.6084,0.6097,0.6125,0.6139,0.6167,0.6233,0.6266,0.6291,0.6341, 0.6345,0.6416,0.6437,0.6467,0.6498,0.6507,0.6526,0.6532,0.6534,0.6534, 0.6544,0.6591,0.6610,0.6613,0.6624,0.6635,0.6659,0.6711,0.6716,0.6757, 0.6857,0.6946,0.6978,0.6983,0.7072,0.7121,0.7140,0.7220,0.7231,0.7232, 0.7242,0.7260,0.7311,0.7321,0.7358,0.7361,0.7410,0.7411,0.7444,0.7444, 0.7497,0.7676,0.7711,0.7732,0.7734,0.7808,0.7887,0.7898,0.7944,0.7949, 0.7982,0.7997,0.8012,0.8069,0.8091,0.8124,0.8316,0.8325,0.8382,0.8427, 0.8432,0.8441,0.8502,0.8533,0.8698,0.8752,0.8784,0.8799,0.8854,0.8887, 0.8918,0.8949,0.8964,0.8966,0.8978,0.9033,0.9061,0.9062,0.9074,0.9091, 0.9131,0.9187,0.9203,0.9269,0.9374,0.9521,0.9634,0.9667,0.9687,0.9691, 0.9720,0.9747,0.9752,0.9770,0.9778,0.9941,0.9975,0.9985,0.9995, Overall p-value after applying KStest on 269 p-values = 0.843567 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.