RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-11-08_02:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.27 50.6354 0.999966 2 to 25 15.74 13.1759 0.275668 3 to 26 15.76 17.0448 0.548662 4 to 27 15.83 21.7347 0.804864 5 to 28 15.86 24.2239 0.886522 6 to 29 15.61 17.3485 0.568989 7 to 30 15.43 24.0918 0.883038 8 to 31 15.80 21.3985 0.791030 9 to 32 15.70 19.3610 0.691794 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.019075 Tough bday spacings test for dh-ranFile-2015-11-08_02:31: 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 13 44 74 105 95 60 50 30 17 7 5 (O-E)^2/E 1.6 1.5 0.0 0.5 0.1 4.2 0.1 0.0 0.3 0.0 0.2 Birthday Spacings: Sum(O-E)^2/E= 8.561, p= 0.426 RESULTS OF GCD FOR dh-ranFile-2015-11-08_02:31 Euclid's algorithm: p-value, steps to gcd: 0.589532 p-value, dist. of gcd's: 0.833910 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-11-08_02:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.446 0.522 0.862 0.715 0.807 0.802 0.152 0.377 Bits 8 to 15---> 0.653 0.684 0.886 0.711 0.790 0.129 0.318 0.895 Bits 16 to 23---> 0.913 0.334 0.921 0.256 0.529 0.524 0.601 0.421 Bits 24 to 31---> 0.967 0.369 0.244 0.855 0.058 0.819 0.597 0.524 KS test for the above 32 p values: 0.845 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-11-08_02:31, p-values for 5 runs: 0.8653, 0.5465, 0.1572, 0.7974, 0.8577 Rank test for binary matrices (31x31) for dh-ranFile-2015-11-08_02:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 237 211.4 3.095 3.095 r= 29 5159 5134.0 0.122 3.217 r= 30 22980 23103.0 0.655 3.872 r= 31 11624 11551.5 0.455 4.327 chi-square = 4.327 with df = 3; p-value = 0.772 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-11-08_02:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 197 211.4 0.983 0.983 r= 30 5201 5134.0 0.874 1.857 r= 31 23193 23103.0 0.350 2.208 r= 32 11409 11551.5 1.758 3.966 chi-square = 3.966 with df = 3; p-value = 0.735 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-11-08_02:31 b-rank test for bits 1 to 8, p=0.12757 b-rank test for bits 2 to 9, p=0.55103 b-rank test for bits 3 to 10, p=0.49946 b-rank test for bits 4 to 11, p=0.67513 b-rank test for bits 5 to 12, p=0.21987 b-rank test for bits 6 to 13, p=0.12382 b-rank test for bits 7 to 14, p=0.15127 b-rank test for bits 8 to 15, p=0.96335 b-rank test for bits 9 to 16, p=0.66483 b-rank test for bits 10 to 17, p=0.37147 b-rank test for bits 11 to 18, p=0.42654 b-rank test for bits 12 to 19, p=0.78024 b-rank test for bits 13 to 20, p=0.82003 b-rank test for bits 14 to 21, p=0.54862 b-rank test for bits 15 to 22, p=0.20006 b-rank test for bits 16 to 23, p=0.05022 b-rank test for bits 17 to 24, p=0.75379 b-rank test for bits 18 to 25, p=0.11926 b-rank test for bits 19 to 26, p=0.86171 b-rank test for bits 20 to 27, p=0.71237 b-rank test for bits 21 to 28, p=0.80547 b-rank test for bits 22 to 29, p=0.65538 b-rank test for bits 23 to 30, p=0.20815 b-rank test for bits 24 to 31, p=0.36674 b-rank test for bits 25 to 32, p=0.73775 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 = 0.869827 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-11-08_02:31 (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 141870 -0.09 0.463392 2 142135 0.53 0.700996 3 141649 -0.61 0.271512 4 142116 0.48 0.685407 5 141399 -1.19 0.116560 6 141919 0.02 0.509013 7 142141 0.54 0.705844 8 142663 1.76 0.960873 9 141630 -0.65 0.256994 10 141639 -0.63 0.263820 11 142792 2.06 0.980411 12 142025 0.27 0.606519 13 141639 -0.63 0.263820 14 142055 0.34 0.633204 15 141964 0.13 0.550820 16 142577 1.56 0.940617 17 142015 0.25 0.597504 18 142816 2.12 0.982929 19 141516 -0.92 0.179049 20 141778 -0.31 0.379480 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-11-08_02:31 Bits used No. missing words z-score p-value 23 to 32 141497 -1.4218 0.077538 22 to 31 141551 -1.2356 0.108300 21 to 30 142010 0.3471 0.635756 20 to 29 141775 -0.4632 0.321608 19 to 28 142121 0.7299 0.767273 18 to 27 141956 0.1609 0.563926 17 to 26 141705 -0.7046 0.240534 16 to 25 141776 -0.4598 0.322845 15 to 24 141713 -0.6770 0.249203 14 to 23 141782 -0.4391 0.330306 13 to 22 141772 -0.4736 0.317910 12 to 21 142229 1.1023 0.864837 11 to 20 142066 0.5402 0.705485 10 to 19 141901 -0.0287 0.488542 9 to 18 141905 -0.0149 0.494044 8 to 17 141439 -1.6218 0.052420 7 to 16 142047 0.4747 0.682508 6 to 15 141786 -0.4253 0.335318 5 to 14 141533 -1.2977 0.097197 4 to 13 141849 -0.2080 0.417601 3 to 12 141850 -0.2046 0.418948 2 to 11 142213 1.0471 0.852482 1 to 10 141866 -0.1494 0.440614 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-11-08_02:31 Bits used No. missing words z-score p-value 28 to 32 142045 0.4599 0.677205 27 to 31 142508 2.0294 0.978791 26 to 30 141656 -0.8587 0.195240 25 to 29 141766 -0.4859 0.313532 24 to 28 141746 -0.5537 0.289905 23 to 27 141951 0.1413 0.556166 22 to 26 142289 1.2870 0.900956 21 to 25 141968 0.1989 0.578822 20 to 24 142280 1.2565 0.895534 19 to 23 142392 1.6362 0.949098 18 to 22 142090 0.6124 0.729877 17 to 21 142214 1.0328 0.849147 16 to 20 141928 0.0633 0.525232 15 to 19 141800 -0.3706 0.355464 14 to 18 141733 -0.5977 0.275010 13 to 17 141619 -0.9842 0.162516 12 to 16 142072 0.5514 0.709328 11 to 15 142258 1.1819 0.881384 10 to 14 141461 -1.5198 0.064285 9 to 13 141707 -0.6859 0.246399 8 to 12 141670 -0.8113 0.208600 7 to 11 141710 -0.6757 0.249617 6 to 10 141929 0.0667 0.526581 5 to 9 141720 -0.6418 0.260503 4 to 8 141379 -1.7977 0.036110 3 to 7 141846 -0.2147 0.415009 2 to 6 141838 -0.2418 0.404469 1 to 5 141506 -1.3672 0.085778 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-11-08_02:31 Bits used No. missing words z-score p-value 31 to 32 142036 0.3737 0.645671 30 to 31 142344 1.2822 0.900116 29 to 30 142390 1.4179 0.921891 28 to 29 141560 -1.0305 0.151394 27 to 28 141559 -1.0334 0.150703 26 to 27 141554 -1.0482 0.147280 25 to 26 142045 0.4002 0.655498 24 to 25 142205 0.8722 0.808446 23 to 24 141578 -0.9774 0.164192 22 to 23 142196 0.8456 0.801122 21 to 22 141698 -0.6234 0.266513 20 to 21 141742 -0.4936 0.310795 19 to 20 141114 -2.3461 0.009485 18 to 19 142261 1.0374 0.850219 17 to 18 141630 -0.8240 0.204975 16 to 17 141938 0.0846 0.533699 15 to 16 141912 0.0079 0.503142 14 to 15 141369 -1.5939 0.055480 13 to 14 141776 -0.3933 0.347048 12 to 13 142139 0.6775 0.750953 11 to 12 142058 0.4386 0.669508 10 to 11 141802 -0.3166 0.375771 9 to 10 141686 -0.6588 0.255015 8 to 9 141275 -1.8712 0.030660 7 to 8 142025 0.3412 0.633527 6 to 7 142251 1.0079 0.843243 5 to 6 141939 0.0875 0.534872 4 to 5 141580 -0.9715 0.165656 3 to 4 141380 -1.5614 0.059209 2 to 3 142367 1.3501 0.911501 1 to 2 141915 0.0167 0.506672 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-11-08_02:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2427.88 -1.020 0.153870 Test results for specific bytes for dh-ranFile-2015-11-08_02:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2454.57 -0.642 0.260286 2 to 9 2609.57 1.549 0.939369 3 to 10 2506.74 0.095 0.537965 4 to 11 2329.72 -2.408 0.008018 5 to 12 2513.37 0.189 0.574980 6 to 13 2437.80 -0.880 0.189531 7 to 14 2586.60 1.225 0.889653 8 to 15 2502.00 0.028 0.511297 9 to 16 2533.32 0.471 0.681255 10 to 17 2463.45 -0.517 0.302615 11 to 18 2367.77 -1.870 0.030743 12 to 19 2415.59 -1.194 0.116301 13 to 20 2553.00 0.749 0.773211 14 to 21 2597.98 1.386 0.917067 15 to 22 2507.39 0.104 0.541606 16 to 23 2457.78 -0.597 0.275210 17 to 24 2548.92 0.692 0.755485 18 to 25 2507.25 0.103 0.540848 19 to 26 2507.41 0.105 0.541736 20 to 27 2422.15 -1.101 0.135444 21 to 28 2491.88 -0.115 0.454273 22 to 29 2420.33 -1.127 0.129930 23 to 30 2479.49 -0.290 0.385861 24 to 31 2518.37 0.260 0.602499 25 to 32 2545.98 0.650 0.742247 CDPARK for dh-ranFile-2015-11-08_02:31: 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 3565 1.9178 0.972432 3521 -0.0913 0.463617 3509 -0.6393 0.261324 3486 -1.6895 0.045562 3512 -0.5023 0.307734 3563 1.8265 0.966111 3545 1.0046 0.842447 3545 1.0046 0.842447 3521 -0.0913 0.463617 3536 0.5936 0.723613 Square side=100, avg. no. parked=3530.30 sample std.=23.80 p-value of the KSTEST for those 10 p-values: 0.428024 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-11-08_02:31 0.4249,0.6377,0.8042,0.9983,0.3762,0.5987,0.2756,0.6608,0.6077,0.7145, The KS test for those 10 p-values: 0.187579 The 3DSPHERES test for dh-ranFile-2015-11-08_02:31 sample no r^3 equiv. uni. 1 3.051 0.096707 2 18.868 0.466843 3 41.630 0.750341 4 41.792 0.751685 5 38.729 0.724998 6 2.906 0.092324 7 6.467 0.193912 8 6.459 0.193702 9 30.921 0.643238 10 0.844 0.027752 11 22.819 0.532635 12 7.188 0.213063 13 2.604 0.083144 14 1.843 0.059570 15 45.127 0.777815 16 15.279 0.399092 17 27.950 0.606097 18 2.396 0.076746 19 20.047 0.487383 20 17.928 0.449863 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.075434 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-11-08_02:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 -0.7 1.3 -0.7 0.0 0.4 1.1 -0.0 -1.2 0.2 0.3 -0.6 -1.2 0.8 -2.0 -0.3 0.9 -0.7 -0.9 -0.1 -1.0 0.2 2.1 1.5 1.7 -0.3 0.4 -0.0 1.5 -0.3 0.2 1.4 -0.4 1.0 -1.3 0.8 0.3 -1.0 -0.8 -0.1 -0.6 1.0 -1.1 Chi-square with 42 degrees of freedom:37.624121 z-score=-0.477448, p-value=0.336642 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-11-08_02:31 Test no p-value 1 0.847325 2 0.395463 3 0.309726 4 0.333548 5 0.002275 6 0.137613 7 0.880817 8 0.245611 9 0.002780 10 0.131671 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.026117 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-11-08_02:31: (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 66878 0.67 66623 0.03 3 25000.00 24900 0.40 25002 0.00 4 6666.67 6661 0.00 6676 0.01 5 1388.89 1287 7.47 1413 0.42 6 238.10 231 0.21 239 0.00 7 34.72 36 0.05 44 2.48 8 4.96 6 0.22 2 1.77 p=0.82789 p=0.41857 Number of rngs required: 687787, p-value: 0.238 RESULTS OF CRAPS TEST for dh-ranFile-2015-11-08_02:31 No. of wins: Observed Expected 98706 98585.9 z-score= 0.537, pvalue=0.70448 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66837 66666.7 0.435 0.435 2 37803 37654.3 0.587 1.022 3 26495 26954.7 7.841 8.863 4 19351 19313.5 0.073 8.936 5 13721 13851.4 1.228 10.164 6 10011 9943.5 0.458 10.622 7 7246 7145.0 1.427 12.049 8 5167 5139.1 0.152 12.201 9 3713 3699.9 0.047 12.247 10 2591 2666.3 2.126 14.374 11 1960 1923.3 0.699 15.073 12 1350 1388.7 1.081 16.154 13 1043 1003.7 1.538 17.691 14 729 726.1 0.011 17.702 15 518 525.8 0.117 17.819 16 420 381.2 3.960 21.779 17 270 276.5 0.155 21.934 18 207 200.8 0.190 22.123 19 150 146.0 0.110 22.234 20 114 106.2 0.571 22.804 21 304 287.1 0.993 23.797 Chisq= 23.80 for 20 degrees of freedom, p= 0.74864 SUMMARY of craptest p-value for no. of wins: 0.704484 p-value for throws/game: 0.748644 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-11-08_02:31 No. of wins: Observed Expected 98836 98585.9 z-score= 1.119, pvalue=0.86838 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66828 66666.7 0.390 0.390 2 37643 37654.3 0.003 0.394 3 26806 26954.7 0.821 1.215 4 19473 19313.5 1.318 2.532 5 13795 13851.4 0.230 2.762 6 9942 9943.5 0.000 2.762 7 7205 7145.0 0.503 3.266 8 4961 5139.1 6.170 9.436 9 3736 3699.9 0.353 9.789 10 2714 2666.3 0.853 10.643 11 1852 1923.3 2.645 13.288 12 1393 1388.7 0.013 13.301 13 982 1003.7 0.470 13.771 14 737 726.1 0.162 13.933 15 546 525.8 0.773 14.706 16 374 381.2 0.134 14.840 17 251 276.5 2.359 17.199 18 193 200.8 0.305 17.504 19 172 146.0 4.636 22.141 20 95 106.2 1.184 23.325 21 302 287.1 0.772 24.097 Chisq= 24.10 for 20 degrees of freedom, p= 0.76180 SUMMARY of craptest p-value for no. of wins: 0.868383 p-value for throws/game: 0.761804 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0023,0.0028,0.0080,0.0095,0.0191,0.0261,0.0278,0.0307,0.0307,0.0361, 0.0456,0.0502,0.0524,0.0555,0.0580,0.0592,0.0596,0.0643,0.0754,0.0767, 0.0775,0.0831,0.0858,0.0923,0.0967,0.0972,0.1083,0.1163,0.1166,0.1193, 0.1238,0.1276,0.1287,0.1299,0.1317,0.1354,0.1376,0.1473,0.1507,0.1513, 0.1514,0.1524,0.1539,0.1572,0.1625,0.1642,0.1657,0.1790,0.1876,0.1895, 0.1937,0.1939,0.1952,0.2001,0.2050,0.2082,0.2086,0.2131,0.2199,0.2385, 0.2405,0.2435,0.2456,0.2464,0.2492,0.2496,0.2550,0.2563,0.2570,0.2603, 0.2605,0.2613,0.2638,0.2638,0.2665,0.2715,0.2750,0.2752,0.2756,0.2757, 0.2899,0.3026,0.3077,0.3097,0.3108,0.3135,0.3179,0.3183,0.3216,0.3228, 0.3303,0.3335,0.3341,0.3353,0.3366,0.3470,0.3555,0.3667,0.3687,0.3715, 0.3758,0.3762,0.3768,0.3795,0.3859,0.3955,0.3991,0.4045,0.4150,0.4176, 0.4186,0.4189,0.4209,0.4249,0.4258,0.4265,0.4280,0.4406,0.4461,0.4499, 0.4543,0.4634,0.4636,0.4636,0.4668,0.4874,0.4885,0.4940,0.4995,0.5031, 0.5067,0.5090,0.5113,0.5216,0.5236,0.5241,0.5252,0.5266,0.5290,0.5326, 0.5337,0.5349,0.5380,0.5408,0.5416,0.5417,0.5465,0.5486,0.5487,0.5508, 0.5510,0.5562,0.5639,0.5690,0.5750,0.5788,0.5895,0.5969,0.5975,0.5987, 0.6008,0.6025,0.6061,0.6065,0.6077,0.6332,0.6335,0.6358,0.6377,0.6432, 0.6457,0.6533,0.6554,0.6555,0.6608,0.6648,0.6695,0.6751,0.6772,0.6813, 0.6825,0.6842,0.6854,0.6918,0.7010,0.7045,0.7055,0.7058,0.7093,0.7114, 0.7124,0.7145,0.7150,0.7236,0.7250,0.7299,0.7348,0.7377,0.7422,0.7486, 0.7503,0.7510,0.7517,0.7538,0.7555,0.7618,0.7673,0.7718,0.7732,0.7778, 0.7802,0.7898,0.7910,0.7974,0.8011,0.8023,0.8042,0.8049,0.8055,0.8065, 0.8084,0.8187,0.8200,0.8279,0.8339,0.8424,0.8424,0.8432,0.8454,0.8473, 0.8491,0.8502,0.8525,0.8549,0.8577,0.8617,0.8620,0.8648,0.8653,0.8684, 0.8698,0.8808,0.8814,0.8830,0.8864,0.8865,0.8897,0.8950,0.8955,0.9001, 0.9010,0.9115,0.9133,0.9171,0.9211,0.9219,0.9394,0.9406,0.9491,0.9609, 0.9634,0.9661,0.9665,0.9724,0.9788,0.9804,0.9829,0.9983,1.0000, Overall p-value after applying KStest on 269 p-values = 0.947744 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.