RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-02-06_20:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.91 26.0149 0.925810 2 to 25 16.02 14.1088 0.340616 3 to 26 15.93 14.6601 0.380050 4 to 27 15.82 12.0506 0.202934 5 to 28 15.74 23.4882 0.865978 6 to 29 15.78 21.0972 0.778029 7 to 30 15.73 18.3788 0.634671 8 to 31 15.49 20.4206 0.746715 9 to 32 15.88 33.6926 0.990803 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.183125 Tough bday spacings test for dh-ranFile-2017-02-06_20:31: 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 38 76 103 79 84 58 36 6 4 2 (O-E)^2/E 2.6 0.1 0.1 0.3 3.6 0.4 0.7 1.3 5.3 1.0 1.0 Birthday Spacings: Sum(O-E)^2/E= 16.375, p= 0.911 RESULTS OF GCD FOR dh-ranFile-2017-02-06_20:31 Euclid's algorithm: p-value, steps to gcd: 0.067888 p-value, dist. of gcd's: 0.752421 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-02-06_20:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.637 0.587 0.531 0.064 0.199 0.841 0.196 0.052 Bits 8 to 15---> 0.429 0.335 0.351 0.415 0.454 0.549 0.992 0.291 Bits 16 to 23---> 0.419 0.811 0.752 0.929 0.159 0.108 0.133 0.704 Bits 24 to 31---> 0.201 0.392 0.916 0.570 0.741 0.962 0.675 0.892 KS test for the above 32 p values: 0.002 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-02-06_20:31, p-values for 5 runs: 0.2768, 0.3438, 0.9954, 0.8301, 0.2049 Rank test for binary matrices (31x31) for dh-ranFile-2017-02-06_20:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 203 211.4 0.335 0.335 r= 29 5179 5134.0 0.394 0.729 r= 30 23192 23103.0 0.342 1.072 r= 31 11426 11551.5 1.364 2.436 chi-square = 2.436 with df = 3; p-value = 0.513 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2017-02-06_20:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 198 211.4 0.852 0.852 r= 30 5088 5134.0 0.412 1.264 r= 31 23230 23103.0 0.698 1.962 r= 32 11484 11551.5 0.395 2.356 chi-square = 2.356 with df = 3; p-value = 0.498 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2017-02-06_20:31 b-rank test for bits 1 to 8, p=0.92546 b-rank test for bits 2 to 9, p=0.83806 b-rank test for bits 3 to 10, p=0.20981 b-rank test for bits 4 to 11, p=0.63979 b-rank test for bits 5 to 12, p=0.60014 b-rank test for bits 6 to 13, p=0.10676 b-rank test for bits 7 to 14, p=0.84599 b-rank test for bits 8 to 15, p=0.83589 b-rank test for bits 9 to 16, p=0.02866 b-rank test for bits 10 to 17, p=0.31457 b-rank test for bits 11 to 18, p=0.12717 b-rank test for bits 12 to 19, p=0.41376 b-rank test for bits 13 to 20, p=0.70489 b-rank test for bits 14 to 21, p=0.89444 b-rank test for bits 15 to 22, p=0.96820 b-rank test for bits 16 to 23, p=0.54945 b-rank test for bits 17 to 24, p=0.63190 b-rank test for bits 18 to 25, p=0.41623 b-rank test for bits 19 to 26, p=0.40411 b-rank test for bits 20 to 27, p=0.43829 b-rank test for bits 21 to 28, p=0.72580 b-rank test for bits 22 to 29, p=0.86153 b-rank test for bits 23 to 30, p=0.33658 b-rank test for bits 24 to 31, p=0.02526 b-rank test for bits 25 to 32, p=0.64494 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 = 0.792853 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-02-06_20:31 (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 142901 2.32 0.989748 2 142175 0.62 0.732610 3 140940 -2.26 0.011763 4 142683 1.81 0.964669 5 142331 0.99 0.837740 6 142208 0.70 0.757357 7 142290 0.89 0.813110 8 141264 -1.51 0.065805 9 142664 1.76 0.961071 10 141859 -0.12 0.453195 11 141319 -1.38 0.083905 12 141694 -0.50 0.307444 13 141529 -0.89 0.187103 14 142195 0.67 0.747759 15 142486 1.35 0.911068 16 142424 1.20 0.885415 17 141997 0.20 0.581150 18 142183 0.64 0.738724 19 142782 2.04 0.979272 20 141341 -1.33 0.092110 ---------------------------------------------------------------- OPSO test for dh-ranFile-2017-02-06_20:31 Bits used No. missing words z-score p-value 23 to 32 142075 0.5713 0.716094 22 to 31 141953 0.1506 0.559849 21 to 30 142354 1.5333 0.937405 20 to 29 141506 -1.3908 0.082144 19 to 28 142085 0.6058 0.727663 18 to 27 142303 1.3575 0.912686 17 to 26 141908 -0.0046 0.498170 16 to 25 142371 1.5920 0.944304 15 to 24 141639 -0.9322 0.175624 14 to 23 141927 0.0609 0.524293 13 to 22 141606 -1.0460 0.147789 12 to 21 142112 0.6989 0.757681 11 to 20 142169 0.8954 0.814717 10 to 19 142015 0.3644 0.642213 9 to 18 141868 -0.1425 0.443336 8 to 17 141910 0.0023 0.500922 7 to 16 142061 0.5230 0.699513 6 to 15 141630 -0.9632 0.167722 5 to 14 141987 0.2678 0.605584 4 to 13 142004 0.3264 0.627957 3 to 12 142203 1.0127 0.844388 2 to 11 142167 0.8885 0.812869 1 to 10 142174 0.9127 0.819288 ----------------------------------------------------------------- OQSO test for dh-ranFile-2017-02-06_20:31 Bits used No. missing words z-score p-value 28 to 32 141814 -0.3232 0.373290 27 to 31 141992 0.2802 0.610352 26 to 30 141799 -0.3740 0.354202 25 to 29 141740 -0.5740 0.282984 24 to 28 141501 -1.3842 0.083153 23 to 27 142147 0.8057 0.789781 22 to 26 141718 -0.6486 0.258306 21 to 25 142013 0.3514 0.637365 20 to 24 142065 0.5277 0.701145 19 to 23 142441 1.8023 0.964249 18 to 22 142153 0.8260 0.795598 17 to 21 141990 0.2735 0.607749 16 to 20 141922 0.0429 0.517129 15 to 19 141342 -1.9232 0.027230 14 to 18 142258 1.1819 0.881384 13 to 17 141688 -0.7503 0.226546 12 to 16 141884 -0.0859 0.465787 11 to 15 141587 -1.0926 0.137275 10 to 14 141268 -2.1740 0.014853 9 to 13 141885 -0.0825 0.467135 8 to 12 142150 0.8158 0.792702 7 to 11 141805 -0.3537 0.361797 6 to 10 141879 -0.1028 0.459056 5 to 9 142171 0.8870 0.812465 4 to 8 142339 1.4565 0.927374 3 to 7 142199 0.9819 0.836933 2 to 6 142443 1.8091 0.964778 1 to 5 142066 0.5311 0.702320 ----------------------------------------------------------------- DNA test for dh-ranFile-2017-02-06_20:31 Bits used No. missing words z-score p-value 31 to 32 142414 1.4887 0.931717 30 to 31 141482 -1.2606 0.103734 29 to 30 142282 1.0993 0.864186 28 to 29 142565 1.9341 0.973451 27 to 28 141768 -0.4169 0.338375 26 to 27 141665 -0.7207 0.235536 25 to 26 141836 -0.2163 0.414372 24 to 25 142219 0.9135 0.819505 23 to 24 142243 0.9843 0.837510 22 to 23 141704 -0.6057 0.272359 21 to 22 142109 0.5890 0.722068 20 to 21 141865 -0.1308 0.447980 19 to 20 142151 0.7129 0.762043 18 to 19 142210 0.8869 0.812442 17 to 18 141150 -2.2399 0.012548 16 to 17 141226 -2.0157 0.021914 15 to 16 142124 0.6332 0.736713 14 to 15 142053 0.4238 0.664146 13 to 14 141773 -0.4022 0.343786 12 to 13 141469 -1.2989 0.096988 11 to 12 141858 -0.1514 0.439824 10 to 11 141884 -0.0747 0.470219 9 to 10 141993 0.2468 0.597474 8 to 9 141747 -0.4788 0.316023 7 to 8 141361 -1.6175 0.052886 6 to 7 141718 -0.5644 0.286243 5 to 6 141241 -1.9715 0.024335 4 to 5 141674 -0.6942 0.243782 3 to 4 141816 -0.2753 0.391539 2 to 3 141848 -0.1809 0.428217 1 to 2 142164 0.7512 0.773746 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2017-02-06_20:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2455.39 -0.631 0.264053 Test results for specific bytes for dh-ranFile-2017-02-06_20:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2524.40 0.345 0.634961 2 to 9 2390.22 -1.552 0.060274 3 to 10 2436.08 -0.904 0.183020 4 to 11 2453.27 -0.661 0.254351 5 to 12 2421.73 -1.107 0.134177 6 to 13 2419.05 -1.145 0.126153 7 to 14 2491.10 -0.126 0.449931 8 to 15 2423.22 -1.086 0.138768 9 to 16 2396.86 -1.459 0.072337 10 to 17 2573.47 1.039 0.850592 11 to 18 2474.45 -0.361 0.358929 12 to 19 2564.51 0.912 0.819182 13 to 20 2580.75 1.142 0.873273 14 to 21 2504.43 0.063 0.524952 15 to 22 2541.71 0.590 0.722344 16 to 23 2472.53 -0.388 0.348847 17 to 24 2484.63 -0.217 0.413990 18 to 25 2683.24 2.591 0.995221 19 to 26 2428.49 -1.011 0.155927 20 to 27 2492.12 -0.111 0.455645 21 to 28 2542.43 0.600 0.725784 22 to 29 2536.79 0.520 0.698592 23 to 30 2409.33 -1.282 0.099883 24 to 31 2549.71 0.703 0.758993 25 to 32 2528.99 0.410 0.659095 CDPARK for dh-ranFile-2017-02-06_20:31: 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 3538 0.6849 0.753306 3502 -0.9589 0.168804 3538 0.6849 0.753306 3520 -0.1370 0.445521 3493 -1.3699 0.085365 3564 1.8721 0.969407 3487 -1.6438 0.050105 3490 -1.5068 0.065925 3543 0.9132 0.819442 3551 1.2785 0.899470 Square side=100, avg. no. parked=3522.60 sample std.=26.55 p-value of the KSTEST for those 10 p-values: 0.410555 Results for the MINIMUM DISTANCE test for dh-ranFile-2017-02-06_20:31 0.5430,0.6387,0.0417,0.7620,0.6914,0.4147,0.2010,0.3385,0.4846,0.3657, The KS test for those 10 p-values: 0.595522 The 3DSPHERES test for dh-ranFile-2017-02-06_20:31 sample no r^3 equiv. uni. 1 31.920 0.654925 2 31.812 0.653688 3 12.887 0.349202 4 1.408 0.045842 5 33.782 0.675689 6 12.678 0.344653 7 47.038 0.791526 8 0.314 0.010412 9 75.040 0.918023 10 108.743 0.973344 11 21.881 0.517781 12 10.959 0.306003 13 60.171 0.865432 14 61.097 0.869526 15 11.484 0.318051 16 10.118 0.286280 17 10.118 0.286279 18 3.751 0.117533 19 30.086 0.633174 20 8.436 0.245125 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.951003 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-02-06_20:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 1.3 -0.3 -1.8 -0.3 -1.2 0.5 -0.5 1.9 2.1 1.2 -0.8 2.1 -1.7 1.2 1.0 0.1 0.0 -0.0 -0.6 1.6 -0.9 -0.6 -0.6 -0.9 0.8 -1.7 -0.9 -0.8 -2.2 -0.7 -1.1 2.1 -0.1 -1.3 -0.6 0.4 -0.2 -1.3 0.9 1.0 -0.6 0.0 -0.1 Chi-square with 42 degrees of freedom:54.845340 z-score=1.401542, p-value=0.911632 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2017-02-06_20:31 Test no p-value 1 0.019586 2 0.664515 3 0.540016 4 0.653944 5 0.851754 6 0.504242 7 0.305650 8 0.270681 9 0.039849 10 0.115856 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.391714 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-02-06_20:31: (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 66853 0.52 66632 0.02 3 25000.00 24938 0.15 25030 0.04 4 6666.67 6558 1.77 6599 0.69 5 1388.89 1368 0.31 1447 2.43 6 238.10 246 0.26 251 0.70 7 34.72 34 0.01 29 0.94 8 4.96 2 1.77 11 7.36 p=0.43081 p=0.94170 Number of rngs required: 690150, p-value: 0.981 RESULTS OF CRAPS TEST for dh-ranFile-2017-02-06_20:31 No. of wins: Observed Expected 98573 98585.9 z-score=-0.058, pvalue=0.47707 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66825 66666.7 0.376 0.376 2 37533 37654.3 0.391 0.767 3 27134 26954.7 1.192 1.959 4 19229 19313.5 0.369 2.329 5 13868 13851.4 0.020 2.348 6 9922 9943.5 0.047 2.395 7 6951 7145.0 5.269 7.664 8 5151 5139.1 0.028 7.692 9 3652 3699.9 0.619 8.311 10 2701 2666.3 0.452 8.762 11 1921 1923.3 0.003 8.765 12 1425 1388.7 0.947 9.712 13 1020 1003.7 0.264 9.976 14 741 726.1 0.304 10.280 15 555 525.8 1.618 11.898 16 382 381.2 0.002 11.900 17 277 276.5 0.001 11.901 18 197 200.8 0.073 11.974 19 140 146.0 0.245 12.219 20 93 106.2 1.644 13.863 21 283 287.1 0.059 13.922 Chisq= 13.92 for 20 degrees of freedom, p= 0.16557 SUMMARY of craptest p-value for no. of wins: 0.477069 p-value for throws/game: 0.165573 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2017-02-06_20:31 No. of wins: Observed Expected 98581 98585.9 z-score=-0.022, pvalue=0.49133 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66694 66666.7 0.011 0.011 2 37560 37654.3 0.236 0.247 3 26815 26954.7 0.724 0.972 4 19583 19313.5 3.762 4.734 5 13939 13851.4 0.554 5.287 6 9955 9943.5 0.013 5.300 7 7076 7145.0 0.667 5.967 8 5173 5139.1 0.224 6.191 9 3620 3699.9 1.724 7.915 10 2657 2666.3 0.032 7.948 11 1900 1923.3 0.283 8.231 12 1363 1388.7 0.477 8.708 13 982 1003.7 0.470 9.178 14 740 726.1 0.265 9.442 15 566 525.8 3.068 12.510 16 364 381.2 0.772 13.282 17 267 276.5 0.329 13.611 18 222 200.8 2.232 15.842 19 140 146.0 0.245 16.088 20 117 106.2 1.095 17.183 21 267 287.1 1.409 18.592 Chisq= 18.59 for 20 degrees of freedom, p= 0.45151 SUMMARY of craptest p-value for no. of wins: 0.491331 p-value for throws/game: 0.451511 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0019,0.0104,0.0118,0.0125,0.0149,0.0196,0.0219,0.0243,0.0253,0.0272, 0.0287,0.0398,0.0417,0.0458,0.0501,0.0516,0.0529,0.0603,0.0642,0.0658, 0.0659,0.0679,0.0723,0.0821,0.0832,0.0839,0.0854,0.0921,0.0970,0.0999, 0.1037,0.1068,0.1076,0.1159,0.1175,0.1262,0.1272,0.1325,0.1342,0.1373, 0.1388,0.1478,0.1559,0.1586,0.1656,0.1677,0.1688,0.1756,0.1830,0.1831, 0.1871,0.1960,0.1992,0.2008,0.2010,0.2029,0.2049,0.2098,0.2265,0.2355, 0.2438,0.2451,0.2544,0.2583,0.2641,0.2707,0.2724,0.2768,0.2830,0.2862, 0.2863,0.2863,0.2910,0.3057,0.3060,0.3074,0.3146,0.3160,0.3181,0.3349, 0.3366,0.3384,0.3385,0.3406,0.3438,0.3438,0.3447,0.3488,0.3492,0.3515, 0.3542,0.3589,0.3618,0.3657,0.3733,0.3801,0.3915,0.3917,0.3921,0.4041, 0.4106,0.4138,0.4140,0.4144,0.4147,0.4147,0.4162,0.4193,0.4282,0.4291, 0.4308,0.4383,0.4398,0.4433,0.4455,0.4480,0.4499,0.4515,0.4532,0.4544, 0.4556,0.4591,0.4658,0.4671,0.4702,0.4771,0.4846,0.4913,0.4982,0.4982, 0.5009,0.5042,0.5130,0.5171,0.5178,0.5243,0.5250,0.5315,0.5400,0.5430, 0.5488,0.5494,0.5598,0.5702,0.5812,0.5872,0.5955,0.5975,0.6001,0.6056, 0.6077,0.6104,0.6280,0.6319,0.6332,0.6347,0.6350,0.6370,0.6374,0.6387, 0.6398,0.6422,0.6449,0.6537,0.6539,0.6549,0.6591,0.6641,0.6645,0.6747, 0.6757,0.6914,0.6986,0.6995,0.7011,0.7023,0.7038,0.7049,0.7161,0.7221, 0.7223,0.7258,0.7258,0.7277,0.7326,0.7367,0.7387,0.7413,0.7467,0.7478, 0.7519,0.7524,0.7533,0.7533,0.7574,0.7577,0.7590,0.7620,0.7620,0.7737, 0.7780,0.7898,0.7915,0.7927,0.7929,0.7956,0.8109,0.8124,0.8125,0.8129, 0.8131,0.8147,0.8192,0.8193,0.8194,0.8195,0.8301,0.8359,0.8369,0.8375, 0.8377,0.8381,0.8408,0.8444,0.8460,0.8506,0.8518,0.8615,0.8642,0.8654, 0.8660,0.8695,0.8733,0.8814,0.8854,0.8916,0.8944,0.8995,0.9106,0.9111, 0.9116,0.9127,0.9160,0.9180,0.9255,0.9258,0.9274,0.9293,0.9317,0.9374, 0.9417,0.9443,0.9510,0.9611,0.9621,0.9642,0.9647,0.9648,0.9682,0.9694, 0.9733,0.9735,0.9793,0.9805,0.9897,0.9908,0.9915,0.9952,0.9954, Overall p-value after applying KStest on 269 p-values = 0.338818 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.