RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-06-09_13:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.80 12.0487 0.202822 2 to 25 15.85 18.6710 0.652258 3 to 26 15.61 22.4669 0.832576 4 to 27 15.85 22.4083 0.830477 5 to 28 15.67 32.5763 0.987252 6 to 29 15.61 28.7597 0.963193 7 to 30 15.78 19.8245 0.716696 8 to 31 15.82 22.7479 0.842360 9 to 32 15.72 17.2785 0.564342 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.020104 Tough bday spacings test for dh-ranFile-2015-06-09_13:31: 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 9 40 76 94 102 65 62 26 18 2 6 (O-E)^2/E 0.0 0.3 0.1 0.1 0.2 2.2 1.9 0.5 0.7 3.2 0.9 Birthday Spacings: Sum(O-E)^2/E= 10.108, p= 0.569 RESULTS OF GCD FOR dh-ranFile-2015-06-09_13:31 Euclid's algorithm: p-value, steps to gcd: 0.893257 p-value, dist. of gcd's: 0.525849 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-06-09_13:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.695 0.001 0.692 0.637 0.101 0.138 0.322 0.928 Bits 8 to 15---> 0.639 0.505 0.891 0.084 0.119 0.309 0.882 0.206 Bits 16 to 23---> 0.555 0.423 0.120 0.880 0.775 0.774 0.785 0.139 Bits 24 to 31---> 0.247 0.833 0.725 0.599 0.668 0.223 0.167 0.151 KS test for the above 32 p values: 0.463 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-06-09_13:31, p-values for 5 runs: 0.7555, 0.1906, 0.1669, 0.9817, 0.0584 Rank test for binary matrices (31x31) for dh-ranFile-2015-06-09_13:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 199 211.4 0.729 0.729 r= 29 5185 5134.0 0.506 1.236 r= 30 23009 23103.0 0.383 1.619 r= 31 11607 11551.5 0.266 1.885 chi-square = 1.885 with df = 3; p-value = 0.403 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-06-09_13:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 191 211.4 1.972 1.972 r= 30 5268 5134.0 3.497 5.469 r= 31 23061 23103.0 0.077 5.545 r= 32 11480 11551.5 0.443 5.988 chi-square = 5.988 with df = 3; p-value = 0.888 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-06-09_13:31 b-rank test for bits 1 to 8, p=0.36356 b-rank test for bits 2 to 9, p=0.99932 b-rank test for bits 3 to 10, p=0.55343 b-rank test for bits 4 to 11, p=0.58366 b-rank test for bits 5 to 12, p=0.71793 b-rank test for bits 6 to 13, p=0.99531 b-rank test for bits 7 to 14, p=0.65477 b-rank test for bits 8 to 15, p=0.53511 b-rank test for bits 9 to 16, p=0.34936 b-rank test for bits 10 to 17, p=0.10565 b-rank test for bits 11 to 18, p=0.43831 b-rank test for bits 12 to 19, p=0.98355 b-rank test for bits 13 to 20, p=0.87443 b-rank test for bits 14 to 21, p=0.51276 b-rank test for bits 15 to 22, p=0.88970 b-rank test for bits 16 to 23, p=0.31099 b-rank test for bits 17 to 24, p=0.60571 b-rank test for bits 18 to 25, p=0.78552 b-rank test for bits 19 to 26, p=0.58575 b-rank test for bits 20 to 27, p=0.86412 b-rank test for bits 21 to 28, p=0.02260 b-rank test for bits 22 to 29, p=0.17972 b-rank test for bits 23 to 30, p=0.85708 b-rank test for bits 24 to 31, p=0.11755 b-rank test for bits 25 to 32, p=0.17334 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 = 0.289007 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-06-09_13:31 (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 141031 -2.05 0.020076 2 142482 1.34 0.909554 3 142231 0.75 0.773844 4 142436 1.23 0.890752 5 142228 0.74 0.771730 6 142375 1.09 0.861706 7 142310 0.94 0.825401 8 142052 0.33 0.630562 9 142549 1.49 0.932485 10 141947 0.09 0.535067 11 141962 0.12 0.548971 12 141988 0.18 0.572918 13 141952 0.10 0.539707 14 141833 -0.18 0.429228 15 141630 -0.65 0.256994 16 141708 -0.47 0.319036 17 142565 1.53 0.937231 18 141987 0.18 0.572001 19 142192 0.66 0.745516 20 141891 -0.04 0.482920 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-06-09_13:31 Bits used No. missing words z-score p-value 23 to 32 141672 -0.8184 0.206570 22 to 31 141981 0.2471 0.597599 21 to 30 141859 -0.1736 0.431109 20 to 29 142356 1.5402 0.938249 19 to 28 141433 -1.6425 0.050241 18 to 27 141964 0.1885 0.574764 17 to 26 142138 0.7885 0.784803 16 to 25 142102 0.6644 0.746776 15 to 24 142387 1.6471 0.950235 14 to 23 141695 -0.7391 0.229933 13 to 22 142157 0.8540 0.803457 12 to 21 142078 0.5816 0.719589 11 to 20 142028 0.4092 0.658806 10 to 19 142404 1.7058 0.955973 9 to 18 142150 0.8299 0.796701 8 to 17 141967 0.1989 0.578815 7 to 16 142038 0.4437 0.671367 6 to 15 141633 -0.9529 0.170330 5 to 14 141859 -0.1736 0.431109 4 to 13 141636 -0.9425 0.172964 3 to 12 141626 -0.9770 0.164285 2 to 11 141924 0.0506 0.520172 1 to 10 142216 1.0575 0.854854 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-06-09_13:31 Bits used No. missing words z-score p-value 28 to 32 141971 0.2091 0.582796 27 to 31 142153 0.8260 0.795598 26 to 30 141992 0.2802 0.610352 25 to 29 141978 0.2328 0.592034 24 to 28 141784 -0.4248 0.335474 23 to 27 142420 1.7311 0.958282 22 to 26 141580 -1.1164 0.132131 21 to 25 141748 -0.5469 0.292230 20 to 24 141608 -1.0215 0.153519 19 to 23 141967 0.1955 0.577496 18 to 22 141936 0.0904 0.536018 17 to 21 142151 0.8192 0.793670 16 to 20 141607 -1.0248 0.152718 15 to 19 141730 -0.6079 0.271628 14 to 18 141973 0.2158 0.585440 13 to 17 141639 -0.9164 0.179736 12 to 16 142345 1.4768 0.930142 11 to 15 142145 0.7989 0.787820 10 to 14 141935 0.0870 0.534671 9 to 13 142247 1.1446 0.873822 8 to 12 142408 1.6904 0.954525 7 to 11 142091 0.6158 0.730997 6 to 10 141911 0.0057 0.502258 5 to 9 141881 -0.0960 0.461747 4 to 8 142122 0.7209 0.764519 3 to 7 141980 0.2396 0.594664 2 to 6 141822 -0.2960 0.383602 1 to 5 141720 -0.6418 0.260503 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-06-09_13:31 Bits used No. missing words z-score p-value 31 to 32 142208 0.8810 0.810850 30 to 31 141717 -0.5673 0.285240 29 to 30 142128 0.6450 0.740551 28 to 29 142019 0.3235 0.626846 27 to 28 142067 0.4651 0.679071 26 to 27 142163 0.7483 0.772857 25 to 26 141679 -0.6794 0.248430 24 to 25 141681 -0.6735 0.250302 23 to 24 141489 -1.2399 0.107504 22 to 23 141529 -1.1219 0.130949 21 to 22 141939 0.0875 0.534872 20 to 21 141885 -0.0718 0.471393 19 to 20 142464 1.6362 0.949101 18 to 19 142002 0.2734 0.607713 17 to 18 141691 -0.6440 0.259774 16 to 17 141747 -0.4788 0.316023 15 to 16 141394 -1.5201 0.064237 14 to 15 141489 -1.2399 0.107504 13 to 14 142050 0.4150 0.660913 12 to 13 142353 1.3088 0.904692 11 to 12 142335 1.2557 0.895381 10 to 11 141499 -1.2104 0.113060 9 to 10 141777 -0.3904 0.348137 8 to 9 142122 0.6273 0.734784 7 to 8 142101 0.5654 0.714099 6 to 7 142353 1.3088 0.904692 5 to 6 141706 -0.5998 0.274322 4 to 5 141855 -0.1603 0.436336 3 to 4 142145 0.6952 0.756532 2 to 3 142578 1.9725 0.975722 1 to 2 142117 0.6126 0.729928 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-06-09_13:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2518.35 0.259 0.602360 Test results for specific bytes for dh-ranFile-2015-06-09_13:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2537.73 0.534 0.703169 2 to 9 2527.33 0.386 0.650427 3 to 10 2453.73 -0.654 0.256439 4 to 11 2399.86 -1.416 0.078368 5 to 12 2524.81 0.351 0.637136 6 to 13 2488.91 -0.157 0.437684 7 to 14 2586.85 1.228 0.890318 8 to 15 2415.11 -1.200 0.114981 9 to 16 2478.86 -0.299 0.382468 10 to 17 2590.43 1.279 0.899538 11 to 18 2473.26 -0.378 0.352644 12 to 19 2470.45 -0.418 0.338019 13 to 20 2570.46 0.997 0.840497 14 to 21 2552.69 0.745 0.771895 15 to 22 2504.99 0.071 0.528134 16 to 23 2618.79 1.680 0.953519 17 to 24 2533.64 0.476 0.682866 18 to 25 2533.12 0.468 0.680234 19 to 26 2660.09 2.264 0.988214 20 to 27 2539.85 0.564 0.713480 21 to 28 2515.68 0.222 0.587720 22 to 29 2471.34 -0.405 0.342617 23 to 30 2628.22 1.813 0.965111 24 to 31 2374.03 -1.781 0.037421 25 to 32 2487.37 -0.179 0.429127 CDPARK for dh-ranFile-2015-06-09_13:31: 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 3502 -0.9589 0.168804 3541 0.8219 0.794438 3520 -0.1370 0.445521 3516 -0.3196 0.374623 3563 1.8265 0.966111 3511 -0.5479 0.291865 3513 -0.4566 0.323972 3512 -0.5023 0.307734 3532 0.4110 0.659449 3528 0.2283 0.590298 Square side=100, avg. no. parked=3523.80 sample std.=16.99 p-value of the KSTEST for those 10 p-values: 0.759948 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-06-09_13:31 0.9325,0.7324,0.8505,0.9451,0.3193,0.0663,0.7571,0.1078,0.8568,0.2859, The KS test for those 10 p-values: 0.320700 The 3DSPHERES test for dh-ranFile-2015-06-09_13:31 sample no r^3 equiv. uni. 1 9.425 0.269605 2 41.626 0.750310 3 35.347 0.692174 4 14.829 0.390002 5 78.372 0.926641 6 34.743 0.685919 7 14.483 0.382931 8 75.616 0.919584 9 4.194 0.130456 10 117.248 0.979925 11 4.603 0.142249 12 62.355 0.874884 13 3.307 0.104376 14 0.531 0.017553 15 1.169 0.038228 16 2.400 0.076889 17 3.466 0.109109 18 45.556 0.780964 19 80.411 0.931462 20 38.685 0.724587 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.275858 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-06-09_13:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 0.9 -0.6 1.2 0.7 -0.5 -0.4 0.0 0.0 -0.5 -0.2 -0.6 0.8 -0.8 0.9 0.2 1.8 0.6 -1.1 1.1 -3.3 0.1 -0.4 0.4 0.5 -0.6 0.3 -0.3 1.4 -0.9 -0.4 -1.5 1.7 0.2 -0.9 0.2 1.4 1.1 2.1 1.5 -0.6 0.0 -0.1 Chi-square with 42 degrees of freedom:43.537818 z-score=0.167790, p-value=0.594210 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-06-09_13:31 Test no p-value 1 0.781914 2 0.348757 3 0.025704 4 0.006442 5 0.251576 6 0.460332 7 0.010509 8 0.128728 9 0.004739 10 0.413344 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000850 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-06-09_13:31: (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 66565 0.16 66582 0.11 3 25000.00 24947 0.11 25078 0.24 4 6666.67 6833 4.15 6689 0.07 5 1388.89 1398 0.06 1379 0.07 6 238.10 217 1.87 233 0.11 7 34.72 32 0.21 33 0.09 8 4.96 7 0.84 5 0.00 p=0.71441 p=0.00531 Number of rngs required: 689800, p-value: 0.949 RESULTS OF CRAPS TEST for dh-ranFile-2015-06-09_13:31 No. of wins: Observed Expected 98631 98585.9 z-score= 0.202, pvalue=0.58000 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66659 66666.7 0.001 0.001 2 37939 37654.3 2.152 2.153 3 26744 26954.7 1.648 3.801 4 19295 19313.5 0.018 3.818 5 13849 13851.4 0.000 3.819 6 9829 9943.5 1.319 5.138 7 7207 7145.0 0.538 5.676 8 5117 5139.1 0.095 5.771 9 3761 3699.9 1.010 6.781 10 2688 2666.3 0.177 6.957 11 1948 1923.3 0.316 7.274 12 1369 1388.7 0.281 7.554 13 1002 1003.7 0.003 7.557 14 744 726.1 0.439 7.997 15 523 525.8 0.015 8.012 16 354 381.2 1.934 9.946 17 267 276.5 0.329 10.275 18 185 200.8 1.248 11.523 19 136 146.0 0.683 12.206 20 105 106.2 0.014 12.220 21 279 287.1 0.229 12.449 Chisq= 12.45 for 20 degrees of freedom, p= 0.10024 SUMMARY of craptest p-value for no. of wins: 0.580002 p-value for throws/game: 0.100238 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-06-09_13:31 No. of wins: Observed Expected 98604 98585.9 z-score= 0.081, pvalue=0.53233 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66872 66666.7 0.632 0.632 2 37772 37654.3 0.368 1.000 3 26540 26954.7 6.381 7.381 4 19360 19313.5 0.112 7.494 5 13930 13851.4 0.446 7.939 6 9989 9943.5 0.208 8.147 7 7143 7145.0 0.001 8.148 8 5106 5139.1 0.213 8.361 9 3758 3699.9 0.913 9.274 10 2563 2666.3 4.002 13.276 11 1952 1923.3 0.427 13.703 12 1386 1388.7 0.005 13.709 13 1001 1003.7 0.007 13.716 14 723 726.1 0.014 13.730 15 545 525.8 0.698 14.428 16 338 381.2 4.885 19.313 17 255 276.5 1.678 20.991 18 196 200.8 0.116 21.107 19 158 146.0 0.989 22.096 20 125 106.2 3.322 25.418 21 288 287.1 0.003 25.421 Chisq= 25.42 for 20 degrees of freedom, p= 0.81420 SUMMARY of craptest p-value for no. of wins: 0.532334 p-value for throws/game: 0.814203 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0006,0.0009,0.0047,0.0053,0.0064,0.0105,0.0176,0.0201,0.0201,0.0226, 0.0257,0.0374,0.0382,0.0502,0.0584,0.0642,0.0663,0.0769,0.0784,0.0835, 0.1002,0.1008,0.1044,0.1056,0.1075,0.1075,0.1078,0.1091,0.1131,0.1150, 0.1175,0.1191,0.1198,0.1287,0.1305,0.1309,0.1321,0.1380,0.1387,0.1422, 0.1513,0.1527,0.1535,0.1643,0.1667,0.1669,0.1688,0.1703,0.1730,0.1733, 0.1797,0.1797,0.1906,0.2028,0.2061,0.2066,0.2234,0.2299,0.2466,0.2484, 0.2503,0.2516,0.2564,0.2570,0.2598,0.2605,0.2696,0.2716,0.2743,0.2759, 0.2852,0.2859,0.2890,0.2919,0.2922,0.3077,0.3092,0.3110,0.3160,0.3190, 0.3193,0.3207,0.3218,0.3240,0.3355,0.3380,0.3426,0.3481,0.3488,0.3494, 0.3526,0.3636,0.3746,0.3825,0.3829,0.3836,0.3900,0.4034,0.4133,0.4235, 0.4291,0.4292,0.4311,0.4311,0.4363,0.4377,0.4383,0.4455,0.4603,0.4617, 0.4631,0.4714,0.4829,0.5023,0.5051,0.5128,0.5202,0.5258,0.5281,0.5323, 0.5347,0.5349,0.5351,0.5351,0.5360,0.5397,0.5490,0.5534,0.5547,0.5643, 0.5689,0.5720,0.5729,0.5748,0.5775,0.5788,0.5800,0.5828,0.5837,0.5854, 0.5857,0.5877,0.5903,0.5920,0.5942,0.5947,0.5976,0.5992,0.6024,0.6057, 0.6077,0.6104,0.6268,0.6306,0.6371,0.6374,0.6387,0.6504,0.6523,0.6548, 0.6588,0.6594,0.6609,0.6685,0.6714,0.6791,0.6802,0.6829,0.6859,0.6922, 0.6924,0.6952,0.7032,0.7135,0.7141,0.7144,0.7167,0.7179,0.7196,0.7246, 0.7248,0.7299,0.7310,0.7324,0.7348,0.7406,0.7455,0.7468,0.7503,0.7555, 0.7565,0.7571,0.7599,0.7645,0.7717,0.7719,0.7729,0.7738,0.7738,0.7747, 0.7810,0.7819,0.7848,0.7851,0.7855,0.7878,0.7937,0.7944,0.7956,0.7967, 0.8035,0.8108,0.8142,0.8254,0.8305,0.8326,0.8331,0.8405,0.8424,0.8505, 0.8549,0.8568,0.8571,0.8617,0.8641,0.8738,0.8744,0.8749,0.8805,0.8825, 0.8878,0.8897,0.8903,0.8908,0.8912,0.8933,0.8954,0.8995,0.9047,0.9047, 0.9096,0.9196,0.9266,0.9283,0.9301,0.9315,0.9325,0.9325,0.9372,0.9382, 0.9451,0.9491,0.9491,0.9502,0.9535,0.9545,0.9560,0.9583,0.9632,0.9651, 0.9661,0.9757,0.9799,0.9817,0.9836,0.9873,0.9882,0.9953,0.9993, Overall p-value after applying KStest on 269 p-values = 0.070694 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.