RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-03-20_10:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.77 15.3284 0.428162 2 to 25 15.60 31.8446 0.984269 3 to 26 15.51 29.4990 0.969807 4 to 27 15.98 15.3597 0.430408 5 to 28 15.84 7.7313 0.028041 6 to 29 15.99 6.0508 0.007162 7 to 30 15.99 13.9098 0.326527 8 to 31 15.69 17.2366 0.561552 9 to 32 15.45 26.5608 0.935169 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.198011 Tough bday spacings test for dh-ranFile-2016-03-20_10:31: 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 35 71 97 113 72 46 28 15 6 6 (O-E)^2/E 0.4 0.1 0.1 0.0 2.4 0.5 0.7 0.1 0.0 0.1 0.9 Birthday Spacings: Sum(O-E)^2/E= 5.200, p= 0.123 RESULTS OF GCD FOR dh-ranFile-2016-03-20_10:31 Euclid's algorithm: p-value, steps to gcd: 0.000929 p-value, dist. of gcd's: 0.114386 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-03-20_10:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.335 0.104 0.310 0.095 0.563 0.812 0.788 0.278 Bits 8 to 15---> 0.587 0.156 0.962 0.589 0.277 0.704 0.323 0.267 Bits 16 to 23---> 0.670 0.123 0.193 0.178 0.091 0.350 0.007 0.822 Bits 24 to 31---> 0.180 0.763 0.953 0.537 0.915 0.127 0.463 0.398 KS test for the above 32 p values: 0.688 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-03-20_10:31, p-values for 5 runs: 0.2403, 0.6217, 0.4984, 0.0097, 0.7692 Rank test for binary matrices (31x31) for dh-ranFile-2016-03-20_10:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 221 211.4 0.434 0.434 r= 29 5089 5134.0 0.395 0.829 r= 30 23259 23103.0 1.053 1.882 r= 31 11431 11551.5 1.257 3.139 chi-square = 3.139 with df = 3; p-value = 0.629 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-03-20_10:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 207 211.4 0.092 0.092 r= 30 5083 5134.0 0.507 0.599 r= 31 23066 23103.0 0.059 0.659 r= 32 11644 11551.5 0.740 1.399 chi-square = 1.399 with df = 3; p-value = 0.294 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-03-20_10:31 b-rank test for bits 1 to 8, p=0.10226 b-rank test for bits 2 to 9, p=0.20408 b-rank test for bits 3 to 10, p=0.52823 b-rank test for bits 4 to 11, p=0.65001 b-rank test for bits 5 to 12, p=0.20236 b-rank test for bits 6 to 13, p=0.59697 b-rank test for bits 7 to 14, p=0.04844 b-rank test for bits 8 to 15, p=0.51466 b-rank test for bits 9 to 16, p=0.75954 b-rank test for bits 10 to 17, p=0.67183 b-rank test for bits 11 to 18, p=0.92029 b-rank test for bits 12 to 19, p=0.24567 b-rank test for bits 13 to 20, p=0.63546 b-rank test for bits 14 to 21, p=0.21213 b-rank test for bits 15 to 22, p=0.44522 b-rank test for bits 16 to 23, p=0.39737 b-rank test for bits 17 to 24, p=0.50169 b-rank test for bits 18 to 25, p=0.76163 b-rank test for bits 19 to 26, p=0.80972 b-rank test for bits 20 to 27, p=0.29110 b-rank test for bits 21 to 28, p=0.27213 b-rank test for bits 22 to 29, p=0.92527 b-rank test for bits 23 to 30, p=0.56042 b-rank test for bits 24 to 31, p=0.55903 b-rank test for bits 25 to 32, p=0.41728 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 = 0.665023 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-03-20_10:31 (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 142244 0.78 0.782875 2 142244 0.78 0.782875 3 142619 1.66 0.951352 4 142538 1.47 0.929064 5 142201 0.68 0.752214 6 141734 -0.41 0.341032 7 141676 -0.55 0.292821 8 142400 1.15 0.874190 9 141773 -0.32 0.375042 10 141373 -1.25 0.105083 11 141331 -1.35 0.088310 12 141570 -0.79 0.213939 13 141393 -1.21 0.113836 14 141665 -0.57 0.284046 15 142414 1.18 0.880828 16 141818 -0.21 0.415512 17 141614 -0.69 0.245090 18 141858 -0.12 0.452269 19 141844 -0.15 0.439341 20 142385 1.11 0.866797 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-03-20_10:31 Bits used No. missing words z-score p-value 23 to 32 142051 0.4885 0.687408 22 to 31 141886 -0.0804 0.467940 21 to 30 142045 0.4678 0.680046 20 to 29 141711 -0.6839 0.247020 19 to 28 141695 -0.7391 0.229933 18 to 27 141796 -0.3908 0.347975 17 to 26 142199 0.9989 0.841069 16 to 25 141866 -0.1494 0.440614 15 to 24 142325 1.4333 0.924120 14 to 23 142458 1.8920 0.970752 13 to 22 142504 2.0506 0.979846 12 to 21 141960 0.1747 0.569352 11 to 20 141980 0.2437 0.596264 10 to 19 141784 -0.4322 0.332808 9 to 18 142580 2.3127 0.989629 8 to 17 142007 0.3368 0.631864 7 to 16 141933 0.0816 0.532526 6 to 15 141715 -0.6701 0.251396 5 to 14 142032 0.4230 0.663852 4 to 13 141480 -1.4804 0.069377 3 to 12 142073 0.5644 0.713752 2 to 11 142172 0.9058 0.817468 1 to 10 141881 -0.0977 0.461089 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-03-20_10:31 Bits used No. missing words z-score p-value 28 to 32 141580 -1.1164 0.132131 27 to 31 141923 0.0463 0.518480 26 to 30 141625 -0.9638 0.167565 25 to 29 142009 0.3379 0.632267 24 to 28 141883 -0.0893 0.464440 23 to 27 142057 0.5006 0.691665 22 to 26 141912 0.0091 0.503611 21 to 25 141693 -0.7333 0.231681 20 to 24 142137 0.7718 0.779873 19 to 23 142131 0.7514 0.773801 18 to 22 141574 -1.1367 0.127829 17 to 21 141916 0.0226 0.509019 16 to 20 142146 0.8023 0.788802 15 to 19 141843 -0.2248 0.411049 14 to 18 142104 0.6599 0.745341 13 to 17 141756 -0.5198 0.301615 12 to 16 141852 -0.1943 0.422955 11 to 15 141883 -0.0893 0.464440 10 to 14 141555 -1.2011 0.114853 9 to 13 142354 1.5074 0.934140 8 to 12 141513 -1.3435 0.089556 7 to 11 141758 -0.5130 0.303982 6 to 10 141899 -0.0350 0.486033 5 to 9 141814 -0.3232 0.373290 4 to 8 141471 -1.4859 0.068658 3 to 7 141979 0.2362 0.593349 2 to 6 141940 0.1040 0.541402 1 to 5 142002 0.3141 0.623291 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-03-20_10:31 Bits used No. missing words z-score p-value 31 to 32 141816 -0.2753 0.391539 30 to 31 141994 0.2498 0.598615 29 to 30 142199 0.8545 0.803582 28 to 29 142736 2.4386 0.992627 27 to 28 141628 -0.8299 0.203303 26 to 27 142157 0.7306 0.767485 25 to 26 141694 -0.6352 0.262652 24 to 25 141515 -1.1632 0.122371 23 to 24 141510 -1.1780 0.119405 22 to 23 141875 -0.1013 0.459669 21 to 22 142361 1.3324 0.908629 20 to 21 142106 0.5801 0.719092 19 to 20 142096 0.5506 0.709063 18 to 19 141733 -0.5201 0.301480 17 to 18 141891 -0.0541 0.478439 16 to 17 142028 0.3501 0.636853 15 to 16 142097 0.5536 0.710073 14 to 15 142114 0.6037 0.726994 13 to 14 142096 0.5506 0.709063 12 to 13 142514 1.7837 0.962763 11 to 12 141720 -0.5585 0.288253 10 to 11 141912 0.0079 0.503142 9 to 10 142438 1.5595 0.940561 8 to 9 142043 0.3943 0.653323 7 to 8 141871 -0.1131 0.454988 6 to 7 141782 -0.3756 0.353605 5 to 6 141854 -0.1632 0.435174 4 to 5 141262 -1.9095 0.028097 3 to 4 141146 -2.2517 0.012170 2 to 3 141461 -1.3225 0.093000 1 to 2 142593 2.0167 0.978138 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-03-20_10:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2589.99 1.273 0.898417 Test results for specific bytes for dh-ranFile-2016-03-20_10:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2460.54 -0.558 0.288393 2 to 9 2448.37 -0.730 0.232656 3 to 10 2416.53 -1.180 0.118916 4 to 11 2429.48 -0.997 0.159304 5 to 12 2526.29 0.372 0.644953 6 to 13 2505.26 0.074 0.529653 7 to 14 2478.70 -0.301 0.381617 8 to 15 2571.26 1.008 0.843229 9 to 16 2415.11 -1.201 0.114960 10 to 17 2435.35 -0.914 0.180278 11 to 18 2480.01 -0.283 0.388702 12 to 19 2557.73 0.816 0.792855 13 to 20 2646.97 2.078 0.981167 14 to 21 2456.73 -0.612 0.270285 15 to 22 2398.07 -1.441 0.074722 16 to 23 2501.54 0.022 0.508660 17 to 24 2611.69 1.580 0.942894 18 to 25 2351.44 -2.101 0.017822 19 to 26 2511.89 0.168 0.566744 20 to 27 2505.54 0.078 0.531209 21 to 28 2425.23 -1.057 0.145156 22 to 29 2508.86 0.125 0.549841 23 to 30 2576.12 1.076 0.859135 24 to 31 2632.47 1.873 0.969499 25 to 32 2554.12 0.765 0.777972 CDPARK for dh-ranFile-2016-03-20_10:31: 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 3533 0.4566 0.676028 3495 -1.2785 0.100530 3508 -0.6849 0.246694 3533 0.4566 0.676028 3554 1.4155 0.921543 3527 0.1826 0.572463 3474 -2.2374 0.012629 3501 -1.0046 0.157553 3520 -0.1370 0.445521 3467 -2.5571 0.005278 Square side=100, avg. no. parked=3511.20 sample std.=26.12 p-value of the KSTEST for those 10 p-values: 0.161060 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-03-20_10:31 0.3348,0.8059,0.1031,0.7023,0.3949,0.5960,0.3656,0.4400,0.0531,0.0079, The KS test for those 10 p-values: 0.271898 The 3DSPHERES test for dh-ranFile-2016-03-20_10:31 sample no r^3 equiv. uni. 1 0.845 0.027768 2 48.416 0.800886 3 18.819 0.465960 4 35.825 0.697044 5 35.900 0.697805 6 3.006 0.095345 7 11.888 0.327182 8 80.535 0.931745 9 65.506 0.887356 10 4.351 0.134994 11 5.258 0.160758 12 18.629 0.462583 13 3.148 0.099609 14 19.563 0.479057 15 34.284 0.681078 16 23.314 0.540271 17 3.685 0.115599 18 6.807 0.202998 19 50.763 0.815871 20 62.302 0.874660 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.829551 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-03-20_10:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 2.2 0.1 0.0 -2.4 1.4 -0.5 0.6 0.6 -0.1 -0.5 -1.4 -0.0 0.5 1.3 -0.5 -1.5 -0.6 1.1 0.2 -0.7 -1.3 0.7 0.9 1.0 0.1 -0.5 1.4 -0.8 1.4 0.5 0.2 0.6 -0.9 0.8 -0.5 1.9 -1.0 0.1 0.4 -1.3 -1.0 -0.1 Chi-square with 42 degrees of freedom:43.665150 z-score=0.181683, p-value=0.599449 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-03-20_10:31 Test no p-value 1 0.006770 2 0.151072 3 0.053903 4 0.586473 5 0.761510 6 0.301834 7 0.428399 8 0.972931 9 0.077992 10 0.977425 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.227622 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-03-20_10:31: (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 66746 0.09 66867 0.60 3 25000.00 24951 0.10 24809 1.46 4 6666.67 6628 0.22 6654 0.02 5 1388.89 1405 0.19 1410 0.32 6 238.10 228 0.43 227 0.52 7 34.72 32 0.21 30 0.64 8 4.96 9 3.29 2 1.77 p=0.39511 p=0.49792 Number of rngs required: 688922, p-value: 0.725 RESULTS OF CRAPS TEST for dh-ranFile-2016-03-20_10:31 No. of wins: Observed Expected 98870 98585.9 z-score= 1.271, pvalue=0.89811 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66529 66666.7 0.284 0.284 2 37713 37654.3 0.091 0.376 3 26932 26954.7 0.019 0.395 4 19340 19313.5 0.036 0.431 5 14030 13851.4 2.302 2.734 6 9890 9943.5 0.288 3.022 7 7191 7145.0 0.296 3.318 8 5183 5139.1 0.375 3.693 9 3603 3699.9 2.536 6.229 10 2651 2666.3 0.088 6.317 11 1894 1923.3 0.447 6.764 12 1361 1388.7 0.554 7.318 13 1017 1003.7 0.176 7.494 14 705 726.1 0.615 8.110 15 498 525.8 1.474 9.583 16 417 381.2 3.372 12.955 17 280 276.5 0.043 12.998 18 210 200.8 0.419 13.417 19 142 146.0 0.109 13.526 20 104 106.2 0.046 13.572 21 310 287.1 1.824 15.396 Chisq= 15.40 for 20 degrees of freedom, p= 0.24670 SUMMARY of craptest p-value for no. of wins: 0.898108 p-value for throws/game: 0.246703 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-03-20_10:31 No. of wins: Observed Expected 98834 98585.9 z-score= 1.110, pvalue=0.86646 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66717 66666.7 0.038 0.038 2 37866 37654.3 1.190 1.228 3 27312 26954.7 4.735 5.963 4 19178 19313.5 0.950 6.913 5 13602 13851.4 4.491 11.405 6 10000 9943.5 0.321 11.725 7 7160 7145.0 0.031 11.757 8 5164 5139.1 0.121 11.878 9 3652 3699.9 0.619 12.497 10 2467 2666.3 14.897 27.394 11 1905 1923.3 0.175 27.568 12 1291 1388.7 6.879 34.447 13 981 1003.7 0.514 34.961 14 743 726.1 0.391 35.353 15 548 525.8 0.934 36.287 16 389 381.2 0.162 36.449 17 299 276.5 1.824 38.273 18 176 200.8 3.070 41.343 19 154 146.0 0.440 41.783 20 110 106.2 0.135 41.918 21 286 287.1 0.004 41.922 Chisq= 41.92 for 20 degrees of freedom, p= 0.99717 SUMMARY of craptest p-value for no. of wins: 0.866465 p-value for throws/game: 0.997169 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0009,0.0053,0.0067,0.0068,0.0072,0.0079,0.0097,0.0122,0.0126,0.0178, 0.0278,0.0280,0.0281,0.0484,0.0531,0.0539,0.0687,0.0694,0.0747,0.0780, 0.0883,0.0896,0.0910,0.0930,0.0952,0.0953,0.0996,0.1005,0.1023,0.1031, 0.1036,0.1051,0.1138,0.1144,0.1149,0.1150,0.1156,0.1189,0.1194,0.1224, 0.1226,0.1232,0.1265,0.1278,0.1321,0.1350,0.1452,0.1511,0.1555,0.1576, 0.1593,0.1608,0.1611,0.1676,0.1783,0.1796,0.1803,0.1925,0.1980,0.2024, 0.2030,0.2033,0.2041,0.2121,0.2139,0.2276,0.2299,0.2317,0.2327,0.2403, 0.2451,0.2457,0.2467,0.2467,0.2470,0.2514,0.2627,0.2671,0.2703,0.2719, 0.2721,0.2775,0.2777,0.2840,0.2883,0.2884,0.2911,0.2928,0.2942,0.3015, 0.3016,0.3018,0.3040,0.3105,0.3229,0.3265,0.3272,0.3328,0.3348,0.3353, 0.3410,0.3480,0.3501,0.3536,0.3656,0.3733,0.3750,0.3816,0.3887,0.3915, 0.3949,0.3951,0.3974,0.3975,0.4110,0.4155,0.4173,0.4230,0.4282,0.4284, 0.4304,0.4352,0.4393,0.4400,0.4406,0.4452,0.4455,0.4523,0.4550,0.4597, 0.4611,0.4626,0.4633,0.4644,0.4644,0.4660,0.4679,0.4784,0.4791,0.4860, 0.4979,0.4984,0.5017,0.5031,0.5036,0.5087,0.5090,0.5147,0.5185,0.5282, 0.5297,0.5312,0.5325,0.5367,0.5403,0.5414,0.5498,0.5590,0.5604,0.5616, 0.5635,0.5667,0.5694,0.5725,0.5865,0.5868,0.5886,0.5933,0.5960,0.5963, 0.5970,0.5986,0.5994,0.6217,0.6233,0.6293,0.6319,0.6323,0.6355,0.6369, 0.6450,0.6500,0.6533,0.6639,0.6650,0.6702,0.6718,0.6760,0.6760,0.6800, 0.6811,0.6874,0.6878,0.6917,0.6970,0.6978,0.7023,0.7045,0.7091,0.7091, 0.7101,0.7138,0.7191,0.7253,0.7270,0.7453,0.7522,0.7595,0.7615,0.7616, 0.7629,0.7675,0.7692,0.7738,0.7780,0.7799,0.7829,0.7829,0.7875,0.7888, 0.7929,0.8009,0.8036,0.8059,0.8097,0.8121,0.8159,0.8175,0.8224,0.8296, 0.8411,0.8432,0.8591,0.8665,0.8668,0.8742,0.8747,0.8808,0.8874,0.8981, 0.8984,0.9086,0.9154,0.9203,0.9215,0.9241,0.9253,0.9291,0.9317,0.9341, 0.9352,0.9406,0.9429,0.9514,0.9531,0.9617,0.9628,0.9695,0.9698,0.9708, 0.9729,0.9774,0.9781,0.9798,0.9812,0.9843,0.9896,0.9926,0.9972, Overall p-value after applying KStest on 269 p-values = 0.416241 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.