RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-12-02_16:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.73 10.2807 0.108571 2 to 25 15.74 16.1486 0.486675 3 to 26 15.70 9.3517 0.071423 4 to 27 15.74 23.5724 0.868474 5 to 28 15.50 29.5938 0.970572 6 to 29 15.91 24.2002 0.885903 7 to 30 16.14 22.4831 0.833152 8 to 31 15.76 9.2306 0.067252 9 to 32 15.78 20.0143 0.726502 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.289128 Tough bday spacings test for dh-ranFile-2015-12-02_16:31: 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 11 37 63 110 85 91 52 28 16 4 3 (O-E)^2/E 0.4 0.0 1.4 1.6 1.6 2.1 0.0 0.1 0.1 1.0 0.3 Birthday Spacings: Sum(O-E)^2/E= 8.628, p= 0.432 RESULTS OF GCD FOR dh-ranFile-2015-12-02_16:31 Euclid's algorithm: p-value, steps to gcd: 0.655079 p-value, dist. of gcd's: 0.158421 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-12-02_16:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.508 0.948 0.533 0.296 0.623 0.786 0.263 0.926 Bits 8 to 15---> 0.671 0.652 0.218 0.482 0.372 0.825 0.828 0.948 Bits 16 to 23---> 0.450 0.829 0.221 0.190 0.586 0.822 0.637 0.152 Bits 24 to 31---> 0.487 0.470 0.076 0.340 0.553 0.602 0.853 0.463 KS test for the above 32 p values: 0.673 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-12-02_16:31, p-values for 5 runs: 0.5586, 0.5263, 0.7166, 0.2615, 0.8020 Rank test for binary matrices (31x31) for dh-ranFile-2015-12-02_16:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 203 211.4 0.335 0.335 r= 29 5082 5134.0 0.527 0.862 r= 30 23088 23103.0 0.010 0.872 r= 31 11627 11551.5 0.493 1.365 chi-square = 1.365 with df = 3; p-value = 0.286 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-12-02_16:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 219 211.4 0.272 0.272 r= 30 5042 5134.0 1.649 1.921 r= 31 23242 23103.0 0.836 2.757 r= 32 11497 11551.5 0.257 3.014 chi-square = 3.014 with df = 3; p-value = 0.611 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-12-02_16:31 b-rank test for bits 1 to 8, p=0.69192 b-rank test for bits 2 to 9, p=0.92924 b-rank test for bits 3 to 10, p=0.88778 b-rank test for bits 4 to 11, p=0.25620 b-rank test for bits 5 to 12, p=0.30786 b-rank test for bits 6 to 13, p=0.31453 b-rank test for bits 7 to 14, p=0.44475 b-rank test for bits 8 to 15, p=0.62419 b-rank test for bits 9 to 16, p=0.65002 b-rank test for bits 10 to 17, p=0.03494 b-rank test for bits 11 to 18, p=0.81030 b-rank test for bits 12 to 19, p=0.60255 b-rank test for bits 13 to 20, p=0.04590 b-rank test for bits 14 to 21, p=0.28065 b-rank test for bits 15 to 22, p=0.91851 b-rank test for bits 16 to 23, p=0.51536 b-rank test for bits 17 to 24, p=0.21422 b-rank test for bits 18 to 25, p=0.48205 b-rank test for bits 19 to 26, p=0.35227 b-rank test for bits 20 to 27, p=0.13601 b-rank test for bits 21 to 28, p=0.64897 b-rank test for bits 22 to 29, p=0.40527 b-rank test for bits 23 to 30, p=0.22266 b-rank test for bits 24 to 31, p=0.40865 b-rank test for bits 25 to 32, p=0.00668 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 = 0.592510 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-12-02_16:31 (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 141905 -0.01 0.495964 2 141318 -1.38 0.083545 3 141766 -0.33 0.368857 4 141711 -0.46 0.321543 5 142268 0.84 0.798989 6 142065 0.36 0.641965 7 141180 -1.70 0.044187 8 142475 1.32 0.906859 9 141631 -0.65 0.257748 10 142066 0.37 0.642837 11 142148 0.56 0.711455 12 142579 1.56 0.941167 13 141236 -1.57 0.057836 14 142059 0.35 0.636717 15 141668 -0.56 0.286426 16 142058 0.35 0.635840 17 142389 1.12 0.868797 18 141892 -0.04 0.483851 19 142501 1.38 0.916577 20 141538 -0.87 0.192808 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-12-02_16:31 Bits used No. missing words z-score p-value 23 to 32 141492 -1.4391 0.075066 22 to 31 141789 -0.4149 0.339096 21 to 30 141735 -0.6011 0.273874 20 to 29 142124 0.7402 0.770423 19 to 28 142522 2.1127 0.982685 18 to 27 142488 1.9954 0.977001 17 to 26 142030 0.4161 0.661333 16 to 25 141558 -1.2115 0.112855 15 to 24 142363 1.5644 0.941136 14 to 23 142599 2.3782 0.991301 13 to 22 141673 -0.8149 0.207556 12 to 21 141693 -0.7460 0.227844 11 to 20 141923 0.0471 0.518798 10 to 19 141633 -0.9529 0.170330 9 to 18 142147 0.8196 0.793764 8 to 17 142055 0.5023 0.692275 7 to 16 141791 -0.4080 0.341624 6 to 15 141756 -0.5287 0.298498 5 to 14 142027 0.4058 0.657540 4 to 13 142035 0.4333 0.667618 3 to 12 142047 0.4747 0.682508 2 to 11 141677 -0.8011 0.211526 1 to 10 141767 -0.4908 0.311786 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-12-02_16:31 Bits used No. missing words z-score p-value 28 to 32 141864 -0.1537 0.438939 27 to 31 141477 -1.4655 0.071389 26 to 30 142374 1.5752 0.942389 25 to 29 141732 -0.6011 0.273881 24 to 28 141511 -1.3503 0.088465 23 to 27 141894 -0.0520 0.479278 22 to 26 141786 -0.4181 0.337949 21 to 25 142233 1.0972 0.863720 20 to 24 141908 -0.0045 0.498201 19 to 23 141710 -0.6757 0.249617 18 to 22 141665 -0.8282 0.203768 17 to 21 141912 0.0091 0.503611 16 to 20 141729 -0.6113 0.270504 15 to 19 141944 0.1175 0.546778 14 to 18 142420 1.7311 0.958282 13 to 17 141752 -0.5333 0.296905 12 to 16 141394 -1.7469 0.040329 11 to 15 141371 -1.8248 0.034012 10 to 14 141438 -1.5977 0.055052 9 to 13 141848 -0.2079 0.417654 8 to 12 141568 -1.1571 0.123626 7 to 11 141408 -1.6994 0.044620 6 to 10 142148 0.8091 0.790757 5 to 9 142484 1.9480 0.974295 4 to 8 142149 0.8124 0.791731 3 to 7 141333 -1.9537 0.025371 2 to 6 141948 0.1311 0.552146 1 to 5 141610 -1.0147 0.155130 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-12-02_16:31 Bits used No. missing words z-score p-value 31 to 32 141397 -1.5113 0.065356 30 to 31 141952 0.1259 0.550083 29 to 30 142310 1.1819 0.881381 28 to 29 142218 0.9105 0.818729 27 to 28 142542 1.8663 0.968999 26 to 27 142228 0.9400 0.826399 25 to 26 141915 0.0167 0.506672 24 to 25 141754 -0.4582 0.323404 23 to 24 141359 -1.6234 0.052253 22 to 23 141799 -0.3255 0.372418 21 to 22 141947 0.1111 0.544240 20 to 21 142507 1.7630 0.961053 19 to 20 141202 -2.0865 0.018466 18 to 19 141694 -0.6352 0.262652 17 to 18 141593 -0.9331 0.175377 16 to 17 141787 -0.3609 0.359104 15 to 16 141817 -0.2724 0.392673 14 to 15 142098 0.5565 0.711082 13 to 14 141938 0.0846 0.533699 12 to 13 142208 0.8810 0.810850 11 to 12 141787 -0.3609 0.359104 10 to 11 142332 1.2468 0.893767 9 to 10 141794 -0.3402 0.366851 8 to 9 141693 -0.6381 0.261691 7 to 8 142006 0.2852 0.612240 6 to 7 142360 1.3294 0.908144 5 to 6 141518 -1.1544 0.124175 4 to 5 141861 -0.1426 0.443316 3 to 4 141635 -0.8092 0.209191 2 to 3 142132 0.6568 0.744359 1 to 2 141595 -0.9272 0.176904 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-12-02_16:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2495.79 -0.060 0.476273 Test results for specific bytes for dh-ranFile-2015-12-02_16:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2464.22 -0.506 0.306404 2 to 9 2531.94 0.452 0.674237 3 to 10 2580.61 1.140 0.872869 4 to 11 2425.62 -1.052 0.146428 5 to 12 2551.34 0.726 0.766083 6 to 13 2573.21 1.035 0.849751 7 to 14 2443.85 -0.794 0.213572 8 to 15 2457.80 -0.597 0.275312 9 to 16 2294.55 -2.906 0.001833 10 to 17 2441.12 -0.833 0.202503 11 to 18 2482.26 -0.251 0.400942 12 to 19 2469.83 -0.427 0.334833 13 to 20 2368.73 -1.856 0.031696 14 to 21 2359.00 -1.994 0.023075 15 to 22 2521.25 0.301 0.618110 16 to 23 2544.92 0.635 0.737389 17 to 24 2502.64 0.037 0.514885 18 to 25 2460.61 -0.557 0.288748 19 to 26 2506.99 0.099 0.539355 20 to 27 2518.84 0.266 0.605024 21 to 28 2499.75 -0.004 0.498594 22 to 29 2595.21 1.346 0.910929 23 to 30 2538.45 0.544 0.706696 24 to 31 2463.62 -0.514 0.303469 25 to 32 2682.64 2.583 0.995102 CDPARK for dh-ranFile-2015-12-02_16:31: 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 3454 -3.1507 0.000814 3483 -1.8265 0.033889 3498 -1.1416 0.126820 3474 -2.2374 0.012629 3561 1.7352 0.958644 3531 0.3653 0.642555 3494 -1.3242 0.092718 3558 1.5982 0.944998 3541 0.8219 0.794438 3484 -1.7808 0.037471 Square side=100, avg. no. parked=3507.80 sample std.=35.35 p-value of the KSTEST for those 10 p-values: 0.004588 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-12-02_16:31 0.7062,0.4731,0.0222,0.9027,0.6311,0.5035,0.1086,0.2052,0.8233,0.6065, The KS test for those 10 p-values: 0.962369 The 3DSPHERES test for dh-ranFile-2015-12-02_16:31 sample no r^3 equiv. uni. 1 41.888 0.752482 2 23.688 0.545976 3 3.586 0.112655 4 28.794 0.617028 5 106.856 0.971614 6 11.118 0.309671 7 4.277 0.132879 8 31.358 0.648399 9 5.574 0.169547 10 45.474 0.780369 11 196.924 0.998590 12 44.092 0.770012 13 23.134 0.537510 14 8.348 0.242901 15 7.055 0.209555 16 11.922 0.327932 17 118.828 0.980955 18 5.929 0.179335 19 15.893 0.411261 20 24.858 0.563333 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.611547 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-12-02_16:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 2.6 0.3 -1.0 0.4 -0.9 0.2 1.9 -0.6 0.2 0.4 -0.4 -1.4 -0.5 2.3 1.2 -0.4 -1.1 0.8 0.2 -1.1 -0.1 0.5 -1.5 -0.8 0.6 0.2 -0.0 -0.1 -0.1 0.6 0.8 -0.4 1.1 0.2 0.2 0.0 -1.3 0.1 -1.3 0.1 0.0 -0.1 Chi-square with 42 degrees of freedom:34.601019 z-score=-0.807295, p-value=0.215841 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-12-02_16:31 Test no p-value 1 0.514076 2 0.564465 3 0.986085 4 0.451328 5 0.075194 6 0.041343 7 0.257650 8 0.408335 9 0.098616 10 0.274937 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.196440 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-12-02_16:31: (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 66603 0.06 66741 0.08 3 25000.00 25161 1.04 24930 0.20 4 6666.67 6589 0.90 6628 0.22 5 1388.89 1388 0.00 1446 2.35 6 238.10 218 1.70 222 1.09 7 34.72 35 0.00 28 1.30 8 4.96 5 0.00 4 0.19 p=0.28303 p=0.50955 Number of rngs required: 688771, p-value: 0.664 RESULTS OF CRAPS TEST for dh-ranFile-2015-12-02_16:31 No. of wins: Observed Expected 98841 98585.9 z-score= 1.141, pvalue=0.87309 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66716 66666.7 0.037 0.037 2 37660 37654.3 0.001 0.037 3 26925 26954.7 0.033 0.070 4 19503 19313.5 1.860 1.930 5 13788 13851.4 0.290 2.221 6 9908 9943.5 0.127 2.348 7 7090 7145.0 0.424 2.771 8 5117 5139.1 0.095 2.866 9 3713 3699.9 0.047 2.913 10 2577 2666.3 2.991 5.904 11 1928 1923.3 0.011 5.915 12 1410 1388.7 0.325 6.240 13 1021 1003.7 0.298 6.538 14 700 726.1 0.941 7.479 15 518 525.8 0.117 7.596 16 382 381.2 0.002 7.598 17 296 276.5 1.369 8.967 18 203 200.8 0.023 8.991 19 138 146.0 0.437 9.427 20 111 106.2 0.216 9.643 21 296 287.1 0.275 9.918 Chisq= 9.92 for 20 degrees of freedom, p= 0.03036 SUMMARY of craptest p-value for no. of wins: 0.873094 p-value for throws/game: 0.030363 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-12-02_16:31 No. of wins: Observed Expected 98434 98585.9 z-score=-0.679, pvalue=0.24851 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66893 66666.7 0.768 0.768 2 37491 37654.3 0.708 1.477 3 26634 26954.7 3.816 5.293 4 19209 19313.5 0.565 5.858 5 13929 13851.4 0.435 6.293 6 9852 9943.5 0.843 7.135 7 7187 7145.0 0.247 7.382 8 5229 5139.1 1.574 8.956 9 3769 3699.9 1.292 10.248 10 2623 2666.3 0.703 10.951 11 1962 1923.3 0.778 11.728 12 1392 1388.7 0.008 11.736 13 1042 1003.7 1.460 13.196 14 771 726.1 2.771 15.967 15 534 525.8 0.127 16.094 16 410 381.2 2.184 18.278 17 287 276.5 0.396 18.673 18 206 200.8 0.133 18.807 19 163 146.0 1.983 20.790 20 121 106.2 2.058 22.848 21 296 287.1 0.275 23.123 Chisq= 23.12 for 20 degrees of freedom, p= 0.71720 SUMMARY of craptest p-value for no. of wins: 0.248506 p-value for throws/game: 0.717199 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0008,0.0018,0.0046,0.0067,0.0126,0.0185,0.0222,0.0231,0.0254,0.0304, 0.0317,0.0339,0.0340,0.0349,0.0375,0.0403,0.0413,0.0442,0.0446,0.0459, 0.0523,0.0551,0.0578,0.0654,0.0673,0.0714,0.0714,0.0751,0.0752,0.0761, 0.0835,0.0885,0.0927,0.0986,0.1086,0.1086,0.1127,0.1129,0.1236,0.1242, 0.1268,0.1329,0.1360,0.1464,0.1521,0.1551,0.1584,0.1695,0.1703,0.1754, 0.1769,0.1793,0.1898,0.1928,0.1964,0.2025,0.2038,0.2052,0.2076,0.2092, 0.2096,0.2115,0.2136,0.2142,0.2158,0.2184,0.2211,0.2227,0.2278,0.2429, 0.2485,0.2496,0.2562,0.2576,0.2577,0.2615,0.2617,0.2627,0.2631,0.2705, 0.2739,0.2739,0.2749,0.2753,0.2806,0.2830,0.2862,0.2864,0.2887,0.2891, 0.2962,0.2969,0.2985,0.3035,0.3064,0.3079,0.3097,0.3118,0.3145,0.3215, 0.3234,0.3279,0.3348,0.3379,0.3391,0.3399,0.3416,0.3523,0.3591,0.3591, 0.3669,0.3689,0.3722,0.3724,0.3927,0.4009,0.4053,0.4083,0.4086,0.4113, 0.4177,0.4323,0.4389,0.4433,0.4448,0.4498,0.4513,0.4632,0.4699,0.4731, 0.4763,0.4793,0.4820,0.4821,0.4839,0.4865,0.4867,0.4960,0.4982,0.4986, 0.5035,0.5036,0.5067,0.5082,0.5096,0.5141,0.5149,0.5154,0.5188,0.5263, 0.5327,0.5337,0.5375,0.5394,0.5442,0.5460,0.5468,0.5501,0.5521,0.5530, 0.5586,0.5633,0.5645,0.5858,0.5925,0.6019,0.6026,0.6050,0.6065,0.6105, 0.6115,0.6122,0.6170,0.6181,0.6231,0.6242,0.6311,0.6358,0.6367,0.6367, 0.6420,0.6426,0.6428,0.6484,0.6490,0.6500,0.6522,0.6551,0.6575,0.6613, 0.6642,0.6676,0.6713,0.6725,0.6742,0.6825,0.6919,0.6923,0.7062,0.7067, 0.7111,0.7115,0.7166,0.7172,0.7265,0.7374,0.7444,0.7525,0.7661,0.7700, 0.7704,0.7804,0.7858,0.7908,0.7917,0.7938,0.7944,0.7990,0.8020,0.8103, 0.8108,0.8187,0.8215,0.8233,0.8252,0.8264,0.8278,0.8287,0.8332,0.8498, 0.8531,0.8637,0.8685,0.8688,0.8729,0.8731,0.8814,0.8859,0.8878,0.8938, 0.9027,0.9069,0.9081,0.9109,0.9166,0.9185,0.9257,0.9292,0.9411,0.9412, 0.9424,0.9450,0.9478,0.9485,0.9583,0.9586,0.9611,0.9624,0.9690,0.9706, 0.9716,0.9743,0.9770,0.9810,0.9827,0.9861,0.9913,0.9951,0.9986, Overall p-value after applying KStest on 269 p-values = 0.333475 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.