RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-07-06_04:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.96 15.4495 0.436862 2 to 25 15.65 11.6930 0.181643 3 to 26 15.80 36.7675 0.996382 4 to 27 15.70 15.3273 0.428083 5 to 28 15.71 19.3146 0.689222 6 to 29 15.65 19.3324 0.690212 7 to 30 15.84 23.7255 0.872912 8 to 31 15.70 19.3060 0.688745 9 to 32 15.76 14.0327 0.335217 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.430838 Tough bday spacings test for dh-ranFile-2015-07-06_04:31: 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 50 72 92 89 71 55 34 8 13 2 (O-E)^2/E 2.6 4.9 0.0 0.3 0.8 0.7 0.2 0.6 3.2 6.2 1.0 Birthday Spacings: Sum(O-E)^2/E= 20.376, p= 0.974 RESULTS OF GCD FOR dh-ranFile-2015-07-06_04:31 Euclid's algorithm: p-value, steps to gcd: 0.274780 p-value, dist. of gcd's: 0.324480 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-07-06_04:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.220 0.840 0.229 0.805 0.714 0.754 0.652 0.492 Bits 8 to 15---> 0.539 0.538 0.398 0.803 0.889 0.592 0.632 0.045 Bits 16 to 23---> 0.840 0.454 0.989 0.020 0.843 0.503 0.167 0.666 Bits 24 to 31---> 0.569 0.078 0.283 0.191 0.906 0.688 0.623 0.672 KS test for the above 32 p values: 0.600 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-07-06_04:31, p-values for 5 runs: 0.0790, 0.8313, 0.3643, 0.0953, 0.8530 Rank test for binary matrices (31x31) for dh-ranFile-2015-07-06_04:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 207 211.4 0.092 0.092 r= 29 5067 5134.0 0.875 0.967 r= 30 23025 23103.0 0.264 1.231 r= 31 11701 11551.5 1.934 3.165 chi-square = 3.165 with df = 3; p-value = 0.633 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-07-06_04:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 229 211.4 1.462 1.462 r= 30 5150 5134.0 0.050 1.512 r= 31 23081 23103.0 0.021 1.533 r= 32 11540 11551.5 0.011 1.544 chi-square = 1.544 with df = 3; p-value = 0.328 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-07-06_04:31 b-rank test for bits 1 to 8, p=0.88419 b-rank test for bits 2 to 9, p=0.63295 b-rank test for bits 3 to 10, p=0.94655 b-rank test for bits 4 to 11, p=0.55019 b-rank test for bits 5 to 12, p=0.04291 b-rank test for bits 6 to 13, p=0.41936 b-rank test for bits 7 to 14, p=0.60273 b-rank test for bits 8 to 15, p=0.37361 b-rank test for bits 9 to 16, p=0.63514 b-rank test for bits 10 to 17, p=0.52436 b-rank test for bits 11 to 18, p=0.62445 b-rank test for bits 12 to 19, p=0.90539 b-rank test for bits 13 to 20, p=0.25454 b-rank test for bits 14 to 21, p=0.48121 b-rank test for bits 15 to 22, p=0.47912 b-rank test for bits 16 to 23, p=0.39336 b-rank test for bits 17 to 24, p=0.32062 b-rank test for bits 18 to 25, p=0.52552 b-rank test for bits 19 to 26, p=0.11393 b-rank test for bits 20 to 27, p=0.24197 b-rank test for bits 21 to 28, p=0.50313 b-rank test for bits 22 to 29, p=0.44941 b-rank test for bits 23 to 30, p=0.01579 b-rank test for bits 24 to 31, p=0.01681 b-rank test for bits 25 to 32, p=0.31146 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 = 0.296279 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-07-06_04:31 (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 141466 -1.04 0.150144 2 141472 -1.02 0.153438 3 141865 -0.10 0.458753 4 141956 0.11 0.543415 5 142619 1.66 0.951352 6 142380 1.10 0.864268 7 141944 0.08 0.532281 8 142157 0.58 0.718594 9 141625 -0.66 0.253242 10 141208 -1.64 0.050646 11 141624 -0.67 0.252495 12 141543 -0.86 0.196023 13 141895 -0.03 0.486645 14 141434 -1.11 0.133374 15 141969 0.14 0.555439 16 142219 0.72 0.765322 17 142150 0.56 0.713049 18 142197 0.67 0.749248 19 141826 -0.19 0.422815 20 141837 -0.17 0.432900 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-07-06_04:31 Bits used No. missing words z-score p-value 23 to 32 141671 -0.8218 0.205588 22 to 31 141715 -0.6701 0.251396 21 to 30 142046 0.4713 0.681278 20 to 29 142279 1.2747 0.898797 19 to 28 142494 2.0161 0.978105 18 to 27 142154 0.8437 0.800579 17 to 26 141925 0.0540 0.521546 16 to 25 142034 0.4299 0.666365 15 to 24 141877 -0.1115 0.455617 14 to 23 141684 -0.7770 0.218579 13 to 22 141822 -0.3011 0.381655 12 to 21 142051 0.4885 0.687408 11 to 20 142753 2.9092 0.998188 10 to 19 142049 0.4816 0.684962 9 to 18 141816 -0.3218 0.373792 8 to 17 142275 1.2609 0.896333 7 to 16 142018 0.3747 0.646067 6 to 15 141556 -1.2184 0.111540 5 to 14 141867 -0.1460 0.441974 4 to 13 142107 0.6816 0.752261 3 to 12 141667 -0.8356 0.201684 2 to 11 141960 0.1747 0.569352 1 to 10 141323 -2.0218 0.021597 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-07-06_04:31 Bits used No. missing words z-score p-value 28 to 32 141298 -2.0723 0.019119 27 to 31 141714 -0.6621 0.253942 26 to 30 141858 -0.1740 0.430933 25 to 29 142112 0.6870 0.753964 24 to 28 142122 0.7209 0.764519 23 to 27 141816 -0.3164 0.375860 22 to 26 141774 -0.4587 0.323208 21 to 25 141609 -1.0181 0.154323 20 to 24 141275 -2.1503 0.015767 19 to 23 141648 -0.8859 0.187845 18 to 22 142131 0.7514 0.773801 17 to 21 141811 -0.3333 0.369446 16 to 20 141797 -0.3808 0.351683 15 to 19 141718 -0.6486 0.258306 14 to 18 142317 1.3819 0.916504 13 to 17 142355 1.5107 0.934573 12 to 16 141798 -0.3774 0.352942 11 to 15 141670 -0.8113 0.208600 10 to 14 141859 -0.1706 0.432265 9 to 13 141609 -1.0181 0.154323 8 to 12 141497 -1.3977 0.081097 7 to 11 141987 0.2633 0.603836 6 to 10 141117 -2.6859 0.003617 5 to 9 141850 -0.2011 0.420303 4 to 8 142132 0.7548 0.774820 3 to 7 142226 1.0735 0.858467 2 to 6 142459 1.8633 0.968789 1 to 5 141888 -0.0723 0.471180 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-07-06_04:31 Bits used No. missing words z-score p-value 31 to 32 142081 0.5064 0.693713 30 to 31 141797 -0.3314 0.370187 29 to 30 142293 1.1318 0.871134 28 to 29 142028 0.3501 0.636853 27 to 28 141680 -0.6765 0.249365 26 to 27 142062 0.4504 0.673772 25 to 26 141184 -2.1396 0.016193 24 to 25 141814 -0.2812 0.389275 23 to 24 141655 -0.7502 0.226556 22 to 23 142464 1.6362 0.949101 21 to 22 142264 1.0462 0.852271 20 to 21 141889 -0.0600 0.476090 19 to 20 142066 0.4622 0.678014 18 to 19 141546 -1.0718 0.141912 17 to 18 141317 -1.7473 0.040294 16 to 17 141993 0.2468 0.597474 15 to 16 142298 1.1465 0.874210 14 to 15 141236 -1.9862 0.023504 13 to 14 142245 0.9902 0.838956 12 to 13 141664 -0.7237 0.234629 11 to 12 141260 -1.9154 0.027719 10 to 11 142211 0.8899 0.813235 9 to 10 142219 0.9135 0.819505 8 to 9 142340 1.2704 0.898031 7 to 8 141597 -0.9213 0.178440 6 to 7 141479 -1.2694 0.102147 5 to 6 141526 -1.1308 0.129077 4 to 5 141824 -0.2517 0.400632 3 to 4 142427 1.5271 0.936626 2 to 3 141305 -1.7827 0.037319 1 to 2 141811 -0.2901 0.385886 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-07-06_04:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2477.37 -0.320 0.374467 Test results for specific bytes for dh-ranFile-2015-07-06_04:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2454.92 -0.637 0.261902 2 to 9 2440.73 -0.838 0.200959 3 to 10 2544.31 0.627 0.734531 4 to 11 2351.20 -2.104 0.017672 5 to 12 2528.16 0.398 0.654780 6 to 13 2506.78 0.096 0.538210 7 to 14 2537.99 0.537 0.704479 8 to 15 2524.65 0.349 0.636323 9 to 16 2476.93 -0.326 0.372123 10 to 17 2551.86 0.733 0.768329 11 to 18 2393.17 -1.511 0.065414 12 to 19 2524.13 0.341 0.633567 13 to 20 2413.87 -1.218 0.111599 14 to 21 2691.39 2.707 0.996603 15 to 22 2663.21 2.308 0.989506 16 to 23 2513.38 0.189 0.575029 17 to 24 2502.56 0.036 0.514419 18 to 25 2564.91 0.918 0.820672 19 to 26 2543.05 0.609 0.728675 20 to 27 2584.74 1.198 0.884620 21 to 28 2418.29 -1.156 0.123936 22 to 29 2549.86 0.705 0.759615 23 to 30 2547.59 0.673 0.749540 24 to 31 2510.14 0.143 0.557003 25 to 32 2636.63 1.932 0.973331 CDPARK for dh-ranFile-2015-07-06_04:31: 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 3536 0.5936 0.723613 3508 -0.6849 0.246694 3517 -0.2740 0.392053 3519 -0.1826 0.427537 3561 1.7352 0.958644 3508 -0.6849 0.246694 3538 0.6849 0.753306 3509 -0.6393 0.261324 3546 1.0502 0.853193 3538 0.6849 0.753306 Square side=100, avg. no. parked=3528.00 sample std.=17.44 p-value of the KSTEST for those 10 p-values: 0.632953 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-07-06_04:31 0.6738,0.5717,0.5427,0.4023,0.4234,0.9935,0.5102,0.4456,0.4352,0.7834, The KS test for those 10 p-values: 0.176661 The 3DSPHERES test for dh-ranFile-2015-07-06_04:31 sample no r^3 equiv. uni. 1 8.119 0.237107 2 22.037 0.520288 3 1.758 0.056913 4 0.820 0.026955 5 1.721 0.055748 6 9.047 0.260337 7 10.565 0.296831 8 62.768 0.876594 9 64.658 0.884126 10 4.504 0.139419 11 10.279 0.290109 12 8.311 0.241971 13 62.678 0.876224 14 10.263 0.289722 15 8.611 0.249513 16 4.134 0.128730 17 30.605 0.639461 18 32.513 0.661676 19 11.454 0.317360 20 20.975 0.502996 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.070556 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-07-06_04:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 0.1 0.1 0.0 1.3 0.5 -1.5 -0.3 -0.3 -1.1 -0.2 -1.0 0.5 1.4 0.2 -0.1 0.7 0.9 -0.4 -0.7 0.3 0.2 -0.1 -1.1 -0.6 -0.5 0.1 -0.3 1.1 0.2 0.0 0.6 0.6 0.0 0.2 0.6 -0.5 -0.1 1.7 -0.1 0.1 -1.0 0.8 Chi-square with 42 degrees of freedom:20.611598 z-score=-2.333666, p-value=0.002254 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-07-06_04:31 Test no p-value 1 0.991661 2 0.369499 3 0.017373 4 0.484775 5 0.000068 6 0.729244 7 0.335949 8 0.753586 9 0.191866 10 0.663328 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.245103 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-07-06_04:31: (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 66668 0.00 66685 0.01 3 25000.00 25096 0.37 24868 0.70 4 6666.67 6592 0.84 6794 2.43 5 1388.89 1366 0.38 1383 0.02 6 238.10 242 0.06 227 0.52 7 34.72 33 0.09 35 0.00 8 4.96 2 1.77 7 0.84 p=0.25576 p=0.39296 Number of rngs required: 689058, p-value: 0.775 RESULTS OF CRAPS TEST for dh-ranFile-2015-07-06_04:31 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 66809 66666.7 0.304 0.304 2 37831 37654.3 0.829 1.133 3 26722 26954.7 2.009 3.142 4 19269 19313.5 0.102 3.245 5 13817 13851.4 0.086 3.330 6 9986 9943.5 0.181 3.512 7 6953 7145.0 5.161 8.672 8 5163 5139.1 0.111 8.784 9 3767 3699.9 1.218 10.002 10 2718 2666.3 1.003 11.004 11 1947 1923.3 0.291 11.296 12 1379 1388.7 0.068 11.364 13 999 1003.7 0.022 11.386 14 762 726.1 1.771 13.157 15 504 525.8 0.907 14.064 16 376 381.2 0.070 14.133 17 271 276.5 0.111 14.244 18 188 200.8 0.820 15.064 19 151 146.0 0.172 15.236 20 122 106.2 2.346 17.582 21 266 287.1 1.553 19.135 Chisq= 19.13 for 20 degrees of freedom, p= 0.48692 SUMMARY of craptest p-value for no. of wins: 0.873094 p-value for throws/game: 0.486925 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-07-06_04:31 No. of wins: Observed Expected 98874 98585.9 z-score= 1.289, pvalue=0.90126 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66761 66666.7 0.133 0.133 2 37461 37654.3 0.993 1.126 3 27143 26954.7 1.315 2.441 4 19456 19313.5 1.052 3.493 5 13825 13851.4 0.050 3.543 6 10002 9943.5 0.344 3.887 7 7010 7145.0 2.552 6.439 8 5056 5139.1 1.343 7.782 9 3632 3699.9 1.245 9.026 10 2706 2666.3 0.591 9.618 11 1918 1923.3 0.015 9.632 12 1374 1388.7 0.156 9.789 13 995 1003.7 0.076 9.864 14 727 726.1 0.001 9.865 15 499 525.8 1.370 11.235 16 405 381.2 1.492 12.727 17 286 276.5 0.324 13.051 18 209 200.8 0.332 13.383 19 157 146.0 0.831 14.215 20 90 106.2 2.475 16.690 21 288 287.1 0.003 16.693 Chisq= 16.69 for 20 degrees of freedom, p= 0.32718 SUMMARY of craptest p-value for no. of wins: 0.901255 p-value for throws/game: 0.327176 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0001,0.0023,0.0036,0.0158,0.0158,0.0162,0.0168,0.0174,0.0177,0.0191, 0.0199,0.0216,0.0235,0.0270,0.0277,0.0373,0.0403,0.0429,0.0446,0.0506, 0.0557,0.0569,0.0654,0.0706,0.0777,0.0790,0.0811,0.0953,0.1021,0.1115, 0.1116,0.1139,0.1239,0.1287,0.1291,0.1334,0.1394,0.1419,0.1501,0.1534, 0.1543,0.1543,0.1666,0.1767,0.1784,0.1816,0.1878,0.1906,0.1919,0.1960, 0.2010,0.2017,0.2056,0.2086,0.2186,0.2195,0.2266,0.2286,0.2346,0.2371, 0.2420,0.2420,0.2451,0.2467,0.2467,0.2494,0.2495,0.2514,0.2525,0.2532, 0.2539,0.2545,0.2558,0.2583,0.2603,0.2613,0.2619,0.2748,0.2830,0.2897, 0.2901,0.2963,0.2968,0.3115,0.3174,0.3206,0.3232,0.3245,0.3272,0.3280, 0.3352,0.3359,0.3517,0.3529,0.3643,0.3694,0.3695,0.3702,0.3721,0.3736, 0.3738,0.3745,0.3759,0.3817,0.3859,0.3893,0.3921,0.3930,0.3934,0.3980, 0.4006,0.4023,0.4194,0.4203,0.4228,0.4234,0.4275,0.4281,0.4308,0.4309, 0.4323,0.4329,0.4352,0.4369,0.4420,0.4456,0.4494,0.4535,0.4556,0.4588, 0.4712,0.4761,0.4791,0.4812,0.4848,0.4866,0.4869,0.4920,0.5028,0.5030, 0.5031,0.5102,0.5144,0.5203,0.5215,0.5244,0.5255,0.5323,0.5379,0.5382, 0.5395,0.5427,0.5434,0.5502,0.5554,0.5570,0.5688,0.5694,0.5717,0.5750, 0.5920,0.5975,0.6002,0.6027,0.6038,0.6235,0.6245,0.6321,0.6330,0.6330, 0.6331,0.6336,0.6351,0.6363,0.6369,0.6395,0.6461,0.6518,0.6548,0.6617, 0.6633,0.6661,0.6664,0.6719,0.6738,0.6738,0.6780,0.6813,0.6850,0.6874, 0.6877,0.6887,0.6892,0.6902,0.6937,0.7045,0.7130,0.7144,0.7186,0.7236, 0.7287,0.7292,0.7345,0.7492,0.7495,0.7523,0.7533,0.7533,0.7536,0.7537, 0.7540,0.7596,0.7645,0.7653,0.7683,0.7738,0.7748,0.7754,0.7834,0.8006, 0.8032,0.8048,0.8132,0.8195,0.8207,0.8313,0.8390,0.8398,0.8400,0.8425, 0.8523,0.8530,0.8532,0.8585,0.8643,0.8711,0.8729,0.8731,0.8742,0.8762, 0.8766,0.8841,0.8842,0.8846,0.8893,0.8963,0.8980,0.8988,0.9013,0.9054, 0.9059,0.9165,0.9346,0.9366,0.9466,0.9491,0.9514,0.9586,0.9688,0.9733, 0.9741,0.9781,0.9890,0.9895,0.9917,0.9935,0.9964,0.9966,0.9982, Overall p-value after applying KStest on 269 p-values = 0.706168 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.