RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-08-27_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 15.83 18.4053 0.636286 2 to 25 15.82 20.0616 0.728911 3 to 26 15.40 29.6373 0.970918 4 to 27 15.20 28.4733 0.960297 5 to 28 15.71 16.8222 0.533529 6 to 29 15.96 21.5512 0.797399 7 to 30 16.11 19.5888 0.704202 8 to 31 15.86 20.5093 0.750986 9 to 32 15.76 17.4007 0.572444 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.016368 Tough bday spacings test for dh-ranFile-2016-08-27_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 14 37 72 97 107 81 41 27 13 8 3 (O-E)^2/E 2.6 0.0 0.0 0.0 0.9 0.1 2.4 0.3 0.2 0.3 0.3 Birthday Spacings: Sum(O-E)^2/E= 7.013, p= 0.276 RESULTS OF GCD FOR dh-ranFile-2016-08-27_01:31 Euclid's algorithm: p-value, steps to gcd: 0.510885 p-value, dist. of gcd's: 0.795953 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-08-27_01:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.630 0.736 0.527 0.083 0.658 0.251 0.934 0.478 Bits 8 to 15---> 0.873 0.161 0.585 0.197 0.072 0.044 0.700 0.112 Bits 16 to 23---> 0.338 0.585 0.823 0.932 0.883 0.281 0.400 0.473 Bits 24 to 31---> 0.492 0.343 0.682 0.877 0.626 0.240 0.685 0.109 KS test for the above 32 p values: 0.027 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-08-27_01:31, p-values for 5 runs: 0.5755, 0.5780, 0.1039, 0.3820, 0.6195 Rank test for binary matrices (31x31) for dh-ranFile-2016-08-27_01:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 217 211.4 0.147 0.147 r= 29 5138 5134.0 0.003 0.150 r= 30 22981 23103.0 0.645 0.795 r= 31 11664 11551.5 1.095 1.890 chi-square = 1.890 with df = 3; p-value = 0.405 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-08-27_01:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 184 211.4 3.556 3.556 r= 30 5236 5134.0 2.026 5.582 r= 31 22981 23103.0 0.645 6.227 r= 32 11599 11551.5 0.195 6.422 chi-square = 6.422 with df = 3; p-value = 0.907 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-08-27_01:31 b-rank test for bits 1 to 8, p=0.38047 b-rank test for bits 2 to 9, p=0.02575 b-rank test for bits 3 to 10, p=0.13318 b-rank test for bits 4 to 11, p=0.44651 b-rank test for bits 5 to 12, p=0.28588 b-rank test for bits 6 to 13, p=0.78604 b-rank test for bits 7 to 14, p=0.25191 b-rank test for bits 8 to 15, p=0.50142 b-rank test for bits 9 to 16, p=0.07204 b-rank test for bits 10 to 17, p=0.93727 b-rank test for bits 11 to 18, p=0.99002 b-rank test for bits 12 to 19, p=0.41318 b-rank test for bits 13 to 20, p=0.38553 b-rank test for bits 14 to 21, p=0.86748 b-rank test for bits 15 to 22, p=0.85095 b-rank test for bits 16 to 23, p=0.12776 b-rank test for bits 17 to 24, p=0.84565 b-rank test for bits 18 to 25, p=0.29916 b-rank test for bits 19 to 26, p=0.99354 b-rank test for bits 20 to 27, p=0.54391 b-rank test for bits 21 to 28, p=0.68033 b-rank test for bits 22 to 29, p=0.05935 b-rank test for bits 23 to 30, p=0.27405 b-rank test for bits 24 to 31, p=0.63778 b-rank test for bits 25 to 32, p=0.27545 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 = 0.773294 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-08-27_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 142025 0.27 0.606519 2 141508 -0.94 0.174203 3 142237 0.77 0.778038 4 141557 -0.82 0.205197 5 141652 -0.60 0.273841 6 141887 -0.05 0.479196 7 141273 -1.49 0.068540 8 142204 0.69 0.754425 9 141558 -0.82 0.205862 10 141593 -0.74 0.229927 11 141631 -0.65 0.257748 12 142022 0.26 0.603820 13 142105 0.46 0.676227 14 142370 1.08 0.859111 15 141202 -1.65 0.049202 16 141687 -0.52 0.301719 17 141932 0.05 0.521121 18 142654 1.74 0.959060 19 141919 0.02 0.509013 20 141653 -0.60 0.274619 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-08-27_01:31 Bits used No. missing words z-score p-value 23 to 32 142148 0.8230 0.794746 22 to 31 142090 0.6230 0.733358 21 to 30 141743 -0.5736 0.283136 20 to 29 141973 0.2196 0.586890 19 to 28 141466 -1.5287 0.063166 18 to 27 142250 1.1747 0.879947 17 to 26 142285 1.2954 0.902411 16 to 25 142345 1.5023 0.933492 15 to 24 141842 -0.2322 0.408202 14 to 23 141562 -1.1977 0.115519 13 to 22 141324 -2.0184 0.021776 12 to 21 141750 -0.5494 0.291361 11 to 20 141692 -0.7494 0.226804 10 to 19 142085 0.6058 0.727663 9 to 18 142198 0.9954 0.840233 8 to 17 141505 -1.3942 0.081622 7 to 16 142336 1.4713 0.929392 6 to 15 141948 0.1333 0.553040 5 to 14 141381 -1.8218 0.034241 4 to 13 141754 -0.5356 0.296110 3 to 12 142171 0.9023 0.816554 2 to 11 142321 1.4196 0.922131 1 to 10 142195 0.9851 0.837705 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-08-27_01:31 Bits used No. missing words z-score p-value 28 to 32 141665 -0.8282 0.203768 27 to 31 141704 -0.6960 0.243204 26 to 30 141978 0.2328 0.592034 25 to 29 142126 0.7345 0.768670 24 to 28 141559 -1.1876 0.117504 23 to 27 142131 0.7514 0.773801 22 to 26 141587 -1.0926 0.137275 21 to 25 141508 -1.3604 0.086845 20 to 24 141942 0.1107 0.544091 19 to 23 141872 -0.1265 0.449651 18 to 22 142223 1.0633 0.856174 17 to 21 141411 -1.6893 0.045585 16 to 20 141759 -0.5096 0.305168 15 to 19 142322 1.3989 0.919076 14 to 18 142070 0.5446 0.707001 13 to 17 141883 -0.0893 0.464440 12 to 16 142116 0.7006 0.758216 11 to 15 141454 -1.5435 0.061356 10 to 14 141649 -0.8825 0.188760 9 to 13 141657 -0.8554 0.196177 8 to 12 142179 0.9141 0.819677 7 to 11 141638 -0.9198 0.178848 6 to 10 141926 0.0565 0.522532 5 to 9 141657 -0.8554 0.196177 4 to 8 142012 0.3480 0.636093 3 to 7 141491 -1.4181 0.078086 2 to 6 141749 -0.5435 0.293396 1 to 5 142277 1.2463 0.893680 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-08-27_01:31 Bits used No. missing words z-score p-value 31 to 32 141539 -1.0924 0.137325 30 to 31 141440 -1.3845 0.083110 29 to 30 141778 -0.3874 0.349229 28 to 29 142069 0.4710 0.681181 27 to 28 141590 -0.9420 0.173102 26 to 27 142005 0.2822 0.611110 25 to 26 142318 1.2055 0.885998 24 to 25 141677 -0.6853 0.246565 23 to 24 142178 0.7925 0.785976 22 to 23 141596 -0.9243 0.177671 21 to 22 141370 -1.5909 0.055811 20 to 21 142153 0.7188 0.763865 19 to 20 141371 -1.5880 0.056144 18 to 19 142247 0.9961 0.840394 17 to 18 141642 -0.7886 0.215178 16 to 17 142090 0.5329 0.702966 15 to 16 141765 -0.4258 0.335144 14 to 15 141933 0.0698 0.527833 13 to 14 141534 -1.1072 0.134111 12 to 13 142169 0.7660 0.778158 11 to 12 142192 0.8338 0.797813 10 to 11 142250 1.0049 0.842534 9 to 10 141896 -0.0393 0.484317 8 to 9 141539 -1.0924 0.137325 7 to 8 141412 -1.4671 0.071181 6 to 7 141980 0.2085 0.582568 5 to 6 141851 -0.1721 0.431693 4 to 5 142070 0.4740 0.682233 3 to 4 141561 -1.0275 0.152087 2 to 3 142243 0.9843 0.837510 1 to 2 141580 -0.9715 0.165656 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-08-27_01:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2468.76 -0.442 0.329329 Test results for specific bytes for dh-ranFile-2016-08-27_01:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2423.67 -1.080 0.140180 2 to 9 2597.41 1.378 0.915829 3 to 10 2477.79 -0.314 0.376722 4 to 11 2462.65 -0.528 0.298681 5 to 12 2507.24 0.102 0.540794 6 to 13 2522.17 0.314 0.623088 7 to 14 2463.75 -0.513 0.304073 8 to 15 2495.09 -0.070 0.472294 9 to 16 2449.97 -0.708 0.239600 10 to 17 2421.51 -1.110 0.133502 11 to 18 2538.57 0.545 0.707287 12 to 19 2493.38 -0.094 0.462694 13 to 20 2524.02 0.340 0.632941 14 to 21 2556.34 0.797 0.787218 15 to 22 2596.27 1.361 0.913310 16 to 23 2502.06 0.029 0.511635 17 to 24 2528.45 0.402 0.656266 18 to 25 2542.04 0.594 0.723899 19 to 26 2553.13 0.751 0.773801 20 to 27 2510.74 0.152 0.560345 21 to 28 2568.61 0.970 0.834043 22 to 29 2451.46 -0.687 0.246190 23 to 30 2565.06 0.920 0.821220 24 to 31 2509.52 0.135 0.553548 25 to 32 2541.53 0.587 0.721526 CDPARK for dh-ranFile-2016-08-27_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 3533 0.4566 0.676028 3495 -1.2785 0.100530 3539 0.7306 0.767486 3502 -0.9589 0.168804 3529 0.2740 0.607947 3518 -0.2283 0.409702 3511 -0.5479 0.291865 3531 0.3653 0.642555 3536 0.5936 0.723613 3523 0.0000 0.500000 Square side=100, avg. no. parked=3521.70 sample std.=14.15 p-value of the KSTEST for those 10 p-values: 0.717175 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-08-27_01:31 0.3925,0.7731,0.6661,0.8539,0.3446,0.2557,0.8303,0.0298,0.9174,0.6023, The KS test for those 10 p-values: 0.755813 The 3DSPHERES test for dh-ranFile-2016-08-27_01:31 sample no r^3 equiv. uni. 1 13.329 0.358728 2 21.064 0.504474 3 19.108 0.471087 4 26.054 0.580400 5 27.160 0.595596 6 26.153 0.581786 7 15.855 0.410506 8 5.873 0.177807 9 2.148 0.069092 10 4.279 0.132939 11 26.605 0.588041 12 4.088 0.127402 13 16.245 0.418129 14 88.530 0.947712 15 46.245 0.785941 16 28.224 0.609681 17 98.520 0.962522 18 25.920 0.578534 19 35.664 0.695416 20 18.929 0.467931 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.507844 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-08-27_01:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.1 -1.3 1.8 0.2 -0.6 -0.7 -0.1 0.4 1.3 -2.0 0.3 0.4 -1.5 -0.8 0.3 0.8 1.9 -0.2 -1.5 0.3 0.1 0.0 0.7 0.9 -0.5 -0.8 -1.2 0.2 -0.0 0.5 0.4 0.0 -0.4 1.3 1.3 -0.7 0.2 -2.0 -0.1 0.1 1.0 1.8 Chi-square with 42 degrees of freedom:38.400152 z-score=-0.392776, p-value=0.370231 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-08-27_01:31 Test no p-value 1 0.798812 2 0.618433 3 0.295867 4 0.019989 5 0.282887 6 0.705808 7 0.060719 8 0.045351 9 0.070004 10 0.325328 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.047849 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-08-27_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 66718 0.04 66464 0.62 3 25000.00 24988 0.01 25200 1.60 4 6666.67 6676 0.01 6659 0.01 5 1388.89 1341 1.65 1383 0.02 6 238.10 242 0.06 253 0.93 7 34.72 30 0.64 37 0.15 8 4.96 4 0.19 3 0.77 p=0.14302 p=0.33783 Number of rngs required: 687522, p-value: 0.154 RESULTS OF CRAPS TEST for dh-ranFile-2016-08-27_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 66436 66666.7 0.798 0.798 2 37508 37654.3 0.569 1.367 3 26871 26954.7 0.260 1.627 4 19365 19313.5 0.138 1.764 5 13967 13851.4 0.964 2.729 6 10062 9943.5 1.411 4.140 7 6932 7145.0 6.351 10.491 8 5187 5139.1 0.447 10.938 9 3771 3699.9 1.368 12.306 10 2784 2666.3 5.196 17.502 11 1962 1923.3 0.778 18.279 12 1414 1388.7 0.459 18.739 13 1041 1003.7 1.385 20.124 14 765 726.1 2.080 22.203 15 550 525.8 1.110 23.314 16 374 381.2 0.134 23.448 17 288 276.5 0.475 23.923 18 212 200.8 0.621 24.544 19 142 146.0 0.109 24.653 20 100 106.2 0.364 25.017 21 269 287.1 1.143 26.159 Chisq= 26.16 for 20 degrees of freedom, p= 0.83939 SUMMARY of craptest p-value for no. of wins: 0.025357 p-value for throws/game: 0.839388 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-08-27_01:31 No. of wins: Observed Expected 98901 98585.9 z-score= 1.409, pvalue=0.92066 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66563 66666.7 0.161 0.161 2 37595 37654.3 0.093 0.255 3 27237 26954.7 2.956 3.211 4 19177 19313.5 0.964 4.175 5 13762 13851.4 0.577 4.752 6 9983 9943.5 0.157 4.909 7 7165 7145.0 0.056 4.964 8 5161 5139.1 0.094 5.058 9 3797 3699.9 2.550 7.608 10 2629 2666.3 0.522 8.130 11 1864 1923.3 1.830 9.960 12 1413 1388.7 0.424 10.384 13 1013 1003.7 0.086 10.470 14 730 726.1 0.021 10.490 15 525 525.8 0.001 10.492 16 368 381.2 0.454 10.945 17 282 276.5 0.108 11.053 18 192 200.8 0.388 11.441 19 148 146.0 0.028 11.469 20 127 106.2 4.067 15.536 21 269 287.1 1.143 16.679 Chisq= 16.68 for 20 degrees of freedom, p= 0.32630 SUMMARY of craptest p-value for no. of wins: 0.920656 p-value for throws/game: 0.326304 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0164,0.0200,0.0218,0.0254,0.0258,0.0268,0.0298,0.0342,0.0443,0.0454, 0.0456,0.0478,0.0492,0.0558,0.0561,0.0594,0.0607,0.0614,0.0632,0.0685, 0.0691,0.0700,0.0712,0.0717,0.0720,0.0781,0.0816,0.0831,0.0831,0.0868, 0.1005,0.1039,0.1089,0.1121,0.1155,0.1175,0.1274,0.1278,0.1329,0.1332, 0.1335,0.1341,0.1373,0.1373,0.1373,0.1402,0.1430,0.1521,0.1536,0.1607, 0.1657,0.1688,0.1731,0.1742,0.1777,0.1778,0.1788,0.1888,0.1962,0.1962, 0.1970,0.2038,0.2052,0.2059,0.2152,0.2268,0.2299,0.2396,0.2402,0.2432, 0.2462,0.2466,0.2505,0.2519,0.2557,0.2577,0.2738,0.2740,0.2746,0.2755, 0.2758,0.2807,0.2829,0.2831,0.2859,0.2914,0.2919,0.2934,0.2959,0.2961, 0.2987,0.2992,0.3017,0.3041,0.3052,0.3253,0.3263,0.3293,0.3351,0.3378, 0.3380,0.3427,0.3446,0.3492,0.3587,0.3702,0.3767,0.3805,0.3820,0.3855, 0.3925,0.4003,0.4045,0.4082,0.4097,0.4105,0.4132,0.4181,0.4317,0.4465, 0.4497,0.4627,0.4644,0.4679,0.4711,0.4723,0.4729,0.4785,0.4792,0.4843, 0.4919,0.5000,0.5014,0.5045,0.5078,0.5090,0.5109,0.5116,0.5211,0.5225, 0.5274,0.5278,0.5335,0.5408,0.5439,0.5441,0.5530,0.5535,0.5603,0.5724, 0.5755,0.5780,0.5785,0.5804,0.5818,0.5826,0.5845,0.5854,0.5869,0.5880, 0.5920,0.5956,0.6023,0.6038,0.6065,0.6079,0.6097,0.6111,0.6184,0.6195, 0.6231,0.6257,0.6304,0.6329,0.6361,0.6363,0.6378,0.6426,0.6563,0.6584, 0.6661,0.6760,0.6762,0.6803,0.6812,0.6817,0.6822,0.6853,0.6954,0.6997, 0.7030,0.7042,0.7058,0.7070,0.7073,0.7172,0.7215,0.7236,0.7239,0.7277, 0.7289,0.7334,0.7357,0.7510,0.7544,0.7558,0.7582,0.7639,0.7675,0.7687, 0.7731,0.7733,0.7738,0.7738,0.7780,0.7782,0.7859,0.7860,0.7860,0.7872, 0.7947,0.7960,0.7974,0.7978,0.7988,0.8166,0.8197,0.8212,0.8225,0.8303, 0.8340,0.8375,0.8377,0.8394,0.8402,0.8404,0.8425,0.8457,0.8509,0.8539, 0.8562,0.8591,0.8675,0.8726,0.8773,0.8799,0.8828,0.8860,0.8937,0.9024, 0.9072,0.9133,0.9158,0.9174,0.9191,0.9207,0.9221,0.9294,0.9320,0.9335, 0.9338,0.9373,0.9477,0.9591,0.9603,0.9625,0.9709,0.9900,0.9935, Overall p-value after applying KStest on 269 p-values = 0.369696 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.