RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-07-19_21:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.56 21.7835 0.806812 2 to 25 15.39 29.5812 0.970472 3 to 26 15.63 12.3254 0.219952 4 to 27 15.83 17.1367 0.554859 5 to 28 15.99 22.5077 0.834026 6 to 29 15.71 14.0754 0.338245 7 to 30 15.81 10.1907 0.104577 8 to 31 16.08 21.0610 0.776426 9 to 32 15.66 34.7751 0.993342 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.210746 Tough bday spacings test for dh-ranFile-2015-07-19_21:31: 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 42 71 106 92 77 56 24 9 6 5 (O-E)^2/E 0.9 0.8 0.1 0.7 0.3 0.0 0.3 1.1 2.3 0.1 0.2 Birthday Spacings: Sum(O-E)^2/E= 6.804, p= 0.256 RESULTS OF GCD FOR dh-ranFile-2015-07-19_21:31 Euclid's algorithm: p-value, steps to gcd: 0.038199 p-value, dist. of gcd's: 0.612804 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-07-19_21:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.260 0.072 0.729 0.005 0.898 0.194 0.934 0.572 Bits 8 to 15---> 0.845 0.806 0.350 0.305 0.136 0.673 0.123 0.958 Bits 16 to 23---> 0.123 0.764 0.965 0.262 0.136 0.981 0.464 0.870 Bits 24 to 31---> 0.696 0.930 0.101 0.677 0.932 0.382 0.956 0.514 KS test for the above 32 p values: 0.836 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-07-19_21:31, p-values for 5 runs: 0.8066, 0.6619, 0.0541, 0.2317, 0.4188 Rank test for binary matrices (31x31) for dh-ranFile-2015-07-19_21:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 201 211.4 0.513 0.513 r= 29 5107 5134.0 0.142 0.655 r= 30 23158 23103.0 0.131 0.786 r= 31 11534 11551.5 0.027 0.813 chi-square = 0.813 with df = 3; p-value = 0.154 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-07-19_21:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 203 211.4 0.335 0.335 r= 30 5047 5134.0 1.475 1.810 r= 31 23179 23103.0 0.250 2.060 r= 32 11571 11551.5 0.033 2.092 chi-square = 2.092 with df = 3; p-value = 0.447 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-07-19_21:31 b-rank test for bits 1 to 8, p=0.88027 b-rank test for bits 2 to 9, p=0.53887 b-rank test for bits 3 to 10, p=0.68572 b-rank test for bits 4 to 11, p=0.99322 b-rank test for bits 5 to 12, p=0.86209 b-rank test for bits 6 to 13, p=0.52744 b-rank test for bits 7 to 14, p=0.82183 b-rank test for bits 8 to 15, p=0.69552 b-rank test for bits 9 to 16, p=0.26013 b-rank test for bits 10 to 17, p=0.63740 b-rank test for bits 11 to 18, p=0.03494 b-rank test for bits 12 to 19, p=0.18327 b-rank test for bits 13 to 20, p=0.35817 b-rank test for bits 14 to 21, p=0.07333 b-rank test for bits 15 to 22, p=0.94457 b-rank test for bits 16 to 23, p=0.32693 b-rank test for bits 17 to 24, p=0.65057 b-rank test for bits 18 to 25, p=0.54072 b-rank test for bits 19 to 26, p=0.88377 b-rank test for bits 20 to 27, p=0.17906 b-rank test for bits 21 to 28, p=0.25506 b-rank test for bits 22 to 29, p=0.36938 b-rank test for bits 23 to 30, p=0.88844 b-rank test for bits 24 to 31, p=0.38914 b-rank test for bits 25 to 32, p=0.38005 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 = 0.863497 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-07-19_21:31 (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 141439 -1.10 0.135905 2 141701 -0.49 0.313217 3 141220 -1.61 0.053635 4 141889 -0.05 0.481057 5 141407 -1.17 0.120264 6 142414 1.18 0.880828 7 141989 0.19 0.573834 8 141656 -0.59 0.276961 9 142082 0.40 0.656686 10 142071 0.38 0.647186 11 141587 -0.75 0.225693 12 142040 0.31 0.619933 13 141876 -0.08 0.468964 14 141811 -0.23 0.409146 15 141464 -1.04 0.149056 16 142669 1.77 0.962045 17 142012 0.24 0.594790 18 141900 -0.02 0.491304 19 141996 0.20 0.580237 20 141574 -0.78 0.216672 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-07-19_21:31 Bits used No. missing words z-score p-value 23 to 32 141702 -0.7149 0.237326 22 to 31 141882 -0.0942 0.462459 21 to 30 141657 -0.8701 0.192122 20 to 29 141559 -1.2080 0.113517 19 to 28 141868 -0.1425 0.443336 18 to 27 141514 -1.3632 0.086409 17 to 26 142086 0.6092 0.728806 16 to 25 142346 1.5058 0.933935 15 to 24 142055 0.5023 0.692275 14 to 23 141729 -0.6218 0.267028 13 to 22 142125 0.7437 0.771468 12 to 21 142757 2.9230 0.998267 11 to 20 141996 0.2989 0.617477 10 to 19 142055 0.5023 0.692275 9 to 18 141752 -0.5425 0.293731 8 to 17 141674 -0.8115 0.208544 7 to 16 142452 1.8713 0.969347 6 to 15 141947 0.1299 0.551676 5 to 14 141391 -1.7873 0.036941 4 to 13 141571 -1.1667 0.121675 3 to 12 141771 -0.4770 0.316681 2 to 11 142134 0.7747 0.780749 1 to 10 142147 0.8196 0.793764 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-07-19_21:31 Bits used No. missing words z-score p-value 28 to 32 141650 -0.8791 0.189678 27 to 31 142107 0.6701 0.748593 26 to 30 141977 0.2294 0.590717 25 to 29 141841 -0.2316 0.408414 24 to 28 141438 -1.5977 0.055052 23 to 27 141279 -2.1367 0.016311 22 to 26 141817 -0.3130 0.377147 21 to 25 142011 0.3446 0.634819 20 to 24 141971 0.2091 0.582796 19 to 23 142099 0.6429 0.739872 18 to 22 142123 0.7243 0.765561 17 to 21 141843 -0.2248 0.411049 16 to 20 141813 -0.3265 0.372007 15 to 19 142108 0.6735 0.749672 14 to 18 141821 -0.2994 0.382308 13 to 17 141452 -1.5503 0.060538 12 to 16 141867 -0.1435 0.442951 11 to 15 142291 1.2938 0.902132 10 to 14 142360 1.5277 0.936706 9 to 13 141888 -0.0723 0.471180 8 to 12 141836 -0.2486 0.401844 7 to 11 142175 0.9006 0.816093 6 to 10 142208 1.0124 0.844336 5 to 9 141692 -0.7367 0.230649 4 to 8 141796 -0.3842 0.350426 3 to 7 142276 1.2429 0.893057 2 to 6 142194 0.9650 0.832723 1 to 5 142124 0.7277 0.766600 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-07-19_21:31 Bits used No. missing words z-score p-value 31 to 32 141874 -0.1042 0.458498 30 to 31 141837 -0.2134 0.415522 29 to 30 141915 0.0167 0.506672 28 to 29 141634 -0.8122 0.208343 27 to 28 141236 -1.9862 0.023504 26 to 27 141792 -0.3461 0.364632 25 to 26 142389 1.4150 0.921459 24 to 25 142123 0.6303 0.735749 23 to 24 141987 0.2291 0.590610 22 to 23 141947 0.1111 0.544240 21 to 22 141908 -0.0039 0.498435 20 to 21 142033 0.3648 0.642373 19 to 20 142295 1.1377 0.872371 18 to 19 141368 -1.5968 0.055150 17 to 18 141924 0.0433 0.517259 16 to 17 141604 -0.9007 0.183880 15 to 16 142473 1.6627 0.951818 14 to 15 141735 -0.5142 0.303539 13 to 14 142087 0.5241 0.699896 12 to 13 141572 -0.9951 0.159850 11 to 12 141481 -1.2635 0.103203 10 to 11 141969 0.1760 0.569860 9 to 10 141977 0.1996 0.579110 8 to 9 141875 -0.1013 0.459669 7 to 8 142227 0.9371 0.825641 6 to 7 142300 1.1524 0.875426 5 to 6 142109 0.5890 0.722068 4 to 5 142207 0.8781 0.810051 3 to 4 141635 -0.8092 0.209191 2 to 3 142043 0.3943 0.653323 1 to 2 141831 -0.2311 0.408633 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-07-19_21:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2560.21 0.852 0.802768 Test results for specific bytes for dh-ranFile-2015-07-19_21:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2589.75 1.269 0.897833 2 to 9 2608.73 1.538 0.937940 3 to 10 2515.73 0.222 0.588005 4 to 11 2452.60 -0.670 0.251306 5 to 12 2320.41 -2.540 0.005546 6 to 13 2540.77 0.577 0.717897 7 to 14 2425.36 -1.056 0.145580 8 to 15 2653.98 2.178 0.985281 9 to 16 2490.38 -0.136 0.445879 10 to 17 2429.60 -0.996 0.159722 11 to 18 2557.62 0.815 0.792444 12 to 19 2537.63 0.532 0.702690 13 to 20 2564.94 0.918 0.820787 14 to 21 2399.16 -1.426 0.076924 15 to 22 2537.56 0.531 0.702340 16 to 23 2431.57 -0.968 0.166580 17 to 24 2495.82 -0.059 0.476427 18 to 25 2577.40 1.095 0.863167 19 to 26 2538.11 0.539 0.705025 20 to 27 2469.17 -0.436 0.331400 21 to 28 2633.84 1.893 0.970803 22 to 29 2587.19 1.233 0.891221 23 to 30 2463.88 -0.511 0.304738 24 to 31 2549.56 0.701 0.758290 25 to 32 2425.26 -1.057 0.145249 CDPARK for dh-ranFile-2015-07-19_21:31: 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 3527 0.1826 0.572463 3545 1.0046 0.842447 3523 0.0000 0.500000 3516 -0.3196 0.374623 3523 0.0000 0.500000 3543 0.9132 0.819442 3523 0.0000 0.500000 3516 -0.3196 0.374623 3535 0.5479 0.708135 3496 -1.2329 0.108811 Square side=100, avg. no. parked=3524.70 sample std.=13.57 p-value of the KSTEST for those 10 p-values: 0.556201 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-07-19_21:31 0.6774,0.8839,0.3522,0.9014,0.2021,0.8629,0.3538,0.5900,0.3486,0.6095, The KS test for those 10 p-values: 0.521736 The 3DSPHERES test for dh-ranFile-2015-07-19_21:31 sample no r^3 equiv. uni. 1 53.628 0.832638 2 87.025 0.945023 3 64.203 0.882357 4 45.032 0.777111 5 32.350 0.659842 6 2.843 0.090400 7 5.773 0.175045 8 30.172 0.634223 9 8.938 0.257653 10 40.911 0.744287 11 29.301 0.623446 12 14.252 0.378155 13 16.770 0.428216 14 19.686 0.481184 15 6.689 0.199861 16 24.867 0.563477 17 7.182 0.212899 18 10.914 0.304966 19 6.587 0.197137 20 4.320 0.134114 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.877877 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-07-19_21:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 -1.2 -1.3 -0.7 1.2 -0.8 0.6 1.5 -1.1 -0.3 0.8 -0.6 0.5 1.1 -0.1 0.4 -0.4 -0.3 0.3 -1.2 -0.6 0.3 1.3 0.2 -0.1 -0.8 0.4 1.5 -1.1 -1.5 -0.4 0.0 -0.5 -0.9 -0.5 -0.5 -0.7 -0.4 0.5 1.0 0.1 -1.0 -1.1 Chi-square with 42 degrees of freedom:28.436898 z-score=-1.479856, p-value=0.054452 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-07-19_21:31 Test no p-value 1 0.652914 2 0.702699 3 0.004269 4 0.289741 5 0.714565 6 0.929853 7 0.121654 8 0.180503 9 0.042798 10 0.058006 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.098558 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-07-19_21:31: (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 66647 0.01 66623 0.03 3 25000.00 25018 0.01 25003 0.00 4 6666.67 6721 0.44 6698 0.15 5 1388.89 1370 0.26 1408 0.26 6 238.10 202 5.47 226 0.61 7 34.72 35 0.00 37 0.15 8 4.96 6 0.22 4 0.19 p=0.62122 p=0.03348 Number of rngs required: 687666, p-value: 0.197 RESULTS OF CRAPS TEST for dh-ranFile-2015-07-19_21:31 No. of wins: Observed Expected 98638 98585.9 z-score= 0.233, pvalue=0.59220 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66558 66666.7 0.177 0.177 2 37764 37654.3 0.319 0.497 3 27182 26954.7 1.916 2.413 4 19305 19313.5 0.004 2.417 5 13879 13851.4 0.055 2.471 6 9814 9943.5 1.688 4.159 7 7031 7145.0 1.820 5.979 8 5154 5139.1 0.043 6.022 9 3683 3699.9 0.077 6.099 10 2667 2666.3 0.000 6.099 11 1940 1923.3 0.144 6.244 12 1466 1388.7 4.298 10.542 13 976 1003.7 0.765 11.307 14 710 726.1 0.359 11.666 15 533 525.8 0.098 11.764 16 373 381.2 0.174 11.938 17 284 276.5 0.201 12.139 18 186 200.8 1.095 13.234 19 121 146.0 4.276 17.510 20 115 106.2 0.727 18.237 21 259 287.1 2.753 20.990 Chisq= 20.99 for 20 degrees of freedom, p= 0.60226 SUMMARY of craptest p-value for no. of wins: 0.592200 p-value for throws/game: 0.602255 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-07-19_21:31 No. of wins: Observed Expected 98766 98585.9 z-score= 0.806, pvalue=0.78979 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67021 66666.7 1.883 1.883 2 37521 37654.3 0.472 2.355 3 26858 26954.7 0.347 2.702 4 19219 19313.5 0.462 3.164 5 13692 13851.4 1.835 4.999 6 9923 9943.5 0.042 5.042 7 7127 7145.0 0.045 5.087 8 5218 5139.1 1.212 6.299 9 3798 3699.9 2.603 8.902 10 2634 2666.3 0.391 9.294 11 1955 1923.3 0.522 9.815 12 1416 1388.7 0.535 10.350 13 961 1003.7 1.818 12.168 14 728 726.1 0.005 12.173 15 548 525.8 0.934 13.107 16 396 381.2 0.579 13.686 17 268 276.5 0.264 13.949 18 200 200.8 0.003 13.953 19 127 146.0 2.469 16.421 20 126 106.2 3.685 20.107 21 264 287.1 1.861 21.968 Chisq= 21.97 for 20 degrees of freedom, p= 0.65773 SUMMARY of craptest p-value for no. of wins: 0.789791 p-value for throws/game: 0.657725 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0043,0.0046,0.0055,0.0163,0.0235,0.0335,0.0349,0.0369,0.0382,0.0428, 0.0536,0.0541,0.0545,0.0551,0.0552,0.0580,0.0605,0.0715,0.0733,0.0769, 0.0864,0.0904,0.0986,0.1006,0.1032,0.1046,0.1088,0.1135,0.1203,0.1217, 0.1217,0.1228,0.1232,0.1341,0.1357,0.1359,0.1359,0.1452,0.1456,0.1491, 0.1536,0.1597,0.1599,0.1666,0.1750,0.1791,0.1805,0.1833,0.1839,0.1897, 0.1921,0.1937,0.1970,0.1971,0.1999,0.2021,0.2083,0.2085,0.2092,0.2107, 0.2129,0.2167,0.2200,0.2257,0.2306,0.2317,0.2373,0.2513,0.2551,0.2562, 0.2577,0.2598,0.2601,0.2619,0.2670,0.2770,0.2897,0.2937,0.3035,0.3047, 0.3049,0.3050,0.3132,0.3167,0.3269,0.3314,0.3382,0.3486,0.3501,0.3504, 0.3522,0.3538,0.3582,0.3646,0.3694,0.3720,0.3746,0.3746,0.3771,0.3782, 0.3801,0.3822,0.3823,0.3891,0.4018,0.4084,0.4086,0.4091,0.4110,0.4155, 0.4188,0.4282,0.4430,0.4433,0.4459,0.4465,0.4585,0.4597,0.4625,0.4643, 0.4690,0.4712,0.4764,0.4811,0.4812,0.4913,0.4984,0.5000,0.5000,0.5000, 0.5067,0.5143,0.5173,0.5217,0.5274,0.5389,0.5407,0.5442,0.5517,0.5549, 0.5562,0.5635,0.5699,0.5718,0.5725,0.5738,0.5791,0.5802,0.5828,0.5880, 0.5900,0.5906,0.5907,0.5922,0.5948,0.6023,0.6095,0.6128,0.6175,0.6199, 0.6212,0.6234,0.6342,0.6348,0.6374,0.6424,0.6472,0.6506,0.6529,0.6533, 0.6567,0.6577,0.6598,0.6619,0.6733,0.6773,0.6774,0.6857,0.6923,0.6923, 0.6955,0.6956,0.6999,0.7023,0.7027,0.7027,0.7050,0.7081,0.7146,0.7179, 0.7221,0.7288,0.7290,0.7357,0.7399,0.7443,0.7486,0.7497,0.7583,0.7642, 0.7656,0.7666,0.7715,0.7764,0.7771,0.7807,0.7898,0.7924,0.7938,0.8028, 0.8056,0.8066,0.8068,0.8101,0.8161,0.8194,0.8208,0.8218,0.8256,0.8326, 0.8327,0.8340,0.8363,0.8424,0.8443,0.8454,0.8621,0.8629,0.8632,0.8635, 0.8698,0.8724,0.8754,0.8779,0.8803,0.8808,0.8824,0.8838,0.8839,0.8884, 0.8912,0.8931,0.8978,0.8979,0.9014,0.9021,0.9215,0.9299,0.9305,0.9316, 0.9336,0.9339,0.9367,0.9379,0.9446,0.9450,0.9518,0.9561,0.9577,0.9620, 0.9646,0.9693,0.9705,0.9708,0.9807,0.9853,0.9932,0.9933,0.9983, Overall p-value after applying KStest on 269 p-values = 0.847881 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.