RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-07-23_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 22.2679 0.825365 2 to 25 15.85 29.2071 0.967337 3 to 26 15.81 24.5740 0.895341 4 to 27 15.65 22.0836 0.818473 5 to 28 15.70 29.6092 0.970695 6 to 29 15.66 18.2067 0.624086 7 to 30 15.98 11.1732 0.152579 8 to 31 15.82 21.1544 0.780541 9 to 32 15.86 10.5177 0.119489 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.041038 Tough bday spacings test for dh-ranFile-2015-07-23_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 12 30 67 97 107 85 39 40 16 7 0 (O-E)^2/E 0.9 1.2 0.5 0.0 0.9 0.6 3.3 3.5 0.1 0.0 4.1 Birthday Spacings: Sum(O-E)^2/E= 15.092, p= 0.871 RESULTS OF GCD FOR dh-ranFile-2015-07-23_23:31 Euclid's algorithm: p-value, steps to gcd: 0.992046 p-value, dist. of gcd's: 0.436083 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-07-23_23:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.247 0.368 0.362 0.716 0.922 0.731 0.514 0.666 Bits 8 to 15---> 0.269 0.468 0.974 0.350 0.179 0.962 0.696 0.329 Bits 16 to 23---> 0.676 0.973 0.920 0.939 0.166 0.217 0.084 0.565 Bits 24 to 31---> 0.136 0.119 0.287 0.261 0.958 0.442 0.266 0.008 KS test for the above 32 p values: 0.522 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-07-23_23:31, p-values for 5 runs: 0.7397, 0.3076, 0.5497, 0.5877, 0.5255 Rank test for binary matrices (31x31) for dh-ranFile-2015-07-23_23:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 223 211.4 0.634 0.634 r= 29 5212 5134.0 1.185 1.819 r= 30 23014 23103.0 0.343 2.162 r= 31 11551 11551.5 0.000 2.162 chi-square = 2.162 with df = 3; p-value = 0.461 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-07-23_23:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 203 211.4 0.335 0.335 r= 30 5107 5134.0 0.142 0.477 r= 31 23074 23103.0 0.037 0.514 r= 32 11616 11551.5 0.360 0.874 chi-square = 0.874 with df = 3; p-value = 0.168 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-07-23_23:31 b-rank test for bits 1 to 8, p=0.29670 b-rank test for bits 2 to 9, p=0.18029 b-rank test for bits 3 to 10, p=0.17717 b-rank test for bits 4 to 11, p=0.75771 b-rank test for bits 5 to 12, p=0.00890 b-rank test for bits 6 to 13, p=0.43593 b-rank test for bits 7 to 14, p=0.70123 b-rank test for bits 8 to 15, p=0.99232 b-rank test for bits 9 to 16, p=0.84539 b-rank test for bits 10 to 17, p=0.49876 b-rank test for bits 11 to 18, p=0.59919 b-rank test for bits 12 to 19, p=0.22436 b-rank test for bits 13 to 20, p=0.01635 b-rank test for bits 14 to 21, p=0.61866 b-rank test for bits 15 to 22, p=0.32345 b-rank test for bits 16 to 23, p=0.37237 b-rank test for bits 17 to 24, p=0.72039 b-rank test for bits 18 to 25, p=0.40167 b-rank test for bits 19 to 26, p=0.23117 b-rank test for bits 20 to 27, p=0.34819 b-rank test for bits 21 to 28, p=0.71958 b-rank test for bits 22 to 29, p=0.68846 b-rank test for bits 23 to 30, p=0.06992 b-rank test for bits 24 to 31, p=0.63130 b-rank test for bits 25 to 32, p=0.85275 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 = 0.785395 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-07-23_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 141700 -0.49 0.312389 2 141941 0.07 0.529493 3 141783 -0.30 0.383935 4 141493 -0.97 0.165343 5 141778 -0.31 0.379480 6 142161 0.59 0.721739 7 142410 1.17 0.878957 8 141220 -1.61 0.053635 9 141355 -1.30 0.097632 10 141900 -0.02 0.491304 11 142601 1.62 0.946958 12 141466 -1.04 0.150144 13 141335 -1.34 0.089815 14 141769 -0.33 0.371504 15 142538 1.47 0.929064 16 142559 1.52 0.935483 17 141582 -0.76 0.222198 18 142208 0.70 0.757357 19 141773 -0.32 0.375042 20 141498 -0.96 0.168263 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-07-23_23:31 Bits used No. missing words z-score p-value 23 to 32 141849 -0.2080 0.417601 22 to 31 141648 -0.9011 0.183758 21 to 30 141993 0.2885 0.613525 20 to 29 142040 0.4506 0.673856 19 to 28 141866 -0.1494 0.440614 18 to 27 142204 1.0161 0.845210 17 to 26 142223 1.0816 0.860289 16 to 25 141706 -0.7011 0.241609 15 to 24 141934 0.0851 0.533897 14 to 23 141962 0.1816 0.572060 13 to 22 141915 0.0196 0.507800 12 to 21 141640 -0.9287 0.176516 11 to 20 141664 -0.8460 0.198786 10 to 19 141697 -0.7322 0.232032 9 to 18 141948 0.1333 0.553040 8 to 17 142142 0.8023 0.788813 7 to 16 141567 -1.1804 0.118911 6 to 15 141717 -0.6632 0.253599 5 to 14 142323 1.4264 0.923131 4 to 13 142531 2.1437 0.983971 3 to 12 141966 0.1954 0.577466 2 to 11 141137 -2.6632 0.003870 1 to 10 142022 0.3885 0.651183 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-07-23_23:31 Bits used No. missing words z-score p-value 28 to 32 141448 -1.5638 0.058929 27 to 31 141958 0.1650 0.565521 26 to 30 142017 0.3650 0.642438 25 to 29 141819 -0.3062 0.379725 24 to 28 141924 0.0497 0.519831 23 to 27 141861 -0.1638 0.434932 22 to 26 141875 -0.1164 0.453679 21 to 25 141816 -0.3164 0.375860 20 to 24 141892 -0.0587 0.476577 19 to 23 141864 -0.1537 0.438939 18 to 22 141925 0.0531 0.521181 17 to 21 142086 0.5989 0.725374 16 to 20 141780 -0.4384 0.330546 15 to 19 142166 0.8701 0.807868 14 to 18 142088 0.6057 0.727630 13 to 17 142497 1.9921 0.976820 12 to 16 142350 1.4938 0.932386 11 to 15 142393 1.6396 0.949452 10 to 14 141873 -0.1232 0.450993 9 to 13 141839 -0.2384 0.405783 8 to 12 141870 -0.1333 0.446969 7 to 11 142342 1.4667 0.928768 6 to 10 141682 -0.7706 0.220469 5 to 9 141989 0.2701 0.606446 4 to 8 142240 1.1209 0.868838 3 to 7 142058 0.5040 0.692857 2 to 6 141842 -0.2282 0.409731 1 to 5 142105 0.6633 0.746427 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-07-23_23:31 Bits used No. missing words z-score p-value 31 to 32 141361 -1.6175 0.052886 30 to 31 142067 0.4651 0.679071 29 to 30 141715 -0.5732 0.283240 28 to 29 142054 0.4268 0.665221 27 to 28 141781 -0.3786 0.352509 26 to 27 142071 0.4769 0.683284 25 to 26 142182 0.8043 0.789399 24 to 25 142426 1.5241 0.936258 23 to 24 142536 1.8486 0.967741 22 to 23 142455 1.6096 0.946262 21 to 22 141823 -0.2547 0.399493 20 to 21 141799 -0.3255 0.372418 19 to 20 142017 0.3176 0.624610 18 to 19 142124 0.6332 0.736713 17 to 18 142505 1.7571 0.960553 16 to 17 141633 -0.8151 0.207498 15 to 16 141976 0.1967 0.577956 14 to 15 142176 0.7866 0.784253 13 to 14 142600 2.0374 0.979194 12 to 13 142547 1.8810 0.970016 11 to 12 141720 -0.5585 0.288253 10 to 11 141538 -1.0954 0.136678 9 to 10 142510 1.7719 0.961793 8 to 9 142174 0.7807 0.782522 7 to 8 142002 0.2734 0.607713 6 to 7 141863 -0.1367 0.445647 5 to 6 142561 1.9223 0.972718 4 to 5 141847 -0.1839 0.427060 3 to 4 141365 -1.6057 0.054171 2 to 3 141838 -0.2104 0.416673 1 to 2 142077 0.4946 0.689559 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-07-23_23:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2493.55 -0.091 0.463636 Test results for specific bytes for dh-ranFile-2015-07-23_23:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2666.15 2.350 0.990605 2 to 9 2485.06 -0.211 0.416353 3 to 10 2564.34 0.910 0.818569 4 to 11 2409.83 -1.275 0.101119 5 to 12 2503.94 0.056 0.522236 6 to 13 2572.54 1.026 0.847537 7 to 14 2468.35 -0.448 0.327246 8 to 15 2473.82 -0.370 0.355575 9 to 16 2555.27 0.782 0.782798 10 to 17 2458.03 -0.594 0.276423 11 to 18 2499.74 -0.004 0.498512 12 to 19 2475.67 -0.344 0.365410 13 to 20 2564.41 0.911 0.818830 14 to 21 2418.96 -1.146 0.125896 15 to 22 2453.40 -0.659 0.254960 16 to 23 2508.09 0.114 0.545541 17 to 24 2527.16 0.384 0.649532 18 to 25 2407.01 -1.315 0.094251 19 to 26 2397.74 -1.446 0.074055 20 to 27 2535.90 0.508 0.694191 21 to 28 2515.11 0.214 0.584590 22 to 29 2609.37 1.547 0.939028 23 to 30 2474.90 -0.355 0.361328 24 to 31 2525.37 0.359 0.640147 25 to 32 2532.85 0.465 0.678894 CDPARK for dh-ranFile-2015-07-23_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 3513 -0.4566 0.323972 3538 0.6849 0.753306 3477 -2.1005 0.017844 3508 -0.6849 0.246694 3505 -0.8219 0.205562 3518 -0.2283 0.409702 3506 -0.7763 0.218799 3578 2.5114 0.993988 3529 0.2740 0.607947 3561 1.7352 0.958644 Square side=100, avg. no. parked=3523.30 sample std.=27.94 p-value of the KSTEST for those 10 p-values: 0.593712 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-07-23_23:31 0.4826,0.3577,0.2187,0.7215,0.6447,0.5806,0.9308,0.6801,0.9295,0.8987, The KS test for those 10 p-values: 0.182341 The 3DSPHERES test for dh-ranFile-2015-07-23_23:31 sample no r^3 equiv. uni. 1 12.499 0.340737 2 3.871 0.121044 3 39.608 0.732936 4 3.383 0.106638 5 39.082 0.728211 6 17.186 0.436096 7 24.178 0.553325 8 49.445 0.807596 9 0.014 0.000470 10 26.619 0.588232 11 82.864 0.936843 12 44.438 0.772648 13 2.195 0.070559 14 53.014 0.829177 15 4.096 0.127609 16 19.601 0.479709 17 16.026 0.413862 18 26.848 0.591370 19 59.544 0.862591 20 2.765 0.088038 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.639966 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-07-23_23:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 2.6 0.6 -1.1 1.5 -0.8 -0.1 -1.6 1.0 1.2 -0.8 0.2 0.3 0.7 0.3 -0.1 0.5 -2.3 0.1 0.5 0.9 -0.9 0.6 0.6 -1.7 1.2 -0.7 -0.8 0.4 -0.4 0.8 -0.4 0.4 0.4 -1.2 0.6 -2.1 -0.4 3.8 -0.7 1.6 0.0 0.8 Chi-square with 42 degrees of freedom:57.912504 z-score=1.736197, p-value=0.948048 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-07-23_23:31 Test no p-value 1 0.397423 2 0.014958 3 0.194996 4 0.829893 5 0.197374 6 0.893897 7 0.079167 8 0.338809 9 0.541455 10 0.273505 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.289070 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-07-23_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 66762 0.14 66508 0.38 3 25000.00 24827 1.20 25104 0.43 4 6666.67 6769 1.57 6721 0.44 5 1388.89 1379 0.07 1392 0.01 6 238.10 228 0.43 236 0.02 7 34.72 31 0.40 34 0.01 8 4.96 3 0.77 4 0.19 p=0.40074 p=0.03913 Number of rngs required: 688653, p-value: 0.613 RESULTS OF CRAPS TEST for dh-ranFile-2015-07-23_23:31 No. of wins: Observed Expected 98594 98585.9 z-score= 0.036, pvalue=0.51452 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66657 66666.7 0.001 0.001 2 37462 37654.3 0.982 0.984 3 26883 26954.7 0.191 1.175 4 19335 19313.5 0.024 1.199 5 13808 13851.4 0.136 1.335 6 10033 9943.5 0.805 2.140 7 7275 7145.0 2.364 4.504 8 5113 5139.1 0.132 4.636 9 3645 3699.9 0.814 5.450 10 2715 2666.3 0.890 6.339 11 1953 1923.3 0.458 6.797 12 1424 1388.7 0.895 7.692 13 1012 1003.7 0.068 7.761 14 731 726.1 0.033 7.793 15 502 525.8 1.080 8.874 16 404 381.2 1.370 10.243 17 274 276.5 0.023 10.267 18 217 200.8 1.302 11.569 19 153 146.0 0.337 11.906 20 118 106.2 1.308 13.213 21 286 287.1 0.004 13.218 Chisq= 13.22 for 20 degrees of freedom, p= 0.13215 SUMMARY of craptest p-value for no. of wins: 0.514524 p-value for throws/game: 0.132152 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-07-23_23:31 No. of wins: Observed Expected 98453 98585.9 z-score=-0.594, pvalue=0.27618 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66377 66666.7 1.259 1.259 2 37878 37654.3 1.329 2.587 3 26977 26954.7 0.018 2.606 4 19650 19313.5 5.864 8.470 5 13848 13851.4 0.001 8.471 6 10021 9943.5 0.603 9.074 7 7006 7145.0 2.705 11.779 8 5058 5139.1 1.279 13.058 9 3652 3699.9 0.619 13.677 10 2600 2666.3 1.648 15.326 11 1930 1923.3 0.023 15.349 12 1347 1388.7 1.255 16.604 13 974 1003.7 0.880 17.483 14 719 726.1 0.070 17.554 15 521 525.8 0.044 17.598 16 406 381.2 1.620 19.218 17 269 276.5 0.206 19.424 18 181 200.8 1.958 21.382 19 144 146.0 0.027 21.409 20 110 106.2 0.135 21.543 21 332 287.1 7.017 28.561 Chisq= 28.56 for 20 degrees of freedom, p= 0.90322 SUMMARY of craptest p-value for no. of wins: 0.276182 p-value for throws/game: 0.903224 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0005,0.0039,0.0084,0.0089,0.0150,0.0164,0.0178,0.0391,0.0410,0.0529, 0.0536,0.0542,0.0589,0.0699,0.0706,0.0741,0.0792,0.0835,0.0880,0.0898, 0.0943,0.0976,0.1011,0.1066,0.1186,0.1189,0.1195,0.1210,0.1259,0.1276, 0.1322,0.1365,0.1367,0.1501,0.1526,0.1653,0.1664,0.1682,0.1683,0.1765, 0.1772,0.1795,0.1803,0.1823,0.1838,0.1950,0.1974,0.1988,0.2056,0.2075, 0.2172,0.2187,0.2188,0.2205,0.2222,0.2244,0.2312,0.2320,0.2416,0.2467, 0.2472,0.2536,0.2550,0.2609,0.2658,0.2693,0.2735,0.2762,0.2764,0.2832, 0.2870,0.2883,0.2891,0.2967,0.3076,0.3124,0.3234,0.3240,0.3272,0.3288, 0.3305,0.3388,0.3407,0.3482,0.3498,0.3525,0.3556,0.3577,0.3613,0.3619, 0.3654,0.3683,0.3715,0.3724,0.3724,0.3750,0.3759,0.3795,0.3797,0.3839, 0.3974,0.3995,0.4007,0.4017,0.4058,0.4097,0.4097,0.4139,0.4164,0.4167, 0.4176,0.4271,0.4349,0.4359,0.4361,0.4361,0.4389,0.4406,0.4421,0.4456, 0.4470,0.4510,0.4537,0.4606,0.4636,0.4676,0.4766,0.4797,0.4826,0.4913, 0.4985,0.4988,0.5078,0.5139,0.5145,0.5198,0.5212,0.5217,0.5222,0.5255, 0.5295,0.5339,0.5415,0.5455,0.5497,0.5530,0.5533,0.5651,0.5655,0.5721, 0.5775,0.5780,0.5806,0.5846,0.5877,0.5882,0.5914,0.5937,0.5992,0.6064, 0.6077,0.6079,0.6132,0.6135,0.6187,0.6241,0.6246,0.6313,0.6400,0.6401, 0.6424,0.6447,0.6495,0.6512,0.6652,0.6658,0.6739,0.6756,0.6789,0.6791, 0.6801,0.6833,0.6885,0.6896,0.6929,0.6942,0.6962,0.7012,0.7157,0.7196, 0.7204,0.7215,0.7217,0.7254,0.7276,0.7282,0.7312,0.7329,0.7367,0.7397, 0.7464,0.7533,0.7574,0.7577,0.7726,0.7805,0.7825,0.7828,0.7843,0.7854, 0.7888,0.7894,0.8076,0.8079,0.8185,0.8186,0.8188,0.8254,0.8292,0.8299, 0.8452,0.8454,0.8475,0.8528,0.8603,0.8626,0.8688,0.8713,0.8790,0.8939, 0.8953,0.8987,0.9032,0.9203,0.9216,0.9231,0.9288,0.9291,0.9295,0.9308, 0.9324,0.9355,0.9363,0.9368,0.9387,0.9390,0.9463,0.9470,0.9480,0.9495, 0.9578,0.9586,0.9606,0.9618,0.9623,0.9673,0.9677,0.9700,0.9707,0.9727, 0.9730,0.9738,0.9768,0.9792,0.9840,0.9906,0.9920,0.9923,0.9940, Overall p-value after applying KStest on 269 p-values = 0.367446 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.