RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-27_04:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.44 21.1411 0.779958 2 to 25 15.77 16.3513 0.500919 3 to 26 15.56 15.1503 0.415344 4 to 27 15.68 33.0714 0.988961 5 to 28 15.80 18.2779 0.628483 6 to 29 15.67 11.2717 0.157901 7 to 30 15.72 19.2740 0.686969 8 to 31 15.85 14.3822 0.360114 9 to 32 16.18 23.4098 0.863623 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.548942 Tough bday spacings test for dh-ranFile-2018-06-27_04:31: 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 17 35 62 107 95 84 49 28 18 3 2 (O-E)^2/E 6.7 0.1 1.7 0.9 0.1 0.4 0.2 0.1 0.7 2.0 1.0 Birthday Spacings: Sum(O-E)^2/E= 13.887, p= 0.822 RESULTS OF GCD FOR dh-ranFile-2018-06-27_04:31 Euclid's algorithm: p-value, steps to gcd: 0.354227 p-value, dist. of gcd's: 0.104837 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-27_04:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.614 0.959 0.032 0.175 0.712 0.939 0.595 0.709 Bits 8 to 15---> 0.613 0.029 0.935 0.296 0.377 0.742 0.869 0.080 Bits 16 to 23---> 0.054 0.360 0.718 0.741 0.476 0.553 0.748 0.507 Bits 24 to 31---> 0.715 0.557 0.149 0.095 0.694 0.945 0.858 0.167 KS test for the above 32 p values: 0.442 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-27_04:31, p-values for 5 runs: 0.6031, 0.9766, 0.8904, 0.7089, 0.8501 Rank test for binary matrices (31x31) for dh-ranFile-2018-06-27_04:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 217 211.4 0.147 0.147 r= 29 5055 5134.0 1.216 1.363 r= 30 23277 23103.0 1.310 2.673 r= 31 11451 11551.5 0.875 3.548 chi-square = 3.548 with df = 3; p-value = 0.685 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-06-27_04:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 217 211.4 0.147 0.147 r= 30 5182 5134.0 0.449 0.596 r= 31 22862 23103.0 2.515 3.111 r= 32 11739 11551.5 3.043 6.154 chi-square = 6.154 with df = 3; p-value = 0.896 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-06-27_04:31 b-rank test for bits 1 to 8, p=0.52823 b-rank test for bits 2 to 9, p=0.10386 b-rank test for bits 3 to 10, p=0.09416 b-rank test for bits 4 to 11, p=0.35817 b-rank test for bits 5 to 12, p=0.21663 b-rank test for bits 6 to 13, p=0.07328 b-rank test for bits 7 to 14, p=0.75701 b-rank test for bits 8 to 15, p=0.75769 b-rank test for bits 9 to 16, p=0.85758 b-rank test for bits 10 to 17, p=0.84469 b-rank test for bits 11 to 18, p=0.23881 b-rank test for bits 12 to 19, p=0.06209 b-rank test for bits 13 to 20, p=0.84236 b-rank test for bits 14 to 21, p=0.90000 b-rank test for bits 15 to 22, p=0.25505 b-rank test for bits 16 to 23, p=0.57169 b-rank test for bits 17 to 24, p=0.34032 b-rank test for bits 18 to 25, p=0.09143 b-rank test for bits 19 to 26, p=0.39749 b-rank test for bits 20 to 27, p=0.10420 b-rank test for bits 21 to 28, p=0.37117 b-rank test for bits 22 to 29, p=0.53741 b-rank test for bits 23 to 30, p=0.25364 b-rank test for bits 24 to 31, p=0.47828 b-rank test for bits 25 to 32, p=0.38888 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 = 0.205326 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-27_04:31 (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 141259 -1.52 0.064323 2 141899 -0.02 0.490372 3 140881 -2.40 0.008139 4 141153 -1.77 0.038604 5 142293 0.90 0.814987 6 141866 -0.10 0.459681 7 141920 0.02 0.509945 8 142684 1.81 0.964850 9 142352 1.03 0.849496 10 142703 1.85 0.968157 11 141619 -0.68 0.248778 12 141781 -0.30 0.382151 13 142029 0.28 0.610109 14 142079 0.40 0.654104 15 141477 -1.01 0.156220 16 141490 -0.98 0.163607 17 142260 0.82 0.793699 18 142384 1.11 0.866294 19 142038 0.30 0.618152 20 141168 -1.73 0.041630 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-06-27_04:31 Bits used No. missing words z-score p-value 23 to 32 141661 -0.8563 0.195913 22 to 31 141712 -0.6804 0.248110 21 to 30 142237 1.1299 0.870740 20 to 29 141605 -1.0494 0.146994 19 to 28 141540 -1.2736 0.101411 18 to 27 142449 1.8609 0.968623 17 to 26 141749 -0.5529 0.290179 16 to 25 141775 -0.4632 0.321608 15 to 24 142201 1.0058 0.842734 14 to 23 142002 0.3196 0.625346 13 to 22 142488 1.9954 0.977001 12 to 21 141836 -0.2529 0.400187 11 to 20 141426 -1.6667 0.047792 10 to 19 141721 -0.6494 0.258036 9 to 18 141955 0.1575 0.562568 8 to 17 141902 -0.0253 0.489918 7 to 16 142161 0.8678 0.807256 6 to 15 142308 1.3747 0.915392 5 to 14 142400 1.6920 0.954674 4 to 13 142258 1.2023 0.885378 3 to 12 141603 -1.0563 0.145413 2 to 11 141721 -0.6494 0.258036 1 to 10 141626 -0.9770 0.164285 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-06-27_04:31 Bits used No. missing words z-score p-value 28 to 32 142240 1.1209 0.868838 27 to 31 142302 1.3311 0.908419 26 to 30 141717 -0.6520 0.257212 25 to 29 141878 -0.1062 0.457711 24 to 28 141804 -0.3571 0.360527 23 to 27 141548 -1.2248 0.110316 22 to 26 142591 2.3107 0.989577 21 to 25 142041 0.4463 0.672324 20 to 24 141686 -0.7571 0.224510 19 to 23 141739 -0.5774 0.281838 18 to 22 141841 -0.2316 0.408414 17 to 21 142076 0.5650 0.713957 16 to 20 142331 1.4294 0.923554 15 to 19 142192 0.9582 0.831020 14 to 18 142040 0.4429 0.671099 13 to 17 141005 -3.0655 0.001086 12 to 16 141704 -0.6960 0.243204 11 to 15 142112 0.6870 0.753964 10 to 14 141995 0.2904 0.614248 9 to 13 142489 1.9650 0.975292 8 to 12 141615 -0.9977 0.159205 7 to 11 142315 1.3752 0.915458 6 to 10 142152 0.8226 0.794635 5 to 9 141930 0.0701 0.527930 4 to 8 141228 -2.3096 0.010455 3 to 7 142133 0.7582 0.775835 2 to 6 142324 1.4057 0.920088 1 to 5 141862 -0.1604 0.436267 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-06-27_04:31 Bits used No. missing words z-score p-value 31 to 32 141520 -1.1485 0.125388 30 to 31 142066 0.4622 0.678014 29 to 30 142108 0.5860 0.721078 28 to 29 141603 -0.9036 0.183096 27 to 28 141898 -0.0334 0.486669 26 to 27 141507 -1.1868 0.117650 25 to 26 142229 0.9430 0.827154 24 to 25 141648 -0.7709 0.220388 23 to 24 141392 -1.5260 0.063499 22 to 23 142560 1.9194 0.972532 21 to 22 142004 0.2793 0.609978 20 to 21 142116 0.6096 0.728952 19 to 20 142365 1.3442 0.910552 18 to 19 142142 0.6863 0.753751 17 to 18 142271 1.0669 0.856985 16 to 17 141786 -0.3638 0.358002 15 to 16 141997 0.2586 0.602033 14 to 15 142775 2.5536 0.994669 13 to 14 141964 0.1613 0.564059 12 to 13 141491 -1.2340 0.108599 11 to 12 141444 -1.3727 0.084930 10 to 11 141998 0.2616 0.603171 9 to 10 142158 0.7335 0.768385 8 to 9 141299 -1.8004 0.035900 7 to 8 141759 -0.4435 0.328720 6 to 7 142184 0.8102 0.791098 5 to 6 141856 -0.1573 0.437498 4 to 5 141943 0.0993 0.539559 3 to 4 141605 -0.8977 0.184665 2 to 3 141341 -1.6765 0.046821 1 to 2 141541 -1.0865 0.138625 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-27_04:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2565.70 0.929 0.823604 Test results for specific bytes for dh-ranFile-2018-06-27_04:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2593.76 1.326 0.907576 2 to 9 2542.03 0.594 0.723868 3 to 10 2615.61 1.635 0.948968 4 to 11 2387.27 -1.594 0.055435 5 to 12 2528.56 0.404 0.656847 6 to 13 2519.90 0.281 0.610785 7 to 14 2541.49 0.587 0.721317 8 to 15 2440.04 -0.848 0.198212 9 to 16 2512.30 0.174 0.569021 10 to 17 2444.36 -0.787 0.215694 11 to 18 2487.09 -0.183 0.427553 12 to 19 2579.24 1.121 0.868769 13 to 20 2504.15 0.059 0.523380 14 to 21 2453.94 -0.651 0.257405 15 to 22 2363.75 -1.927 0.026999 16 to 23 2608.23 1.531 0.937069 17 to 24 2430.42 -0.984 0.162550 18 to 25 2507.14 0.101 0.540215 19 to 26 2588.43 1.251 0.894450 20 to 27 2442.48 -0.814 0.207964 21 to 28 2527.04 0.382 0.648902 22 to 29 2423.40 -1.083 0.139331 23 to 30 2492.37 -0.108 0.457018 24 to 31 2496.05 -0.056 0.477698 25 to 32 2495.24 -0.067 0.473161 CDPARK for dh-ranFile-2018-06-27_04:31: 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 3528 0.2283 0.590298 3519 -0.1826 0.427537 3532 0.4110 0.659449 3522 -0.0457 0.481790 3519 -0.1826 0.427537 3521 -0.0913 0.463617 3491 -1.4612 0.071982 3541 0.8219 0.794438 3519 -0.1826 0.427537 3491 -1.4612 0.071982 Square side=100, avg. no. parked=3518.30 sample std.=15.20 p-value of the KSTEST for those 10 p-values: 0.378757 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-27_04:31 0.3858,0.2165,0.1484,0.6501,0.0294,0.3288,0.6806,0.7280,0.1245,0.4524, The KS test for those 10 p-values: 0.298577 The 3DSPHERES test for dh-ranFile-2018-06-27_04:31 sample no r^3 equiv. uni. 1 5.388 0.164399 2 2.931 0.093090 3 36.794 0.706673 4 10.686 0.299656 5 17.924 0.449797 6 5.831 0.176653 7 152.472 0.993795 8 6.177 0.186083 9 49.730 0.809416 10 8.577 0.248654 11 14.012 0.373161 12 27.539 0.600668 13 62.645 0.876086 14 21.594 0.513157 15 35.926 0.698061 16 13.659 0.365743 17 26.307 0.583928 18 27.974 0.606424 19 2.093 0.067391 20 4.118 0.128259 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.662228 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-27_04:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 1.3 -0.4 -0.5 -1.0 0.1 0.9 -0.1 -0.9 -0.8 -1.8 -0.3 1.9 0.6 -0.3 0.8 -0.2 -0.5 0.3 -0.0 -0.5 0.2 -1.4 -0.1 1.5 0.8 1.1 0.1 0.2 -2.1 0.9 -0.3 0.8 -1.3 0.3 1.3 0.0 -0.1 -0.4 -0.7 1.6 -1.0 0.8 Chi-square with 42 degrees of freedom:35.070033 z-score=-0.756121, p-value=0.233195 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-06-27_04:31 Test no p-value 1 0.010050 2 0.181969 3 0.640968 4 0.362403 5 0.319772 6 0.293531 7 0.549648 8 0.160814 9 0.861542 10 0.093232 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.164900 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-27_04:31: (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 66598 0.07 67029 1.97 3 25000.00 25153 0.94 24857 0.82 4 6666.67 6584 1.03 6539 2.44 5 1388.89 1378 0.09 1319 3.52 6 238.10 242 0.06 204 4.88 7 34.72 37 0.15 44 2.48 8 4.96 7 0.84 7 0.84 p=0.21283 p=0.99053 Number of rngs required: 688820, p-value: 0.685 RESULTS OF CRAPS TEST for dh-ranFile-2018-06-27_04:31 No. of wins: Observed Expected 98533 98585.9 z-score=-0.236, pvalue=0.40656 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66867 66666.7 0.602 0.602 2 37669 37654.3 0.006 0.608 3 26799 26954.7 0.900 1.507 4 19163 19313.5 1.172 2.680 5 14019 13851.4 2.027 4.707 6 9911 9943.5 0.107 4.814 7 7211 7145.0 0.609 5.423 8 5147 5139.1 0.012 5.435 9 3700 3699.9 0.000 5.435 10 2629 2666.3 0.522 5.957 11 1867 1923.3 1.650 7.606 12 1345 1388.7 1.378 8.984 13 1009 1003.7 0.028 9.012 14 739 726.1 0.228 9.240 15 532 525.8 0.072 9.312 16 363 381.2 0.864 10.176 17 289 276.5 0.561 10.738 18 199 200.8 0.017 10.754 19 159 146.0 1.160 11.915 20 113 106.2 0.433 12.348 21 270 287.1 1.020 13.368 Chisq= 13.37 for 20 degrees of freedom, p= 0.13898 SUMMARY of craptest p-value for no. of wins: 0.406556 p-value for throws/game: 0.138975 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-27_04:31 No. of wins: Observed Expected 98328 98585.9 z-score=-1.153, pvalue=0.12439 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66606 66666.7 0.055 0.055 2 37939 37654.3 2.152 2.207 3 26845 26954.7 0.447 2.654 4 19393 19313.5 0.328 2.982 5 13636 13851.4 3.350 6.332 6 9951 9943.5 0.006 6.338 7 7150 7145.0 0.003 6.341 8 5068 5139.1 0.983 7.324 9 3755 3699.9 0.822 8.146 10 2743 2666.3 2.207 10.352 11 1903 1923.3 0.215 10.567 12 1384 1388.7 0.016 10.583 13 961 1003.7 1.818 12.401 14 731 726.1 0.033 12.434 15 551 525.8 1.204 13.638 16 371 381.2 0.270 13.908 17 298 276.5 1.665 15.574 18 179 200.8 2.373 17.946 19 137 146.0 0.553 18.499 20 115 106.2 0.727 19.226 21 284 287.1 0.034 19.260 Chisq= 19.26 for 20 degrees of freedom, p= 0.49499 SUMMARY of craptest p-value for no. of wins: 0.124395 p-value for throws/game: 0.494990 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0011,0.0081,0.0101,0.0105,0.0270,0.0290,0.0294,0.0320,0.0359,0.0386, 0.0416,0.0468,0.0478,0.0543,0.0554,0.0621,0.0635,0.0643,0.0674,0.0720, 0.0720,0.0733,0.0805,0.0849,0.0914,0.0931,0.0932,0.0942,0.0947,0.1014, 0.1039,0.1042,0.1048,0.1086,0.1103,0.1177,0.1244,0.1245,0.1254,0.1283, 0.1386,0.1390,0.1393,0.1454,0.1470,0.1484,0.1493,0.1562,0.1579,0.1592, 0.1608,0.1626,0.1636,0.1643,0.1644,0.1649,0.1670,0.1754,0.1767,0.1820, 0.1831,0.1847,0.1861,0.1959,0.1982,0.2053,0.2080,0.2128,0.2157,0.2165, 0.2166,0.2204,0.2245,0.2332,0.2388,0.2432,0.2481,0.2487,0.2488,0.2536, 0.2550,0.2572,0.2574,0.2580,0.2580,0.2818,0.2902,0.2935,0.2962,0.2986, 0.2997,0.3198,0.3216,0.3287,0.3288,0.3403,0.3542,0.3580,0.3582,0.3601, 0.3603,0.3605,0.3624,0.3657,0.3712,0.3732,0.3772,0.3788,0.3822,0.3858, 0.3889,0.3975,0.4002,0.4066,0.4084,0.4153,0.4275,0.4275,0.4275,0.4276, 0.4363,0.4375,0.4423,0.4498,0.4524,0.4570,0.4577,0.4597,0.4636,0.4732, 0.4765,0.4777,0.4783,0.4818,0.4867,0.4899,0.4904,0.4950,0.5009,0.5066, 0.5099,0.5132,0.5234,0.5279,0.5282,0.5374,0.5396,0.5402,0.5489,0.5496, 0.5526,0.5569,0.5626,0.5641,0.5690,0.5717,0.5839,0.5903,0.5949,0.6007, 0.6020,0.6031,0.6032,0.6064,0.6100,0.6101,0.6108,0.6126,0.6136,0.6142, 0.6182,0.6253,0.6285,0.6410,0.6489,0.6501,0.6541,0.6568,0.6594,0.6622, 0.6711,0.6723,0.6780,0.6806,0.6846,0.6854,0.6870,0.6936,0.6981,0.7067, 0.7089,0.7093,0.7116,0.7140,0.7150,0.7184,0.7211,0.7213,0.7239,0.7280, 0.7290,0.7406,0.7423,0.7485,0.7538,0.7540,0.7570,0.7577,0.7684,0.7758, 0.7800,0.7911,0.7937,0.7944,0.7946,0.8073,0.8094,0.8150,0.8218,0.8236, 0.8272,0.8310,0.8424,0.8427,0.8447,0.8495,0.8501,0.8570,0.8576,0.8580, 0.8615,0.8636,0.8663,0.8688,0.8688,0.8688,0.8707,0.8761,0.8854,0.8904, 0.8944,0.8956,0.9000,0.9076,0.9084,0.9106,0.9154,0.9155,0.9201,0.9236, 0.9354,0.9371,0.9389,0.9447,0.9490,0.9547,0.9591,0.9649,0.9682,0.9686, 0.9725,0.9753,0.9766,0.9770,0.9890,0.9896,0.9905,0.9938,0.9947, Overall p-value after applying KStest on 269 p-values = 0.702257 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.