RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-10-23_01:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.51 27.5508 0.949532 2 to 25 15.44 20.0826 0.729973 3 to 26 15.79 16.0205 0.477618 4 to 27 15.49 21.4111 0.791560 5 to 28 15.93 10.3413 0.111308 6 to 29 15.76 14.5318 0.370833 7 to 30 15.49 24.3320 0.889308 8 to 31 15.43 22.8641 0.846272 9 to 32 16.06 10.3476 0.111597 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.515816 Tough bday spacings test for dh-ranFile-2015-10-23_01:31: 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 11 30 69 88 122 77 58 27 8 6 4 (O-E)^2/E 0.4 1.2 0.2 1.0 6.1 0.0 0.7 0.3 3.2 0.1 0.0 Birthday Spacings: Sum(O-E)^2/E= 13.018, p= 0.777 RESULTS OF GCD FOR dh-ranFile-2015-10-23_01:31 Euclid's algorithm: p-value, steps to gcd: 0.963625 p-value, dist. of gcd's: 0.195503 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-10-23_01:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.989 0.637 0.211 0.246 0.312 0.251 0.447 0.577 Bits 8 to 15---> 0.017 0.793 0.876 0.607 0.720 0.725 0.962 0.771 Bits 16 to 23---> 0.711 0.910 0.477 0.853 0.947 0.957 0.140 0.971 Bits 24 to 31---> 0.291 0.449 0.713 0.897 0.355 0.861 0.163 0.446 KS test for the above 32 p values: 0.938 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-10-23_01:31, p-values for 5 runs: 0.2794, 0.5367, 0.5659, 0.3714, 0.6468 Rank test for binary matrices (31x31) for dh-ranFile-2015-10-23_01:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 221 211.4 0.434 0.434 r= 29 5129 5134.0 0.005 0.439 r= 30 23305 23103.0 1.765 2.205 r= 31 11345 11551.5 3.692 5.897 chi-square = 5.897 with df = 3; p-value = 0.883 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-10-23_01:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 202 211.4 0.420 0.420 r= 30 5099 5134.0 0.239 0.658 r= 31 23290 23103.0 1.513 2.171 r= 32 11409 11551.5 1.758 3.930 chi-square = 3.930 with df = 3; p-value = 0.731 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-10-23_01:31 b-rank test for bits 1 to 8, p=0.11845 b-rank test for bits 2 to 9, p=0.86339 b-rank test for bits 3 to 10, p=0.38684 b-rank test for bits 4 to 11, p=0.18916 b-rank test for bits 5 to 12, p=0.51559 b-rank test for bits 6 to 13, p=0.75515 b-rank test for bits 7 to 14, p=0.81380 b-rank test for bits 8 to 15, p=0.89316 b-rank test for bits 9 to 16, p=0.43768 b-rank test for bits 10 to 17, p=0.61348 b-rank test for bits 11 to 18, p=0.66532 b-rank test for bits 12 to 19, p=0.29636 b-rank test for bits 13 to 20, p=0.78226 b-rank test for bits 14 to 21, p=0.64310 b-rank test for bits 15 to 22, p=0.10981 b-rank test for bits 16 to 23, p=0.75423 b-rank test for bits 17 to 24, p=0.78400 b-rank test for bits 18 to 25, p=0.07523 b-rank test for bits 19 to 26, p=0.04801 b-rank test for bits 20 to 27, p=0.77124 b-rank test for bits 21 to 28, p=0.11490 b-rank test for bits 22 to 29, p=0.09744 b-rank test for bits 23 to 30, p=0.85588 b-rank test for bits 24 to 31, p=0.79945 b-rank test for bits 25 to 32, p=0.88604 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 = 0.337837 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-10-23_01:31 (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 141744 -0.39 0.349643 2 141663 -0.58 0.282464 3 141369 -1.26 0.103393 4 141620 -0.68 0.249519 5 141436 -1.11 0.134382 6 142222 0.73 0.767469 7 142624 1.67 0.952520 8 141841 -0.16 0.436579 9 141452 -1.07 0.142641 10 142009 0.23 0.592070 11 142050 0.33 0.628797 12 142401 1.15 0.874673 13 141923 0.03 0.512740 14 141845 -0.15 0.440263 15 141997 0.20 0.581150 16 142866 2.24 0.987298 17 142279 0.86 0.806128 18 142324 0.97 0.833691 19 140551 -3.17 0.000753 20 142166 0.60 0.725646 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-10-23_01:31 Bits used No. missing words z-score p-value 23 to 32 141939 0.1023 0.540745 22 to 31 142235 1.1230 0.869281 21 to 30 141904 -0.0184 0.492668 20 to 29 142198 0.9954 0.840233 19 to 28 142229 1.1023 0.864837 18 to 27 141783 -0.4356 0.331556 17 to 26 141996 0.2989 0.617477 16 to 25 142000 0.3127 0.622729 15 to 24 142268 1.2368 0.891918 14 to 23 142194 0.9816 0.836857 13 to 22 142314 1.3954 0.918554 12 to 21 142082 0.5954 0.724217 11 to 20 142004 0.3264 0.627957 10 to 19 142315 1.3989 0.919073 9 to 18 141924 0.0506 0.520172 8 to 17 142268 1.2368 0.891918 7 to 16 141384 -1.8115 0.035033 6 to 15 142184 0.9471 0.828216 5 to 14 141393 -1.7804 0.037501 4 to 13 141994 0.2920 0.614844 3 to 12 141985 0.2609 0.602927 2 to 11 142190 0.9678 0.833435 1 to 10 142197 0.9920 0.839393 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-10-23_01:31 Bits used No. missing words z-score p-value 28 to 32 141923 0.0463 0.518480 27 to 31 142107 0.6701 0.748593 26 to 30 142253 1.1650 0.877987 25 to 29 141935 0.0870 0.534671 24 to 28 141965 0.1887 0.574841 23 to 27 142336 1.4463 0.925959 22 to 26 141958 0.1650 0.565521 21 to 25 141751 -0.5367 0.295733 20 to 24 141860 -0.1672 0.433598 19 to 23 141618 -0.9876 0.161684 18 to 22 142054 0.4904 0.688077 17 to 21 142004 0.3209 0.625863 16 to 20 141836 -0.2486 0.401844 15 to 19 142093 0.6226 0.733230 14 to 18 142138 0.7752 0.780875 13 to 17 141526 -1.2994 0.096899 12 to 16 141899 -0.0350 0.486033 11 to 15 141606 -1.0282 0.151919 10 to 14 142102 0.6531 0.743160 9 to 13 142236 1.1074 0.865930 8 to 12 141841 -0.2316 0.408414 7 to 11 142239 1.1175 0.868115 6 to 10 141671 -0.8079 0.209575 5 to 9 141415 -1.6757 0.046899 4 to 8 141766 -0.4859 0.313532 3 to 7 141830 -0.2689 0.393998 2 to 6 141923 0.0463 0.518480 1 to 5 142317 1.3819 0.916504 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-10-23_01:31 Bits used No. missing words z-score p-value 31 to 32 142005 0.2822 0.611110 30 to 31 142166 0.7571 0.775517 29 to 30 142184 0.8102 0.791098 28 to 29 141882 -0.0806 0.467872 27 to 28 141969 0.1760 0.569860 26 to 27 142019 0.3235 0.626846 25 to 26 141968 0.1731 0.568701 24 to 25 141957 0.1406 0.555915 23 to 24 142355 1.3147 0.905688 22 to 23 142287 1.1141 0.867376 21 to 22 142254 1.0167 0.845358 20 to 21 141586 -0.9538 0.170099 19 to 20 142065 0.4592 0.676956 18 to 19 142716 2.3796 0.991333 17 to 18 141886 -0.0688 0.472566 16 to 17 142027 0.3471 0.635745 15 to 16 142433 1.5447 0.938797 14 to 15 142251 1.0079 0.843243 13 to 14 141755 -0.4553 0.324464 12 to 13 142115 0.6067 0.727974 11 to 12 141908 -0.0039 0.498435 10 to 11 141985 0.2232 0.588316 9 to 10 141819 -0.2665 0.394942 8 to 9 142094 0.5447 0.707037 7 to 8 141551 -1.0570 0.145251 6 to 7 141861 -0.1426 0.443316 5 to 6 141931 0.0639 0.525484 4 to 5 142137 0.6716 0.749079 3 to 4 141728 -0.5349 0.296361 2 to 3 141501 -1.2045 0.114196 1 to 2 141747 -0.4788 0.316023 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-10-23_01:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2571.02 1.004 0.842385 Test results for specific bytes for dh-ranFile-2015-10-23_01:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2560.12 0.850 0.802420 2 to 9 2557.57 0.814 0.792236 3 to 10 2433.57 -0.939 0.173739 4 to 11 2334.39 -2.342 0.009587 5 to 12 2430.79 -0.979 0.163850 6 to 13 2530.63 0.433 0.667561 7 to 14 2461.48 -0.545 0.292983 8 to 15 2387.21 -1.595 0.055340 9 to 16 2357.09 -2.021 0.021639 10 to 17 2497.36 -0.037 0.485113 11 to 18 2531.52 0.446 0.672109 12 to 19 2528.28 0.400 0.655392 13 to 20 2568.62 0.970 0.834080 14 to 21 2498.78 -0.017 0.493123 15 to 22 2489.66 -0.146 0.441845 16 to 23 2561.28 0.867 0.806916 17 to 24 2671.10 2.420 0.992235 18 to 25 2491.87 -0.115 0.454211 19 to 26 2652.31 2.154 0.984377 20 to 27 2431.10 -0.974 0.164948 21 to 28 2423.56 -1.081 0.139841 22 to 29 2405.31 -1.339 0.090277 23 to 30 2453.57 -0.657 0.255691 24 to 31 2388.00 -1.584 0.056605 25 to 32 2529.76 0.421 0.663090 CDPARK for dh-ranFile-2015-10-23_01:31: 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 3543 0.9132 0.819442 3536 0.5936 0.723613 3542 0.8676 0.807188 3541 0.8219 0.794438 3508 -0.6849 0.246694 3534 0.5023 0.692266 3505 -0.8219 0.205562 3539 0.7306 0.767486 3481 -1.9178 0.027568 3535 0.5479 0.708135 Square side=100, avg. no. parked=3526.40 sample std.=19.93 p-value of the KSTEST for those 10 p-values: 0.239012 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-10-23_01:31 0.1742,0.1741,0.8100,0.5966,0.7206,0.5482,0.6453,0.4516,0.0446,0.0767, The KS test for those 10 p-values: 0.577730 The 3DSPHERES test for dh-ranFile-2015-10-23_01:31 sample no r^3 equiv. uni. 1 25.170 0.567855 2 2.151 0.069180 3 63.255 0.878579 4 3.792 0.118734 5 54.321 0.836459 6 58.173 0.856166 7 11.619 0.321110 8 17.285 0.437952 9 62.761 0.876565 10 2.726 0.086862 11 44.036 0.769585 12 158.102 0.994857 13 45.367 0.779581 14 54.910 0.839639 15 21.948 0.518857 16 10.417 0.293362 17 60.219 0.865649 18 2.003 0.064576 19 9.856 0.280029 20 11.072 0.308621 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.453278 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-10-23_01:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -0.7 2.3 -0.5 -0.1 0.2 -0.3 -0.6 -0.2 0.2 1.0 0.1 0.6 0.4 -1.0 -0.8 1.6 0.7 -0.8 0.4 -0.1 0.7 -2.0 -0.0 -0.8 -0.2 -0.2 -0.3 1.3 0.6 0.1 -0.8 -1.1 1.5 -0.4 -1.2 1.2 -0.4 0.5 1.0 0.1 -1.0 -1.1 Chi-square with 42 degrees of freedom:31.998897 z-score=-1.091210, p-value=0.131801 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-10-23_01:31 Test no p-value 1 0.032182 2 0.247845 3 0.031913 4 0.006686 5 0.236655 6 0.022870 7 0.483400 8 0.298452 9 0.335563 10 0.480442 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.001148 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-10-23_01:31: (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 66810 0.31 66463 0.62 3 25000.00 24936 0.16 25124 0.62 4 6666.67 6636 0.14 6698 0.15 5 1388.89 1341 1.65 1432 1.34 6 238.10 241 0.04 251 0.70 7 34.72 32 0.21 29 0.94 8 4.96 3 0.77 2 1.77 p=0.22800 p=0.59131 Number of rngs required: 688841, p-value: 0.693 RESULTS OF CRAPS TEST for dh-ranFile-2015-10-23_01:31 No. of wins: Observed Expected 98263 98585.9 z-score=-1.444, pvalue=0.07437 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66716 66666.7 0.037 0.037 2 37935 37654.3 2.092 2.129 3 26747 26954.7 1.601 3.730 4 19398 19313.5 0.370 4.100 5 13566 13851.4 5.881 9.981 6 9939 9943.5 0.002 9.983 7 7113 7145.0 0.144 10.127 8 5134 5139.1 0.005 10.132 9 3758 3699.9 0.913 11.045 10 2667 2666.3 0.000 11.045 11 1944 1923.3 0.222 11.267 12 1427 1388.7 1.054 12.321 13 984 1003.7 0.387 12.709 14 729 726.1 0.011 12.720 15 553 525.8 1.403 14.123 16 380 381.2 0.003 14.127 17 292 276.5 0.864 14.991 18 197 200.8 0.073 15.064 19 137 146.0 0.553 15.617 20 101 106.2 0.256 15.873 21 283 287.1 0.059 15.932 Chisq= 15.93 for 20 degrees of freedom, p= 0.27917 SUMMARY of craptest p-value for no. of wins: 0.074368 p-value for throws/game: 0.279171 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-10-23_01:31 No. of wins: Observed Expected 98149 98585.9 z-score=-1.954, pvalue=0.02536 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66886 66666.7 0.722 0.722 2 37497 37654.3 0.657 1.379 3 27098 26954.7 0.761 2.140 4 19327 19313.5 0.009 2.150 5 13747 13851.4 0.787 2.937 6 10099 9943.5 2.430 5.367 7 7118 7145.0 0.102 5.470 8 4996 5139.1 3.983 9.453 9 3705 3699.9 0.007 9.460 10 2607 2666.3 1.319 10.779 11 1927 1923.3 0.007 10.786 12 1354 1388.7 0.869 11.655 13 960 1003.7 1.904 13.559 14 695 726.1 1.335 14.894 15 550 525.8 1.110 16.005 16 400 381.2 0.932 16.937 17 262 276.5 0.764 17.701 18 218 200.8 1.468 19.169 19 143 146.0 0.061 19.230 20 94 106.2 1.405 20.635 21 317 287.1 3.111 23.746 Chisq= 23.75 for 20 degrees of freedom, p= 0.74633 SUMMARY of craptest p-value for no. of wins: 0.025357 p-value for throws/game: 0.746330 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0008,0.0011,0.0067,0.0096,0.0166,0.0216,0.0229,0.0254,0.0276,0.0319, 0.0322,0.0350,0.0375,0.0446,0.0469,0.0480,0.0553,0.0566,0.0646,0.0692, 0.0744,0.0752,0.0767,0.0869,0.0903,0.0969,0.0974,0.1034,0.1098,0.1113, 0.1116,0.1142,0.1149,0.1185,0.1187,0.1318,0.1344,0.1398,0.1401,0.1426, 0.1453,0.1519,0.1617,0.1629,0.1639,0.1649,0.1701,0.1737,0.1741,0.1742, 0.1892,0.1955,0.2056,0.2096,0.2108,0.2280,0.2367,0.2390,0.2464,0.2467, 0.2478,0.2495,0.2506,0.2557,0.2792,0.2794,0.2800,0.2825,0.2907,0.2930, 0.2934,0.2957,0.2964,0.2964,0.2985,0.3086,0.3122,0.3135,0.3160,0.3211, 0.3245,0.3316,0.3356,0.3378,0.3496,0.3552,0.3708,0.3714,0.3868,0.3940, 0.3949,0.4018,0.4084,0.4336,0.4366,0.4377,0.4380,0.4403,0.4418,0.4433, 0.4463,0.4474,0.4490,0.4516,0.4533,0.4542,0.4679,0.4726,0.4772,0.4776, 0.4804,0.4834,0.4851,0.4860,0.4927,0.4931,0.4984,0.5127,0.5156,0.5158, 0.5185,0.5185,0.5189,0.5202,0.5255,0.5347,0.5367,0.5407,0.5482,0.5559, 0.5655,0.5659,0.5679,0.5687,0.5699,0.5748,0.5766,0.5777,0.5812,0.5883, 0.5913,0.5921,0.5966,0.6029,0.6071,0.6111,0.6135,0.6148,0.6175,0.6227, 0.6259,0.6268,0.6280,0.6288,0.6357,0.6368,0.6431,0.6453,0.6468,0.6554, 0.6631,0.6653,0.6676,0.6721,0.6770,0.6881,0.6923,0.6931,0.7070,0.7081, 0.7110,0.7134,0.7195,0.7206,0.7236,0.7242,0.7249,0.7256,0.7280,0.7300, 0.7308,0.7332,0.7432,0.7463,0.7486,0.7491,0.7542,0.7552,0.7675,0.7675, 0.7696,0.7712,0.7713,0.7755,0.7774,0.7796,0.7809,0.7823,0.7840,0.7911, 0.7916,0.7922,0.7932,0.7944,0.7995,0.8024,0.8061,0.8069,0.8072,0.8100, 0.8138,0.8194,0.8282,0.8334,0.8337,0.8341,0.8365,0.8369,0.8394,0.8396, 0.8402,0.8424,0.8432,0.8454,0.8463,0.8528,0.8559,0.8562,0.8614,0.8634, 0.8648,0.8656,0.8659,0.8674,0.8681,0.8693,0.8747,0.8757,0.8766,0.8780, 0.8786,0.8833,0.8860,0.8893,0.8919,0.8919,0.8932,0.8967,0.9057,0.9096, 0.9165,0.9186,0.9191,0.9260,0.9381,0.9388,0.9472,0.9495,0.9525,0.9568, 0.9618,0.9636,0.9705,0.9844,0.9873,0.9887,0.9913,0.9922,0.9949, Overall p-value after applying KStest on 269 p-values = 0.041623 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.