RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-11-25_23:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.83 15.2397 0.421782 2 to 25 15.86 13.0092 0.264427 3 to 26 15.82 20.9680 0.772276 4 to 27 15.75 14.4387 0.364157 5 to 28 15.60 16.6393 0.520948 6 to 29 15.56 31.9334 0.984663 7 to 30 15.75 24.0877 0.882929 8 to 31 15.80 16.4405 0.507147 9 to 32 15.76 23.8434 0.876248 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.306400 Tough bday spacings test for dh-ranFile-2015-11-25_23:31: 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 38 80 105 87 78 46 32 15 6 2 (O-E)^2/E 0.4 0.1 0.6 0.5 1.2 0.0 0.7 0.2 0.0 0.1 1.0 Birthday Spacings: Sum(O-E)^2/E= 4.747, p= 0.093 RESULTS OF GCD FOR dh-ranFile-2015-11-25_23:31 Euclid's algorithm: p-value, steps to gcd: 0.889911 p-value, dist. of gcd's: 0.727778 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-11-25_23:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.778 0.347 0.906 0.586 0.746 0.107 0.170 0.516 Bits 8 to 15---> 0.083 0.166 0.531 0.683 0.490 0.191 0.279 0.661 Bits 16 to 23---> 0.052 0.129 0.298 0.844 0.515 0.041 0.200 0.729 Bits 24 to 31---> 0.161 0.415 0.670 0.305 0.270 0.819 0.573 0.989 KS test for the above 32 p values: 0.508 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-11-25_23:31, p-values for 5 runs: 0.7118, 0.0406, 0.5624, 0.5087, 0.3389 Rank test for binary matrices (31x31) for dh-ranFile-2015-11-25_23:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 193 211.4 1.605 1.605 r= 29 5171 5134.0 0.267 1.871 r= 30 23107 23103.0 0.001 1.872 r= 31 11529 11551.5 0.044 1.916 chi-square = 1.916 with df = 3; p-value = 0.410 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-11-25_23:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 201 211.4 0.513 0.513 r= 30 5106 5134.0 0.153 0.666 r= 31 23200 23103.0 0.407 1.073 r= 32 11493 11551.5 0.297 1.370 chi-square = 1.370 with df = 3; p-value = 0.287 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-11-25_23:31 b-rank test for bits 1 to 8, p=0.87053 b-rank test for bits 2 to 9, p=0.80871 b-rank test for bits 3 to 10, p=0.77503 b-rank test for bits 4 to 11, p=0.12157 b-rank test for bits 5 to 12, p=0.73401 b-rank test for bits 6 to 13, p=0.13104 b-rank test for bits 7 to 14, p=0.31861 b-rank test for bits 8 to 15, p=0.95045 b-rank test for bits 9 to 16, p=0.57358 b-rank test for bits 10 to 17, p=0.25191 b-rank test for bits 11 to 18, p=0.93730 b-rank test for bits 12 to 19, p=0.96478 b-rank test for bits 13 to 20, p=0.42933 b-rank test for bits 14 to 21, p=0.05953 b-rank test for bits 15 to 22, p=0.44444 b-rank test for bits 16 to 23, p=0.03010 b-rank test for bits 17 to 24, p=0.85639 b-rank test for bits 18 to 25, p=0.01784 b-rank test for bits 19 to 26, p=0.07354 b-rank test for bits 20 to 27, p=0.01681 b-rank test for bits 21 to 28, p=0.66641 b-rank test for bits 22 to 29, p=0.50820 b-rank test for bits 23 to 30, p=0.74471 b-rank test for bits 24 to 31, p=0.94984 b-rank test for bits 25 to 32, p=0.79227 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 = 0.247790 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-11-25_23:31 (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 142702 1.85 0.967989 2 141686 -0.52 0.300905 3 141643 -0.62 0.266883 4 142239 0.77 0.779426 5 142634 1.69 0.954787 6 141846 -0.15 0.441184 7 142219 0.72 0.765322 8 142169 0.61 0.727977 9 141601 -0.72 0.235640 10 141738 -0.40 0.344466 11 142397 1.14 0.872735 12 142124 0.50 0.692013 13 142403 1.15 0.875634 14 141210 -1.63 0.051135 15 142240 0.77 0.780119 16 142453 1.27 0.898003 17 141404 -1.18 0.118865 18 141683 -0.53 0.298469 19 142310 0.94 0.825401 20 142171 0.61 0.729526 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-11-25_23:31 Bits used No. missing words z-score p-value 23 to 32 141814 -0.3287 0.371182 22 to 31 142063 0.5299 0.701908 21 to 30 142026 0.4023 0.656272 20 to 29 141881 -0.0977 0.461089 19 to 28 141953 0.1506 0.559849 18 to 27 141677 -0.8011 0.211526 17 to 26 141845 -0.2218 0.412224 16 to 25 141616 -1.0115 0.155893 15 to 24 141532 -1.3011 0.096606 14 to 23 141848 -0.2115 0.416255 13 to 22 142513 2.0816 0.981311 12 to 21 141762 -0.5080 0.305715 11 to 20 141709 -0.6908 0.244848 10 to 19 141890 -0.0667 0.473428 9 to 18 142233 1.1161 0.867811 8 to 17 142653 2.5644 0.994832 7 to 16 142312 1.3885 0.917510 6 to 15 142455 1.8816 0.970056 5 to 14 142308 1.3747 0.915392 4 to 13 141519 -1.3460 0.089157 3 to 12 142195 0.9851 0.837705 2 to 11 141781 -0.4425 0.329058 1 to 10 142390 1.6575 0.951289 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-11-25_23:31 Bits used No. missing words z-score p-value 28 to 32 141993 0.2836 0.611652 27 to 31 141750 -0.5401 0.294564 26 to 30 141546 -1.2316 0.109044 25 to 29 141904 -0.0181 0.492792 24 to 28 141714 -0.6621 0.253942 23 to 27 142276 1.2429 0.893057 22 to 26 141795 -0.3876 0.349171 21 to 25 141855 -0.1842 0.426940 20 to 24 141746 -0.5537 0.289905 19 to 23 141723 -0.6316 0.263815 18 to 22 141650 -0.8791 0.189678 17 to 21 141930 0.0701 0.527930 16 to 20 142501 2.0057 0.977554 15 to 19 141940 0.1040 0.541402 14 to 18 142256 1.1752 0.880033 13 to 17 141725 -0.6248 0.266036 12 to 16 141810 -0.3367 0.368167 11 to 15 141761 -0.5028 0.307548 10 to 14 141587 -1.0926 0.137275 9 to 13 141582 -1.1096 0.133587 8 to 12 142143 0.7921 0.785849 7 to 11 142032 0.4158 0.661233 6 to 10 141970 0.2057 0.581472 5 to 9 141873 -0.1232 0.450993 4 to 8 142160 0.8497 0.802262 3 to 7 141939 0.1006 0.540057 2 to 6 141856 -0.1808 0.428270 1 to 5 142300 1.3243 0.907299 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-11-25_23:31 Bits used No. missing words z-score p-value 31 to 32 142083 0.5123 0.695780 30 to 31 141796 -0.3343 0.369074 29 to 30 141911 0.0049 0.501965 28 to 29 142069 0.4710 0.681181 27 to 28 141993 0.2468 0.597474 26 to 27 142204 0.8692 0.807640 25 to 26 141802 -0.3166 0.375771 24 to 25 141728 -0.5349 0.296361 23 to 24 142008 0.2911 0.614498 22 to 23 141423 -1.4346 0.075700 21 to 22 141905 -0.0128 0.494905 20 to 21 142135 0.6657 0.747196 19 to 20 141527 -1.1278 0.129699 18 to 19 141511 -1.1750 0.119994 17 to 18 141895 -0.0423 0.483141 16 to 17 141896 -0.0393 0.484317 15 to 16 142620 2.0964 0.981975 14 to 15 142296 1.1406 0.872986 13 to 14 142035 0.3707 0.644573 12 to 13 141529 -1.1219 0.130949 11 to 12 142329 1.2380 0.892135 10 to 11 141513 -1.1691 0.121179 9 to 10 141782 -0.3756 0.353605 8 to 9 142032 0.3619 0.641271 7 to 8 141665 -0.7207 0.235536 6 to 7 142109 0.5890 0.722068 5 to 6 141533 -1.1101 0.133474 4 to 5 141729 -0.5319 0.297381 3 to 4 142155 0.7247 0.765679 2 to 3 142025 0.3412 0.633527 1 to 2 141669 -0.7089 0.239182 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-11-25_23:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2462.77 -0.526 0.299281 Test results for specific bytes for dh-ranFile-2015-11-25_23:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2473.89 -0.369 0.355958 2 to 9 2577.30 1.093 0.862830 3 to 10 2467.46 -0.460 0.322702 4 to 11 2591.96 1.301 0.903287 5 to 12 2553.40 0.755 0.774936 6 to 13 2424.37 -1.070 0.142393 7 to 14 2441.60 -0.826 0.204414 8 to 15 2466.18 -0.478 0.316212 9 to 16 2509.34 0.132 0.552563 10 to 17 2452.61 -0.670 0.251346 11 to 18 2429.48 -0.997 0.159317 12 to 19 2429.13 -1.002 0.158114 13 to 20 2469.54 -0.431 0.333334 14 to 21 2426.96 -1.033 0.150807 15 to 22 2387.71 -1.588 0.056133 16 to 23 2542.71 0.604 0.727096 17 to 24 2557.67 0.816 0.792625 18 to 25 2372.26 -1.806 0.035423 19 to 26 2519.47 0.275 0.608450 20 to 27 2519.47 0.275 0.608452 21 to 28 2438.12 -0.875 0.190773 22 to 29 2510.98 0.155 0.561696 23 to 30 2672.89 2.445 0.992758 24 to 31 2544.28 0.626 0.734426 25 to 32 2553.35 0.754 0.774724 CDPARK for dh-ranFile-2015-11-25_23:31: 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 3507 -0.7306 0.232514 3522 -0.0457 0.481790 3535 0.5479 0.708135 3525 0.0913 0.536383 3532 0.4110 0.659449 3519 -0.1826 0.427537 3494 -1.3242 0.092718 3504 -0.8676 0.192812 3529 0.2740 0.607947 3551 1.2785 0.899470 Square side=100, avg. no. parked=3521.80 sample std.=15.84 p-value of the KSTEST for those 10 p-values: 0.907968 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-11-25_23:31 0.9889,0.1291,0.3523,0.3998,0.3359,0.6217,0.0440,0.9369,0.6486,0.6058, The KS test for those 10 p-values: 0.888400 The 3DSPHERES test for dh-ranFile-2015-11-25_23:31 sample no r^3 equiv. uni. 1 64.688 0.884244 2 24.055 0.551490 3 21.115 0.505312 4 15.805 0.409529 5 109.878 0.974334 6 1.019 0.033399 7 0.613 0.020216 8 20.857 0.501048 9 3.126 0.098953 10 1.006 0.032985 11 22.788 0.532141 12 38.700 0.724725 13 15.076 0.395014 14 19.243 0.473462 15 45.980 0.784039 16 81.561 0.934039 17 15.655 0.406559 18 168.988 0.996422 19 9.224 0.264702 20 36.856 0.707276 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.606546 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-11-25_23:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -0.3 -1.3 1.1 0.9 1.1 -0.1 0.7 0.4 -1.6 0.4 2.3 0.1 -1.1 -1.6 0.2 -0.5 -0.7 -0.3 -0.8 0.6 0.8 0.6 1.9 -0.1 -0.4 0.2 0.6 -0.5 0.3 -0.5 -2.0 0.2 0.0 0.3 1.5 -0.2 -0.4 -1.2 0.4 0.1 0.0 0.8 Chi-square with 42 degrees of freedom:33.402653 z-score=-0.938047, p-value=0.174419 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-11-25_23:31 Test no p-value 1 0.003789 2 0.103449 3 0.034033 4 0.001857 5 0.975778 6 0.032463 7 0.537905 8 0.991520 9 0.361795 10 0.135895 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.001528 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-11-25_23:31: (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 66608 0.05 66807 0.30 3 25000.00 24865 0.73 24831 1.14 4 6666.67 6824 3.71 6673 0.01 5 1388.89 1426 0.99 1408 0.26 6 238.10 243 0.10 248 0.41 7 34.72 29 0.94 26 2.19 8 4.96 4 0.19 6 0.22 p=0.65192 p=0.39425 Number of rngs required: 689153, p-value: 0.807 RESULTS OF CRAPS TEST for dh-ranFile-2015-11-25_23:31 No. of wins: Observed Expected 98877 98585.9 z-score= 1.302, pvalue=0.90357 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66576 66666.7 0.123 0.123 2 37546 37654.3 0.312 0.435 3 27015 26954.7 0.135 0.570 4 19317 19313.5 0.001 0.570 5 13890 13851.4 0.107 0.678 6 9821 9943.5 1.510 2.188 7 7406 7145.0 9.532 11.720 8 5175 5139.1 0.251 11.971 9 3643 3699.9 0.874 12.845 10 2722 2666.3 1.164 14.009 11 1912 1923.3 0.067 14.076 12 1361 1388.7 0.554 14.630 13 1031 1003.7 0.742 15.372 14 730 726.1 0.021 15.392 15 486 525.8 3.018 18.410 16 388 381.2 0.123 18.533 17 294 276.5 1.102 19.635 18 203 200.8 0.023 19.659 19 136 146.0 0.683 20.342 20 100 106.2 0.364 20.705 21 248 287.1 5.329 26.034 Chisq= 26.03 for 20 degrees of freedom, p= 0.83531 SUMMARY of craptest p-value for no. of wins: 0.903568 p-value for throws/game: 0.835309 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-11-25_23:31 No. of wins: Observed Expected 98712 98585.9 z-score= 0.564, pvalue=0.71368 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66671 66666.7 0.000 0.000 2 37851 37654.3 1.027 1.028 3 27234 26954.7 2.893 3.921 4 19141 19313.5 1.540 5.461 5 13743 13851.4 0.849 6.310 6 9734 9943.5 4.416 10.725 7 7127 7145.0 0.045 10.771 8 5191 5139.1 0.525 11.296 9 3580 3699.9 3.883 15.179 10 2731 2666.3 1.570 16.749 11 1999 1923.3 2.977 19.726 12 1385 1388.7 0.010 19.736 13 962 1003.7 1.734 21.470 14 751 726.1 0.851 22.321 15 533 525.8 0.098 22.419 16 357 381.2 1.530 23.949 17 289 276.5 0.561 24.510 18 208 200.8 0.256 24.766 19 141 146.0 0.170 24.936 20 97 106.2 0.800 25.736 21 275 287.1 0.511 26.247 Chisq= 26.25 for 20 degrees of freedom, p= 0.84219 SUMMARY of craptest p-value for no. of wins: 0.713683 p-value for throws/game: 0.842195 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0015,0.0019,0.0038,0.0168,0.0178,0.0202,0.0301,0.0325,0.0330,0.0334, 0.0340,0.0354,0.0406,0.0414,0.0440,0.0511,0.0525,0.0561,0.0595,0.0735, 0.0757,0.0833,0.0892,0.0926,0.0927,0.0966,0.0990,0.1034,0.1069,0.1090, 0.1189,0.1200,0.1212,0.1216,0.1285,0.1291,0.1297,0.1309,0.1310,0.1335, 0.1336,0.1359,0.1373,0.1424,0.1508,0.1559,0.1581,0.1593,0.1609,0.1660, 0.1700,0.1744,0.1897,0.1908,0.1911,0.1928,0.2004,0.2044,0.2115,0.2325, 0.2355,0.2356,0.2392,0.2448,0.2478,0.2513,0.2519,0.2539,0.2638,0.2644, 0.2647,0.2660,0.2669,0.2696,0.2791,0.2873,0.2899,0.2946,0.2964,0.2974, 0.2980,0.2985,0.2993,0.3009,0.3048,0.3057,0.3064,0.3075,0.3162,0.3186, 0.3227,0.3291,0.3333,0.3359,0.3389,0.3445,0.3471,0.3492,0.3523,0.3536, 0.3560,0.3618,0.3642,0.3682,0.3691,0.3712,0.3758,0.3943,0.3950,0.3998, 0.4066,0.4095,0.4099,0.4122,0.4154,0.4163,0.4218,0.4269,0.4275,0.4283, 0.4293,0.4412,0.4444,0.4510,0.4611,0.4734,0.4735,0.4818,0.4831,0.4843, 0.4898,0.4928,0.4949,0.5010,0.5020,0.5053,0.5071,0.5077,0.5082,0.5087, 0.5154,0.5155,0.5209,0.5279,0.5315,0.5321,0.5364,0.5379,0.5401,0.5414, 0.5515,0.5526,0.5598,0.5617,0.5624,0.5725,0.5736,0.5815,0.5863,0.5975, 0.6058,0.6065,0.6079,0.6084,0.6085,0.6117,0.6145,0.6217,0.6335,0.6413, 0.6446,0.6486,0.6519,0.6563,0.6594,0.6608,0.6612,0.6664,0.6700,0.6812, 0.6829,0.6920,0.6958,0.7019,0.7073,0.7081,0.7118,0.7137,0.7221,0.7247, 0.7271,0.7278,0.7280,0.7289,0.7295,0.7340,0.7344,0.7447,0.7458,0.7472, 0.7653,0.7657,0.7723,0.7747,0.7749,0.7750,0.7781,0.7794,0.7801,0.7840, 0.7858,0.7923,0.7926,0.8023,0.8072,0.8076,0.8087,0.8191,0.8254,0.8353, 0.8377,0.8422,0.8440,0.8564,0.8628,0.8678,0.8705,0.8727,0.8730,0.8756, 0.8762,0.8800,0.8829,0.8842,0.8884,0.8899,0.8921,0.8931,0.8980,0.8995, 0.9033,0.9036,0.9061,0.9073,0.9080,0.9154,0.9175,0.9340,0.9369,0.9373, 0.9498,0.9505,0.9513,0.9548,0.9648,0.9680,0.9701,0.9743,0.9758,0.9776, 0.9813,0.9820,0.9847,0.9889,0.9894,0.9915,0.9928,0.9948,0.9964, Overall p-value after applying KStest on 269 p-values = 0.911927 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.