RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-06-09_09:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.84 15.9531 0.472839 2 to 25 15.69 15.9535 0.472863 3 to 26 15.73 16.3091 0.497961 4 to 27 15.76 18.6713 0.652281 5 to 28 15.84 24.0964 0.883160 6 to 29 15.89 16.2870 0.496410 7 to 30 15.85 7.9661 0.032735 8 to 31 15.78 14.9536 0.401175 9 to 32 15.44 30.4962 0.977019 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.582339 Tough bday spacings test for dh-ranFile-2015-06-09_09:31: 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 8 46 82 98 98 54 54 32 17 7 4 (O-E)^2/E 0.1 2.4 1.0 0.0 0.0 7.5 0.1 0.2 0.3 0.0 0.0 Birthday Spacings: Sum(O-E)^2/E= 11.608, p= 0.688 RESULTS OF GCD FOR dh-ranFile-2015-06-09_09:31 Euclid's algorithm: p-value, steps to gcd: 0.715309 p-value, dist. of gcd's: 0.283471 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-06-09_09:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.779 0.935 0.226 0.604 0.325 0.986 0.472 0.771 Bits 8 to 15---> 0.929 0.989 0.846 0.535 0.921 0.689 0.434 0.107 Bits 16 to 23---> 0.099 0.657 0.852 0.514 0.082 0.251 0.430 0.469 Bits 24 to 31---> 0.256 0.299 0.465 0.285 0.325 0.364 0.618 0.764 KS test for the above 32 p values: 0.406 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-06-09_09:31, p-values for 5 runs: 0.4740, 0.4007, 0.0139, 0.2411, 0.7452 Rank test for binary matrices (31x31) for dh-ranFile-2015-06-09_09:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 186 211.4 3.056 3.056 r= 29 5180 5134.0 0.412 3.468 r= 30 23069 23103.0 0.050 3.518 r= 31 11565 11551.5 0.016 3.534 chi-square = 3.534 with df = 3; p-value = 0.684 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-06-09_09:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 196 211.4 1.124 1.124 r= 30 5007 5134.0 3.142 4.267 r= 31 23221 23103.0 0.602 4.869 r= 32 11576 11551.5 0.052 4.921 chi-square = 4.921 with df = 3; p-value = 0.822 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-06-09_09:31 b-rank test for bits 1 to 8, p=0.45058 b-rank test for bits 2 to 9, p=0.75714 b-rank test for bits 3 to 10, p=0.78813 b-rank test for bits 4 to 11, p=0.54551 b-rank test for bits 5 to 12, p=0.60852 b-rank test for bits 6 to 13, p=0.00650 b-rank test for bits 7 to 14, p=0.27525 b-rank test for bits 8 to 15, p=0.00301 b-rank test for bits 9 to 16, p=0.17255 b-rank test for bits 10 to 17, p=0.47167 b-rank test for bits 11 to 18, p=0.38131 b-rank test for bits 12 to 19, p=0.33278 b-rank test for bits 13 to 20, p=0.26307 b-rank test for bits 14 to 21, p=0.60591 b-rank test for bits 15 to 22, p=0.04291 b-rank test for bits 16 to 23, p=0.07823 b-rank test for bits 17 to 24, p=0.89408 b-rank test for bits 18 to 25, p=0.54883 b-rank test for bits 19 to 26, p=0.35596 b-rank test for bits 20 to 27, p=0.40814 b-rank test for bits 21 to 28, p=0.90946 b-rank test for bits 22 to 29, p=0.35490 b-rank test for bits 23 to 30, p=0.36293 b-rank test for bits 24 to 31, p=0.84294 b-rank test for bits 25 to 32, p=0.50340 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 = 0.295116 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-06-09_09:31 (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 142489 1.35 0.912191 2 141934 0.06 0.522982 3 141706 -0.48 0.317369 4 141902 -0.02 0.493168 5 142889 2.29 0.988959 6 142398 1.14 0.873222 7 141806 -0.24 0.404613 8 142225 0.74 0.769605 9 142541 1.48 0.930010 10 141757 -0.36 0.360954 11 142414 1.18 0.880828 12 141626 -0.66 0.253990 13 141437 -1.10 0.134889 14 141315 -1.39 0.082474 15 141862 -0.11 0.455973 16 141231 -1.58 0.056496 17 141593 -0.74 0.229927 18 141799 -0.26 0.398288 19 141864 -0.11 0.457826 20 142002 0.22 0.585708 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-06-09_09:31 Bits used No. missing words z-score p-value 23 to 32 141841 -0.2356 0.406864 22 to 31 142091 0.6264 0.734490 21 to 30 142430 1.7954 0.963706 20 to 29 142350 1.5196 0.935688 19 to 28 141801 -0.3736 0.354369 18 to 27 141364 -1.8804 0.030024 17 to 26 141436 -1.6322 0.051322 16 to 25 141907 -0.0080 0.496795 15 to 24 142162 0.8713 0.808198 14 to 23 142043 0.4609 0.677576 13 to 22 141774 -0.4667 0.320373 12 to 21 141986 0.2644 0.604256 11 to 20 142104 0.6713 0.748978 10 to 19 141783 -0.4356 0.331556 9 to 18 141367 -1.8701 0.030735 8 to 17 142187 0.9575 0.830838 7 to 16 141833 -0.2632 0.396196 6 to 15 142273 1.2540 0.895085 5 to 14 142057 0.5092 0.694696 4 to 13 141923 0.0471 0.518798 3 to 12 141721 -0.6494 0.258036 2 to 11 141790 -0.4115 0.340359 1 to 10 142044 0.4644 0.678812 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-06-09_09:31 Bits used No. missing words z-score p-value 28 to 32 142041 0.4463 0.672324 27 to 31 141610 -1.0147 0.155130 26 to 30 141516 -1.3333 0.091213 25 to 29 142086 0.5989 0.725374 24 to 28 141987 0.2633 0.603836 23 to 27 141800 -0.3706 0.355464 22 to 26 141912 0.0091 0.503611 21 to 25 141535 -1.2689 0.102236 20 to 24 142166 0.8701 0.807868 19 to 23 141562 -1.1774 0.119520 18 to 22 142097 0.6362 0.737667 17 to 21 141839 -0.2384 0.405783 16 to 20 142280 1.2565 0.895534 15 to 19 142017 0.3650 0.642438 14 to 18 142505 2.0192 0.978268 13 to 17 141503 -1.3774 0.084196 12 to 16 142452 1.8396 0.967084 11 to 15 142142 0.7887 0.784860 10 to 14 142066 0.5311 0.702320 9 to 13 141994 0.2870 0.612950 8 to 12 142145 0.7989 0.787820 7 to 11 141457 -1.5333 0.062598 6 to 10 142022 0.3819 0.648744 5 to 9 141454 -1.5435 0.061356 4 to 8 142531 2.1074 0.982457 3 to 7 142065 0.5277 0.701145 2 to 6 142144 0.7955 0.786836 1 to 5 142053 0.4870 0.686877 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-06-09_09:31 Bits used No. missing words z-score p-value 31 to 32 141481 -1.2635 0.103203 30 to 31 141916 0.0197 0.507849 29 to 30 142083 0.5123 0.695780 28 to 29 141664 -0.7237 0.234629 27 to 28 141903 -0.0187 0.492551 26 to 27 141380 -1.5614 0.059209 25 to 26 142188 0.8220 0.794472 24 to 25 142592 2.0138 0.977983 23 to 24 141218 -2.0393 0.020709 22 to 23 141691 -0.6440 0.259774 21 to 22 141512 -1.1721 0.120586 20 to 21 141905 -0.0128 0.494905 19 to 20 141859 -0.1485 0.440988 18 to 19 141579 -0.9744 0.164923 17 to 18 142176 0.7866 0.784253 16 to 17 142203 0.8663 0.806833 15 to 16 141312 -1.7620 0.039032 14 to 15 141607 -0.8918 0.186242 13 to 14 141319 -1.7414 0.040808 12 to 13 141479 -1.2694 0.102147 11 to 12 142256 1.0226 0.846758 10 to 11 142055 0.4297 0.666295 9 to 10 142018 0.3206 0.625728 8 to 9 142388 1.4120 0.921026 7 to 8 141919 0.0285 0.511378 6 to 7 141663 -0.7266 0.233724 5 to 6 141543 -1.0806 0.139933 4 to 5 142574 1.9607 0.975042 3 to 4 141808 -0.2989 0.382505 2 to 3 141571 -0.9980 0.159134 1 to 2 142097 0.5536 0.710073 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-06-09_09:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2518.10 0.256 0.601022 Test results for specific bytes for dh-ranFile-2015-06-09_09:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2498.56 -0.020 0.491851 2 to 9 2297.23 -2.868 0.002068 3 to 10 2482.68 -0.245 0.403245 4 to 11 2473.42 -0.376 0.353506 5 to 12 2530.01 0.424 0.664381 6 to 13 2488.85 -0.158 0.437336 7 to 14 2414.11 -1.215 0.112253 8 to 15 2620.44 1.703 0.955742 9 to 16 2514.65 0.207 0.582065 10 to 17 2621.50 1.718 0.957121 11 to 18 2424.27 -1.071 0.142078 12 to 19 2503.04 0.043 0.517157 13 to 20 2542.36 0.599 0.725412 14 to 21 2406.00 -1.329 0.091875 15 to 22 2526.02 0.368 0.643553 16 to 23 2469.25 -0.435 0.331837 17 to 24 2358.49 -2.001 0.022683 18 to 25 2467.39 -0.461 0.322332 19 to 26 2532.72 0.463 0.678242 20 to 27 2581.96 1.159 0.876799 21 to 28 2510.91 0.154 0.561331 22 to 29 2507.85 0.111 0.544189 23 to 30 2498.42 -0.022 0.491081 24 to 31 2496.50 -0.050 0.480235 25 to 32 2458.94 -0.581 0.280708 CDPARK for dh-ranFile-2015-06-09_09:31: 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 3498 -1.1416 0.126820 3537 0.6393 0.738676 3562 1.7808 0.962529 3500 -1.0502 0.146807 3494 -1.3242 0.092718 3528 0.2283 0.590298 3489 -1.5525 0.060270 3520 -0.1370 0.445521 3546 1.0502 0.853193 3501 -1.0046 0.157553 Square side=100, avg. no. parked=3517.50 sample std.=23.69 p-value of the KSTEST for those 10 p-values: 0.348466 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-06-09_09:31 0.2249,0.8954,0.1282,0.6196,0.1384,0.2443,0.5928,0.2808,0.6131,0.0143, The KS test for those 10 p-values: 0.261324 The 3DSPHERES test for dh-ranFile-2015-06-09_09:31 sample no r^3 equiv. uni. 1 66.615 0.891447 2 24.133 0.552653 3 11.242 0.312529 4 1.810 0.058554 5 1.965 0.063390 6 47.583 0.795280 7 6.024 0.181915 8 3.684 0.115554 9 27.397 0.598773 10 9.598 0.273808 11 62.446 0.875259 12 10.445 0.294020 13 28.511 0.613400 14 4.009 0.125088 15 29.784 0.629462 16 135.190 0.988961 17 5.739 0.174117 18 33.658 0.674346 19 45.090 0.777536 20 81.339 0.933551 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.878522 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-06-09_09:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 -1.6 -0.1 0.3 -0.6 -1.4 0.2 1.6 -0.6 -0.3 -1.3 -0.9 0.7 -1.0 0.0 1.1 1.1 0.1 -0.4 -0.7 -0.4 0.4 0.5 -0.0 0.8 0.1 -0.1 -0.2 1.0 -1.0 -0.5 -1.3 0.8 1.0 -0.6 -0.5 -0.2 0.2 -1.2 1.5 2.4 0.0 -1.1 Chi-square with 42 degrees of freedom:35.314241 z-score=-0.729476, p-value=0.242464 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-06-09_09:31 Test no p-value 1 0.130514 2 0.051143 3 0.102258 4 0.926264 5 0.459307 6 0.876765 7 0.981255 8 0.100591 9 0.267655 10 0.523501 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.325270 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-06-09_09:31: (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 66660 0.00 66732 0.06 3 25000.00 24995 0.00 25005 0.00 4 6666.67 6674 0.01 6625 0.26 5 1388.89 1423 0.84 1346 1.32 6 238.10 214 2.44 247 0.33 7 34.72 28 1.30 34 0.01 8 4.96 5 0.00 10 5.12 p=0.40222 p=0.69004 Number of rngs required: 687897, p-value: 0.280 RESULTS OF CRAPS TEST for dh-ranFile-2015-06-09_09:31 No. of wins: Observed Expected 98464 98585.9 z-score=-0.545, pvalue=0.29287 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66446 66666.7 0.730 0.730 2 37843 37654.3 0.945 1.676 3 26751 26954.7 1.540 3.216 4 19472 19313.5 1.301 4.517 5 13923 13851.4 0.370 4.887 6 9915 9943.5 0.082 4.969 7 7127 7145.0 0.045 5.014 8 5180 5139.1 0.326 5.340 9 3699 3699.9 0.000 5.341 10 2692 2666.3 0.248 5.588 11 1938 1923.3 0.112 5.700 12 1310 1388.7 4.465 10.165 13 1049 1003.7 2.043 12.208 14 732 726.1 0.047 12.255 15 544 525.8 0.627 12.883 16 352 381.2 2.229 15.112 17 295 276.5 1.232 16.344 18 214 200.8 0.864 17.208 19 147 146.0 0.007 17.215 20 99 106.2 0.490 17.705 21 272 287.1 0.796 18.501 Chisq= 18.50 for 20 degrees of freedom, p= 0.44555 SUMMARY of craptest p-value for no. of wins: 0.292869 p-value for throws/game: 0.445552 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-06-09_09:31 No. of wins: Observed Expected 98228 98585.9 z-score=-1.601, pvalue=0.05474 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66636 66666.7 0.014 0.014 2 37421 37654.3 1.446 1.460 3 27237 26954.7 2.956 4.416 4 19257 19313.5 0.165 4.581 5 13839 13851.4 0.011 4.592 6 9836 9943.5 1.163 5.755 7 7123 7145.0 0.068 5.823 8 5273 5139.1 3.490 9.313 9 3616 3699.9 1.901 11.214 10 2746 2666.3 2.383 13.597 11 1974 1923.3 1.335 14.932 12 1417 1388.7 0.575 15.507 13 999 1003.7 0.022 15.529 14 734 726.1 0.085 15.614 15 513 525.8 0.313 15.927 16 364 381.2 0.772 16.699 17 273 276.5 0.045 16.744 18 203 200.8 0.023 16.768 19 141 146.0 0.170 16.938 20 102 106.2 0.167 17.105 21 296 287.1 0.275 17.380 Chisq= 17.38 for 20 degrees of freedom, p= 0.37183 SUMMARY of craptest p-value for no. of wins: 0.054738 p-value for throws/game: 0.371835 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0021,0.0030,0.0065,0.0139,0.0143,0.0207,0.0227,0.0300,0.0307,0.0327, 0.0390,0.0408,0.0429,0.0511,0.0513,0.0547,0.0565,0.0586,0.0592,0.0603, 0.0614,0.0626,0.0634,0.0782,0.0821,0.0825,0.0842,0.0912,0.0919,0.0927, 0.0994,0.1006,0.1021,0.1022,0.1023,0.1032,0.1068,0.1123,0.1156,0.1195, 0.1206,0.1251,0.1268,0.1282,0.1305,0.1349,0.1384,0.1399,0.1421,0.1468, 0.1551,0.1576,0.1591,0.1649,0.1726,0.1741,0.1819,0.1862,0.2249,0.2255, 0.2299,0.2337,0.2346,0.2411,0.2425,0.2443,0.2514,0.2540,0.2556,0.2580, 0.2598,0.2613,0.2631,0.2677,0.2738,0.2752,0.2798,0.2807,0.2808,0.2835, 0.2847,0.2929,0.2940,0.2951,0.2994,0.3125,0.3174,0.3204,0.3223,0.3245, 0.3253,0.3253,0.3316,0.3318,0.3328,0.3404,0.3485,0.3535,0.3544,0.3549, 0.3555,0.3560,0.3610,0.3629,0.3638,0.3718,0.3813,0.3825,0.3962,0.3983, 0.4007,0.4012,0.4022,0.4032,0.4046,0.4058,0.4060,0.4069,0.4081,0.4298, 0.4335,0.4373,0.4410,0.4455,0.4456,0.4506,0.4560,0.4578,0.4593,0.4655, 0.4691,0.4717,0.4720,0.4728,0.4729,0.4740,0.4802,0.4911,0.4919,0.4926, 0.4932,0.4949,0.4964,0.4968,0.4980,0.5034,0.5036,0.5078,0.5114,0.5136, 0.5172,0.5188,0.5230,0.5235,0.5351,0.5442,0.5455,0.5488,0.5527,0.5613, 0.5821,0.5823,0.5857,0.5903,0.5928,0.5988,0.6010,0.6038,0.6039,0.6043, 0.6059,0.6085,0.6130,0.6131,0.6134,0.6181,0.6196,0.6257,0.6295,0.6424, 0.6436,0.6487,0.6523,0.6572,0.6644,0.6663,0.6723,0.6743,0.6776,0.6782, 0.6788,0.6836,0.6869,0.6879,0.6886,0.6900,0.6947,0.6958,0.7011,0.7023, 0.7101,0.7153,0.7254,0.7254,0.7345,0.7377,0.7387,0.7452,0.7490,0.7571, 0.7642,0.7696,0.7712,0.7775,0.7794,0.7843,0.7849,0.7868,0.7878,0.7881, 0.7945,0.7953,0.8068,0.8079,0.8082,0.8223,0.8308,0.8429,0.8456,0.8468, 0.8525,0.8532,0.8732,0.8753,0.8768,0.8768,0.8785,0.8808,0.8832,0.8914, 0.8941,0.8951,0.8954,0.8955,0.9095,0.9122,0.9210,0.9211,0.9263,0.9290, 0.9300,0.9336,0.9352,0.9357,0.9557,0.9571,0.9625,0.9637,0.9671,0.9750, 0.9770,0.9780,0.9783,0.9813,0.9825,0.9859,0.9890,0.9890,0.9891, Overall p-value after applying KStest on 269 p-values = 0.542120 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.