RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-03-03_08:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.85 7.6225 0.026033 2 to 25 15.70 22.5065 0.833985 3 to 26 15.72 18.5713 0.646316 4 to 27 15.59 11.8943 0.193505 5 to 28 15.73 13.2849 0.283088 6 to 29 15.80 21.3763 0.790090 7 to 30 15.72 13.1435 0.273474 8 to 31 15.90 15.5674 0.445320 9 to 32 15.69 24.9163 0.903401 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.979227 Tough bday spacings test for dh-ranFile-2016-03-03_08:31: 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 8 30 70 90 114 80 51 35 14 4 4 (O-E)^2/E 0.1 1.2 0.1 0.6 2.7 0.0 0.0 0.9 0.1 1.0 0.0 Birthday Spacings: Sum(O-E)^2/E= 6.896, p= 0.265 RESULTS OF GCD FOR dh-ranFile-2016-03-03_08:31 Euclid's algorithm: p-value, steps to gcd: 0.990049 p-value, dist. of gcd's: 0.139780 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-03-03_08:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.747 0.161 0.761 0.690 0.231 0.786 0.402 0.325 Bits 8 to 15---> 0.114 0.316 0.087 0.834 0.862 0.404 0.306 0.018 Bits 16 to 23---> 0.176 0.306 0.532 0.200 0.730 0.928 0.293 0.319 Bits 24 to 31---> 0.517 0.232 0.377 0.914 0.556 0.451 0.785 0.488 KS test for the above 32 p values: 0.449 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-03-03_08:31, p-values for 5 runs: 0.3696, 0.3935, 0.0580, 0.0503, 0.3672 Rank test for binary matrices (31x31) for dh-ranFile-2016-03-03_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 198 211.4 0.852 0.852 r= 29 5267 5134.0 3.445 4.297 r= 30 23129 23103.0 0.029 4.326 r= 31 11406 11551.5 1.833 6.159 chi-square = 6.159 with df = 3; p-value = 0.896 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-03-03_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 187 211.4 2.820 2.820 r= 30 5227 5134.0 1.684 4.504 r= 31 23074 23103.0 0.037 4.541 r= 32 11512 11551.5 0.135 4.676 chi-square = 4.676 with df = 3; p-value = 0.803 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-03-03_08:31 b-rank test for bits 1 to 8, p=0.76709 b-rank test for bits 2 to 9, p=0.80559 b-rank test for bits 3 to 10, p=0.83101 b-rank test for bits 4 to 11, p=0.15555 b-rank test for bits 5 to 12, p=0.54812 b-rank test for bits 6 to 13, p=0.67278 b-rank test for bits 7 to 14, p=0.22261 b-rank test for bits 8 to 15, p=0.54518 b-rank test for bits 9 to 16, p=0.33335 b-rank test for bits 10 to 17, p=0.63665 b-rank test for bits 11 to 18, p=0.28773 b-rank test for bits 12 to 19, p=0.05916 b-rank test for bits 13 to 20, p=0.94975 b-rank test for bits 14 to 21, p=0.69186 b-rank test for bits 15 to 22, p=0.82684 b-rank test for bits 16 to 23, p=0.48129 b-rank test for bits 17 to 24, p=0.16545 b-rank test for bits 18 to 25, p=0.23735 b-rank test for bits 19 to 26, p=0.42806 b-rank test for bits 20 to 27, p=0.17778 b-rank test for bits 21 to 28, p=0.77394 b-rank test for bits 22 to 29, p=0.15036 b-rank test for bits 23 to 30, p=0.44301 b-rank test for bits 24 to 31, p=0.05141 b-rank test for bits 25 to 32, p=0.21691 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 = 0.695274 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-03-03_08:31 (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 142254 0.81 0.789678 2 141817 -0.22 0.414601 3 142131 0.52 0.697743 4 141866 -0.10 0.459681 5 141829 -0.19 0.425561 6 141928 0.04 0.517397 7 142035 0.29 0.615476 8 141604 -0.71 0.237803 9 142291 0.89 0.813737 10 142392 1.13 0.870284 11 142078 0.39 0.653242 12 142251 0.80 0.787650 13 141828 -0.19 0.424645 14 142059 0.35 0.636717 15 142129 0.51 0.696111 16 141682 -0.53 0.297659 17 141636 -0.64 0.261535 18 141617 -0.68 0.247299 19 141992 0.19 0.576581 20 141918 0.02 0.508081 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-03-03_08:31 Bits used No. missing words z-score p-value 23 to 32 141722 -0.6460 0.259151 22 to 31 141745 -0.5667 0.285474 21 to 30 141815 -0.3253 0.372486 20 to 29 142554 2.2230 0.986892 19 to 28 141964 0.1885 0.574764 18 to 27 142203 1.0127 0.844388 17 to 26 142097 0.6471 0.741229 16 to 25 142080 0.5885 0.721907 15 to 24 141965 0.1920 0.576115 14 to 23 142211 1.0402 0.850886 13 to 22 141242 -2.3011 0.010692 12 to 21 141785 -0.4287 0.334062 11 to 20 142097 0.6471 0.741229 10 to 19 141779 -0.4494 0.326567 9 to 18 142427 1.7851 0.962875 8 to 17 141887 -0.0770 0.469312 7 to 16 141123 -2.7115 0.003349 6 to 15 141885 -0.0839 0.466569 5 to 14 141627 -0.9736 0.165140 4 to 13 142219 1.0678 0.857201 3 to 12 141941 0.1092 0.543481 2 to 11 141710 -0.6873 0.245933 1 to 10 142252 1.1816 0.881322 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-03-03_08:31 Bits used No. missing words z-score p-value 28 to 32 141872 -0.1265 0.449651 27 to 31 141856 -0.1808 0.428270 26 to 30 142127 0.7379 0.769702 25 to 29 141741 -0.5706 0.284132 24 to 28 141854 -0.1876 0.425611 23 to 27 141526 -1.2994 0.096899 22 to 26 141880 -0.0994 0.460401 21 to 25 142235 1.1040 0.865196 20 to 24 141712 -0.6689 0.251775 19 to 23 141664 -0.8316 0.202810 18 to 22 141984 0.2531 0.599912 17 to 21 141809 -0.3401 0.366890 16 to 20 141836 -0.2486 0.401844 15 to 19 141855 -0.1842 0.426940 14 to 18 142067 0.5345 0.703493 13 to 17 141732 -0.6011 0.273881 12 to 16 141913 0.0124 0.504963 11 to 15 141942 0.1107 0.544091 10 to 14 142046 0.4633 0.678421 9 to 13 141446 -1.5706 0.058137 8 to 12 141841 -0.2316 0.408414 7 to 11 141789 -0.4079 0.341674 6 to 10 142144 0.7955 0.786836 5 to 9 142228 1.0802 0.859982 4 to 8 141839 -0.2384 0.405783 3 to 7 142080 0.5785 0.718551 2 to 6 142076 0.5650 0.713957 1 to 5 141365 -1.8452 0.032505 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-03-03_08:31 Bits used No. missing words z-score p-value 31 to 32 142237 0.9666 0.833123 30 to 31 141533 -1.1101 0.133474 29 to 30 142642 2.1613 0.984663 28 to 29 142309 1.1790 0.880794 27 to 28 141504 -1.1957 0.115914 26 to 27 142056 0.4327 0.667367 25 to 26 141740 -0.4995 0.308714 24 to 25 141935 0.0757 0.530180 23 to 24 141992 0.2439 0.596332 22 to 23 141664 -0.7237 0.234629 21 to 22 142077 0.4946 0.689559 20 to 21 142306 1.1701 0.879023 19 to 20 141929 0.0580 0.523135 18 to 19 141749 -0.4729 0.318125 17 to 18 141779 -0.3845 0.350321 16 to 17 142100 0.5624 0.713095 15 to 16 141920 0.0315 0.512555 14 to 15 141413 -1.4641 0.071583 13 to 14 142050 0.4150 0.660913 12 to 13 142364 1.3412 0.910074 11 to 12 141409 -1.4759 0.069985 10 to 11 141920 0.0315 0.512555 9 to 10 142108 0.5860 0.721078 8 to 9 141986 0.2262 0.589464 7 to 8 141391 -1.5290 0.063133 6 to 7 141217 -2.0423 0.020562 5 to 6 141383 -1.5526 0.060260 4 to 5 141516 -1.1603 0.122970 3 to 4 141468 -1.3019 0.096482 2 to 3 141842 -0.1986 0.421283 1 to 2 142055 0.4297 0.666295 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-03-03_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2483.00 -0.240 0.405025 Test results for specific bytes for dh-ranFile-2016-03-03_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2546.12 0.652 0.742872 2 to 9 2554.68 0.773 0.780324 3 to 10 2652.93 2.163 0.984718 4 to 11 2538.31 0.542 0.706034 5 to 12 2479.94 -0.284 0.388327 6 to 13 2413.27 -1.227 0.109985 7 to 14 2410.21 -1.270 0.102068 8 to 15 2422.51 -1.096 0.136575 9 to 16 2549.30 0.697 0.757175 10 to 17 2447.06 -0.749 0.227032 11 to 18 2447.86 -0.737 0.230455 12 to 19 2471.71 -0.400 0.344573 13 to 20 2403.99 -1.358 0.087272 14 to 21 2578.52 1.110 0.866604 15 to 22 2357.99 -2.008 0.022306 16 to 23 2392.03 -1.527 0.063387 17 to 24 2575.32 1.065 0.856595 18 to 25 2579.78 1.128 0.870397 19 to 26 2492.35 -0.108 0.456938 20 to 27 2515.23 0.215 0.585253 21 to 28 2522.93 0.324 0.627113 22 to 29 2541.47 0.586 0.721216 23 to 30 2537.88 0.536 0.703911 24 to 31 2600.91 1.427 0.923224 25 to 32 2487.15 -0.182 0.427912 CDPARK for dh-ranFile-2016-03-03_08:31: 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 3506 -0.7763 0.218799 3519 -0.1826 0.427537 3490 -1.5068 0.065925 3488 -1.5982 0.055002 3519 -0.1826 0.427537 3551 1.2785 0.899470 3520 -0.1370 0.445521 3506 -0.7763 0.218799 3507 -0.7306 0.232514 3570 2.1461 0.984068 Square side=100, avg. no. parked=3517.60 sample std.=24.27 p-value of the KSTEST for those 10 p-values: 0.266936 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-03-03_08:31 0.5602,0.7665,0.9022,0.7154,0.1485,0.4948,0.8815,0.6651,0.0438,0.7146, The KS test for those 10 p-values: 0.423710 The 3DSPHERES test for dh-ranFile-2016-03-03_08:31 sample no r^3 equiv. uni. 1 57.732 0.854038 2 12.340 0.337241 3 27.768 0.603712 4 4.966 0.152559 5 3.287 0.103781 6 16.386 0.420849 7 2.146 0.069023 8 81.793 0.934548 9 43.165 0.762797 10 31.104 0.645418 11 12.852 0.348452 12 14.337 0.379913 13 26.141 0.581625 14 23.464 0.542570 15 39.567 0.732572 16 55.486 0.842687 17 35.523 0.693974 18 5.609 0.170526 19 3.564 0.112002 20 0.662 0.021838 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.898705 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-03-03_08:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -1.2 -0.1 0.6 1.0 2.4 -1.7 -1.3 -0.5 -1.3 -0.9 -0.2 0.5 -0.9 -0.2 0.1 1.6 0.7 -0.4 -0.3 0.5 -0.6 -0.4 -0.1 0.4 0.4 0.6 -0.1 0.2 0.9 2.0 -0.8 -1.1 2.0 -0.8 1.3 -1.2 -1.3 -1.6 -0.1 0.9 3.0 -0.1 Chi-square with 42 degrees of freedom:50.581467 z-score=0.936315, p-value=0.829165 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-03-03_08:31 Test no p-value 1 0.009048 2 0.047243 3 0.862575 4 0.046017 5 0.226902 6 0.138894 7 0.253778 8 0.039414 9 0.625571 10 0.138194 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.001720 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-03-03_08:31: (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 66626 0.02 66596 0.07 3 25000.00 24975 0.03 25112 0.50 4 6666.67 6734 0.68 6630 0.20 5 1388.89 1386 0.01 1394 0.02 6 238.10 247 0.33 225 0.72 7 34.72 27 1.72 35 0.00 8 4.96 4 0.19 7 0.84 p=0.18755 p=0.11607 Number of rngs required: 688907, p-value: 0.719 RESULTS OF CRAPS TEST for dh-ranFile-2016-03-03_08:31 No. of wins: Observed Expected 98984 98585.9 z-score= 1.781, pvalue=0.96252 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66704 66666.7 0.021 0.021 2 37376 37654.3 2.057 2.078 3 26827 26954.7 0.605 2.683 4 19473 19313.5 1.318 4.001 5 14005 13851.4 1.703 5.704 6 9946 9943.5 0.001 5.705 7 7154 7145.0 0.011 5.716 8 5158 5139.1 0.070 5.786 9 3721 3699.9 0.121 5.906 10 2668 2666.3 0.001 5.908 11 1911 1923.3 0.079 5.987 12 1416 1388.7 0.535 6.522 13 974 1003.7 0.880 7.401 14 697 726.1 1.169 8.571 15 560 525.8 2.220 10.790 16 393 381.2 0.368 11.159 17 260 276.5 0.989 12.148 18 209 200.8 0.332 12.480 19 139 146.0 0.334 12.815 20 105 106.2 0.014 12.828 21 304 287.1 0.993 13.822 Chisq= 13.82 for 20 degrees of freedom, p= 0.16058 SUMMARY of craptest p-value for no. of wins: 0.962521 p-value for throws/game: 0.160575 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-03-03_08:31 No. of wins: Observed Expected 98643 98585.9 z-score= 0.256, pvalue=0.60086 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66981 66666.7 1.482 1.482 2 37573 37654.3 0.176 1.658 3 26725 26954.7 1.958 3.616 4 19171 19313.5 1.051 4.667 5 13663 13851.4 2.563 7.230 6 9974 9943.5 0.093 7.323 7 7249 7145.0 1.513 8.836 8 5210 5139.1 0.979 9.815 9 3735 3699.9 0.334 10.149 10 2722 2666.3 1.164 11.312 11 1893 1923.3 0.478 11.790 12 1373 1388.7 0.178 11.969 13 1021 1003.7 0.298 12.267 14 758 726.1 1.398 13.664 15 539 525.8 0.330 13.994 16 366 381.2 0.602 14.596 17 302 276.5 2.344 16.940 18 223 200.8 2.447 19.388 19 121 146.0 4.276 23.664 20 107 106.2 0.006 23.669 21 294 287.1 0.165 23.835 Chisq= 23.83 for 20 degrees of freedom, p= 0.75031 SUMMARY of craptest p-value for no. of wins: 0.600858 p-value for throws/game: 0.750306 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0017,0.0033,0.0090,0.0107,0.0178,0.0206,0.0218,0.0223,0.0260,0.0325, 0.0394,0.0438,0.0460,0.0472,0.0503,0.0514,0.0550,0.0580,0.0581,0.0592, 0.0603,0.0631,0.0634,0.0659,0.0690,0.0700,0.0716,0.0873,0.0874,0.0965, 0.0969,0.1021,0.1038,0.1100,0.1120,0.1141,0.1159,0.1161,0.1230,0.1335, 0.1366,0.1382,0.1389,0.1398,0.1485,0.1504,0.1526,0.1556,0.1606,0.1609, 0.1651,0.1654,0.1705,0.1763,0.1778,0.1875,0.1935,0.2003,0.2028,0.2169, 0.2188,0.2188,0.2226,0.2269,0.2270,0.2305,0.2310,0.2320,0.2325,0.2346, 0.2374,0.2378,0.2459,0.2473,0.2518,0.2538,0.2592,0.2615,0.2647,0.2669, 0.2735,0.2739,0.2831,0.2841,0.2855,0.2877,0.2929,0.2977,0.3057,0.3063, 0.3087,0.3161,0.3181,0.3194,0.3250,0.3266,0.3334,0.3341,0.3372,0.3417, 0.3446,0.3485,0.3503,0.3669,0.3672,0.3696,0.3725,0.3773,0.3799,0.3883, 0.3935,0.4018,0.4020,0.4038,0.4050,0.4058,0.4084,0.4146,0.4208,0.4213, 0.4237,0.4246,0.4256,0.4256,0.4269,0.4275,0.4275,0.4279,0.4281,0.4283, 0.4430,0.4453,0.4455,0.4485,0.4497,0.4506,0.4569,0.4597,0.4604,0.4666, 0.4693,0.4813,0.4881,0.4948,0.5050,0.5081,0.5126,0.5126,0.5174,0.5174, 0.5231,0.5302,0.5316,0.5426,0.5435,0.5441,0.5452,0.5481,0.5558,0.5602, 0.5748,0.5761,0.5766,0.5816,0.5853,0.5895,0.5963,0.5999,0.6009,0.6037, 0.6155,0.6256,0.6271,0.6367,0.6367,0.6454,0.6463,0.6532,0.6609,0.6651, 0.6663,0.6674,0.6728,0.6784,0.6896,0.6897,0.6919,0.6940,0.6953,0.6961, 0.6977,0.7035,0.7039,0.7060,0.7131,0.7140,0.7146,0.7154,0.7186,0.7194, 0.7211,0.7212,0.7219,0.7296,0.7326,0.7412,0.7412,0.7429,0.7470,0.7503, 0.7572,0.7609,0.7628,0.7665,0.7671,0.7697,0.7739,0.7803,0.7851,0.7857, 0.7868,0.7877,0.7897,0.7901,0.8029,0.8056,0.8137,0.8268,0.8292,0.8310, 0.8331,0.8339,0.8340,0.8427,0.8444,0.8509,0.8540,0.8566,0.8572,0.8600, 0.8622,0.8626,0.8652,0.8666,0.8703,0.8704,0.8790,0.8808,0.8813,0.8815, 0.8959,0.8987,0.8995,0.9022,0.9034,0.9101,0.9141,0.9232,0.9285,0.9345, 0.9497,0.9625,0.9629,0.9792,0.9841,0.9847,0.9847,0.9869,0.9900, Overall p-value after applying KStest on 269 p-values = 0.259606 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.