RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-01-12_16:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.52 20.1317 0.732450 2 to 25 15.50 21.4125 0.791621 3 to 26 15.67 22.9142 0.847937 4 to 27 16.00 6.7100 0.012997 5 to 28 15.71 17.3912 0.571817 6 to 29 15.51 18.2585 0.627292 7 to 30 15.66 36.3678 0.995905 8 to 31 15.86 21.7011 0.803509 9 to 32 15.67 31.2975 0.981630 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.020537 Tough bday spacings test for dh-ranFile-2017-01-12_16:31: 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 4 39 75 102 96 79 47 25 15 8 10 (O-E)^2/E 2.9 0.2 0.0 0.2 0.0 0.0 0.5 0.8 0.0 0.3 8.7 Birthday Spacings: Sum(O-E)^2/E= 13.542, p= 0.805 RESULTS OF GCD FOR dh-ranFile-2017-01-12_16:31 Euclid's algorithm: p-value, steps to gcd: 0.714812 p-value, dist. of gcd's: 0.273078 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-01-12_16:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.883 0.585 0.962 0.820 0.070 0.888 0.366 0.966 Bits 8 to 15---> 0.346 0.193 0.915 0.317 0.908 0.382 0.978 0.280 Bits 16 to 23---> 0.765 0.530 0.536 0.853 0.642 0.283 0.427 0.782 Bits 24 to 31---> 0.703 0.852 0.602 0.508 0.028 0.997 0.137 0.003 KS test for the above 32 p values: 0.857 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-01-12_16:31, p-values for 5 runs: 0.9779, 0.7269, 0.1029, 0.8941, 0.9602 Rank test for binary matrices (31x31) for dh-ranFile-2017-01-12_16:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 205 211.4 0.195 0.195 r= 29 5224 5134.0 1.577 1.772 r= 30 23076 23103.0 0.032 1.804 r= 31 11495 11551.5 0.277 2.080 chi-square = 2.080 with df = 3; p-value = 0.444 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2017-01-12_16:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 220 211.4 0.348 0.348 r= 30 5178 5134.0 0.377 0.725 r= 31 23006 23103.0 0.408 1.133 r= 32 11596 11551.5 0.171 1.304 chi-square = 1.304 with df = 3; p-value = 0.272 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2017-01-12_16:31 b-rank test for bits 1 to 8, p=0.67381 b-rank test for bits 2 to 9, p=0.63763 b-rank test for bits 3 to 10, p=0.74408 b-rank test for bits 4 to 11, p=0.84741 b-rank test for bits 5 to 12, p=0.49680 b-rank test for bits 6 to 13, p=0.58260 b-rank test for bits 7 to 14, p=0.80977 b-rank test for bits 8 to 15, p=0.14032 b-rank test for bits 9 to 16, p=0.29333 b-rank test for bits 10 to 17, p=0.27918 b-rank test for bits 11 to 18, p=0.41051 b-rank test for bits 12 to 19, p=0.18760 b-rank test for bits 13 to 20, p=0.38017 b-rank test for bits 14 to 21, p=0.41622 b-rank test for bits 15 to 22, p=0.26260 b-rank test for bits 16 to 23, p=0.71568 b-rank test for bits 17 to 24, p=0.68818 b-rank test for bits 18 to 25, p=0.91768 b-rank test for bits 19 to 26, p=0.81526 b-rank test for bits 20 to 27, p=0.41805 b-rank test for bits 21 to 28, p=0.63483 b-rank test for bits 22 to 29, p=0.08169 b-rank test for bits 23 to 30, p=0.92691 b-rank test for bits 24 to 31, p=0.76451 b-rank test for bits 25 to 32, p=0.69055 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 = 0.402785 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-01-12_16:31 (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 142633 1.69 0.954564 3 142187 0.65 0.741754 4 141890 -0.05 0.481989 5 142007 0.23 0.590255 6 142198 0.67 0.749991 7 141708 -0.47 0.319036 8 141885 -0.06 0.477334 9 142238 0.77 0.778733 10 142012 0.24 0.594790 11 141804 -0.25 0.402803 12 142223 0.73 0.768182 13 140918 -2.32 0.010274 14 141993 0.20 0.577496 15 141450 -1.07 0.141591 16 143038 2.64 0.995819 17 141187 -1.69 0.045736 18 141594 -0.74 0.230637 19 142023 0.27 0.604720 20 141620 -0.68 0.249519 ---------------------------------------------------------------- OPSO test for dh-ranFile-2017-01-12_16:31 Bits used No. missing words z-score p-value 23 to 32 142425 1.7782 0.962312 22 to 31 142029 0.4127 0.660070 21 to 30 142188 0.9609 0.831707 20 to 29 141714 -0.6736 0.250298 19 to 28 141847 -0.2149 0.414911 18 to 27 141722 -0.6460 0.259151 17 to 26 141950 0.1402 0.555765 16 to 25 141427 -1.6632 0.048136 15 to 24 142299 1.3437 0.910476 14 to 23 141681 -0.7873 0.215540 13 to 22 142306 1.3678 0.914317 12 to 21 142151 0.8333 0.797675 11 to 20 142170 0.8989 0.815637 10 to 19 141986 0.2644 0.604256 9 to 18 141750 -0.5494 0.291361 8 to 17 141410 -1.7218 0.042550 7 to 16 141638 -0.9356 0.174734 6 to 15 142051 0.4885 0.687408 5 to 14 141630 -0.9632 0.167722 4 to 13 141426 -1.6667 0.047792 3 to 12 141673 -0.8149 0.207556 2 to 11 141692 -0.7494 0.226804 1 to 10 141687 -0.7667 0.221643 ----------------------------------------------------------------- OQSO test for dh-ranFile-2017-01-12_16:31 Bits used No. missing words z-score p-value 28 to 32 141905 -0.0147 0.494145 27 to 31 141523 -1.3096 0.095167 26 to 30 142284 1.2701 0.897970 25 to 29 141852 -0.1943 0.422955 24 to 28 142028 0.4023 0.656258 23 to 27 142441 1.8023 0.964249 22 to 26 142356 1.5141 0.935004 21 to 25 141484 -1.4418 0.074680 20 to 24 141868 -0.1401 0.444290 19 to 23 142000 0.3074 0.620714 18 to 22 141850 -0.2011 0.420303 17 to 21 141858 -0.1740 0.430933 16 to 20 141938 0.0972 0.538711 15 to 19 141404 -1.7130 0.043358 14 to 18 141441 -1.5876 0.056193 13 to 17 141824 -0.2893 0.386193 12 to 16 141639 -0.9164 0.179736 11 to 15 142105 0.6633 0.746427 10 to 14 141942 0.1107 0.544091 9 to 13 141561 -1.1808 0.118845 8 to 12 141768 -0.4791 0.315939 7 to 11 142453 1.8429 0.967332 6 to 10 141321 -1.9943 0.023058 5 to 9 142026 0.3955 0.653760 4 to 8 141956 0.1582 0.562852 3 to 7 141785 -0.4215 0.336711 2 to 6 142413 1.7074 0.956122 1 to 5 142052 0.4836 0.685675 ----------------------------------------------------------------- DNA test for dh-ranFile-2017-01-12_16:31 Bits used No. missing words z-score p-value 31 to 32 141794 -0.3402 0.366851 30 to 31 142234 0.9577 0.830900 29 to 30 142355 1.3147 0.905688 28 to 29 141799 -0.3255 0.372418 27 to 28 141241 -1.9715 0.024335 26 to 27 142294 1.1347 0.871754 25 to 26 141628 -0.8299 0.203303 24 to 25 142518 1.7955 0.963712 23 to 24 141488 -1.2429 0.106959 22 to 23 141412 -1.4671 0.071181 21 to 22 141242 -1.9685 0.024504 20 to 21 141543 -1.0806 0.139933 19 to 20 142254 1.0167 0.845358 18 to 19 142171 0.7719 0.779910 17 to 18 141884 -0.0747 0.470219 16 to 17 142004 0.2793 0.609978 15 to 16 141417 -1.4523 0.073209 14 to 15 141591 -0.9390 0.173859 13 to 14 141762 -0.4346 0.331926 12 to 13 142343 1.2793 0.899598 11 to 12 141902 -0.0216 0.491375 10 to 11 142050 0.4150 0.660913 9 to 10 141740 -0.4995 0.308714 8 to 9 142235 0.9607 0.831643 7 to 8 142094 0.5447 0.707037 6 to 7 141802 -0.3166 0.375771 5 to 6 142391 1.4209 0.922321 4 to 5 141804 -0.3107 0.378011 3 to 4 141714 -0.5762 0.282242 2 to 3 141642 -0.7886 0.215178 1 to 2 141509 -1.1809 0.118818 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2017-01-12_16:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2537.91 0.536 0.704066 Test results for specific bytes for dh-ranFile-2017-01-12_16:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2640.49 1.987 0.976531 2 to 9 2455.80 -0.625 0.265980 3 to 10 2426.45 -1.040 0.149149 4 to 11 2588.43 1.251 0.894453 5 to 12 2536.60 0.518 0.697623 6 to 13 2471.14 -0.408 0.341610 7 to 14 2481.92 -0.256 0.399078 8 to 15 2486.62 -0.189 0.424940 9 to 16 2502.52 0.036 0.514201 10 to 17 2487.90 -0.171 0.432043 11 to 18 2337.07 -2.304 0.010608 12 to 19 2691.38 2.706 0.996600 13 to 20 2397.86 -1.444 0.074299 14 to 21 2472.94 -0.383 0.350995 15 to 22 2598.97 1.400 0.919191 16 to 23 2424.33 -1.070 0.142266 17 to 24 2576.54 1.082 0.860479 18 to 25 2370.79 -1.827 0.033830 19 to 26 2464.57 -0.501 0.308169 20 to 27 2490.63 -0.133 0.447278 21 to 28 2519.69 0.278 0.609647 22 to 29 2640.35 1.985 0.976420 23 to 30 2514.06 0.199 0.578787 24 to 31 2291.30 -2.952 0.001581 25 to 32 2500.51 0.007 0.502875 CDPARK for dh-ranFile-2017-01-12_16:31: 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 3510 -0.5936 0.276387 3519 -0.1826 0.427537 3545 1.0046 0.842447 3497 -1.1872 0.117571 3454 -3.1507 0.000814 3537 0.6393 0.738676 3510 -0.5936 0.276387 3507 -0.7306 0.232514 3523 0.0000 0.500000 3522 -0.0457 0.481790 Square side=100, avg. no. parked=3512.40 sample std.=23.67 p-value of the KSTEST for those 10 p-values: 0.271861 Results for the MINIMUM DISTANCE test for dh-ranFile-2017-01-12_16:31 0.4226,0.4449,0.5303,0.4189,0.3030,0.6272,0.7324,0.7051,0.4088,0.3267, The KS test for those 10 p-values: 0.203757 The 3DSPHERES test for dh-ranFile-2017-01-12_16:31 sample no r^3 equiv. uni. 1 4.667 0.144076 2 4.470 0.138418 3 42.908 0.760754 4 7.055 0.209562 5 36.548 0.704261 6 3.178 0.100512 7 70.416 0.904362 8 21.791 0.516334 9 25.908 0.578354 10 5.159 0.157987 11 41.501 0.749270 12 14.115 0.375318 13 12.148 0.332980 14 7.464 0.220269 15 16.996 0.432508 16 0.359 0.011906 17 82.729 0.936558 18 42.723 0.759276 19 0.656 0.021623 20 2.419 0.077468 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.200668 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-01-12_16:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 2.0 0.1 0.3 0.0 -1.1 -0.2 0.0 0.3 -0.5 0.1 -0.2 1.1 0.4 0.5 0.4 0.6 -0.2 -1.3 0.8 -0.9 -1.0 0.6 -0.6 0.4 0.8 -1.8 -0.3 1.3 1.2 1.1 -0.3 -1.5 -0.5 -1.1 0.1 0.8 0.5 -0.4 -0.4 0.4 -0.6 1.0 0.8 Chi-square with 42 degrees of freedom:28.945004 z-score=-1.424417, p-value=0.062827 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2017-01-12_16:31 Test no p-value 1 0.582783 2 0.599132 3 0.009043 4 0.287231 5 0.552902 6 0.117570 7 0.727262 8 0.060306 9 0.389497 10 0.025346 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.068908 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-01-12_16:31: (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 66671 0.00 66337 1.63 3 25000.00 25064 0.16 25294 3.46 4 6666.67 6685 0.05 6618 0.36 5 1388.89 1324 3.03 1477 5.59 6 238.10 216 2.05 232 0.16 7 34.72 31 0.40 39 0.53 8 4.96 8 1.86 2 1.77 p=0.72773 p=0.96402 Number of rngs required: 689525, p-value: 0.904 RESULTS OF CRAPS TEST for dh-ranFile-2017-01-12_16:31 No. of wins: Observed Expected 98519 98585.9 z-score=-0.299, pvalue=0.38246 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66817 66666.7 0.339 0.339 2 37254 37654.3 4.256 4.595 3 27146 26954.7 1.357 5.952 4 19266 19313.5 0.117 6.069 5 13924 13851.4 0.380 6.449 6 9834 9943.5 1.207 7.656 7 7233 7145.0 1.083 8.739 8 5116 5139.1 0.104 8.843 9 3731 3699.9 0.262 9.105 10 2641 2666.3 0.240 9.345 11 1944 1923.3 0.222 9.567 12 1417 1388.7 0.575 10.142 13 1018 1003.7 0.203 10.345 14 728 726.1 0.005 10.350 15 532 525.8 0.072 10.422 16 378 381.2 0.026 10.448 17 272 276.5 0.075 10.523 18 215 200.8 1.000 11.523 19 136 146.0 0.683 12.206 20 103 106.2 0.097 12.303 21 295 287.1 0.217 12.519 Chisq= 12.52 for 20 degrees of freedom, p= 0.10296 SUMMARY of craptest p-value for no. of wins: 0.382458 p-value for throws/game: 0.102962 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2017-01-12_16:31 No. of wins: Observed Expected 98416 98585.9 z-score=-0.760, pvalue=0.22371 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66667 66666.7 0.000 0.000 2 37785 37654.3 0.454 0.454 3 26791 26954.7 0.995 1.448 4 19306 19313.5 0.003 1.451 5 13846 13851.4 0.002 1.453 6 9902 9943.5 0.174 1.627 7 7213 7145.0 0.647 2.273 8 5040 5139.1 1.910 4.183 9 3719 3699.9 0.099 4.282 10 2698 2666.3 0.377 4.659 11 1915 1923.3 0.036 4.695 12 1423 1388.7 0.845 5.540 13 1028 1003.7 0.588 6.128 14 706 726.1 0.559 6.687 15 531 525.8 0.051 6.737 16 397 381.2 0.659 7.396 17 291 276.5 0.756 8.153 18 207 200.8 0.190 8.342 19 146 146.0 0.000 8.342 20 104 106.2 0.046 8.388 21 285 287.1 0.016 8.404 Chisq= 8.40 for 20 degrees of freedom, p= 0.01116 SUMMARY of craptest p-value for no. of wins: 0.223715 p-value for throws/game: 0.011160 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0008,0.0016,0.0030,0.0090,0.0103,0.0106,0.0112,0.0119,0.0130,0.0205, 0.0216,0.0231,0.0243,0.0245,0.0253,0.0277,0.0338,0.0426,0.0434,0.0457, 0.0478,0.0481,0.0562,0.0603,0.0628,0.0689,0.0705,0.0712,0.0732,0.0743, 0.0747,0.0775,0.0817,0.0952,0.1005,0.1029,0.1030,0.1070,0.1176,0.1176, 0.1188,0.1188,0.1374,0.1384,0.1399,0.1403,0.1416,0.1423,0.1441,0.1491, 0.1580,0.1677,0.1739,0.1747,0.1797,0.1876,0.1928,0.2007,0.2033,0.2038, 0.2076,0.2096,0.2152,0.2155,0.2203,0.2216,0.2237,0.2268,0.2306,0.2325, 0.2495,0.2503,0.2592,0.2626,0.2660,0.2719,0.2719,0.2731,0.2764,0.2764, 0.2792,0.2804,0.2822,0.2832,0.2872,0.2914,0.2933,0.3030,0.3082,0.3087, 0.3159,0.3165,0.3190,0.3267,0.3319,0.3330,0.3367,0.3416,0.3461,0.3510, 0.3657,0.3669,0.3724,0.3753,0.3758,0.3780,0.3802,0.3821,0.3825,0.3862, 0.3895,0.3991,0.4028,0.4028,0.4088,0.4105,0.4149,0.4162,0.4181,0.4189, 0.4203,0.4226,0.4230,0.4249,0.4267,0.4275,0.4309,0.4320,0.4325,0.4441, 0.4443,0.4449,0.4473,0.4702,0.4773,0.4818,0.4820,0.4914,0.4941,0.4968, 0.5000,0.5029,0.5077,0.5142,0.5163,0.5298,0.5303,0.5356,0.5387,0.5441, 0.5471,0.5529,0.5558,0.5629,0.5718,0.5775,0.5784,0.5788,0.5826,0.5828, 0.5851,0.5903,0.5948,0.5991,0.6025,0.6043,0.6047,0.6096,0.6100,0.6207, 0.6272,0.6273,0.6348,0.6376,0.6416,0.6538,0.6563,0.6601,0.6609,0.6738, 0.6857,0.6874,0.6882,0.6905,0.6976,0.7034,0.7041,0.7043,0.7051,0.7070, 0.7148,0.7157,0.7269,0.7273,0.7277,0.7324,0.7324,0.7387,0.7418,0.7441, 0.7464,0.7493,0.7500,0.7593,0.7608,0.7645,0.7650,0.7682,0.7787,0.7799, 0.7824,0.7916,0.7977,0.8035,0.8051,0.8098,0.8153,0.8156,0.8199,0.8309, 0.8316,0.8317,0.8424,0.8454,0.8474,0.8479,0.8516,0.8531,0.8572,0.8605, 0.8718,0.8829,0.8875,0.8941,0.8945,0.8980,0.8996,0.9043,0.9044,0.9057, 0.9085,0.9105,0.9143,0.9149,0.9177,0.9192,0.9223,0.9269,0.9350,0.9366, 0.9546,0.9561,0.9602,0.9622,0.9623,0.9637,0.9640,0.9642,0.9658,0.9673, 0.9764,0.9765,0.9777,0.9779,0.9816,0.9958,0.9959,0.9966,0.9966, Overall p-value after applying KStest on 269 p-values = 0.361456 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.