RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-07-23_17:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 16.03 16.4632 0.508733 2 to 25 15.74 23.9018 0.877871 3 to 26 15.62 20.1216 0.731941 4 to 27 15.55 31.1556 0.980881 5 to 28 15.80 31.6420 0.983335 6 to 29 15.72 13.3659 0.288633 7 to 30 15.84 14.4919 0.367969 8 to 31 15.60 17.9881 0.610411 9 to 32 15.63 13.9955 0.332582 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.183549 Tough bday spacings test for dh-ranFile-2016-07-23_17:31: 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 6 25 79 104 86 75 61 34 14 8 8 (O-E)^2/E 1.1 3.7 0.4 0.4 1.4 0.1 1.5 0.6 0.1 0.3 3.8 Birthday Spacings: Sum(O-E)^2/E= 13.434, p= 0.800 RESULTS OF GCD FOR dh-ranFile-2016-07-23_17:31 Euclid's algorithm: p-value, steps to gcd: 0.035640 p-value, dist. of gcd's: 0.833761 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-07-23_17:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.231 0.201 0.469 0.086 0.929 0.666 0.988 0.158 Bits 8 to 15---> 0.237 0.929 0.176 0.348 0.117 0.177 0.077 0.760 Bits 16 to 23---> 0.363 0.962 0.485 0.990 0.797 0.614 0.540 0.444 Bits 24 to 31---> 0.689 0.531 0.461 0.967 0.081 0.364 0.801 0.134 KS test for the above 32 p values: 0.450 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-07-23_17:31, p-values for 5 runs: 0.9423, 0.0929, 0.4901, 0.6515, 0.2205 Rank test for binary matrices (31x31) for dh-ranFile-2016-07-23_17:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 233 211.4 2.203 2.203 r= 29 5137 5134.0 0.002 2.205 r= 30 23019 23103.0 0.306 2.511 r= 31 11611 11551.5 0.306 2.817 chi-square = 2.817 with df = 3; p-value = 0.579 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-07-23_17:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 201 211.4 0.513 0.513 r= 30 5136 5134.0 0.001 0.514 r= 31 23087 23103.0 0.011 0.525 r= 32 11576 11551.5 0.052 0.577 chi-square = 0.577 with df = 3; p-value = 0.098 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-07-23_17:31 b-rank test for bits 1 to 8, p=0.87381 b-rank test for bits 2 to 9, p=0.45488 b-rank test for bits 3 to 10, p=0.82883 b-rank test for bits 4 to 11, p=0.98431 b-rank test for bits 5 to 12, p=0.34298 b-rank test for bits 6 to 13, p=0.76733 b-rank test for bits 7 to 14, p=0.76588 b-rank test for bits 8 to 15, p=0.43305 b-rank test for bits 9 to 16, p=0.19535 b-rank test for bits 10 to 17, p=0.00520 b-rank test for bits 11 to 18, p=0.78266 b-rank test for bits 12 to 19, p=0.20907 b-rank test for bits 13 to 20, p=0.52331 b-rank test for bits 14 to 21, p=0.09143 b-rank test for bits 15 to 22, p=0.48880 b-rank test for bits 16 to 23, p=0.04458 b-rank test for bits 17 to 24, p=0.43137 b-rank test for bits 18 to 25, p=0.67785 b-rank test for bits 19 to 26, p=0.48587 b-rank test for bits 20 to 27, p=0.64940 b-rank test for bits 21 to 28, p=0.10993 b-rank test for bits 22 to 29, p=0.11516 b-rank test for bits 23 to 30, p=0.03465 b-rank test for bits 24 to 31, p=0.78864 b-rank test for bits 25 to 32, p=0.22434 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 = 0.586783 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-07-23_17:31 (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 142848 2.19 0.985852 2 141471 -1.02 0.152886 3 141366 -1.27 0.102138 4 141749 -0.37 0.353978 5 141978 0.16 0.563734 6 142454 1.27 0.898419 7 142190 0.66 0.744014 8 141522 -0.90 0.182739 9 141586 -0.76 0.224991 10 142095 0.43 0.667786 11 141838 -0.17 0.433819 12 141404 -1.18 0.118865 13 141230 -1.59 0.056231 14 142078 0.39 0.653242 15 141426 -1.13 0.129391 16 141960 0.12 0.547120 17 141764 -0.34 0.367095 18 141905 -0.01 0.495964 19 141793 -0.27 0.392888 20 141835 -0.17 0.431063 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-07-23_17:31 Bits used No. missing words z-score p-value 23 to 32 142316 1.4023 0.919589 22 to 31 142114 0.7058 0.759831 21 to 30 142186 0.9540 0.829967 20 to 29 141971 0.2127 0.584202 19 to 28 141877 -0.1115 0.455617 18 to 27 141908 -0.0046 0.498170 17 to 26 141509 -1.3804 0.083724 16 to 25 141452 -1.5770 0.057398 15 to 24 141630 -0.9632 0.167722 14 to 23 141817 -0.3184 0.375099 13 to 22 141976 0.2299 0.590914 12 to 21 142090 0.6230 0.733358 11 to 20 142518 2.0989 0.982085 10 to 19 141922 0.0437 0.517424 9 to 18 142224 1.0851 0.861054 8 to 17 142198 0.9954 0.840233 7 to 16 141761 -0.5115 0.304507 6 to 15 142384 1.6368 0.949163 5 to 14 141974 0.2230 0.588232 4 to 13 141867 -0.1460 0.441974 3 to 12 141578 -1.1425 0.126620 2 to 11 141997 0.3023 0.618792 1 to 10 141987 0.2678 0.605584 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-07-23_17:31 Bits used No. missing words z-score p-value 28 to 32 142310 1.3582 0.912800 27 to 31 142468 1.8938 0.970874 26 to 30 141809 -0.3401 0.366890 25 to 29 141770 -0.4723 0.318355 24 to 28 141458 -1.5299 0.063017 23 to 27 141548 -1.2248 0.110316 22 to 26 141748 -0.5469 0.292230 21 to 25 142085 0.5955 0.724243 20 to 24 141959 0.1684 0.566855 19 to 23 142040 0.4429 0.671099 18 to 22 141717 -0.6520 0.257212 17 to 21 141837 -0.2452 0.403156 16 to 20 142115 0.6972 0.757157 15 to 19 142296 1.3107 0.905028 14 to 18 141897 -0.0418 0.483330 13 to 17 141700 -0.7096 0.238978 12 to 16 141745 -0.5571 0.288746 11 to 15 142148 0.8091 0.790757 10 to 14 142196 0.9718 0.834416 9 to 13 142233 1.0972 0.863720 8 to 12 141863 -0.1571 0.437602 7 to 11 142125 0.7311 0.767636 6 to 10 141593 -1.0723 0.141792 5 to 9 141225 -2.3198 0.010177 4 to 8 141320 -1.9977 0.022873 3 to 7 141979 0.2362 0.593349 2 to 6 142046 0.4633 0.678421 1 to 5 142189 0.9480 0.828444 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-07-23_17:31 Bits used No. missing words z-score p-value 31 to 32 141294 -1.8151 0.034752 30 to 31 141687 -0.6558 0.255963 29 to 30 142052 0.4209 0.663070 28 to 29 141810 -0.2930 0.384758 27 to 28 141959 0.1465 0.558244 26 to 27 141183 -2.1426 0.016074 25 to 26 141993 0.2468 0.597474 24 to 25 141737 -0.5083 0.305605 23 to 24 141853 -0.1662 0.434014 22 to 23 141407 -1.4818 0.069197 21 to 22 141782 -0.3756 0.353605 20 to 21 142038 0.3796 0.647863 19 to 20 141767 -0.4199 0.337297 18 to 19 142055 0.4297 0.666295 17 to 18 141491 -1.2340 0.108599 16 to 17 142528 1.8250 0.965998 15 to 16 141892 -0.0511 0.479615 14 to 15 141976 0.1967 0.577956 13 to 14 141861 -0.1426 0.443316 12 to 13 141770 -0.4110 0.340535 11 to 12 141798 -0.3284 0.371302 10 to 11 142051 0.4179 0.661992 9 to 10 142757 2.5005 0.993799 8 to 9 141915 0.0167 0.506672 7 to 8 141683 -0.6676 0.252182 6 to 7 142132 0.6568 0.744359 5 to 6 142506 1.7601 0.960804 4 to 5 141943 0.0993 0.539559 3 to 4 141693 -0.6381 0.261691 2 to 3 142137 0.6716 0.749079 1 to 2 142204 0.8692 0.807640 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-07-23_17:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2576.89 1.087 0.861556 Test results for specific bytes for dh-ranFile-2016-07-23_17:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2393.79 -1.502 0.066536 2 to 9 2383.82 -1.643 0.050187 3 to 10 2581.05 1.146 0.874146 4 to 11 2549.64 0.702 0.758662 5 to 12 2440.28 -0.845 0.199189 6 to 13 2452.81 -0.667 0.252254 7 to 14 2474.65 -0.358 0.359996 8 to 15 2504.21 0.059 0.523713 9 to 16 2571.18 1.007 0.842929 10 to 17 2594.10 1.331 0.908375 11 to 18 2541.87 0.592 0.723101 12 to 19 2452.39 -0.673 0.250395 13 to 20 2443.51 -0.799 0.212182 14 to 21 2444.92 -0.779 0.218018 15 to 22 2411.55 -1.251 0.105479 16 to 23 2547.67 0.674 0.749897 17 to 24 2476.43 -0.333 0.369433 18 to 25 2457.45 -0.602 0.273691 19 to 26 2423.12 -1.087 0.138459 20 to 27 2484.09 -0.225 0.410978 21 to 28 2585.56 1.210 0.886860 22 to 29 2482.41 -0.249 0.401763 23 to 30 2442.77 -0.809 0.209147 24 to 31 2536.80 0.520 0.698597 25 to 32 2544.21 0.625 0.734068 CDPARK for dh-ranFile-2016-07-23_17:31: 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 3537 0.6393 0.738676 3512 -0.5023 0.307734 3542 0.8676 0.807188 3514 -0.4110 0.340551 3554 1.4155 0.921543 3515 -0.3653 0.357445 3553 1.3699 0.914635 3547 1.0959 0.863437 3550 1.2329 0.891189 3506 -0.7763 0.218799 Square side=100, avg. no. parked=3533.00 sample std.=18.11 p-value of the KSTEST for those 10 p-values: 0.136776 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-07-23_17:31 0.5038,0.2180,0.2789,0.1032,0.5766,0.4163,0.3256,0.5844,0.4231,0.0598, The KS test for those 10 p-values: 0.119887 The 3DSPHERES test for dh-ranFile-2016-07-23_17:31 sample no r^3 equiv. uni. 1 125.012 0.984502 2 22.931 0.534373 3 31.888 0.654563 4 8.135 0.237508 5 33.882 0.676770 6 36.049 0.699297 7 3.045 0.096527 8 18.944 0.468194 9 4.244 0.131902 10 42.492 0.757414 11 106.478 0.971254 12 13.964 0.372163 13 22.206 0.522984 14 25.763 0.576317 15 14.773 0.388863 16 7.436 0.219533 17 30.680 0.640361 18 3.444 0.108449 19 6.699 0.200133 20 38.663 0.724390 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.827312 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-07-23_17:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -0.3 -0.1 1.2 -1.4 0.7 0.7 -0.8 0.3 -0.7 -0.7 0.0 0.8 0.8 0.6 0.7 0.2 -0.1 1.2 -0.8 0.0 0.1 -0.4 -1.2 -1.7 -1.1 -0.3 -1.5 0.8 -0.0 0.7 -0.3 0.5 1.2 0.5 1.0 0.3 1.1 0.5 1.0 0.1 0.0 -1.1 Chi-square with 42 degrees of freedom:26.273407 z-score=-1.715912, p-value=0.027516 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-07-23_17:31 Test no p-value 1 0.173363 2 0.044650 3 0.054055 4 0.116626 5 0.028844 6 0.603533 7 0.137679 8 0.456700 9 0.066639 10 0.874549 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.003491 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-07-23_17:31: (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 66724 0.05 66659 0.00 3 25000.00 25033 0.04 24995 0.00 4 6666.67 6574 1.29 6697 0.14 5 1388.89 1397 0.05 1371 0.23 6 238.10 246 0.26 237 0.01 7 34.72 23 3.96 34 0.01 8 4.96 2 1.77 6 0.22 p=0.71570 p=0.00374 Number of rngs required: 687860, p-value: 0.266 RESULTS OF CRAPS TEST for dh-ranFile-2016-07-23_17:31 No. of wins: Observed Expected 98561 98585.9 z-score=-0.111, pvalue=0.45574 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66349 66666.7 1.514 1.514 2 37640 37654.3 0.005 1.519 3 27156 26954.7 1.503 3.022 4 19209 19313.5 0.565 3.587 5 13910 13851.4 0.248 3.835 6 10198 9943.5 6.512 10.346 7 7129 7145.0 0.036 10.382 8 5192 5139.1 0.545 10.927 9 3740 3699.9 0.435 11.363 10 2566 2666.3 3.773 15.136 11 1850 1923.3 2.796 17.931 12 1361 1388.7 0.554 18.485 13 1015 1003.7 0.127 18.612 14 741 726.1 0.304 18.916 15 551 525.8 1.204 20.121 16 385 381.2 0.039 20.160 17 267 276.5 0.329 20.489 18 194 200.8 0.232 20.721 19 169 146.0 3.629 24.349 20 98 106.2 0.635 24.985 21 280 287.1 0.176 25.161 Chisq= 25.16 for 20 degrees of freedom, p= 0.80467 SUMMARY of craptest p-value for no. of wins: 0.455736 p-value for throws/game: 0.804665 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-07-23_17:31 No. of wins: Observed Expected 98673 98585.9 z-score= 0.390, pvalue=0.65164 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66739 66666.7 0.078 0.078 2 37479 37654.3 0.816 0.895 3 27172 26954.7 1.751 2.646 4 19196 19313.5 0.714 3.360 5 13995 13851.4 1.488 4.849 6 9920 9943.5 0.056 4.905 7 7173 7145.0 0.110 5.014 8 5193 5139.1 0.566 5.580 9 3689 3699.9 0.032 5.612 10 2592 2666.3 2.070 7.682 11 1861 1923.3 2.020 9.702 12 1374 1388.7 0.156 9.859 13 991 1003.7 0.161 10.020 14 680 726.1 2.932 12.951 15 550 525.8 1.110 14.062 16 385 381.2 0.039 14.101 17 238 276.5 5.371 19.472 18 239 200.8 7.255 26.726 19 165 146.0 2.477 29.203 20 116 106.2 0.901 30.105 21 253 287.1 4.053 34.158 Chisq= 34.16 for 20 degrees of freedom, p= 0.97493 SUMMARY of craptest p-value for no. of wins: 0.651638 p-value for throws/game: 0.974925 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0035,0.0037,0.0052,0.0102,0.0161,0.0229,0.0275,0.0288,0.0347,0.0348, 0.0356,0.0446,0.0446,0.0502,0.0541,0.0562,0.0574,0.0598,0.0630,0.0665, 0.0666,0.0692,0.0769,0.0808,0.0837,0.0860,0.0914,0.0929,0.0965,0.0984, 0.1021,0.1032,0.1055,0.1084,0.1086,0.1099,0.1103,0.1152,0.1166,0.1167, 0.1189,0.1199,0.1266,0.1294,0.1319,0.1341,0.1368,0.1377,0.1385,0.1418, 0.1529,0.1580,0.1677,0.1734,0.1755,0.1771,0.1827,0.1835,0.1954,0.1992, 0.2001,0.2008,0.2091,0.2091,0.2122,0.2180,0.2180,0.2188,0.2195,0.2205, 0.2243,0.2250,0.2307,0.2372,0.2375,0.2390,0.2504,0.2522,0.2523,0.2560, 0.2572,0.2617,0.2655,0.2737,0.2789,0.2886,0.2887,0.2922,0.3045,0.3056, 0.3077,0.3184,0.3256,0.3326,0.3373,0.3405,0.3406,0.3430,0.3479,0.3536, 0.3540,0.3574,0.3600,0.3634,0.3636,0.3669,0.3671,0.3680,0.3694,0.3713, 0.3722,0.3751,0.3848,0.3889,0.3929,0.4018,0.4032,0.4110,0.4163,0.4231, 0.4311,0.4314,0.4331,0.4338,0.4340,0.4376,0.4420,0.4433,0.4435,0.4497, 0.4549,0.4556,0.4557,0.4567,0.4609,0.4682,0.4690,0.4796,0.4833,0.4855, 0.4859,0.4888,0.4901,0.4960,0.4982,0.5038,0.5067,0.5087,0.5174,0.5230, 0.5233,0.5237,0.5313,0.5344,0.5396,0.5400,0.5471,0.5582,0.5637,0.5669, 0.5763,0.5766,0.5780,0.5793,0.5842,0.5844,0.5868,0.5882,0.5909,0.5933, 0.5975,0.6035,0.6056,0.6104,0.6140,0.6188,0.6404,0.6479,0.6494,0.6515, 0.6516,0.6532,0.6546,0.6620,0.6631,0.6663,0.6663,0.6678,0.6711,0.6768, 0.6779,0.6784,0.6893,0.6986,0.6993,0.7157,0.7231,0.7242,0.7244,0.7319, 0.7334,0.7341,0.7387,0.7440,0.7444,0.7491,0.7499,0.7572,0.7574,0.7587, 0.7598,0.7601,0.7659,0.7673,0.7676,0.7827,0.7886,0.7908,0.7967,0.7996, 0.8008,0.8047,0.8072,0.8076,0.8273,0.8284,0.8288,0.8300,0.8338,0.8344, 0.8402,0.8429,0.8611,0.8616,0.8634,0.8637,0.8738,0.8741,0.8745,0.8779, 0.8869,0.8912,0.8984,0.9050,0.9084,0.9128,0.9146,0.9196,0.9215,0.9289, 0.9292,0.9423,0.9492,0.9608,0.9625,0.9660,0.9667,0.9709,0.9713,0.9749, 0.9809,0.9821,0.9833,0.9843,0.9845,0.9859,0.9884,0.9904,0.9938, Overall p-value after applying KStest on 269 p-values = 0.391460 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.