RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-05-18_02:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.80 14.1902 0.346405 2 to 25 15.62 22.4330 0.831365 3 to 26 15.56 10.1532 0.102937 4 to 27 15.61 19.4270 0.695422 5 to 28 15.55 17.9295 0.606699 6 to 29 15.71 9.9427 0.094004 7 to 30 15.60 22.4917 0.833460 8 to 31 15.60 24.7267 0.899003 9 to 32 15.71 18.9076 0.666139 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.643118 Tough bday spacings test for dh-ranFile-2016-05-18_02:31: 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 5 45 73 97 103 89 44 22 13 6 3 (O-E)^2/E 1.9 1.9 0.0 0.0 0.3 1.5 1.3 2.0 0.2 0.1 0.3 Birthday Spacings: Sum(O-E)^2/E= 9.464, p= 0.511 RESULTS OF GCD FOR dh-ranFile-2016-05-18_02:31 Euclid's algorithm: p-value, steps to gcd: 0.042133 p-value, dist. of gcd's: 0.591929 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-05-18_02:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.271 0.086 0.600 0.388 0.881 0.369 0.276 0.983 Bits 8 to 15---> 0.848 0.051 0.645 0.440 0.420 0.108 0.121 0.229 Bits 16 to 23---> 0.227 0.006 0.606 0.700 0.502 0.953 0.296 0.572 Bits 24 to 31---> 0.261 0.469 0.102 0.870 0.426 0.244 0.169 0.759 KS test for the above 32 p values: 0.659 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-05-18_02:31, p-values for 5 runs: 0.2589, 0.2238, 0.6141, 0.9379, 0.5352 Rank test for binary matrices (31x31) for dh-ranFile-2016-05-18_02:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 216 211.4 0.099 0.099 r= 29 5124 5134.0 0.020 0.119 r= 30 23053 23103.0 0.108 0.227 r= 31 11607 11551.5 0.266 0.494 chi-square = 0.494 with df = 3; p-value = 0.080 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-05-18_02:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 213 211.4 0.012 0.012 r= 30 5208 5134.0 1.066 1.078 r= 31 23016 23103.0 0.328 1.406 r= 32 11563 11551.5 0.011 1.418 chi-square = 1.418 with df = 3; p-value = 0.299 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-05-18_02:31 b-rank test for bits 1 to 8, p=0.96127 b-rank test for bits 2 to 9, p=0.88024 b-rank test for bits 3 to 10, p=0.64466 b-rank test for bits 4 to 11, p=0.45250 b-rank test for bits 5 to 12, p=0.42257 b-rank test for bits 6 to 13, p=0.14181 b-rank test for bits 7 to 14, p=0.66155 b-rank test for bits 8 to 15, p=0.35274 b-rank test for bits 9 to 16, p=0.58990 b-rank test for bits 10 to 17, p=0.22115 b-rank test for bits 11 to 18, p=0.35363 b-rank test for bits 12 to 19, p=0.71312 b-rank test for bits 13 to 20, p=0.93483 b-rank test for bits 14 to 21, p=0.00016 b-rank test for bits 15 to 22, p=0.31809 b-rank test for bits 16 to 23, p=0.55144 b-rank test for bits 17 to 24, p=0.81652 b-rank test for bits 18 to 25, p=0.17908 b-rank test for bits 19 to 26, p=0.17850 b-rank test for bits 20 to 27, p=0.51175 b-rank test for bits 21 to 28, p=0.65735 b-rank test for bits 22 to 29, p=0.64767 b-rank test for bits 23 to 30, p=0.11798 b-rank test for bits 24 to 31, p=0.23525 b-rank test for bits 25 to 32, p=0.23273 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 = 0.712835 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-05-18_02:31 (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 141727 -0.43 0.335052 2 141474 -1.02 0.154547 3 141378 -1.24 0.107224 4 141237 -1.57 0.058107 5 141196 -1.67 0.047791 6 141816 -0.22 0.413691 7 141812 -0.23 0.410054 8 141855 -0.13 0.449494 9 141773 -0.32 0.375042 10 142011 0.24 0.593884 11 142062 0.36 0.639344 12 141917 0.02 0.507149 13 141924 0.03 0.513671 14 141609 -0.70 0.241431 15 141578 -0.77 0.219425 16 142401 1.15 0.874673 17 141131 -1.82 0.034492 18 141977 0.16 0.562814 19 141977 0.16 0.562814 20 142571 1.55 0.938943 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-05-18_02:31 Bits used No. missing words z-score p-value 23 to 32 141430 -1.6529 0.049179 22 to 31 141537 -1.2839 0.099589 21 to 30 142215 1.0540 0.854066 20 to 29 141820 -0.3080 0.379028 19 to 28 142111 0.6954 0.756602 18 to 27 142374 1.6023 0.945457 17 to 26 141680 -0.7908 0.214532 16 to 25 141815 -0.3253 0.372486 15 to 24 141776 -0.4598 0.322845 14 to 23 141947 0.1299 0.551676 13 to 22 141920 0.0368 0.514675 12 to 21 141865 -0.1529 0.439254 11 to 20 141755 -0.5322 0.297303 10 to 19 141729 -0.6218 0.267028 9 to 18 141755 -0.5322 0.297303 8 to 17 141488 -1.4529 0.073131 7 to 16 141879 -0.1046 0.458352 6 to 15 142064 0.5333 0.703103 5 to 14 141673 -0.8149 0.207556 4 to 13 141916 0.0230 0.509175 3 to 12 142391 1.6609 0.951636 2 to 11 142639 2.5161 0.994067 1 to 10 141577 -1.1460 0.125905 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-05-18_02:31 Bits used No. missing words z-score p-value 28 to 32 141720 -0.6418 0.260503 27 to 31 141574 -1.1367 0.127829 26 to 30 141215 -2.3537 0.009295 25 to 29 141588 -1.0893 0.138021 24 to 28 142010 0.3413 0.633544 23 to 27 141687 -0.7537 0.225526 22 to 26 141677 -0.7876 0.215477 21 to 25 142037 0.4328 0.667413 20 to 24 142116 0.7006 0.758216 19 to 23 142012 0.3480 0.636093 18 to 22 141844 -0.2215 0.412368 17 to 21 141793 -0.3943 0.346665 16 to 20 141862 -0.1604 0.436267 15 to 19 141675 -0.7943 0.213499 14 to 18 142319 1.3887 0.917540 13 to 17 141565 -1.1672 0.121561 12 to 16 141802 -0.3638 0.357992 11 to 15 141628 -0.9537 0.170128 10 to 14 141559 -1.1876 0.117504 9 to 13 141851 -0.1977 0.421629 8 to 12 141951 0.1413 0.556166 7 to 11 141881 -0.0960 0.461747 6 to 10 142105 0.6633 0.746427 5 to 9 141733 -0.5977 0.275010 4 to 8 141873 -0.1232 0.450993 3 to 7 141827 -0.2791 0.390090 2 to 6 141982 0.2463 0.597290 1 to 5 141870 -0.1333 0.446969 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-05-18_02:31 Bits used No. missing words z-score p-value 31 to 32 141624 -0.8417 0.199983 30 to 31 141598 -0.9184 0.179211 29 to 30 141725 -0.5437 0.293308 28 to 29 141723 -0.5496 0.291281 27 to 28 142057 0.4356 0.668438 26 to 27 142372 1.3648 0.913843 25 to 26 142397 1.4386 0.924862 24 to 25 141540 -1.0895 0.137974 23 to 24 142394 1.4297 0.923599 22 to 23 141878 -0.0924 0.463183 21 to 22 141960 0.1495 0.559408 20 to 21 141394 -1.5201 0.064237 19 to 20 141791 -0.3491 0.363524 18 to 19 141618 -0.8594 0.195065 17 to 18 142123 0.6303 0.735749 16 to 17 141572 -0.9951 0.159850 15 to 16 142139 0.6775 0.750953 14 to 15 142042 0.3914 0.652233 13 to 14 142231 0.9489 0.828659 12 to 13 142231 0.9489 0.828659 11 to 12 141940 0.0905 0.536044 10 to 11 141722 -0.5526 0.290270 9 to 10 141074 -2.4641 0.006868 8 to 9 141999 0.2645 0.604308 7 to 8 141511 -1.1750 0.119994 6 to 7 141136 -2.2812 0.011268 5 to 6 141933 0.0698 0.527833 4 to 5 142068 0.4681 0.680127 3 to 4 142385 1.4032 0.919715 2 to 3 142250 1.0049 0.842534 1 to 2 142041 0.3884 0.651143 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-05-18_02:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2533.12 0.468 0.680267 Test results for specific bytes for dh-ranFile-2016-05-18_02:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2464.94 -0.496 0.310012 2 to 9 2614.33 1.617 0.947046 3 to 10 2484.88 -0.214 0.415320 4 to 11 2507.77 0.110 0.543744 5 to 12 2404.34 -1.353 0.088058 6 to 13 2527.82 0.393 0.652987 7 to 14 2498.74 -0.018 0.492907 8 to 15 2528.82 0.408 0.658182 9 to 16 2415.47 -1.195 0.115970 10 to 17 2579.28 1.121 0.868901 11 to 18 2440.99 -0.834 0.202011 12 to 19 2475.76 -0.343 0.365893 13 to 20 2529.57 0.418 0.662079 14 to 21 2550.55 0.715 0.762665 15 to 22 2505.63 0.080 0.531731 16 to 23 2502.83 0.040 0.515974 17 to 24 2517.30 0.245 0.596627 18 to 25 2550.70 0.717 0.763294 19 to 26 2506.09 0.086 0.534344 20 to 27 2437.35 -0.886 0.187790 21 to 28 2444.02 -0.792 0.214255 22 to 29 2501.54 0.022 0.508676 23 to 30 2549.07 0.694 0.756147 24 to 31 2425.23 -1.057 0.145161 25 to 32 2457.66 -0.599 0.274650 CDPARK for dh-ranFile-2016-05-18_02:31: 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 3509 -0.6393 0.261324 3537 0.6393 0.738676 3524 0.0457 0.518210 3527 0.1826 0.572463 3526 0.1370 0.554479 3516 -0.3196 0.374623 3553 1.3699 0.914635 3495 -1.2785 0.100530 3567 2.0091 0.977738 3523 0.0000 0.500000 Square side=100, avg. no. parked=3527.70 sample std.=19.66 p-value of the KSTEST for those 10 p-values: 0.788180 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-05-18_02:31 0.7812,0.9027,0.1901,0.6705,0.7254,0.1842,0.8538,0.3292,0.6313,0.5967, The KS test for those 10 p-values: 0.492172 The 3DSPHERES test for dh-ranFile-2016-05-18_02:31 sample no r^3 equiv. uni. 1 18.163 0.454166 2 1.683 0.054545 3 14.332 0.379811 4 54.428 0.837044 5 7.667 0.225519 6 12.128 0.332543 7 37.249 0.711088 8 17.423 0.440538 9 2.078 0.066907 10 6.889 0.205180 11 2.793 0.088891 12 6.139 0.185054 13 24.844 0.563138 14 42.595 0.758242 15 155.292 0.994352 16 8.003 0.234158 17 33.974 0.677759 18 48.846 0.803720 19 1.976 0.063729 20 30.236 0.635006 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.514105 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-05-18_02:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 1.3 -3.0 0.5 -0.2 0.3 -0.4 -0.3 -1.9 -0.5 -0.6 1.4 -0.3 0.2 0.9 -1.2 0.4 -1.2 0.5 -0.1 1.1 -1.3 -0.2 1.4 1.0 0.5 -1.0 0.4 -0.7 0.8 0.5 0.8 0.0 -1.5 0.1 2.0 0.7 -0.4 -2.0 -0.7 -0.6 0.0 -0.1 Chi-square with 42 degrees of freedom:42.980990 z-score=0.107035, p-value=0.570989 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-05-18_02:31 Test no p-value 1 0.114953 2 0.400013 3 0.533049 4 0.338116 5 0.491015 6 0.676316 7 0.389991 8 0.001378 9 0.572602 10 0.848416 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.430453 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-05-18_02:31: (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 66465 0.61 66955 1.25 3 25000.00 25313 3.92 24641 5.16 4 6666.67 6544 2.26 6722 0.46 5 1388.89 1388 0.00 1403 0.14 6 238.10 247 0.33 242 0.06 7 34.72 38 0.31 34 0.01 8 4.96 4 0.19 2 1.77 p=0.73234 p=0.81782 Number of rngs required: 687614, p-value: 0.181 RESULTS OF CRAPS TEST for dh-ranFile-2016-05-18_02:31 No. of wins: Observed Expected 98386 98585.9 z-score=-0.894, pvalue=0.18569 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66668 66666.7 0.000 0.000 2 37756 37654.3 0.275 0.275 3 26704 26954.7 2.332 2.607 4 19404 19313.5 0.424 3.031 5 13785 13851.4 0.318 3.350 6 9859 9943.5 0.719 4.069 7 7336 7145.0 5.104 9.173 8 5115 5139.1 0.113 9.286 9 3743 3699.9 0.503 9.789 10 2741 2666.3 2.093 11.882 11 1885 1923.3 0.764 12.646 12 1434 1388.7 1.475 14.121 13 999 1003.7 0.022 14.143 14 696 726.1 1.251 15.394 15 482 525.8 3.654 19.048 16 400 381.2 0.932 19.980 17 267 276.5 0.329 20.309 18 179 200.8 2.373 22.682 19 158 146.0 0.989 23.671 20 120 106.2 1.789 25.460 21 269 287.1 1.143 26.603 Chisq= 26.60 for 20 degrees of freedom, p= 0.85319 SUMMARY of craptest p-value for no. of wins: 0.185692 p-value for throws/game: 0.853194 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-05-18_02:31 No. of wins: Observed Expected 98622 98585.9 z-score= 0.162, pvalue=0.56421 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66988 66666.7 1.549 1.549 2 37591 37654.3 0.106 1.655 3 26823 26954.7 0.644 2.299 4 19288 19313.5 0.034 2.333 5 13946 13851.4 0.646 2.978 6 9853 9943.5 0.824 3.803 7 7084 7145.0 0.521 4.324 8 5118 5139.1 0.086 4.411 9 3685 3699.9 0.060 4.470 10 2623 2666.3 0.703 5.173 11 1900 1923.3 0.283 5.456 12 1398 1388.7 0.062 5.518 13 990 1003.7 0.187 5.706 14 820 726.1 12.132 17.838 15 523 525.8 0.015 17.853 16 369 381.2 0.387 18.240 17 289 276.5 0.561 18.802 18 198 200.8 0.040 18.842 19 134 146.0 0.984 19.825 20 107 106.2 0.006 19.831 21 273 287.1 0.694 20.525 Chisq= 20.53 for 20 degrees of freedom, p= 0.57445 SUMMARY of craptest p-value for no. of wins: 0.564207 p-value for throws/game: 0.574452 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0002,0.0014,0.0064,0.0069,0.0093,0.0113,0.0345,0.0421,0.0478,0.0492, 0.0508,0.0545,0.0581,0.0637,0.0642,0.0669,0.0731,0.0797,0.0859,0.0881, 0.0889,0.0940,0.0996,0.1005,0.1023,0.1029,0.1072,0.1081,0.1150,0.1160, 0.1175,0.1180,0.1200,0.1206,0.1216,0.1259,0.1278,0.1380,0.1380,0.1418, 0.1452,0.1545,0.1599,0.1694,0.1701,0.1785,0.1791,0.1792,0.1806,0.1842, 0.1851,0.1857,0.1878,0.1901,0.1951,0.2000,0.2020,0.2052,0.2076,0.2135, 0.2143,0.2145,0.2155,0.2194,0.2211,0.2238,0.2255,0.2255,0.2267,0.2286, 0.2327,0.2342,0.2352,0.2414,0.2443,0.2589,0.2605,0.2607,0.2613,0.2670, 0.2714,0.2746,0.2750,0.2760,0.2903,0.2913,0.2933,0.2955,0.2973,0.2973, 0.2986,0.3100,0.3181,0.3228,0.3292,0.3325,0.3351,0.3381,0.3464,0.3467, 0.3527,0.3536,0.3580,0.3635,0.3659,0.3693,0.3725,0.3746,0.3750,0.3790, 0.3798,0.3878,0.3900,0.3901,0.4000,0.4101,0.4124,0.4137,0.4153,0.4203, 0.4216,0.4226,0.4255,0.4305,0.4363,0.4393,0.4399,0.4405,0.4470,0.4495, 0.4510,0.4525,0.4542,0.4584,0.4617,0.4632,0.4690,0.4910,0.4922,0.4929, 0.5000,0.5023,0.5071,0.5087,0.5092,0.5113,0.5117,0.5137,0.5141,0.5147, 0.5160,0.5182,0.5278,0.5317,0.5330,0.5343,0.5352,0.5360,0.5437,0.5514, 0.5517,0.5545,0.5562,0.5594,0.5628,0.5628,0.5631,0.5642,0.5710,0.5718, 0.5725,0.5726,0.5745,0.5899,0.5919,0.5939,0.5966,0.5967,0.5973,0.6003, 0.6043,0.6063,0.6067,0.6141,0.6313,0.6335,0.6350,0.6361,0.6393,0.6431, 0.6447,0.6448,0.6477,0.6511,0.6522,0.6530,0.6573,0.6582,0.6594,0.6615, 0.6621,0.6661,0.6674,0.6684,0.6705,0.6763,0.6778,0.6801,0.6803,0.6954, 0.7000,0.7031,0.7111,0.7128,0.7131,0.7254,0.7323,0.7357,0.7387,0.7464, 0.7510,0.7561,0.7566,0.7582,0.7582,0.7586,0.7627,0.7633,0.7812,0.7882, 0.8037,0.8165,0.8178,0.8287,0.8287,0.8314,0.8335,0.8370,0.8425,0.8475, 0.8484,0.8532,0.8538,0.8541,0.8689,0.8703,0.8747,0.8802,0.8811,0.8990, 0.9027,0.9138,0.9146,0.9175,0.9197,0.9236,0.9249,0.9348,0.9379,0.9389, 0.9455,0.9470,0.9516,0.9529,0.9613,0.9777,0.9826,0.9941,0.9944, Overall p-value after applying KStest on 269 p-values = 0.038215 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.