RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-10-19_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 16.12 17.7638 0.596116 2 to 25 15.91 14.9598 0.401624 3 to 26 15.47 23.0037 0.850870 4 to 27 15.88 19.8964 0.720436 5 to 28 15.57 25.5503 0.916947 6 to 29 15.41 22.1191 0.819819 7 to 30 15.66 17.4963 0.578739 8 to 31 15.92 11.9584 0.197349 9 to 32 15.68 16.1760 0.488604 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.355685 Tough bday spacings test for dh-ranFile-2015-10-19_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 12 39 70 89 100 74 62 23 17 9 5 (O-E)^2/E 0.9 0.2 0.1 0.8 0.1 0.2 1.9 1.5 0.3 0.9 0.2 Birthday Spacings: Sum(O-E)^2/E= 7.024, p= 0.277 RESULTS OF GCD FOR dh-ranFile-2015-10-19_12:31 Euclid's algorithm: p-value, steps to gcd: 0.590166 p-value, dist. of gcd's: 0.431706 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-10-19_12:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.166 0.446 0.056 0.316 0.790 0.023 0.931 0.263 Bits 8 to 15---> 0.178 0.425 0.343 0.253 0.545 0.671 0.031 0.303 Bits 16 to 23---> 0.395 0.503 0.691 0.188 0.478 0.108 0.277 0.015 Bits 24 to 31---> 0.691 0.662 0.325 0.216 0.094 0.020 0.429 0.773 KS test for the above 32 p values: 0.989 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-10-19_12:31, p-values for 5 runs: 0.6980, 0.7772, 0.9865, 0.3277, 0.6026 Rank test for binary matrices (31x31) for dh-ranFile-2015-10-19_12:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 200 211.4 0.617 0.617 r= 29 5224 5134.0 1.577 2.194 r= 30 23104 23103.0 0.000 2.194 r= 31 11472 11551.5 0.547 2.741 chi-square = 2.741 with df = 3; p-value = 0.567 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-10-19_12:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 224 211.4 0.749 0.749 r= 30 5067 5134.0 0.875 1.623 r= 31 23079 23103.0 0.025 1.648 r= 32 11630 11551.5 0.533 2.182 chi-square = 2.182 with df = 3; p-value = 0.464 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-10-19_12:31 b-rank test for bits 1 to 8, p=0.09287 b-rank test for bits 2 to 9, p=0.18723 b-rank test for bits 3 to 10, p=0.69942 b-rank test for bits 4 to 11, p=0.84787 b-rank test for bits 5 to 12, p=0.63814 b-rank test for bits 6 to 13, p=0.73963 b-rank test for bits 7 to 14, p=0.91155 b-rank test for bits 8 to 15, p=0.56377 b-rank test for bits 9 to 16, p=0.78695 b-rank test for bits 10 to 17, p=0.68130 b-rank test for bits 11 to 18, p=0.75840 b-rank test for bits 12 to 19, p=0.03044 b-rank test for bits 13 to 20, p=0.77694 b-rank test for bits 14 to 21, p=0.32553 b-rank test for bits 15 to 22, p=0.42174 b-rank test for bits 16 to 23, p=0.56880 b-rank test for bits 17 to 24, p=0.07574 b-rank test for bits 18 to 25, p=0.50312 b-rank test for bits 19 to 26, p=0.30121 b-rank test for bits 20 to 27, p=0.28176 b-rank test for bits 21 to 28, p=0.03521 b-rank test for bits 22 to 29, p=0.20001 b-rank test for bits 23 to 30, p=0.70751 b-rank test for bits 24 to 31, p=0.16109 b-rank test for bits 25 to 32, p=0.41828 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 = 0.760374 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-10-19_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 141927 0.04 0.516466 2 141903 -0.01 0.494100 3 141964 0.13 0.550820 4 142177 0.63 0.734145 5 141838 -0.17 0.433819 6 141148 -1.78 0.037636 7 140886 -2.39 0.008402 8 142140 0.54 0.705039 9 141769 -0.33 0.371504 10 141688 -0.52 0.302534 11 141843 -0.15 0.438420 12 142821 2.13 0.983417 13 141757 -0.36 0.360954 14 142705 1.86 0.968489 15 141495 -0.97 0.166507 16 141785 -0.29 0.385720 17 141608 -0.70 0.240703 18 141380 -1.24 0.108090 19 142037 0.30 0.617261 20 141207 -1.64 0.050403 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-10-19_12:31 Bits used No. missing words z-score p-value 23 to 32 141766 -0.4942 0.310568 22 to 31 142181 0.9368 0.825568 21 to 30 142417 1.7506 0.959991 20 to 29 142343 1.4954 0.932597 19 to 28 142012 0.3540 0.638344 18 to 27 142070 0.5540 0.710222 17 to 26 141902 -0.0253 0.489918 16 to 25 141963 0.1851 0.573413 15 to 24 142054 0.4989 0.691062 14 to 23 142226 1.0920 0.862576 13 to 22 142306 1.3678 0.914317 12 to 21 141149 -2.6218 0.004373 11 to 20 141455 -1.5667 0.058598 10 to 19 141630 -0.9632 0.167722 9 to 18 141630 -0.9632 0.167722 8 to 17 142058 0.5127 0.695904 7 to 16 141644 -0.9149 0.180114 6 to 15 142442 1.8368 0.966880 5 to 14 142270 1.2437 0.893193 4 to 13 142344 1.4989 0.933045 3 to 12 141532 -1.3011 0.096606 2 to 11 142130 0.7609 0.776651 1 to 10 142369 1.5851 0.943525 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-10-19_12:31 Bits used No. missing words z-score p-value 28 to 32 141721 -0.6384 0.261605 27 to 31 141513 -1.3435 0.089556 26 to 30 141826 -0.2825 0.388790 25 to 29 141479 -1.4587 0.072318 24 to 28 141995 0.2904 0.614248 23 to 27 142026 0.3955 0.653760 22 to 26 142147 0.8057 0.789781 21 to 25 141909 -0.0011 0.499554 20 to 24 141817 -0.3130 0.377147 19 to 23 142218 1.0463 0.852298 18 to 22 141848 -0.2079 0.417654 17 to 21 142098 0.6396 0.738770 16 to 20 141983 0.2497 0.598602 15 to 19 141471 -1.4859 0.068658 14 to 18 141993 0.2836 0.611652 13 to 17 141660 -0.8452 0.199003 12 to 16 141452 -1.5503 0.060538 11 to 15 141403 -1.7164 0.043047 10 to 14 141603 -1.0384 0.149540 9 to 13 142028 0.4023 0.656258 8 to 12 141774 -0.4587 0.323208 7 to 11 141692 -0.7367 0.230649 6 to 10 142008 0.3345 0.630989 5 to 9 141528 -1.2926 0.098067 4 to 8 141241 -2.2655 0.011740 3 to 7 141944 0.1175 0.546778 2 to 6 141440 -1.5909 0.055811 1 to 5 142064 0.5243 0.699967 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-10-19_12:31 Bits used No. missing words z-score p-value 31 to 32 142460 1.6244 0.947854 30 to 31 141891 -0.0541 0.478439 29 to 30 142203 0.8663 0.806833 28 to 29 141793 -0.3432 0.365740 27 to 28 141989 0.2350 0.592901 26 to 27 141322 -1.7325 0.041589 25 to 26 141675 -0.6912 0.244708 24 to 25 142238 0.9695 0.833859 23 to 24 142169 0.7660 0.778158 22 to 23 141975 0.1937 0.576801 21 to 22 141414 -1.4612 0.071987 20 to 21 141926 0.0492 0.519610 19 to 20 142087 0.5241 0.699896 18 to 19 142074 0.4858 0.686429 17 to 18 142616 2.0846 0.981446 16 to 17 142008 0.2911 0.614498 15 to 16 141565 -1.0157 0.154881 14 to 15 141800 -0.3225 0.373534 13 to 14 141046 -2.5467 0.005437 12 to 13 141991 0.2409 0.595189 11 to 12 141796 -0.3343 0.369074 10 to 11 142401 1.4504 0.926520 9 to 10 141753 -0.4612 0.322345 8 to 9 141695 -0.6322 0.263614 7 to 8 141610 -0.8830 0.188624 6 to 7 142239 0.9725 0.834594 5 to 6 141559 -1.0334 0.150703 4 to 5 142139 0.6775 0.750953 3 to 4 141945 0.1052 0.541900 2 to 3 141943 0.0993 0.539559 1 to 2 141921 0.0344 0.513731 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-10-19_12:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2390.99 -1.542 0.061577 Test results for specific bytes for dh-ranFile-2015-10-19_12:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2542.04 0.594 0.723902 2 to 9 2453.89 -0.652 0.257161 3 to 10 2550.87 0.719 0.764059 4 to 11 2494.12 -0.083 0.466885 5 to 12 2430.41 -0.984 0.162538 6 to 13 2460.63 -0.557 0.288837 7 to 14 2384.13 -1.639 0.050636 8 to 15 2596.59 1.366 0.914025 9 to 16 2363.08 -1.936 0.026415 10 to 17 2550.43 0.713 0.762149 11 to 18 2580.72 1.142 0.873174 12 to 19 2606.53 1.507 0.934035 13 to 20 2608.09 1.529 0.936819 14 to 21 2508.70 0.123 0.548980 15 to 22 2475.84 -0.342 0.366281 16 to 23 2462.09 -0.536 0.295955 17 to 24 2347.01 -2.164 0.015248 18 to 25 2685.63 2.625 0.995670 19 to 26 2501.47 0.021 0.508313 20 to 27 2375.21 -1.765 0.038794 21 to 28 2538.92 0.550 0.708997 22 to 29 2436.31 -0.901 0.183858 23 to 30 2349.40 -2.130 0.016593 24 to 31 2542.18 0.597 0.724581 25 to 32 2524.80 0.351 0.637113 CDPARK for dh-ranFile-2015-10-19_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 3531 0.3653 0.642555 3507 -0.7306 0.232514 3502 -0.9589 0.168804 3540 0.7763 0.781201 3523 0.0000 0.500000 3548 1.1416 0.873180 3550 1.2329 0.891189 3555 1.4612 0.928018 3532 0.4110 0.659449 3489 -1.5525 0.060270 Square side=100, avg. no. parked=3527.70 sample std.=21.08 p-value of the KSTEST for those 10 p-values: 0.644318 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-10-19_12:31 0.6952,0.5399,0.8747,0.7547,0.5106,0.5401,0.5812,0.6272,0.1075,0.8414, The KS test for those 10 p-values: 0.215691 The 3DSPHERES test for dh-ranFile-2015-10-19_12:31 sample no r^3 equiv. uni. 1 11.423 0.316662 2 2.632 0.083991 3 53.280 0.830684 4 106.100 0.970890 5 23.954 0.549978 6 62.406 0.875093 7 29.025 0.619973 8 35.106 0.689694 9 21.788 0.516292 10 4.451 0.137893 11 16.249 0.418208 12 0.909 0.029833 13 48.684 0.802653 14 57.646 0.853619 15 22.519 0.527927 16 1.125 0.036808 17 61.026 0.869216 18 18.300 0.456653 19 47.525 0.794883 20 49.927 0.810663 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.420957 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-10-19_12:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 0.5 -0.6 -0.8 2.3 -0.2 -0.5 0.9 0.1 0.5 0.4 -0.5 -0.5 1.4 1.5 0.8 -0.2 -2.3 0.1 -0.9 -0.4 0.4 0.2 -0.3 -0.0 1.6 -1.8 -0.8 1.0 -0.4 -0.1 -0.5 0.1 0.2 0.8 -0.3 -0.7 0.8 -0.4 -0.7 0.9 1.0 -1.1 Chi-square with 42 degrees of freedom:34.016130 z-score=-0.871112, p-value=0.195078 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-10-19_12:31 Test no p-value 1 0.023687 2 0.825528 3 0.841788 4 0.344148 5 0.048169 6 0.510659 7 0.353539 8 0.575119 9 0.397191 10 0.310847 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.533180 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-10-19_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 66910 0.89 66879 0.68 3 25000.00 24831 1.14 24742 2.66 4 6666.67 6640 0.11 6619 0.34 5 1388.89 1341 1.65 1469 4.62 6 238.10 241 0.04 235 0.04 7 34.72 31 0.40 50 6.72 8 4.96 5 0.00 5 0.00 p=0.35346 p=0.98025 Number of rngs required: 687358, p-value: 0.112 RESULTS OF CRAPS TEST for dh-ranFile-2015-10-19_12:31 No. of wins: Observed Expected 98358 98585.9 z-score=-1.019, pvalue=0.15407 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66281 66666.7 2.231 2.231 2 37641 37654.3 0.005 2.236 3 27186 26954.7 1.984 4.220 4 19465 19313.5 1.189 5.409 5 13753 13851.4 0.699 6.108 6 9837 9943.5 1.142 7.250 7 7205 7145.0 0.503 7.753 8 5183 5139.1 0.375 8.129 9 3762 3699.9 1.043 9.172 10 2713 2666.3 0.818 9.990 11 1959 1923.3 0.662 10.652 12 1398 1388.7 0.062 10.714 13 994 1003.7 0.094 10.808 14 732 726.1 0.047 10.855 15 517 525.8 0.148 11.003 16 374 381.2 0.134 11.138 17 299 276.5 1.824 12.962 18 178 200.8 2.595 15.557 19 131 146.0 1.538 17.095 20 112 106.2 0.315 17.410 21 280 287.1 0.176 17.586 Chisq= 17.59 for 20 degrees of freedom, p= 0.38537 SUMMARY of craptest p-value for no. of wins: 0.154074 p-value for throws/game: 0.385372 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-10-19_12:31 No. of wins: Observed Expected 98941 98585.9 z-score= 1.588, pvalue=0.94390 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66968 66666.7 1.362 1.362 2 37437 37654.3 1.254 2.616 3 27105 26954.7 0.838 3.454 4 19324 19313.5 0.006 3.460 5 13806 13851.4 0.149 3.609 6 10036 9943.5 0.860 4.468 7 7024 7145.0 2.050 6.518 8 5196 5139.1 0.631 7.149 9 3610 3699.9 2.183 9.332 10 2599 2666.3 1.699 11.030 11 1907 1923.3 0.139 11.169 12 1348 1388.7 1.195 12.364 13 1032 1003.7 0.797 13.161 14 724 726.1 0.006 13.167 15 504 525.8 0.907 14.074 16 366 381.2 0.602 14.676 17 303 276.5 2.532 17.208 18 186 200.8 1.095 18.303 19 135 146.0 0.827 19.130 20 115 106.2 0.727 19.856 21 275 287.1 0.511 20.368 Chisq= 20.37 for 20 degrees of freedom, p= 0.56484 SUMMARY of craptest p-value for no. of wins: 0.943902 p-value for throws/game: 0.564842 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0044,0.0054,0.0084,0.0117,0.0152,0.0152,0.0166,0.0202,0.0227,0.0237, 0.0264,0.0298,0.0304,0.0314,0.0352,0.0368,0.0376,0.0388,0.0416,0.0430, 0.0482,0.0504,0.0506,0.0556,0.0558,0.0586,0.0603,0.0605,0.0616,0.0687, 0.0720,0.0723,0.0757,0.0840,0.0896,0.0929,0.0943,0.0966,0.0981,0.1075, 0.1076,0.1081,0.1122,0.1379,0.1495,0.1507,0.1541,0.1549,0.1611,0.1625, 0.1660,0.1665,0.1677,0.1677,0.1688,0.1782,0.1801,0.1839,0.1872,0.1883, 0.1886,0.1951,0.1973,0.1990,0.2000,0.2157,0.2161,0.2306,0.2325,0.2407, 0.2447,0.2533,0.2572,0.2616,0.2632,0.2636,0.2768,0.2775,0.2818,0.2888, 0.2960,0.3012,0.3025,0.3030,0.3106,0.3108,0.3164,0.3167,0.3223,0.3232, 0.3245,0.3255,0.3277,0.3429,0.3441,0.3535,0.3535,0.3557,0.3610,0.3657, 0.3663,0.3691,0.3715,0.3735,0.3771,0.3854,0.3857,0.3888,0.3954,0.3972, 0.4016,0.4177,0.4182,0.4183,0.4210,0.4217,0.4247,0.4293,0.4317,0.4338, 0.4384,0.4457,0.4567,0.4644,0.4669,0.4777,0.4784,0.4886,0.4899,0.4941, 0.4996,0.5000,0.5028,0.5031,0.5083,0.5106,0.5107,0.5137,0.5163,0.5165, 0.5196,0.5279,0.5332,0.5396,0.5399,0.5401,0.5419,0.5447,0.5468,0.5490, 0.5500,0.5508,0.5638,0.5648,0.5668,0.5688,0.5734,0.5751,0.5768,0.5787, 0.5812,0.5902,0.5929,0.5952,0.5961,0.5986,0.6026,0.6117,0.6142,0.6145, 0.6173,0.6200,0.6272,0.6310,0.6371,0.6381,0.6383,0.6426,0.6443,0.6538, 0.6563,0.6594,0.6616,0.6706,0.6813,0.6864,0.6897,0.6905,0.6909,0.6911, 0.6952,0.6959,0.6980,0.6994,0.6999,0.7000,0.7050,0.7075,0.7090,0.7102, 0.7204,0.7239,0.7246,0.7341,0.7388,0.7396,0.7510,0.7547,0.7584,0.7604, 0.7621,0.7641,0.7734,0.7767,0.7769,0.7772,0.7782,0.7812,0.7870,0.7898, 0.7902,0.7949,0.8027,0.8068,0.8107,0.8198,0.8255,0.8256,0.8307,0.8339, 0.8346,0.8414,0.8418,0.8479,0.8509,0.8523,0.8536,0.8626,0.8692,0.8732, 0.8732,0.8747,0.8751,0.8912,0.8932,0.9115,0.9140,0.9143,0.9169,0.9265, 0.9280,0.9308,0.9326,0.9330,0.9340,0.9368,0.9435,0.9439,0.9479,0.9600, 0.9669,0.9685,0.9709,0.9802,0.9814,0.9834,0.9865,0.9892,0.9957, Overall p-value after applying KStest on 269 p-values = 0.367497 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.