RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-11-27_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 15.60 13.3858 0.289998 2 to 25 15.80 10.0782 0.099701 3 to 26 15.84 13.5449 0.300984 4 to 27 15.74 18.0427 0.613848 5 to 28 15.70 22.7849 0.843615 6 to 29 15.87 24.2424 0.887003 7 to 30 15.59 18.4434 0.638602 8 to 31 15.62 21.7864 0.806928 9 to 32 15.93 15.3986 0.433206 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.905028 Tough bday spacings test for dh-ranFile-2016-11-27_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 9 33 69 104 101 90 49 24 14 5 2 (O-E)^2/E 0.0 0.4 0.2 0.4 0.1 1.8 0.2 1.1 0.1 0.4 1.0 Birthday Spacings: Sum(O-E)^2/E= 5.729, p= 0.163 RESULTS OF GCD FOR dh-ranFile-2016-11-27_10:31 Euclid's algorithm: p-value, steps to gcd: 0.042562 p-value, dist. of gcd's: 0.986200 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-11-27_10:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.340 0.739 0.183 0.127 0.496 0.044 0.436 0.032 Bits 8 to 15---> 0.463 0.841 0.872 0.706 0.580 0.650 0.608 0.339 Bits 16 to 23---> 0.506 0.804 0.296 0.519 0.354 0.826 0.016 0.721 Bits 24 to 31---> 0.329 0.729 0.544 0.853 0.894 0.833 0.836 0.392 KS test for the above 32 p values: 0.498 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-11-27_10:31, p-values for 5 runs: 0.5472, 0.4965, 0.3465, 0.3524, 0.4192 Rank test for binary matrices (31x31) for dh-ranFile-2016-11-27_10:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 177 211.4 5.603 5.603 r= 29 5123 5134.0 0.024 5.627 r= 30 23250 23103.0 0.935 6.561 r= 31 11450 11551.5 0.892 7.454 chi-square = 7.454 with df = 3; p-value = 0.941 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-11-27_10:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 220 211.4 0.348 0.348 r= 30 5136 5134.0 0.001 0.349 r= 31 23131 23103.0 0.034 0.383 r= 32 11513 11551.5 0.128 0.511 chi-square = 0.511 with df = 3; p-value = 0.084 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-11-27_10:31 b-rank test for bits 1 to 8, p=0.58777 b-rank test for bits 2 to 9, p=0.17342 b-rank test for bits 3 to 10, p=0.67194 b-rank test for bits 4 to 11, p=0.81234 b-rank test for bits 5 to 12, p=0.08453 b-rank test for bits 6 to 13, p=0.95598 b-rank test for bits 7 to 14, p=0.36666 b-rank test for bits 8 to 15, p=0.44674 b-rank test for bits 9 to 16, p=0.25795 b-rank test for bits 10 to 17, p=0.41173 b-rank test for bits 11 to 18, p=0.59748 b-rank test for bits 12 to 19, p=0.85911 b-rank test for bits 13 to 20, p=0.86980 b-rank test for bits 14 to 21, p=0.17833 b-rank test for bits 15 to 22, p=0.44057 b-rank test for bits 16 to 23, p=0.36183 b-rank test for bits 17 to 24, p=0.53047 b-rank test for bits 18 to 25, p=0.91888 b-rank test for bits 19 to 26, p=0.05526 b-rank test for bits 20 to 27, p=0.83492 b-rank test for bits 21 to 28, p=0.70811 b-rank test for bits 22 to 29, p=0.11690 b-rank test for bits 23 to 30, p=0.01286 b-rank test for bits 24 to 31, p=0.09610 b-rank test for bits 25 to 32, p=0.18660 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 = 0.836467 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-11-27_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 141495 -0.97 0.166507 2 141797 -0.26 0.396486 3 141603 -0.72 0.237081 4 141896 -0.03 0.487577 5 141322 -1.37 0.084990 6 141646 -0.62 0.269193 7 141566 -0.80 0.211227 8 141681 -0.53 0.296850 9 141991 0.19 0.575666 10 142553 1.50 0.933697 11 141729 -0.42 0.336756 12 141945 0.08 0.533210 13 142380 1.10 0.864268 14 142238 0.77 0.778733 15 142281 0.87 0.807409 16 142106 0.46 0.677066 17 142716 1.88 0.970268 18 141400 -1.19 0.117019 19 141334 -1.34 0.089437 20 142550 1.50 0.932789 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-11-27_10:31 Bits used No. missing words z-score p-value 23 to 32 141612 -1.0253 0.152617 22 to 31 141796 -0.3908 0.347975 21 to 30 141868 -0.1425 0.443336 20 to 29 141957 0.1644 0.565284 19 to 28 142107 0.6816 0.752261 18 to 27 142032 0.4230 0.663852 17 to 26 141752 -0.5425 0.293731 16 to 25 142154 0.8437 0.800579 15 to 24 142145 0.8127 0.791792 14 to 23 141953 0.1506 0.559849 13 to 22 141777 -0.4563 0.324083 12 to 21 141710 -0.6873 0.245933 11 to 20 141273 -2.1942 0.014109 10 to 19 141591 -1.0977 0.136170 9 to 18 141415 -1.7046 0.044136 8 to 17 141668 -0.8322 0.202656 7 to 16 142049 0.4816 0.684962 6 to 15 141529 -1.3115 0.094847 5 to 14 141727 -0.6287 0.264765 4 to 13 141755 -0.5322 0.297303 3 to 12 142106 0.6782 0.751169 2 to 11 142022 0.3885 0.651183 1 to 10 141951 0.1437 0.557127 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-11-27_10:31 Bits used No. missing words z-score p-value 28 to 32 141703 -0.6994 0.242144 27 to 31 141901 -0.0282 0.488737 26 to 30 141865 -0.1503 0.440275 25 to 29 141925 0.0531 0.521181 24 to 28 142413 1.7074 0.956122 23 to 27 141859 -0.1706 0.432265 22 to 26 141764 -0.4926 0.311132 21 to 25 141544 -1.2384 0.107783 20 to 24 141770 -0.4723 0.318355 19 to 23 142069 0.5413 0.705834 18 to 22 142248 1.1480 0.874523 17 to 21 141979 0.2362 0.593349 16 to 20 141708 -0.6825 0.247470 15 to 19 141818 -0.3096 0.378435 14 to 18 141205 -2.3876 0.008480 13 to 17 141637 -0.9232 0.177964 12 to 16 142640 2.4768 0.993373 11 to 15 141880 -0.0994 0.460401 10 to 14 141768 -0.4791 0.315939 9 to 13 141799 -0.3740 0.354202 8 to 12 141639 -0.9164 0.179736 7 to 11 141675 -0.7943 0.213499 6 to 10 142106 0.6667 0.747511 5 to 9 142051 0.4802 0.684471 4 to 8 142135 0.7650 0.777859 3 to 7 142393 1.6396 0.949452 2 to 6 141881 -0.0960 0.461747 1 to 5 142073 0.5548 0.710489 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-11-27_10:31 Bits used No. missing words z-score p-value 31 to 32 141442 -1.3786 0.084016 30 to 31 141751 -0.4671 0.320232 29 to 30 142156 0.7276 0.766583 28 to 29 141432 -1.4081 0.079558 27 to 28 142192 0.8338 0.797813 26 to 27 142011 0.2999 0.617878 25 to 26 141514 -1.1662 0.121774 24 to 25 141757 -0.4494 0.326589 23 to 24 141373 -1.5821 0.056814 22 to 23 142552 1.8958 0.971006 21 to 22 142257 1.0256 0.847454 20 to 21 141913 0.0108 0.504319 19 to 20 141946 0.1082 0.543070 18 to 19 142545 1.8751 0.969613 17 to 18 141760 -0.4405 0.329787 16 to 17 141731 -0.5260 0.299428 15 to 16 141669 -0.7089 0.239182 14 to 15 141794 -0.3402 0.366851 13 to 14 141534 -1.1072 0.134111 12 to 13 142932 3.0167 0.998722 11 to 12 141618 -0.8594 0.195065 10 to 11 142289 1.1200 0.868637 9 to 10 142046 0.4032 0.656583 8 to 9 141409 -1.4759 0.069985 7 to 8 141829 -0.2370 0.406343 6 to 7 141921 0.0344 0.513731 5 to 6 141510 -1.1780 0.119405 4 to 5 142045 0.4002 0.655498 3 to 4 141364 -1.6086 0.053847 2 to 3 141369 -1.5939 0.055480 1 to 2 141533 -1.1101 0.133474 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-11-27_10:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2431.34 -0.971 0.165764 Test results for specific bytes for dh-ranFile-2016-11-27_10:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2539.03 0.552 0.709526 2 to 9 2454.39 -0.645 0.259444 3 to 10 2451.30 -0.689 0.245508 4 to 11 2389.66 -1.560 0.059323 5 to 12 2284.35 -3.050 0.001145 6 to 13 2455.52 -0.629 0.264649 7 to 14 2560.30 0.853 0.803097 8 to 15 2428.05 -1.018 0.154455 9 to 16 2474.52 -0.360 0.359279 10 to 17 2410.33 -1.268 0.102368 11 to 18 2502.65 0.037 0.514936 12 to 19 2522.64 0.320 0.625575 13 to 20 2398.32 -1.438 0.075214 14 to 21 2425.58 -1.053 0.146280 15 to 22 2450.25 -0.704 0.240867 16 to 23 2529.26 0.414 0.660484 17 to 24 2408.81 -1.290 0.098582 18 to 25 2606.27 1.503 0.933567 19 to 26 2605.47 1.492 0.932090 20 to 27 2455.40 -0.631 0.264104 21 to 28 2501.46 0.021 0.508238 22 to 29 2475.12 -0.352 0.362481 23 to 30 2440.41 -0.843 0.199696 24 to 31 2460.43 -0.560 0.287873 25 to 32 2386.92 -1.599 0.054884 CDPARK for dh-ranFile-2016-11-27_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 3504 -0.8676 0.192812 3549 1.1872 0.882429 3517 -0.2740 0.392053 3492 -1.4155 0.078457 3525 0.0913 0.536383 3602 3.6073 0.999845 3553 1.3699 0.914635 3558 1.5982 0.944998 3538 0.6849 0.753306 3551 1.2785 0.899470 Square side=100, avg. no. parked=3538.90 sample std.=29.81 p-value of the KSTEST for those 10 p-values: 0.037589 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-11-27_10:31 0.4564,0.6016,0.6899,0.8526,0.8482,0.1075,0.9137,0.4784,0.9637,0.4969, The KS test for those 10 p-values: 0.204903 The 3DSPHERES test for dh-ranFile-2016-11-27_10:31 sample no r^3 equiv. uni. 1 31.947 0.655236 2 6.601 0.197511 3 0.331 0.010967 4 42.242 0.755385 5 1.368 0.044590 6 24.356 0.555976 7 19.603 0.479744 8 6.047 0.182539 9 21.239 0.507354 10 45.037 0.777146 11 6.754 0.201589 12 1.473 0.047908 13 11.349 0.314978 14 32.875 0.665734 15 8.834 0.255080 16 0.387 0.012805 17 15.892 0.411240 18 51.773 0.821962 19 38.985 0.727330 20 1.090 0.035683 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.061197 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-11-27_10:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -0.3 0.6 1.2 -0.1 0.3 0.4 -0.3 0.3 1.0 -0.1 0.4 -0.9 -0.1 0.8 1.2 -0.6 -0.2 -1.9 1.3 0.3 0.2 -1.2 2.4 -2.6 -1.8 -0.8 1.5 0.1 0.6 0.7 -0.1 -0.9 2.3 0.5 -1.7 0.3 1.5 -1.2 1.0 0.9 0.0 0.8 Chi-square with 42 degrees of freedom:48.439240 z-score=0.702579, p-value=0.770809 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-11-27_10:31 Test no p-value 1 0.028567 2 0.008674 3 0.003542 4 0.072454 5 0.472368 6 0.524855 7 0.916000 8 0.903707 9 0.410212 10 0.011728 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.003879 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-11-27_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 66715 0.04 66608 0.05 3 25000.00 24827 1.20 25030 0.04 4 6666.67 6776 1.79 6672 0.00 5 1388.89 1392 0.01 1406 0.21 6 238.10 255 1.20 240 0.02 7 34.72 31 0.40 35 0.00 8 4.96 3 0.77 8 1.86 p=0.50704 p=0.09792 Number of rngs required: 687606, p-value: 0.178 RESULTS OF CRAPS TEST for dh-ranFile-2016-11-27_10:31 No. of wins: Observed Expected 98856 98585.9 z-score= 1.208, pvalue=0.88652 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66750 66666.7 0.104 0.104 2 37467 37654.3 0.932 1.036 3 26910 26954.7 0.074 1.110 4 19338 19313.5 0.031 1.141 5 13708 13851.4 1.485 2.626 6 10040 9943.5 0.936 3.562 7 7074 7145.0 0.706 4.268 8 5182 5139.1 0.359 4.627 9 3785 3699.9 1.959 6.586 10 2721 2666.3 1.122 7.708 11 1934 1923.3 0.059 7.767 12 1412 1388.7 0.390 8.157 13 1029 1003.7 0.637 8.794 14 715 726.1 0.171 8.965 15 498 525.8 1.474 10.438 16 371 381.2 0.270 10.709 17 271 276.5 0.111 10.820 18 208 200.8 0.256 11.075 19 141 146.0 0.170 11.246 20 124 106.2 2.978 14.224 21 322 287.1 4.239 18.462 Chisq= 18.46 for 20 degrees of freedom, p= 0.44303 SUMMARY of craptest p-value for no. of wins: 0.886521 p-value for throws/game: 0.443026 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-11-27_10:31 No. of wins: Observed Expected 98474 98585.9 z-score=-0.500, pvalue=0.30843 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66785 66666.7 0.210 0.210 2 37589 37654.3 0.113 0.323 3 27030 26954.7 0.210 0.534 4 19152 19313.5 1.350 1.883 5 13843 13851.4 0.005 1.888 6 10024 9943.5 0.651 2.539 7 7127 7145.0 0.045 2.585 8 5155 5139.1 0.049 2.634 9 3735 3699.9 0.334 2.968 10 2687 2666.3 0.161 3.129 11 1913 1923.3 0.055 3.184 12 1408 1388.7 0.267 3.451 13 985 1003.7 0.349 3.800 14 711 726.1 0.316 4.116 15 537 525.8 0.237 4.353 16 382 381.2 0.002 4.355 17 257 276.5 1.381 5.735 18 202 200.8 0.007 5.742 19 139 146.0 0.334 6.076 20 91 106.2 2.180 8.256 21 248 287.1 5.329 13.585 Chisq= 13.58 for 20 degrees of freedom, p= 0.14908 SUMMARY of craptest p-value for no. of wins: 0.308433 p-value for throws/game: 0.149082 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0011,0.0035,0.0039,0.0085,0.0087,0.0110,0.0117,0.0128,0.0129,0.0141, 0.0161,0.0286,0.0322,0.0357,0.0376,0.0426,0.0437,0.0441,0.0446,0.0479, 0.0538,0.0549,0.0553,0.0555,0.0568,0.0593,0.0612,0.0700,0.0725,0.0752, 0.0785,0.0796,0.0836,0.0840,0.0845,0.0850,0.0894,0.0948,0.0961,0.0979, 0.0986,0.0997,0.1024,0.1075,0.1078,0.1169,0.1170,0.1194,0.1218,0.1274, 0.1335,0.1341,0.1362,0.1463,0.1491,0.1526,0.1545,0.1625,0.1658,0.1665, 0.1734,0.1780,0.1781,0.1783,0.1797,0.1825,0.1831,0.1866,0.1928,0.1951, 0.1975,0.1997,0.2016,0.2027,0.2049,0.2112,0.2135,0.2371,0.2392,0.2409, 0.2421,0.2455,0.2459,0.2475,0.2551,0.2579,0.2594,0.2641,0.2646,0.2648, 0.2692,0.2879,0.2900,0.2937,0.2957,0.2969,0.2973,0.2994,0.3010,0.3084, 0.3111,0.3150,0.3159,0.3184,0.3202,0.3241,0.3266,0.3286,0.3298,0.3368, 0.3390,0.3397,0.3465,0.3480,0.3524,0.3542,0.3542,0.3593,0.3618,0.3625, 0.3667,0.3669,0.3784,0.3916,0.3921,0.3965,0.4063,0.4102,0.4112,0.4117, 0.4192,0.4323,0.4332,0.4362,0.4403,0.4406,0.4430,0.4433,0.4467,0.4564, 0.4604,0.4617,0.4629,0.4724,0.4784,0.4797,0.4876,0.4887,0.4957,0.4965, 0.4969,0.4984,0.5043,0.5063,0.5070,0.5074,0.5082,0.5137,0.5149,0.5192, 0.5212,0.5249,0.5305,0.5332,0.5364,0.5431,0.5443,0.5472,0.5560,0.5571, 0.5598,0.5653,0.5757,0.5802,0.5878,0.5933,0.5975,0.6016,0.6085,0.6138, 0.6179,0.6256,0.6386,0.6499,0.6512,0.6552,0.6555,0.6566,0.6605,0.6639, 0.6657,0.6719,0.6771,0.6845,0.6850,0.6899,0.7058,0.7060,0.7081,0.7095, 0.7105,0.7208,0.7273,0.7289,0.7394,0.7475,0.7512,0.7523,0.7533,0.7554, 0.7666,0.7708,0.7771,0.7779,0.7787,0.7918,0.7978,0.8006,0.8031,0.8035, 0.8069,0.8074,0.8123,0.8220,0.8257,0.8334,0.8349,0.8358,0.8365,0.8410, 0.8436,0.8475,0.8482,0.8526,0.8530,0.8591,0.8643,0.8686,0.8698,0.8715, 0.8745,0.8824,0.8865,0.8870,0.8940,0.8995,0.9037,0.9050,0.9137,0.9146, 0.9160,0.9189,0.9321,0.9328,0.9336,0.9337,0.9412,0.9450,0.9495,0.9560, 0.9561,0.9637,0.9696,0.9703,0.9710,0.9862,0.9934,0.9987,0.9998, Overall p-value after applying KStest on 269 p-values = 0.012744 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.