RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-11-27_18:31 (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 20.3498 0.743270 2 to 25 15.50 18.5640 0.645876 3 to 26 15.81 20.9350 0.770788 4 to 27 15.94 14.2958 0.353934 5 to 28 15.59 22.4282 0.831193 6 to 29 15.83 16.2474 0.493632 7 to 30 15.97 20.5610 0.753454 8 to 31 15.75 18.8703 0.663974 9 to 32 15.84 17.3013 0.565856 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.089631 Tough bday spacings test for dh-ranFile-2016-11-27_18:31: 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 11 41 66 100 101 80 61 22 11 4 3 (O-E)^2/E 0.4 0.5 0.7 0.1 0.1 0.0 1.5 2.0 1.0 1.0 0.3 Birthday Spacings: Sum(O-E)^2/E= 7.700, p= 0.342 RESULTS OF GCD FOR dh-ranFile-2016-11-27_18:31 Euclid's algorithm: p-value, steps to gcd: 0.389188 p-value, dist. of gcd's: 0.478515 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-11-27_18:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.678 0.614 0.732 0.097 0.586 0.601 0.882 0.102 Bits 8 to 15---> 0.157 0.759 0.107 0.472 0.384 0.424 0.237 0.611 Bits 16 to 23---> 0.489 0.806 0.273 0.605 0.628 0.562 0.703 0.974 Bits 24 to 31---> 0.217 0.674 0.159 0.544 0.747 0.664 0.526 0.376 KS test for the above 32 p values: 0.706 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-11-27_18:31, p-values for 5 runs: 0.3850, 0.5936, 0.8607, 0.6166, 0.5841 Rank test for binary matrices (31x31) for dh-ranFile-2016-11-27_18:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 197 211.4 0.983 0.983 r= 29 5117 5134.0 0.056 1.040 r= 30 23016 23103.0 0.328 1.368 r= 31 11670 11551.5 1.215 2.583 chi-square = 2.583 with df = 3; p-value = 0.539 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-11-27_18:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 216 211.4 0.099 0.099 r= 30 5186 5134.0 0.526 0.626 r= 31 23098 23103.0 0.001 0.627 r= 32 11500 11551.5 0.230 0.857 chi-square = 0.857 with df = 3; p-value = 0.164 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-11-27_18:31 b-rank test for bits 1 to 8, p=0.45754 b-rank test for bits 2 to 9, p=0.06013 b-rank test for bits 3 to 10, p=0.09741 b-rank test for bits 4 to 11, p=0.68548 b-rank test for bits 5 to 12, p=0.28890 b-rank test for bits 6 to 13, p=0.00443 b-rank test for bits 7 to 14, p=0.30108 b-rank test for bits 8 to 15, p=0.23633 b-rank test for bits 9 to 16, p=0.93018 b-rank test for bits 10 to 17, p=0.61659 b-rank test for bits 11 to 18, p=0.77075 b-rank test for bits 12 to 19, p=0.89085 b-rank test for bits 13 to 20, p=0.02044 b-rank test for bits 14 to 21, p=0.91889 b-rank test for bits 15 to 22, p=0.20548 b-rank test for bits 16 to 23, p=0.81444 b-rank test for bits 17 to 24, p=0.76485 b-rank test for bits 18 to 25, p=0.13812 b-rank test for bits 19 to 26, p=0.01982 b-rank test for bits 20 to 27, p=0.76857 b-rank test for bits 21 to 28, p=0.62066 b-rank test for bits 22 to 29, p=0.21520 b-rank test for bits 23 to 30, p=0.08181 b-rank test for bits 24 to 31, p=0.72053 b-rank test for bits 25 to 32, p=0.28694 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 = 0.188592 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-11-27_18:31 (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 142119 0.49 0.687892 2 142181 0.63 0.737202 3 141512 -0.93 0.176615 4 142742 1.95 0.974142 5 140561 -3.15 0.000816 6 142661 1.76 0.960476 7 142344 1.02 0.845086 8 142606 1.63 0.948209 9 141668 -0.56 0.286426 10 142488 1.35 0.911818 11 141389 -1.22 0.112045 12 141969 0.14 0.555439 13 142209 0.70 0.758087 14 141706 -0.48 0.317369 15 142371 1.08 0.859632 16 141711 -0.46 0.321543 17 141406 -1.18 0.119797 18 142753 1.97 0.975649 19 141426 -1.13 0.129391 20 141931 0.05 0.520190 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-11-27_18:31 Bits used No. missing words z-score p-value 23 to 32 141713 -0.6770 0.249203 22 to 31 141839 -0.2425 0.404190 21 to 30 141846 -0.2184 0.413567 20 to 29 141787 -0.4218 0.336575 19 to 28 142022 0.3885 0.651183 18 to 27 141929 0.0678 0.527039 17 to 26 142011 0.3506 0.637051 16 to 25 141577 -1.1460 0.125905 15 to 24 142022 0.3885 0.651183 14 to 23 142045 0.4678 0.680046 13 to 22 142341 1.4885 0.931693 12 to 21 142129 0.7575 0.775620 11 to 20 141601 -1.0632 0.143844 10 to 19 142238 1.1333 0.871465 9 to 18 142287 1.3023 0.903595 8 to 17 141876 -0.1149 0.454250 7 to 16 141947 0.1299 0.551676 6 to 15 141905 -0.0149 0.494044 5 to 14 142003 0.3230 0.626652 4 to 13 141922 0.0437 0.517424 3 to 12 142017 0.3713 0.644784 2 to 11 142252 1.1816 0.881322 1 to 10 141612 -1.0253 0.152617 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-11-27_18:31 Bits used No. missing words z-score p-value 28 to 32 141554 -1.2045 0.114197 27 to 31 142546 2.1582 0.984544 26 to 30 141921 0.0396 0.515778 25 to 29 141513 -1.3435 0.089556 24 to 28 141599 -1.0520 0.146408 23 to 27 141852 -0.1943 0.422955 22 to 26 141669 -0.8147 0.207628 21 to 25 142160 0.8497 0.802262 20 to 24 141839 -0.2384 0.405783 19 to 23 141619 -0.9842 0.162516 18 to 22 141640 -0.9130 0.180626 17 to 21 142284 1.2701 0.897970 16 to 20 141789 -0.4079 0.341674 15 to 19 142353 1.5040 0.933705 14 to 18 142122 0.7209 0.764519 13 to 17 141953 0.1480 0.558842 12 to 16 141955 0.1548 0.561516 11 to 15 141175 -2.4893 0.006401 10 to 14 141665 -0.8282 0.203768 9 to 13 141744 -0.5604 0.287589 8 to 12 141173 -2.4960 0.006280 7 to 11 142056 0.4972 0.690471 6 to 10 141658 -0.8520 0.197116 5 to 9 142768 2.9107 0.998197 4 to 8 142362 1.5345 0.937544 3 to 7 141567 -1.1604 0.122935 2 to 6 141861 -0.1638 0.434932 1 to 5 141745 -0.5571 0.288746 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-11-27_18:31 Bits used No. missing words z-score p-value 31 to 32 142281 1.0964 0.863542 30 to 31 142152 0.7158 0.762955 29 to 30 141463 -1.3166 0.093985 28 to 29 142334 1.2527 0.894845 27 to 28 142230 0.9459 0.827908 26 to 27 141978 0.2026 0.580263 25 to 26 142184 0.8102 0.791098 24 to 25 141512 -1.1721 0.120586 23 to 24 142204 0.8692 0.807640 22 to 23 141899 -0.0305 0.487845 21 to 22 141383 -1.5526 0.060260 20 to 21 141896 -0.0393 0.484317 19 to 20 142008 0.2911 0.614498 18 to 19 142023 0.3353 0.631304 17 to 18 142007 0.2881 0.613370 16 to 17 142518 1.7955 0.963712 15 to 16 141986 0.2262 0.589464 14 to 15 142973 3.1377 0.999149 13 to 14 142199 0.8545 0.803582 12 to 13 141829 -0.2370 0.406343 11 to 12 141937 0.0816 0.532527 10 to 11 141666 -0.7178 0.236444 9 to 10 141763 -0.4317 0.332997 8 to 9 142452 1.6008 0.945289 7 to 8 141517 -1.1573 0.123572 6 to 7 141981 0.2114 0.583719 5 to 6 141454 -1.3432 0.089611 4 to 5 141854 -0.1632 0.435174 3 to 4 141978 0.2026 0.580263 2 to 3 142010 0.2970 0.616752 1 to 2 142746 2.4681 0.993207 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-11-27_18:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2586.65 1.225 0.889789 Test results for specific bytes for dh-ranFile-2016-11-27_18:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2489.37 -0.150 0.440261 2 to 9 2457.81 -0.597 0.275347 3 to 10 2482.46 -0.248 0.402054 4 to 11 2486.12 -0.196 0.422211 5 to 12 2502.16 0.031 0.512183 6 to 13 2494.69 -0.075 0.470055 7 to 14 2522.52 0.318 0.624930 8 to 15 2403.65 -1.363 0.086503 9 to 16 2515.04 0.213 0.584221 10 to 17 2545.44 0.643 0.739746 11 to 18 2565.53 0.927 0.822978 12 to 19 2356.14 -2.035 0.020948 13 to 20 2513.06 0.185 0.573253 14 to 21 2458.55 -0.586 0.278850 15 to 22 2456.84 -0.610 0.270819 16 to 23 2473.88 -0.369 0.355938 17 to 24 2490.02 -0.141 0.443889 18 to 25 2610.69 1.565 0.941249 19 to 26 2680.90 2.558 0.994740 20 to 27 2457.68 -0.599 0.274742 21 to 28 2464.15 -0.507 0.306072 22 to 29 2444.53 -0.784 0.216397 23 to 30 2540.92 0.579 0.718592 24 to 31 2483.57 -0.232 0.408109 25 to 32 2597.99 1.386 0.917101 CDPARK for dh-ranFile-2016-11-27_18:31: 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 3527 0.1826 0.572463 3483 -1.8265 0.033889 3518 -0.2283 0.409702 3503 -0.9132 0.180558 3528 0.2283 0.590298 3516 -0.3196 0.374623 3529 0.2740 0.607947 3519 -0.1826 0.427537 3511 -0.5479 0.291865 3556 1.5068 0.934075 Square side=100, avg. no. parked=3519.00 sample std.=18.00 p-value of the KSTEST for those 10 p-values: 0.655711 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-11-27_18:31 0.9214,0.5878,0.0387,0.0032,0.1479,0.0828,0.8029,0.3439,0.0298,0.9801, The KS test for those 10 p-values: 0.051984 The 3DSPHERES test for dh-ranFile-2016-11-27_18:31 sample no r^3 equiv. uni. 1 7.196 0.213257 2 35.551 0.694261 3 22.475 0.527239 4 0.750 0.024690 5 28.403 0.612006 6 47.713 0.796160 7 40.035 0.736711 8 43.572 0.765994 9 48.132 0.798990 10 40.668 0.742207 11 15.478 0.403050 12 2.871 0.091251 13 23.193 0.538419 14 47.546 0.795027 15 18.135 0.453648 16 121.314 0.982469 17 11.918 0.327852 18 25.539 0.573134 19 27.888 0.605294 20 36.174 0.700551 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.251677 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-11-27_18:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 2.0 1.8 0.6 -0.1 1.0 0.2 0.2 -0.2 0.2 0.4 -2.4 0.2 0.9 -0.0 0.9 -0.4 1.8 -0.1 -1.3 -0.4 0.8 -0.3 -0.9 0.4 -0.7 -0.8 -0.7 1.0 1.1 0.7 0.6 0.0 -2.4 0.5 -0.8 0.4 -1.4 -1.0 0.1 0.4 -0.6 0.0 -1.1 Chi-square with 42 degrees of freedom:39.389251 z-score=-0.284856, p-value=0.413801 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-11-27_18:31 Test no p-value 1 0.013190 2 0.347754 3 0.727125 4 0.331012 5 0.569571 6 0.281136 7 0.004430 8 0.299080 9 0.007041 10 0.270065 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.007179 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-11-27_18:31: (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 66717 0.04 66612 0.04 3 25000.00 24873 0.65 24965 0.05 4 6666.67 6727 0.55 6680 0.03 5 1388.89 1430 1.22 1452 2.87 6 238.10 226 0.61 247 0.33 7 34.72 24 3.31 34 0.01 8 4.96 2 1.77 9 3.29 p=0.77174 p=0.64325 Number of rngs required: 689398, p-value: 0.876 RESULTS OF CRAPS TEST for dh-ranFile-2016-11-27_18:31 No. of wins: Observed Expected 98404 98585.9 z-score=-0.813, pvalue=0.20800 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66385 66666.7 1.190 1.190 2 37764 37654.3 0.319 1.510 3 27117 26954.7 0.977 2.486 4 19331 19313.5 0.016 2.502 5 13795 13851.4 0.230 2.732 6 9913 9943.5 0.094 2.826 7 7220 7145.0 0.787 3.613 8 5121 5139.1 0.064 3.676 9 3675 3699.9 0.167 3.843 10 2761 2666.3 3.364 7.207 11 1911 1923.3 0.079 7.286 12 1383 1388.7 0.024 7.310 13 1001 1003.7 0.007 7.317 14 691 726.1 1.701 9.018 15 533 525.8 0.098 9.115 16 373 381.2 0.174 9.290 17 278 276.5 0.008 9.297 18 194 200.8 0.232 9.530 19 136 146.0 0.683 10.212 20 116 106.2 0.901 11.114 21 302 287.1 0.772 11.886 Chisq= 11.89 for 20 degrees of freedom, p= 0.08004 SUMMARY of craptest p-value for no. of wins: 0.208001 p-value for throws/game: 0.080043 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-11-27_18:31 No. of wins: Observed Expected 98379 98585.9 z-score=-0.925, pvalue=0.17743 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66466 66666.7 0.604 0.604 2 37682 37654.3 0.020 0.624 3 26794 26954.7 0.958 1.583 4 19412 19313.5 0.503 2.086 5 14062 13851.4 3.201 5.287 6 9920 9943.5 0.056 5.343 7 7265 7145.0 2.015 7.357 8 5151 5139.1 0.028 7.385 9 3760 3699.9 0.977 8.362 10 2700 2666.3 0.426 8.788 11 1901 1923.3 0.259 9.048 12 1349 1388.7 1.137 10.185 13 943 1003.7 3.673 13.857 14 694 726.1 1.423 15.280 15 520 525.8 0.065 15.345 16 382 381.2 0.002 15.347 17 273 276.5 0.045 15.392 18 197 200.8 0.073 15.465 19 146 146.0 0.000 15.465 20 105 106.2 0.014 15.479 21 278 287.1 0.289 15.768 Chisq= 15.77 for 20 degrees of freedom, p= 0.26911 SUMMARY of craptest p-value for no. of wins: 0.177433 p-value for throws/game: 0.269107 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0008,0.0032,0.0044,0.0044,0.0063,0.0064,0.0070,0.0072,0.0132,0.0198, 0.0204,0.0209,0.0247,0.0298,0.0339,0.0387,0.0520,0.0601,0.0603,0.0800, 0.0818,0.0828,0.0865,0.0896,0.0896,0.0896,0.0913,0.0940,0.0974,0.0975, 0.1016,0.1066,0.1120,0.1142,0.1198,0.1206,0.1229,0.1236,0.1259,0.1294, 0.1381,0.1438,0.1464,0.1479,0.1526,0.1566,0.1586,0.1625,0.1641,0.1766, 0.1774,0.1806,0.1806,0.1886,0.1971,0.2038,0.2055,0.2076,0.2080,0.2133, 0.2152,0.2164,0.2172,0.2363,0.2364,0.2374,0.2492,0.2517,0.2691,0.2701, 0.2708,0.2726,0.2747,0.2753,0.2788,0.2811,0.2864,0.2869,0.2876,0.2887, 0.2889,0.2919,0.2991,0.3011,0.3061,0.3174,0.3215,0.3279,0.3310,0.3330, 0.3366,0.3417,0.3419,0.3439,0.3478,0.3539,0.3559,0.3746,0.3757,0.3836, 0.3850,0.3892,0.4021,0.4030,0.4042,0.4058,0.4063,0.4081,0.4097,0.4136, 0.4138,0.4222,0.4230,0.4236,0.4275,0.4349,0.4352,0.4403,0.4439,0.4536, 0.4542,0.4575,0.4701,0.4718,0.4785,0.4843,0.4878,0.4894,0.4936,0.4940, 0.5122,0.5158,0.5174,0.5202,0.5255,0.5270,0.5272,0.5325,0.5384,0.5395, 0.5439,0.5517,0.5554,0.5588,0.5615,0.5617,0.5659,0.5696,0.5725,0.5731, 0.5733,0.5803,0.5803,0.5837,0.5841,0.5842,0.5862,0.5878,0.5895,0.5903, 0.5936,0.6014,0.6053,0.6054,0.6079,0.6107,0.6120,0.6134,0.6144,0.6145, 0.6166,0.6166,0.6168,0.6207,0.6249,0.6267,0.6281,0.6313,0.6371,0.6433, 0.6448,0.6459,0.6512,0.6512,0.6557,0.6640,0.6640,0.6739,0.6781,0.6800, 0.6855,0.6879,0.6905,0.6943,0.7006,0.7030,0.7056,0.7186,0.7205,0.7271, 0.7315,0.7367,0.7372,0.7397,0.7422,0.7433,0.7468,0.7535,0.7581,0.7589, 0.7630,0.7645,0.7648,0.7660,0.7686,0.7708,0.7708,0.7717,0.7756,0.7911, 0.7950,0.7962,0.7990,0.8023,0.8029,0.8036,0.8058,0.8076,0.8144,0.8230, 0.8279,0.8312,0.8451,0.8596,0.8607,0.8635,0.8715,0.8761,0.8813,0.8821, 0.8898,0.8908,0.8948,0.8980,0.9036,0.9118,0.9171,0.9189,0.9214,0.9302, 0.9317,0.9337,0.9341,0.9375,0.9412,0.9453,0.9482,0.9605,0.9637,0.9736, 0.9741,0.9756,0.9801,0.9825,0.9845,0.9932,0.9947,0.9982,0.9991, Overall p-value after applying KStest on 269 p-values = 0.649021 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.