RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-12-21_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 15.59 12.7380 0.246457 2 to 25 15.73 22.8446 0.845622 3 to 26 15.71 15.9136 0.470030 4 to 27 15.77 17.1962 0.558849 5 to 28 15.78 18.1920 0.623173 6 to 29 15.93 15.0227 0.406155 7 to 30 15.82 18.6088 0.648555 8 to 31 15.61 19.1437 0.679656 9 to 32 15.96 20.2397 0.737847 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.305458 Tough bday spacings test for dh-ranFile-2015-12-21_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 8 38 72 92 98 89 54 26 13 7 3 (O-E)^2/E 0.1 0.1 0.0 0.3 0.0 1.5 0.1 0.5 0.2 0.0 0.3 Birthday Spacings: Sum(O-E)^2/E= 3.146, p= 0.022 RESULTS OF GCD FOR dh-ranFile-2015-12-21_02:31 Euclid's algorithm: p-value, steps to gcd: 0.398624 p-value, dist. of gcd's: 0.872462 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-12-21_02:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.439 0.097 0.106 0.141 0.137 0.521 0.371 0.249 Bits 8 to 15---> 0.649 0.822 0.118 0.546 0.301 0.419 0.798 0.507 Bits 16 to 23---> 0.694 0.851 0.862 0.843 0.855 0.382 0.566 0.931 Bits 24 to 31---> 0.448 0.398 0.275 0.420 0.259 0.091 0.913 0.523 KS test for the above 32 p values: 0.296 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-12-21_02:31, p-values for 5 runs: 0.8809, 0.8083, 0.7162, 0.0017, 0.6039 Rank test for binary matrices (31x31) for dh-ranFile-2015-12-21_02:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 235 211.4 2.630 2.630 r= 29 5181 5134.0 0.430 3.060 r= 30 23168 23103.0 0.183 3.243 r= 31 11416 11551.5 1.590 4.833 chi-square = 4.833 with df = 3; p-value = 0.816 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-12-21_02:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 226 211.4 1.006 1.006 r= 30 5136 5134.0 0.001 1.007 r= 31 23168 23103.0 0.183 1.189 r= 32 11470 11551.5 0.575 1.764 chi-square = 1.764 with df = 3; p-value = 0.377 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-12-21_02:31 b-rank test for bits 1 to 8, p=0.44217 b-rank test for bits 2 to 9, p=0.23403 b-rank test for bits 3 to 10, p=0.18689 b-rank test for bits 4 to 11, p=0.55038 b-rank test for bits 5 to 12, p=0.81687 b-rank test for bits 6 to 13, p=0.51034 b-rank test for bits 7 to 14, p=0.30147 b-rank test for bits 8 to 15, p=0.09887 b-rank test for bits 9 to 16, p=0.90288 b-rank test for bits 10 to 17, p=0.86990 b-rank test for bits 11 to 18, p=0.49304 b-rank test for bits 12 to 19, p=0.06351 b-rank test for bits 13 to 20, p=0.21701 b-rank test for bits 14 to 21, p=0.47303 b-rank test for bits 15 to 22, p=0.76997 b-rank test for bits 16 to 23, p=0.99312 b-rank test for bits 17 to 24, p=0.98398 b-rank test for bits 18 to 25, p=0.68442 b-rank test for bits 19 to 26, p=0.52583 b-rank test for bits 20 to 27, p=0.47220 b-rank test for bits 21 to 28, p=0.74089 b-rank test for bits 22 to 29, p=0.87209 b-rank test for bits 23 to 30, p=0.46311 b-rank test for bits 24 to 31, p=0.58372 b-rank test for bits 25 to 32, p=0.17933 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 = 0.721419 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-12-21_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 141960 0.12 0.547120 2 141911 0.00 0.501557 3 141099 -1.89 0.029159 4 141852 -0.13 0.446722 5 142212 0.71 0.760271 6 142485 1.35 0.910691 7 142234 0.76 0.775947 8 141602 -0.72 0.236360 9 141460 -1.05 0.146897 10 141628 -0.66 0.255490 11 141447 -1.08 0.140024 12 141843 -0.15 0.438420 13 142589 1.59 0.943858 14 141618 -0.68 0.248038 15 141991 0.19 0.575666 16 141557 -0.82 0.205197 17 142190 0.66 0.744014 18 141773 -0.32 0.375042 19 141888 -0.05 0.480126 20 141459 -1.05 0.146360 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-12-21_02:31 Bits used No. missing words z-score p-value 23 to 32 141977 0.2333 0.592253 22 to 31 142291 1.3161 0.905930 21 to 30 141481 -1.4770 0.069838 20 to 29 142208 1.0299 0.848471 19 to 28 142031 0.4196 0.662594 18 to 27 141948 0.1333 0.553040 17 to 26 141871 -0.1322 0.447424 16 to 25 141632 -0.9563 0.169458 15 to 24 142015 0.3644 0.642213 14 to 23 142062 0.5264 0.700712 13 to 22 141779 -0.4494 0.326567 12 to 21 142174 0.9127 0.819288 11 to 20 142342 1.4920 0.932146 10 to 19 142566 2.2644 0.988225 9 to 18 142472 1.9402 0.973825 8 to 17 141945 0.1230 0.548947 7 to 16 142156 0.8506 0.802500 6 to 15 142247 1.1644 0.877865 5 to 14 142328 1.4437 0.925587 4 to 13 142198 0.9954 0.840233 3 to 12 141992 0.2851 0.612204 2 to 11 142300 1.3471 0.911032 1 to 10 142557 2.2333 0.987237 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-12-21_02:31 Bits used No. missing words z-score p-value 28 to 32 141918 0.0294 0.511723 27 to 31 141088 -2.7842 0.002683 26 to 30 142016 0.3616 0.641172 25 to 29 141685 -0.7604 0.223496 24 to 28 141877 -0.1096 0.456366 23 to 27 141940 0.1040 0.541402 22 to 26 141638 -0.9198 0.178848 21 to 25 141469 -1.4926 0.067765 20 to 24 141971 0.2091 0.582796 19 to 23 141847 -0.2113 0.416331 18 to 22 141702 -0.7028 0.241086 17 to 21 141504 -1.3740 0.084721 16 to 20 142153 0.8260 0.795598 15 to 19 142045 0.4599 0.677205 14 to 18 142172 0.8904 0.813376 13 to 17 142222 1.0599 0.855405 12 to 16 141628 -0.9537 0.170128 11 to 15 141637 -0.9232 0.177964 10 to 14 141770 -0.4723 0.318355 9 to 13 141502 -1.3808 0.083673 8 to 12 142110 0.6802 0.751823 7 to 11 141961 0.1752 0.569520 6 to 10 141797 -0.3808 0.351683 5 to 9 141885 -0.0825 0.467135 4 to 8 141800 -0.3706 0.355464 3 to 7 142231 1.0904 0.862233 2 to 6 142090 0.6124 0.729877 1 to 5 141738 -0.5808 0.280695 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-12-21_02:31 Bits used No. missing words z-score p-value 31 to 32 141907 -0.0069 0.497258 30 to 31 141844 -0.1927 0.423592 29 to 30 141405 -1.4877 0.068415 28 to 29 141872 -0.1101 0.456158 27 to 28 141429 -1.4169 0.078256 26 to 27 142143 0.6893 0.754680 25 to 26 141974 0.1908 0.575646 24 to 25 141775 -0.3963 0.345959 23 to 24 141827 -0.2429 0.404056 22 to 23 141778 -0.3874 0.349229 21 to 22 141994 0.2498 0.598615 20 to 21 142274 1.0757 0.858974 19 to 20 141148 -2.2458 0.012358 18 to 19 142226 0.9341 0.824882 17 to 18 141349 -1.6529 0.049177 16 to 17 141682 -0.6706 0.251241 15 to 16 142306 1.1701 0.879023 14 to 15 141586 -0.9538 0.170099 13 to 14 140890 -3.0069 0.001320 12 to 13 142098 0.5565 0.711082 11 to 12 141982 0.2144 0.584869 10 to 11 142017 0.3176 0.624610 9 to 10 142455 1.6096 0.946262 8 to 9 141730 -0.5290 0.298404 7 to 8 141796 -0.3343 0.369074 6 to 7 142122 0.6273 0.734784 5 to 6 141567 -1.0098 0.156290 4 to 5 142048 0.4091 0.658751 3 to 4 142159 0.7365 0.769284 2 to 3 142125 0.6362 0.737675 1 to 2 142012 0.3029 0.619002 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-12-21_02:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2458.69 -0.584 0.279516 Test results for specific bytes for dh-ranFile-2015-12-21_02:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2600.19 1.417 0.921736 2 to 9 2612.09 1.585 0.943542 3 to 10 2563.47 0.898 0.815307 4 to 11 2516.03 0.227 0.589673 5 to 12 2535.83 0.507 0.693803 6 to 13 2593.62 1.324 0.907236 7 to 14 2683.42 2.594 0.995256 8 to 15 2515.78 0.223 0.588313 9 to 16 2515.65 0.221 0.587562 10 to 17 2412.78 -1.234 0.108690 11 to 18 2535.60 0.503 0.692670 12 to 19 2497.14 -0.040 0.483890 13 to 20 2473.80 -0.371 0.355490 14 to 21 2371.30 -1.820 0.034375 15 to 22 2464.17 -0.507 0.306166 16 to 23 2455.79 -0.625 0.265909 17 to 24 2557.78 0.817 0.793085 18 to 25 2439.91 -0.850 0.197737 19 to 26 2410.28 -1.269 0.102239 20 to 27 2454.05 -0.650 0.257908 21 to 28 2407.00 -1.315 0.094214 22 to 29 2433.39 -0.942 0.173104 23 to 30 2456.78 -0.611 0.270543 24 to 31 2386.89 -1.600 0.054849 25 to 32 2467.49 -0.460 0.322845 CDPARK for dh-ranFile-2015-12-21_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 3531 0.3653 0.642555 3508 -0.6849 0.246694 3516 -0.3196 0.374623 3510 -0.5936 0.276387 3482 -1.8721 0.030593 3545 1.0046 0.842447 3523 0.0000 0.500000 3549 1.1872 0.882429 3487 -1.6438 0.050105 3524 0.0457 0.518210 Square side=100, avg. no. parked=3517.50 sample std.=20.84 p-value of the KSTEST for those 10 p-values: 0.781516 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-12-21_02:31 0.1553,0.4163,0.7751,0.8654,0.9707,0.5518,0.7455,0.8848,0.1443,0.1193, The KS test for those 10 p-values: 0.619134 The 3DSPHERES test for dh-ranFile-2015-12-21_02:31 sample no r^3 equiv. uni. 1 12.016 0.330032 2 28.037 0.607245 3 19.596 0.479616 4 20.360 0.492704 5 5.801 0.175829 6 65.736 0.888217 7 18.177 0.454413 8 12.383 0.338193 9 49.099 0.805365 10 22.551 0.528430 11 9.318 0.266999 12 15.766 0.408752 13 18.136 0.453667 14 36.531 0.704086 15 24.993 0.565298 16 17.401 0.440117 17 96.955 0.960515 18 13.753 0.367736 19 21.518 0.511923 20 34.596 0.684376 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.183259 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-12-21_02:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 0.9 0.8 0.9 0.5 -0.1 -0.8 -1.0 -1.1 1.2 2.4 0.2 0.2 0.0 -2.1 -2.2 -0.3 -0.6 0.2 0.8 0.9 0.3 0.6 -0.1 1.1 0.3 0.1 0.9 -1.1 -0.0 -0.5 -0.3 1.6 1.3 -0.1 0.1 -0.2 -0.7 -0.8 -1.3 0.1 1.0 -1.1 Chi-square with 42 degrees of freedom:37.491269 z-score=-0.491943, p-value=0.330966 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-12-21_02:31 Test no p-value 1 0.018255 2 0.007745 3 0.333765 4 0.935854 5 0.634241 6 0.089947 7 0.269248 8 0.137893 9 0.480996 10 0.221770 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.042454 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-12-21_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 66712 0.03 66343 1.57 3 25000.00 25030 0.04 25148 0.88 4 6666.67 6600 0.67 6841 4.56 5 1388.89 1368 0.31 1390 0.00 6 238.10 246 0.26 237 0.01 7 34.72 38 0.31 36 0.05 8 4.96 5 0.00 4 0.19 p=0.04890 p=0.70123 Number of rngs required: 687884, p-value: 0.275 RESULTS OF CRAPS TEST for dh-ranFile-2015-12-21_02:31 No. of wins: Observed Expected 98576 98585.9 z-score=-0.044, pvalue=0.48241 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66859 66666.7 0.555 0.555 2 37448 37654.3 1.131 1.685 3 27090 26954.7 0.679 2.364 4 19216 19313.5 0.492 2.856 5 14037 13851.4 2.486 5.342 6 9910 9943.5 0.113 5.456 7 6992 7145.0 3.277 8.733 8 5220 5139.1 1.274 10.007 9 3665 3699.9 0.329 10.336 10 2579 2666.3 2.858 13.194 11 1886 1923.3 0.725 13.919 12 1398 1388.7 0.062 13.980 13 1018 1003.7 0.203 14.184 14 737 726.1 0.162 14.346 15 504 525.8 0.907 15.253 16 367 381.2 0.525 15.778 17 288 276.5 0.475 16.253 18 221 200.8 2.026 18.279 19 154 146.0 0.440 18.719 20 97 106.2 0.800 19.518 21 314 287.1 2.518 22.036 Chisq= 22.04 for 20 degrees of freedom, p= 0.66145 SUMMARY of craptest p-value for no. of wins: 0.482415 p-value for throws/game: 0.661448 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-12-21_02:31 No. of wins: Observed Expected 98818 98585.9 z-score= 1.038, pvalue=0.85043 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66976 66666.7 1.435 1.435 2 37392 37654.3 1.827 3.263 3 26947 26954.7 0.002 3.265 4 19135 19313.5 1.649 4.914 5 13989 13851.4 1.367 6.281 6 10048 9943.5 1.097 7.378 7 7087 7145.0 0.471 7.849 8 5059 5139.1 1.248 9.097 9 3709 3699.9 0.023 9.119 10 2697 2666.3 0.354 9.473 11 1905 1923.3 0.175 9.647 12 1416 1388.7 0.535 10.183 13 1000 1003.7 0.014 10.196 14 734 726.1 0.085 10.281 15 516 525.8 0.184 10.465 16 339 381.2 4.661 15.127 17 288 276.5 0.475 15.602 18 209 200.8 0.332 15.934 19 156 146.0 0.687 16.621 20 105 106.2 0.014 16.635 21 293 287.1 0.121 16.756 Chisq= 16.76 for 20 degrees of freedom, p= 0.33123 SUMMARY of craptest p-value for no. of wins: 0.850428 p-value for throws/game: 0.331229 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0013,0.0017,0.0027,0.0077,0.0124,0.0183,0.0222,0.0292,0.0306,0.0344, 0.0425,0.0489,0.0492,0.0501,0.0548,0.0635,0.0678,0.0684,0.0698,0.0783, 0.0837,0.0847,0.0899,0.0908,0.0942,0.0966,0.0989,0.1022,0.1064,0.1087, 0.1182,0.1193,0.1374,0.1379,0.1400,0.1406,0.1443,0.1464,0.1469,0.1553, 0.1563,0.1695,0.1701,0.1701,0.1731,0.1758,0.1780,0.1788,0.1793,0.1833, 0.1869,0.1977,0.2052,0.2170,0.2218,0.2235,0.2340,0.2364,0.2411,0.2465, 0.2467,0.2480,0.2487,0.2512,0.2555,0.2579,0.2591,0.2659,0.2670,0.2692, 0.2705,0.2747,0.2755,0.2764,0.2795,0.2807,0.2956,0.2984,0.3014,0.3015, 0.3055,0.3062,0.3184,0.3228,0.3266,0.3300,0.3310,0.3312,0.3338,0.3382, 0.3460,0.3492,0.3517,0.3555,0.3555,0.3677,0.3691,0.3714,0.3746,0.3750, 0.3773,0.3824,0.3977,0.3986,0.4041,0.4062,0.4088,0.4163,0.4163,0.4190, 0.4195,0.4236,0.4384,0.4392,0.4401,0.4422,0.4467,0.4474,0.4478,0.4537, 0.4544,0.4562,0.4564,0.4631,0.4671,0.4700,0.4722,0.4730,0.4796,0.4801, 0.4810,0.4824,0.4839,0.4927,0.4930,0.4973,0.5000,0.5016,0.5075,0.5103, 0.5117,0.5119,0.5182,0.5210,0.5233,0.5258,0.5284,0.5414,0.5459,0.5471, 0.5489,0.5504,0.5518,0.5530,0.5588,0.5653,0.5662,0.5695,0.5756,0.5757, 0.5828,0.5837,0.5849,0.5876,0.5883,0.5897,0.5923,0.5986,0.6039,0.6072, 0.6122,0.6190,0.6191,0.6232,0.6246,0.6342,0.6412,0.6422,0.6426,0.6486, 0.6489,0.6588,0.6614,0.6626,0.6772,0.6797,0.6844,0.6844,0.6927,0.6938, 0.6943,0.7007,0.7012,0.7041,0.7111,0.7162,0.7214,0.7299,0.7348,0.7377, 0.7378,0.7409,0.7440,0.7455,0.7518,0.7547,0.7603,0.7693,0.7700,0.7751, 0.7759,0.7815,0.7931,0.7956,0.7982,0.8025,0.8054,0.8083,0.8134,0.8153, 0.8156,0.8169,0.8193,0.8222,0.8249,0.8402,0.8424,0.8435,0.8456,0.8485, 0.8504,0.8510,0.8552,0.8554,0.8590,0.8619,0.8622,0.8654,0.8699,0.8721, 0.8725,0.8779,0.8790,0.8809,0.8824,0.8848,0.8882,0.9029,0.9059,0.9072, 0.9107,0.9110,0.9131,0.9217,0.9256,0.9313,0.9321,0.9359,0.9435,0.9439, 0.9463,0.9605,0.9707,0.9738,0.9840,0.9872,0.9882,0.9931,0.9953, Overall p-value after applying KStest on 269 p-values = 0.903719 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.