RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-10-18_17:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 16.02 17.0847 0.551361 2 to 25 16.02 7.2393 0.019767 3 to 26 15.82 10.4058 0.114265 4 to 27 15.82 13.0876 0.269699 5 to 28 16.00 12.5720 0.235667 6 to 29 16.08 11.3067 0.159817 7 to 30 15.68 14.9204 0.398788 8 to 31 15.90 18.2010 0.623731 9 to 32 15.70 10.7979 0.133124 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.034818 Tough bday spacings test for dh-ranFile-2016-10-18_17:31: 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 14 46 63 100 96 80 47 29 18 6 1 (O-E)^2/E 2.6 2.4 1.4 0.1 0.0 0.0 0.5 0.0 0.7 0.1 2.3 Birthday Spacings: Sum(O-E)^2/E= 10.062, p= 0.565 RESULTS OF GCD FOR dh-ranFile-2016-10-18_17:31 Euclid's algorithm: p-value, steps to gcd: 0.195226 p-value, dist. of gcd's: 0.648813 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-10-18_17:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.575 0.745 0.124 0.941 0.544 0.286 0.968 0.041 Bits 8 to 15---> 0.777 0.579 0.471 0.399 0.389 0.051 0.619 0.216 Bits 16 to 23---> 0.834 0.556 0.251 0.467 0.808 0.121 0.407 0.631 Bits 24 to 31---> 0.289 0.253 0.237 0.696 0.082 0.198 0.976 0.014 KS test for the above 32 p values: 0.288 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-10-18_17:31, p-values for 5 runs: 0.9877, 0.9581, 0.7935, 0.5211, 0.5416 Rank test for binary matrices (31x31) for dh-ranFile-2016-10-18_17:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 234 211.4 2.412 2.412 r= 29 5203 5134.0 0.927 3.339 r= 30 23006 23103.0 0.408 3.747 r= 31 11557 11551.5 0.003 3.749 chi-square = 3.749 with df = 3; p-value = 0.710 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-10-18_17:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 204 211.4 0.260 0.260 r= 30 5078 5134.0 0.611 0.871 r= 31 23222 23103.0 0.612 1.484 r= 32 11496 11551.5 0.267 1.751 chi-square = 1.751 with df = 3; p-value = 0.374 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-10-18_17:31 b-rank test for bits 1 to 8, p=0.34186 b-rank test for bits 2 to 9, p=0.56369 b-rank test for bits 3 to 10, p=0.55914 b-rank test for bits 4 to 11, p=0.38192 b-rank test for bits 5 to 12, p=0.90775 b-rank test for bits 6 to 13, p=0.99939 b-rank test for bits 7 to 14, p=0.26830 b-rank test for bits 8 to 15, p=0.43915 b-rank test for bits 9 to 16, p=0.63286 b-rank test for bits 10 to 17, p=0.70600 b-rank test for bits 11 to 18, p=0.30080 b-rank test for bits 12 to 19, p=0.95781 b-rank test for bits 13 to 20, p=0.94502 b-rank test for bits 14 to 21, p=0.85124 b-rank test for bits 15 to 22, p=0.91775 b-rank test for bits 16 to 23, p=0.28458 b-rank test for bits 17 to 24, p=0.19648 b-rank test for bits 18 to 25, p=0.89340 b-rank test for bits 19 to 26, p=0.30931 b-rank test for bits 20 to 27, p=0.89463 b-rank test for bits 21 to 28, p=0.12706 b-rank test for bits 22 to 29, p=0.94483 b-rank test for bits 23 to 30, p=0.88353 b-rank test for bits 24 to 31, p=0.69228 b-rank test for bits 25 to 32, p=0.15680 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 = 0.046213 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-10-18_17:31 (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 141760 -0.35 0.363582 2 141524 -0.90 0.183979 3 141228 -1.59 0.055704 4 141896 -0.03 0.487577 5 141029 -2.06 0.019851 6 142270 0.84 0.800298 7 141678 -0.54 0.294429 8 141781 -0.30 0.382151 9 142162 0.59 0.722522 10 142330 0.98 0.837165 11 142132 0.52 0.698558 12 142097 0.44 0.669481 13 142902 2.32 0.989811 14 142116 0.48 0.685407 15 142220 0.73 0.766039 16 142519 1.42 0.922844 17 141964 0.13 0.550820 18 142421 1.20 0.884052 19 141672 -0.55 0.289615 20 142114 0.48 0.683746 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-10-18_17:31 Bits used No. missing words z-score p-value 23 to 32 141431 -1.6494 0.049531 22 to 31 141514 -1.3632 0.086409 21 to 30 141669 -0.8287 0.203630 20 to 29 141916 0.0230 0.509175 19 to 28 142092 0.6299 0.735619 18 to 27 141987 0.2678 0.605584 17 to 26 141973 0.2196 0.586890 16 to 25 141698 -0.7287 0.233085 15 to 24 141638 -0.9356 0.174734 14 to 23 141680 -0.7908 0.214532 13 to 22 141687 -0.7667 0.221643 12 to 21 142043 0.4609 0.677576 11 to 20 141730 -0.6184 0.268163 10 to 19 141914 0.0161 0.506424 9 to 18 142082 0.5954 0.724217 8 to 17 141871 -0.1322 0.447424 7 to 16 142096 0.6437 0.740112 6 to 15 141697 -0.7322 0.232032 5 to 14 142241 1.1437 0.873624 4 to 13 141939 0.1023 0.540745 3 to 12 142133 0.7713 0.779728 2 to 11 141960 0.1747 0.569352 1 to 10 141733 -0.6080 0.271582 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-10-18_17:31 Bits used No. missing words z-score p-value 28 to 32 141567 -1.1604 0.122935 27 to 31 141768 -0.4791 0.315939 26 to 30 141736 -0.5876 0.278414 25 to 29 141203 -2.3943 0.008325 24 to 28 142133 0.7582 0.775835 23 to 27 141896 -0.0452 0.481979 22 to 26 141614 -1.0011 0.158385 21 to 25 142116 0.7006 0.758216 20 to 24 141686 -0.7571 0.224510 19 to 23 142111 0.6836 0.752895 18 to 22 142505 2.0192 0.978268 17 to 21 141664 -0.8316 0.202810 16 to 20 141658 -0.8520 0.197116 15 to 19 142463 1.8768 0.969731 14 to 18 141740 -0.5740 0.282984 13 to 17 142498 1.9955 0.977005 12 to 16 142140 0.7819 0.782873 11 to 15 141495 -1.4045 0.080084 10 to 14 141821 -0.2994 0.382308 9 to 13 142007 0.3311 0.629710 8 to 12 142025 0.3921 0.652509 7 to 11 142147 0.8057 0.789781 6 to 10 142343 1.4701 0.929228 5 to 9 141944 0.1175 0.546778 4 to 8 141953 0.1480 0.558842 3 to 7 141745 -0.5571 0.288746 2 to 6 141920 0.0362 0.514426 1 to 5 141491 -1.4181 0.078086 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-10-18_17:31 Bits used No. missing words z-score p-value 31 to 32 141480 -1.2665 0.102674 30 to 31 142043 0.3943 0.653323 29 to 30 142519 1.7984 0.963946 28 to 29 141457 -1.3343 0.091052 27 to 28 141776 -0.3933 0.347048 26 to 27 141914 0.0138 0.505496 25 to 26 141567 -1.0098 0.156290 24 to 25 142366 1.3471 0.911027 23 to 24 141568 -1.0069 0.156998 22 to 23 141892 -0.0511 0.479615 21 to 22 141844 -0.1927 0.423592 20 to 21 141868 -0.1219 0.451482 19 to 20 141942 0.0964 0.538387 18 to 19 142230 0.9459 0.827908 17 to 18 141780 -0.3815 0.351415 16 to 17 141323 -1.7296 0.041852 15 to 16 141472 -1.2901 0.098515 14 to 15 141633 -0.8151 0.207498 13 to 14 141667 -0.7148 0.237355 12 to 13 141538 -1.0954 0.136678 11 to 12 141892 -0.0511 0.479615 10 to 11 142068 0.4681 0.680127 9 to 10 141922 0.0374 0.514907 8 to 9 142228 0.9400 0.826399 7 to 8 142109 0.5890 0.722068 6 to 7 142329 1.2380 0.892135 5 to 6 142177 0.7896 0.785116 4 to 5 142166 0.7571 0.775517 3 to 4 141843 -0.1957 0.422437 2 to 3 141621 -0.8505 0.197515 1 to 2 142013 0.3058 0.620126 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-10-18_17:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2575.32 1.065 0.856593 Test results for specific bytes for dh-ranFile-2016-10-18_17:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2393.36 -1.508 0.065753 2 to 9 2628.29 1.814 0.965183 3 to 10 2442.63 -0.811 0.208603 4 to 11 2358.99 -1.994 0.023064 5 to 12 2520.91 0.296 0.616257 6 to 13 2645.65 2.060 0.980289 7 to 14 2423.16 -1.087 0.138589 8 to 15 2561.75 0.873 0.808754 9 to 16 2479.53 -0.289 0.386118 10 to 17 2707.07 2.928 0.998296 11 to 18 2646.67 2.074 0.980971 12 to 19 2328.77 -2.422 0.007726 13 to 20 2567.23 0.951 0.829156 14 to 21 2527.39 0.387 0.650760 15 to 22 2565.59 0.928 0.823177 16 to 23 2269.86 -3.255 0.000568 17 to 24 2478.67 -0.302 0.381472 18 to 25 2449.78 -0.710 0.238797 19 to 26 2596.08 1.359 0.912887 20 to 27 2626.58 1.790 0.963283 21 to 28 2377.09 -1.738 0.041086 22 to 29 2666.70 2.357 0.990799 23 to 30 2554.13 0.766 0.778015 24 to 31 2506.79 0.096 0.538224 25 to 32 2446.84 -0.752 0.226104 CDPARK for dh-ranFile-2016-10-18_17:31: 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 3553 1.3699 0.914635 3527 0.1826 0.572463 3525 0.0913 0.536383 3495 -1.2785 0.100530 3521 -0.0913 0.463617 3540 0.7763 0.781201 3518 -0.2283 0.409702 3517 -0.2740 0.392053 3557 1.5525 0.939730 3538 0.6849 0.753306 Square side=100, avg. no. parked=3529.10 sample std.=17.51 p-value of the KSTEST for those 10 p-values: 0.563512 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-10-18_17:31 0.7888,0.8188,0.7139,0.4085,0.1531,0.4713,0.7804,0.9232,0.0759,0.6923, The KS test for those 10 p-values: 0.521693 The 3DSPHERES test for dh-ranFile-2016-10-18_17:31 sample no r^3 equiv. uni. 1 7.443 0.219707 2 119.378 0.981301 3 10.349 0.291764 4 45.389 0.779747 5 42.123 0.754411 6 83.702 0.938583 7 0.687 0.022625 8 6.451 0.193487 9 13.693 0.366457 10 19.705 0.481512 11 8.000 0.234068 12 3.916 0.122359 13 22.281 0.524176 14 10.309 0.290813 15 7.326 0.216672 16 32.609 0.662766 17 9.354 0.267881 18 12.584 0.342599 19 21.036 0.504010 20 70.969 0.906109 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.589176 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-10-18_17:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -1.6 -0.1 0.2 0.3 1.1 -0.2 -0.4 0.1 -0.7 -1.1 0.7 1.2 -0.2 0.7 -1.2 -0.5 0.8 0.8 -0.1 0.6 -0.2 -0.6 -0.7 0.2 -0.6 -0.3 -0.6 1.5 -0.1 -1.6 0.1 0.6 0.5 -0.6 0.4 0.7 0.5 -0.8 -0.1 -0.6 1.0 -0.1 Chi-square with 42 degrees of freedom:22.488948 z-score=-2.128830, p-value=0.005919 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-10-18_17:31 Test no p-value 1 0.262467 2 0.394576 3 0.395649 4 0.560741 5 0.473431 6 0.378419 7 0.816085 8 0.263448 9 0.002045 10 0.000603 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.038129 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-10-18_17:31: (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 66835 0.43 66325 1.75 3 25000.00 24897 0.42 25234 2.19 4 6666.67 6672 0.00 6743 0.87 5 1388.89 1330 2.50 1406 0.21 6 238.10 230 0.28 245 0.20 7 34.72 31 0.40 35 0.00 8 4.96 4 0.19 11 7.36 p=0.35175 p=0.94986 Number of rngs required: 688936, p-value: 0.731 RESULTS OF CRAPS TEST for dh-ranFile-2016-10-18_17:31 No. of wins: Observed Expected 99091 98585.9 z-score= 2.259, pvalue=0.98807 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66668 66666.7 0.000 0.000 2 37872 37654.3 1.258 1.258 3 26886 26954.7 0.175 1.434 4 19295 19313.5 0.018 1.451 5 13641 13851.4 3.197 4.648 6 9916 9943.5 0.076 4.724 7 7174 7145.0 0.117 4.842 8 5039 5139.1 1.949 6.790 9 3709 3699.9 0.023 6.813 10 2673 2666.3 0.017 6.830 11 1987 1923.3 2.108 8.938 12 1379 1388.7 0.068 9.006 13 1045 1003.7 1.698 10.704 14 739 726.1 0.228 10.932 15 563 525.8 2.627 13.558 16 414 381.2 2.831 16.389 17 269 276.5 0.206 16.595 18 226 200.8 3.155 19.750 19 134 146.0 0.984 20.733 20 104 106.2 0.046 20.780 21 267 287.1 1.409 22.189 Chisq= 22.19 for 20 degrees of freedom, p= 0.66964 SUMMARY of craptest p-value for no. of wins: 0.988067 p-value for throws/game: 0.669643 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-10-18_17:31 No. of wins: Observed Expected 98597 98585.9 z-score= 0.050, pvalue=0.51987 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66827 66666.7 0.386 0.386 2 37693 37654.3 0.040 0.425 3 27083 26954.7 0.610 1.036 4 19251 19313.5 0.202 1.238 5 13661 13851.4 2.618 3.855 6 9978 9943.5 0.119 3.975 7 6988 7145.0 3.451 7.426 8 5120 5139.1 0.071 7.497 9 3767 3699.9 1.218 8.715 10 2707 2666.3 0.621 9.336 11 1870 1923.3 1.479 10.815 12 1371 1388.7 0.227 11.041 13 1065 1003.7 3.742 14.783 14 723 726.1 0.014 14.797 15 512 525.8 0.364 15.161 16 362 381.2 0.962 16.123 17 264 276.5 0.569 16.692 18 220 200.8 1.830 18.522 19 162 146.0 1.757 20.279 20 90 106.2 2.475 22.754 21 286 287.1 0.004 22.759 Chisq= 22.76 for 20 degrees of freedom, p= 0.69919 SUMMARY of craptest p-value for no. of wins: 0.519871 p-value for throws/game: 0.699194 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0006,0.0006,0.0020,0.0059,0.0077,0.0083,0.0136,0.0198,0.0199,0.0226, 0.0231,0.0348,0.0381,0.0411,0.0412,0.0419,0.0462,0.0495,0.0513,0.0557, 0.0658,0.0759,0.0781,0.0801,0.0816,0.0864,0.0911,0.0985,0.1005,0.1027, 0.1143,0.1209,0.1224,0.1229,0.1244,0.1271,0.1331,0.1367,0.1386,0.1531, 0.1563,0.1568,0.1570,0.1584,0.1598,0.1747,0.1840,0.1935,0.1952,0.1965, 0.1971,0.1975,0.1977,0.2028,0.2036,0.2075,0.2086,0.2145,0.2159,0.2167, 0.2197,0.2216,0.2245,0.2261,0.2320,0.2331,0.2341,0.2357,0.2370,0.2374, 0.2388,0.2510,0.2528,0.2625,0.2634,0.2679,0.2682,0.2683,0.2697,0.2716, 0.2784,0.2830,0.2846,0.2856,0.2877,0.2887,0.2891,0.2896,0.2908,0.2918, 0.2944,0.3008,0.3093,0.3159,0.3419,0.3426,0.3470,0.3514,0.3518,0.3636, 0.3665,0.3743,0.3784,0.3815,0.3819,0.3822,0.3823,0.3861,0.3890,0.3921, 0.3946,0.3956,0.3988,0.3989,0.4067,0.4085,0.4097,0.4224,0.4236,0.4392, 0.4474,0.4515,0.4636,0.4669,0.4713,0.4713,0.4734,0.4796,0.4796,0.4815, 0.4820,0.4876,0.5040,0.5055,0.5064,0.5092,0.5144,0.5149,0.5199,0.5211, 0.5217,0.5242,0.5364,0.5382,0.5384,0.5407,0.5416,0.5445,0.5468,0.5508, 0.5514,0.5558,0.5588,0.5591,0.5607,0.5635,0.5637,0.5649,0.5694,0.5725, 0.5746,0.5787,0.5869,0.5892,0.6056,0.6163,0.6193,0.6201,0.6237,0.6297, 0.6311,0.6329,0.6488,0.6508,0.6525,0.6533,0.6628,0.6695,0.6696,0.6776, 0.6801,0.6837,0.6854,0.6923,0.6923,0.6962,0.6986,0.6992,0.7060,0.7102, 0.7139,0.7221,0.7225,0.7242,0.7307,0.7356,0.7401,0.7450,0.7529,0.7533, 0.7544,0.7582,0.7660,0.7755,0.7758,0.7770,0.7780,0.7797,0.7797,0.7804, 0.7812,0.7829,0.7851,0.7888,0.7898,0.7935,0.8003,0.8076,0.8088,0.8161, 0.8188,0.8232,0.8264,0.8279,0.8292,0.8338,0.8372,0.8512,0.8566,0.8736, 0.8835,0.8841,0.8921,0.8934,0.8946,0.9061,0.9078,0.9110,0.9129,0.9146, 0.9178,0.9228,0.9232,0.9292,0.9386,0.9397,0.9412,0.9448,0.9450,0.9499, 0.9578,0.9581,0.9633,0.9639,0.9652,0.9676,0.9697,0.9756,0.9770,0.9783, 0.9803,0.9810,0.9813,0.9877,0.9881,0.9898,0.9908,0.9983,0.9994, Overall p-value after applying KStest on 269 p-values = 0.651071 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.