RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-11-26_12:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.45 34.4146 0.992581 2 to 25 15.66 19.9786 0.724673 3 to 26 15.84 29.6564 0.971068 4 to 27 15.71 14.0531 0.336657 5 to 28 15.78 15.5703 0.445523 6 to 29 15.75 20.7703 0.763266 7 to 30 15.92 22.3291 0.827610 8 to 31 15.96 12.1023 0.206096 9 to 32 15.61 17.5433 0.581814 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.165367 Tough bday spacings test for dh-ranFile-2015-11-26_12:31: 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 9 32 75 92 105 69 47 44 13 12 2 (O-E)^2/E 0.0 0.6 0.0 0.3 0.5 1.1 0.5 6.8 0.2 4.4 1.0 Birthday Spacings: Sum(O-E)^2/E= 15.550, p= 0.887 RESULTS OF GCD FOR dh-ranFile-2015-11-26_12:31 Euclid's algorithm: p-value, steps to gcd: 0.131019 p-value, dist. of gcd's: 0.318545 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-11-26_12:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.386 0.217 0.046 0.237 0.925 0.246 0.454 0.040 Bits 8 to 15---> 0.480 0.687 0.348 0.123 0.169 0.194 0.675 0.476 Bits 16 to 23---> 0.039 0.913 0.542 0.860 0.141 0.888 0.509 0.245 Bits 24 to 31---> 0.707 0.729 0.187 0.449 0.924 0.603 0.583 0.712 KS test for the above 32 p values: 0.295 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-11-26_12:31, p-values for 5 runs: 0.4224, 0.0492, 0.2430, 0.9873, 0.0868 Rank test for binary matrices (31x31) for dh-ranFile-2015-11-26_12:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 210 211.4 0.010 0.010 r= 29 5209 5134.0 1.095 1.105 r= 30 23000 23103.0 0.460 1.564 r= 31 11581 11551.5 0.075 1.640 chi-square = 1.640 with df = 3; p-value = 0.350 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-11-26_12:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 208 211.4 0.055 0.055 r= 30 5252 5134.0 2.712 2.767 r= 31 23064 23103.0 0.066 2.833 r= 32 11476 11551.5 0.494 3.327 chi-square = 3.327 with df = 3; p-value = 0.656 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-11-26_12:31 b-rank test for bits 1 to 8, p=0.11713 b-rank test for bits 2 to 9, p=0.38865 b-rank test for bits 3 to 10, p=0.39759 b-rank test for bits 4 to 11, p=0.27857 b-rank test for bits 5 to 12, p=0.03823 b-rank test for bits 6 to 13, p=0.42130 b-rank test for bits 7 to 14, p=0.91720 b-rank test for bits 8 to 15, p=0.77220 b-rank test for bits 9 to 16, p=0.94212 b-rank test for bits 10 to 17, p=0.69545 b-rank test for bits 11 to 18, p=0.50102 b-rank test for bits 12 to 19, p=0.05942 b-rank test for bits 13 to 20, p=0.94895 b-rank test for bits 14 to 21, p=0.94516 b-rank test for bits 15 to 22, p=0.74701 b-rank test for bits 16 to 23, p=0.45898 b-rank test for bits 17 to 24, p=0.38914 b-rank test for bits 18 to 25, p=0.38446 b-rank test for bits 19 to 26, p=0.90109 b-rank test for bits 20 to 27, p=0.64604 b-rank test for bits 21 to 28, p=0.86961 b-rank test for bits 22 to 29, p=0.18290 b-rank test for bits 23 to 30, p=0.30005 b-rank test for bits 24 to 31, p=0.73653 b-rank test for bits 25 to 32, p=0.64760 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 = 0.635533 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-11-26_12:31 (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 141113 -1.86 0.031401 2 141867 -0.10 0.460608 3 142013 0.24 0.595695 4 142037 0.30 0.617261 5 141638 -0.63 0.263057 6 141776 -0.31 0.377703 7 142057 0.35 0.634962 8 142507 1.40 0.918707 9 140712 -2.80 0.002575 10 142573 1.55 0.939505 11 141979 0.16 0.564654 12 141243 -1.56 0.059754 13 141554 -0.83 0.203210 14 141449 -1.08 0.141067 15 142657 1.75 0.959672 16 141778 -0.31 0.379480 17 141148 -1.78 0.037636 18 141969 0.14 0.555439 19 142049 0.33 0.627913 20 141120 -1.84 0.032575 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-11-26_12:31 Bits used No. missing words z-score p-value 23 to 32 142159 0.8609 0.805362 22 to 31 142259 1.2058 0.886045 21 to 30 142070 0.5540 0.710222 20 to 29 141872 -0.1287 0.448788 19 to 28 142198 0.9954 0.840233 18 to 27 142245 1.1575 0.876462 17 to 26 141595 -1.0839 0.139205 16 to 25 141607 -1.0425 0.148586 15 to 24 142426 1.7816 0.962594 14 to 23 142074 0.5678 0.714924 13 to 22 142077 0.5782 0.718426 12 to 21 141996 0.2989 0.617477 11 to 20 141724 -0.6391 0.261389 10 to 19 141771 -0.4770 0.316681 9 to 18 141892 -0.0598 0.476174 8 to 17 142195 0.9851 0.837705 7 to 16 141572 -1.1632 0.122373 6 to 15 141588 -1.1080 0.133923 5 to 14 142014 0.3609 0.640925 4 to 13 141922 0.0437 0.517424 3 to 12 142173 0.9092 0.818380 2 to 11 141741 -0.5804 0.280806 1 to 10 142371 1.5920 0.944304 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-11-26_12:31 Bits used No. missing words z-score p-value 28 to 32 141545 -1.2350 0.108412 27 to 31 141757 -0.5164 0.302797 26 to 30 141626 -0.9604 0.168417 25 to 29 142605 2.3582 0.990818 24 to 28 141701 -0.7062 0.240031 23 to 27 142524 2.0836 0.981403 22 to 26 142599 2.3379 0.990303 21 to 25 141752 -0.5333 0.296905 20 to 24 142066 0.5311 0.702320 19 to 23 141953 0.1480 0.558842 18 to 22 142045 0.4599 0.677205 17 to 21 141813 -0.3265 0.372007 16 to 20 142421 1.7345 0.958583 15 to 19 141759 -0.5096 0.305168 14 to 18 142170 0.8836 0.811551 13 to 17 141145 -2.5909 0.004786 12 to 16 142334 1.4396 0.925004 11 to 15 141937 0.0938 0.537365 10 to 14 141896 -0.0452 0.481979 9 to 13 141720 -0.6418 0.260503 8 to 12 141711 -0.6723 0.250695 7 to 11 142196 0.9718 0.834416 6 to 10 141677 -0.7876 0.215477 5 to 9 142084 0.5921 0.723109 4 to 8 142515 2.0531 0.979969 3 to 7 142047 0.4667 0.679635 2 to 6 141585 -1.0994 0.135792 1 to 5 141353 -1.8859 0.029657 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-11-26_12:31 Bits used No. missing words z-score p-value 31 to 32 141554 -1.0482 0.147280 30 to 31 141685 -0.6617 0.254069 29 to 30 141446 -1.3668 0.085851 28 to 29 142332 1.2468 0.893767 27 to 28 141853 -0.1662 0.434014 26 to 27 141497 -1.2163 0.111933 25 to 26 141953 0.1288 0.551250 24 to 25 141942 0.0964 0.538387 23 to 24 142203 0.8663 0.806833 22 to 23 141976 0.1967 0.577956 21 to 22 142229 0.9430 0.827154 20 to 21 141787 -0.3609 0.359104 19 to 20 142234 0.9577 0.830900 18 to 19 141852 -0.1691 0.432853 17 to 18 142442 1.5713 0.941943 16 to 17 142138 0.6745 0.750017 15 to 16 141366 -1.6027 0.054496 14 to 15 141658 -0.7414 0.229230 13 to 14 142066 0.4622 0.678014 12 to 13 141893 -0.0482 0.480790 11 to 12 141813 -0.2842 0.388144 10 to 11 141841 -0.2016 0.420129 9 to 10 142013 0.3058 0.620126 8 to 9 141668 -0.7119 0.238267 7 to 8 141471 -1.2930 0.098004 6 to 7 141856 -0.1573 0.437498 5 to 6 142747 2.4710 0.993263 4 to 5 141850 -0.1750 0.430534 3 to 4 142260 1.0344 0.849531 2 to 3 142817 2.6775 0.996291 1 to 2 141909 -0.0010 0.499612 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-11-26_12:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2422.78 -1.092 0.137398 Test results for specific bytes for dh-ranFile-2015-11-26_12:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2480.92 -0.270 0.393642 2 to 9 2455.06 -0.635 0.262554 3 to 10 2399.15 -1.426 0.076892 4 to 11 2495.28 -0.067 0.473372 5 to 12 2516.87 0.239 0.594286 6 to 13 2479.74 -0.287 0.387221 7 to 14 2368.06 -1.866 0.031024 8 to 15 2446.89 -0.751 0.226299 9 to 16 2524.72 0.350 0.636699 10 to 17 2441.36 -0.829 0.203486 11 to 18 2445.57 -0.770 0.220725 12 to 19 2428.44 -1.012 0.155771 13 to 20 2629.06 1.825 0.966012 14 to 21 2612.08 1.585 0.943528 15 to 22 2630.53 1.846 0.967549 16 to 23 2535.23 0.498 0.690826 17 to 24 2541.60 0.588 0.721821 18 to 25 2523.20 0.328 0.628578 19 to 26 2509.84 0.139 0.555331 20 to 27 2469.15 -0.436 0.331304 21 to 28 2554.54 0.771 0.779753 22 to 29 2526.33 0.372 0.645163 23 to 30 2540.10 0.567 0.714698 24 to 31 2424.80 -1.064 0.143767 25 to 32 2511.36 0.161 0.563820 CDPARK for dh-ranFile-2015-11-26_12:31: 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 3550 1.2329 0.891189 3493 -1.3699 0.085365 3496 -1.2329 0.108811 3517 -0.2740 0.392053 3535 0.5479 0.708135 3524 0.0457 0.518210 3536 0.5936 0.723613 3473 -2.2831 0.011212 3515 -0.3653 0.357445 3488 -1.5982 0.055002 Square side=100, avg. no. parked=3512.70 sample std.=23.32 p-value of the KSTEST for those 10 p-values: 0.242438 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-11-26_12:31 0.6612,0.2646,0.7583,0.7612,0.1509,0.6159,0.2197,0.4692,0.0266,0.6190, The KS test for those 10 p-values: 0.736389 The 3DSPHERES test for dh-ranFile-2015-11-26_12:31 sample no r^3 equiv. uni. 1 22.787 0.532135 2 50.157 0.812112 3 11.754 0.324153 4 23.828 0.548089 5 6.348 0.190717 6 9.051 0.260428 7 4.256 0.132274 8 8.953 0.258017 9 24.624 0.559916 10 4.129 0.128569 11 45.412 0.779914 12 16.395 0.421021 13 24.488 0.557923 14 3.089 0.097839 15 137.668 0.989836 16 0.133 0.004416 17 40.008 0.736473 18 103.131 0.967861 19 57.093 0.850894 20 32.066 0.656603 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.968730 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-11-26_12:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 -0.7 -0.1 -0.4 0.9 0.7 -0.3 1.0 -0.3 1.1 -0.7 0.8 0.4 1.5 -0.5 0.4 -0.9 -0.3 -1.5 0.4 -1.4 -1.4 0.9 -0.5 0.8 -0.6 -0.9 2.0 0.9 2.5 1.2 0.8 -0.3 0.4 -0.4 2.4 1.4 -0.4 0.1 0.4 -0.6 -1.0 1.8 Chi-square with 42 degrees of freedom:44.750074 z-score=0.300058, p-value=0.642885 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-11-26_12:31 Test no p-value 1 0.979108 2 0.008598 3 0.035091 4 0.695533 5 0.004145 6 0.034089 7 0.014581 8 0.009823 9 0.050081 10 0.321111 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000003 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-11-26_12:31: (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 66834 0.42 66877 0.66 3 25000.00 24719 3.16 24788 1.80 4 6666.67 6739 0.78 6611 0.46 5 1388.89 1425 0.94 1441 1.96 6 238.10 236 0.02 241 0.04 7 34.72 41 1.14 37 0.15 8 4.96 5 0.00 4 0.19 p=0.62598 p=0.48812 Number of rngs required: 688943, p-value: 0.733 RESULTS OF CRAPS TEST for dh-ranFile-2015-11-26_12:31 No. of wins: Observed Expected 98686 98585.9 z-score= 0.448, pvalue=0.67288 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66480 66666.7 0.523 0.523 2 37822 37654.3 0.747 1.269 3 26882 26954.7 0.196 1.466 4 19095 19313.5 2.471 3.937 5 14017 13851.4 1.979 5.916 6 9964 9943.5 0.042 5.958 7 7142 7145.0 0.001 5.959 8 5115 5139.1 0.113 6.072 9 3617 3699.9 1.856 7.928 10 2779 2666.3 4.764 12.692 11 1953 1923.3 0.458 13.150 12 1504 1388.7 9.566 22.716 13 1000 1003.7 0.014 22.730 14 710 726.1 0.359 23.088 15 500 525.8 1.269 24.358 16 380 381.2 0.003 24.361 17 277 276.5 0.001 24.362 18 217 200.8 1.302 25.664 19 149 146.0 0.062 25.726 20 90 106.2 2.475 28.202 21 307 287.1 1.377 29.579 Chisq= 29.58 for 20 degrees of freedom, p= 0.92303 SUMMARY of craptest p-value for no. of wins: 0.672884 p-value for throws/game: 0.923031 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-11-26_12:31 No. of wins: Observed Expected 98296 98585.9 z-score=-1.296, pvalue=0.09742 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66552 66666.7 0.197 0.197 2 37790 37654.3 0.489 0.686 3 26887 26954.7 0.170 0.856 4 19332 19313.5 0.018 0.874 5 13752 13851.4 0.714 1.588 6 9996 9943.5 0.277 1.864 7 7133 7145.0 0.020 1.885 8 5177 5139.1 0.280 2.165 9 3738 3699.9 0.393 2.558 10 2669 2666.3 0.003 2.560 11 1909 1923.3 0.107 2.667 12 1378 1388.7 0.083 2.750 13 1081 1003.7 5.951 8.701 14 682 726.1 2.683 11.384 15 515 525.8 0.223 11.608 16 412 381.2 2.497 14.104 17 278 276.5 0.008 14.112 18 182 200.8 1.765 15.878 19 160 146.0 1.346 17.223 20 105 106.2 0.014 17.237 21 272 287.1 0.796 18.033 Chisq= 18.03 for 20 degrees of freedom, p= 0.41475 SUMMARY of craptest p-value for no. of wins: 0.097416 p-value for throws/game: 0.414753 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0000,0.0026,0.0041,0.0044,0.0048,0.0086,0.0098,0.0112,0.0146,0.0266, 0.0297,0.0310,0.0314,0.0326,0.0341,0.0351,0.0376,0.0382,0.0388,0.0398, 0.0460,0.0492,0.0501,0.0545,0.0550,0.0594,0.0598,0.0769,0.0854,0.0859, 0.0868,0.0974,0.0978,0.0980,0.1084,0.1088,0.1119,0.1171,0.1224,0.1228, 0.1286,0.1310,0.1323,0.1339,0.1358,0.1374,0.1392,0.1411,0.1414,0.1438, 0.1473,0.1486,0.1509,0.1558,0.1654,0.1684,0.1686,0.1829,0.1867,0.1907, 0.1942,0.2032,0.2035,0.2061,0.2155,0.2166,0.2197,0.2207,0.2263,0.2292, 0.2370,0.2383,0.2400,0.2424,0.2430,0.2453,0.2457,0.2507,0.2541,0.2580, 0.2604,0.2605,0.2614,0.2626,0.2631,0.2646,0.2786,0.2808,0.2953,0.2969, 0.3001,0.3028,0.3052,0.3167,0.3185,0.3211,0.3242,0.3313,0.3367,0.3475, 0.3496,0.3574,0.3591,0.3720,0.3777,0.3795,0.3845,0.3864,0.3872,0.3881, 0.3886,0.3891,0.3921,0.3936,0.3976,0.4148,0.4201,0.4210,0.4213,0.4224, 0.4305,0.4329,0.4340,0.4375,0.4455,0.4488,0.4494,0.4543,0.4590,0.4606, 0.4692,0.4734,0.4761,0.4762,0.4799,0.4808,0.4820,0.4881,0.4996,0.5010, 0.5091,0.5174,0.5182,0.5321,0.5374,0.5384,0.5420,0.5481,0.5513,0.5553, 0.5554,0.5579,0.5588,0.5599,0.5638,0.5647,0.5780,0.5818,0.5833,0.5943, 0.5957,0.6027,0.6159,0.6173,0.6175,0.6190,0.6201,0.6260,0.6279,0.6286, 0.6350,0.6355,0.6367,0.6409,0.6429,0.6452,0.6460,0.6476,0.6560,0.6566, 0.6612,0.6729,0.6748,0.6772,0.6780,0.6796,0.6865,0.6908,0.6955,0.6955, 0.7023,0.7066,0.7081,0.7102,0.7116,0.7147,0.7149,0.7184,0.7218,0.7231, 0.7236,0.7247,0.7286,0.7333,0.7364,0.7365,0.7365,0.7470,0.7500,0.7583, 0.7612,0.7633,0.7722,0.7798,0.7799,0.8054,0.8068,0.8116,0.8121,0.8184, 0.8272,0.8276,0.8309,0.8344,0.8377,0.8402,0.8495,0.8509,0.8597,0.8696, 0.8765,0.8860,0.8867,0.8880,0.8912,0.8938,0.9011,0.9128,0.9172,0.9187, 0.9230,0.9244,0.9248,0.9250,0.9395,0.9419,0.9421,0.9435,0.9443,0.9452, 0.9490,0.9586,0.9597,0.9626,0.9660,0.9675,0.9679,0.9687,0.9711,0.9791, 0.9800,0.9814,0.9873,0.9898,0.9903,0.9908,0.9926,0.9933,0.9963, Overall p-value after applying KStest on 269 p-values = 0.241268 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.