RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-08-05_17:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.92 9.0150 0.060210 2 to 25 15.69 25.9637 0.924875 3 to 26 15.67 14.0525 0.336616 4 to 27 16.05 16.8262 0.533802 5 to 28 16.02 13.7319 0.314019 6 to 29 15.72 24.2316 0.886724 7 to 30 15.90 7.6895 0.027257 8 to 31 15.68 18.6815 0.652883 9 to 32 15.80 11.5798 0.175113 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.721038 Tough bday spacings test for dh-ranFile-2015-08-05_17:31: 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 12 32 75 108 76 82 51 26 21 11 6 (O-E)^2/E 0.9 0.6 0.0 1.1 4.8 0.2 0.0 0.5 2.5 2.9 0.9 Birthday Spacings: Sum(O-E)^2/E= 14.440, p= 0.846 RESULTS OF GCD FOR dh-ranFile-2015-08-05_17:31 Euclid's algorithm: p-value, steps to gcd: 0.319428 p-value, dist. of gcd's: 0.635787 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-08-05_17:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.595 0.808 0.629 0.361 0.212 0.946 0.525 0.135 Bits 8 to 15---> 0.275 0.456 0.197 0.918 0.423 0.530 0.032 0.718 Bits 16 to 23---> 0.583 0.201 0.266 0.111 0.381 0.865 0.281 0.556 Bits 24 to 31---> 0.861 0.287 0.392 0.031 0.369 0.772 0.316 0.243 KS test for the above 32 p values: 0.623 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-08-05_17:31, p-values for 5 runs: 0.0701, 0.2904, 0.5425, 0.9002, 0.7793 Rank test for binary matrices (31x31) for dh-ranFile-2015-08-05_17:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 210 211.4 0.010 0.010 r= 29 5194 5134.0 0.701 0.710 r= 30 22962 23103.0 0.861 1.572 r= 31 11634 11551.5 0.589 2.160 chi-square = 2.160 with df = 3; p-value = 0.460 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-08-05_17:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 230 211.4 1.633 1.633 r= 30 5130 5134.0 0.003 1.636 r= 31 23017 23103.0 0.320 1.957 r= 32 11623 11551.5 0.442 2.399 chi-square = 2.399 with df = 3; p-value = 0.506 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-08-05_17:31 b-rank test for bits 1 to 8, p=0.62566 b-rank test for bits 2 to 9, p=0.59764 b-rank test for bits 3 to 10, p=0.40356 b-rank test for bits 4 to 11, p=0.75400 b-rank test for bits 5 to 12, p=0.05274 b-rank test for bits 6 to 13, p=0.57105 b-rank test for bits 7 to 14, p=0.06431 b-rank test for bits 8 to 15, p=0.69887 b-rank test for bits 9 to 16, p=0.68413 b-rank test for bits 10 to 17, p=0.44875 b-rank test for bits 11 to 18, p=0.33075 b-rank test for bits 12 to 19, p=0.00615 b-rank test for bits 13 to 20, p=0.29553 b-rank test for bits 14 to 21, p=0.79386 b-rank test for bits 15 to 22, p=0.99569 b-rank test for bits 16 to 23, p=0.33597 b-rank test for bits 17 to 24, p=0.21140 b-rank test for bits 18 to 25, p=0.72623 b-rank test for bits 19 to 26, p=0.93724 b-rank test for bits 20 to 27, p=0.31631 b-rank test for bits 21 to 28, p=0.75786 b-rank test for bits 22 to 29, p=0.94913 b-rank test for bits 23 to 30, p=0.86695 b-rank test for bits 24 to 31, p=0.87928 b-rank test for bits 25 to 32, p=0.94791 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 = 0.335739 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-08-05_17:31 (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 142390 1.12 0.869294 2 142271 0.85 0.800951 3 141961 0.12 0.548045 4 142097 0.44 0.669481 5 142641 1.71 0.956322 6 142461 1.29 0.901292 7 142315 0.95 0.828391 8 143005 2.56 0.994766 9 142002 0.22 0.585708 10 142586 1.58 0.943062 11 141958 0.11 0.545268 12 141722 -0.44 0.330807 13 142389 1.12 0.868797 14 140878 -2.41 0.007984 15 142093 0.43 0.666088 16 142250 0.80 0.786972 17 142025 0.27 0.606519 18 141294 -1.44 0.075261 19 141983 0.17 0.568331 20 141361 -1.28 0.100071 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-08-05_17:31 Bits used No. missing words z-score p-value 23 to 32 141528 -1.3149 0.094267 22 to 31 141549 -1.2425 0.107023 21 to 30 141828 -0.2804 0.389567 20 to 29 141915 0.0196 0.507800 19 to 28 141467 -1.5253 0.063595 18 to 27 141653 -0.8839 0.188376 17 to 26 141732 -0.6115 0.270440 16 to 25 141874 -0.1218 0.451518 15 to 24 142183 0.9437 0.827336 14 to 23 142124 0.7402 0.770423 13 to 22 142017 0.3713 0.644784 12 to 21 141628 -0.9701 0.165998 11 to 20 141562 -1.1977 0.115519 10 to 19 141923 0.0471 0.518798 9 to 18 141902 -0.0253 0.489918 8 to 17 141613 -1.0218 0.153431 7 to 16 142367 1.5782 0.942737 6 to 15 141681 -0.7873 0.215540 5 to 14 141549 -1.2425 0.107023 4 to 13 141883 -0.0908 0.463829 3 to 12 142082 0.5954 0.724217 2 to 11 142102 0.6644 0.746776 1 to 10 142243 1.1506 0.875049 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-08-05_17:31 Bits used No. missing words z-score p-value 28 to 32 141727 -0.6181 0.268265 27 to 31 142063 0.5209 0.698787 26 to 30 142106 0.6667 0.747511 25 to 29 141680 -0.7774 0.218464 24 to 28 142131 0.7514 0.773801 23 to 27 141922 0.0429 0.517129 22 to 26 141810 -0.3367 0.368167 21 to 25 142038 0.4362 0.668643 20 to 24 142112 0.6870 0.753964 19 to 23 141472 -1.4825 0.069107 18 to 22 141816 -0.3164 0.375860 17 to 21 141153 -2.5638 0.005176 16 to 20 142352 1.5006 0.933267 15 to 19 141868 -0.1401 0.444290 14 to 18 141830 -0.2689 0.393998 13 to 17 142050 0.4768 0.683265 12 to 16 142342 1.4667 0.928768 11 to 15 142275 1.2396 0.892431 10 to 14 142011 0.3446 0.634819 9 to 13 141956 0.1582 0.562852 8 to 12 142274 1.2362 0.891802 7 to 11 142171 0.8870 0.812465 6 to 10 141936 0.0904 0.536018 5 to 9 141857 -0.1774 0.429601 4 to 8 142129 0.7446 0.771757 3 to 7 142055 0.4938 0.689275 2 to 6 142090 0.6124 0.729877 1 to 5 142075 0.5616 0.712803 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-08-05_17:31 Bits used No. missing words z-score p-value 31 to 32 141898 -0.0334 0.486669 30 to 31 141786 -0.3638 0.358002 29 to 30 141814 -0.2812 0.389275 28 to 29 141040 -2.5644 0.005168 27 to 28 142195 0.8427 0.800298 26 to 27 141608 -0.8889 0.187034 25 to 26 141988 0.2321 0.591756 24 to 25 142083 0.5123 0.695780 23 to 24 141907 -0.0069 0.497258 22 to 23 141675 -0.6912 0.244708 21 to 22 141677 -0.6853 0.246565 20 to 21 141910 0.0020 0.500789 19 to 20 142155 0.7247 0.765679 18 to 19 142069 0.4710 0.681181 17 to 18 141875 -0.1013 0.459669 16 to 17 141869 -0.1190 0.452651 15 to 16 142357 1.3206 0.906676 14 to 15 141729 -0.5319 0.297381 13 to 14 141214 -2.0511 0.020128 12 to 13 141936 0.0787 0.531354 11 to 12 141882 -0.0806 0.467872 10 to 11 142209 0.8840 0.811647 9 to 10 142016 0.3147 0.623490 8 to 9 141936 0.0787 0.531354 7 to 8 142139 0.6775 0.750953 6 to 7 142613 2.0757 0.981040 5 to 6 141586 -0.9538 0.170099 4 to 5 141676 -0.6883 0.245635 3 to 4 141588 -0.9479 0.171596 2 to 3 141901 -0.0246 0.490198 1 to 2 142047 0.4061 0.657668 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-08-05_17:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2558.72 0.830 0.796854 Test results for specific bytes for dh-ranFile-2015-08-05_17:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2501.62 0.023 0.509127 2 to 9 2488.69 -0.160 0.436434 3 to 10 2579.51 1.124 0.869595 4 to 11 2457.80 -0.597 0.275319 5 to 12 2411.54 -1.251 0.105453 6 to 13 2555.62 0.787 0.784253 7 to 14 2586.46 1.223 0.889296 8 to 15 2563.38 0.896 0.814958 9 to 16 2540.62 0.574 0.717164 10 to 17 2378.09 -1.724 0.042353 11 to 18 2426.80 -1.035 0.150273 12 to 19 2497.43 -0.036 0.485513 13 to 20 2562.82 0.888 0.812845 14 to 21 2449.28 -0.717 0.236606 15 to 22 2593.09 1.316 0.905986 16 to 23 2570.65 0.999 0.841152 17 to 24 2414.33 -1.212 0.112837 18 to 25 2600.87 1.426 0.923133 19 to 26 2408.30 -1.297 0.097344 20 to 27 2437.63 -0.882 0.188866 21 to 28 2319.58 -2.551 0.005364 22 to 29 2511.36 0.161 0.563801 23 to 30 2566.33 0.938 0.825888 24 to 31 2475.94 -0.340 0.366833 25 to 32 2526.70 0.378 0.647125 CDPARK for dh-ranFile-2015-08-05_17:31: 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 3540 0.7763 0.781201 3507 -0.7306 0.232514 3533 0.4566 0.676028 3511 -0.5479 0.291865 3522 -0.0457 0.481790 3521 -0.0913 0.463617 3502 -0.9589 0.168804 3516 -0.3196 0.374623 3506 -0.7763 0.218799 3532 0.4110 0.659449 Square side=100, avg. no. parked=3519.00 sample std.=12.22 p-value of the KSTEST for those 10 p-values: 0.449268 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-08-05_17:31 0.4611,0.0830,0.2627,0.9938,0.9174,0.0977,0.6672,0.2210,0.8387,0.6434, The KS test for those 10 p-values: 0.824328 The 3DSPHERES test for dh-ranFile-2015-08-05_17:31 sample no r^3 equiv. uni. 1 174.819 0.997054 2 8.427 0.244888 3 1.614 0.052377 4 42.845 0.760248 5 31.260 0.647252 6 3.338 0.105294 7 24.933 0.564430 8 13.475 0.361846 9 7.657 0.225260 10 31.003 0.644218 11 14.018 0.373292 12 49.253 0.806365 13 46.643 0.788764 14 28.051 0.607432 15 0.836 0.027479 16 2.684 0.085584 17 22.494 0.527541 18 15.819 0.409800 19 57.044 0.850651 20 46.064 0.784644 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.924528 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-08-05_17:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 -1.2 0.3 -1.1 -1.1 0.0 0.1 0.6 -0.6 -1.9 0.8 -1.9 -0.6 0.5 -0.6 -0.2 -0.1 -0.5 -0.1 0.9 -0.1 1.0 0.8 0.3 0.5 0.4 0.2 -1.5 1.0 -0.6 2.4 1.6 1.2 -0.1 0.3 0.4 0.3 0.5 -1.2 1.5 0.9 1.0 -1.1 Chi-square with 42 degrees of freedom:39.575231 z-score=-0.264564, p-value=0.422047 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-08-05_17:31 Test no p-value 1 0.037996 2 0.123984 3 0.000384 4 0.323715 5 0.844108 6 0.439155 7 0.005361 8 0.038407 9 0.968832 10 0.228725 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.003630 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-08-05_17:31: (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 66645 0.01 66686 0.01 3 25000.00 25084 0.28 24927 0.21 4 6666.67 6650 0.04 6693 0.10 5 1388.89 1353 0.93 1420 0.70 6 238.10 230 0.28 229 0.35 7 34.72 34 0.01 38 0.31 8 4.96 3 0.77 6 0.22 p=0.11228 p=0.07090 Number of rngs required: 687618, p-value: 0.182 RESULTS OF CRAPS TEST for dh-ranFile-2015-08-05_17:31 No. of wins: Observed Expected 98848 98585.9 z-score= 1.172, pvalue=0.87949 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66458 66666.7 0.653 0.653 2 37879 37654.3 1.341 1.994 3 27158 26954.7 1.533 3.527 4 19193 19313.5 0.751 4.278 5 13900 13851.4 0.170 4.448 6 9954 9943.5 0.011 4.459 7 6988 7145.0 3.451 7.910 8 5087 5139.1 0.528 8.438 9 3676 3699.9 0.154 8.592 10 2733 2666.3 1.669 10.261 11 1908 1923.3 0.122 10.383 12 1392 1388.7 0.008 10.390 13 990 1003.7 0.187 10.578 14 731 726.1 0.033 10.610 15 559 525.8 2.092 12.702 16 371 381.2 0.270 12.972 17 285 276.5 0.259 13.231 18 171 200.8 4.431 17.662 19 152 146.0 0.248 17.910 20 120 106.2 1.789 19.699 21 295 287.1 0.217 19.915 Chisq= 19.92 for 20 degrees of freedom, p= 0.53676 SUMMARY of craptest p-value for no. of wins: 0.879492 p-value for throws/game: 0.536762 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-08-05_17:31 No. of wins: Observed Expected 98474 98585.9 z-score=-0.500, pvalue=0.30843 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66498 66666.7 0.427 0.427 2 37603 37654.3 0.070 0.497 3 26882 26954.7 0.196 0.693 4 19436 19313.5 0.777 1.470 5 14013 13851.4 1.885 3.355 6 9911 9943.5 0.107 3.462 7 7156 7145.0 0.017 3.479 8 5159 5139.1 0.077 3.556 9 3871 3699.9 7.916 11.472 10 2589 2666.3 2.241 13.713 11 1849 1923.3 2.873 16.585 12 1323 1388.7 3.112 19.697 13 1031 1003.7 0.742 20.439 14 755 726.1 1.147 21.586 15 509 525.8 0.539 22.125 16 383 381.2 0.009 22.134 17 305 276.5 2.929 25.063 18 185 200.8 1.248 26.311 19 142 146.0 0.109 26.419 20 113 106.2 0.433 26.853 21 287 287.1 0.000 26.853 Chisq= 26.85 for 20 degrees of freedom, p= 0.86054 SUMMARY of craptest p-value for no. of wins: 0.308433 p-value for throws/game: 0.860543 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0004,0.0036,0.0052,0.0052,0.0054,0.0054,0.0061,0.0080,0.0201,0.0273, 0.0275,0.0315,0.0320,0.0380,0.0384,0.0424,0.0524,0.0527,0.0602,0.0636, 0.0643,0.0691,0.0701,0.0709,0.0753,0.0830,0.0856,0.0943,0.0973,0.0977, 0.1001,0.1053,0.1055,0.1070,0.1070,0.1114,0.1123,0.1128,0.1155,0.1240, 0.1347,0.1503,0.1534,0.1660,0.1688,0.1701,0.1716,0.1751,0.1818,0.1870, 0.1884,0.1889,0.1971,0.2013,0.2114,0.2121,0.2155,0.2185,0.2188,0.2210, 0.2253,0.2287,0.2325,0.2366,0.2430,0.2447,0.2449,0.2456,0.2466,0.2627, 0.2659,0.2683,0.2704,0.2750,0.2753,0.2813,0.2870,0.2904,0.2919,0.2955, 0.2974,0.3084,0.3140,0.3158,0.3163,0.3194,0.3237,0.3308,0.3308,0.3357, 0.3360,0.3366,0.3580,0.3607,0.3618,0.3668,0.3682,0.3691,0.3733,0.3746, 0.3759,0.3815,0.3893,0.3896,0.3922,0.3940,0.4036,0.4098,0.4220,0.4228, 0.4296,0.4364,0.4392,0.4443,0.4488,0.4493,0.4515,0.4527,0.4563,0.4597, 0.4602,0.4611,0.4636,0.4638,0.4679,0.4818,0.4855,0.4867,0.4899,0.4902, 0.4973,0.5008,0.5062,0.5078,0.5091,0.5171,0.5188,0.5254,0.5275,0.5303, 0.5314,0.5314,0.5338,0.5360,0.5368,0.5425,0.5453,0.5480,0.5559,0.5629, 0.5638,0.5644,0.5683,0.5711,0.5833,0.5857,0.5918,0.5951,0.5976,0.6065, 0.6074,0.6235,0.6235,0.6257,0.6288,0.6348,0.6358,0.6434,0.6442,0.6448, 0.6471,0.6473,0.6529,0.6577,0.6594,0.6661,0.6672,0.6686,0.6695,0.6760, 0.6812,0.6833,0.6841,0.6893,0.6958,0.6988,0.6989,0.7128,0.7172,0.7175, 0.7210,0.7242,0.7262,0.7299,0.7468,0.7475,0.7510,0.7540,0.7540,0.7579, 0.7602,0.7657,0.7704,0.7718,0.7720,0.7738,0.7793,0.7812,0.7843,0.7846, 0.7870,0.7888,0.7939,0.7969,0.8003,0.8010,0.8064,0.8075,0.8116,0.8125, 0.8128,0.8150,0.8243,0.8259,0.8273,0.8284,0.8387,0.8412,0.8441,0.8461, 0.8507,0.8605,0.8614,0.8654,0.8669,0.8688,0.8693,0.8696,0.8750,0.8793, 0.8795,0.8867,0.8893,0.8918,0.8924,0.9002,0.9013,0.9060,0.9067,0.9174, 0.9179,0.9231,0.9245,0.9249,0.9288,0.9333,0.9372,0.9427,0.9431,0.9463, 0.9479,0.9491,0.9563,0.9688,0.9810,0.9938,0.9948,0.9957,0.9971, Overall p-value after applying KStest on 269 p-values = 0.807220 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.