RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-12-21_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 15.78 12.8323 0.252661 2 to 25 15.95 24.4441 0.892139 3 to 26 15.93 16.3103 0.498047 4 to 27 15.75 12.9440 0.260073 5 to 28 15.92 16.5435 0.514316 6 to 29 15.84 22.5700 0.836220 7 to 30 15.65 17.6685 0.589966 8 to 31 15.72 12.7351 0.246271 9 to 32 15.97 17.1224 0.553894 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.686265 Tough bday spacings test for dh-ranFile-2015-12-21_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 9 32 77 99 99 83 43 34 19 3 2 (O-E)^2/E 0.0 0.6 0.2 0.0 0.0 0.3 1.6 0.6 1.1 2.0 1.0 Birthday Spacings: Sum(O-E)^2/E= 7.469, p= 0.319 RESULTS OF GCD FOR dh-ranFile-2015-12-21_17:31 Euclid's algorithm: p-value, steps to gcd: 0.212435 p-value, dist. of gcd's: 0.559839 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-12-21_17:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.593 0.096 0.962 0.294 0.139 0.112 0.934 0.153 Bits 8 to 15---> 0.117 0.694 0.172 0.359 0.200 0.429 0.747 0.548 Bits 16 to 23---> 0.043 0.301 0.072 0.151 0.149 0.996 0.929 0.356 Bits 24 to 31---> 0.917 0.283 0.576 0.149 0.393 0.318 0.498 0.114 KS test for the above 32 p values: 0.968 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-12-21_17:31, p-values for 5 runs: 0.7614, 0.6455, 0.8154, 0.1713, 0.7634 Rank test for binary matrices (31x31) for dh-ranFile-2015-12-21_17:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 199 211.4 0.729 0.729 r= 29 5182 5134.0 0.449 1.178 r= 30 23168 23103.0 0.183 1.361 r= 31 11451 11551.5 0.875 2.235 chi-square = 2.235 with df = 3; p-value = 0.475 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-12-21_17:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 199 211.4 0.729 0.729 r= 30 5129 5134.0 0.005 0.734 r= 31 23032 23103.0 0.218 0.953 r= 32 11640 11551.5 0.678 1.630 chi-square = 1.630 with df = 3; p-value = 0.347 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-12-21_17:31 b-rank test for bits 1 to 8, p=0.21248 b-rank test for bits 2 to 9, p=0.26155 b-rank test for bits 3 to 10, p=0.91983 b-rank test for bits 4 to 11, p=0.83852 b-rank test for bits 5 to 12, p=0.70609 b-rank test for bits 6 to 13, p=0.28330 b-rank test for bits 7 to 14, p=0.83745 b-rank test for bits 8 to 15, p=0.41896 b-rank test for bits 9 to 16, p=0.64218 b-rank test for bits 10 to 17, p=0.02824 b-rank test for bits 11 to 18, p=0.97369 b-rank test for bits 12 to 19, p=0.63125 b-rank test for bits 13 to 20, p=0.09898 b-rank test for bits 14 to 21, p=0.16729 b-rank test for bits 15 to 22, p=0.95670 b-rank test for bits 16 to 23, p=0.47960 b-rank test for bits 17 to 24, p=0.06332 b-rank test for bits 18 to 25, p=0.46813 b-rank test for bits 19 to 26, p=0.26336 b-rank test for bits 20 to 27, p=0.53891 b-rank test for bits 21 to 28, p=0.85055 b-rank test for bits 22 to 29, p=0.43906 b-rank test for bits 23 to 30, p=0.82045 b-rank test for bits 24 to 31, p=0.15333 b-rank test for bits 25 to 32, p=0.57092 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 = 0.998219 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-12-21_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 141986 0.18 0.571084 2 142151 0.56 0.713844 3 142706 1.86 0.968655 4 142339 1.00 0.842287 5 141510 -0.93 0.175406 6 141718 -0.45 0.327426 7 141577 -0.78 0.218735 8 142026 0.27 0.607417 9 142567 1.54 0.937806 10 142112 0.47 0.682082 11 142069 0.37 0.645448 12 141557 -0.82 0.205197 13 142078 0.39 0.653242 14 141688 -0.52 0.302534 15 141081 -1.94 0.026474 16 142069 0.37 0.645448 17 142055 0.34 0.633204 18 141518 -0.91 0.180274 19 141939 0.07 0.527634 20 141774 -0.32 0.375929 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-12-21_17:31 Bits used No. missing words z-score p-value 23 to 32 141674 -0.8115 0.208544 22 to 31 142241 1.1437 0.873624 21 to 30 141814 -0.3287 0.371182 20 to 29 141869 -0.1391 0.444698 19 to 28 142118 0.7196 0.764100 18 to 27 141991 0.2816 0.610883 17 to 26 142202 1.0092 0.843562 16 to 25 142484 1.9816 0.976239 15 to 24 141939 0.1023 0.540745 14 to 23 142257 1.1989 0.884709 13 to 22 141387 -1.8011 0.035841 12 to 21 141212 -2.4046 0.008095 11 to 20 141693 -0.7460 0.227844 10 to 19 141561 -1.2011 0.114849 9 to 18 142148 0.8230 0.794746 8 to 17 141579 -1.1391 0.127337 7 to 16 141440 -1.6184 0.052790 6 to 15 141775 -0.4632 0.321608 5 to 14 142150 0.8299 0.796701 4 to 13 142433 1.8058 0.964522 3 to 12 141862 -0.1632 0.435178 2 to 11 141823 -0.2977 0.382970 1 to 10 142082 0.5954 0.724217 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-12-21_17:31 Bits used No. missing words z-score p-value 28 to 32 141797 -0.3808 0.351683 27 to 31 141382 -1.7876 0.036924 26 to 30 142201 0.9887 0.838598 25 to 29 141674 -0.7977 0.212514 24 to 28 142346 1.4802 0.930595 23 to 27 141846 -0.2147 0.415009 22 to 26 142443 1.8091 0.964778 21 to 25 141857 -0.1774 0.429601 20 to 24 141525 -1.3028 0.096319 19 to 23 141671 -0.8079 0.209575 18 to 22 141654 -0.8655 0.193375 17 to 21 142029 0.4057 0.657504 16 to 20 141537 -1.2621 0.103450 15 to 19 142267 1.2124 0.887328 14 to 18 142160 0.8497 0.802262 13 to 17 141720 -0.6418 0.260503 12 to 16 142291 1.2938 0.902132 11 to 15 141879 -0.1028 0.459056 10 to 14 142441 1.8023 0.964249 9 to 13 141844 -0.2215 0.412368 8 to 12 141915 0.0192 0.507667 7 to 11 141917 0.0260 0.510371 6 to 10 142334 1.4396 0.925004 5 to 9 141674 -0.7977 0.212514 4 to 8 141939 0.1006 0.540057 3 to 7 141878 -0.1062 0.457711 2 to 6 141974 0.2192 0.586761 1 to 5 142182 0.9243 0.822336 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-12-21_17:31 Bits used No. missing words z-score p-value 31 to 32 142107 0.5831 0.720086 30 to 31 142022 0.3324 0.630191 29 to 30 142528 1.8250 0.965998 28 to 29 141743 -0.4906 0.311837 27 to 28 142506 1.7601 0.960804 26 to 27 141812 -0.2871 0.387014 25 to 26 141890 -0.0570 0.477264 24 to 25 141561 -1.0275 0.152087 23 to 24 141593 -0.9331 0.175377 22 to 23 142117 0.6126 0.729928 21 to 22 142205 0.8722 0.808446 20 to 21 142242 0.9813 0.836784 19 to 20 141853 -0.1662 0.434014 18 to 19 142006 0.2852 0.612240 17 to 18 141944 0.1023 0.540729 16 to 17 141838 -0.2104 0.416673 15 to 16 142413 1.4858 0.931328 14 to 15 142171 0.7719 0.779910 13 to 14 141698 -0.6234 0.266513 12 to 13 141965 0.1642 0.565220 11 to 12 142242 0.9813 0.836784 10 to 11 141452 -1.3491 0.088660 9 to 10 141934 0.0728 0.529007 8 to 9 141914 0.0138 0.505496 7 to 8 142117 0.6126 0.729928 6 to 7 142291 1.1259 0.869890 5 to 6 142331 1.2439 0.893225 4 to 5 141655 -0.7502 0.226556 3 to 4 141395 -1.5172 0.064608 2 to 3 141722 -0.5526 0.290270 1 to 2 142240 0.9754 0.835326 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-12-21_17:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2573.43 1.038 0.850465 Test results for specific bytes for dh-ranFile-2015-12-21_17:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2457.00 -0.608 0.271564 2 to 9 2589.81 1.270 0.897973 3 to 10 2532.68 0.462 0.678007 4 to 11 2437.66 -0.882 0.188974 5 to 12 2561.86 0.875 0.809182 6 to 13 2407.57 -1.307 0.095568 7 to 14 2486.34 -0.193 0.423434 8 to 15 2573.81 1.044 0.851724 9 to 16 2615.95 1.640 0.949469 10 to 17 2471.67 -0.401 0.344365 11 to 18 2517.64 0.250 0.598520 12 to 19 2574.24 1.050 0.853114 13 to 20 2520.21 0.286 0.612469 14 to 21 2520.99 0.297 0.616689 15 to 22 2524.70 0.349 0.636549 16 to 23 2579.65 1.126 0.869998 17 to 24 2518.30 0.259 0.602097 18 to 25 2522.27 0.315 0.623607 19 to 26 2629.28 1.828 0.966247 20 to 27 2478.70 -0.301 0.381642 21 to 28 2519.80 0.280 0.610264 22 to 29 2406.31 -1.325 0.092593 23 to 30 2525.09 0.355 0.638616 24 to 31 2559.07 0.835 0.798230 25 to 32 2415.07 -1.201 0.114863 CDPARK for dh-ranFile-2015-12-21_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 3536 0.5936 0.723613 3547 1.0959 0.863437 3456 -3.0594 0.001109 3533 0.4566 0.676028 3541 0.8219 0.794438 3553 1.3699 0.914635 3538 0.6849 0.753306 3557 1.5525 0.939730 3553 1.3699 0.914635 3550 1.2329 0.891189 Square side=100, avg. no. parked=3536.40 sample std.=27.88 p-value of the KSTEST for those 10 p-values: 0.002630 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-12-21_17:31 0.4794,0.7800,0.9226,0.5474,0.2092,0.4366,0.2782,0.6287,0.2988,0.3492, The KS test for those 10 p-values: 0.686095 The 3DSPHERES test for dh-ranFile-2015-12-21_17:31 sample no r^3 equiv. uni. 1 42.325 0.756060 2 12.780 0.346890 3 27.190 0.596003 4 78.696 0.927431 5 13.743 0.367519 6 15.294 0.399389 7 92.764 0.954596 8 12.285 0.336020 9 2.555 0.081642 10 109.584 0.974081 11 75.037 0.918016 12 12.749 0.346207 13 8.672 0.251034 14 22.067 0.520763 15 8.761 0.253246 16 20.649 0.497566 17 46.889 0.790487 18 32.951 0.666583 19 8.151 0.237929 20 15.649 0.406455 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.565477 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-12-21_17:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 0.1 -1.8 -0.5 -0.1 0.7 1.9 -0.0 0.3 0.2 0.8 0.0 0.6 0.1 -1.9 0.2 -0.3 1.0 -0.7 0.5 -0.2 0.8 0.5 -1.1 -0.7 -0.3 0.2 -0.6 0.2 0.2 -1.0 1.1 -1.3 0.1 0.3 -1.0 0.3 0.5 0.5 -0.1 0.9 -1.0 -1.1 Chi-square with 42 degrees of freedom:26.467913 z-score=-1.694690, p-value=0.029409 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-12-21_17:31 Test no p-value 1 0.431632 2 0.098709 3 0.032025 4 0.569050 5 0.441132 6 0.555233 7 0.056471 8 0.459535 9 0.053732 10 0.607703 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.053360 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-12-21_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 66531 0.28 66627 0.02 3 25000.00 25088 0.31 24935 0.17 4 6666.67 6688 0.07 6745 0.92 5 1388.89 1389 0.00 1430 1.22 6 238.10 258 1.66 234 0.07 7 34.72 38 0.31 23 3.96 8 4.96 7 0.84 5 0.00 p=0.25165 p=0.61556 Number of rngs required: 688709, p-value: 0.638 RESULTS OF CRAPS TEST for dh-ranFile-2015-12-21_17:31 No. of wins: Observed Expected 98656 98585.9 z-score= 0.314, pvalue=0.62313 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66818 66666.7 0.344 0.344 2 37693 37654.3 0.040 0.383 3 26960 26954.7 0.001 0.384 4 19257 19313.5 0.165 0.549 5 13748 13851.4 0.772 1.322 6 10015 9943.5 0.514 1.835 7 7071 7145.0 0.767 2.602 8 5003 5139.1 3.603 6.205 9 3632 3699.9 1.245 7.450 10 2661 2666.3 0.011 7.460 11 1960 1923.3 0.699 8.159 12 1404 1388.7 0.168 8.327 13 1062 1003.7 3.385 11.712 14 683 726.1 2.563 14.275 15 535 525.8 0.160 14.434 16 434 381.2 7.328 21.762 17 269 276.5 0.206 21.968 18 208 200.8 0.256 22.224 19 170 146.0 3.951 26.175 20 92 106.2 1.902 28.077 21 325 287.1 4.999 33.076 Chisq= 33.08 for 20 degrees of freedom, p= 0.96690 SUMMARY of craptest p-value for no. of wins: 0.623131 p-value for throws/game: 0.966905 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-12-21_17:31 No. of wins: Observed Expected 99058 98585.9 z-score= 2.112, pvalue=0.98264 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66880 66666.7 0.683 0.683 2 37568 37654.3 0.198 0.881 3 27044 26954.7 0.296 1.176 4 19177 19313.5 0.964 2.140 5 13923 13851.4 0.370 2.510 6 9883 9943.5 0.369 2.879 7 7161 7145.0 0.036 2.915 8 4996 5139.1 3.983 6.898 9 3792 3699.9 2.294 9.192 10 2712 2666.3 0.783 9.976 11 1887 1923.3 0.686 10.662 12 1350 1388.7 1.081 11.742 13 1020 1003.7 0.264 12.007 14 714 726.1 0.203 12.210 15 530 525.8 0.033 12.243 16 369 381.2 0.387 12.630 17 265 276.5 0.482 13.111 18 205 200.8 0.087 13.198 19 150 146.0 0.110 13.309 20 97 106.2 0.800 14.108 21 277 287.1 0.356 14.464 Chisq= 14.46 for 20 degrees of freedom, p= 0.19380 SUMMARY of craptest p-value for no. of wins: 0.982644 p-value for throws/game: 0.193804 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0011,0.0026,0.0081,0.0265,0.0282,0.0294,0.0320,0.0358,0.0369,0.0433, 0.0528,0.0534,0.0537,0.0565,0.0633,0.0646,0.0721,0.0816,0.0887,0.0926, 0.0956,0.0956,0.0963,0.0987,0.0990,0.1035,0.1117,0.1142,0.1148,0.1149, 0.1168,0.1273,0.1389,0.1489,0.1493,0.1509,0.1521,0.1527,0.1533,0.1673, 0.1713,0.1716,0.1754,0.1754,0.1803,0.1890,0.1934,0.1938,0.2002,0.2052, 0.2085,0.2092,0.2096,0.2124,0.2125,0.2125,0.2125,0.2187,0.2266,0.2278, 0.2379,0.2463,0.2510,0.2517,0.2527,0.2532,0.2601,0.2605,0.2616,0.2634, 0.2665,0.2716,0.2782,0.2833,0.2834,0.2903,0.2939,0.2988,0.3007,0.3025, 0.3118,0.3176,0.3194,0.3216,0.3274,0.3360,0.3444,0.3462,0.3469,0.3475, 0.3492,0.3517,0.3559,0.3586,0.3675,0.3712,0.3759,0.3816,0.3830,0.3870, 0.3935,0.3994,0.4065,0.4124,0.4150,0.4167,0.4190,0.4234,0.4294,0.4296, 0.4316,0.4340,0.4352,0.4366,0.4391,0.4411,0.4447,0.4577,0.4591,0.4595, 0.4681,0.4750,0.4773,0.4794,0.4796,0.4976,0.4977,0.4980,0.5055,0.5077, 0.5104,0.5143,0.5208,0.5276,0.5290,0.5389,0.5401,0.5407,0.5407,0.5474, 0.5485,0.5539,0.5552,0.5598,0.5652,0.5655,0.5690,0.5709,0.5711,0.5760, 0.5868,0.5900,0.5926,0.5960,0.5985,0.6021,0.6074,0.6077,0.6103,0.6109, 0.6122,0.6125,0.6156,0.6167,0.6231,0.6236,0.6287,0.6302,0.6313,0.6332, 0.6365,0.6377,0.6386,0.6422,0.6454,0.6454,0.6455,0.6532,0.6575,0.6666, 0.6760,0.6780,0.6821,0.6861,0.6863,0.6943,0.7061,0.7138,0.7201,0.7236, 0.7242,0.7299,0.7299,0.7470,0.7533,0.7561,0.7614,0.7634,0.7641,0.7799, 0.7800,0.7905,0.7944,0.7947,0.7967,0.7982,0.8023,0.8084,0.8092,0.8154, 0.8204,0.8223,0.8353,0.8362,0.8368,0.8368,0.8375,0.8385,0.8386,0.8423, 0.8436,0.8505,0.8505,0.8517,0.8531,0.8634,0.8699,0.8700,0.8736,0.8847, 0.8873,0.8912,0.8921,0.8932,0.8980,0.9021,0.9146,0.9146,0.9169,0.9180, 0.9198,0.9226,0.9250,0.9274,0.9291,0.9306,0.9313,0.9335,0.9378,0.9397, 0.9495,0.9546,0.9567,0.9608,0.9617,0.9642,0.9645,0.9648,0.9660,0.9662, 0.9669,0.9677,0.9687,0.9737,0.9741,0.9762,0.9826,0.9964,0.9982, Overall p-value after applying KStest on 269 p-values = 0.490397 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.