RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-12-07_11:31 (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 19.2369 0.684894 2 to 25 15.72 15.8772 0.467442 3 to 26 15.77 13.6764 0.310139 4 to 27 15.72 24.0904 0.882999 5 to 28 15.69 31.7381 0.983784 6 to 29 16.00 21.7522 0.805561 7 to 30 15.84 12.5150 0.231999 8 to 31 15.82 14.3581 0.358388 9 to 32 15.62 14.8283 0.392153 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.645597 Tough bday spacings test for dh-ranFile-2015-12-07_11:31: 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 36 89 86 90 89 51 23 16 8 2 (O-E)^2/E 0.1 0.0 3.4 1.4 0.6 1.5 0.0 1.5 0.1 0.3 1.0 Birthday Spacings: Sum(O-E)^2/E= 9.964, p= 0.556 RESULTS OF GCD FOR dh-ranFile-2015-12-07_11:31 Euclid's algorithm: p-value, steps to gcd: 0.508891 p-value, dist. of gcd's: 0.594882 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-12-07_11:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.789 0.960 0.061 0.216 0.525 0.495 0.828 0.671 Bits 8 to 15---> 0.158 0.793 0.324 0.522 0.406 0.999 0.348 0.451 Bits 16 to 23---> 0.694 0.061 0.106 0.070 0.241 0.998 0.432 0.958 Bits 24 to 31---> 0.546 0.561 0.656 0.121 0.681 0.535 0.676 0.660 KS test for the above 32 p values: 0.438 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-12-07_11:31, p-values for 5 runs: 0.8161, 0.4374, 0.1551, 0.6265, 0.0562 Rank test for binary matrices (31x31) for dh-ranFile-2015-12-07_11:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 191 211.4 1.972 1.972 r= 29 5102 5134.0 0.200 2.171 r= 30 23053 23103.0 0.108 2.280 r= 31 11654 11551.5 0.909 3.189 chi-square = 3.189 with df = 3; p-value = 0.637 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-12-07_11:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 216 211.4 0.099 0.099 r= 30 5132 5134.0 0.001 0.100 r= 31 23017 23103.0 0.320 0.421 r= 32 11635 11551.5 0.603 1.024 chi-square = 1.024 with df = 3; p-value = 0.205 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-12-07_11:31 b-rank test for bits 1 to 8, p=0.67132 b-rank test for bits 2 to 9, p=0.01547 b-rank test for bits 3 to 10, p=0.53807 b-rank test for bits 4 to 11, p=0.94510 b-rank test for bits 5 to 12, p=0.84129 b-rank test for bits 6 to 13, p=0.19751 b-rank test for bits 7 to 14, p=0.91100 b-rank test for bits 8 to 15, p=0.89388 b-rank test for bits 9 to 16, p=0.82707 b-rank test for bits 10 to 17, p=0.60872 b-rank test for bits 11 to 18, p=0.28117 b-rank test for bits 12 to 19, p=0.52732 b-rank test for bits 13 to 20, p=0.41115 b-rank test for bits 14 to 21, p=0.52125 b-rank test for bits 15 to 22, p=0.92023 b-rank test for bits 16 to 23, p=0.45122 b-rank test for bits 17 to 24, p=0.16696 b-rank test for bits 18 to 25, p=0.97175 b-rank test for bits 19 to 26, p=0.97784 b-rank test for bits 20 to 27, p=0.40928 b-rank test for bits 21 to 28, p=0.86735 b-rank test for bits 22 to 29, p=0.98984 b-rank test for bits 23 to 30, p=0.94962 b-rank test for bits 24 to 31, p=0.14916 b-rank test for bits 25 to 32, p=0.58512 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 = 0.023112 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-12-07_11:31 (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 141209 -1.64 0.050890 2 141814 -0.22 0.411871 3 141917 0.02 0.507149 4 142865 2.23 0.987221 5 141922 0.03 0.511808 6 141778 -0.31 0.379480 7 141130 -1.82 0.034314 8 141630 -0.65 0.256994 9 142982 2.51 0.993899 10 142524 1.44 0.924519 11 142646 1.72 0.957392 12 141811 -0.23 0.409146 13 141475 -1.01 0.155103 14 141753 -0.37 0.357460 15 141503 -0.95 0.171216 16 140701 -2.82 0.002377 17 141573 -0.79 0.215987 18 142072 0.38 0.648053 19 142407 1.16 0.877541 20 141810 -0.23 0.408238 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-12-07_11:31 Bits used No. missing words z-score p-value 23 to 32 141582 -1.1287 0.129507 22 to 31 142418 1.7540 0.960288 21 to 30 141548 -1.2460 0.106389 20 to 29 141711 -0.6839 0.247020 19 to 28 141645 -0.9115 0.181021 18 to 27 141778 -0.4529 0.325324 17 to 26 141844 -0.2253 0.410882 16 to 25 141627 -0.9736 0.165140 15 to 24 141882 -0.0942 0.462459 14 to 23 141889 -0.0701 0.472056 13 to 22 141650 -0.8942 0.185596 12 to 21 141995 0.2954 0.616161 11 to 20 141160 -2.5839 0.004885 10 to 19 142283 1.2885 0.901217 9 to 18 142077 0.5782 0.718426 8 to 17 141837 -0.2494 0.401520 7 to 16 142783 3.0127 0.998705 6 to 15 142177 0.9230 0.821996 5 to 14 142105 0.6747 0.750075 4 to 13 142076 0.5747 0.717261 3 to 12 142103 0.6678 0.747878 2 to 11 141418 -1.6942 0.045110 1 to 10 141670 -0.8253 0.204608 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-12-07_11:31 Bits used No. missing words z-score p-value 28 to 32 141770 -0.4723 0.318355 27 to 31 141774 -0.4587 0.323208 26 to 30 142057 0.5006 0.691665 25 to 29 142265 1.2057 0.886026 24 to 28 142025 0.3921 0.652509 23 to 27 142254 1.1684 0.878672 22 to 26 142570 2.2396 0.987440 21 to 25 141889 -0.0689 0.472529 20 to 24 141394 -1.7469 0.040329 19 to 23 142777 2.9413 0.998366 18 to 22 142444 1.8124 0.965041 17 to 21 142171 0.8870 0.812465 16 to 20 142367 1.5514 0.939600 15 to 19 142463 1.8768 0.969731 14 to 18 141688 -0.7503 0.226546 13 to 17 142231 1.0904 0.862233 12 to 16 141653 -0.8689 0.192447 11 to 15 142192 0.9582 0.831020 10 to 14 141675 -0.7943 0.213499 9 to 13 142183 0.9277 0.823217 8 to 12 142114 0.6938 0.756095 7 to 11 141291 -2.0960 0.018040 6 to 10 141945 0.1209 0.548121 5 to 9 142704 2.6938 0.996468 4 to 8 141679 -0.7808 0.217466 3 to 7 141527 -1.2960 0.097482 2 to 6 142499 1.9989 0.977189 1 to 5 141817 -0.3130 0.377147 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-12-07_11:31 Bits used No. missing words z-score p-value 31 to 32 141891 -0.0541 0.478439 30 to 31 141675 -0.6912 0.244708 29 to 30 141192 -2.1160 0.017172 28 to 29 141899 -0.0305 0.487845 27 to 28 141598 -0.9184 0.179211 26 to 27 142032 0.3619 0.641271 25 to 26 142004 0.2793 0.609978 24 to 25 141964 0.1613 0.564059 23 to 24 141563 -1.0216 0.153480 22 to 23 141563 -1.0216 0.153480 21 to 22 141959 0.1465 0.558244 20 to 21 142403 1.4563 0.927339 19 to 20 141895 -0.0423 0.483141 18 to 19 141762 -0.4346 0.331926 17 to 18 141784 -0.3697 0.355801 16 to 17 142201 0.8604 0.805211 15 to 16 142471 1.6568 0.951224 14 to 15 141661 -0.7325 0.231921 13 to 14 142211 0.8899 0.813235 12 to 13 142282 1.0993 0.864186 11 to 12 141787 -0.3609 0.359104 10 to 11 141410 -1.4729 0.070382 9 to 10 141716 -0.5703 0.284239 8 to 9 142110 0.5919 0.723057 7 to 8 142185 0.8132 0.791944 6 to 7 141993 0.2468 0.597474 5 to 6 142060 0.4445 0.671643 4 to 5 142104 0.5742 0.717100 3 to 4 141451 -1.3520 0.088187 2 to 3 141596 -0.9243 0.177671 1 to 2 141941 0.0934 0.537216 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-12-07_11:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2523.02 0.325 0.627598 Test results for specific bytes for dh-ranFile-2015-12-07_11:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2524.50 0.346 0.635516 2 to 9 2577.96 1.103 0.864892 3 to 10 2558.72 0.830 0.796862 4 to 11 2538.54 0.545 0.707128 5 to 12 2523.89 0.338 0.632267 6 to 13 2699.10 2.816 0.997567 7 to 14 2481.02 -0.268 0.394162 8 to 15 2544.46 0.629 0.735251 9 to 16 2528.44 0.402 0.656215 10 to 17 2327.47 -2.440 0.007344 11 to 18 2428.82 -1.007 0.157050 12 to 19 2378.69 -1.716 0.043115 13 to 20 2632.33 1.871 0.969352 14 to 21 2398.29 -1.438 0.075151 15 to 22 2484.55 -0.218 0.413544 16 to 23 2656.81 2.218 0.986711 17 to 24 2474.00 -0.368 0.356526 18 to 25 2480.40 -0.277 0.390835 19 to 26 2512.51 0.177 0.570210 20 to 27 2399.33 -1.424 0.077265 21 to 28 2567.50 0.955 0.830118 22 to 29 2628.48 1.817 0.965391 23 to 30 2549.61 0.702 0.758544 24 to 31 2601.38 1.434 0.924182 25 to 32 2550.17 0.709 0.760975 CDPARK for dh-ranFile-2015-12-07_11:31: 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 3546 1.0502 0.853193 3526 0.1370 0.554479 3513 -0.4566 0.323972 3547 1.0959 0.863437 3550 1.2329 0.891189 3546 1.0502 0.853193 3503 -0.9132 0.180558 3500 -1.0502 0.146807 3496 -1.2329 0.108811 3550 1.2329 0.891189 Square side=100, avg. no. parked=3527.70 sample std.=21.54 p-value of the KSTEST for those 10 p-values: 0.296756 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-12-07_11:31 0.7032,0.3708,0.0409,0.5801,0.3247,0.8716,0.9046,0.7203,0.3880,0.5665, The KS test for those 10 p-values: 0.829850 The 3DSPHERES test for dh-ranFile-2015-12-07_11:31 sample no r^3 equiv. uni. 1 33.613 0.673865 2 40.068 0.736999 3 14.874 0.390918 4 1.544 0.050177 5 4.215 0.131079 6 29.228 0.622529 7 1.652 0.053580 8 3.188 0.100820 9 14.271 0.378543 10 10.144 0.286901 11 14.304 0.379241 12 0.897 0.029460 13 22.222 0.523228 14 8.964 0.258285 15 23.122 0.537319 16 63.324 0.878858 17 15.763 0.408701 18 5.829 0.176591 19 56.073 0.845736 20 2.181 0.070133 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.089149 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-12-07_11:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 0.5 0.1 -0.7 -0.4 -1.9 -1.3 -0.1 0.5 0.2 -1.4 -0.6 0.2 1.2 0.9 2.7 0.1 -0.6 -0.7 0.4 0.8 1.1 -1.2 -1.3 -1.8 -1.8 -0.3 -2.0 1.6 0.5 1.5 0.1 -0.3 -1.0 -0.5 1.0 0.0 -0.1 0.9 1.5 -0.6 -1.0 0.8 Chi-square with 42 degrees of freedom:47.748111 z-score=0.627170, p-value=0.749423 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-12-07_11:31 Test no p-value 1 0.851879 2 0.580321 3 0.229273 4 0.077388 5 0.148965 6 0.312421 7 0.511107 8 0.635828 9 0.434741 10 0.783431 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.929450 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-12-07_11:31: (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 66898 0.80 66774 0.17 3 25000.00 24763 2.25 24791 1.75 4 6666.67 6652 0.03 6743 0.87 5 1388.89 1414 0.45 1414 0.45 6 238.10 237 0.01 243 0.10 7 34.72 32 0.21 29 0.94 8 4.96 3 0.77 5 0.00 p=0.39444 p=0.36273 Number of rngs required: 688291, p-value: 0.449 RESULTS OF CRAPS TEST for dh-ranFile-2015-12-07_11:31 No. of wins: Observed Expected 98536 98585.9 z-score=-0.223, pvalue=0.41177 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66514 66666.7 0.350 0.350 2 37785 37654.3 0.454 0.803 3 27044 26954.7 0.296 1.099 4 19171 19313.5 1.051 2.150 5 13894 13851.4 0.131 2.280 6 9910 9943.5 0.113 2.394 7 7134 7145.0 0.017 2.411 8 5190 5139.1 0.505 2.915 9 3680 3699.9 0.107 3.022 10 2664 2666.3 0.002 3.024 11 1966 1923.3 0.947 3.971 12 1408 1388.7 0.267 4.238 13 971 1003.7 1.066 5.304 14 718 726.1 0.091 5.395 15 547 525.8 0.852 6.247 16 380 381.2 0.003 6.251 17 268 276.5 0.264 6.514 18 211 200.8 0.515 7.029 19 162 146.0 1.757 8.786 20 108 106.2 0.030 8.816 21 275 287.1 0.511 9.328 Chisq= 9.33 for 20 degrees of freedom, p= 0.02121 SUMMARY of craptest p-value for no. of wins: 0.411769 p-value for throws/game: 0.021206 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-12-07_11:31 No. of wins: Observed Expected 98442 98585.9 z-score=-0.643, pvalue=0.25998 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66941 66666.7 1.129 1.129 2 37728 37654.3 0.144 1.273 3 27020 26954.7 0.158 1.431 4 19127 19313.5 1.800 3.231 5 13863 13851.4 0.010 3.241 6 9887 9943.5 0.322 3.562 7 7107 7145.0 0.202 3.765 8 5096 5139.1 0.361 4.126 9 3626 3699.9 1.475 5.601 10 2623 2666.3 0.703 6.304 11 1920 1923.3 0.006 6.309 12 1411 1388.7 0.357 6.666 13 956 1003.7 2.268 8.934 14 712 726.1 0.275 9.210 15 549 525.8 1.020 10.230 16 405 381.2 1.492 11.723 17 260 276.5 0.989 12.712 18 177 200.8 2.828 15.539 19 165 146.0 2.477 18.016 20 111 106.2 0.216 18.232 21 316 287.1 2.906 21.138 Chisq= 21.14 for 20 degrees of freedom, p= 0.61095 SUMMARY of craptest p-value for no. of wins: 0.259976 p-value for throws/game: 0.610951 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0024,0.0049,0.0073,0.0155,0.0172,0.0180,0.0212,0.0231,0.0295,0.0343, 0.0403,0.0409,0.0431,0.0451,0.0502,0.0509,0.0536,0.0562,0.0606,0.0607, 0.0696,0.0701,0.0704,0.0752,0.0773,0.0774,0.0882,0.0891,0.0975,0.1008, 0.1060,0.1064,0.1088,0.1213,0.1295,0.1311,0.1468,0.1490,0.1492,0.1535, 0.1535,0.1551,0.1551,0.1571,0.1581,0.1651,0.1670,0.1712,0.1766,0.1777, 0.1792,0.1806,0.1810,0.1856,0.1924,0.1975,0.2045,0.2046,0.2135,0.2160, 0.2161,0.2175,0.2265,0.2293,0.2319,0.2320,0.2408,0.2447,0.2470,0.2570, 0.2583,0.2600,0.2812,0.2842,0.2869,0.2968,0.3101,0.3124,0.3184,0.3232, 0.3237,0.3240,0.3247,0.3253,0.3319,0.3483,0.3558,0.3565,0.3575,0.3584, 0.3591,0.3627,0.3708,0.3771,0.3785,0.3792,0.3795,0.3880,0.3908,0.3909, 0.3922,0.3942,0.3944,0.4015,0.4064,0.4082,0.4087,0.4091,0.4093,0.4109, 0.4112,0.4118,0.4119,0.4135,0.4316,0.4347,0.4374,0.4381,0.4487,0.4512, 0.4513,0.4625,0.4674,0.4721,0.4725,0.4784,0.4831,0.4878,0.4950,0.5071, 0.5089,0.5111,0.5118,0.5213,0.5224,0.5232,0.5251,0.5273,0.5352,0.5372, 0.5373,0.5381,0.5459,0.5481,0.5545,0.5563,0.5582,0.5611,0.5641,0.5665, 0.5702,0.5801,0.5803,0.5851,0.5949,0.5975,0.6087,0.6100,0.6110,0.6162, 0.6225,0.6265,0.6276,0.6323,0.6355,0.6358,0.6366,0.6413,0.6456,0.6481, 0.6525,0.6560,0.6562,0.6596,0.6713,0.6713,0.6716,0.6739,0.6757,0.6806, 0.6849,0.6917,0.6941,0.7032,0.7071,0.7171,0.7173,0.7184,0.7203,0.7231, 0.7353,0.7370,0.7479,0.7494,0.7501,0.7561,0.7585,0.7610,0.7834,0.7890, 0.7919,0.7928,0.7969,0.8052,0.8056,0.8125,0.8132,0.8161,0.8220,0.8232, 0.8271,0.8276,0.8299,0.8301,0.8310,0.8413,0.8457,0.8519,0.8532,0.8532, 0.8622,0.8634,0.8642,0.8649,0.8673,0.8716,0.8775,0.8787,0.8789,0.8830, 0.8860,0.8912,0.8912,0.8939,0.9012,0.9046,0.9110,0.9202,0.9242,0.9245, 0.9273,0.9295,0.9396,0.9451,0.9496,0.9512,0.9574,0.9584,0.9596,0.9603, 0.9650,0.9654,0.9694,0.9697,0.9717,0.9772,0.9778,0.9838,0.9867,0.9872, 0.9874,0.9898,0.9939,0.9965,0.9976,0.9984,0.9984,0.9987,0.9990, Overall p-value after applying KStest on 269 p-values = 0.192226 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.