RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-01-15_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 15.85 11.8097 0.188480 2 to 25 15.48 19.8586 0.718474 3 to 26 15.74 15.7375 0.457488 4 to 27 15.69 10.8034 0.133402 5 to 28 15.44 23.0052 0.850919 6 to 29 15.66 7.2807 0.020385 7 to 30 15.68 10.3537 0.111874 8 to 31 15.31 31.8462 0.984276 9 to 32 15.62 15.4326 0.435647 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.567657 Tough bday spacings test for dh-ranFile-2017-01-15_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 2 37 69 108 97 85 54 27 16 2 3 (O-E)^2/E 5.6 0.0 0.2 1.1 0.0 0.6 0.1 0.3 0.1 3.2 0.3 Birthday Spacings: Sum(O-E)^2/E= 11.452, p= 0.677 RESULTS OF GCD FOR dh-ranFile-2017-01-15_01:31 Euclid's algorithm: p-value, steps to gcd: 0.044011 p-value, dist. of gcd's: 0.539882 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-01-15_01:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.090 0.916 0.212 0.745 0.870 0.906 0.014 0.356 Bits 8 to 15---> 0.314 0.066 0.450 0.838 0.993 0.385 0.303 0.876 Bits 16 to 23---> 0.378 0.404 0.965 0.943 0.994 0.847 0.757 0.840 Bits 24 to 31---> 0.974 0.424 0.436 0.925 0.680 0.036 0.318 0.372 KS test for the above 32 p values: 0.958 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-01-15_01:31, p-values for 5 runs: 0.4700, 0.0730, 0.0081, 0.7700, 0.8431 Rank test for binary matrices (31x31) for dh-ranFile-2017-01-15_01:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 214 211.4 0.032 0.032 r= 29 5171 5134.0 0.267 0.298 r= 30 23003 23103.0 0.433 0.731 r= 31 11612 11551.5 0.317 1.048 chi-square = 1.048 with df = 3; p-value = 0.210 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2017-01-15_01:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 206 211.4 0.139 0.139 r= 30 5204 5134.0 0.954 1.093 r= 31 23003 23103.0 0.433 1.526 r= 32 11587 11551.5 0.109 1.635 chi-square = 1.635 with df = 3; p-value = 0.349 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2017-01-15_01:31 b-rank test for bits 1 to 8, p=0.36525 b-rank test for bits 2 to 9, p=0.25564 b-rank test for bits 3 to 10, p=0.56374 b-rank test for bits 4 to 11, p=0.81604 b-rank test for bits 5 to 12, p=0.09762 b-rank test for bits 6 to 13, p=0.71823 b-rank test for bits 7 to 14, p=0.30344 b-rank test for bits 8 to 15, p=0.53796 b-rank test for bits 9 to 16, p=0.04149 b-rank test for bits 10 to 17, p=0.34074 b-rank test for bits 11 to 18, p=0.74048 b-rank test for bits 12 to 19, p=0.09843 b-rank test for bits 13 to 20, p=0.79327 b-rank test for bits 14 to 21, p=0.30138 b-rank test for bits 15 to 22, p=0.38125 b-rank test for bits 16 to 23, p=0.93448 b-rank test for bits 17 to 24, p=0.23993 b-rank test for bits 18 to 25, p=0.86623 b-rank test for bits 19 to 26, p=0.51456 b-rank test for bits 20 to 27, p=0.38936 b-rank test for bits 21 to 28, p=0.25345 b-rank test for bits 22 to 29, p=0.08483 b-rank test for bits 23 to 30, p=0.92958 b-rank test for bits 24 to 31, p=0.97340 b-rank test for bits 25 to 32, p=0.95441 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 = 0.871757 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-01-15_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 141999 0.21 0.582975 2 142249 0.79 0.786292 3 141442 -1.09 0.137440 4 141901 -0.02 0.492236 5 141940 0.07 0.528563 6 142243 0.78 0.782188 7 141889 -0.05 0.481057 8 141973 0.15 0.559129 9 141408 -1.17 0.120733 10 142259 0.82 0.793032 11 141394 -1.20 0.114287 12 141729 -0.42 0.336756 13 142081 0.40 0.655826 14 142754 1.97 0.975782 15 141885 -0.06 0.477334 16 141669 -0.56 0.287222 17 141864 -0.11 0.457826 18 141606 -0.71 0.239251 19 142195 0.67 0.747759 20 142136 0.53 0.701806 ---------------------------------------------------------------- OPSO test for dh-ranFile-2017-01-15_01:31 Bits used No. missing words z-score p-value 23 to 32 142198 0.9954 0.840233 22 to 31 141386 -1.8046 0.035570 21 to 30 142241 1.1437 0.873624 20 to 29 141597 -1.0770 0.140740 19 to 28 142269 1.2402 0.892557 18 to 27 141911 0.0058 0.502297 17 to 26 142222 1.0782 0.859522 16 to 25 142017 0.3713 0.644784 15 to 24 141862 -0.1632 0.435178 14 to 23 141835 -0.2563 0.398856 13 to 22 141858 -0.1770 0.429754 12 to 21 142100 0.6575 0.744565 11 to 20 141907 -0.0080 0.496795 10 to 19 141605 -1.0494 0.146994 9 to 18 142005 0.3299 0.629261 8 to 17 141473 -1.5046 0.066215 7 to 16 141805 -0.3598 0.359514 6 to 15 141928 0.0644 0.525666 5 to 14 141586 -1.1149 0.132440 4 to 13 141562 -1.1977 0.115519 3 to 12 141810 -0.3425 0.365981 2 to 11 141858 -0.1770 0.429754 1 to 10 141866 -0.1494 0.440614 ----------------------------------------------------------------- OQSO test for dh-ranFile-2017-01-15_01:31 Bits used No. missing words z-score p-value 28 to 32 142572 2.2463 0.987659 27 to 31 141778 -0.4452 0.328093 26 to 30 141825 -0.2859 0.387491 25 to 29 142036 0.4294 0.666180 24 to 28 142037 0.4328 0.667413 23 to 27 141865 -0.1503 0.440275 22 to 26 141746 -0.5537 0.289905 21 to 25 141895 -0.0486 0.480629 20 to 24 141775 -0.4554 0.324427 19 to 23 141765 -0.4893 0.312331 18 to 22 142292 1.2972 0.902717 17 to 21 141772 -0.4655 0.320778 16 to 20 141854 -0.1876 0.425611 15 to 19 141495 -1.4045 0.080084 14 to 18 142134 0.7616 0.776849 13 to 17 141991 0.2768 0.609051 12 to 16 142119 0.7107 0.761379 11 to 15 141877 -0.1096 0.456366 10 to 14 141851 -0.1977 0.421629 9 to 13 141512 -1.3469 0.089009 8 to 12 142310 1.3582 0.912800 7 to 11 141781 -0.4350 0.331775 6 to 10 142118 0.7074 0.760327 5 to 9 142355 1.5107 0.934573 4 to 8 141702 -0.7028 0.241086 3 to 7 141443 -1.5808 0.056964 2 to 6 141694 -0.7299 0.232716 1 to 5 141696 -0.7232 0.234793 ----------------------------------------------------------------- DNA test for dh-ranFile-2017-01-15_01:31 Bits used No. missing words z-score p-value 31 to 32 142500 1.7424 0.959280 30 to 31 141490 -1.2370 0.108051 29 to 30 141406 -1.4847 0.068805 28 to 29 141796 -0.3343 0.369074 27 to 28 141272 -1.8800 0.030052 26 to 27 142217 0.9076 0.817950 25 to 26 141381 -1.5585 0.059558 24 to 25 141646 -0.7768 0.218643 23 to 24 142079 0.5005 0.691639 22 to 23 141686 -0.6588 0.255015 21 to 22 141450 -1.3550 0.087716 20 to 21 141908 -0.0039 0.498435 19 to 20 141736 -0.5113 0.304571 18 to 19 141910 0.0020 0.500789 17 to 18 142071 0.4769 0.683284 16 to 17 141481 -1.2635 0.103203 15 to 16 141822 -0.2576 0.398354 14 to 15 141296 -1.8092 0.035207 13 to 14 141617 -0.8623 0.194253 12 to 13 141700 -0.6175 0.268455 11 to 12 142073 0.4828 0.685382 10 to 11 142475 1.6686 0.952406 9 to 10 141927 0.0521 0.520785 8 to 9 141816 -0.2753 0.391539 7 to 8 141640 -0.7945 0.213457 6 to 7 141808 -0.2989 0.382505 5 to 6 142429 1.5329 0.937356 4 to 5 142427 1.5271 0.936626 3 to 4 141675 -0.6912 0.244708 2 to 3 141425 -1.4287 0.076545 1 to 2 142411 1.4799 0.930544 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2017-01-15_01:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2551.98 0.735 0.768872 Test results for specific bytes for dh-ranFile-2017-01-15_01:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2481.82 -0.257 0.398539 2 to 9 2496.71 -0.047 0.481433 3 to 10 2401.66 -1.391 0.082143 4 to 11 2420.80 -1.120 0.131355 5 to 12 2470.69 -0.414 0.339277 6 to 13 2506.57 0.093 0.537039 7 to 14 2427.57 -1.024 0.152846 8 to 15 2628.67 1.820 0.965599 9 to 16 2448.88 -0.723 0.234856 10 to 17 2459.33 -0.575 0.282591 11 to 18 2547.11 0.666 0.747371 12 to 19 2500.50 0.007 0.502828 13 to 20 2540.66 0.575 0.717357 14 to 21 2370.57 -1.830 0.033592 15 to 22 2561.02 0.863 0.805911 16 to 23 2612.84 1.596 0.944738 17 to 24 2480.66 -0.273 0.392245 18 to 25 2470.41 -0.418 0.337820 19 to 26 2503.89 0.055 0.521959 20 to 27 2510.28 0.145 0.557799 21 to 28 2482.64 -0.245 0.403051 22 to 29 2375.67 -1.758 0.039344 23 to 30 2551.16 0.724 0.765320 24 to 31 2680.09 2.547 0.994564 25 to 32 2541.39 0.585 0.720847 CDPARK for dh-ranFile-2017-01-15_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 3507 -0.7306 0.232514 3530 0.3196 0.625377 3496 -1.2329 0.108811 3560 1.6895 0.954438 3559 1.6438 0.949895 3547 1.0959 0.863437 3499 -1.0959 0.136563 3514 -0.4110 0.340551 3524 0.0457 0.518210 3517 -0.2740 0.392053 Square side=100, avg. no. parked=3525.30 sample std.=22.17 p-value of the KSTEST for those 10 p-values: 0.872224 Results for the MINIMUM DISTANCE test for dh-ranFile-2017-01-15_01:31 0.3572,0.2951,0.6756,0.4680,0.0572,0.6023,0.7358,0.5594,0.3307,0.4960, The KS test for those 10 p-values: 0.449182 The 3DSPHERES test for dh-ranFile-2017-01-15_01:31 sample no r^3 equiv. uni. 1 7.835 0.229841 2 48.816 0.803520 3 22.098 0.521260 4 39.656 0.733367 5 5.542 0.168676 6 3.579 0.112444 7 46.452 0.787414 8 13.446 0.361232 9 89.020 0.948560 10 4.175 0.129924 11 30.232 0.634954 12 35.945 0.698255 13 5.530 0.168341 14 26.378 0.584915 15 8.911 0.256982 16 0.798 0.026234 17 26.759 0.590154 18 1.975 0.063725 19 1.934 0.062444 20 27.970 0.606369 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.340944 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-01-15_01:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.1 -1.1 -1.1 0.0 0.1 -0.6 -0.6 -1.4 -1.7 -1.1 -0.6 1.4 0.5 -0.1 1.6 0.5 -0.7 0.2 -0.2 -1.6 1.0 -1.4 -0.7 2.8 -1.4 0.5 2.1 0.8 1.2 -0.4 -0.5 -0.7 0.3 1.2 -0.8 -1.2 -0.4 0.1 -1.3 -0.6 -1.0 0.8 Chi-square with 42 degrees of freedom:45.793195 z-score=0.413871, p-value=0.682364 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2017-01-15_01:31 Test no p-value 1 0.614883 2 0.465790 3 0.182194 4 0.179819 5 0.715982 6 0.518055 7 0.023665 8 0.008861 9 0.589701 10 0.273867 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.142052 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-01-15_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 66896 0.79 66608 0.05 3 25000.00 24838 1.05 25043 0.07 4 6666.67 6614 0.42 6711 0.29 5 1388.89 1364 0.45 1361 0.56 6 238.10 250 0.60 243 0.10 7 34.72 34 0.01 27 1.72 8 4.96 3 0.77 6 0.22 p=0.33489 p=0.19317 Number of rngs required: 687752, p-value: 0.226 RESULTS OF CRAPS TEST for dh-ranFile-2017-01-15_01:31 No. of wins: Observed Expected 98556 98585.9 z-score=-0.134, pvalue=0.44688 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66302 66666.7 1.995 1.995 2 37841 37654.3 0.925 2.920 3 27003 26954.7 0.086 3.007 4 19333 19313.5 0.020 3.026 5 13950 13851.4 0.702 3.728 6 10023 9943.5 0.635 4.363 7 7139 7145.0 0.005 4.368 8 5107 5139.1 0.200 4.568 9 3577 3699.9 4.080 8.648 10 2665 2666.3 0.001 8.649 11 2010 1923.3 3.906 12.555 12 1420 1388.7 0.704 13.258 13 979 1003.7 0.609 13.867 14 747 726.1 0.599 14.466 15 478 525.8 4.352 18.818 16 397 381.2 0.659 19.477 17 287 276.5 0.396 19.872 18 192 200.8 0.388 20.261 19 166 146.0 2.744 23.005 20 97 106.2 0.800 23.804 21 287 287.1 0.000 23.804 Chisq= 23.80 for 20 degrees of freedom, p= 0.74896 SUMMARY of craptest p-value for no. of wins: 0.446881 p-value for throws/game: 0.748963 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2017-01-15_01:31 No. of wins: Observed Expected 98526 98585.9 z-score=-0.268, pvalue=0.39446 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66656 66666.7 0.002 0.002 2 37929 37654.3 2.004 2.005 3 26851 26954.7 0.399 2.405 4 19298 19313.5 0.012 2.417 5 13997 13851.4 1.530 3.947 6 9755 9943.5 3.575 7.522 7 7200 7145.0 0.423 7.945 8 5218 5139.1 1.212 9.157 9 3692 3699.9 0.017 9.174 10 2625 2666.3 0.640 9.814 11 1852 1923.3 2.645 12.459 12 1379 1388.7 0.068 12.527 13 937 1003.7 4.434 16.962 14 755 726.1 1.147 18.109 15 507 525.8 0.675 18.783 16 376 381.2 0.070 18.853 17 273 276.5 0.045 18.898 18 180 200.8 2.160 21.059 19 134 146.0 0.984 22.043 20 102 106.2 0.167 22.210 21 284 287.1 0.034 22.244 Chisq= 22.24 for 20 degrees of freedom, p= 0.67256 SUMMARY of craptest p-value for no. of wins: 0.394456 p-value for throws/game: 0.672563 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0081,0.0089,0.0137,0.0204,0.0237,0.0262,0.0301,0.0336,0.0352,0.0356, 0.0364,0.0393,0.0415,0.0440,0.0570,0.0572,0.0596,0.0624,0.0637,0.0658, 0.0662,0.0688,0.0730,0.0765,0.0801,0.0821,0.0848,0.0877,0.0890,0.0901, 0.0976,0.0984,0.1032,0.1081,0.1088,0.1119,0.1124,0.1143,0.1155,0.1207, 0.1299,0.1314,0.1324,0.1334,0.1366,0.1374,0.1407,0.1421,0.1470,0.1528, 0.1683,0.1687,0.1798,0.1822,0.1885,0.1932,0.1943,0.2103,0.2116,0.2135, 0.2186,0.2260,0.2298,0.2325,0.2327,0.2348,0.2349,0.2393,0.2399,0.2411, 0.2447,0.2535,0.2550,0.2556,0.2570,0.2685,0.2739,0.2826,0.2872,0.2899, 0.2951,0.3014,0.3032,0.3034,0.3046,0.3123,0.3141,0.3185,0.3208,0.3244, 0.3281,0.3307,0.3318,0.3349,0.3368,0.3378,0.3393,0.3406,0.3407,0.3409, 0.3486,0.3560,0.3572,0.3595,0.3612,0.3652,0.3660,0.3691,0.3717,0.3780, 0.3812,0.3825,0.3847,0.3875,0.3894,0.3915,0.3921,0.3922,0.3945,0.3984, 0.3985,0.3989,0.4031,0.4037,0.4216,0.4235,0.4256,0.4298,0.4298,0.4352, 0.4356,0.4361,0.4403,0.4406,0.4469,0.4492,0.4498,0.4564,0.4575,0.4578, 0.4658,0.4680,0.4700,0.4773,0.4806,0.4811,0.4814,0.4922,0.4960,0.4968, 0.4984,0.5008,0.5023,0.5028,0.5146,0.5181,0.5182,0.5208,0.5213,0.5220, 0.5257,0.5286,0.5370,0.5380,0.5399,0.5578,0.5591,0.5594,0.5637,0.5677, 0.5830,0.5849,0.5897,0.5902,0.6023,0.6064,0.6091,0.6149,0.6254,0.6293, 0.6350,0.6448,0.6558,0.6662,0.6674,0.6726,0.6756,0.6766,0.6799,0.6824, 0.6833,0.6854,0.6916,0.6983,0.7018,0.7160,0.7174,0.7182,0.7185,0.7208, 0.7334,0.7358,0.7405,0.7446,0.7450,0.7474,0.7478,0.7490,0.7567,0.7603, 0.7614,0.7653,0.7689,0.7700,0.7768,0.7822,0.7863,0.7874,0.7930,0.7933, 0.8035,0.8059,0.8160,0.8180,0.8378,0.8397,0.8402,0.8431,0.8473,0.8509, 0.8595,0.8634,0.8662,0.8699,0.8718,0.8722,0.8736,0.8761,0.8926,0.9027, 0.9059,0.9128,0.9158,0.9246,0.9296,0.9305,0.9345,0.9346,0.9366,0.9374, 0.9429,0.9447,0.9486,0.9499,0.9524,0.9544,0.9544,0.9579,0.9593,0.9646, 0.9656,0.9734,0.9739,0.9758,0.9843,0.9877,0.9930,0.9944,0.9946, Overall p-value after applying KStest on 269 p-values = 0.255618 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.