RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-09-10_12:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.86 9.3680 0.071994 2 to 25 15.66 17.4485 0.575601 3 to 26 15.57 21.7496 0.805460 4 to 27 15.96 16.0280 0.478149 5 to 28 15.81 16.2802 0.495933 6 to 29 15.62 28.5336 0.960923 7 to 30 15.56 20.3938 0.745418 8 to 31 15.52 24.6421 0.896989 9 to 32 15.45 28.6525 0.962132 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.114964 Tough bday spacings test for dh-ranFile-2015-09-10_12:31: 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 6 37 79 101 94 84 49 25 12 7 6 (O-E)^2/E 1.1 0.0 0.4 0.1 0.1 0.4 0.2 0.8 0.6 0.0 0.9 Birthday Spacings: Sum(O-E)^2/E= 4.682, p= 0.089 RESULTS OF GCD FOR dh-ranFile-2015-09-10_12:31 Euclid's algorithm: p-value, steps to gcd: 0.827796 p-value, dist. of gcd's: 0.932468 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-09-10_12:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.168 0.834 0.711 0.154 0.537 0.464 0.181 0.376 Bits 8 to 15---> 0.837 0.097 0.384 0.862 0.073 0.575 0.374 0.831 Bits 16 to 23---> 0.474 0.852 0.542 0.174 0.876 0.605 0.551 0.399 Bits 24 to 31---> 0.859 0.805 0.851 0.371 0.988 0.797 0.532 0.092 KS test for the above 32 p values: 0.525 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-09-10_12:31, p-values for 5 runs: 0.3016, 0.3735, 0.8511, 0.5524, 0.4655 Rank test for binary matrices (31x31) for dh-ranFile-2015-09-10_12:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 202 211.4 0.420 0.420 r= 29 5174 5134.0 0.311 0.731 r= 30 23148 23103.0 0.087 0.818 r= 31 11476 11551.5 0.494 1.312 chi-square = 1.312 with df = 3; p-value = 0.274 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-09-10_12:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 209 211.4 0.028 0.028 r= 30 5074 5134.0 0.701 0.729 r= 31 23011 23103.0 0.367 1.096 r= 32 11706 11551.5 2.066 3.162 chi-square = 3.162 with df = 3; p-value = 0.633 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-09-10_12:31 b-rank test for bits 1 to 8, p=0.75446 b-rank test for bits 2 to 9, p=0.42510 b-rank test for bits 3 to 10, p=0.81954 b-rank test for bits 4 to 11, p=0.40694 b-rank test for bits 5 to 12, p=0.46690 b-rank test for bits 6 to 13, p=0.76247 b-rank test for bits 7 to 14, p=0.41030 b-rank test for bits 8 to 15, p=0.18830 b-rank test for bits 9 to 16, p=0.53081 b-rank test for bits 10 to 17, p=0.64466 b-rank test for bits 11 to 18, p=0.82247 b-rank test for bits 12 to 19, p=0.76710 b-rank test for bits 13 to 20, p=0.23660 b-rank test for bits 14 to 21, p=0.49323 b-rank test for bits 15 to 22, p=0.14611 b-rank test for bits 16 to 23, p=0.40628 b-rank test for bits 17 to 24, p=0.54578 b-rank test for bits 18 to 25, p=0.34154 b-rank test for bits 19 to 26, p=0.86911 b-rank test for bits 20 to 27, p=0.03784 b-rank test for bits 21 to 28, p=0.14877 b-rank test for bits 22 to 29, p=0.72981 b-rank test for bits 23 to 30, p=0.47172 b-rank test for bits 24 to 31, p=0.51956 b-rank test for bits 25 to 32, p=0.24079 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 = 0.467996 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-09-10_12:31 (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 141729 -0.42 0.336756 2 141757 -0.36 0.360954 3 141927 0.04 0.516466 4 142310 0.94 0.825401 5 142339 1.00 0.842287 6 141222 -1.61 0.054147 7 141859 -0.12 0.453195 8 141739 -0.40 0.345327 9 141048 -2.01 0.022086 10 142585 1.58 0.942794 11 142338 1.00 0.841723 12 141537 -0.87 0.192169 13 141769 -0.33 0.371504 14 142014 0.24 0.596600 15 141741 -0.39 0.347051 16 141642 -0.62 0.266116 17 141335 -1.34 0.089815 18 141593 -0.74 0.229927 19 140887 -2.39 0.008456 20 142227 0.74 0.771023 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-09-10_12:31 Bits used No. missing words z-score p-value 23 to 32 141868 -0.1425 0.443336 22 to 31 141334 -1.9839 0.023634 21 to 30 141547 -1.2494 0.105757 20 to 29 142072 0.5609 0.712578 19 to 28 141667 -0.8356 0.201684 18 to 27 141539 -1.2770 0.100801 17 to 26 142496 2.0230 0.978463 16 to 25 141742 -0.5770 0.281970 15 to 24 141859 -0.1736 0.431109 14 to 23 141675 -0.8080 0.209535 13 to 22 142248 1.1678 0.878562 12 to 21 142104 0.6713 0.748978 11 to 20 141975 0.2264 0.589574 10 to 19 141659 -0.8632 0.194012 9 to 18 142305 1.3644 0.913776 8 to 17 142285 1.2954 0.902411 7 to 16 142133 0.7713 0.779728 6 to 15 141560 -1.2046 0.114182 5 to 14 141918 0.0299 0.511925 4 to 13 141627 -0.9736 0.165140 3 to 12 141846 -0.2184 0.413567 2 to 11 142003 0.3230 0.626652 1 to 10 141721 -0.6494 0.258036 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-09-10_12:31 Bits used No. missing words z-score p-value 28 to 32 142319 1.3887 0.917540 27 to 31 141533 -1.2757 0.101032 26 to 30 142061 0.5141 0.696421 25 to 29 141551 -1.2147 0.112244 24 to 28 141900 -0.0316 0.487385 23 to 27 141578 -1.1232 0.130686 22 to 26 141513 -1.3435 0.089556 21 to 25 141750 -0.5401 0.294564 20 to 24 141776 -0.4520 0.325647 19 to 23 142479 1.9311 0.973264 18 to 22 142023 0.3853 0.650001 17 to 21 142462 1.8735 0.969497 16 to 20 142107 0.6701 0.748593 15 to 19 141977 0.2294 0.590717 14 to 18 141947 0.1277 0.550805 13 to 17 141957 0.1616 0.564187 12 to 16 141821 -0.2994 0.382308 11 to 15 141648 -0.8859 0.187845 10 to 14 141624 -0.9672 0.166717 9 to 13 142081 0.5819 0.719694 8 to 12 142447 1.8226 0.965819 7 to 11 141816 -0.3164 0.375860 6 to 10 142181 0.9209 0.821453 5 to 9 142039 0.4396 0.669872 4 to 8 141898 -0.0384 0.484682 3 to 7 141723 -0.6316 0.263815 2 to 6 141908 -0.0045 0.498201 1 to 5 141146 -2.5876 0.004833 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-09-10_12:31 Bits used No. missing words z-score p-value 31 to 32 141842 -0.1986 0.421283 30 to 31 142260 1.0344 0.849531 29 to 30 141329 -1.7119 0.043459 28 to 29 142144 0.6922 0.755607 27 to 28 141771 -0.4081 0.341617 26 to 27 142355 1.3147 0.905688 25 to 26 142174 0.7807 0.782522 24 to 25 142361 1.3324 0.908629 23 to 24 141636 -0.8063 0.210040 22 to 23 141858 -0.1514 0.439824 21 to 22 141769 -0.4140 0.339454 20 to 21 142409 1.4740 0.929753 19 to 20 141003 -2.6735 0.003753 18 to 19 142246 0.9931 0.839676 17 to 18 142551 1.8928 0.970810 16 to 17 142302 1.1583 0.876633 15 to 16 142219 0.9135 0.819505 14 to 15 142285 1.1082 0.866106 13 to 14 141139 -2.2724 0.011532 12 to 13 141744 -0.4877 0.312882 11 to 12 142000 0.2675 0.605444 10 to 11 141653 -0.7561 0.224784 9 to 10 141546 -1.0718 0.141912 8 to 9 141679 -0.6794 0.248430 7 to 8 142313 1.1908 0.883127 6 to 7 142174 0.7807 0.782522 5 to 6 141484 -1.2547 0.104801 4 to 5 142635 2.1406 0.983848 3 to 4 141955 0.1347 0.553583 2 to 3 142393 1.4268 0.923175 1 to 2 141778 -0.3874 0.349229 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-09-10_12:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2534.68 0.490 0.688088 Test results for specific bytes for dh-ranFile-2015-09-10_12:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2524.63 0.348 0.636188 2 to 9 2466.71 -0.471 0.318904 3 to 10 2430.41 -0.984 0.162522 4 to 11 2528.54 0.404 0.656728 5 to 12 2552.53 0.743 0.771230 6 to 13 2553.81 0.761 0.776689 7 to 14 2434.35 -0.928 0.176604 8 to 15 2540.29 0.570 0.715604 9 to 16 2612.69 1.594 0.944501 10 to 17 2487.41 -0.178 0.429366 11 to 18 2493.83 -0.087 0.465214 12 to 19 2335.20 -2.331 0.009885 13 to 20 2553.97 0.763 0.777324 14 to 21 2601.45 1.435 0.924311 15 to 22 2519.38 0.274 0.607997 16 to 23 2420.52 -1.124 0.130500 17 to 24 2485.25 -0.209 0.417378 18 to 25 2501.62 0.023 0.509155 19 to 26 2561.79 0.874 0.808897 20 to 27 2560.76 0.859 0.804892 21 to 28 2552.81 0.747 0.772441 22 to 29 2524.29 0.344 0.634407 23 to 30 2603.60 1.465 0.928554 24 to 31 2553.84 0.761 0.776798 25 to 32 2610.81 1.567 0.941459 CDPARK for dh-ranFile-2015-09-10_12:31: 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 3559 1.6438 0.949895 3532 0.4110 0.659449 3520 -0.1370 0.445521 3509 -0.6393 0.261324 3498 -1.1416 0.126820 3547 1.0959 0.863437 3514 -0.4110 0.340551 3517 -0.2740 0.392053 3524 0.0457 0.518210 3465 -2.6484 0.004044 Square side=100, avg. no. parked=3518.50 sample std.=24.62 p-value of the KSTEST for those 10 p-values: 0.836198 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-09-10_12:31 0.2738,0.5900,0.8272,0.9362,0.3532,0.7878,0.9543,0.4982,0.9169,0.0582, The KS test for those 10 p-values: 0.272522 The 3DSPHERES test for dh-ranFile-2015-09-10_12:31 sample no r^3 equiv. uni. 1 6.505 0.194928 2 3.831 0.119885 3 28.407 0.612057 4 42.680 0.758927 5 68.886 0.899359 6 27.381 0.598565 7 73.230 0.912926 8 15.712 0.407697 9 156.897 0.994646 10 7.902 0.231572 11 20.152 0.489175 12 20.912 0.501957 13 12.931 0.350156 14 4.930 0.151538 15 31.670 0.652043 16 23.350 0.540824 17 2.715 0.086520 18 0.826 0.027172 19 16.122 0.415731 20 18.997 0.469124 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.892760 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-09-10_12:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 0.1 -0.4 0.5 1.9 -1.0 0.3 -1.9 0.9 -0.7 0.3 0.2 0.5 0.2 0.9 -0.2 0.1 -0.6 -0.2 1.0 0.2 -0.7 0.9 -0.6 -1.2 0.5 -0.4 0.2 0.2 -1.3 -0.3 0.9 -1.3 -1.7 1.2 -0.8 0.5 -0.7 -0.8 -0.7 0.1 -1.0 -0.1 Chi-square with 42 degrees of freedom:30.701663 z-score=-1.232750, p-value=0.098503 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-09-10_12:31 Test no p-value 1 0.154266 2 0.712790 3 0.023495 4 0.084321 5 0.045855 6 0.582121 7 0.311252 8 0.611306 9 0.144118 10 0.115414 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.015358 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-09-10_12:31: (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 66676 0.00 66416 0.94 3 25000.00 24989 0.00 25379 5.75 4 6666.67 6612 0.45 6528 2.88 5 1388.89 1427 1.05 1415 0.49 6 238.10 262 2.40 231 0.21 7 34.72 30 0.64 27 1.72 8 4.96 3 0.77 3 0.77 p=0.49608 p=0.95309 Number of rngs required: 688000, p-value: 0.321 RESULTS OF CRAPS TEST for dh-ranFile-2015-09-10_12:31 No. of wins: Observed Expected 98314 98585.9 z-score=-1.216, pvalue=0.11201 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66364 66666.7 1.374 1.374 2 37918 37654.3 1.846 3.221 3 26922 26954.7 0.040 3.260 4 19440 19313.5 0.829 4.089 5 13772 13851.4 0.455 4.545 6 9941 9943.5 0.001 4.545 7 7232 7145.0 1.059 5.604 8 5184 5139.1 0.393 5.997 9 3605 3699.9 2.432 8.429 10 2620 2666.3 0.804 9.233 11 1909 1923.3 0.107 9.340 12 1438 1388.7 1.747 11.087 13 981 1003.7 0.514 11.601 14 684 726.1 2.446 14.047 15 576 525.8 4.786 18.832 16 375 381.2 0.099 18.932 17 286 276.5 0.324 19.255 18 206 200.8 0.133 19.388 19 156 146.0 0.687 20.076 20 106 106.2 0.000 20.076 21 285 287.1 0.016 20.092 Chisq= 20.09 for 20 degrees of freedom, p= 0.54778 SUMMARY of craptest p-value for no. of wins: 0.112010 p-value for throws/game: 0.547783 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-09-10_12:31 No. of wins: Observed Expected 98601 98585.9 z-score= 0.068, pvalue=0.52700 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66389 66666.7 1.156 1.156 2 37806 37654.3 0.611 1.767 3 27019 26954.7 0.153 1.921 4 19315 19313.5 0.000 1.921 5 14036 13851.4 2.460 4.380 6 9965 9943.5 0.046 4.427 7 7018 7145.0 2.258 6.685 8 5121 5139.1 0.064 6.749 9 3682 3699.9 0.086 6.835 10 2650 2666.3 0.100 6.935 11 1960 1923.3 0.699 7.634 12 1387 1388.7 0.002 7.636 13 965 1003.7 1.493 9.129 14 750 726.1 0.784 9.913 15 521 525.8 0.044 9.958 16 386 381.2 0.062 10.019 17 262 276.5 0.764 10.784 18 213 200.8 0.737 11.521 19 147 146.0 0.007 11.528 20 114 106.2 0.571 12.099 21 294 287.1 0.165 12.264 Chisq= 12.26 for 20 degrees of freedom, p= 0.09331 SUMMARY of craptest p-value for no. of wins: 0.526996 p-value for throws/game: 0.093311 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0038,0.0040,0.0048,0.0085,0.0099,0.0115,0.0154,0.0221,0.0235,0.0236, 0.0272,0.0378,0.0435,0.0459,0.0541,0.0582,0.0720,0.0727,0.0843,0.0865, 0.0886,0.0896,0.0898,0.0920,0.0933,0.0974,0.0985,0.1008,0.1010,0.1048, 0.1058,0.1120,0.1122,0.1142,0.1150,0.1154,0.1199,0.1268,0.1305,0.1307, 0.1419,0.1441,0.1461,0.1488,0.1515,0.1543,0.1543,0.1625,0.1651,0.1667, 0.1681,0.1740,0.1766,0.1805,0.1878,0.1883,0.1922,0.1940,0.1949,0.2017, 0.2095,0.2100,0.2248,0.2299,0.2316,0.2366,0.2408,0.2484,0.2580,0.2613, 0.2638,0.2661,0.2725,0.2738,0.2738,0.2820,0.2946,0.3016,0.3113,0.3129, 0.3189,0.3212,0.3256,0.3368,0.3395,0.3406,0.3415,0.3416,0.3453,0.3471, 0.3492,0.3502,0.3532,0.3610,0.3714,0.3715,0.3735,0.3739,0.3759,0.3761, 0.3823,0.3842,0.3921,0.3987,0.4063,0.4069,0.4077,0.4103,0.4136,0.4157, 0.4174,0.4213,0.4251,0.4294,0.4311,0.4398,0.4433,0.4455,0.4532,0.4644, 0.4652,0.4655,0.4669,0.4680,0.4691,0.4717,0.4743,0.4781,0.4847,0.4874, 0.4892,0.4932,0.4959,0.4961,0.4982,0.4982,0.5020,0.5092,0.5119,0.5165, 0.5182,0.5196,0.5249,0.5270,0.5308,0.5317,0.5375,0.5408,0.5416,0.5458, 0.5478,0.5508,0.5511,0.5524,0.5536,0.5642,0.5747,0.5756,0.5821,0.5896, 0.5900,0.5907,0.5966,0.5986,0.6050,0.6054,0.6080,0.6113,0.6121,0.6267, 0.6326,0.6344,0.6362,0.6447,0.6500,0.6520,0.6567,0.6594,0.6699,0.6881, 0.6964,0.7115,0.7126,0.7128,0.7156,0.7197,0.7298,0.7454,0.7486,0.7490, 0.7545,0.7556,0.7589,0.7625,0.7671,0.7710,0.7712,0.7724,0.7767,0.7768, 0.7773,0.7797,0.7825,0.7825,0.7878,0.7970,0.8049,0.8053,0.8055,0.8089, 0.8195,0.8195,0.8215,0.8225,0.8254,0.8272,0.8278,0.8311,0.8335,0.8362, 0.8372,0.8397,0.8417,0.8423,0.8495,0.8507,0.8511,0.8524,0.8588,0.8616, 0.8634,0.8661,0.8691,0.8758,0.8766,0.8786,0.8831,0.8928,0.8970,0.8994, 0.9024,0.9057,0.9086,0.9129,0.9138,0.9169,0.9175,0.9232,0.9243,0.9286, 0.9298,0.9325,0.9362,0.9415,0.9428,0.9445,0.9499,0.9531,0.9543,0.9609, 0.9621,0.9658,0.9695,0.9708,0.9733,0.9785,0.9838,0.9881,0.9946, Overall p-value after applying KStest on 269 p-values = 0.755651 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.