* using log directory 'd:/Rcompile/CRANpkg/local/4.0/DPQ.Rcheck' * using R version 4.0.5 (2021-03-31) * using platform: x86_64-w64-mingw32 (64-bit) * using session charset: ISO8859-1 * checking for file 'DPQ/DESCRIPTION' ... OK * this is package 'DPQ' version '0.5-1' * package encoding: UTF-8 * checking package namespace information ... OK * checking package dependencies ... OK * checking if this is a source package ... OK * checking if there is a namespace ... OK * checking for hidden files and directories ... OK * checking for portable file names ... OK * checking whether package 'DPQ' can be installed ... OK * checking installed package size ... OK * checking package directory ... OK * checking 'build' directory ... OK * checking DESCRIPTION meta-information ... OK * checking top-level files ... OK * checking for left-over files ... OK * checking index information ... OK * checking package subdirectories ... OK * checking R files for non-ASCII characters ... OK * checking R files for syntax errors ... OK * loading checks for arch 'i386' ** checking whether the package can be loaded ... OK ** checking whether the package can be loaded with stated dependencies ... OK ** checking whether the package can be unloaded cleanly ... OK ** checking whether the namespace can be loaded with stated dependencies ... OK ** checking whether the namespace can be unloaded cleanly ... OK ** checking loading without being on the library search path ... OK ** checking use of S3 registration ... OK * loading checks for arch 'x64' ** checking whether the package can be loaded ... OK ** checking whether the package can be loaded with stated dependencies ... OK ** checking whether the package can be unloaded cleanly ... OK ** checking whether the namespace can be loaded with stated dependencies ... OK ** checking whether the namespace can be unloaded cleanly ... OK ** checking loading without being on the library search path ... OK ** checking use of S3 registration ... OK * checking dependencies in R code ... OK * checking S3 generic/method consistency ... OK * checking replacement functions ... OK * checking foreign function calls ... OK * checking R code for possible problems ... [25s] OK * checking Rd files ... OK * checking Rd metadata ... OK * checking Rd cross-references ... OK * checking for missing documentation entries ... OK * checking for code/documentation mismatches ... OK * checking Rd \usage sections ... OK * checking Rd contents ... OK * checking for unstated dependencies in examples ... OK * checking line endings in C/C++/Fortran sources/headers ... OK * checking pragmas in C/C++ headers and code ... OK * checking compiled code ... OK * checking sizes of PDF files under 'inst/doc' ... OK * checking installed files from 'inst/doc' ... OK * checking files in 'vignettes' ... OK * checking examples ... ** running examples for arch 'i386' ... [29s] OK ** running examples for arch 'x64' ... [24s] OK * checking for unstated dependencies in 'tests' ... OK * checking tests ... ** running tests for arch 'i386' ... [391s] ERROR Running 'chisq-nonc-ex.R' [46s] Running 'dnbinom-tst.R' [32s] Running 'dnchisq-tst.R' [1s] Running 'hyper-dist-ex.R' [51s] Running 'pnbeta-tst.R' [1s] Running 'pnt-prec.R' [37s] Running 'ppois-ex.R' [2s] Running 'qPoisBinom-ex.R' [1s] Running 'qbeta-dist.R' [15s] Running 'qbeta-tst.R' [1s] Running 'qgamma-ex.R' [22s] Running 'stirlerr-tst.R' [164s] Running 't-nonc-tst.R' [7s] Running 'wienergerm-pchisq-tst.R' [1s] Running 'wienergerm_nchisq.R' [9s] Running the tests in 'tests/stirlerr-tst.R' failed. Complete output: > #### Testing stirlerr(), bd0(), ebd0(), dpois_raw(), ... > #### =============================================== > > require(DPQ) Loading required package: DPQ > for(pkg in c("Rmpfr", "DPQmpfr")) + if(!requireNamespace(pkg)) { + cat("no CRAN package", sQuote(pkg), " ---> no tests here.\n") + q("no") + } Loading required namespace: Rmpfr Loading required namespace: DPQmpfr > require("Rmpfr") Loading required package: Rmpfr Loading required package: gmp Attaching package: 'gmp' The following objects are masked from 'package:base': %*%, apply, crossprod, matrix, tcrossprod C code of R package 'Rmpfr': GMP using 32 bits per limb Attaching package: 'Rmpfr' The following object is masked from 'package:gmp': outer The following object is masked from 'package:DPQ': log1mexp The following objects are masked from 'package:stats': dbinom, dgamma, dnbinom, dnorm, dpois, dt, pnorm The following objects are masked from 'package:base': cbind, pmax, pmin, rbind > > source(system.file(package="Matrix", "test-tools-1.R", mustWork=TRUE)) Loading required package: tools > ## -> showProc.time(), assertError(), relErrV(), ... > > ##' From ..../sfsmisc/R/relErr.R --- version that *keeps* matrix > ## Componentwise aka "Vectorized" relative error: > ## Must not be NA/NaN unless one of the components is ==> deal with {0, Inf, NA} > relErrV <- function(target, current, eps0 = .Machine$double.xmin) { + n <- length(target <- as.vector(target)) + ## assert( is multiple of ) : + lc <- length(current) + if(!n) { + if(!lc) return(numeric()) # everything length 0 + else stop("length(target) == 0 differing from length(current)") + } else if(!lc) + stop("length(current) == 0 differing from length(target)") + ## else n, lc > 0 + if(lc %% n) + stop("length(current) must be a multiple of length(target)") + recycle <- (lc != n) # explicitly recycle + R <- if(recycle) + target[rep(seq_len(n), length.out=lc)] + else + target # (possibly "mpfr") + R[] <- 0 + ## use *absolute* error when target is zero {and deal with NAs}: + t0 <- abs(target) < eps0 & !(na.t <- is.na(target)) + R[t0] <- current[t0] + ## absolute error also when it is infinite, as (-Inf, Inf) would give NaN: + dInf <- is.infinite(E <- current - target) + R[dInf] <- E[dInf] + useRE <- !dInf & !t0 & (na.t | is.na(current) | (current != target)) + R[useRE] <- (current/target)[useRE] - 1 + if(recycle) { # should also work when target is mpfrArray + if(!is.null(d <- dim(current))) + array(R, dim=d, dimnames=dimnames(current)) + else if(!is.null(nm <- names(current)) && is.null(names(R))) # not needed for mpfr + `names<-`(R, nm) + else R + } else R + } > showProc.time() Time (user system elapsed): 1.62 0.08 1.77 > > cutoffs <- c(15,35,80,500) # cut points, n=*, in the above "algorithm" > ## > n <- c(seq(1,15, by=1/4),seq(16, 25, by=1/2), 26:30, seq(32,50, by=2), seq(55,1000, by=5), + 20*c(51:99), 50*(40:80), 150*(27:48), 500*(15:20)) > st.n <- stirlerr(n)# rather use.halves=TRUE, just here , use.halves=FALSE) > plot(st.n ~ n, log="xy", type="b") ## looks good now > nM <- mpfr(n, 2048) > st.nM <- stirlerr(nM, use.halves=FALSE) ## << on purpose > all.equal(asNumeric(st.nM), st.n)# TRUE [1] TRUE > all.equal(st.nM, as(st.n,"mpfr"))# .. difference: 1.05884..............................e-15 [1] "Mean relative difference: 3.76188328836862237848210671840523134669652278507109803395524851619517133525710813038949864253324335258957995946422636705795318842095018082968414294689177210904242078505467469226107840508716759595731520562809445423582080845132783078190770966884357013373423963183831420177657134945428163130092904941631651286987113921371270172713541623773629860605382909440081832156833672439163785232423191743273755440650299060121762088567869522015326743026183287161491630854095774843808440633833644546114257377272716830527815818340327554735024334315571779348383752605170522238377026508187338666733574758200859673498905046382318912316786e-14" > all.equal(roundMpfr(st.nM, 64), as(st.n,"mpfr"), tol=1e-16)# diff.: 1.05884...e-15 [1] "Mean relative difference: 3.761883442465859304959816110162294641769e-14" > > > ## Very revealing plot showing the *relative* approximation error of stirlerr() > > p.stirlerrDev <- function(n, precBits=2048, stnM = stirlerr(mpfr(n, precBits)), abs=FALSE, + ## cut points, n=*, in the stirlerr() algorithm : + cutoffs = c(15,35,80,500), + type = "b", cex = 1, + col = adjustcolor(1, 3/4), colnB = adjustcolor("orange4", 1/3), + log = if(abs) "xy" else "x", + xlim=NULL, ylim = if(abs) c(8e-18, max(abs(N(relE))))) + { + op <- par(las = 1, mgp=c(2, 0.6, 0)) + on.exit(par(op)) + st <- stirlerr(n, cutoffs=cutoffs) + relE <- sfsmisc::relErrV(stnM, st) + N <- asNumeric + form <- if(abs) abs(N(relE)) ~ n else N(relE) ~ n + plot(form, log=log, type=type, cex=cex, col=col, xlim=xlim, ylim=ylim, + ylab = quote(relErrV(stM, st)), axes=FALSE, frame=TRUE, + main = sprintf("stirlerr(n, cutoffs) rel.error [wrt stirlerr(Rmpfr::mpfr(n, %d))]", + precBits)) + sfsmisc::eaxis(1, sub10=3) + sfsmisc::eaxis(2) + mtext(paste("cutoffs =", deparse(cutoffs))) + ylog <- par("ylog") + if(ylog) { + epsC <- c(1,2,4,8)*2^-52 + epsCxp <- expression(epsilon[C],2*epsilon[C], 4*epsilon[C], 8*epsilon[C]) + } else { + epsC <- (-2:2)*2^-52 + epsCxp <- expression(-2*epsilon[C],-epsilon[C], 0, +epsilon[C], +2*epsilon[C]) + } + dy <- diff(par("usr")[3:4]) + if(diff(range(if(ylog) log10(epsC) else epsC)) > dy/50) { + lw <- rep(1/2, 5); lw[if(ylog) 1 else 3] <- 2 + abline( h=epsC, lty=3, lwd=lw) + axis(4, at=epsC, epsCxp, las=2, cex.axis = 3/4, mgp=c(3/4, 1/4, 0), tck=0) + } else ## only x-axis + abline(h=if(ylog) epsC else 0, lty=3, lwd=2) + abline(v = cutoffs, col=colnB) + axis(3, at=cutoffs, col=colnB, col.axis=colnB, + labels = formatC(cutoffs, digits=3, width=1)) + invisible(relE) + } > > do.pdf <- TRUE > do.pdf <- !dev.interactive(orNone = TRUE) > do.pdf [1] TRUE > if(do.pdf) + pdf("stirlerr-relErr_0.pdf", width=8, height=6) > > showProc.time() Time (user system elapsed): 7.66 0.02 7.75 > > p.stirlerrDev(n=n, stnM=st.nM) # default cutoffs= c(15, 40, 85, 600) > ## show the zoom-in region in next plot > yl2 <- 3e-14*c(-1,1) > abline(h = yl2, col=adjustcolor("tomato", 1/4), lwd=3, lty=2) > > if(do.pdf) { + dev.off() ; pdf("stirlerr-relErr_1.pdf", width=8, height=6) + } > > ## drop small n > p.stirlerrDev(n=n, stnM=st.nM, xlim = c(5, max(n))) # default cutoffs= c(15, 40, 85, 600) > abline(h = yl2, col=adjustcolor("tomato", 1/4), lwd=3, lty=2) > > ## The first plot clearly shows we should do better: > ## Current code is switching to less terms too early, loosing up to 2 decimals precision > p.stirlerrDev(n=n, stnM=st.nM, ylim = yl2) > abline(h = yl2, col=adjustcolor("tomato", 1/4), lwd=3, lty=2) > > if(do.pdf) { + dev.off(); pdf("stirlerr-relErr_6-fin.pdf") + } > > showProc.time() Time (user system elapsed): 0.33 0 0.33 > > ### ~19.April 2021: "This is close to *the* solution" (but ...) > cuts <- c(7, 12, 20, 26, 60, 200, 3300) > st. <- stirlerr(n=n, cutoffs = cuts, verbose=TRUE) stirlerr(n, cutoffs = 7,12,20,26,60,200,3300) : case I (n <= 7), using direct formula for n= num [1:25] 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 3.25 ... case II (n > 7 ), 7 cutoffs: ( 7, 12, 20, 26, 60, 200, 3300 ): n in cutoff intervals: (7,12] (12,20] (20,26] (26,60] (60,200] 20 21 11 16 28 (200,3.3e+03] (3.3e+03,Inf] 236 42 > relE <- asNumeric(sfsmisc::relErrV(st.nM, st.)) > head(cbind(n, relE), 20) n relE [1,] 1.00 8.911677e-16 [2,] 1.25 -1.448799e-15 [3,] 1.50 1.594766e-15 [4,] 1.75 4.066938e-15 [5,] 2.00 -1.439463e-15 [6,] 2.25 3.992641e-15 [7,] 2.50 3.122191e-16 [8,] 2.75 1.178175e-14 [9,] 3.00 -6.421491e-15 [10,] 3.25 -1.844078e-14 [11,] 3.50 -2.035730e-15 [12,] 3.75 -1.035142e-14 [13,] 4.00 1.453032e-14 [14,] 4.25 2.251539e-14 [15,] 4.50 -3.369124e-14 [16,] 4.75 -3.534188e-14 [17,] 5.00 3.069955e-14 [18,] 5.25 -5.701343e-14 [19,] 5.50 6.708174e-15 [20,] 5.75 4.460480e-14 > ## nice printout : > print(cbind(n = format(n, drop0trailing = TRUE), + stirlerr= format(st.,scientific=FALSE, digits=4), + relErr = signif(relE, 4)) + , quote=FALSE) n stirlerr relErr [1,] 1 0.081061467 8.912e-16 [2,] 1.25 0.065431967 -1.449e-15 [3,] 1.5 0.054814121 1.595e-15 [4,] 1.75 0.047140611 4.067e-15 [5,] 2 0.041340696 -1.439e-15 [6,] 2.25 0.036805303 3.993e-15 [7,] 2.5 0.033162874 3.122e-16 [8,] 2.75 0.030174082 1.178e-14 [9,] 3 0.027677926 -6.421e-15 [10,] 3.25 0.025562158 -1.844e-14 [11,] 3.5 0.023746164 -2.036e-15 [12,] 3.75 0.022170565 -1.035e-14 [13,] 4 0.020790672 1.453e-14 [14,] 4.25 0.019572208 2.252e-14 [15,] 4.5 0.018488451 -3.369e-14 [16,] 4.75 0.017518259 -3.534e-14 [17,] 5 0.016644691 3.07e-14 [18,] 5.25 0.015854013 -5.701e-14 [19,] 5.5 0.015134973 6.708e-15 [20,] 5.75 0.014478266 4.46e-14 [21,] 6 0.013876129 -6.719e-15 [22,] 6.25 0.013322037 3.135e-15 [23,] 6.5 0.012810465 -3.891e-15 [24,] 6.75 0.012336703 -5.301e-14 [25,] 7 0.011896710 1.774e-14 [26,] 7.25 0.011487003 -3.257e-14 [27,] 7.5 0.011104560 -1.906e-14 [28,] 7.75 0.010746749 -1.141e-14 [29,] 8 0.010411265 -6.86e-15 [30,] 8.25 0.010096084 -4.267e-15 [31,] 8.5 0.009799416 -2.769e-15 [32,] 8.75 0.009519678 -1.653e-15 [33,] 9 0.009255462 -1.131e-15 [34,] 9.25 0.009005511 -8.71e-16 [35,] 9.5 0.008768700 -5.137e-16 [36,] 9.75 0.008544021 -3.593e-16 [37,] 10 0.008330563 -2.639e-16 [38,] 10.25 0.008127509 -1.544e-16 [39,] 10.5 0.007934115 -2.982e-16 [40,] 10.75 0.007749707 -9.565e-17 [41,] 11 0.007573675 -1.415e-16 [42,] 11.25 0.007405461 -1.027e-16 [43,] 11.5 0.007244554 -2.771e-17 [44,] 11.75 0.007090490 -2.427e-17 [45,] 12 0.006942840 -1.174e-16 [46,] 12.25 0.006801213 2.474e-16 [47,] 12.5 0.006665247 7.289e-17 [48,] 12.75 0.006534610 1.485e-16 [49,] 13 0.006408994 1.166e-17 [50,] 13.25 0.006288116 6.312e-17 [51,] 13.5 0.006171712 -6.452e-18 [52,] 13.75 0.006059539 1.379e-17 [53,] 14 0.005951370 -4.032e-17 [54,] 14.25 0.005846995 -2.056e-17 [55,] 14.5 0.005746217 -3.829e-17 [56,] 14.75 0.005648853 -6.556e-17 [57,] 15 0.005554734 -5.734e-17 [58,] 16 0.005207656 5.537e-19 [59,] 16.5 0.005049887 -4.726e-17 [60,] 17 0.004901396 4.783e-17 [61,] 17.5 0.004761387 -1.976e-16 [62,] 18 0.004629154 -3.698e-17 [63,] 18.5 0.004504066 -7.949e-17 [64,] 19 0.004385560 -2.207e-16 [65,] 19.5 0.004273130 -2.281e-17 [66,] 20 0.004166320 -2.273e-17 [67,] 20.5 0.004064718 -8.882e-17 [68,] 21 0.003967954 -1.583e-16 [69,] 21.5 0.003875690 6.289e-19 [70,] 22 0.003787618 -5.73e-18 [71,] 22.5 0.003703460 -9.793e-17 [72,] 23 0.003622960 -1.029e-16 [73,] 23.5 0.003545885 -2.311e-17 [74,] 24 0.003472021 -4.593e-17 [75,] 24.5 0.003401172 -9.158e-18 [76,] 25 0.003333156 2.703e-17 [77,] 26 0.003204970 -1.109e-16 [78,] 27 0.003086279 -7.897e-17 [79,] 28 0.002976064 -9.417e-18 [80,] 29 0.002873449 -2.472e-17 [81,] 30 0.002777675 3.454e-18 [82,] 32 0.002604082 -4.99e-18 [83,] 34 0.002450910 -5.68e-17 [84,] 36 0.002314755 -2.264e-18 [85,] 38 0.002192932 -3.248e-18 [86,] 40 0.002083290 -2.034e-16 [87,] 42 0.001984089 -7.638e-17 [88,] 44 0.001893907 -1.089e-16 [89,] 46 0.001811566 2.649e-17 [90,] 48 0.001736086 -8.297e-17 [91,] 50 0.001666644 4.193e-17 [92,] 55 0.001515135 -1.209e-16 [93,] 60 0.001388876 -1.322e-16 [94,] 65 0.001282041 -6.821e-17 [95,] 70 0.001190468 -2.89e-17 [96,] 75 0.001111105 -4.77e-17 [97,] 80 0.001041661 -1.163e-16 [98,] 85 0.000980388 -5.347e-17 [99,] 90 0.000925922 -3.745e-17 [100,] 95 0.000877190 -8.095e-17 [101,] 100 0.000833331 -1.496e-17 [102,] 105 0.000793648 -8.561e-17 [103,] 110 0.000757574 -2.762e-17 [104,] 115 0.000724636 6.351e-17 [105,] 120 0.000694443 -6.279e-17 [106,] 125 0.000666665 -4.699e-17 [107,] 130 0.000641024 2.201e-17 [108,] 135 0.000617283 -1.11e-17 [109,] 140 0.000595237 -7.067e-17 [110,] 145 0.000574712 -1.006e-16 [111,] 150 0.000555555 -8.214e-17 [112,] 155 0.000537634 -1.397e-16 [113,] 160 0.000520833 -1.717e-16 [114,] 165 0.000505050 -8.529e-17 [115,] 170 0.000490196 -1.66e-17 [116,] 175 0.000476190 -9.022e-17 [117,] 180 0.000462962 2.137e-17 [118,] 185 0.000450450 -8.115e-17 [119,] 190 0.000438596 -1.624e-17 [120,] 195 0.000427350 8.692e-18 [121,] 200 0.000416666 -6.039e-17 [122,] 205 0.000406504 5.003e-17 [123,] 210 0.000396825 -1.129e-17 [124,] 215 0.000387597 -4.967e-17 [125,] 220 0.000378788 1.949e-17 [126,] 225 0.000370370 -1.198e-16 [127,] 230 0.000362319 5.385e-17 [128,] 235 0.000354610 -1.021e-17 [129,] 240 0.000347222 3.399e-17 [130,] 245 0.000340136 -1.682e-16 [131,] 250 0.000333333 -9.091e-19 [132,] 255 0.000326797 -5.987e-18 [133,] 260 0.000320513 -7.05e-17 [134,] 265 0.000314465 -6.944e-17 [135,] 270 0.000308642 -8.838e-17 [136,] 275 0.000303030 -2.459e-17 [137,] 280 0.000297619 5.586e-18 [138,] 285 0.000292398 -1.002e-16 [139,] 290 0.000287356 -4.698e-17 [140,] 295 0.000282486 3.589e-18 [141,] 300 0.000277778 -8.79e-17 [142,] 305 0.000273224 5.592e-17 [143,] 310 0.000268817 -9.722e-17 [144,] 315 0.000264550 -1.114e-16 [145,] 320 0.000260417 9.132e-17 [146,] 325 0.000256410 -3.948e-17 [147,] 330 0.000252525 -4.325e-17 [148,] 335 0.000248756 -9.059e-17 [149,] 340 0.000245098 -1.621e-16 [150,] 345 0.000241546 1.338e-17 [151,] 350 0.000238095 3.486e-17 [152,] 355 0.000234742 -2.086e-17 [153,] 360 0.000231481 -1.147e-16 [154,] 365 0.000228310 3.977e-17 [155,] 370 0.000225225 -4.736e-17 [156,] 375 0.000222222 -5.641e-17 [157,] 380 0.000219298 -9.447e-17 [158,] 385 0.000216450 -7.211e-17 [159,] 390 0.000213675 -6.235e-18 [160,] 395 0.000210970 4.771e-17 [161,] 400 0.000208333 -1.837e-16 [162,] 405 0.000205761 -9.207e-17 [163,] 410 0.000203252 4.984e-17 [164,] 415 0.000200803 2.075e-17 [165,] 420 0.000198413 -1.513e-16 [166,] 425 0.000196078 -1.915e-16 [167,] 430 0.000193798 -1.057e-16 [168,] 435 0.000191571 -7.294e-17 [169,] 440 0.000189394 -9.068e-17 [170,] 445 0.000187266 -1.479e-17 [171,] 450 0.000185185 -1.037e-16 [172,] 455 0.000183150 -4.903e-17 [173,] 460 0.000181159 -1.496e-19 [174,] 465 0.000179211 -8.755e-17 [175,] 470 0.000177305 -9.812e-17 [176,] 475 0.000175439 1.823e-17 [177,] 480 0.000173611 -1.402e-16 [178,] 485 0.000171821 -1.02e-16 [179,] 490 0.000170068 -1.477e-16 [180,] 495 0.000168350 -8.904e-17 [181,] 500 0.000166667 -1.651e-16 [182,] 505 0.000165016 -2.034e-17 [183,] 510 0.000163399 -2.66e-17 [184,] 515 0.000161812 5.707e-17 [185,] 520 0.000160256 -1.283e-16 [186,] 525 0.000158730 -7.213e-17 [187,] 530 0.000157233 2.542e-17 [188,] 535 0.000155763 9.391e-17 [189,] 540 0.000154321 -1.605e-16 [190,] 545 0.000152905 -1.192e-16 [191,] 550 0.000151515 -3.43e-17 [192,] 555 0.000150150 4.472e-17 [193,] 560 0.000148810 -2.576e-17 [194,] 565 0.000147493 1.196e-16 [195,] 570 0.000146199 1.552e-17 [196,] 575 0.000144928 -2.12e-16 [197,] 580 0.000143678 -1.148e-17 [198,] 585 0.000142450 -1.407e-16 [199,] 590 0.000141243 -8.399e-17 [200,] 595 0.000140056 -5.62e-17 [201,] 600 0.000138889 -9.309e-17 [202,] 605 0.000137741 -1.692e-16 [203,] 610 0.000136612 6.936e-17 [204,] 615 0.000135501 -8.611e-17 [205,] 620 0.000134409 3.987e-17 [206,] 625 0.000133333 -4.148e-17 [207,] 630 0.000132275 -1.1e-16 [208,] 635 0.000131234 -6.594e-17 [209,] 640 0.000130208 -2.265e-17 [210,] 645 0.000129199 2.465e-17 [211,] 650 0.000128205 -5.088e-17 [212,] 655 0.000127226 -5.245e-17 [213,] 660 0.000126263 -1.364e-16 [214,] 665 0.000125313 -1.784e-16 [215,] 670 0.000124378 -4.501e-17 [216,] 675 0.000123457 -3.045e-17 [217,] 680 0.000122549 -7.071e-17 [218,] 685 0.000121654 -8.794e-17 [219,] 690 0.000120773 -9.828e-17 [220,] 695 0.000119904 -7.036e-17 [221,] 700 0.000119048 -1.581e-17 [222,] 705 0.000118203 -3.835e-17 [223,] 710 0.000117371 -5.492e-17 [224,] 715 0.000116550 -2.908e-17 [225,] 720 0.000115741 -3.447e-17 [226,] 725 0.000114943 5.42e-17 [227,] 730 0.000114155 -1.388e-16 [228,] 735 0.000113379 -1.045e-16 [229,] 740 0.000112613 -3.46e-17 [230,] 745 0.000111857 1.05e-17 [231,] 750 0.000111111 -3.025e-17 [232,] 755 0.000110375 -1.144e-16 [233,] 760 0.000109649 -2.414e-17 [234,] 765 0.000108932 -7.09e-17 [235,] 770 0.000108225 -4.449e-17 [236,] 775 0.000107527 -1.123e-16 [237,] 780 0.000106838 -3.249e-18 [238,] 785 0.000106157 2.321e-17 [239,] 790 0.000105485 5.064e-17 [240,] 795 0.000104822 -1.233e-16 [241,] 800 0.000104167 -1.748e-16 [242,] 805 0.000103520 -1.378e-16 [243,] 810 0.000102881 -9.075e-17 [244,] 815 0.000102249 -1.586e-16 [245,] 820 0.000101626 -7.227e-17 [246,] 825 0.000101010 -3.838e-17 [247,] 830 0.000100402 -2.964e-17 [248,] 835 0.000099800 -1.876e-16 [249,] 840 0.000099206 -2.759e-17 [250,] 845 0.000098619 -1.536e-16 [251,] 850 0.000098039 -8.679e-17 [252,] 855 0.000097466 -1.494e-16 [253,] 860 0.000096899 -1.483e-16 [254,] 865 0.000096339 2.876e-17 [255,] 870 0.000095785 -3.176e-17 [256,] 875 0.000095238 2.357e-17 [257,] 880 0.000094697 -1.091e-16 [258,] 885 0.000094162 -5.772e-17 [259,] 890 0.000093633 -1.744e-16 [260,] 895 0.000093110 -1.181e-16 [261,] 900 0.000092593 -1.335e-16 [262,] 905 0.000092081 -5.527e-17 [263,] 910 0.000091575 -1.198e-16 [264,] 915 0.000091075 -1.207e-16 [265,] 920 0.000090580 -5.728e-17 [266,] 925 0.000090090 -4.742e-19 [267,] 930 0.000089606 -5.574e-17 [268,] 935 0.000089127 8.545e-17 [269,] 940 0.000088652 -1.068e-16 [270,] 945 0.000088183 -1.4e-17 [271,] 950 0.000087719 -4.414e-17 [272,] 955 0.000087260 -7.53e-17 [273,] 960 0.000086806 -1.683e-16 [274,] 965 0.000086356 3.832e-17 [275,] 970 0.000085911 -7.401e-17 [276,] 975 0.000085470 -5.156e-17 [277,] 980 0.000085034 -7.189e-17 [278,] 985 0.000084602 -6.9e-17 [279,] 990 0.000084175 -6.533e-17 [280,] 995 0.000083752 -1.062e-16 [281,] 1000 0.000083333 4.47e-17 [282,] 1020 0.000081699 -2.043e-16 [283,] 1040 0.000080128 3.465e-17 [284,] 1060 0.000078616 1.744e-17 [285,] 1080 0.000077160 2.023e-19 [286,] 1100 0.000075758 -8.344e-17 [287,] 1120 0.000074405 4.223e-18 [288,] 1140 0.000073099 1.678e-17 [289,] 1160 0.000071839 1.405e-17 [290,] 1180 0.000070621 1.336e-17 [291,] 1200 0.000069444 -3.825e-18 [292,] 1220 0.000068306 -1.316e-16 [293,] 1240 0.000067204 4.497e-17 [294,] 1260 0.000066138 8.852e-17 [295,] 1280 0.000065104 -4.096e-17 [296,] 1300 0.000064103 -1.05e-16 [297,] 1320 0.000063131 -1.565e-17 [298,] 1340 0.000062189 8.636e-17 [299,] 1360 0.000061275 -8.111e-17 [300,] 1380 0.000060386 -4.864e-17 [301,] 1400 0.000059524 -1.377e-16 [302,] 1420 0.000058685 -4.785e-17 [303,] 1440 0.000057870 7.827e-17 [304,] 1460 0.000057078 -3.29e-17 [305,] 1480 0.000056306 -2.93e-17 [306,] 1500 0.000055556 3.087e-17 [307,] 1520 0.000054825 1.479e-17 [308,] 1540 0.000054113 -6.619e-17 [309,] 1560 0.000053419 -6.097e-17 [310,] 1580 0.000052743 -1.745e-16 [311,] 1600 0.000052083 -1.245e-16 [312,] 1620 0.000051440 -3.918e-17 [313,] 1640 0.000050813 -6.98e-17 [314,] 1660 0.000050201 -9.32e-17 [315,] 1680 0.000049603 -6.853e-18 [316,] 1700 0.000049020 -8.787e-17 [317,] 1720 0.000048450 3.516e-17 [318,] 1740 0.000047893 -4.948e-17 [319,] 1760 0.000047348 1.593e-17 [320,] 1780 0.000046816 -6.248e-17 [321,] 1800 0.000046296 5.308e-17 [322,] 1820 0.000045788 -5.345e-17 [323,] 1840 0.000045290 -5.611e-17 [324,] 1860 0.000044803 -1.23e-16 [325,] 1880 0.000044326 -2.026e-17 [326,] 1900 0.000043860 7.87e-17 [327,] 1920 0.000043403 -5.773e-17 [328,] 1940 0.000042955 4.493e-18 [329,] 1960 0.000042517 -4.638e-17 [330,] 1980 0.000042088 -4.982e-17 [331,] 2000 0.000041667 -1.709e-17 [332,] 2050 0.000040650 1.564e-17 [333,] 2100 0.000039683 5.082e-17 [334,] 2150 0.000038760 -5.206e-17 [335,] 2200 0.000037879 3.535e-17 [336,] 2250 0.000037037 -2.37e-17 [337,] 2300 0.000036232 -1.453e-16 [338,] 2350 0.000035461 -1.478e-16 [339,] 2400 0.000034722 7.893e-17 [340,] 2450 0.000034014 1.053e-16 [341,] 2500 0.000033333 -1.249e-16 [342,] 2550 0.000032680 -2.632e-17 [343,] 2600 0.000032051 -3.594e-17 [344,] 2650 0.000031447 -2.662e-17 [345,] 2700 0.000030864 -1.459e-16 [346,] 2750 0.000030303 -1.228e-16 [347,] 2800 0.000029762 2.86e-18 [348,] 2850 0.000029240 1.979e-17 [349,] 2900 0.000028736 -8.976e-18 [350,] 2950 0.000028249 -8.074e-17 [351,] 3000 0.000027778 3.047e-17 [352,] 3050 0.000027322 -8.783e-17 [353,] 3100 0.000026882 -9.946e-17 [354,] 3150 0.000026455 -5.146e-17 [355,] 3200 0.000026042 -3.577e-17 [356,] 3250 0.000025641 -9.052e-17 [357,] 3300 0.000025253 -7.322e-17 [358,] 3350 0.000024876 -1.866e-16 [359,] 3400 0.000024510 -1.21e-17 [360,] 3450 0.000024155 -1.608e-16 [361,] 3500 0.000023810 9.896e-18 [362,] 3550 0.000023474 -1.422e-16 [363,] 3600 0.000023148 -7.342e-17 [364,] 3650 0.000022831 -1.147e-16 [365,] 3700 0.000022523 -1.354e-16 [366,] 3750 0.000022222 -7.032e-17 [367,] 3800 0.000021930 -9.196e-17 [368,] 3850 0.000021645 -1.068e-16 [369,] 3900 0.000021368 -1.001e-16 [370,] 3950 0.000021097 -8.581e-18 [371,] 4000 0.000020833 -8.034e-17 [372,] 4050 0.000020576 -1.234e-16 [373,] 4200 0.000019841 -1.95e-16 [374,] 4350 0.000019157 -1.488e-16 [375,] 4500 0.000018519 -1.747e-16 [376,] 4650 0.000017921 -1.313e-16 [377,] 4800 0.000017361 -7.346e-17 [378,] 4950 0.000016835 -1.846e-16 [379,] 5100 0.000016340 4.508e-18 [380,] 5250 0.000015873 -1.385e-16 [381,] 5400 0.000015432 -9.5e-17 [382,] 5550 0.000015015 -3.488e-17 [383,] 5700 0.000014620 -2.353e-17 [384,] 5850 0.000014245 -3.92e-17 [385,] 6000 0.000013889 -1.174e-16 [386,] 6150 0.000013550 -1.588e-16 [387,] 6300 0.000013228 -2.74e-17 [388,] 6450 0.000012920 -2.363e-17 [389,] 6600 0.000012626 -7.098e-17 [390,] 6750 0.000012346 -8.038e-18 [391,] 6900 0.000012077 -4.655e-17 [392,] 7050 0.000011820 -6.789e-17 [393,] 7200 0.000011574 -4.496e-17 [394,] 7500 0.000011111 -4.884e-17 [395,] 8000 0.000010417 -7.881e-17 [396,] 8500 0.000009804 -9.742e-19 [397,] 9000 0.000009259 -3.391e-18 [398,] 9500 0.000008772 6.364e-17 [399,] 10000 0.000008333 -3.753e-17 > > if(do.pdf) { + dev.off(); pdf("stirlerr-relErr_6-fin-1.pdf") + } > > p.stirlerrDev(n=n, stnM=st.nM, cex=1/4, type="o", cutoffs = cuts) > > if(do.pdf) { dev.off(); pdf("stirlerr-relErr_6-fin-2.pdf") } > > ## zoom in ==> {good for n >= 10} > p.stirlerrDev(n=n, stnM=st.nM, cex=1/4, type="o", ylim = 2e-15*c(-1,1), + cutoffs = cuts)## old default cutoffs = c(15,35, 80, 500) > > if(do.pdf) { dev.off(); pdf("stirlerr-tst_others.pdf") } > > ##-- April 20: we more terms up to S10 in stirlerr() -- more cutoffs > n <- sfsmisc::lseq(1/16, 5000, length=4096) > nM <- mpfr(n, 2048) > st.nM <- stirlerr(nM, use.halves=FALSE) ## << on purpose > > cuts <- c(5.4, 7.5, 8.5, 10.625, 12.125, 20, 26, 60, 200, 3300) > p.stirlerrDev(n=n, stnM=st.nM, cex=1/4, type="o", cutoffs = cuts) > p.stirlerrDev(n=n, stnM=st.nM, cex=1/4, type="o", cutoffs = cuts, abs=TRUE) > ## using exact values sferr_halves[] > lines((0:30)/2, abs(stirlerr((0:30)/2, cutoffs=cuts, verbose=TRUE)/DPQ:::sferr_halves - 1), type="o", col=2,lwd=2) stirlerr(n, cutoffs = 5.4,7.5,8.5,10.62,12.12,20,26,60,200,3300) : case I (n <= 5.4), using direct formula for n= num [1:11] 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 ... case II (n > 5.4 ), 10 cutoffs: ( 5.4, 7.5, 8.5, 10.625, 12.125, 20, 26, 60, 200, 3300 ): n in cutoff intervals: (5.4,7.5] (7.5,8.5] (8.5,10.6] (10.6,12.1] (12.1,20] 5 2 4 3 6 (20,26] (26,60] (60,200] (200,3.3e+03] (3.3e+03,Inf] 0 0 0 0 0 > ## should we e.g., use interpolation spline through sfserr_halves[] for n <= 7.5 > ## -- doing the interpolation on the log(1 - 12*x*stirlerr(x)) vs log2(x) scale -- maybe ? > curve(1-12*x*stirlerr(x, verbose=TRUE), 1/64, 8, log="xy", n=2048) stirlerr(n, scheme = "R3") : case I (n <= 15), using direct formula for n= num [1:2048] 0.0156 0.0157 0.0157 0.0158 0.0158 ... > ## just need "true" values for x = 2^-(6,5,4,3,2) in addition to those we already have at x = 1/2, 1.5, 2, 2.5, ..., 7.5, 8 > > p.stirlerrDev(n=n, stnM=st.nM, cex=1/4, type="o", cutoffs = cuts, ylim=c(-1,1)*4e-14) > p.stirlerrDev(n=n, stnM=st.nM, cex=1/4, type="o", cutoffs = cuts, ylim=c(-1,1)*1e-15) > > st. <- stirlerr(n=n, cutoffs = cuts, verbose=TRUE) stirlerr(n, cutoffs = 5.4,7.5,8.5,10.62,12.12,20,26,60,200,3300) : case I (n <= 5.4), using direct formula for n= num [1:1618] 0.0625 0.0627 0.0628 0.063 0.0632 ... case II (n > 5.4 ), 10 cutoffs: ( 5.4, 7.5, 8.5, 10.625, 12.125, 20, 26, 60, 200, 3300 ): n in cutoff intervals: (5.4,7.5] (7.5,8.5] (8.5,10.6] (10.6,12.1] (12.1,20] 119 45 81 48 182 (20,26] (26,60] (60,200] (200,3.3e+03] (3.3e+03,Inf] 95 303 437 1017 151 > relE <- asNumeric(sfsmisc::relErrV(st.nM, st.)) > head(cbind(n, relE), 20) n relE [1,] 0.06250000 1.145349e-16 [2,] 0.06267255 2.991784e-16 [3,] 0.06284557 -8.156474e-17 [4,] 0.06301908 1.528496e-16 [5,] 0.06319306 9.174643e-17 [6,] 0.06336752 -7.677091e-17 [7,] 0.06354246 5.967122e-17 [8,] 0.06371789 4.722483e-16 [9,] 0.06389380 1.721318e-16 [10,] 0.06407019 3.924397e-16 [11,] 0.06424708 -1.777654e-16 [12,] 0.06442445 5.391117e-16 [13,] 0.06460231 3.499214e-16 [14,] 0.06478066 1.961559e-16 [15,] 0.06495951 -9.756855e-17 [16,] 0.06513885 2.139647e-16 [17,] 0.06531868 1.273413e-16 [18,] 0.06549901 2.265762e-16 [19,] 0.06567984 2.202612e-16 [20,] 0.06586116 2.793055e-16 > ## nice printout : > print(cbind(n = format(n, drop0trailing = TRUE), + stirlerr= format(st.,scientific=FALSE, digits=4), + relErr = signif(asNumeric(sfsmisc::relErrV(st.nM, st.)), 4)) + , quote=FALSE) n stirlerr relErr [1,] 6.250000e-02 0.67018552 1.145e-16 [2,] 6.267255e-02 0.66920260 2.992e-16 [3,] 6.284557e-02 0.66822034 -8.156e-17 [4,] 6.301908e-02 0.66723875 1.528e-16 [5,] 6.319306e-02 0.66625781 9.175e-17 [6,] 6.336752e-02 0.66527753 -7.677e-17 [7,] 6.354246e-02 0.66429792 5.967e-17 [8,] 6.371789e-02 0.66331897 4.722e-16 [9,] 6.389380e-02 0.66234069 1.721e-16 [10,] 6.407019e-02 0.66136307 3.924e-16 [11,] 6.424708e-02 0.66038612 -1.778e-16 [12,] 6.442445e-02 0.65940984 5.391e-16 [13,] 6.460231e-02 0.65843422 3.499e-16 [14,] 6.478066e-02 0.65745927 1.962e-16 [15,] 6.495951e-02 0.65648499 -9.757e-17 [16,] 6.513885e-02 0.65551138 2.14e-16 [17,] 6.531868e-02 0.65453844 1.273e-16 [18,] 6.549901e-02 0.65356617 2.266e-16 [19,] 6.567984e-02 0.65259457 2.203e-16 [20,] 6.586116e-02 0.65162365 2.793e-16 [21,] 6.604299e-02 0.65065339 1.932e-16 [22,] 6.622532e-02 0.64968382 7.097e-16 [23,] 6.640815e-02 0.64871491 -1.901e-17 [24,] 6.659149e-02 0.64774669 -1.838e-16 [25,] 6.677534e-02 0.64677914 -1.391e-16 [26,] 6.695969e-02 0.64581226 -1.213e-16 [27,] 6.714455e-02 0.64484607 2.032e-16 [28,] 6.732992e-02 0.64388055 -1.909e-16 [29,] 6.751580e-02 0.64291571 -2.471e-16 [30,] 6.770220e-02 0.64195156 5.63e-16 [31,] 6.788911e-02 0.64098808 2.884e-16 [32,] 6.807653e-02 0.64002528 3.839e-16 [33,] 6.826448e-02 0.63906317 -1.54e-17 [34,] 6.845294e-02 0.63810174 -1.624e-16 [35,] 6.864192e-02 0.63714099 3.531e-16 [36,] 6.883143e-02 0.63618093 -3.276e-16 [37,] 6.902145e-02 0.63522155 3.731e-16 [38,] 6.921201e-02 0.63426286 1.101e-17 [39,] 6.940309e-02 0.63330486 2.713e-16 [40,] 6.959469e-02 0.63234754 -3.426e-16 [41,] 6.978683e-02 0.63139091 4.905e-16 [42,] 6.997949e-02 0.63043497 4.93e-16 [43,] 7.017269e-02 0.62947972 1.414e-16 [44,] 7.036642e-02 0.62852516 -2.749e-16 [45,] 7.056069e-02 0.62757129 1.261e-16 [46,] 7.075549e-02 0.62661811 1.128e-16 [47,] 7.095083e-02 0.62566562 2.61e-16 [48,] 7.114671e-02 0.62471383 -4.31e-17 [49,] 7.134313e-02 0.62376273 -1.228e-17 [50,] 7.154009e-02 0.62281233 -2.894e-16 [51,] 7.173759e-02 0.62186262 -1.316e-16 [52,] 7.193564e-02 0.62091361 3.339e-16 [53,] 7.213424e-02 0.61996529 -1.485e-16 [54,] 7.233339e-02 0.61901767 -1.836e-16 [55,] 7.253308e-02 0.61807075 2.161e-16 [56,] 7.273333e-02 0.61712453 -2.776e-16 [57,] 7.293413e-02 0.61617901 3.135e-16 [58,] 7.313549e-02 0.61523418 2.281e-16 [59,] 7.333740e-02 0.61429006 5.148e-16 [60,] 7.353986e-02 0.61334664 3.787e-16 [61,] 7.374289e-02 0.61240393 -4.606e-17 [62,] 7.394648e-02 0.61146191 -7.132e-17 [63,] 7.415063e-02 0.61052061 -3.845e-17 [64,] 7.435534e-02 0.60958000 7.328e-17 [65,] 7.456062e-02 0.60864010 -4.679e-17 [66,] 7.476646e-02 0.60770091 2.763e-16 [67,] 7.497288e-02 0.60676242 2.448e-16 [68,] 7.517986e-02 0.60582464 -4.094e-16 [69,] 7.538741e-02 0.60488757 -5.742e-17 [70,] 7.559554e-02 0.60395121 -8.479e-18 [71,] 7.580424e-02 0.60301555 -5.085e-17 [72,] 7.601352e-02 0.60208061 -2.045e-16 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0.01661895 -5.103e-14 [1592,] 5.021590 0.01657331 3.576e-14 [1593,] 5.035453 0.01652780 1.084e-14 [1594,] 5.049355 0.01648242 6.429e-14 [1595,] 5.063295 0.01643715 1.895e-14 [1596,] 5.077274 0.01639201 -1.663e-14 [1597,] 5.091291 0.01634700 -1.755e-14 [1598,] 5.105347 0.01630210 -3.623e-14 [1599,] 5.119441 0.01625733 7.705e-14 [1600,] 5.133575 0.01621269 8.107e-14 [1601,] 5.147748 0.01616816 -5.02e-14 [1602,] 5.161959 0.01612376 -6.217e-14 [1603,] 5.176210 0.01607947 -1.751e-14 [1604,] 5.190501 0.01603531 -1.608e-14 [1605,] 5.204831 0.01599127 -2.249e-14 [1606,] 5.219200 0.01594735 3.152e-14 [1607,] 5.233609 0.01590355 2.939e-14 [1608,] 5.248058 0.01585987 1.076e-14 [1609,] 5.262546 0.01581631 6.705e-14 [1610,] 5.277075 0.01577286 1.029e-14 [1611,] 5.291644 0.01572954 5.312e-14 [1612,] 5.306253 0.01568633 -8.552e-14 [1613,] 5.320902 0.01564325 6.729e-14 [1614,] 5.335592 0.01560028 -1.031e-14 [1615,] 5.350322 0.01555743 -1.604e-14 [1616,] 5.365093 0.01551469 1.058e-13 [1617,] 5.379905 0.01547207 5.09e-14 [1618,] 5.394758 0.01542957 1.946e-14 [1619,] 5.409652 0.01538719 9.621e-14 [1620,] 5.424586 0.01534492 9.065e-14 [1621,] 5.439562 0.01530276 8.538e-14 [1622,] 5.454580 0.01526073 8.059e-14 [1623,] 5.469639 0.01521880 7.582e-14 [1624,] 5.484739 0.01517699 7.153e-14 [1625,] 5.499881 0.01513530 6.751e-14 [1626,] 5.515065 0.01509372 6.365e-14 [1627,] 5.530291 0.01505225 6e-14 [1628,] 5.545559 0.01501090 5.648e-14 [1629,] 5.560869 0.01496966 5.319e-14 [1630,] 5.576221 0.01492853 5.026e-14 [1631,] 5.591616 0.01488752 4.74e-14 [1632,] 5.607053 0.01484662 4.472e-14 [1633,] 5.622533 0.01480583 4.205e-14 [1634,] 5.638055 0.01476515 3.96e-14 [1635,] 5.653621 0.01472458 3.732e-14 [1636,] 5.669229 0.01468412 3.523e-14 [1637,] 5.684881 0.01464378 3.318e-14 [1638,] 5.700575 0.01460354 3.131e-14 [1639,] 5.716313 0.01456342 2.948e-14 [1640,] 5.732095 0.01452340 2.786e-14 [1641,] 5.747920 0.01448350 2.608e-14 [1642,] 5.763788 0.01444370 2.469e-14 [1643,] 5.779701 0.01440401 2.329e-14 [1644,] 5.795657 0.01436443 2.191e-14 [1645,] 5.811658 0.01432496 2.066e-14 [1646,] 5.827702 0.01428560 1.948e-14 [1647,] 5.843791 0.01424634 1.828e-14 [1648,] 5.859925 0.01420720 1.729e-14 [1649,] 5.876103 0.01416816 1.636e-14 [1650,] 5.892325 0.01412922 1.538e-14 [1651,] 5.908593 0.01409040 1.446e-14 [1652,] 5.924905 0.01405167 1.372e-14 [1653,] 5.941262 0.01401306 1.288e-14 [1654,] 5.957665 0.01397455 1.203e-14 [1655,] 5.974112 0.01393615 1.145e-14 [1656,] 5.990605 0.01389785 1.08e-14 [1657,] 6.007144 0.01385966 1.003e-14 [1658,] 6.023729 0.01382157 9.508e-15 [1659,] 6.040359 0.01378358 9.021e-15 [1660,] 6.057035 0.01374570 8.534e-15 [1661,] 6.073757 0.01370793 7.955e-15 [1662,] 6.090525 0.01367025 7.403e-15 [1663,] 6.107340 0.01363268 6.97e-15 [1664,] 6.124201 0.01359522 6.675e-15 [1665,] 6.141108 0.01355785 6.239e-15 [1666,] 6.158062 0.01352059 5.955e-15 [1667,] 6.175063 0.01348343 5.494e-15 [1668,] 6.192111 0.01344637 5.252e-15 [1669,] 6.209206 0.01340941 4.995e-15 [1670,] 6.226348 0.01337256 4.568e-15 [1671,] 6.243538 0.01333580 4.355e-15 [1672,] 6.260775 0.01329915 4.07e-15 [1673,] 6.278060 0.01326259 4.011e-15 [1674,] 6.295392 0.01322614 3.663e-15 [1675,] 6.312772 0.01318979 3.446e-15 [1676,] 6.330200 0.01315353 3.286e-15 [1677,] 6.347676 0.01311738 3.085e-15 [1678,] 6.365201 0.01308132 2.747e-15 [1679,] 6.382774 0.01304537 2.705e-15 [1680,] 6.400395 0.01300951 2.549e-15 [1681,] 6.418065 0.01297375 2.425e-15 [1682,] 6.435784 0.01293809 2.28e-15 [1683,] 6.453552 0.01290252 2.132e-15 [1684,] 6.471368 0.01286705 2.002e-15 [1685,] 6.489234 0.01283168 1.88e-15 [1686,] 6.507150 0.01279641 1.846e-15 [1687,] 6.525114 0.01276124 1.664e-15 [1688,] 6.543129 0.01272616 1.497e-15 [1689,] 6.561193 0.01269117 1.562e-15 [1690,] 6.579307 0.01265628 1.381e-15 [1691,] 6.597471 0.01262149 1.384e-15 [1692,] 6.615685 0.01258680 1.241e-15 [1693,] 6.633949 0.01255219 1.224e-15 [1694,] 6.652264 0.01251769 1.121e-15 [1695,] 6.670629 0.01248328 9.35e-16 [1696,] 6.689046 0.01244896 9.259e-16 [1697,] 6.707512 0.01241473 8.073e-16 [1698,] 6.726030 0.01238060 7.786e-16 [1699,] 6.744599 0.01234657 8.528e-16 [1700,] 6.763220 0.01231262 6.848e-16 [1701,] 6.781891 0.01227877 7.067e-16 [1702,] 6.800615 0.01224502 6.823e-16 [1703,] 6.819390 0.01221135 6.953e-16 [1704,] 6.838216 0.01217778 4.6e-16 [1705,] 6.857095 0.01214430 4.165e-16 [1706,] 6.876026 0.01211091 3.989e-16 [1707,] 6.895009 0.01207761 4.197e-16 [1708,] 6.914045 0.01204441 4.496e-16 [1709,] 6.933133 0.01201129 2.82e-16 [1710,] 6.952274 0.01197827 4.606e-16 [1711,] 6.971467 0.01194533 3.791e-16 [1712,] 6.990714 0.01191249 2.57e-16 [1713,] 7.010014 0.01187974 2.866e-16 [1714,] 7.029367 0.01184708 3.743e-16 [1715,] 7.048773 0.01181450 3.281e-16 [1716,] 7.068233 0.01178202 2.185e-16 [1717,] 7.087747 0.01174962 3.291e-16 [1718,] 7.107315 0.01171732 2.477e-16 [1719,] 7.126936 0.01168510 2.109e-16 [1720,] 7.146612 0.01165297 2.017e-16 [1721,] 7.166342 0.01162093 6.539e-17 [1722,] 7.186127 0.01158897 1.037e-16 [1723,] 7.205966 0.01155711 1.101e-16 [1724,] 7.225860 0.01152533 1.341e-17 [1725,] 7.245809 0.01149364 1.204e-16 [1726,] 7.265813 0.01146203 4.788e-17 [1727,] 7.285872 0.01143052 1.286e-16 [1728,] 7.305987 0.01139909 1.012e-16 [1729,] 7.326157 0.01136774 8.558e-17 [1730,] 7.346383 0.01133648 1.444e-16 [1731,] 7.366665 0.01130531 -1.294e-17 [1732,] 7.387002 0.01127422 8.415e-17 [1733,] 7.407396 0.01124322 5.994e-17 [1734,] 7.427846 0.01121230 3.653e-17 [1735,] 7.448353 0.01118147 1.144e-16 [1736,] 7.468916 0.01115072 8.587e-18 [1737,] 7.489536 0.01112006 1.529e-16 [1738,] 7.510213 0.01108948 -4.146e-16 [1739,] 7.530947 0.01105898 -4.109e-16 [1740,] 7.551738 0.01102857 -4.397e-16 [1741,] 7.572587 0.01099824 -2.923e-16 [1742,] 7.593493 0.01096800 -3.568e-16 [1743,] 7.614457 0.01093783 -3.542e-16 [1744,] 7.635479 0.01090775 -3.314e-16 [1745,] 7.656558 0.01087776 -2.319e-16 [1746,] 7.677696 0.01084784 -1.937e-16 [1747,] 7.698893 0.01081801 -3.779e-16 [1748,] 7.720148 0.01078826 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0.01004275 -2.556e-16 [1775,] 8.316751 0.01001513 -2.442e-16 [1776,] 8.339711 0.00998758 -2.471e-17 [1777,] 8.362735 0.00996011 -2.17e-16 [1778,] 8.385823 0.00993272 -1.558e-16 [1779,] 8.408974 0.00990539 -1.62e-17 [1780,] 8.432189 0.00987815 -1.539e-16 [1781,] 8.455469 0.00985098 -1.104e-16 [1782,] 8.478812 0.00982388 4.677e-17 [1783,] 8.502220 0.00979686 1.204e-16 [1784,] 8.525693 0.00976991 1.811e-16 [1785,] 8.549231 0.00974304 8.497e-17 [1786,] 8.572833 0.00971624 1.501e-16 [1787,] 8.596501 0.00968951 5.23e-17 [1788,] 8.620234 0.00966286 1.735e-16 [1789,] 8.644032 0.00963628 4.978e-17 [1790,] 8.667896 0.00960977 1.398e-17 [1791,] 8.691827 0.00958334 1.379e-16 [1792,] 8.715823 0.00955698 1.98e-16 [1793,] 8.739885 0.00953069 1.847e-16 [1794,] 8.764014 0.00950447 1.555e-16 [1795,] 8.788209 0.00947832 6.017e-17 [1796,] 8.812472 0.00945225 1.039e-16 [1797,] 8.836801 0.00942625 -1.388e-17 [1798,] 8.861197 0.00940032 2.376e-17 [1799,] 8.885661 0.00937446 6.669e-17 [1800,] 8.910192 0.00934867 1.162e-16 [1801,] 8.934791 0.00932296 -1.462e-17 [1802,] 8.959458 0.00929731 5.874e-19 [1803,] 8.984193 0.00927173 -5.881e-17 [1804,] 9.008996 0.00924623 -2.404e-17 [1805,] 9.033868 0.00922079 1.485e-16 [1806,] 9.058809 0.00919543 1.256e-16 [1807,] 9.083818 0.00917013 -3.139e-17 [1808,] 9.108896 0.00914490 8.469e-17 [1809,] 9.134044 0.00911975 -6.71e-19 [1810,] 9.159261 0.00909466 1.242e-17 [1811,] 9.184548 0.00906964 3.433e-18 [1812,] 9.209904 0.00904469 -3.947e-17 [1813,] 9.235330 0.00901980 -4.689e-17 [1814,] 9.260827 0.00899499 1.167e-16 [1815,] 9.286394 0.00897024 5.882e-17 [1816,] 9.312032 0.00894557 1.5e-17 [1817,] 9.337740 0.00892096 -1.168e-16 [1818,] 9.363519 0.00889641 1.749e-17 [1819,] 9.389370 0.00887194 -1.304e-16 [1820,] 9.415292 0.00884753 -3.264e-17 [1821,] 9.441285 0.00882319 -2.846e-17 [1822,] 9.467351 0.00879892 -1.343e-16 [1823,] 9.493488 0.00877471 2.75e-17 [1824,] 9.519697 0.00875057 1.389e-17 [1825,] 9.545979 0.00872650 -9.471e-18 [1826,] 9.572333 0.00870249 -1.314e-17 [1827,] 9.598760 0.00867855 7.487e-17 [1828,] 9.625260 0.00865467 1.187e-17 [1829,] 9.651833 0.00863086 -1.369e-16 [1830,] 9.678480 0.00860711 -3.837e-17 [1831,] 9.705200 0.00858343 -2.653e-17 [1832,] 9.731994 0.00855982 1.415e-16 [1833,] 9.758861 0.00853627 8.007e-17 [1834,] 9.785803 0.00851278 -1.995e-17 [1835,] 9.812820 0.00848936 -8.4e-17 [1836,] 9.839911 0.00846600 -1.04e-17 [1837,] 9.867076 0.00844271 -3.402e-17 [1838,] 9.894317 0.00841948 -1.135e-16 [1839,] 9.921633 0.00839632 -2.318e-17 [1840,] 9.949025 0.00837322 4.748e-17 [1841,] 9.976492 0.00835018 -6.795e-17 [1842,] 1.000403e+01 0.00832721 3.842e-17 [1843,] 1.003165e+01 0.00830430 4.107e-17 [1844,] 1.005935e+01 0.00828145 9.206e-17 [1845,] 1.008712e+01 0.00825866 -1.059e-16 [1846,] 1.011497e+01 0.00823594 -5.163e-17 [1847,] 1.014289e+01 0.00821328 -5.503e-17 [1848,] 1.017090e+01 0.00819068 6.677e-17 [1849,] 1.019897e+01 0.00816814 -1.815e-16 [1850,] 1.022713e+01 0.00814567 7.084e-17 [1851,] 1.025537e+01 0.00812326 -1.878e-17 [1852,] 1.028368e+01 0.00810091 -5.638e-17 [1853,] 1.031207e+01 0.00807862 6.926e-18 [1854,] 1.034054e+01 0.00805639 -9.775e-17 [1855,] 1.036909e+01 0.00803422 -5.051e-17 [1856,] 1.039771e+01 0.00801212 -1.397e-16 [1857,] 1.042642e+01 0.00799007 -1.683e-17 [1858,] 1.045520e+01 0.00796809 8.494e-17 [1859,] 1.048407e+01 0.00794616 -5.612e-17 [1860,] 1.051301e+01 0.00792430 5.178e-17 [1861,] 1.054204e+01 0.00790250 3.639e-17 [1862,] 1.057114e+01 0.00788075 -1.239e-16 [1863,] 1.060033e+01 0.00785907 -5.24e-17 [1864,] 1.062959e+01 0.00783744 -1.61e-16 [1865,] 1.065894e+01 0.00781588 -1.936e-16 [1866,] 1.068836e+01 0.00779437 -1.577e-16 [1867,] 1.071787e+01 0.00777292 2.622e-18 [1868,] 1.074746e+01 0.00775154 -5.205e-17 [1869,] 1.077713e+01 0.00773021 -1.411e-16 [1870,] 1.080689e+01 0.00770894 -1.529e-16 [1871,] 1.083672e+01 0.00768773 -5.368e-17 [1872,] 1.086664e+01 0.00766657 -7.389e-17 [1873,] 1.089664e+01 0.00764548 -1.113e-16 [1874,] 1.092672e+01 0.00762444 -5.381e-17 [1875,] 1.095689e+01 0.00760346 -8.969e-17 [1876,] 1.098714e+01 0.00758254 -4.332e-17 [1877,] 1.101747e+01 0.00756167 -3.428e-17 [1878,] 1.104789e+01 0.00754086 1.961e-17 [1879,] 1.107839e+01 0.00752011 -1.036e-16 [1880,] 1.110897e+01 0.00749942 -6.48e-17 [1881,] 1.113964e+01 0.00747879 -1.48e-16 [1882,] 1.117040e+01 0.00745821 -1.848e-16 [1883,] 1.120124e+01 0.00743768 -4.813e-17 [1884,] 1.123216e+01 0.00741722 -1.039e-16 [1885,] 1.126317e+01 0.00739681 -1.243e-16 [1886,] 1.129426e+01 0.00737645 -1.41e-16 [1887,] 1.132545e+01 0.00735615 -4.483e-17 [1888,] 1.135671e+01 0.00733591 -3.847e-17 [1889,] 1.138807e+01 0.00731573 -1.765e-16 [1890,] 1.141951e+01 0.00729559 -5.919e-17 [1891,] 1.145103e+01 0.00727552 -1.412e-16 [1892,] 1.148265e+01 0.00725550 -1.079e-16 [1893,] 1.151435e+01 0.00723553 -1.41e-16 [1894,] 1.154614e+01 0.00721562 -1.136e-16 [1895,] 1.157801e+01 0.00719577 -1.192e-16 [1896,] 1.160998e+01 0.00717596 4.681e-17 [1897,] 1.164203e+01 0.00715622 -1.651e-16 [1898,] 1.167417e+01 0.00713652 -1.101e-16 [1899,] 1.170640e+01 0.00711689 -8.113e-17 [1900,] 1.173872e+01 0.00709730 -1.512e-16 [1901,] 1.177113e+01 0.00707777 -1.474e-16 [1902,] 1.180362e+01 0.00705829 -9.768e-17 [1903,] 1.183621e+01 0.00703887 -7.933e-17 [1904,] 1.186889e+01 0.00701950 3.457e-17 [1905,] 1.190165e+01 0.00700018 1.787e-17 [1906,] 1.193451e+01 0.00698092 3.691e-17 [1907,] 1.196746e+01 0.00696171 -1.819e-17 [1908,] 1.200050e+01 0.00694255 -1.1e-16 [1909,] 1.203363e+01 0.00692345 2.361e-17 [1910,] 1.206685e+01 0.00690439 4.718e-17 [1911,] 1.210017e+01 0.00688539 -1.019e-16 [1912,] 1.213357e+01 0.00686644 1.179e-16 [1913,] 1.216707e+01 0.00684755 1.086e-16 [1914,] 1.220066e+01 0.00682870 1.867e-16 [1915,] 1.223434e+01 0.00680991 1.018e-16 [1916,] 1.226812e+01 0.00679117 1.738e-16 [1917,] 1.230199e+01 0.00677248 4.797e-17 [1918,] 1.233595e+01 0.00675385 2.418e-17 [1919,] 1.237001e+01 0.00673526 2.535e-17 [1920,] 1.240416e+01 0.00671672 1.171e-16 [1921,] 1.243841e+01 0.00669824 8.973e-17 [1922,] 1.247274e+01 0.00667981 1.108e-16 [1923,] 1.250718e+01 0.00666142 -2.753e-17 [1924,] 1.254171e+01 0.00664309 1.31e-16 [1925,] 1.257633e+01 0.00662481 3.372e-17 [1926,] 1.261105e+01 0.00660658 8.811e-17 [1927,] 1.264587e+01 0.00658840 1.354e-16 [1928,] 1.268078e+01 0.00657026 1.844e-17 [1929,] 1.271579e+01 0.00655218 1.096e-16 [1930,] 1.275090e+01 0.00653415 8.427e-17 [1931,] 1.278610e+01 0.00651617 8.817e-17 [1932,] 1.282140e+01 0.00649824 4.359e-17 [1933,] 1.285680e+01 0.00648035 7.854e-17 [1934,] 1.289229e+01 0.00646252 3.333e-17 [1935,] 1.292788e+01 0.00644473 5.688e-17 [1936,] 1.296357e+01 0.00642700 1.234e-16 [1937,] 1.299936e+01 0.00640931 7.49e-17 [1938,] 1.303525e+01 0.00639167 9.276e-17 [1939,] 1.307124e+01 0.00637408 5.967e-17 [1940,] 1.310733e+01 0.00635654 -1.096e-16 [1941,] 1.314351e+01 0.00633904 -1.116e-17 [1942,] 1.317980e+01 0.00632160 6.359e-17 [1943,] 1.321618e+01 0.00630420 -4.362e-18 [1944,] 1.325267e+01 0.00628685 1.946e-17 [1945,] 1.328926e+01 0.00626955 6.637e-17 [1946,] 1.332595e+01 0.00625229 -5.855e-17 [1947,] 1.336274e+01 0.00623508 5.636e-17 [1948,] 1.339963e+01 0.00621793 -9.854e-17 [1949,] 1.343662e+01 0.00620081 2.668e-17 [1950,] 1.347372e+01 0.00618375 -1.729e-17 [1951,] 1.351092e+01 0.00616673 -3.522e-17 [1952,] 1.354822e+01 0.00614976 -2.041e-17 [1953,] 1.358562e+01 0.00613283 1.176e-17 [1954,] 1.362313e+01 0.00611595 -4.01e-17 [1955,] 1.366074e+01 0.00609912 -8.449e-17 [1956,] 1.369845e+01 0.00608233 6.346e-17 [1957,] 1.373627e+01 0.00606559 1.837e-17 [1958,] 1.377419e+01 0.00604890 -3.592e-17 [1959,] 1.381222e+01 0.00603225 -8.856e-18 [1960,] 1.385035e+01 0.00601565 -6.647e-17 [1961,] 1.388859e+01 0.00599909 3.621e-18 [1962,] 1.392693e+01 0.00598258 -6.722e-17 [1963,] 1.396538e+01 0.00596612 -9.877e-17 [1964,] 1.400394e+01 0.00594970 -2.662e-17 [1965,] 1.404260e+01 0.00593332 2.319e-17 [1966,] 1.408137e+01 0.00591699 -7.307e-17 [1967,] 1.412024e+01 0.00590071 6.137e-17 [1968,] 1.415922e+01 0.00588447 -3.574e-17 [1969,] 1.419832e+01 0.00586827 -3.63e-17 [1970,] 1.423751e+01 0.00585212 -5.372e-17 [1971,] 1.427682e+01 0.00583601 -8.689e-17 [1972,] 1.431624e+01 0.00581995 -4.634e-17 [1973,] 1.435576e+01 0.00580393 -5.897e-17 [1974,] 1.439539e+01 0.00578796 -7.167e-17 [1975,] 1.443513e+01 0.00577203 6.173e-17 [1976,] 1.447499e+01 0.00575614 -4.044e-17 [1977,] 1.451495e+01 0.00574030 2.463e-17 [1978,] 1.455502e+01 0.00572450 -6.677e-17 [1979,] 1.459520e+01 0.00570875 -6.493e-17 [1980,] 1.463550e+01 0.00569303 -3.427e-17 [1981,] 1.467590e+01 0.00567736 -1.003e-17 [1982,] 1.471642e+01 0.00566174 -5.983e-17 [1983,] 1.475705e+01 0.00564616 2.222e-17 [1984,] 1.479779e+01 0.00563062 2.28e-17 [1985,] 1.483864e+01 0.00561512 -1.098e-16 [1986,] 1.487961e+01 0.00559966 -7.868e-18 [1987,] 1.492069e+01 0.00558425 -6.327e-17 [1988,] 1.496188e+01 0.00556888 -1.04e-16 [1989,] 1.500319e+01 0.00555355 2.548e-17 [1990,] 1.504461e+01 0.00553827 -7.335e-17 [1991,] 1.508614e+01 0.00552303 -1.296e-17 [1992,] 1.512779e+01 0.00550782 -3.03e-17 [1993,] 1.516956e+01 0.00549266 7.078e-17 [1994,] 1.521144e+01 0.00547755 -4.144e-18 [1995,] 1.525343e+01 0.00546247 1.816e-18 [1996,] 1.529554e+01 0.00544744 3.829e-17 [1997,] 1.533777e+01 0.00543244 -5.778e-17 [1998,] 1.538011e+01 0.00541749 1.961e-17 [1999,] 1.542257e+01 0.00540258 1.976e-17 [2000,] 1.546515e+01 0.00538771 8.565e-17 [2001,] 1.550785e+01 0.00537288 -5.308e-17 [2002,] 1.555066e+01 0.00535809 -8.871e-17 [2003,] 1.559359e+01 0.00534334 3.356e-17 [2004,] 1.563664e+01 0.00532864 -1.687e-16 [2005,] 1.567981e+01 0.00531397 -9.577e-18 [2006,] 1.572310e+01 0.00529934 -4.947e-17 [2007,] 1.576651e+01 0.00528476 -1.163e-16 [2008,] 1.581004e+01 0.00527021 -2.078e-17 [2009,] 1.585369e+01 0.00525570 4.32e-17 [2010,] 1.589745e+01 0.00524124 1.276e-18 [2011,] 1.594134e+01 0.00522681 8.286e-17 [2012,] 1.598535e+01 0.00521243 4.246e-18 [2013,] 1.602949e+01 0.00519808 -8.425e-17 [2014,] 1.607374e+01 0.00518377 1.77e-17 [2015,] 1.611812e+01 0.00516950 -1.656e-16 [2016,] 1.616261e+01 0.00515527 4.461e-17 [2017,] 1.620724e+01 0.00514108 -9.962e-17 [2018,] 1.625198e+01 0.00512693 -6.854e-17 [2019,] 1.629685e+01 0.00511282 -1.134e-16 [2020,] 1.634184e+01 0.00509875 4.852e-17 [2021,] 1.638696e+01 0.00508472 -5.987e-17 [2022,] 1.643220e+01 0.00507072 -1.361e-16 [2023,] 1.647756e+01 0.00505676 -5.319e-18 [2024,] 1.652305e+01 0.00504284 -1.526e-17 [2025,] 1.656867e+01 0.00502896 4.312e-17 [2026,] 1.661441e+01 0.00501512 -8.638e-17 [2027,] 1.666028e+01 0.00500132 -1.513e-16 [2028,] 1.670628e+01 0.00498755 3.846e-17 [2029,] 1.675240e+01 0.00497382 -9.375e-17 [2030,] 1.679865e+01 0.00496013 5.155e-18 [2031,] 1.684502e+01 0.00494648 -7.903e-17 [2032,] 1.689153e+01 0.00493286 -6.641e-17 [2033,] 1.693816e+01 0.00491929 -5.549e-17 [2034,] 1.698493e+01 0.00490575 -2.278e-18 [2035,] 1.703182e+01 0.00489224 3.901e-17 [2036,] 1.707884e+01 0.00487878 -9.192e-17 [2037,] 1.712599e+01 0.00486535 -4.879e-18 [2038,] 1.717327e+01 0.00485195 9.207e-17 [2039,] 1.722068e+01 0.00483860 -5.966e-17 [2040,] 1.726822e+01 0.00482528 9.654e-17 [2041,] 1.731590e+01 0.00481200 9.568e-17 [2042,] 1.736370e+01 0.00479875 -1.056e-17 [2043,] 1.741164e+01 0.00478554 -7.328e-18 [2044,] 1.745971e+01 0.00477237 -9.762e-17 [2045,] 1.750791e+01 0.00475924 -1.138e-17 [2046,] 1.755625e+01 0.00474614 -1.058e-16 [2047,] 1.760472e+01 0.00473307 -5.018e-17 [2048,] 1.765332e+01 0.00472004 4.424e-17 [2049,] 1.770205e+01 0.00470705 -6.861e-18 [2050,] 1.775093e+01 0.00469409 -5.499e-17 [2051,] 1.779993e+01 0.00468117 4.379e-17 [2052,] 1.784907e+01 0.00466829 -8.447e-17 [2053,] 1.789835e+01 0.00465544 4.407e-17 [2054,] 1.794776e+01 0.00464262 1.823e-17 [2055,] 1.799731e+01 0.00462984 -3.046e-17 [2056,] 1.804700e+01 0.00461710 -7.409e-17 [2057,] 1.809682e+01 0.00460439 -1.609e-17 [2058,] 1.814679e+01 0.00459172 -3.871e-17 [2059,] 1.819688e+01 0.00457908 -1.089e-16 [2060,] 1.824712e+01 0.00456647 -5.247e-17 [2061,] 1.829750e+01 0.00455390 5.46e-17 [2062,] 1.834801e+01 0.00454137 -2.091e-16 [2063,] 1.839867e+01 0.00452887 -2.247e-17 [2064,] 1.844946e+01 0.00451640 -4.334e-17 [2065,] 1.850040e+01 0.00450397 -4.428e-17 [2066,] 1.855147e+01 0.00449157 -5.642e-17 [2067,] 1.860269e+01 0.00447921 -7.311e-17 [2068,] 1.865405e+01 0.00446688 -8.131e-18 [2069,] 1.870555e+01 0.00445458 -1.434e-16 [2070,] 1.875719e+01 0.00444232 -7.461e-17 [2071,] 1.880897e+01 0.00443009 -9.759e-17 [2072,] 1.886090e+01 0.00441790 -1.179e-16 [2073,] 1.891297e+01 0.00440574 -4.526e-17 [2074,] 1.896518e+01 0.00439361 2.184e-19 [2075,] 1.901754e+01 0.00438152 5.326e-17 [2076,] 1.907005e+01 0.00436945 -2.399e-17 [2077,] 1.912269e+01 0.00435743 5.05e-17 [2078,] 1.917549e+01 0.00434543 6.714e-17 [2079,] 1.922843e+01 0.00433347 -2.294e-17 [2080,] 1.928151e+01 0.00432154 -4.095e-17 [2081,] 1.933474e+01 0.00430965 3.615e-18 [2082,] 1.938812e+01 0.00429778 -4.997e-17 [2083,] 1.944165e+01 0.00428595 1.603e-17 [2084,] 1.949532e+01 0.00427415 -1.55e-16 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1.633339e+02 0.00051020 6.654e-17 [2856,] 1.637848e+02 0.00050880 -7.254e-17 [2857,] 1.642370e+02 0.00050740 -8.123e-17 [2858,] 1.646904e+02 0.00050600 -3.608e-17 [2859,] 1.651451e+02 0.00050461 -6.361e-17 [2860,] 1.656010e+02 0.00050322 -1.22e-16 [2861,] 1.660582e+02 0.00050183 -5.553e-17 [2862,] 1.665166e+02 0.00050045 -5.51e-17 [2863,] 1.669764e+02 0.00049907 6.464e-17 [2864,] 1.674373e+02 0.00049770 2.795e-17 [2865,] 1.678996e+02 0.00049633 -1.351e-16 [2866,] 1.683631e+02 0.00049496 3.86e-17 [2867,] 1.688279e+02 0.00049360 -3.305e-17 [2868,] 1.692940e+02 0.00049224 -1.124e-16 [2869,] 1.697614e+02 0.00049088 -1.161e-16 [2870,] 1.702301e+02 0.00048953 -2.685e-17 [2871,] 1.707001e+02 0.00048819 1.435e-17 [2872,] 1.711713e+02 0.00048684 -1.619e-17 [2873,] 1.716439e+02 0.00048550 -8.423e-17 [2874,] 1.721178e+02 0.00048416 -8.609e-17 [2875,] 1.725929e+02 0.00048283 -5.218e-17 [2876,] 1.730694e+02 0.00048150 -1.197e-16 [2877,] 1.735472e+02 0.00048018 -4.316e-17 [2878,] 1.740264e+02 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2.116537e+02 0.00039372 1.648e-17 [2950,] 2.122380e+02 0.00039264 -9.598e-17 [2951,] 2.128240e+02 0.00039156 1.043e-16 [2952,] 2.134115e+02 0.00039048 -6.339e-18 [2953,] 2.140007e+02 0.00038941 7.703e-17 [2954,] 2.145915e+02 0.00038833 1.032e-16 [2955,] 2.151840e+02 0.00038727 1.364e-16 [2956,] 2.157780e+02 0.00038620 -6.379e-17 [2957,] 2.163737e+02 0.00038514 7.119e-17 [2958,] 2.169711e+02 0.00038408 2.173e-17 [2959,] 2.175701e+02 0.00038302 9.425e-18 [2960,] 2.181708e+02 0.00038196 -2.002e-17 [2961,] 2.187731e+02 0.00038091 1.261e-16 [2962,] 2.193771e+02 0.00037986 7.865e-17 [2963,] 2.199827e+02 0.00037882 -3.272e-17 [2964,] 2.205900e+02 0.00037777 5.71e-17 [2965,] 2.211990e+02 0.00037673 -2.395e-17 [2966,] 2.218097e+02 0.00037570 8.566e-17 [2967,] 2.224221e+02 0.00037466 9.883e-17 [2968,] 2.230361e+02 0.00037363 5.203e-17 [2969,] 2.236519e+02 0.00037260 1.101e-17 [2970,] 2.242694e+02 0.00037158 -8.405e-17 [2971,] 2.248885e+02 0.00037055 -1.012e-17 [2972,] 2.255094e+02 0.00036953 5.965e-17 [2973,] 2.261320e+02 0.00036852 -1.362e-17 [2974,] 2.267563e+02 0.00036750 -7.84e-18 [2975,] 2.273823e+02 0.00036649 8.281e-17 [2976,] 2.280100e+02 0.00036548 -2.544e-17 [2977,] 2.286395e+02 0.00036447 -8.031e-18 [2978,] 2.292707e+02 0.00036347 -1.281e-16 [2979,] 2.299037e+02 0.00036247 6.645e-17 [2980,] 2.305384e+02 0.00036147 -7.303e-17 [2981,] 2.311749e+02 0.00036048 -1.339e-17 [2982,] 2.318131e+02 0.00035948 -4.778e-17 [2983,] 2.324531e+02 0.00035850 -8.137e-17 [2984,] 2.330948e+02 0.00035751 -1.089e-16 [2985,] 2.337383e+02 0.00035652 -1.408e-17 [2986,] 2.343836e+02 0.00035554 2.106e-17 [2987,] 2.350307e+02 0.00035456 -3.665e-17 [2988,] 2.356796e+02 0.00035359 -7.411e-17 [2989,] 2.363302e+02 0.00035261 -8.284e-17 [2990,] 2.369827e+02 0.00035164 -8.285e-17 [2991,] 2.376370e+02 0.00035067 -1.029e-16 [2992,] 2.382930e+02 0.00034971 2.841e-17 [2993,] 2.389509e+02 0.00034875 -5.204e-17 [2994,] 2.396106e+02 0.00034779 -1.076e-16 [2995,] 2.402721e+02 0.00034683 -3.36e-17 [2996,] 2.409354e+02 0.00034587 -3.663e-17 [2997,] 2.416006e+02 0.00034492 3.698e-18 [2998,] 2.422676e+02 0.00034397 -1.854e-17 [2999,] 2.429364e+02 0.00034303 -6.268e-17 [3000,] 2.436071e+02 0.00034208 -5.22e-17 [3001,] 2.442797e+02 0.00034114 3.741e-17 [3002,] 2.449541e+02 0.00034020 -9.428e-17 [3003,] 2.456303e+02 0.00033926 -1.251e-17 [3004,] 2.463085e+02 0.00033833 -3.348e-17 [3005,] 2.469885e+02 0.00033740 2.887e-17 [3006,] 2.476703e+02 0.00033647 -5.896e-17 [3007,] 2.483541e+02 0.00033554 -6.896e-17 [3008,] 2.490398e+02 0.00033462 -3.259e-17 [3009,] 2.497273e+02 0.00033370 9.402e-17 [3010,] 2.504167e+02 0.00033278 2.598e-17 [3011,] 2.511081e+02 0.00033186 -9.439e-17 [3012,] 2.518013e+02 0.00033095 -3.64e-17 [3013,] 2.524965e+02 0.00033004 -7.669e-17 [3014,] 2.531936e+02 0.00032913 1.122e-16 [3015,] 2.538926e+02 0.00032822 -8.772e-17 [3016,] 2.545935e+02 0.00032732 -1.098e-16 [3017,] 2.552964e+02 0.00032642 3.69e-17 [3018,] 2.560012e+02 0.00032552 -6.246e-17 [3019,] 2.567080e+02 0.00032462 -4.632e-17 [3020,] 2.574167e+02 0.00032373 3.849e-17 [3021,] 2.581274e+02 0.00032284 9.765e-17 [3022,] 2.588400e+02 0.00032195 -6.194e-17 [3023,] 2.595546e+02 0.00032106 5.816e-17 [3024,] 2.602712e+02 0.00032018 7.125e-17 [3025,] 2.609897e+02 0.00031930 3.951e-17 [3026,] 2.617102e+02 0.00031842 -9.708e-17 [3027,] 2.624328e+02 0.00031754 -1.197e-16 [3028,] 2.631573e+02 0.00031667 3.842e-17 [3029,] 2.638838e+02 0.00031580 -1.073e-17 [3030,] 2.646123e+02 0.00031493 -1.307e-16 [3031,] 2.653429e+02 0.00031406 -4.761e-17 [3032,] 2.660754e+02 0.00031319 -1.81e-16 [3033,] 2.668100e+02 0.00031233 -3.332e-17 [3034,] 2.675466e+02 0.00031147 -5.84e-17 [3035,] 2.682852e+02 0.00031061 -2.396e-17 [3036,] 2.690259e+02 0.00030976 -7.558e-17 [3037,] 2.697686e+02 0.00030891 3.772e-17 [3038,] 2.705134e+02 0.00030806 1.146e-16 [3039,] 2.712602e+02 0.00030721 -5.47e-17 [3040,] 2.720091e+02 0.00030636 5.547e-18 [3041,] 2.727601e+02 0.00030552 1.835e-18 [3042,] 2.735131e+02 0.00030468 -4.651e-17 [3043,] 2.742682e+02 0.00030384 -2.431e-17 [3044,] 2.750254e+02 0.00030300 -1.28e-16 [3045,] 2.757847e+02 0.00030217 6.474e-18 [3046,] 2.765460e+02 0.00030134 -8.83e-18 [3047,] 2.773095e+02 0.00030051 -3.663e-17 [3048,] 2.780751e+02 0.00029968 -1.382e-16 [3049,] 2.788428e+02 0.00029885 2.125e-17 [3050,] 2.796126e+02 0.00029803 -3.38e-17 [3051,] 2.803846e+02 0.00029721 -1.678e-16 [3052,] 2.811587e+02 0.00029639 -1.773e-17 [3053,] 2.819349e+02 0.00029558 -5.007e-17 [3054,] 2.827132e+02 0.00029476 -5.878e-17 [3055,] 2.834937e+02 0.00029395 6.112e-18 [3056,] 2.842764e+02 0.00029314 7.043e-17 [3057,] 2.850612e+02 0.00029233 -1.603e-16 [3058,] 2.858482e+02 0.00029153 -7.767e-17 [3059,] 2.866374e+02 0.00029073 -1.666e-16 [3060,] 2.874287e+02 0.00028993 -1.831e-17 [3061,] 2.882222e+02 0.00028913 -6.988e-17 [3062,] 2.890179e+02 0.00028833 -1.013e-16 [3063,] 2.898159e+02 0.00028754 -3.311e-17 [3064,] 2.906160e+02 0.00028675 -1.263e-16 [3065,] 2.914183e+02 0.00028596 -1.438e-16 [3066,] 2.922228e+02 0.00028517 9.157e-17 [3067,] 2.930296e+02 0.00028439 -5.526e-17 [3068,] 2.938386e+02 0.00028360 8.919e-17 [3069,] 2.946498e+02 0.00028282 -2.728e-17 [3070,] 2.954633e+02 0.00028204 -4.895e-17 [3071,] 2.962790e+02 0.00028127 -1.449e-16 [3072,] 2.970969e+02 0.00028049 -4.763e-17 [3073,] 2.979172e+02 0.00027972 6.71e-17 [3074,] 2.987396e+02 0.00027895 -6.536e-17 [3075,] 2.995644e+02 0.00027818 3.488e-17 [3076,] 3.003914e+02 0.00027742 -1.053e-17 [3077,] 3.012207e+02 0.00027665 -5.712e-17 [3078,] 3.020523e+02 0.00027589 -7.668e-17 [3079,] 3.028862e+02 0.00027513 1.665e-17 [3080,] 3.037224e+02 0.00027437 5.536e-17 [3081,] 3.045609e+02 0.00027362 -1.532e-16 [3082,] 3.054018e+02 0.00027286 -4.959e-17 [3083,] 3.062449e+02 0.00027211 -7.754e-17 [3084,] 3.070904e+02 0.00027136 -1.113e-16 [3085,] 3.079382e+02 0.00027062 -1.182e-16 [3086,] 3.087883e+02 0.00026987 -1.472e-16 [3087,] 3.096408e+02 0.00026913 -3.797e-18 [3088,] 3.104957e+02 0.00026839 -1.209e-16 [3089,] 3.113529e+02 0.00026765 -6.033e-17 [3090,] 3.122125e+02 0.00026691 2.64e-17 [3091,] 3.130744e+02 0.00026618 4.426e-17 [3092,] 3.139387e+02 0.00026544 9.726e-17 [3093,] 3.148054e+02 0.00026471 4.725e-17 [3094,] 3.156745e+02 0.00026398 4.91e-17 [3095,] 3.165460e+02 0.00026326 -8.602e-17 [3096,] 3.174200e+02 0.00026253 6.398e-18 [3097,] 3.182963e+02 0.00026181 -7.652e-17 [3098,] 3.191750e+02 0.00026109 -5.484e-17 [3099,] 3.200562e+02 0.00026037 -1.258e-16 [3100,] 3.209398e+02 0.00025965 2.295e-17 [3101,] 3.218258e+02 0.00025894 1.024e-16 [3102,] 3.227143e+02 0.00025823 4.926e-17 [3103,] 3.236053e+02 0.00025752 -4.786e-17 [3104,] 3.244987e+02 0.00025681 -4.623e-17 [3105,] 3.253945e+02 0.00025610 1.138e-16 [3106,] 3.262929e+02 0.00025539 -1.53e-16 [3107,] 3.271937e+02 0.00025469 -3.162e-17 [3108,] 3.280970e+02 0.00025399 -8.803e-17 [3109,] 3.290028e+02 0.00025329 -4.047e-17 [3110,] 3.299111e+02 0.00025259 -3.968e-17 [3111,] 3.308219e+02 0.00025190 -9.965e-17 [3112,] 3.317352e+02 0.00025120 -9.531e-17 [3113,] 3.326511e+02 0.00025051 -3.367e-17 [3114,] 3.335695e+02 0.00024982 -5.184e-17 [3115,] 3.344904e+02 0.00024914 -3.57e-17 [3116,] 3.354138e+02 0.00024845 9.073e-19 [3117,] 3.363398e+02 0.00024777 1.056e-16 [3118,] 3.372684e+02 0.00024708 -1.103e-16 [3119,] 3.381995e+02 0.00024640 -7.439e-17 [3120,] 3.391332e+02 0.00024572 -1.251e-16 [3121,] 3.400695e+02 0.00024505 -1.61e-16 [3122,] 3.410083e+02 0.00024437 -4.495e-17 [3123,] 3.419498e+02 0.00024370 -9.272e-17 [3124,] 3.428938e+02 0.00024303 -1.393e-17 [3125,] 3.438405e+02 0.00024236 -3.886e-18 [3126,] 3.447897e+02 0.00024169 6.661e-17 [3127,] 3.457416e+02 0.00024103 -8.998e-17 [3128,] 3.466961e+02 0.00024036 -6.72e-17 [3129,] 3.476533e+02 0.00023970 2.197e-17 [3130,] 3.486131e+02 0.00023904 -2.422e-17 [3131,] 3.495755e+02 0.00023838 -4.427e-17 [3132,] 3.505406e+02 0.00023773 -5.503e-17 [3133,] 3.515084e+02 0.00023707 -4.625e-17 [3134,] 3.524788e+02 0.00023642 -3.431e-17 [3135,] 3.534519e+02 0.00023577 2.116e-17 [3136,] 3.544277e+02 0.00023512 -9.155e-17 [3137,] 3.554062e+02 0.00023447 -7.349e-17 [3138,] 3.563874e+02 0.00023383 -7.913e-17 [3139,] 3.573713e+02 0.00023318 1.346e-17 [3140,] 3.583579e+02 0.00023254 -7.706e-17 [3141,] 3.593473e+02 0.00023190 2.197e-17 [3142,] 3.603393e+02 0.00023126 -1.027e-16 [3143,] 3.613342e+02 0.00023063 4.423e-17 [3144,] 3.623317e+02 0.00022999 -8.581e-17 [3145,] 3.633320e+02 0.00022936 2.299e-17 [3146,] 3.643351e+02 0.00022873 -3.696e-17 [3147,] 3.653410e+02 0.00022810 -2.913e-17 [3148,] 3.663496e+02 0.00022747 -2.14e-17 [3149,] 3.673610e+02 0.00022684 4.508e-17 [3150,] 3.683752e+02 0.00022622 3.907e-17 [3151,] 3.693922e+02 0.00022560 6.563e-17 [3152,] 3.704120e+02 0.00022497 -1.702e-17 [3153,] 3.714346e+02 0.00022436 -1.014e-16 [3154,] 3.724601e+02 0.00022374 -6.374e-17 [3155,] 3.734883e+02 0.00022312 -6.3e-17 [3156,] 3.745195e+02 0.00022251 -1.232e-16 [3157,] 3.755534e+02 0.00022189 -1.312e-16 [3158,] 3.765902e+02 0.00022128 -1.686e-17 [3159,] 3.776299e+02 0.00022067 7.184e-17 [3160,] 3.786725e+02 0.00022007 -7.672e-18 [3161,] 3.797179e+02 0.00021946 -4.089e-17 [3162,] 3.807662e+02 0.00021886 -7.667e-17 [3163,] 3.818174e+02 0.00021825 -6.623e-17 [3164,] 3.828715e+02 0.00021765 1.601e-17 [3165,] 3.839285e+02 0.00021705 -1.342e-16 [3166,] 3.849885e+02 0.00021646 -9.454e-17 [3167,] 3.860513e+02 0.00021586 -6.855e-17 [3168,] 3.871171e+02 0.00021527 -1.51e-16 [3169,] 3.881859e+02 0.00021467 -2.663e-17 [3170,] 3.892576e+02 0.00021408 2.853e-17 [3171,] 3.903322e+02 0.00021349 6.447e-17 [3172,] 3.914099e+02 0.00021291 -1.663e-16 [3173,] 3.924904e+02 0.00021232 1.011e-18 [3174,] 3.935740e+02 0.00021173 -2.993e-17 [3175,] 3.946606e+02 0.00021115 2.985e-17 [3176,] 3.957502e+02 0.00021057 6.267e-18 [3177,] 3.968427e+02 0.00020999 -4.186e-17 [3178,] 3.979383e+02 0.00020941 -1.624e-16 [3179,] 3.990369e+02 0.00020884 -7.564e-17 [3180,] 4.001386e+02 0.00020826 -1.039e-16 [3181,] 4.012433e+02 0.00020769 -5.516e-17 [3182,] 4.023510e+02 0.00020712 -4.639e-17 [3183,] 4.034618e+02 0.00020655 -3.623e-17 [3184,] 4.045757e+02 0.00020598 -1.891e-16 [3185,] 4.056926e+02 0.00020541 -4.818e-17 [3186,] 4.068127e+02 0.00020484 5.664e-18 [3187,] 4.079358e+02 0.00020428 -1.371e-16 [3188,] 4.090620e+02 0.00020372 -1.856e-16 [3189,] 4.101913e+02 0.00020316 -1.023e-17 [3190,] 4.113238e+02 0.00020260 -6.758e-17 [3191,] 4.124593e+02 0.00020204 2.558e-17 [3192,] 4.135980e+02 0.00020148 -8.471e-17 [3193,] 4.147399e+02 0.00020093 -5.963e-17 [3194,] 4.158849e+02 0.00020038 -4.848e-17 [3195,] 4.170330e+02 0.00019982 -3.666e-17 [3196,] 4.181844e+02 0.00019927 -8.505e-17 [3197,] 4.193389e+02 0.00019873 -6.804e-17 [3198,] 4.204966e+02 0.00019818 -3.212e-17 [3199,] 4.216575e+02 0.00019763 -1.981e-16 [3200,] 4.228216e+02 0.00019709 -8.592e-17 [3201,] 4.239889e+02 0.00019655 -1.278e-18 [3202,] 4.251594e+02 0.00019600 -1.548e-16 [3203,] 4.263332e+02 0.00019547 -7.169e-17 [3204,] 4.275102e+02 0.00019493 -5.047e-17 [3205,] 4.286905e+02 0.00019439 3.067e-18 [3206,] 4.298740e+02 0.00019386 -4.713e-17 [3207,] 4.310608e+02 0.00019332 -9.108e-17 [3208,] 4.322508e+02 0.00019279 -8.318e-17 [3209,] 4.334442e+02 0.00019226 -1.158e-17 [3210,] 4.346408e+02 0.00019173 -2.501e-17 [3211,] 4.358408e+02 0.00019120 2.143e-17 [3212,] 4.370440e+02 0.00019067 -9.98e-17 [3213,] 4.382506e+02 0.00019015 -1.008e-17 [3214,] 4.394605e+02 0.00018963 -4.925e-17 [3215,] 4.406738e+02 0.00018910 -1.123e-16 [3216,] 4.418904e+02 0.00018858 -5.392e-17 [3217,] 4.431103e+02 0.00018806 -1.288e-17 [3218,] 4.443336e+02 0.00018755 -7.625e-17 [3219,] 4.455603e+02 0.00018703 1.435e-17 [3220,] 4.467904e+02 0.00018652 -1.251e-16 [3221,] 4.480239e+02 0.00018600 -1.209e-16 [3222,] 4.492608e+02 0.00018549 -6.749e-17 [3223,] 4.505011e+02 0.00018498 -1.468e-16 [3224,] 4.517449e+02 0.00018447 -1.7e-16 [3225,] 4.529920e+02 0.00018396 -8.036e-17 [3226,] 4.542426e+02 0.00018346 -6.679e-17 [3227,] 4.554967e+02 0.00018295 -1.824e-16 [3228,] 4.567542e+02 0.00018245 -1.614e-16 [3229,] 4.580152e+02 0.00018194 3.054e-17 [3230,] 4.592797e+02 0.00018144 -2.468e-17 [3231,] 4.605476e+02 0.00018094 2.835e-17 [3232,] 4.618191e+02 0.00018045 -4.072e-17 [3233,] 4.630941e+02 0.00017995 -1.136e-16 [3234,] 4.643726e+02 0.00017945 -1.015e-16 [3235,] 4.656546e+02 0.00017896 -5.394e-17 [3236,] 4.669402e+02 0.00017847 -7.107e-17 [3237,] 4.682293e+02 0.00017798 -1.178e-16 [3238,] 4.695220e+02 0.00017749 2.291e-17 [3239,] 4.708182e+02 0.00017700 -1.252e-16 [3240,] 4.721180e+02 0.00017651 -3.294e-17 [3241,] 4.734214e+02 0.00017602 -7.005e-17 [3242,] 4.747284e+02 0.00017554 -4.084e-17 [3243,] 4.760391e+02 0.00017506 1.074e-17 [3244,] 4.773533e+02 0.00017457 -7.374e-17 [3245,] 4.786712e+02 0.00017409 -9.595e-17 [3246,] 4.799927e+02 0.00017361 -5.068e-17 [3247,] 4.813178e+02 0.00017314 -3.426e-17 [3248,] 4.826466e+02 0.00017266 -5.479e-17 [3249,] 4.839791e+02 0.00017218 -8.043e-17 [3250,] 4.853153e+02 0.00017171 -2.932e-17 [3251,] 4.866551e+02 0.00017124 2.377e-17 [3252,] 4.879986e+02 0.00017077 -4.807e-17 [3253,] 4.893459e+02 0.00017030 -2.771e-17 [3254,] 4.906969e+02 0.00016983 -3.767e-17 [3255,] 4.920516e+02 0.00016936 -4.442e-19 [3256,] 4.934100e+02 0.00016889 6.933e-17 [3257,] 4.947722e+02 0.00016843 2.431e-17 [3258,] 4.961382e+02 0.00016796 -5.991e-17 [3259,] 4.975079e+02 0.00016750 -1.574e-16 [3260,] 4.988814e+02 0.00016704 -3.947e-17 [3261,] 5.002587e+02 0.00016658 9.75e-17 [3262,] 5.016398e+02 0.00016612 -9.109e-17 [3263,] 5.030247e+02 0.00016566 1.603e-17 [3264,] 5.044134e+02 0.00016521 -4.013e-17 [3265,] 5.058060e+02 0.00016475 -1.915e-16 [3266,] 5.072024e+02 0.00016430 -5.446e-19 [3267,] 5.086027e+02 0.00016385 2.557e-17 [3268,] 5.100068e+02 0.00016340 -1.063e-16 [3269,] 5.114148e+02 0.00016295 -2.758e-17 [3270,] 5.128267e+02 0.00016250 -5.037e-17 [3271,] 5.142425e+02 0.00016205 -1.513e-16 [3272,] 5.156622e+02 0.00016160 -4.719e-17 [3273,] 5.170859e+02 0.00016116 8.855e-18 [3274,] 5.185134e+02 0.00016072 -4.955e-17 [3275,] 5.199449e+02 0.00016027 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[3392,] 7.178697e+02 0.00011608 5.068e-17 [3393,] 7.198516e+02 0.00011576 -1.328e-16 [3394,] 7.218389e+02 0.00011545 -1.57e-16 [3395,] 7.238317e+02 0.00011513 -1.155e-17 [3396,] 7.258301e+02 0.00011481 -1.291e-16 [3397,] 7.278339e+02 0.00011449 -1.333e-16 [3398,] 7.298433e+02 0.00011418 4.501e-18 [3399,] 7.318582e+02 0.00011387 -7.179e-17 [3400,] 7.338787e+02 0.00011355 -4.703e-17 [3401,] 7.359048e+02 0.00011324 -2.595e-17 [3402,] 7.379365e+02 0.00011293 -9.92e-17 [3403,] 7.399738e+02 0.00011262 -1.134e-16 [3404,] 7.420166e+02 0.00011231 -1.173e-16 [3405,] 7.440652e+02 0.00011200 -1.714e-16 [3406,] 7.461194e+02 0.00011169 6.674e-17 [3407,] 7.481792e+02 0.00011138 -6.101e-17 [3408,] 7.502448e+02 0.00011107 -1.06e-16 [3409,] 7.523161e+02 0.00011077 -7.932e-17 [3410,] 7.543930e+02 0.00011046 4.919e-17 [3411,] 7.564757e+02 0.00011016 -9.229e-17 [3412,] 7.585642e+02 0.00010986 -1.197e-16 [3413,] 7.606584e+02 0.00010955 -2.465e-17 [3414,] 7.627584e+02 0.00010925 -3.703e-17 [3415,] 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0.00010226 4.072e-17 [3439,] 8.171850e+02 0.00010198 3.439e-17 [3440,] 8.194411e+02 0.00010170 7.043e-17 [3441,] 8.217034e+02 0.00010142 -6.385e-18 [3442,] 8.239719e+02 0.00010114 5.402e-17 [3443,] 8.262467e+02 0.00010086 -4.516e-17 [3444,] 8.285278e+02 0.00010058 -9.339e-18 [3445,] 8.308152e+02 0.00010030 -4.78e-17 [3446,] 8.331089e+02 0.00010003 1.332e-17 [3447,] 8.354089e+02 0.00009975 6.238e-17 [3448,] 8.377153e+02 0.00009948 -8.603e-17 [3449,] 8.400280e+02 0.00009920 -1.276e-16 [3450,] 8.423471e+02 0.00009893 7.224e-18 [3451,] 8.446726e+02 0.00009866 -9.149e-17 [3452,] 8.470046e+02 0.00009839 -1.192e-16 [3453,] 8.493430e+02 0.00009812 3.696e-17 [3454,] 8.516878e+02 0.00009784 -1.641e-16 [3455,] 8.540391e+02 0.00009758 -1.681e-16 [3456,] 8.563969e+02 0.00009731 -4.664e-17 [3457,] 8.587613e+02 0.00009704 3.416e-17 [3458,] 8.611321e+02 0.00009677 4.015e-17 [3459,] 8.635095e+02 0.00009651 -9.166e-17 [3460,] 8.658934e+02 0.00009624 -5.044e-17 [3461,] 8.682840e+02 0.00009597 -3.161e-17 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9.276793e+02 0.00008983 9.319e-18 [3486,] 9.302404e+02 0.00008958 3.402e-18 [3487,] 9.328086e+02 0.00008934 -4.291e-17 [3488,] 9.353838e+02 0.00008909 -7.383e-17 [3489,] 9.379662e+02 0.00008884 -4.606e-17 [3490,] 9.405557e+02 0.00008860 2.586e-17 [3491,] 9.431524e+02 0.00008836 -2.485e-17 [3492,] 9.457562e+02 0.00008811 5.294e-17 [3493,] 9.483672e+02 0.00008787 -1.099e-16 [3494,] 9.509854e+02 0.00008763 -9.246e-17 [3495,] 9.536109e+02 0.00008739 -8.41e-17 [3496,] 9.562436e+02 0.00008715 7.258e-17 [3497,] 9.588836e+02 0.00008691 -8.784e-17 [3498,] 9.615308e+02 0.00008667 -9.904e-17 [3499,] 9.641854e+02 0.00008643 4.825e-17 [3500,] 9.668473e+02 0.00008619 -1.726e-16 [3501,] 9.695165e+02 0.00008595 -1.128e-16 [3502,] 9.721931e+02 0.00008572 -1.323e-17 [3503,] 9.748772e+02 0.00008548 1.214e-17 [3504,] 9.775686e+02 0.00008525 -1.257e-16 [3505,] 9.802674e+02 0.00008501 -7.217e-17 [3506,] 9.829737e+02 0.00008478 3.875e-17 [3507,] 9.856875e+02 0.00008454 -4.374e-17 [3508,] 9.884087e+02 0.00008431 -1.239e-16 [3509,] 9.911375e+02 0.00008408 4.307e-17 [3510,] 9.938738e+02 0.00008385 -2.654e-17 [3511,] 9.966177e+02 0.00008362 -7.125e-17 [3512,] 9.993691e+02 0.00008339 -1.05e-16 [3513,] 1.002128e+03 0.00008316 1.283e-17 [3514,] 1.004895e+03 0.00008293 -5.225e-17 [3515,] 1.007669e+03 0.00008270 8.561e-18 [3516,] 1.010451e+03 0.00008247 7.41e-17 [3517,] 1.013241e+03 0.00008224 -6.368e-17 [3518,] 1.016038e+03 0.00008202 -1.199e-16 [3519,] 1.018843e+03 0.00008179 -6.802e-17 [3520,] 1.021656e+03 0.00008157 -4.685e-17 [3521,] 1.024476e+03 0.00008134 -9.203e-17 [3522,] 1.027305e+03 0.00008112 -7.811e-17 [3523,] 1.030141e+03 0.00008090 1.843e-17 [3524,] 1.032985e+03 0.00008067 -8.243e-17 [3525,] 1.035837e+03 0.00008045 1.449e-17 [3526,] 1.038696e+03 0.00008023 1.603e-17 [3527,] 1.041564e+03 0.00008001 -1.343e-16 [3528,] 1.044439e+03 0.00007979 -1.936e-17 [3529,] 1.047323e+03 0.00007957 -3.234e-17 [3530,] 1.050214e+03 0.00007935 -3.308e-17 [3531,] 1.053114e+03 0.00007913 2.076e-17 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0.00007406 -4.818e-17 [3556,] 1.128259e+03 0.00007386 -2.69e-17 [3557,] 1.131374e+03 0.00007366 -4.402e-17 [3558,] 1.134497e+03 0.00007345 -9.457e-17 [3559,] 1.137629e+03 0.00007325 2.813e-17 [3560,] 1.140770e+03 0.00007305 2.951e-17 [3561,] 1.143919e+03 0.00007285 -7.519e-17 [3562,] 1.147077e+03 0.00007265 1.254e-17 [3563,] 1.150244e+03 0.00007245 -5.445e-17 [3564,] 1.153420e+03 0.00007225 -5.351e-17 [3565,] 1.156604e+03 0.00007205 -1.232e-16 [3566,] 1.159797e+03 0.00007185 7.292e-17 [3567,] 1.162999e+03 0.00007165 -2.661e-17 [3568,] 1.166210e+03 0.00007146 -9.814e-17 [3569,] 1.169430e+03 0.00007126 3.908e-17 [3570,] 1.172658e+03 0.00007106 -1.007e-16 [3571,] 1.175895e+03 0.00007087 -6.215e-17 [3572,] 1.179142e+03 0.00007067 -1.397e-16 [3573,] 1.182397e+03 0.00007048 -1.648e-16 [3574,] 1.185662e+03 0.00007028 -9.662e-17 [3575,] 1.188935e+03 0.00007009 -1.616e-16 [3576,] 1.192217e+03 0.00006990 6.107e-17 [3577,] 1.195509e+03 0.00006971 -6.574e-17 [3578,] 1.198809e+03 0.00006951 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1.280814e+03 0.00006506 -2.973e-17 [3603,] 1.284350e+03 0.00006488 -9.017e-17 [3604,] 1.287896e+03 0.00006471 -4.654e-17 [3605,] 1.291452e+03 0.00006453 -1.275e-16 [3606,] 1.295017e+03 0.00006435 -7.327e-17 [3607,] 1.298592e+03 0.00006417 -7.18e-17 [3608,] 1.302177e+03 0.00006400 -1.443e-17 [3609,] 1.305772e+03 0.00006382 -5.26e-17 [3610,] 1.309377e+03 0.00006364 -5.119e-17 [3611,] 1.312992e+03 0.00006347 8.597e-18 [3612,] 1.316617e+03 0.00006329 -2.577e-18 [3613,] 1.320252e+03 0.00006312 -1.754e-16 [3614,] 1.323897e+03 0.00006295 -2.514e-18 [3615,] 1.327552e+03 0.00006277 -1.007e-16 [3616,] 1.331217e+03 0.00006260 -4.041e-17 [3617,] 1.334892e+03 0.00006243 -1.074e-16 [3618,] 1.338577e+03 0.00006226 -3.49e-17 [3619,] 1.342273e+03 0.00006208 -1.103e-16 [3620,] 1.345979e+03 0.00006191 -1.983e-16 [3621,] 1.349695e+03 0.00006174 -5.009e-17 [3622,] 1.353421e+03 0.00006157 -5.021e-17 [3623,] 1.357157e+03 0.00006140 -9.781e-17 [3624,] 1.360904e+03 0.00006123 -8.599e-18 [3625,] 1.364661e+03 0.00006107 -1.226e-16 [3626,] 1.368429e+03 0.00006090 1.292e-17 [3627,] 1.372207e+03 0.00006073 -4.177e-17 [3628,] 1.375995e+03 0.00006056 -1.236e-16 [3629,] 1.379794e+03 0.00006040 -7.051e-17 [3630,] 1.383603e+03 0.00006023 -5.291e-17 [3631,] 1.387423e+03 0.00006006 -1.394e-16 [3632,] 1.391253e+03 0.00005990 -1.138e-16 [3633,] 1.395094e+03 0.00005973 1.939e-17 [3634,] 1.398946e+03 0.00005957 -2.074e-17 [3635,] 1.402808e+03 0.00005940 -1.164e-16 [3636,] 1.406681e+03 0.00005924 -1.161e-16 [3637,] 1.410564e+03 0.00005908 7.402e-18 [3638,] 1.414459e+03 0.00005892 -1.71e-17 [3639,] 1.418364e+03 0.00005875 1.1e-17 [3640,] 1.422279e+03 0.00005859 -5.402e-17 [3641,] 1.426206e+03 0.00005843 -6.225e-17 [3642,] 1.430143e+03 0.00005827 -7.527e-17 [3643,] 1.434092e+03 0.00005811 -4.165e-18 [3644,] 1.438051e+03 0.00005795 -1.201e-16 [3645,] 1.442021e+03 0.00005779 -7.807e-17 [3646,] 1.446002e+03 0.00005763 -7.517e-17 [3647,] 1.449994e+03 0.00005747 -5.211e-17 [3648,] 1.453997e+03 0.00005731 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1.553458e+03 0.00005364 -1.398e-16 [3673,] 1.557747e+03 0.00005350 -8.396e-17 [3674,] 1.562048e+03 0.00005335 -8.01e-17 [3675,] 1.566360e+03 0.00005320 3.27e-18 [3676,] 1.570685e+03 0.00005306 -8.454e-17 [3677,] 1.575021e+03 0.00005291 -9.309e-17 [3678,] 1.579369e+03 0.00005276 3.71e-18 [3679,] 1.583729e+03 0.00005262 -1.028e-16 [3680,] 1.588102e+03 0.00005247 -3.304e-17 [3681,] 1.592486e+03 0.00005233 1.414e-17 [3682,] 1.596883e+03 0.00005219 4.96e-17 [3683,] 1.601291e+03 0.00005204 -1.989e-17 [3684,] 1.605712e+03 0.00005190 -1.148e-16 [3685,] 1.610145e+03 0.00005176 -9.93e-17 [3686,] 1.614590e+03 0.00005161 6.555e-17 [3687,] 1.619048e+03 0.00005147 -4.606e-17 [3688,] 1.623518e+03 0.00005133 -1.228e-16 [3689,] 1.628000e+03 0.00005119 -3.384e-17 [3690,] 1.632494e+03 0.00005105 -5.306e-17 [3691,] 1.637001e+03 0.00005091 -5.957e-17 [3692,] 1.641521e+03 0.00005077 -1.269e-16 [3693,] 1.646053e+03 0.00005063 -1.347e-18 [3694,] 1.650597e+03 0.00005049 -6.426e-17 [3695,] 1.655154e+03 0.00005035 -1.485e-17 [3696,] 1.659723e+03 0.00005021 -8.448e-17 [3697,] 1.664305e+03 0.00005007 -8.628e-17 [3698,] 1.668900e+03 0.00004993 1.57e-17 [3699,] 1.673508e+03 0.00004980 -1.264e-16 [3700,] 1.678128e+03 0.00004966 -4.379e-17 [3701,] 1.682761e+03 0.00004952 -1.681e-16 [3702,] 1.687406e+03 0.00004939 -7.267e-17 [3703,] 1.692065e+03 0.00004925 -4.469e-17 [3704,] 1.696736e+03 0.00004911 1.699e-18 [3705,] 1.701421e+03 0.00004898 -8.43e-17 [3706,] 1.706118e+03 0.00004884 1.148e-17 [3707,] 1.710828e+03 0.00004871 5.592e-17 [3708,] 1.715551e+03 0.00004858 -1.781e-16 [3709,] 1.720288e+03 0.00004844 -1.004e-16 [3710,] 1.725037e+03 0.00004831 -7.922e-17 [3711,] 1.729799e+03 0.00004818 -9.019e-17 [3712,] 1.734575e+03 0.00004804 -8.536e-17 [3713,] 1.739364e+03 0.00004791 -1.432e-16 [3714,] 1.744166e+03 0.00004778 -3.821e-17 [3715,] 1.748981e+03 0.00004765 -1.478e-16 [3716,] 1.753809e+03 0.00004752 -7.768e-17 [3717,] 1.758651e+03 0.00004738 -1.376e-16 [3718,] 1.763507e+03 0.00004725 -4.8e-17 [3719,] 1.768375e+03 0.00004712 -1.547e-17 [3720,] 1.773257e+03 0.00004699 -1.38e-16 [3721,] 1.778153e+03 0.00004687 -1.882e-17 [3722,] 1.783062e+03 0.00004674 9.053e-17 [3723,] 1.787985e+03 0.00004661 -4.799e-17 [3724,] 1.792921e+03 0.00004648 -1.432e-16 [3725,] 1.797871e+03 0.00004635 -1.745e-16 [3726,] 1.802834e+03 0.00004622 -4.057e-17 [3727,] 1.807811e+03 0.00004610 5.468e-17 [3728,] 1.812802e+03 0.00004597 8.185e-17 [3729,] 1.817807e+03 0.00004584 2.446e-17 [3730,] 1.822826e+03 0.00004572 -3.867e-17 [3731,] 1.827858e+03 0.00004559 -1.978e-17 [3732,] 1.832904e+03 0.00004547 -1.174e-16 [3733,] 1.837965e+03 0.00004534 -1.222e-16 [3734,] 1.843039e+03 0.00004522 1.095e-17 [3735,] 1.848127e+03 0.00004509 2.118e-17 [3736,] 1.853229e+03 0.00004497 -1.28e-16 [3737,] 1.858346e+03 0.00004484 -1.205e-17 [3738,] 1.863476e+03 0.00004472 -7.78e-17 [3739,] 1.868621e+03 0.00004460 -7.91e-17 [3740,] 1.873779e+03 0.00004447 -1.533e-16 [3741,] 1.878953e+03 0.00004435 -6.876e-17 [3742,] 1.884140e+03 0.00004423 3.756e-17 [3743,] 1.889342e+03 0.00004411 -1.339e-16 [3744,] 1.894558e+03 0.00004399 -5.592e-17 [3745,] 1.899788e+03 0.00004386 -1.816e-16 [3746,] 1.905033e+03 0.00004374 -4.077e-17 [3747,] 1.910292e+03 0.00004362 -1.185e-16 [3748,] 1.915566e+03 0.00004350 8.353e-17 [3749,] 1.920855e+03 0.00004338 -1.96e-17 [3750,] 1.926158e+03 0.00004326 4.506e-17 [3751,] 1.931475e+03 0.00004314 -1.721e-16 [3752,] 1.936808e+03 0.00004303 -4.33e-17 [3753,] 1.942155e+03 0.00004291 -7.382e-17 [3754,] 1.947517e+03 0.00004279 -1.666e-16 [3755,] 1.952893e+03 0.00004267 -8.824e-17 [3756,] 1.958285e+03 0.00004255 -5.414e-17 [3757,] 1.963691e+03 0.00004244 -4.423e-17 [3758,] 1.969112e+03 0.00004232 -7.708e-17 [3759,] 1.974549e+03 0.00004220 -6.857e-17 [3760,] 1.980000e+03 0.00004209 -2.063e-17 [3761,] 1.985466e+03 0.00004197 -5.418e-17 [3762,] 1.990948e+03 0.00004186 2.622e-17 [3763,] 1.996444e+03 0.00004174 5.325e-17 [3764,] 2.001956e+03 0.00004163 2.516e-17 [3765,] 2.007483e+03 0.00004151 -5.529e-17 [3766,] 2.013025e+03 0.00004140 -1.241e-16 [3767,] 2.018583e+03 0.00004128 -1.264e-16 [3768,] 2.024155e+03 0.00004117 -1.83e-16 [3769,] 2.029744e+03 0.00004106 -1.265e-17 [3770,] 2.035347e+03 0.00004094 -1.199e-16 [3771,] 2.040967e+03 0.00004083 3.137e-17 [3772,] 2.046601e+03 0.00004072 6.408e-17 [3773,] 2.052251e+03 0.00004061 -1.794e-16 [3774,] 2.057917e+03 0.00004049 -1.398e-16 [3775,] 2.063599e+03 0.00004038 -1.53e-16 [3776,] 2.069296e+03 0.00004027 -1.067e-16 [3777,] 2.075009e+03 0.00004016 -3.429e-17 [3778,] 2.080737e+03 0.00004005 2.818e-17 [3779,] 2.086482e+03 0.00003994 -3.002e-17 [3780,] 2.092242e+03 0.00003983 -1.098e-16 [3781,] 2.098018e+03 0.00003972 -8.385e-17 [3782,] 2.103810e+03 0.00003961 -1.109e-16 [3783,] 2.109618e+03 0.00003950 -5.542e-17 [3784,] 2.115443e+03 0.00003939 -4.32e-17 [3785,] 2.121283e+03 0.00003928 -4.265e-17 [3786,] 2.127139e+03 0.00003918 -2.706e-17 [3787,] 2.133012e+03 0.00003907 -9.061e-17 [3788,] 2.138901e+03 0.00003896 -4.783e-17 [3789,] 2.144806e+03 0.00003885 4.278e-17 [3790,] 2.150727e+03 0.00003875 -8.23e-17 [3791,] 2.156665e+03 0.00003864 3.203e-17 [3792,] 2.162619e+03 0.00003853 -1.468e-16 [3793,] 2.168589e+03 0.00003843 -1.271e-16 [3794,] 2.174576e+03 0.00003832 1.288e-17 [3795,] 2.180580e+03 0.00003822 -2.009e-16 [3796,] 2.186600e+03 0.00003811 -1.604e-16 [3797,] 2.192636e+03 0.00003801 -1.649e-16 [3798,] 2.198690e+03 0.00003790 9.436e-17 [3799,] 2.204760e+03 0.00003780 -1.263e-16 [3800,] 2.210847e+03 0.00003769 -5.122e-17 [3801,] 2.216950e+03 0.00003759 -1.515e-17 [3802,] 2.223071e+03 0.00003749 -6.323e-18 [3803,] 2.229208e+03 0.00003738 -2.742e-17 [3804,] 2.235362e+03 0.00003728 -1.252e-16 [3805,] 2.241534e+03 0.00003718 -1.667e-16 [3806,] 2.247722e+03 0.00003707 -2.962e-17 [3807,] 2.253928e+03 0.00003697 -7.133e-17 [3808,] 2.260150e+03 0.00003687 -8.941e-17 [3809,] 2.266390e+03 0.00003677 -4.322e-17 [3810,] 2.272647e+03 0.00003667 -1.375e-17 [3811,] 2.278921e+03 0.00003657 -9.648e-17 [3812,] 2.285213e+03 0.00003647 8.282e-18 [3813,] 2.291522e+03 0.00003637 -1.517e-16 [3814,] 2.297848e+03 0.00003627 4.639e-17 [3815,] 2.304192e+03 0.00003617 -2.149e-16 [3816,] 2.310553e+03 0.00003607 -4.747e-17 [3817,] 2.316932e+03 0.00003597 3.533e-17 [3818,] 2.323329e+03 0.00003587 -6.234e-17 [3819,] 2.329743e+03 0.00003577 -1.657e-16 [3820,] 2.336175e+03 0.00003567 -1.056e-16 [3821,] 2.342624e+03 0.00003557 -7.014e-17 [3822,] 2.349092e+03 0.00003547 4.553e-17 [3823,] 2.355577e+03 0.00003538 -1.434e-16 [3824,] 2.362080e+03 0.00003528 -9.902e-17 [3825,] 2.368602e+03 0.00003518 5.665e-17 [3826,] 2.375141e+03 0.00003509 -3.357e-17 [3827,] 2.381698e+03 0.00003499 -6.653e-17 [3828,] 2.388273e+03 0.00003489 -3.208e-17 [3829,] 2.394867e+03 0.00003480 -1.136e-16 [3830,] 2.401478e+03 0.00003470 8.225e-17 [3831,] 2.408108e+03 0.00003461 -1.761e-16 [3832,] 2.414757e+03 0.00003451 -1.53e-17 [3833,] 2.421423e+03 0.00003442 -7.309e-17 [3834,] 2.428108e+03 0.00003432 -3.593e-18 [3835,] 2.434812e+03 0.00003423 -2.661e-17 [3836,] 2.441534e+03 0.00003413 -4.315e-17 [3837,] 2.448274e+03 0.00003404 -3.709e-18 [3838,] 2.455033e+03 0.00003394 9.43e-17 [3839,] 2.461811e+03 0.00003385 6.451e-17 [3840,] 2.468608e+03 0.00003376 -1.044e-16 [3841,] 2.475423e+03 0.00003366 -1.568e-17 [3842,] 2.482257e+03 0.00003357 3.081e-17 [3843,] 2.489110e+03 0.00003348 -1.407e-16 [3844,] 2.495982e+03 0.00003339 -2.143e-17 [3845,] 2.502872e+03 0.00003330 -1.687e-16 [3846,] 2.509782e+03 0.00003320 -1.942e-16 [3847,] 2.516711e+03 0.00003311 -1.674e-16 [3848,] 2.523659e+03 0.00003302 -3.108e-17 [3849,] 2.530627e+03 0.00003293 -5.116e-18 [3850,] 2.537613e+03 0.00003284 1.024e-16 [3851,] 2.544619e+03 0.00003275 -6.132e-17 [3852,] 2.551644e+03 0.00003266 -2.067e-17 [3853,] 2.558688e+03 0.00003257 -1.49e-16 [3854,] 2.565752e+03 0.00003248 -2.265e-18 [3855,] 2.572836e+03 0.00003239 -1.26e-16 [3856,] 2.579939e+03 0.00003230 -1.5e-16 [3857,] 2.587062e+03 0.00003221 -3.873e-17 [3858,] 2.594204e+03 0.00003212 -1.138e-16 [3859,] 2.601366e+03 0.00003203 2.455e-17 [3860,] 2.608548e+03 0.00003195 -1.328e-16 [3861,] 2.615749e+03 0.00003186 -1.788e-16 [3862,] 2.622971e+03 0.00003177 2.765e-17 [3863,] 2.630212e+03 0.00003168 -1.051e-16 [3864,] 2.637474e+03 0.00003160 -8.401e-17 [3865,] 2.644755e+03 0.00003151 -1.15e-17 [3866,] 2.652057e+03 0.00003142 -1.428e-17 [3867,] 2.659378e+03 0.00003134 -6.852e-17 [3868,] 2.666720e+03 0.00003125 -1.503e-16 [3869,] 2.674082e+03 0.00003116 -1.898e-16 [3870,] 2.681465e+03 0.00003108 -2.05e-16 [3871,] 2.688868e+03 0.00003099 -1.661e-16 [3872,] 2.696291e+03 0.00003091 -1.44e-16 [3873,] 2.703735e+03 0.00003082 -1.424e-16 [3874,] 2.711199e+03 0.00003074 -5.327e-17 [3875,] 2.718684e+03 0.00003065 -4.684e-17 [3876,] 2.726190e+03 0.00003057 -8.534e-17 [3877,] 2.733716e+03 0.00003048 2.874e-17 [3878,] 2.741264e+03 0.00003040 -4.514e-17 [3879,] 2.748832e+03 0.00003032 -4.852e-17 [3880,] 2.756421e+03 0.00003023 -9.1e-17 [3881,] 2.764030e+03 0.00003015 -3.573e-17 [3882,] 2.771661e+03 0.00003007 -7.354e-17 [3883,] 2.779313e+03 0.00002998 -1.243e-16 [3884,] 2.786986e+03 0.00002990 -1.503e-17 [3885,] 2.794680e+03 0.00002982 -1.47e-16 [3886,] 2.802396e+03 0.00002974 -1.236e-16 [3887,] 2.810133e+03 0.00002965 -5.11e-17 [3888,] 2.817891e+03 0.00002957 -7.118e-17 [3889,] 2.825670e+03 0.00002949 -6.658e-17 [3890,] 2.833471e+03 0.00002941 -8.621e-17 [3891,] 2.841294e+03 0.00002933 -4.303e-17 [3892,] 2.849138e+03 0.00002925 9.666e-18 [3893,] 2.857004e+03 0.00002917 -9.295e-18 [3894,] 2.864891e+03 0.00002909 -1.061e-16 [3895,] 2.872801e+03 0.00002901 -9.266e-17 [3896,] 2.880732e+03 0.00002893 -7.724e-17 [3897,] 2.888685e+03 0.00002885 -8.863e-17 [3898,] 2.896660e+03 0.00002877 -1.62e-16 [3899,] 2.904657e+03 0.00002869 -1.184e-16 [3900,] 2.912676e+03 0.00002861 -2.713e-17 [3901,] 2.920717e+03 0.00002853 -1.873e-17 [3902,] 2.928781e+03 0.00002845 6.231e-18 [3903,] 2.936866e+03 0.00002837 -4.134e-17 [3904,] 2.944974e+03 0.00002830 9.059e-18 [3905,] 2.953105e+03 0.00002822 -3.359e-17 [3906,] 2.961258e+03 0.00002814 -1.068e-16 [3907,] 2.969433e+03 0.00002806 -1.376e-16 [3908,] 2.977631e+03 0.00002799 -1.098e-16 [3909,] 2.985852e+03 0.00002791 -8.982e-17 [3910,] 2.994095e+03 0.00002783 -1.466e-16 [3911,] 3.002361e+03 0.00002776 -1.928e-17 [3912,] 3.010650e+03 0.00002768 -5.71e-17 [3913,] 3.018961e+03 0.00002760 -1.69e-17 [3914,] 3.027296e+03 0.00002753 5.728e-17 [3915,] 3.035654e+03 0.00002745 -5.086e-17 [3916,] 3.044034e+03 0.00002738 -9.653e-17 [3917,] 3.052438e+03 0.00002730 -6.01e-17 [3918,] 3.060865e+03 0.00002723 -9.807e-17 [3919,] 3.069316e+03 0.00002715 -7.126e-17 [3920,] 3.077789e+03 0.00002708 -7.521e-17 [3921,] 3.086287e+03 0.00002700 -6.537e-17 [3922,] 3.094807e+03 0.00002693 -3.102e-17 [3923,] 3.103351e+03 0.00002685 8.157e-18 [3924,] 3.111919e+03 0.00002678 -1.65e-16 [3925,] 3.120510e+03 0.00002671 3.413e-17 [3926,] 3.129125e+03 0.00002663 -2.298e-17 [3927,] 3.137764e+03 0.00002656 -3.973e-17 [3928,] 3.146427e+03 0.00002649 -8.173e-17 [3929,] 3.155113e+03 0.00002641 -9.081e-17 [3930,] 3.163824e+03 0.00002634 -6.771e-17 [3931,] 3.172558e+03 0.00002627 -1.732e-16 [3932,] 3.181317e+03 0.00002619 -7.4e-17 [3933,] 3.190100e+03 0.00002612 -1.064e-16 [3934,] 3.198907e+03 0.00002605 -7.915e-17 [3935,] 3.207738e+03 0.00002598 -2.359e-17 [3936,] 3.216594e+03 0.00002591 3.617e-17 [3937,] 3.225475e+03 0.00002584 -5.183e-17 [3938,] 3.234379e+03 0.00002576 2.238e-17 [3939,] 3.243309e+03 0.00002569 -3.87e-17 [3940,] 3.252263e+03 0.00002562 5.682e-17 [3941,] 3.261241e+03 0.00002555 -1.871e-16 [3942,] 3.270245e+03 0.00002548 -7.423e-17 [3943,] 3.279273e+03 0.00002541 4.821e-17 [3944,] 3.288327e+03 0.00002534 -3.775e-17 [3945,] 3.297405e+03 0.00002527 -1.375e-16 [3946,] 3.306508e+03 0.00002520 -1.905e-16 [3947,] 3.315637e+03 0.00002513 -7.664e-17 [3948,] 3.324791e+03 0.00002506 -1.868e-16 [3949,] 3.333970e+03 0.00002500 -7.517e-18 [3950,] 3.343174e+03 0.00002493 -7.008e-18 [3951,] 3.352404e+03 0.00002486 -2.239e-16 [3952,] 3.361659e+03 0.00002479 -2.46e-16 [3953,] 3.370940e+03 0.00002472 -8.345e-17 [3954,] 3.380246e+03 0.00002465 -1.515e-16 [3955,] 3.389578e+03 0.00002459 -2.221e-16 [3956,] 3.398936e+03 0.00002452 -1.989e-16 [3957,] 3.408320e+03 0.00002445 -1.686e-16 [3958,] 3.417729e+03 0.00002438 -2.022e-16 [3959,] 3.427165e+03 0.00002432 -1.277e-16 [3960,] 3.436627e+03 0.00002425 -1.29e-16 [3961,] 3.446114e+03 0.00002418 -8.84e-17 [3962,] 3.455628e+03 0.00002412 -2.065e-16 [3963,] 3.465168e+03 0.00002405 -1.83e-16 [3964,] 3.474735e+03 0.00002398 -8.013e-17 [3965,] 3.484328e+03 0.00002392 -6.687e-17 [3966,] 3.493947e+03 0.00002385 -1.904e-16 [3967,] 3.503593e+03 0.00002379 -1.784e-16 [3968,] 3.513266e+03 0.00002372 -6.836e-17 [3969,] 3.522965e+03 0.00002365 -5.854e-17 [3970,] 3.532691e+03 0.00002359 -7.628e-17 [3971,] 3.542444e+03 0.00002352 -1.713e-16 [3972,] 3.552224e+03 0.00002346 -1.799e-17 [3973,] 3.562031e+03 0.00002339 -5.029e-17 [3974,] 3.571865e+03 0.00002333 -1.563e-16 [3975,] 3.581726e+03 0.00002327 -9.322e-17 [3976,] 3.591614e+03 0.00002320 -3.243e-17 [3977,] 3.601530e+03 0.00002314 -1.165e-16 [3978,] 3.611473e+03 0.00002307 -1.538e-16 [3979,] 3.621444e+03 0.00002301 -1.074e-16 [3980,] 3.631442e+03 0.00002295 -9.083e-17 [3981,] 3.641467e+03 0.00002288 -2.047e-16 [3982,] 3.651520e+03 0.00002282 -9.817e-17 [3983,] 3.661601e+03 0.00002276 -1.738e-16 [3984,] 3.671710e+03 0.00002270 -5.416e-17 [3985,] 3.681847e+03 0.00002263 -7.673e-17 [3986,] 3.692012e+03 0.00002257 -1.504e-16 [3987,] 3.702205e+03 0.00002251 -1.021e-16 [3988,] 3.712425e+03 0.00002245 -1.176e-16 [3989,] 3.722675e+03 0.00002239 -3.748e-17 [3990,] 3.732952e+03 0.00002232 -1.269e-16 [3991,] 3.743258e+03 0.00002226 -9.194e-17 [3992,] 3.753592e+03 0.00002220 -5.19e-17 [3993,] 3.763955e+03 0.00002214 -2.043e-18 [3994,] 3.774346e+03 0.00002208 -1.161e-16 [3995,] 3.784767e+03 0.00002202 -1.667e-16 [3996,] 3.795215e+03 0.00002196 -3.703e-17 [3997,] 3.805693e+03 0.00002190 -2.044e-16 [3998,] 3.816200e+03 0.00002184 -1.83e-16 [3999,] 3.826735e+03 0.00002178 -6.466e-17 [4000,] 3.837300e+03 0.00002172 -1.668e-17 [4001,] 3.847894e+03 0.00002166 -1.121e-16 [4002,] 3.858517e+03 0.00002160 -2.22e-16 [4003,] 3.869170e+03 0.00002154 -1.216e-16 [4004,] 3.879852e+03 0.00002148 -7.758e-17 [4005,] 3.890563e+03 0.00002142 -2.035e-16 [4006,] 3.901304e+03 0.00002136 -8.265e-17 [4007,] 3.912075e+03 0.00002130 -1.707e-16 [4008,] 3.922875e+03 0.00002124 -2.187e-16 [4009,] 3.933705e+03 0.00002118 -1.613e-16 [4010,] 3.944565e+03 0.00002113 -1.033e-16 [4011,] 3.955455e+03 0.00002107 -4.871e-17 [4012,] 3.966375e+03 0.00002101 -8.547e-17 [4013,] 3.977326e+03 0.00002095 -6.591e-17 [4014,] 3.988306e+03 0.00002089 -1.161e-16 [4015,] 3.999317e+03 0.00002084 -2.176e-16 [4016,] 4.010358e+03 0.00002078 -9.896e-17 [4017,] 4.021430e+03 0.00002072 -2.761e-17 [4018,] 4.032532e+03 0.00002067 -2.111e-16 [4019,] 4.043665e+03 0.00002061 -2.239e-16 [4020,] 4.054828e+03 0.00002055 -1.33e-16 [4021,] 4.066023e+03 0.00002050 -1.28e-16 [4022,] 4.077248e+03 0.00002044 -3.278e-17 [4023,] 4.088505e+03 0.00002038 -1.874e-16 [4024,] 4.099792e+03 0.00002033 -1.027e-16 [4025,] 4.111111e+03 0.00002027 -1.565e-16 [4026,] 4.122460e+03 0.00002021 -8.387e-18 [4027,] 4.133842e+03 0.00002016 -1.622e-16 [4028,] 4.145254e+03 0.00002010 -8.65e-17 [4029,] 4.156698e+03 0.00002005 -1.526e-16 [4030,] 4.168174e+03 0.00001999 -3.823e-17 [4031,] 4.179681e+03 0.00001994 -7.698e-17 [4032,] 4.191221e+03 0.00001988 -2.121e-17 [4033,] 4.202792e+03 0.00001983 2.608e-18 [4034,] 4.214394e+03 0.00001977 -6.998e-17 [4035,] 4.226029e+03 0.00001972 -7.092e-18 [4036,] 4.237697e+03 0.00001966 -1.532e-16 [4037,] 4.249396e+03 0.00001961 -1.991e-16 [4038,] 4.261128e+03 0.00001956 -1.183e-16 [4039,] 4.272892e+03 0.00001950 -4.438e-17 [4040,] 4.284688e+03 0.00001945 -1.07e-17 [4041,] 4.296517e+03 0.00001940 -2.231e-17 [4042,] 4.308379e+03 0.00001934 -1.759e-17 [4043,] 4.320273e+03 0.00001929 3.073e-17 [4044,] 4.332200e+03 0.00001924 -1.112e-16 [4045,] 4.344161e+03 0.00001918 -2.853e-17 [4046,] 4.356154e+03 0.00001913 -3.555e-17 [4047,] 4.368180e+03 0.00001908 -2.883e-17 [4048,] 4.380240e+03 0.00001902 -3.857e-17 [4049,] 4.392333e+03 0.00001897 1.474e-17 [4050,] 4.404459e+03 0.00001892 -1.236e-16 [4051,] 4.416619e+03 0.00001887 -3.911e-17 [4052,] 4.428812e+03 0.00001882 -4.843e-17 [4053,] 4.441039e+03 0.00001876 -3.831e-17 [4054,] 4.453299e+03 0.00001871 -4.747e-17 [4055,] 4.465594e+03 0.00001866 5.526e-17 [4056,] 4.477923e+03 0.00001861 6.7e-17 [4057,] 4.490285e+03 0.00001856 -9.339e-17 [4058,] 4.502682e+03 0.00001851 -2.023e-18 [4059,] 4.515113e+03 0.00001846 -1.519e-16 [4060,] 4.527578e+03 0.00001841 -1.627e-16 [4061,] 4.540077e+03 0.00001836 -1.978e-16 [4062,] 4.552611e+03 0.00001830 -1.005e-16 [4063,] 4.565180e+03 0.00001825 -1.556e-16 [4064,] 4.577784e+03 0.00001820 -1.269e-17 [4065,] 4.590422e+03 0.00001815 -8.607e-17 [4066,] 4.603095e+03 0.00001810 -5.355e-17 [4067,] 4.615803e+03 0.00001805 -2.019e-16 [4068,] 4.628546e+03 0.00001800 -2.226e-16 [4069,] 4.641325e+03 0.00001795 -5.26e-17 [4070,] 4.654138e+03 0.00001791 -6.697e-17 [4071,] 4.666987e+03 0.00001786 2.034e-18 [4072,] 4.679872e+03 0.00001781 -1.175e-16 [4073,] 4.692792e+03 0.00001776 6.692e-18 [4074,] 4.705747e+03 0.00001771 -6.696e-17 [4075,] 4.718739e+03 0.00001766 -8.089e-17 [4076,] 4.731766e+03 0.00001761 -8.559e-17 [4077,] 4.744830e+03 0.00001756 -4.276e-17 [4078,] 4.757929e+03 0.00001751 -1.058e-16 [4079,] 4.771065e+03 0.00001747 -4.105e-17 [4080,] 4.784236e+03 0.00001742 -1.158e-16 [4081,] 4.797445e+03 0.00001737 -1.687e-16 [4082,] 4.810689e+03 0.00001732 6.829e-17 [4083,] 4.823970e+03 0.00001727 -6.768e-17 [4084,] 4.837288e+03 0.00001723 -5.583e-18 [4085,] 4.850643e+03 0.00001718 -1.494e-16 [4086,] 4.864034e+03 0.00001713 -1.535e-16 [4087,] 4.877463e+03 0.00001709 -1.776e-16 [4088,] 4.890929e+03 0.00001704 -1.214e-16 [4089,] 4.904431e+03 0.00001699 3.946e-18 [4090,] 4.917971e+03 0.00001694 4.615e-17 [4091,] 4.931549e+03 0.00001690 -5.954e-17 [4092,] 4.945164e+03 0.00001685 -9.589e-19 [4093,] 4.958816e+03 0.00001681 -1.529e-17 [4094,] 4.972506e+03 0.00001676 -6.325e-17 [4095,] 4.986234e+03 0.00001671 -7.555e-17 [4096,] 5.000000e+03 0.00001667 1.57e-17 > > showProc.time() Time (user system elapsed): 98.98 0.07 100.31 > > ## below, 7 "it's okay, but not perfect:" ===> need more terms in stirlerr() __or__ ?? > ## April 20: MM added more terms up to S10 > x <- sfsmisc::lseq(1, 7, length=2048) > system.time(stM <- DPQmpfr::stirlerrM(Rmpfr::mpfr(x,2048))) # 1.52 sec elapsed user system elapsed 50.09 0.00 50.60 > plot(x, stirlerr(x, use.halves=FALSE) - stM, type="l", log="x", main="absolute Error") > plot(x, stirlerr(x, use.halves=FALSE) / stM - 1, type="l", log="x", main="relative Error") > plot(x, abs(stirlerr(x, use.halves=FALSE) / stM - 1), type="l", log="xy",main="|relative Error|") > abline(h=c(1,2,4)*.Machine$double.eps, lty=3) > ## lgammacor() does *NOT* help, as it is *designed* for x >= 10! > lines(x, abs(lgammacor(x, 5) / stM - 1), col=2) > ## maybe look at it for x >= 9 or so ? > ## > ## ==> Need another chebyshev() or rational-approx. for x in [.1, 7] or so !! > > showProc.time() Time (user system elapsed): 50.76 0 51.27 > > > > > ###--------------- bd0() & ebd0() ------------------------------------------------------ > > > ## ebd0 constants: the column sums of "bd0_scale": log(n / 1024) for all these n > ## ---- according to the *comments* in the C code -- so here I test that at least the *sums* are correct > bd0.n <- c(2048,2032,2016,2001,1986,1971,1956,1942,1928,1913,1900,1886,1872,1859, + 1846,1833,1820,1808,1796,1783,1771,1759,1748,1736,1725,1713,1702,1691, + 1680,1670,1659,1649,1638,1628,1618,1608,1598,1589,1579,1570,1560,1551, + 1542,1533,1524,1515,1507,1498,1489,1481,1473,1464,1456,1448,1440,1432, + 1425,1417,1409,1402,1394,1387,1380,1372,1365,1358,1351,1344,1337,1331, + 1324,1317,1311,1304,1298,1291,1285,1279,1273,1266,1260,1254,1248,1242, + 1237,1231,1225,1219,1214,1208,1202,1197,1192,1186,1181,1176,1170,1165, + 1160,1155,1150,1145,1140,1135,1130,1125,1120,1116,1111,1106,1101,1097, + 1092,1088,1083,1079,1074,1070,1066,1061,1057,1053,1049,1044,1040,1036, + 1032,1028,1024) > > stopifnot( + all.equal(bd0.n, + 1024 * exp(colSums(DPQ:::logf_mat))) + ) ## on lynne (64-bit, Fedora 32, 2021) they are even *identical* > identical(bd0.n, 1024 * exp(colSums(DPQ:::logf_mat))) # amazingly to me [1] TRUE > > ## Also, the numbers themselves decrease monotonely, > ## their differences are close to, but *not* monotone: > diff(bd0.n) # -16 -16 -15 -15 -15 -15 -14 -14 -15 -13 -14 ... [1] -16 -16 -15 -15 -15 -15 -14 -14 -15 -13 -14 -14 -13 -13 -13 -13 -12 -12 [19] -13 -12 -12 -11 -12 -11 -12 -11 -11 -11 -10 -11 -10 -11 -10 -10 -10 -10 [37] -9 -10 -9 -10 -9 -9 -9 -9 -9 -8 -9 -9 -8 -8 -9 -8 -8 -8 [55] -8 -7 -8 -8 -7 -8 -7 -7 -8 -7 -7 -7 -7 -7 -6 -7 -7 -6 [73] -7 -6 -7 -6 -6 -6 -7 -6 -6 -6 -6 -5 -6 -6 -6 -5 -6 -6 [91] -5 -5 -6 -5 -5 -6 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -4 -5 [109] -5 -5 -4 -5 -4 -5 -4 -5 -4 -4 -5 -4 -4 -4 -5 -4 -4 -4 [127] -4 -4 > # ^^^^^^^^^^^^^^ (etc) > > if(do.pdf) { dev.off(); pdf("diff-bd0_tab.pdf") } > > plot(diff(bd0.n), type="b") > c2 <- adjustcolor(2, 1/2) > par(new=TRUE) > plot(diff(bd0.n, differences = 2), type="b", col=c2, axes=FALSE, ann=FALSE) > axis(4, at=-1:2, col=c2, col.axis=c2) > > showProc.time() Time (user system elapsed): 0.02 0 0.02 > > ## close to over-/underflow ------- > > ### Large lambda == np == M ------- > > if(do.pdf) { dev.off(); pdf("stirlerr-bd0-ebd0.pdf") } > ##-- FIXME: use functionality from ~/R/MM/NUMERICS/dpq-functions/15628-dpois_raw_accuracy.R > ##-- ----- *or* move to vignette > > LL <- 1e20 > dput(x1 <- 1e20 - 2e11) # 9.99999998e+19 9.99999998e+19 > > (P1 <- dpois (x1, LL)) # was 3.989455e-11; now 5.520993e-98 [1] 5.520993e-98 > (P1m <- Rmpfr::dpois(mpfr(x1, 128), LL)) # 5.52099285934214335003128935..e-98 1 'mpfr' number of precision 128 bits [1] 5.520992859342143350031289352677120249641e-98 > ## However -- the ebd0() version > (P1e <- dpois_raw(x1, LL, version="ebd0_v1")) [1] 5.520993e-98 > ## was 3.989455e-11, but now good! > stopifnot(exprs = { + all.equal(P1 , 5.520992859342e-98, tol=1e-12) + all.equal(P1e, P1, tol=1e-12) + all.equal(P1m, P1, tol=1e-12) + }) > > options(digits=9) > > ## indeed: regular bd0() works "ok" --- but ebd0() does non-sense !! > (bd.1 <- bd0(x1, LL, verbose=2)) bd0(1e+20, 1e+20): T.series w/ 2 terms -> bd0=200 [1] 199.999992 > ## bd0(1e+20, 1e+20): T.series w/ 2 terms -> bd0=200 > ## [1] 200 > (bd.1M <- bd0(x1, mpfr(LL, 128), verbose=2)) bd0(1e+20, 1e+20): T.series w/ 3 terms -> bd0=200 1 'mpfr' number of precision 128 bits [1] 199.9999919413334091607468236761591740489 > ## bd0(1e+20, 1e+20): T.series w/ 3 terms -> bd0=200 > ## ---> 199.9999919413334091607468236761591740489 > asNumeric(bd.1 / bd.1M - 1)# -1.82e-17 -- suggests bd0() is really accurate here [1] -1.8200191e-17 > stopifnot(abs(bd.1 / bd.1M - 1) < 3e-16, + all.equal(199.999991941333, bd.1, tol=1e-14)) > > ebd0(x1, LL, verbose=TRUE)# fixed since June 6, 2021 ebd0(x=1e+20, M=1e+20): M/x = (r=0.500000001) * 2^(e=1); i=0, f=2048, fg=f*2^-(e+10)=1 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = 1.99999996304e-09 1a. before adding -x * log1pmx(.) = -x * -2e-18 = 200 1. after A.(-x*l..): yl,yh = ( -8.05867e-06, 200); yl+yh= 200 ___ fg = 1 ___ skipping further steps [,1] yh 2.00000000e+02 yl -8.05866662e-06 > > showProc.time() Time (user system elapsed): 0.06 0 0.06 > > ### Large x -- small np == M ------------------------------------ > > > mpfrPrec <- 1024 > mpfrPrec <- 256 > > yy <- bd0 (1e307, 10^(-5:1), verbose=TRUE) > yhl <- ebd0 (1e307, 10^(-5:1), verbose=TRUE) ebd0(x=1e+307, M=1e-05): M/x = (r=0.736335108038475) * 2^(e=-1036); i=61, f=1387, fg=f*2^-(e+10)=Inf --> fg = +Inf --> return( +Inf ) ebd0(x=1e+307, M=0.0001): M/x = (r=0.920418885049457) * 2^(e=-1033); i=108, f=1111, fg=f*2^-(e+10)=Inf --> fg = +Inf --> return( +Inf ) ebd0(x=1e+307, M=0.001): M/x = (r=0.575261803155939) * 2^(e=-1029); i=19, f=1783, fg=f*2^-(e+10)=Inf --> fg = +Inf --> return( +Inf ) ebd0(x=1e+307, M=0.01): M/x = (r=0.719077253944928) * 2^(e=-1026); i=56, f=1425, fg=f*2^-(e+10)=Inf --> fg = +Inf --> return( +Inf ) ebd0(x=1e+307, M=0.1): M/x = (r=0.898846567431158) * 2^(e=-1023); i=102, f=1140, fg=f*2^-(e+10)=1.00067e+308 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.107312 -4.72853e-09 -4.29763e-16 5.35114e-24 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = 0.0006690301479688298 1a. before adding -x * log1pmx(.) = -x * -2.23701e-07 = 2.23701e+300 1. after A.(-x*l..): yl,yh = ( 0, 2.23701e+300); yl+yh= 2.23701e+300 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 1.07312e+306); ( NaN, Inf); yl+yh= NaN non-finite yh --> return((yh=Inf, yl=0)) ebd0(x=1e+307, M=1): M/x = (r=0.561779104644474) * 2^(e=-1019); i=16, f=1820, fg=f*2^-(e+10)=9.98475e+306 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419479548646 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( NaN, Inf); yl+yh= NaN non-finite yh --> return((yh=Inf, yl=0)) ebd0(x=1e+307, M=10): M/x = (r=0.702223880805592) * 2^(e=-1016); i=52, f=1456, fg=f*2^-(e+10)=9.98475e+305 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.351976 2.85039e-08 -9.56643e-16 -6.4096e-24 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419479548646 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 3.51978e+306); ( NaN, Inf); yl+yh= NaN non-finite yh --> return((yh=Inf, yl=0)) > yhlC<- ebd0C(1e307, 10^(-5:1)) > stopifnot(yy == Inf, colSums(yhl) == Inf, yhlC == yhl) > yM <- bd0(mpfr(1e307, mpfrPrec), 10^(-5:1)) > roundMpfr(range(yM), 12) ## 7.0363e+309 7.1739e+309 -- *are* larger than DBL_MAX 2 'mpfr' numbers of precision 12 bits [1] 7.0363e+309 7.1739e+309 > > > ### Now *BOTH* x and lambda are large : --------------------------------------- > ## (FIXME?? Small loss for ebd0, see below) <<< ??? > ## is bd0(, *) really accurate ??? > ## it uses it's own convergent series approxmation for |x-np| < .. ???? > > x. <- 1e307 > ebd0(x., 10^(300:308)) [,1] [,2] [,3] [,4] yh 1.51180958e+308 1.28155116e+308 1.05129355e+308 8.21044037e+307 yl 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00 [,5] [,6] [,7] [,8] [,9] yh 5.90875528e+307 3.61517019e+307 1.40258509e+307 0 6.69741491e+307 yl 0.00000000e+00 0.00000000e+00 0.00000000e+00 0 0.00000000e+00 > > stopifnot(is.finite(Llam <- 2^(990:1024 - 1e-12))) > > bd0ver <- function(x, np, mpfrPrec, chkVerb=TRUE, keepMpfr=FALSE) { + stopifnot(length(mpfrPrec <- as.integer(mpfrPrec)) == 1, + !is.na(mpfrPrec), mpfrPrec >= 64, + x >= 0, np >= 0) + yy <- bd0 (x, np) + yhl <- ebd0 (x, np) + yhlC <- ebd0C(x, np) + if(chkVerb) { + yhl. <- ebd0 (x, np, verbose=TRUE) + yhlC. <- ebd0C(x, np, verbose=TRUE) + stopifnot(identical(yhl., yhl), + identical(yhlC., yhlC)) + } + epsC <- .Machine$double.eps + aeq0 <- all.equal(yhl, yhlC, tol = 0) + aeq4 <- all.equal(yhl, yhlC, tol = 4*epsC) + if(!isTRUE(aeq4)) warning("the C and R versions of ebd0() differ:", aeq4) + stopifnot(is.whole(yhl ["yh",]), + is.whole(yhlC["yh",])) + yM <- bd0(mpfr(x, mpfrPrec), + mpfr(np,mpfrPrec), verbose=chkVerb)# more accurate ! (?? always ??) + relE <- relErrV(target = yM, # the mpfr one + cbind(ebd0 = yhl ["yh",] + yhl ["yl",], + ebd0C= yhlC["yh",] + yhlC["yl",], + bd0 = yy)) + relE <- structure(asNumeric(relE), dim=dim(relE), dimnames=dimnames(relE)) + ## return: + list(x=x, np=np, bd0=yy, ebd0=yhl, ebd0C=yhlC, + bd0M=if(keepMpfr) yM, # <- expensive + aeq0=aeq0, aeq4=aeq4, relE = relE) + } > > bd0v.8 <- bd0ver(x., Llam, mpfrPrec = 256) ebd0(x=1e+307, M=1.0464e+298): M/x = (r=0.561779104644075) * 2^(e=-29); i=16, f=1820, fg=f*2^-(e+10)=9.54204e+08 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( NaN, Inf); yl+yh= NaN non-finite yh --> return((yh=Inf, yl=0)) ebd0(x=1e+307, M=2.09279e+298): M/x = (r=0.561779104644075) * 2^(e=-28); i=16, f=1820, fg=f*2^-(e+10)=4.77102e+08 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( NaN, Inf); yl+yh= NaN non-finite yh --> return((yh=Inf, yl=0)) ebd0(x=1e+307, M=4.18558e+298): M/x = (r=0.561779104644075) * 2^(e=-27); i=16, f=1820, fg=f*2^-(e+10)=2.38551e+08 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( NaN, Inf); yl+yh= NaN non-finite yh --> return((yh=Inf, yl=0)) ebd0(x=1e+307, M=8.37116e+298): M/x = (r=0.561779104644075) * 2^(e=-26); i=16, f=1820, fg=f*2^-(e+10)=1.19276e+08 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( NaN, Inf); yl+yh= NaN non-finite yh --> return((yh=Inf, yl=0)) ebd0(x=1e+307, M=1.67423e+299): M/x = (r=0.561779104644075) * 2^(e=-25); i=16, f=1820, fg=f*2^-(e+10)=5.96378e+07 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 1.79038e+308); yl+yh= 1.79038e+308 j=2: ( 0, 1.79038e+308); ( 0, 1.79038e+308); yl+yh= 1.79038e+308 j=3: ( 0, 1.79038e+308); ( 0, 1.79038e+308); yl+yh= 1.79038e+308 j=4: ( 0, 1.79038e+308); ( 0, 1.79038e+308); yl+yh= 1.79038e+308 3. after ADD1(M): yl,yh = ( 0, 1.79038e+308); yl+yh= 1.79038e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.69053e+308); yl+yh= 1.69053e+308 ebd0(x=1e+307, M=3.34846e+299): M/x = (r=0.561779104644075) * 2^(e=-24); i=16, f=1820, fg=f*2^-(e+10)=2.98189e+07 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 1.72107e+308); yl+yh= 1.72107e+308 j=2: ( 0, 1.72107e+308); ( 0, 1.72107e+308); yl+yh= 1.72107e+308 j=3: ( 0, 1.72107e+308); ( 0, 1.72107e+308); yl+yh= 1.72107e+308 j=4: ( 0, 1.72107e+308); ( 0, 1.72107e+308); yl+yh= 1.72107e+308 3. after ADD1(M): yl,yh = ( 0, 1.72107e+308); yl+yh= 1.72107e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.62122e+308); yl+yh= 1.62122e+308 ebd0(x=1e+307, M=6.69693e+299): M/x = (r=0.561779104644075) * 2^(e=-23); i=16, f=1820, fg=f*2^-(e+10)=1.49094e+07 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 1.65175e+308); yl+yh= 1.65175e+308 j=2: ( 0, 1.65175e+308); ( 0, 1.65175e+308); yl+yh= 1.65175e+308 j=3: ( 0, 1.65175e+308); ( 0, 1.65175e+308); yl+yh= 1.65175e+308 j=4: ( 0, 1.65175e+308); ( 0, 1.65175e+308); yl+yh= 1.65175e+308 3. after ADD1(M): yl,yh = ( 0, 1.65175e+308); yl+yh= 1.65175e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.5519e+308); yl+yh= 1.5519e+308 ebd0(x=1e+307, M=1.33939e+300): M/x = (r=0.561779104644075) * 2^(e=-22); i=16, f=1820, fg=f*2^-(e+10)=7.45472e+06 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 1.58244e+308); yl+yh= 1.58244e+308 j=2: ( 0, 1.58244e+308); ( 0, 1.58244e+308); yl+yh= 1.58244e+308 j=3: ( 0, 1.58244e+308); ( 0, 1.58244e+308); yl+yh= 1.58244e+308 j=4: ( 0, 1.58244e+308); ( 0, 1.58244e+308); yl+yh= 1.58244e+308 3. after ADD1(M): yl,yh = ( 0, 1.58244e+308); yl+yh= 1.58244e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.48259e+308); yl+yh= 1.48259e+308 ebd0(x=1e+307, M=2.67877e+300): M/x = (r=0.561779104644075) * 2^(e=-21); i=16, f=1820, fg=f*2^-(e+10)=3.72736e+06 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 1.51312e+308); yl+yh= 1.51312e+308 j=2: ( 0, 1.51312e+308); ( 0, 1.51312e+308); yl+yh= 1.51312e+308 j=3: ( 0, 1.51312e+308); ( 0, 1.51312e+308); yl+yh= 1.51312e+308 j=4: ( 0, 1.51312e+308); ( 0, 1.51312e+308); yl+yh= 1.51312e+308 3. after ADD1(M): yl,yh = ( 0, 1.51312e+308); yl+yh= 1.51312e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.41327e+308); yl+yh= 1.41327e+308 ebd0(x=1e+307, M=5.35754e+300): M/x = (r=0.561779104644075) * 2^(e=-20); i=16, f=1820, fg=f*2^-(e+10)=1.86368e+06 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 1.44381e+308); yl+yh= 1.44381e+308 j=2: ( 0, 1.44381e+308); ( 0, 1.44381e+308); yl+yh= 1.44381e+308 j=3: ( 0, 1.44381e+308); ( 0, 1.44381e+308); yl+yh= 1.44381e+308 j=4: ( 0, 1.44381e+308); ( 0, 1.44381e+308); yl+yh= 1.44381e+308 3. after ADD1(M): yl,yh = ( 0, 1.44381e+308); yl+yh= 1.44381e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.34396e+308); yl+yh= 1.34396e+308 ebd0(x=1e+307, M=1.07151e+301): M/x = (r=0.561779104644075) * 2^(e=-19); i=16, f=1820, fg=f*2^-(e+10)=931840 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 1.37449e+308); yl+yh= 1.37449e+308 j=2: ( 0, 1.37449e+308); ( 0, 1.37449e+308); yl+yh= 1.37449e+308 j=3: ( 0, 1.37449e+308); ( 0, 1.37449e+308); yl+yh= 1.37449e+308 j=4: ( 0, 1.37449e+308); ( 0, 1.37449e+308); yl+yh= 1.37449e+308 3. after ADD1(M): yl,yh = ( 0, 1.37449e+308); yl+yh= 1.37449e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.27464e+308); yl+yh= 1.27464e+308 ebd0(x=1e+307, M=2.14302e+301): M/x = (r=0.561779104644075) * 2^(e=-18); i=16, f=1820, fg=f*2^-(e+10)=465920 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 1.30518e+308); yl+yh= 1.30518e+308 j=2: ( 0, 1.30518e+308); ( 0, 1.30518e+308); yl+yh= 1.30518e+308 j=3: ( 0, 1.30518e+308); ( 0, 1.30518e+308); yl+yh= 1.30518e+308 j=4: ( 0, 1.30518e+308); ( 0, 1.30518e+308); yl+yh= 1.30518e+308 3. after ADD1(M): yl,yh = ( 0, 1.30518e+308); yl+yh= 1.30518e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.20533e+308); yl+yh= 1.20533e+308 ebd0(x=1e+307, M=4.28603e+301): M/x = (r=0.561779104644075) * 2^(e=-17); i=16, f=1820, fg=f*2^-(e+10)=232960 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 1.23586e+308); yl+yh= 1.23586e+308 j=2: ( 0, 1.23586e+308); ( 0, 1.23586e+308); yl+yh= 1.23586e+308 j=3: ( 0, 1.23586e+308); ( 0, 1.23586e+308); yl+yh= 1.23586e+308 j=4: ( 0, 1.23586e+308); ( 0, 1.23586e+308); yl+yh= 1.23586e+308 3. after ADD1(M): yl,yh = ( 0, 1.23586e+308); yl+yh= 1.23586e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.13602e+308); yl+yh= 1.13602e+308 ebd0(x=1e+307, M=8.57207e+301): M/x = (r=0.561779104644075) * 2^(e=-16); i=16, f=1820, fg=f*2^-(e+10)=116480 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 1.16655e+308); yl+yh= 1.16655e+308 j=2: ( 0, 1.16655e+308); ( 0, 1.16655e+308); yl+yh= 1.16655e+308 j=3: ( 0, 1.16655e+308); ( 0, 1.16655e+308); yl+yh= 1.16655e+308 j=4: ( 0, 1.16655e+308); ( 0, 1.16655e+308); yl+yh= 1.16655e+308 3. after ADD1(M): yl,yh = ( 0, 1.16655e+308); yl+yh= 1.16655e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.0667e+308); yl+yh= 1.0667e+308 ebd0(x=1e+307, M=1.71441e+302): M/x = (r=0.561779104644075) * 2^(e=-15); i=16, f=1820, fg=f*2^-(e+10)=58240 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 1.09723e+308); yl+yh= 1.09723e+308 j=2: ( 0, 1.09723e+308); ( 0, 1.09723e+308); yl+yh= 1.09723e+308 j=3: ( 0, 1.09723e+308); ( 0, 1.09723e+308); yl+yh= 1.09723e+308 j=4: ( 0, 1.09723e+308); ( 0, 1.09723e+308); yl+yh= 1.09723e+308 3. after ADD1(M): yl,yh = ( 0, 1.09723e+308); yl+yh= 1.09723e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 9.97387e+307); yl+yh= 9.97387e+307 ebd0(x=1e+307, M=3.42883e+302): M/x = (r=0.561779104644075) * 2^(e=-14); i=16, f=1820, fg=f*2^-(e+10)=29120 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 1.02792e+308); yl+yh= 1.02792e+308 j=2: ( 0, 1.02792e+308); ( 0, 1.02792e+308); yl+yh= 1.02792e+308 j=3: ( 0, 1.02792e+308); ( 0, 1.02792e+308); yl+yh= 1.02792e+308 j=4: ( 0, 1.02792e+308); ( 0, 1.02792e+308); yl+yh= 1.02792e+308 3. after ADD1(M): yl,yh = ( 0, 1.02792e+308); yl+yh= 1.02792e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 9.28074e+307); yl+yh= 9.28074e+307 ebd0(x=1e+307, M=6.85766e+302): M/x = (r=0.561779104644075) * 2^(e=-13); i=16, f=1820, fg=f*2^-(e+10)=14560 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 9.58603e+307); yl+yh= 9.58603e+307 j=2: ( 0, 9.58603e+307); ( 0, 9.58603e+307); yl+yh= 9.58603e+307 j=3: ( 0, 9.58603e+307); ( 0, 9.58603e+307); yl+yh= 9.58603e+307 j=4: ( 0, 9.58603e+307); ( 0, 9.58603e+307); yl+yh= 9.58603e+307 3. after ADD1(M): yl,yh = ( 0, 9.5861e+307); yl+yh= 9.5861e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 8.58763e+307); yl+yh= 8.58763e+307 ebd0(x=1e+307, M=1.37153e+303): M/x = (r=0.561779104644075) * 2^(e=-12); i=16, f=1820, fg=f*2^-(e+10)=7280 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 8.89289e+307); yl+yh= 8.89289e+307 j=2: ( 0, 8.89289e+307); ( 0, 8.89289e+307); yl+yh= 8.89289e+307 j=3: ( 0, 8.89289e+307); ( 0, 8.89289e+307); yl+yh= 8.89289e+307 j=4: ( 0, 8.89289e+307); ( 0, 8.89289e+307); yl+yh= 8.89289e+307 3. after ADD1(M): yl,yh = ( 0, 8.89302e+307); yl+yh= 8.89302e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 7.89455e+307); yl+yh= 7.89455e+307 ebd0(x=1e+307, M=2.74306e+303): M/x = (r=0.561779104644075) * 2^(e=-11); i=16, f=1820, fg=f*2^-(e+10)=3640 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 8.19974e+307); yl+yh= 8.19974e+307 j=2: ( 0, 8.19974e+307); ( 0, 8.19974e+307); yl+yh= 8.19974e+307 j=3: ( 0, 8.19974e+307); ( 0, 8.19974e+307); yl+yh= 8.19974e+307 j=4: ( 0, 8.19974e+307); ( 0, 8.19974e+307); yl+yh= 8.19974e+307 3. after ADD1(M): yl,yh = ( 0, 8.20001e+307); yl+yh= 8.20001e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 7.20154e+307); yl+yh= 7.20154e+307 ebd0(x=1e+307, M=5.48612e+303): M/x = (r=0.561779104644075) * 2^(e=-10); i=16, f=1820, fg=f*2^-(e+10)=1820 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 7.50659e+307); yl+yh= 7.50659e+307 j=2: ( 0, 7.50659e+307); ( 0, 7.50659e+307); yl+yh= 7.50659e+307 j=3: ( 0, 7.50659e+307); ( 0, 7.50659e+307); yl+yh= 7.50659e+307 j=4: ( 0, 7.50659e+307); ( 0, 7.50659e+307); yl+yh= 7.50659e+307 3. after ADD1(M): yl,yh = ( 0, 7.50714e+307); yl+yh= 7.50714e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 6.50867e+307); yl+yh= 6.50867e+307 ebd0(x=1e+307, M=1.09722e+304): M/x = (r=0.561779104644075) * 2^(e=-9); i=16, f=1820, fg=f*2^-(e+10)=910 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 6.81345e+307); yl+yh= 6.81345e+307 j=2: ( 0, 6.81345e+307); ( 0, 6.81345e+307); yl+yh= 6.81345e+307 j=3: ( 0, 6.81345e+307); ( 0, 6.81345e+307); yl+yh= 6.81345e+307 j=4: ( 0, 6.81345e+307); ( 0, 6.81345e+307); yl+yh= 6.81345e+307 3. after ADD1(M): yl,yh = ( 0, 6.81454e+307); yl+yh= 6.81454e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 5.81607e+307); yl+yh= 5.81607e+307 ebd0(x=1e+307, M=2.19445e+304): M/x = (r=0.561779104644075) * 2^(e=-8); i=16, f=1820, fg=f*2^-(e+10)=455 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 6.1203e+307); yl+yh= 6.1203e+307 j=2: ( 0, 6.1203e+307); ( 0, 6.1203e+307); yl+yh= 6.1203e+307 j=3: ( 0, 6.1203e+307); ( 0, 6.1203e+307); yl+yh= 6.1203e+307 j=4: ( 0, 6.1203e+307); ( 0, 6.1203e+307); yl+yh= 6.1203e+307 3. after ADD1(M): yl,yh = ( 0, 6.12249e+307); yl+yh= 6.12249e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 5.12402e+307); yl+yh= 5.12402e+307 ebd0(x=1e+307, M=4.3889e+304): M/x = (r=0.561779104644075) * 2^(e=-7); i=16, f=1820, fg=f*2^-(e+10)=227.5 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 5.42715e+307); yl+yh= 5.42715e+307 j=2: ( 0, 5.42715e+307); ( 0, 5.42715e+307); yl+yh= 5.42715e+307 j=3: ( 0, 5.42715e+307); ( 0, 5.42715e+307); yl+yh= 5.42715e+307 j=4: ( 0, 5.42715e+307); ( 0, 5.42715e+307); yl+yh= 5.42715e+307 3. after ADD1(M): yl,yh = ( 0, 5.43154e+307); yl+yh= 5.43154e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 4.43307e+307); yl+yh= 4.43307e+307 ebd0(x=1e+307, M=8.7778e+304): M/x = (r=0.561779104644075) * 2^(e=-6); i=16, f=1820, fg=f*2^-(e+10)=113.75 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 4.734e+307); yl+yh= 4.734e+307 j=2: ( 0, 4.734e+307); ( 0, 4.734e+307); yl+yh= 4.734e+307 j=3: ( 0, 4.734e+307); ( 0, 4.734e+307); yl+yh= 4.734e+307 j=4: ( 0, 4.734e+307); ( 0, 4.734e+307); yl+yh= 4.734e+307 3. after ADD1(M): yl,yh = ( 0, 4.74278e+307); yl+yh= 4.74278e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 3.74431e+307); yl+yh= 3.74431e+307 ebd0(x=1e+307, M=1.75556e+305): M/x = (r=0.561779104644075) * 2^(e=-5); i=16, f=1820, fg=f*2^-(e+10)=56.875 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 4.04086e+307); yl+yh= 4.04086e+307 j=2: ( 0, 4.04086e+307); ( 0, 4.04086e+307); yl+yh= 4.04086e+307 j=3: ( 0, 4.04086e+307); ( 0, 4.04086e+307); yl+yh= 4.04086e+307 j=4: ( 0, 4.04086e+307); ( 0, 4.04086e+307); yl+yh= 4.04086e+307 3. after ADD1(M): yl,yh = ( 0, 4.05841e+307); yl+yh= 4.05841e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 3.05994e+307); yl+yh= 3.05994e+307 ebd0(x=1e+307, M=3.51112e+305): M/x = (r=0.561779104644075) * 2^(e=-4); i=16, f=1820, fg=f*2^-(e+10)=28.4375 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 3.34771e+307); yl+yh= 3.34771e+307 j=2: ( 0, 3.34771e+307); ( 0, 3.34771e+307); yl+yh= 3.34771e+307 j=3: ( 0, 3.34771e+307); ( 0, 3.34771e+307); yl+yh= 3.34771e+307 j=4: ( 0, 3.34771e+307); ( 0, 3.34771e+307); yl+yh= 3.34771e+307 3. after ADD1(M): yl,yh = ( 0, 3.38282e+307); yl+yh= 3.38282e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 2.38435e+307); yl+yh= 2.38435e+307 ebd0(x=1e+307, M=7.02224e+305): M/x = (r=0.561779104644075) * 2^(e=-3); i=16, f=1820, fg=f*2^-(e+10)=14.2188 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 2.65456e+307); yl+yh= 2.65456e+307 j=2: ( 0, 2.65456e+307); ( 0, 2.65456e+307); yl+yh= 2.65456e+307 j=3: ( 0, 2.65456e+307); ( 0, 2.65456e+307); yl+yh= 2.65456e+307 j=4: ( 0, 2.65456e+307); ( 0, 2.65456e+307); yl+yh= 2.65456e+307 3. after ADD1(M): yl,yh = ( 0, 2.72479e+307); yl+yh= 2.72479e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 1.72631e+307); yl+yh= 1.72631e+307 ebd0(x=1e+307, M=1.40445e+306): M/x = (r=0.561779104644075) * 2^(e=-2); i=16, f=1820, fg=f*2^-(e+10)=7.10938 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 1.96142e+307); yl+yh= 1.96142e+307 j=2: ( 0, 1.96142e+307); ( 0, 1.96142e+307); yl+yh= 1.96142e+307 j=3: ( 0, 1.96142e+307); ( 0, 1.96142e+307); yl+yh= 1.96142e+307 j=4: ( 0, 1.96142e+307); ( 0, 1.96142e+307); yl+yh= 1.96142e+307 3. after ADD1(M): yl,yh = ( 0, 2.10186e+307); yl+yh= 2.10186e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 1.10339e+307); yl+yh= 1.10339e+307 ebd0(x=1e+307, M=2.8089e+306): M/x = (r=0.561779104644075) * 2^(e=-1); i=16, f=1820, fg=f*2^-(e+10)=3.55469 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 1.26827e+307); yl+yh= 1.26827e+307 j=2: ( 0, 1.26827e+307); ( 0, 1.26827e+307); yl+yh= 1.26827e+307 j=3: ( 0, 1.26827e+307); ( 0, 1.26827e+307); yl+yh= 1.26827e+307 j=4: ( 0, 1.26827e+307); ( 0, 1.26827e+307); yl+yh= 1.26827e+307 3. after ADD1(M): yl,yh = ( 0, 1.54916e+307); yl+yh= 1.54916e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 5.50683e+306); yl+yh= 5.50683e+306 ebd0(x=1e+307, M=5.61779e+306): M/x = (r=0.561779104644075) * 2^(e=0); i=16, f=1820, fg=f*2^-(e+10)=1.77734 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 5.75121e+306); yl+yh= 5.75121e+306 j=2: ( 0, 5.75121e+306); ( 0, 5.75121e+306); yl+yh= 5.75121e+306 j=3: ( 0, 5.75121e+306); ( 0, 5.75121e+306); yl+yh= 5.75121e+306 j=4: ( 0, 5.75121e+306); ( 0, 5.75121e+306); yl+yh= 5.75121e+306 3. after ADD1(M): yl,yh = ( 0, 1.1369e+307); yl+yh= 1.1369e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 1.38426e+306); yl+yh= 1.38426e+306 ebd0(x=1e+307, M=1.12356e+307): M/x = (r=0.561779104644075) * 2^(e=1); i=16, f=1820, fg=f*2^-(e+10)=0.888672 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, -1.18026e+306); yl+yh= -1.18026e+306 j=2: ( 0, -1.18026e+306); ( 0, -1.18026e+306); yl+yh= -1.18026e+306 j=3: ( 0, -1.18026e+306); ( 0, -1.18026e+306); yl+yh= -1.18026e+306 j=4: ( 0, -1.18026e+306); ( 0, -1.18026e+306); yl+yh= -1.18026e+306 3. after ADD1(M): yl,yh = ( 0, 1.00553e+307); yl+yh= 1.00553e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 7.05759e+304); yl+yh= 7.05759e+304 ebd0(x=1e+307, M=2.24712e+307): M/x = (r=0.561779104644075) * 2^(e=2); i=16, f=1820, fg=f*2^-(e+10)=0.444336 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, -8.11173e+306); yl+yh= -8.11173e+306 j=2: ( 0, -8.11173e+306); ( 0, -8.11173e+306); yl+yh= -8.11173e+306 j=3: ( 0, -8.11173e+306); ( 0, -8.11173e+306); yl+yh= -8.11173e+306 j=4: ( 0, -8.11173e+306); ( 0, -8.11173e+306); yl+yh= -8.11173e+306 3. after ADD1(M): yl,yh = ( 0, 1.43594e+307); yl+yh= 1.43594e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 4.37469e+306); yl+yh= 4.37469e+306 ebd0(x=1e+307, M=4.49423e+307): M/x = (r=0.561779104644075) * 2^(e=3); i=16, f=1820, fg=f*2^-(e+10)=0.222168 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, -1.50432e+307); yl+yh= -1.50432e+307 j=2: ( 0, -1.50432e+307); ( 0, -1.50432e+307); yl+yh= -1.50432e+307 j=3: ( 0, -1.50432e+307); ( 0, -1.50432e+307); yl+yh= -1.50432e+307 j=4: ( 0, -1.50432e+307); ( 0, -1.50432e+307); yl+yh= -1.50432e+307 3. after ADD1(M): yl,yh = ( 0, 2.98991e+307); yl+yh= 2.98991e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 1.99144e+307); yl+yh= 1.99144e+307 ebd0(x=1e+307, M=8.98847e+307): M/x = (r=0.561779104644075) * 2^(e=4); i=16, f=1820, fg=f*2^-(e+10)=0.111084 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, -2.19747e+307); yl+yh= -2.19747e+307 j=2: ( 0, -2.19747e+307); ( 0, -2.19747e+307); yl+yh= -2.19747e+307 j=3: ( 0, -2.19747e+307); ( 0, -2.19747e+307); yl+yh= -2.19747e+307 j=4: ( 0, -2.19747e+307); ( 0, -2.19747e+307); yl+yh= -2.19747e+307 3. after ADD1(M): yl,yh = ( 0, 6.791e+307); yl+yh= 6.791e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 5.79252e+307); yl+yh= 5.79252e+307 ebd0(x=1e+307, M=1.79769e+308): M/x = (r=0.561779104644075) * 2^(e=5); i=16, f=1820, fg=f*2^-(e+10)=0.055542 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, -2.89061e+307); yl+yh= -2.89061e+307 j=2: ( 0, -2.89061e+307); ( 0, -2.89061e+307); yl+yh= -2.89061e+307 j=3: ( 0, -2.89061e+307); ( 0, -2.89061e+307); yl+yh= -2.89061e+307 j=4: ( 0, -2.89061e+307); ( 0, -2.89061e+307); yl+yh= -2.89061e+307 3. after ADD1(M): yl,yh = ( 0, 1.50863e+308); yl+yh= 1.50863e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.40878e+308); yl+yh= 1.40878e+308 dpq_ebd0(x[1:1], np[1:35], ... ): ebd0(x=1e+307, M=4.18558e+298): M/x = (r=0.561779104644075) * 2^(e=-27); i=16, f=1820, fg=f*2^-(e+10)=2.38551e+08 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( nan, inf); yl+yh= nan non-finite yh --> return((yh=Inf, yl=0)) ebd0(x=1e+307, M=8.37116e+298): M/x = (r=0.561779104644075) * 2^(e=-26); i=16, f=1820, fg=f*2^-(e+10)=1.19276e+08 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( nan, inf); yl+yh= nan non-finite yh --> return((yh=Inf, yl=0)) ebd0(x=1e+307, M=1.67423e+299): M/x = (r=0.561779104644075) * 2^(e=-25); i=16, f=1820, fg=f*2^-(e+10)=5.96378e+07 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 1.79038e+308); yl+yh= 1.79038e+308 j=1: ( 0, 1.79038e+308); ( 0, 1.79038e+308); yl+yh= 1.79038e+308 j=2: ( 0, 1.79038e+308); ( 0, 1.79038e+308); yl+yh= 1.79038e+308 j=3: ( 0, 1.79038e+308); ( 0, 1.79038e+308); yl+yh= 1.79038e+308 3. after ADD1(M): yl,yh = ( 0, 1.79038e+308); yl+yh= 1.79038e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.69053e+308); yl+yh= 1.69053e+308 ebd0(x=1e+307, M=3.34846e+299): M/x = (r=0.561779104644075) * 2^(e=-24); i=16, f=1820, fg=f*2^-(e+10)=2.98189e+07 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 1.72107e+308); yl+yh= 1.72107e+308 j=1: ( 0, 1.72107e+308); ( 0, 1.72107e+308); yl+yh= 1.72107e+308 j=2: ( 0, 1.72107e+308); ( 0, 1.72107e+308); yl+yh= 1.72107e+308 j=3: ( 0, 1.72107e+308); ( 0, 1.72107e+308); yl+yh= 1.72107e+308 3. after ADD1(M): yl,yh = ( 0, 1.72107e+308); yl+yh= 1.72107e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.62122e+308); yl+yh= 1.62122e+308 ebd0(x=1e+307, M=6.69693e+299): M/x = (r=0.561779104644075) * 2^(e=-23); i=16, f=1820, fg=f*2^-(e+10)=1.49094e+07 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 1.65175e+308); yl+yh= 1.65175e+308 j=1: ( 0, 1.65175e+308); ( 0, 1.65175e+308); yl+yh= 1.65175e+308 j=2: ( 0, 1.65175e+308); ( 0, 1.65175e+308); yl+yh= 1.65175e+308 j=3: ( 0, 1.65175e+308); ( 0, 1.65175e+308); yl+yh= 1.65175e+308 3. after ADD1(M): yl,yh = ( 0, 1.65175e+308); yl+yh= 1.65175e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.5519e+308); yl+yh= 1.5519e+308 ebd0(x=1e+307, M=1.33939e+300): M/x = (r=0.561779104644075) * 2^(e=-22); i=16, f=1820, fg=f*2^-(e+10)=7.45472e+06 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 1.58244e+308); yl+yh= 1.58244e+308 j=1: ( 0, 1.58244e+308); ( 0, 1.58244e+308); yl+yh= 1.58244e+308 j=2: ( 0, 1.58244e+308); ( 0, 1.58244e+308); yl+yh= 1.58244e+308 j=3: ( 0, 1.58244e+308); ( 0, 1.58244e+308); yl+yh= 1.58244e+308 3. after ADD1(M): yl,yh = ( 0, 1.58244e+308); yl+yh= 1.58244e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.48259e+308); yl+yh= 1.48259e+308 ebd0(x=1e+307, M=2.67877e+300): M/x = (r=0.561779104644075) * 2^(e=-21); i=16, f=1820, fg=f*2^-(e+10)=3.72736e+06 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 1.51312e+308); yl+yh= 1.51312e+308 j=1: ( 0, 1.51312e+308); ( 0, 1.51312e+308); yl+yh= 1.51312e+308 j=2: ( 0, 1.51312e+308); ( 0, 1.51312e+308); yl+yh= 1.51312e+308 j=3: ( 0, 1.51312e+308); ( 0, 1.51312e+308); yl+yh= 1.51312e+308 3. after ADD1(M): yl,yh = ( 0, 1.51312e+308); yl+yh= 1.51312e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.41327e+308); yl+yh= 1.41327e+308 ebd0(x=1e+307, M=5.35754e+300): M/x = (r=0.561779104644075) * 2^(e=-20); i=16, f=1820, fg=f*2^-(e+10)=1.86368e+06 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 1.44381e+308); yl+yh= 1.44381e+308 j=1: ( 0, 1.44381e+308); ( 0, 1.44381e+308); yl+yh= 1.44381e+308 j=2: ( 0, 1.44381e+308); ( 0, 1.44381e+308); yl+yh= 1.44381e+308 j=3: ( 0, 1.44381e+308); ( 0, 1.44381e+308); yl+yh= 1.44381e+308 3. after ADD1(M): yl,yh = ( 0, 1.44381e+308); yl+yh= 1.44381e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.34396e+308); yl+yh= 1.34396e+308 ebd0(x=1e+307, M=1.07151e+301): M/x = (r=0.561779104644075) * 2^(e=-19); i=16, f=1820, fg=f*2^-(e+10)=931840 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 1.37449e+308); yl+yh= 1.37449e+308 j=1: ( 0, 1.37449e+308); ( 0, 1.37449e+308); yl+yh= 1.37449e+308 j=2: ( 0, 1.37449e+308); ( 0, 1.37449e+308); yl+yh= 1.37449e+308 j=3: ( 0, 1.37449e+308); ( 0, 1.37449e+308); yl+yh= 1.37449e+308 3. after ADD1(M): yl,yh = ( 0, 1.37449e+308); yl+yh= 1.37449e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.27464e+308); yl+yh= 1.27464e+308 ebd0(x=1e+307, M=2.14302e+301): M/x = (r=0.561779104644075) * 2^(e=-18); i=16, f=1820, fg=f*2^-(e+10)=465920 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 1.30518e+308); yl+yh= 1.30518e+308 j=1: ( 0, 1.30518e+308); ( 0, 1.30518e+308); yl+yh= 1.30518e+308 j=2: ( 0, 1.30518e+308); ( 0, 1.30518e+308); yl+yh= 1.30518e+308 j=3: ( 0, 1.30518e+308); ( 0, 1.30518e+308); yl+yh= 1.30518e+308 3. after ADD1(M): yl,yh = ( 0, 1.30518e+308); yl+yh= 1.30518e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.20533e+308); yl+yh= 1.20533e+308 ebd0(x=1e+307, M=4.28603e+301): M/x = (r=0.561779104644075) * 2^(e=-17); i=16, f=1820, fg=f*2^-(e+10)=232960 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 1.23586e+308); yl+yh= 1.23586e+308 j=1: ( 0, 1.23586e+308); ( 0, 1.23586e+308); yl+yh= 1.23586e+308 j=2: ( 0, 1.23586e+308); ( 0, 1.23586e+308); yl+yh= 1.23586e+308 j=3: ( 0, 1.23586e+308); ( 0, 1.23586e+308); yl+yh= 1.23586e+308 3. after ADD1(M): yl,yh = ( 0, 1.23586e+308); yl+yh= 1.23586e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.13602e+308); yl+yh= 1.13602e+308 ebd0(x=1e+307, M=8.57207e+301): M/x = (r=0.561779104644075) * 2^(e=-16); i=16, f=1820, fg=f*2^-(e+10)=116480 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 1.16655e+308); yl+yh= 1.16655e+308 j=1: ( 0, 1.16655e+308); ( 0, 1.16655e+308); yl+yh= 1.16655e+308 j=2: ( 0, 1.16655e+308); ( 0, 1.16655e+308); yl+yh= 1.16655e+308 j=3: ( 0, 1.16655e+308); ( 0, 1.16655e+308); yl+yh= 1.16655e+308 3. after ADD1(M): yl,yh = ( 0, 1.16655e+308); yl+yh= 1.16655e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.0667e+308); yl+yh= 1.0667e+308 ebd0(x=1e+307, M=1.71441e+302): M/x = (r=0.561779104644075) * 2^(e=-15); i=16, f=1820, fg=f*2^-(e+10)=58240 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 1.09723e+308); yl+yh= 1.09723e+308 j=1: ( 0, 1.09723e+308); ( 0, 1.09723e+308); yl+yh= 1.09723e+308 j=2: ( 0, 1.09723e+308); ( 0, 1.09723e+308); yl+yh= 1.09723e+308 j=3: ( 0, 1.09723e+308); ( 0, 1.09723e+308); yl+yh= 1.09723e+308 3. after ADD1(M): yl,yh = ( 0, 1.09723e+308); yl+yh= 1.09723e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 9.97387e+307); yl+yh= 9.97387e+307 ebd0(x=1e+307, M=3.42883e+302): M/x = (r=0.561779104644075) * 2^(e=-14); i=16, f=1820, fg=f*2^-(e+10)=29120 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 1.02792e+308); yl+yh= 1.02792e+308 j=1: ( 0, 1.02792e+308); ( 0, 1.02792e+308); yl+yh= 1.02792e+308 j=2: ( 0, 1.02792e+308); ( 0, 1.02792e+308); yl+yh= 1.02792e+308 j=3: ( 0, 1.02792e+308); ( 0, 1.02792e+308); yl+yh= 1.02792e+308 3. after ADD1(M): yl,yh = ( 0, 1.02792e+308); yl+yh= 1.02792e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 9.28074e+307); yl+yh= 9.28074e+307 ebd0(x=1e+307, M=6.85766e+302): M/x = (r=0.561779104644075) * 2^(e=-13); i=16, f=1820, fg=f*2^-(e+10)=14560 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 9.58603e+307); yl+yh= 9.58603e+307 j=1: ( 0, 9.58603e+307); ( 0, 9.58603e+307); yl+yh= 9.58603e+307 j=2: ( 0, 9.58603e+307); ( 0, 9.58603e+307); yl+yh= 9.58603e+307 j=3: ( 0, 9.58603e+307); ( 0, 9.58603e+307); yl+yh= 9.58603e+307 3. after ADD1(M): yl,yh = ( 0, 9.5861e+307); yl+yh= 9.5861e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 8.58763e+307); yl+yh= 8.58763e+307 ebd0(x=1e+307, M=1.37153e+303): M/x = (r=0.561779104644075) * 2^(e=-12); i=16, f=1820, fg=f*2^-(e+10)=7280 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 8.89289e+307); yl+yh= 8.89289e+307 j=1: ( 0, 8.89289e+307); ( 0, 8.89289e+307); yl+yh= 8.89289e+307 j=2: ( 0, 8.89289e+307); ( 0, 8.89289e+307); yl+yh= 8.89289e+307 j=3: ( 0, 8.89289e+307); ( 0, 8.89289e+307); yl+yh= 8.89289e+307 3. after ADD1(M): yl,yh = ( 0, 8.89302e+307); yl+yh= 8.89302e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 7.89455e+307); yl+yh= 7.89455e+307 ebd0(x=1e+307, M=2.74306e+303): M/x = (r=0.561779104644075) * 2^(e=-11); i=16, f=1820, fg=f*2^-(e+10)=3640 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 8.19974e+307); yl+yh= 8.19974e+307 j=1: ( 0, 8.19974e+307); ( 0, 8.19974e+307); yl+yh= 8.19974e+307 j=2: ( 0, 8.19974e+307); ( 0, 8.19974e+307); yl+yh= 8.19974e+307 j=3: ( 0, 8.19974e+307); ( 0, 8.19974e+307); yl+yh= 8.19974e+307 3. after ADD1(M): yl,yh = ( 0, 8.20001e+307); yl+yh= 8.20001e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 7.20154e+307); yl+yh= 7.20154e+307 ebd0(x=1e+307, M=5.48612e+303): M/x = (r=0.561779104644075) * 2^(e=-10); i=16, f=1820, fg=f*2^-(e+10)=1820 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 7.50659e+307); yl+yh= 7.50659e+307 j=1: ( 0, 7.50659e+307); ( 0, 7.50659e+307); yl+yh= 7.50659e+307 j=2: ( 0, 7.50659e+307); ( 0, 7.50659e+307); yl+yh= 7.50659e+307 j=3: ( 0, 7.50659e+307); ( 0, 7.50659e+307); yl+yh= 7.50659e+307 3. after ADD1(M): yl,yh = ( 0, 7.50714e+307); yl+yh= 7.50714e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 6.50867e+307); yl+yh= 6.50867e+307 ebd0(x=1e+307, M=1.09722e+304): M/x = (r=0.561779104644075) * 2^(e=-9); i=16, f=1820, fg=f*2^-(e+10)=910 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 6.81345e+307); yl+yh= 6.81345e+307 j=1: ( 0, 6.81345e+307); ( 0, 6.81345e+307); yl+yh= 6.81345e+307 j=2: ( 0, 6.81345e+307); ( 0, 6.81345e+307); yl+yh= 6.81345e+307 j=3: ( 0, 6.81345e+307); ( 0, 6.81345e+307); yl+yh= 6.81345e+307 3. after ADD1(M): yl,yh = ( 0, 6.81454e+307); yl+yh= 6.81454e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 5.81607e+307); yl+yh= 5.81607e+307 ebd0(x=1e+307, M=2.19445e+304): M/x = (r=0.561779104644075) * 2^(e=-8); i=16, f=1820, fg=f*2^-(e+10)=455 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 6.1203e+307); yl+yh= 6.1203e+307 j=1: ( 0, 6.1203e+307); ( 0, 6.1203e+307); yl+yh= 6.1203e+307 j=2: ( 0, 6.1203e+307); ( 0, 6.1203e+307); yl+yh= 6.1203e+307 j=3: ( 0, 6.1203e+307); ( 0, 6.1203e+307); yl+yh= 6.1203e+307 3. after ADD1(M): yl,yh = ( 0, 6.12249e+307); yl+yh= 6.12249e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 5.12402e+307); yl+yh= 5.12402e+307 ebd0(x=1e+307, M=4.3889e+304): M/x = (r=0.561779104644075) * 2^(e=-7); i=16, f=1820, fg=f*2^-(e+10)=227.5 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 5.42715e+307); yl+yh= 5.42715e+307 j=1: ( 0, 5.42715e+307); ( 0, 5.42715e+307); yl+yh= 5.42715e+307 j=2: ( 0, 5.42715e+307); ( 0, 5.42715e+307); yl+yh= 5.42715e+307 j=3: ( 0, 5.42715e+307); ( 0, 5.42715e+307); yl+yh= 5.42715e+307 3. after ADD1(M): yl,yh = ( 0, 5.43154e+307); yl+yh= 5.43154e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 4.43307e+307); yl+yh= 4.43307e+307 ebd0(x=1e+307, M=8.7778e+304): M/x = (r=0.561779104644075) * 2^(e=-6); i=16, f=1820, fg=f*2^-(e+10)=113.75 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 4.734e+307); yl+yh= 4.734e+307 j=1: ( 0, 4.734e+307); ( 0, 4.734e+307); yl+yh= 4.734e+307 j=2: ( 0, 4.734e+307); ( 0, 4.734e+307); yl+yh= 4.734e+307 j=3: ( 0, 4.734e+307); ( 0, 4.734e+307); yl+yh= 4.734e+307 3. after ADD1(M): yl,yh = ( 0, 4.74278e+307); yl+yh= 4.74278e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 3.74431e+307); yl+yh= 3.74431e+307 ebd0(x=1e+307, M=1.75556e+305): M/x = (r=0.561779104644075) * 2^(e=-5); i=16, f=1820, fg=f*2^-(e+10)=56.875 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 4.04086e+307); yl+yh= 4.04086e+307 j=1: ( 0, 4.04086e+307); ( 0, 4.04086e+307); yl+yh= 4.04086e+307 j=2: ( 0, 4.04086e+307); ( 0, 4.04086e+307); yl+yh= 4.04086e+307 j=3: ( 0, 4.04086e+307); ( 0, 4.04086e+307); yl+yh= 4.04086e+307 3. after ADD1(M): yl,yh = ( 0, 4.05841e+307); yl+yh= 4.05841e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 3.05994e+307); yl+yh= 3.05994e+307 ebd0(x=1e+307, M=3.51112e+305): M/x = (r=0.561779104644075) * 2^(e=-4); i=16, f=1820, fg=f*2^-(e+10)=28.4375 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 3.34771e+307); yl+yh= 3.34771e+307 j=1: ( 0, 3.34771e+307); ( 0, 3.34771e+307); yl+yh= 3.34771e+307 j=2: ( 0, 3.34771e+307); ( 0, 3.34771e+307); yl+yh= 3.34771e+307 j=3: ( 0, 3.34771e+307); ( 0, 3.34771e+307); yl+yh= 3.34771e+307 3. after ADD1(M): yl,yh = ( 0, 3.38282e+307); yl+yh= 3.38282e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 2.38435e+307); yl+yh= 2.38435e+307 ebd0(x=1e+307, M=7.02224e+305): M/x = (r=0.561779104644075) * 2^(e=-3); i=16, f=1820, fg=f*2^-(e+10)=14.2188 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 2.65456e+307); yl+yh= 2.65456e+307 j=1: ( 0, 2.65456e+307); ( 0, 2.65456e+307); yl+yh= 2.65456e+307 j=2: ( 0, 2.65456e+307); ( 0, 2.65456e+307); yl+yh= 2.65456e+307 j=3: ( 0, 2.65456e+307); ( 0, 2.65456e+307); yl+yh= 2.65456e+307 3. after ADD1(M): yl,yh = ( 0, 2.72479e+307); yl+yh= 2.72479e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 1.72631e+307); yl+yh= 1.72631e+307 ebd0(x=1e+307, M=1.40445e+306): M/x = (r=0.561779104644075) * 2^(e=-2); i=16, f=1820, fg=f*2^-(e+10)=7.10938 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 1.96142e+307); yl+yh= 1.96142e+307 j=1: ( 0, 1.96142e+307); ( 0, 1.96142e+307); yl+yh= 1.96142e+307 j=2: ( 0, 1.96142e+307); ( 0, 1.96142e+307); yl+yh= 1.96142e+307 j=3: ( 0, 1.96142e+307); ( 0, 1.96142e+307); yl+yh= 1.96142e+307 3. after ADD1(M): yl,yh = ( 0, 2.10186e+307); yl+yh= 2.10186e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 1.10339e+307); yl+yh= 1.10339e+307 ebd0(x=1e+307, M=2.8089e+306): M/x = (r=0.561779104644075) * 2^(e=-1); i=16, f=1820, fg=f*2^-(e+10)=3.55469 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 1.26827e+307); yl+yh= 1.26827e+307 j=1: ( 0, 1.26827e+307); ( 0, 1.26827e+307); yl+yh= 1.26827e+307 j=2: ( 0, 1.26827e+307); ( 0, 1.26827e+307); yl+yh= 1.26827e+307 j=3: ( 0, 1.26827e+307); ( 0, 1.26827e+307); yl+yh= 1.26827e+307 3. after ADD1(M): yl,yh = ( 0, 1.54916e+307); yl+yh= 1.54916e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 5.50683e+306); yl+yh= 5.50683e+306 ebd0(x=1e+307, M=5.61779e+306): M/x = (r=0.561779104644075) * 2^(e=0); i=16, f=1820, fg=f*2^-(e+10)=1.77734 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 5.75121e+306); yl+yh= 5.75121e+306 j=1: ( 0, 5.75121e+306); ( 0, 5.75121e+306); yl+yh= 5.75121e+306 j=2: ( 0, 5.75121e+306); ( 0, 5.75121e+306); yl+yh= 5.75121e+306 j=3: ( 0, 5.75121e+306); ( 0, 5.75121e+306); yl+yh= 5.75121e+306 3. after ADD1(M): yl,yh = ( 0, 1.1369e+307); yl+yh= 1.1369e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 1.38426e+306); yl+yh= 1.38426e+306 ebd0(x=1e+307, M=1.12356e+307): M/x = (r=0.561779104644075) * 2^(e=1); i=16, f=1820, fg=f*2^-(e+10)=0.888672 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, -1.18026e+306); yl+yh= -1.18026e+306 j=1: ( 0, -1.18026e+306); ( 0, -1.18026e+306); yl+yh= -1.18026e+306 j=2: ( 0, -1.18026e+306); ( 0, -1.18026e+306); yl+yh= -1.18026e+306 j=3: ( 0, -1.18026e+306); ( 0, -1.18026e+306); yl+yh= -1.18026e+306 3. after ADD1(M): yl,yh = ( 0, 1.00553e+307); yl+yh= 1.00553e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 7.05759e+304); yl+yh= 7.05759e+304 ebd0(x=1e+307, M=2.24712e+307): M/x = (r=0.561779104644075) * 2^(e=2); i=16, f=1820, fg=f*2^-(e+10)=0.444336 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, -8.11173e+306); yl+yh= -8.11173e+306 j=1: ( 0, -8.11173e+306); ( 0, -8.11173e+306); yl+yh= -8.11173e+306 j=2: ( 0, -8.11173e+306); ( 0, -8.11173e+306); yl+yh= -8.11173e+306 j=3: ( 0, -8.11173e+306); ( 0, -8.11173e+306); yl+yh= -8.11173e+306 3. after ADD1(M): yl,yh = ( 0, 1.43594e+307); yl+yh= 1.43594e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 4.37469e+306); yl+yh= 4.37469e+306 ebd0(x=1e+307, M=4.49423e+307): M/x = (r=0.561779104644075) * 2^(e=3); i=16, f=1820, fg=f*2^-(e+10)=0.222168 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, -1.50432e+307); yl+yh= -1.50432e+307 j=1: ( 0, -1.50432e+307); ( 0, -1.50432e+307); yl+yh= -1.50432e+307 j=2: ( 0, -1.50432e+307); ( 0, -1.50432e+307); yl+yh= -1.50432e+307 j=3: ( 0, -1.50432e+307); ( 0, -1.50432e+307); yl+yh= -1.50432e+307 3. after ADD1(M): yl,yh = ( 0, 2.98991e+307); yl+yh= 2.98991e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 1.99144e+307); yl+yh= 1.99144e+307 ebd0(x=1e+307, M=8.98847e+307): M/x = (r=0.561779104644075) * 2^(e=4); i=16, f=1820, fg=f*2^-(e+10)=0.111084 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, -2.19747e+307); yl+yh= -2.19747e+307 j=1: ( 0, -2.19747e+307); ( 0, -2.19747e+307); yl+yh= -2.19747e+307 j=2: ( 0, -2.19747e+307); ( 0, -2.19747e+307); yl+yh= -2.19747e+307 j=3: ( 0, -2.19747e+307); ( 0, -2.19747e+307); yl+yh= -2.19747e+307 3. after ADD1(M): yl,yh = ( 0, 6.791e+307); yl+yh= 6.791e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 5.79252e+307); yl+yh= 5.79252e+307 ebd0(x=1e+307, M=1.79769e+308): M/x = (r=0.561779104644075) * 2^(e=5); i=16, f=1820, fg=f*2^-(e+10)=0.055542 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, -2.89061e+307); yl+yh= -2.89061e+307 j=1: ( 0, -2.89061e+307); ( 0, -2.89061e+307); yl+yh= -2.89061e+307 j=2: ( 0, -2.89061e+307); ( 0, -2.89061e+307); yl+yh= -2.89061e+307 j=3: ( 0, -2.89061e+307); ( 0, -2.89061e+307); yl+yh= -2.89061e+307 3. after ADD1(M): yl,yh = ( 0, 1.50863e+308); yl+yh= 1.50863e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.40878e+308); yl+yh= 1.40878e+308 bd0(1e+307, 1.12356e+307): T.series w/ 32 terms -> bd0=7.05759e+304 > bd0v.10 <- bd0ver(x., Llam, mpfrPrec = 1024) ebd0(x=1e+307, M=1.0464e+298): M/x = (r=0.561779104644075) * 2^(e=-29); i=16, f=1820, fg=f*2^-(e+10)=9.54204e+08 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( NaN, Inf); yl+yh= NaN non-finite yh --> return((yh=Inf, yl=0)) ebd0(x=1e+307, M=2.09279e+298): M/x = (r=0.561779104644075) * 2^(e=-28); i=16, f=1820, fg=f*2^-(e+10)=4.77102e+08 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( NaN, Inf); yl+yh= NaN non-finite yh --> return((yh=Inf, yl=0)) ebd0(x=1e+307, M=4.18558e+298): M/x = (r=0.561779104644075) * 2^(e=-27); i=16, f=1820, fg=f*2^-(e+10)=2.38551e+08 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( NaN, Inf); yl+yh= NaN non-finite yh --> return((yh=Inf, yl=0)) ebd0(x=1e+307, M=8.37116e+298): M/x = (r=0.561779104644075) * 2^(e=-26); i=16, f=1820, fg=f*2^-(e+10)=1.19276e+08 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( NaN, Inf); yl+yh= NaN non-finite yh --> return((yh=Inf, yl=0)) ebd0(x=1e+307, M=1.67423e+299): M/x = (r=0.561779104644075) * 2^(e=-25); i=16, f=1820, fg=f*2^-(e+10)=5.96378e+07 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 1.79038e+308); yl+yh= 1.79038e+308 j=2: ( 0, 1.79038e+308); ( 0, 1.79038e+308); yl+yh= 1.79038e+308 j=3: ( 0, 1.79038e+308); ( 0, 1.79038e+308); yl+yh= 1.79038e+308 j=4: ( 0, 1.79038e+308); ( 0, 1.79038e+308); yl+yh= 1.79038e+308 3. after ADD1(M): yl,yh = ( 0, 1.79038e+308); yl+yh= 1.79038e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.69053e+308); yl+yh= 1.69053e+308 ebd0(x=1e+307, M=3.34846e+299): M/x = (r=0.561779104644075) * 2^(e=-24); i=16, f=1820, fg=f*2^-(e+10)=2.98189e+07 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 1.72107e+308); yl+yh= 1.72107e+308 j=2: ( 0, 1.72107e+308); ( 0, 1.72107e+308); yl+yh= 1.72107e+308 j=3: ( 0, 1.72107e+308); ( 0, 1.72107e+308); yl+yh= 1.72107e+308 j=4: ( 0, 1.72107e+308); ( 0, 1.72107e+308); yl+yh= 1.72107e+308 3. after ADD1(M): yl,yh = ( 0, 1.72107e+308); yl+yh= 1.72107e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.62122e+308); yl+yh= 1.62122e+308 ebd0(x=1e+307, M=6.69693e+299): M/x = (r=0.561779104644075) * 2^(e=-23); i=16, f=1820, fg=f*2^-(e+10)=1.49094e+07 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 1.65175e+308); yl+yh= 1.65175e+308 j=2: ( 0, 1.65175e+308); ( 0, 1.65175e+308); yl+yh= 1.65175e+308 j=3: ( 0, 1.65175e+308); ( 0, 1.65175e+308); yl+yh= 1.65175e+308 j=4: ( 0, 1.65175e+308); ( 0, 1.65175e+308); yl+yh= 1.65175e+308 3. after ADD1(M): yl,yh = ( 0, 1.65175e+308); yl+yh= 1.65175e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.5519e+308); yl+yh= 1.5519e+308 ebd0(x=1e+307, M=1.33939e+300): M/x = (r=0.561779104644075) * 2^(e=-22); i=16, f=1820, fg=f*2^-(e+10)=7.45472e+06 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 1.58244e+308); yl+yh= 1.58244e+308 j=2: ( 0, 1.58244e+308); ( 0, 1.58244e+308); yl+yh= 1.58244e+308 j=3: ( 0, 1.58244e+308); ( 0, 1.58244e+308); yl+yh= 1.58244e+308 j=4: ( 0, 1.58244e+308); ( 0, 1.58244e+308); yl+yh= 1.58244e+308 3. after ADD1(M): yl,yh = ( 0, 1.58244e+308); yl+yh= 1.58244e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.48259e+308); yl+yh= 1.48259e+308 ebd0(x=1e+307, M=2.67877e+300): M/x = (r=0.561779104644075) * 2^(e=-21); i=16, f=1820, fg=f*2^-(e+10)=3.72736e+06 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 1.51312e+308); yl+yh= 1.51312e+308 j=2: ( 0, 1.51312e+308); ( 0, 1.51312e+308); yl+yh= 1.51312e+308 j=3: ( 0, 1.51312e+308); ( 0, 1.51312e+308); yl+yh= 1.51312e+308 j=4: ( 0, 1.51312e+308); ( 0, 1.51312e+308); yl+yh= 1.51312e+308 3. after ADD1(M): yl,yh = ( 0, 1.51312e+308); yl+yh= 1.51312e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.41327e+308); yl+yh= 1.41327e+308 ebd0(x=1e+307, M=5.35754e+300): M/x = (r=0.561779104644075) * 2^(e=-20); i=16, f=1820, fg=f*2^-(e+10)=1.86368e+06 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 1.44381e+308); yl+yh= 1.44381e+308 j=2: ( 0, 1.44381e+308); ( 0, 1.44381e+308); yl+yh= 1.44381e+308 j=3: ( 0, 1.44381e+308); ( 0, 1.44381e+308); yl+yh= 1.44381e+308 j=4: ( 0, 1.44381e+308); ( 0, 1.44381e+308); yl+yh= 1.44381e+308 3. after ADD1(M): yl,yh = ( 0, 1.44381e+308); yl+yh= 1.44381e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.34396e+308); yl+yh= 1.34396e+308 ebd0(x=1e+307, M=1.07151e+301): M/x = (r=0.561779104644075) * 2^(e=-19); i=16, f=1820, fg=f*2^-(e+10)=931840 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 1.37449e+308); yl+yh= 1.37449e+308 j=2: ( 0, 1.37449e+308); ( 0, 1.37449e+308); yl+yh= 1.37449e+308 j=3: ( 0, 1.37449e+308); ( 0, 1.37449e+308); yl+yh= 1.37449e+308 j=4: ( 0, 1.37449e+308); ( 0, 1.37449e+308); yl+yh= 1.37449e+308 3. after ADD1(M): yl,yh = ( 0, 1.37449e+308); yl+yh= 1.37449e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.27464e+308); yl+yh= 1.27464e+308 ebd0(x=1e+307, M=2.14302e+301): M/x = (r=0.561779104644075) * 2^(e=-18); i=16, f=1820, fg=f*2^-(e+10)=465920 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 1.30518e+308); yl+yh= 1.30518e+308 j=2: ( 0, 1.30518e+308); ( 0, 1.30518e+308); yl+yh= 1.30518e+308 j=3: ( 0, 1.30518e+308); ( 0, 1.30518e+308); yl+yh= 1.30518e+308 j=4: ( 0, 1.30518e+308); ( 0, 1.30518e+308); yl+yh= 1.30518e+308 3. after ADD1(M): yl,yh = ( 0, 1.30518e+308); yl+yh= 1.30518e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.20533e+308); yl+yh= 1.20533e+308 ebd0(x=1e+307, M=4.28603e+301): M/x = (r=0.561779104644075) * 2^(e=-17); i=16, f=1820, fg=f*2^-(e+10)=232960 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 1.23586e+308); yl+yh= 1.23586e+308 j=2: ( 0, 1.23586e+308); ( 0, 1.23586e+308); yl+yh= 1.23586e+308 j=3: ( 0, 1.23586e+308); ( 0, 1.23586e+308); yl+yh= 1.23586e+308 j=4: ( 0, 1.23586e+308); ( 0, 1.23586e+308); yl+yh= 1.23586e+308 3. after ADD1(M): yl,yh = ( 0, 1.23586e+308); yl+yh= 1.23586e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.13602e+308); yl+yh= 1.13602e+308 ebd0(x=1e+307, M=8.57207e+301): M/x = (r=0.561779104644075) * 2^(e=-16); i=16, f=1820, fg=f*2^-(e+10)=116480 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 1.16655e+308); yl+yh= 1.16655e+308 j=2: ( 0, 1.16655e+308); ( 0, 1.16655e+308); yl+yh= 1.16655e+308 j=3: ( 0, 1.16655e+308); ( 0, 1.16655e+308); yl+yh= 1.16655e+308 j=4: ( 0, 1.16655e+308); ( 0, 1.16655e+308); yl+yh= 1.16655e+308 3. after ADD1(M): yl,yh = ( 0, 1.16655e+308); yl+yh= 1.16655e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.0667e+308); yl+yh= 1.0667e+308 ebd0(x=1e+307, M=1.71441e+302): M/x = (r=0.561779104644075) * 2^(e=-15); i=16, f=1820, fg=f*2^-(e+10)=58240 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 1.09723e+308); yl+yh= 1.09723e+308 j=2: ( 0, 1.09723e+308); ( 0, 1.09723e+308); yl+yh= 1.09723e+308 j=3: ( 0, 1.09723e+308); ( 0, 1.09723e+308); yl+yh= 1.09723e+308 j=4: ( 0, 1.09723e+308); ( 0, 1.09723e+308); yl+yh= 1.09723e+308 3. after ADD1(M): yl,yh = ( 0, 1.09723e+308); yl+yh= 1.09723e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 9.97387e+307); yl+yh= 9.97387e+307 ebd0(x=1e+307, M=3.42883e+302): M/x = (r=0.561779104644075) * 2^(e=-14); i=16, f=1820, fg=f*2^-(e+10)=29120 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 1.02792e+308); yl+yh= 1.02792e+308 j=2: ( 0, 1.02792e+308); ( 0, 1.02792e+308); yl+yh= 1.02792e+308 j=3: ( 0, 1.02792e+308); ( 0, 1.02792e+308); yl+yh= 1.02792e+308 j=4: ( 0, 1.02792e+308); ( 0, 1.02792e+308); yl+yh= 1.02792e+308 3. after ADD1(M): yl,yh = ( 0, 1.02792e+308); yl+yh= 1.02792e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 9.28074e+307); yl+yh= 9.28074e+307 ebd0(x=1e+307, M=6.85766e+302): M/x = (r=0.561779104644075) * 2^(e=-13); i=16, f=1820, fg=f*2^-(e+10)=14560 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 9.58603e+307); yl+yh= 9.58603e+307 j=2: ( 0, 9.58603e+307); ( 0, 9.58603e+307); yl+yh= 9.58603e+307 j=3: ( 0, 9.58603e+307); ( 0, 9.58603e+307); yl+yh= 9.58603e+307 j=4: ( 0, 9.58603e+307); ( 0, 9.58603e+307); yl+yh= 9.58603e+307 3. after ADD1(M): yl,yh = ( 0, 9.5861e+307); yl+yh= 9.5861e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 8.58763e+307); yl+yh= 8.58763e+307 ebd0(x=1e+307, M=1.37153e+303): M/x = (r=0.561779104644075) * 2^(e=-12); i=16, f=1820, fg=f*2^-(e+10)=7280 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 8.89289e+307); yl+yh= 8.89289e+307 j=2: ( 0, 8.89289e+307); ( 0, 8.89289e+307); yl+yh= 8.89289e+307 j=3: ( 0, 8.89289e+307); ( 0, 8.89289e+307); yl+yh= 8.89289e+307 j=4: ( 0, 8.89289e+307); ( 0, 8.89289e+307); yl+yh= 8.89289e+307 3. after ADD1(M): yl,yh = ( 0, 8.89302e+307); yl+yh= 8.89302e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 7.89455e+307); yl+yh= 7.89455e+307 ebd0(x=1e+307, M=2.74306e+303): M/x = (r=0.561779104644075) * 2^(e=-11); i=16, f=1820, fg=f*2^-(e+10)=3640 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 8.19974e+307); yl+yh= 8.19974e+307 j=2: ( 0, 8.19974e+307); ( 0, 8.19974e+307); yl+yh= 8.19974e+307 j=3: ( 0, 8.19974e+307); ( 0, 8.19974e+307); yl+yh= 8.19974e+307 j=4: ( 0, 8.19974e+307); ( 0, 8.19974e+307); yl+yh= 8.19974e+307 3. after ADD1(M): yl,yh = ( 0, 8.20001e+307); yl+yh= 8.20001e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 7.20154e+307); yl+yh= 7.20154e+307 ebd0(x=1e+307, M=5.48612e+303): M/x = (r=0.561779104644075) * 2^(e=-10); i=16, f=1820, fg=f*2^-(e+10)=1820 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 7.50659e+307); yl+yh= 7.50659e+307 j=2: ( 0, 7.50659e+307); ( 0, 7.50659e+307); yl+yh= 7.50659e+307 j=3: ( 0, 7.50659e+307); ( 0, 7.50659e+307); yl+yh= 7.50659e+307 j=4: ( 0, 7.50659e+307); ( 0, 7.50659e+307); yl+yh= 7.50659e+307 3. after ADD1(M): yl,yh = ( 0, 7.50714e+307); yl+yh= 7.50714e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 6.50867e+307); yl+yh= 6.50867e+307 ebd0(x=1e+307, M=1.09722e+304): M/x = (r=0.561779104644075) * 2^(e=-9); i=16, f=1820, fg=f*2^-(e+10)=910 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 6.81345e+307); yl+yh= 6.81345e+307 j=2: ( 0, 6.81345e+307); ( 0, 6.81345e+307); yl+yh= 6.81345e+307 j=3: ( 0, 6.81345e+307); ( 0, 6.81345e+307); yl+yh= 6.81345e+307 j=4: ( 0, 6.81345e+307); ( 0, 6.81345e+307); yl+yh= 6.81345e+307 3. after ADD1(M): yl,yh = ( 0, 6.81454e+307); yl+yh= 6.81454e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 5.81607e+307); yl+yh= 5.81607e+307 ebd0(x=1e+307, M=2.19445e+304): M/x = (r=0.561779104644075) * 2^(e=-8); i=16, f=1820, fg=f*2^-(e+10)=455 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 6.1203e+307); yl+yh= 6.1203e+307 j=2: ( 0, 6.1203e+307); ( 0, 6.1203e+307); yl+yh= 6.1203e+307 j=3: ( 0, 6.1203e+307); ( 0, 6.1203e+307); yl+yh= 6.1203e+307 j=4: ( 0, 6.1203e+307); ( 0, 6.1203e+307); yl+yh= 6.1203e+307 3. after ADD1(M): yl,yh = ( 0, 6.12249e+307); yl+yh= 6.12249e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 5.12402e+307); yl+yh= 5.12402e+307 ebd0(x=1e+307, M=4.3889e+304): M/x = (r=0.561779104644075) * 2^(e=-7); i=16, f=1820, fg=f*2^-(e+10)=227.5 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 5.42715e+307); yl+yh= 5.42715e+307 j=2: ( 0, 5.42715e+307); ( 0, 5.42715e+307); yl+yh= 5.42715e+307 j=3: ( 0, 5.42715e+307); ( 0, 5.42715e+307); yl+yh= 5.42715e+307 j=4: ( 0, 5.42715e+307); ( 0, 5.42715e+307); yl+yh= 5.42715e+307 3. after ADD1(M): yl,yh = ( 0, 5.43154e+307); yl+yh= 5.43154e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 4.43307e+307); yl+yh= 4.43307e+307 ebd0(x=1e+307, M=8.7778e+304): M/x = (r=0.561779104644075) * 2^(e=-6); i=16, f=1820, fg=f*2^-(e+10)=113.75 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 4.734e+307); yl+yh= 4.734e+307 j=2: ( 0, 4.734e+307); ( 0, 4.734e+307); yl+yh= 4.734e+307 j=3: ( 0, 4.734e+307); ( 0, 4.734e+307); yl+yh= 4.734e+307 j=4: ( 0, 4.734e+307); ( 0, 4.734e+307); yl+yh= 4.734e+307 3. after ADD1(M): yl,yh = ( 0, 4.74278e+307); yl+yh= 4.74278e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 3.74431e+307); yl+yh= 3.74431e+307 ebd0(x=1e+307, M=1.75556e+305): M/x = (r=0.561779104644075) * 2^(e=-5); i=16, f=1820, fg=f*2^-(e+10)=56.875 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 4.04086e+307); yl+yh= 4.04086e+307 j=2: ( 0, 4.04086e+307); ( 0, 4.04086e+307); yl+yh= 4.04086e+307 j=3: ( 0, 4.04086e+307); ( 0, 4.04086e+307); yl+yh= 4.04086e+307 j=4: ( 0, 4.04086e+307); ( 0, 4.04086e+307); yl+yh= 4.04086e+307 3. after ADD1(M): yl,yh = ( 0, 4.05841e+307); yl+yh= 4.05841e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 3.05994e+307); yl+yh= 3.05994e+307 ebd0(x=1e+307, M=3.51112e+305): M/x = (r=0.561779104644075) * 2^(e=-4); i=16, f=1820, fg=f*2^-(e+10)=28.4375 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 3.34771e+307); yl+yh= 3.34771e+307 j=2: ( 0, 3.34771e+307); ( 0, 3.34771e+307); yl+yh= 3.34771e+307 j=3: ( 0, 3.34771e+307); ( 0, 3.34771e+307); yl+yh= 3.34771e+307 j=4: ( 0, 3.34771e+307); ( 0, 3.34771e+307); yl+yh= 3.34771e+307 3. after ADD1(M): yl,yh = ( 0, 3.38282e+307); yl+yh= 3.38282e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 2.38435e+307); yl+yh= 2.38435e+307 ebd0(x=1e+307, M=7.02224e+305): M/x = (r=0.561779104644075) * 2^(e=-3); i=16, f=1820, fg=f*2^-(e+10)=14.2188 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 2.65456e+307); yl+yh= 2.65456e+307 j=2: ( 0, 2.65456e+307); ( 0, 2.65456e+307); yl+yh= 2.65456e+307 j=3: ( 0, 2.65456e+307); ( 0, 2.65456e+307); yl+yh= 2.65456e+307 j=4: ( 0, 2.65456e+307); ( 0, 2.65456e+307); yl+yh= 2.65456e+307 3. after ADD1(M): yl,yh = ( 0, 2.72479e+307); yl+yh= 2.72479e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 1.72631e+307); yl+yh= 1.72631e+307 ebd0(x=1e+307, M=1.40445e+306): M/x = (r=0.561779104644075) * 2^(e=-2); i=16, f=1820, fg=f*2^-(e+10)=7.10938 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 1.96142e+307); yl+yh= 1.96142e+307 j=2: ( 0, 1.96142e+307); ( 0, 1.96142e+307); yl+yh= 1.96142e+307 j=3: ( 0, 1.96142e+307); ( 0, 1.96142e+307); yl+yh= 1.96142e+307 j=4: ( 0, 1.96142e+307); ( 0, 1.96142e+307); yl+yh= 1.96142e+307 3. after ADD1(M): yl,yh = ( 0, 2.10186e+307); yl+yh= 2.10186e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 1.10339e+307); yl+yh= 1.10339e+307 ebd0(x=1e+307, M=2.8089e+306): M/x = (r=0.561779104644075) * 2^(e=-1); i=16, f=1820, fg=f*2^-(e+10)=3.55469 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 1.26827e+307); yl+yh= 1.26827e+307 j=2: ( 0, 1.26827e+307); ( 0, 1.26827e+307); yl+yh= 1.26827e+307 j=3: ( 0, 1.26827e+307); ( 0, 1.26827e+307); yl+yh= 1.26827e+307 j=4: ( 0, 1.26827e+307); ( 0, 1.26827e+307); yl+yh= 1.26827e+307 3. after ADD1(M): yl,yh = ( 0, 1.54916e+307); yl+yh= 1.54916e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 5.50683e+306); yl+yh= 5.50683e+306 ebd0(x=1e+307, M=5.61779e+306): M/x = (r=0.561779104644075) * 2^(e=0); i=16, f=1820, fg=f*2^-(e+10)=1.77734 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 5.75121e+306); yl+yh= 5.75121e+306 j=2: ( 0, 5.75121e+306); ( 0, 5.75121e+306); yl+yh= 5.75121e+306 j=3: ( 0, 5.75121e+306); ( 0, 5.75121e+306); yl+yh= 5.75121e+306 j=4: ( 0, 5.75121e+306); ( 0, 5.75121e+306); yl+yh= 5.75121e+306 3. after ADD1(M): yl,yh = ( 0, 1.1369e+307); yl+yh= 1.1369e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 1.38426e+306); yl+yh= 1.38426e+306 ebd0(x=1e+307, M=1.12356e+307): M/x = (r=0.561779104644075) * 2^(e=1); i=16, f=1820, fg=f*2^-(e+10)=0.888672 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, -1.18026e+306); yl+yh= -1.18026e+306 j=2: ( 0, -1.18026e+306); ( 0, -1.18026e+306); yl+yh= -1.18026e+306 j=3: ( 0, -1.18026e+306); ( 0, -1.18026e+306); yl+yh= -1.18026e+306 j=4: ( 0, -1.18026e+306); ( 0, -1.18026e+306); yl+yh= -1.18026e+306 3. after ADD1(M): yl,yh = ( 0, 1.00553e+307); yl+yh= 1.00553e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 7.05759e+304); yl+yh= 7.05759e+304 ebd0(x=1e+307, M=2.24712e+307): M/x = (r=0.561779104644075) * 2^(e=2); i=16, f=1820, fg=f*2^-(e+10)=0.444336 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, -8.11173e+306); yl+yh= -8.11173e+306 j=2: ( 0, -8.11173e+306); ( 0, -8.11173e+306); yl+yh= -8.11173e+306 j=3: ( 0, -8.11173e+306); ( 0, -8.11173e+306); yl+yh= -8.11173e+306 j=4: ( 0, -8.11173e+306); ( 0, -8.11173e+306); yl+yh= -8.11173e+306 3. after ADD1(M): yl,yh = ( 0, 1.43594e+307); yl+yh= 1.43594e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 4.37469e+306); yl+yh= 4.37469e+306 ebd0(x=1e+307, M=4.49423e+307): M/x = (r=0.561779104644075) * 2^(e=3); i=16, f=1820, fg=f*2^-(e+10)=0.222168 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, -1.50432e+307); yl+yh= -1.50432e+307 j=2: ( 0, -1.50432e+307); ( 0, -1.50432e+307); yl+yh= -1.50432e+307 j=3: ( 0, -1.50432e+307); ( 0, -1.50432e+307); yl+yh= -1.50432e+307 j=4: ( 0, -1.50432e+307); ( 0, -1.50432e+307); yl+yh= -1.50432e+307 3. after ADD1(M): yl,yh = ( 0, 2.98991e+307); yl+yh= 2.98991e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 1.99144e+307); yl+yh= 1.99144e+307 ebd0(x=1e+307, M=8.98847e+307): M/x = (r=0.561779104644075) * 2^(e=4); i=16, f=1820, fg=f*2^-(e+10)=0.111084 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, -2.19747e+307); yl+yh= -2.19747e+307 j=2: ( 0, -2.19747e+307); ( 0, -2.19747e+307); yl+yh= -2.19747e+307 j=3: ( 0, -2.19747e+307); ( 0, -2.19747e+307); yl+yh= -2.19747e+307 j=4: ( 0, -2.19747e+307); ( 0, -2.19747e+307); yl+yh= -2.19747e+307 3. after ADD1(M): yl,yh = ( 0, 6.791e+307); yl+yh= 6.791e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 5.79252e+307); yl+yh= 5.79252e+307 ebd0(x=1e+307, M=1.79769e+308): M/x = (r=0.561779104644075) * 2^(e=5); i=16, f=1820, fg=f*2^-(e+10)=0.055542 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, -2.89061e+307); yl+yh= -2.89061e+307 j=2: ( 0, -2.89061e+307); ( 0, -2.89061e+307); yl+yh= -2.89061e+307 j=3: ( 0, -2.89061e+307); ( 0, -2.89061e+307); yl+yh= -2.89061e+307 j=4: ( 0, -2.89061e+307); ( 0, -2.89061e+307); yl+yh= -2.89061e+307 3. after ADD1(M): yl,yh = ( 0, 1.50863e+308); yl+yh= 1.50863e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.40878e+308); yl+yh= 1.40878e+308 dpq_ebd0(x[1:1], np[1:35], ... ): ebd0(x=1e+307, M=4.18558e+298): M/x = (r=0.561779104644075) * 2^(e=-27); i=16, f=1820, fg=f*2^-(e+10)=2.38551e+08 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( nan, inf); yl+yh= nan non-finite yh --> return((yh=Inf, yl=0)) ebd0(x=1e+307, M=8.37116e+298): M/x = (r=0.561779104644075) * 2^(e=-26); i=16, f=1820, fg=f*2^-(e+10)=1.19276e+08 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( nan, inf); yl+yh= nan non-finite yh --> return((yh=Inf, yl=0)) ebd0(x=1e+307, M=1.67423e+299): M/x = (r=0.561779104644075) * 2^(e=-25); i=16, f=1820, fg=f*2^-(e+10)=5.96378e+07 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 1.79038e+308); yl+yh= 1.79038e+308 j=1: ( 0, 1.79038e+308); ( 0, 1.79038e+308); yl+yh= 1.79038e+308 j=2: ( 0, 1.79038e+308); ( 0, 1.79038e+308); yl+yh= 1.79038e+308 j=3: ( 0, 1.79038e+308); ( 0, 1.79038e+308); yl+yh= 1.79038e+308 3. after ADD1(M): yl,yh = ( 0, 1.79038e+308); yl+yh= 1.79038e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.69053e+308); yl+yh= 1.69053e+308 ebd0(x=1e+307, M=3.34846e+299): M/x = (r=0.561779104644075) * 2^(e=-24); i=16, f=1820, fg=f*2^-(e+10)=2.98189e+07 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 1.72107e+308); yl+yh= 1.72107e+308 j=1: ( 0, 1.72107e+308); ( 0, 1.72107e+308); yl+yh= 1.72107e+308 j=2: ( 0, 1.72107e+308); ( 0, 1.72107e+308); yl+yh= 1.72107e+308 j=3: ( 0, 1.72107e+308); ( 0, 1.72107e+308); yl+yh= 1.72107e+308 3. after ADD1(M): yl,yh = ( 0, 1.72107e+308); yl+yh= 1.72107e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.62122e+308); yl+yh= 1.62122e+308 ebd0(x=1e+307, M=6.69693e+299): M/x = (r=0.561779104644075) * 2^(e=-23); i=16, f=1820, fg=f*2^-(e+10)=1.49094e+07 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 1.65175e+308); yl+yh= 1.65175e+308 j=1: ( 0, 1.65175e+308); ( 0, 1.65175e+308); yl+yh= 1.65175e+308 j=2: ( 0, 1.65175e+308); ( 0, 1.65175e+308); yl+yh= 1.65175e+308 j=3: ( 0, 1.65175e+308); ( 0, 1.65175e+308); yl+yh= 1.65175e+308 3. after ADD1(M): yl,yh = ( 0, 1.65175e+308); yl+yh= 1.65175e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.5519e+308); yl+yh= 1.5519e+308 ebd0(x=1e+307, M=1.33939e+300): M/x = (r=0.561779104644075) * 2^(e=-22); i=16, f=1820, fg=f*2^-(e+10)=7.45472e+06 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 1.58244e+308); yl+yh= 1.58244e+308 j=1: ( 0, 1.58244e+308); ( 0, 1.58244e+308); yl+yh= 1.58244e+308 j=2: ( 0, 1.58244e+308); ( 0, 1.58244e+308); yl+yh= 1.58244e+308 j=3: ( 0, 1.58244e+308); ( 0, 1.58244e+308); yl+yh= 1.58244e+308 3. after ADD1(M): yl,yh = ( 0, 1.58244e+308); yl+yh= 1.58244e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.48259e+308); yl+yh= 1.48259e+308 ebd0(x=1e+307, M=2.67877e+300): M/x = (r=0.561779104644075) * 2^(e=-21); i=16, f=1820, fg=f*2^-(e+10)=3.72736e+06 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 1.51312e+308); yl+yh= 1.51312e+308 j=1: ( 0, 1.51312e+308); ( 0, 1.51312e+308); yl+yh= 1.51312e+308 j=2: ( 0, 1.51312e+308); ( 0, 1.51312e+308); yl+yh= 1.51312e+308 j=3: ( 0, 1.51312e+308); ( 0, 1.51312e+308); yl+yh= 1.51312e+308 3. after ADD1(M): yl,yh = ( 0, 1.51312e+308); yl+yh= 1.51312e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.41327e+308); yl+yh= 1.41327e+308 ebd0(x=1e+307, M=5.35754e+300): M/x = (r=0.561779104644075) * 2^(e=-20); i=16, f=1820, fg=f*2^-(e+10)=1.86368e+06 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 1.44381e+308); yl+yh= 1.44381e+308 j=1: ( 0, 1.44381e+308); ( 0, 1.44381e+308); yl+yh= 1.44381e+308 j=2: ( 0, 1.44381e+308); ( 0, 1.44381e+308); yl+yh= 1.44381e+308 j=3: ( 0, 1.44381e+308); ( 0, 1.44381e+308); yl+yh= 1.44381e+308 3. after ADD1(M): yl,yh = ( 0, 1.44381e+308); yl+yh= 1.44381e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.34396e+308); yl+yh= 1.34396e+308 ebd0(x=1e+307, M=1.07151e+301): M/x = (r=0.561779104644075) * 2^(e=-19); i=16, f=1820, fg=f*2^-(e+10)=931840 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 1.37449e+308); yl+yh= 1.37449e+308 j=1: ( 0, 1.37449e+308); ( 0, 1.37449e+308); yl+yh= 1.37449e+308 j=2: ( 0, 1.37449e+308); ( 0, 1.37449e+308); yl+yh= 1.37449e+308 j=3: ( 0, 1.37449e+308); ( 0, 1.37449e+308); yl+yh= 1.37449e+308 3. after ADD1(M): yl,yh = ( 0, 1.37449e+308); yl+yh= 1.37449e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.27464e+308); yl+yh= 1.27464e+308 ebd0(x=1e+307, M=2.14302e+301): M/x = (r=0.561779104644075) * 2^(e=-18); i=16, f=1820, fg=f*2^-(e+10)=465920 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 1.30518e+308); yl+yh= 1.30518e+308 j=1: ( 0, 1.30518e+308); ( 0, 1.30518e+308); yl+yh= 1.30518e+308 j=2: ( 0, 1.30518e+308); ( 0, 1.30518e+308); yl+yh= 1.30518e+308 j=3: ( 0, 1.30518e+308); ( 0, 1.30518e+308); yl+yh= 1.30518e+308 3. after ADD1(M): yl,yh = ( 0, 1.30518e+308); yl+yh= 1.30518e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.20533e+308); yl+yh= 1.20533e+308 ebd0(x=1e+307, M=4.28603e+301): M/x = (r=0.561779104644075) * 2^(e=-17); i=16, f=1820, fg=f*2^-(e+10)=232960 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 1.23586e+308); yl+yh= 1.23586e+308 j=1: ( 0, 1.23586e+308); ( 0, 1.23586e+308); yl+yh= 1.23586e+308 j=2: ( 0, 1.23586e+308); ( 0, 1.23586e+308); yl+yh= 1.23586e+308 j=3: ( 0, 1.23586e+308); ( 0, 1.23586e+308); yl+yh= 1.23586e+308 3. after ADD1(M): yl,yh = ( 0, 1.23586e+308); yl+yh= 1.23586e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.13602e+308); yl+yh= 1.13602e+308 ebd0(x=1e+307, M=8.57207e+301): M/x = (r=0.561779104644075) * 2^(e=-16); i=16, f=1820, fg=f*2^-(e+10)=116480 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 1.16655e+308); yl+yh= 1.16655e+308 j=1: ( 0, 1.16655e+308); ( 0, 1.16655e+308); yl+yh= 1.16655e+308 j=2: ( 0, 1.16655e+308); ( 0, 1.16655e+308); yl+yh= 1.16655e+308 j=3: ( 0, 1.16655e+308); ( 0, 1.16655e+308); yl+yh= 1.16655e+308 3. after ADD1(M): yl,yh = ( 0, 1.16655e+308); yl+yh= 1.16655e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.0667e+308); yl+yh= 1.0667e+308 ebd0(x=1e+307, M=1.71441e+302): M/x = (r=0.561779104644075) * 2^(e=-15); i=16, f=1820, fg=f*2^-(e+10)=58240 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 1.09723e+308); yl+yh= 1.09723e+308 j=1: ( 0, 1.09723e+308); ( 0, 1.09723e+308); yl+yh= 1.09723e+308 j=2: ( 0, 1.09723e+308); ( 0, 1.09723e+308); yl+yh= 1.09723e+308 j=3: ( 0, 1.09723e+308); ( 0, 1.09723e+308); yl+yh= 1.09723e+308 3. after ADD1(M): yl,yh = ( 0, 1.09723e+308); yl+yh= 1.09723e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 9.97387e+307); yl+yh= 9.97387e+307 ebd0(x=1e+307, M=3.42883e+302): M/x = (r=0.561779104644075) * 2^(e=-14); i=16, f=1820, fg=f*2^-(e+10)=29120 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 1.02792e+308); yl+yh= 1.02792e+308 j=1: ( 0, 1.02792e+308); ( 0, 1.02792e+308); yl+yh= 1.02792e+308 j=2: ( 0, 1.02792e+308); ( 0, 1.02792e+308); yl+yh= 1.02792e+308 j=3: ( 0, 1.02792e+308); ( 0, 1.02792e+308); yl+yh= 1.02792e+308 3. after ADD1(M): yl,yh = ( 0, 1.02792e+308); yl+yh= 1.02792e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 9.28074e+307); yl+yh= 9.28074e+307 ebd0(x=1e+307, M=6.85766e+302): M/x = (r=0.561779104644075) * 2^(e=-13); i=16, f=1820, fg=f*2^-(e+10)=14560 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 9.58603e+307); yl+yh= 9.58603e+307 j=1: ( 0, 9.58603e+307); ( 0, 9.58603e+307); yl+yh= 9.58603e+307 j=2: ( 0, 9.58603e+307); ( 0, 9.58603e+307); yl+yh= 9.58603e+307 j=3: ( 0, 9.58603e+307); ( 0, 9.58603e+307); yl+yh= 9.58603e+307 3. after ADD1(M): yl,yh = ( 0, 9.5861e+307); yl+yh= 9.5861e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 8.58763e+307); yl+yh= 8.58763e+307 ebd0(x=1e+307, M=1.37153e+303): M/x = (r=0.561779104644075) * 2^(e=-12); i=16, f=1820, fg=f*2^-(e+10)=7280 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 8.89289e+307); yl+yh= 8.89289e+307 j=1: ( 0, 8.89289e+307); ( 0, 8.89289e+307); yl+yh= 8.89289e+307 j=2: ( 0, 8.89289e+307); ( 0, 8.89289e+307); yl+yh= 8.89289e+307 j=3: ( 0, 8.89289e+307); ( 0, 8.89289e+307); yl+yh= 8.89289e+307 3. after ADD1(M): yl,yh = ( 0, 8.89302e+307); yl+yh= 8.89302e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 7.89455e+307); yl+yh= 7.89455e+307 ebd0(x=1e+307, M=2.74306e+303): M/x = (r=0.561779104644075) * 2^(e=-11); i=16, f=1820, fg=f*2^-(e+10)=3640 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 8.19974e+307); yl+yh= 8.19974e+307 j=1: ( 0, 8.19974e+307); ( 0, 8.19974e+307); yl+yh= 8.19974e+307 j=2: ( 0, 8.19974e+307); ( 0, 8.19974e+307); yl+yh= 8.19974e+307 j=3: ( 0, 8.19974e+307); ( 0, 8.19974e+307); yl+yh= 8.19974e+307 3. after ADD1(M): yl,yh = ( 0, 8.20001e+307); yl+yh= 8.20001e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 7.20154e+307); yl+yh= 7.20154e+307 ebd0(x=1e+307, M=5.48612e+303): M/x = (r=0.561779104644075) * 2^(e=-10); i=16, f=1820, fg=f*2^-(e+10)=1820 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 7.50659e+307); yl+yh= 7.50659e+307 j=1: ( 0, 7.50659e+307); ( 0, 7.50659e+307); yl+yh= 7.50659e+307 j=2: ( 0, 7.50659e+307); ( 0, 7.50659e+307); yl+yh= 7.50659e+307 j=3: ( 0, 7.50659e+307); ( 0, 7.50659e+307); yl+yh= 7.50659e+307 3. after ADD1(M): yl,yh = ( 0, 7.50714e+307); yl+yh= 7.50714e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 6.50867e+307); yl+yh= 6.50867e+307 ebd0(x=1e+307, M=1.09722e+304): M/x = (r=0.561779104644075) * 2^(e=-9); i=16, f=1820, fg=f*2^-(e+10)=910 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 6.81345e+307); yl+yh= 6.81345e+307 j=1: ( 0, 6.81345e+307); ( 0, 6.81345e+307); yl+yh= 6.81345e+307 j=2: ( 0, 6.81345e+307); ( 0, 6.81345e+307); yl+yh= 6.81345e+307 j=3: ( 0, 6.81345e+307); ( 0, 6.81345e+307); yl+yh= 6.81345e+307 3. after ADD1(M): yl,yh = ( 0, 6.81454e+307); yl+yh= 6.81454e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 5.81607e+307); yl+yh= 5.81607e+307 ebd0(x=1e+307, M=2.19445e+304): M/x = (r=0.561779104644075) * 2^(e=-8); i=16, f=1820, fg=f*2^-(e+10)=455 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 6.1203e+307); yl+yh= 6.1203e+307 j=1: ( 0, 6.1203e+307); ( 0, 6.1203e+307); yl+yh= 6.1203e+307 j=2: ( 0, 6.1203e+307); ( 0, 6.1203e+307); yl+yh= 6.1203e+307 j=3: ( 0, 6.1203e+307); ( 0, 6.1203e+307); yl+yh= 6.1203e+307 3. after ADD1(M): yl,yh = ( 0, 6.12249e+307); yl+yh= 6.12249e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 5.12402e+307); yl+yh= 5.12402e+307 ebd0(x=1e+307, M=4.3889e+304): M/x = (r=0.561779104644075) * 2^(e=-7); i=16, f=1820, fg=f*2^-(e+10)=227.5 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 5.42715e+307); yl+yh= 5.42715e+307 j=1: ( 0, 5.42715e+307); ( 0, 5.42715e+307); yl+yh= 5.42715e+307 j=2: ( 0, 5.42715e+307); ( 0, 5.42715e+307); yl+yh= 5.42715e+307 j=3: ( 0, 5.42715e+307); ( 0, 5.42715e+307); yl+yh= 5.42715e+307 3. after ADD1(M): yl,yh = ( 0, 5.43154e+307); yl+yh= 5.43154e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 4.43307e+307); yl+yh= 4.43307e+307 ebd0(x=1e+307, M=8.7778e+304): M/x = (r=0.561779104644075) * 2^(e=-6); i=16, f=1820, fg=f*2^-(e+10)=113.75 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 4.734e+307); yl+yh= 4.734e+307 j=1: ( 0, 4.734e+307); ( 0, 4.734e+307); yl+yh= 4.734e+307 j=2: ( 0, 4.734e+307); ( 0, 4.734e+307); yl+yh= 4.734e+307 j=3: ( 0, 4.734e+307); ( 0, 4.734e+307); yl+yh= 4.734e+307 3. after ADD1(M): yl,yh = ( 0, 4.74278e+307); yl+yh= 4.74278e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 3.74431e+307); yl+yh= 3.74431e+307 ebd0(x=1e+307, M=1.75556e+305): M/x = (r=0.561779104644075) * 2^(e=-5); i=16, f=1820, fg=f*2^-(e+10)=56.875 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 4.04086e+307); yl+yh= 4.04086e+307 j=1: ( 0, 4.04086e+307); ( 0, 4.04086e+307); yl+yh= 4.04086e+307 j=2: ( 0, 4.04086e+307); ( 0, 4.04086e+307); yl+yh= 4.04086e+307 j=3: ( 0, 4.04086e+307); ( 0, 4.04086e+307); yl+yh= 4.04086e+307 3. after ADD1(M): yl,yh = ( 0, 4.05841e+307); yl+yh= 4.05841e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 3.05994e+307); yl+yh= 3.05994e+307 ebd0(x=1e+307, M=3.51112e+305): M/x = (r=0.561779104644075) * 2^(e=-4); i=16, f=1820, fg=f*2^-(e+10)=28.4375 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 3.34771e+307); yl+yh= 3.34771e+307 j=1: ( 0, 3.34771e+307); ( 0, 3.34771e+307); yl+yh= 3.34771e+307 j=2: ( 0, 3.34771e+307); ( 0, 3.34771e+307); yl+yh= 3.34771e+307 j=3: ( 0, 3.34771e+307); ( 0, 3.34771e+307); yl+yh= 3.34771e+307 3. after ADD1(M): yl,yh = ( 0, 3.38282e+307); yl+yh= 3.38282e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 2.38435e+307); yl+yh= 2.38435e+307 ebd0(x=1e+307, M=7.02224e+305): M/x = (r=0.561779104644075) * 2^(e=-3); i=16, f=1820, fg=f*2^-(e+10)=14.2188 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 2.65456e+307); yl+yh= 2.65456e+307 j=1: ( 0, 2.65456e+307); ( 0, 2.65456e+307); yl+yh= 2.65456e+307 j=2: ( 0, 2.65456e+307); ( 0, 2.65456e+307); yl+yh= 2.65456e+307 j=3: ( 0, 2.65456e+307); ( 0, 2.65456e+307); yl+yh= 2.65456e+307 3. after ADD1(M): yl,yh = ( 0, 2.72479e+307); yl+yh= 2.72479e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 1.72631e+307); yl+yh= 1.72631e+307 ebd0(x=1e+307, M=1.40445e+306): M/x = (r=0.561779104644075) * 2^(e=-2); i=16, f=1820, fg=f*2^-(e+10)=7.10938 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 1.96142e+307); yl+yh= 1.96142e+307 j=1: ( 0, 1.96142e+307); ( 0, 1.96142e+307); yl+yh= 1.96142e+307 j=2: ( 0, 1.96142e+307); ( 0, 1.96142e+307); yl+yh= 1.96142e+307 j=3: ( 0, 1.96142e+307); ( 0, 1.96142e+307); yl+yh= 1.96142e+307 3. after ADD1(M): yl,yh = ( 0, 2.10186e+307); yl+yh= 2.10186e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 1.10339e+307); yl+yh= 1.10339e+307 ebd0(x=1e+307, M=2.8089e+306): M/x = (r=0.561779104644075) * 2^(e=-1); i=16, f=1820, fg=f*2^-(e+10)=3.55469 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 1.26827e+307); yl+yh= 1.26827e+307 j=1: ( 0, 1.26827e+307); ( 0, 1.26827e+307); yl+yh= 1.26827e+307 j=2: ( 0, 1.26827e+307); ( 0, 1.26827e+307); yl+yh= 1.26827e+307 j=3: ( 0, 1.26827e+307); ( 0, 1.26827e+307); yl+yh= 1.26827e+307 3. after ADD1(M): yl,yh = ( 0, 1.54916e+307); yl+yh= 1.54916e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 5.50683e+306); yl+yh= 5.50683e+306 ebd0(x=1e+307, M=5.61779e+306): M/x = (r=0.561779104644075) * 2^(e=0); i=16, f=1820, fg=f*2^-(e+10)=1.77734 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 5.75121e+306); yl+yh= 5.75121e+306 j=1: ( 0, 5.75121e+306); ( 0, 5.75121e+306); yl+yh= 5.75121e+306 j=2: ( 0, 5.75121e+306); ( 0, 5.75121e+306); yl+yh= 5.75121e+306 j=3: ( 0, 5.75121e+306); ( 0, 5.75121e+306); yl+yh= 5.75121e+306 3. after ADD1(M): yl,yh = ( 0, 1.1369e+307); yl+yh= 1.1369e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 1.38426e+306); yl+yh= 1.38426e+306 ebd0(x=1e+307, M=1.12356e+307): M/x = (r=0.561779104644075) * 2^(e=1); i=16, f=1820, fg=f*2^-(e+10)=0.888672 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, -1.18026e+306); yl+yh= -1.18026e+306 j=1: ( 0, -1.18026e+306); ( 0, -1.18026e+306); yl+yh= -1.18026e+306 j=2: ( 0, -1.18026e+306); ( 0, -1.18026e+306); yl+yh= -1.18026e+306 j=3: ( 0, -1.18026e+306); ( 0, -1.18026e+306); yl+yh= -1.18026e+306 3. after ADD1(M): yl,yh = ( 0, 1.00553e+307); yl+yh= 1.00553e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 7.05759e+304); yl+yh= 7.05759e+304 ebd0(x=1e+307, M=2.24712e+307): M/x = (r=0.561779104644075) * 2^(e=2); i=16, f=1820, fg=f*2^-(e+10)=0.444336 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, -8.11173e+306); yl+yh= -8.11173e+306 j=1: ( 0, -8.11173e+306); ( 0, -8.11173e+306); yl+yh= -8.11173e+306 j=2: ( 0, -8.11173e+306); ( 0, -8.11173e+306); yl+yh= -8.11173e+306 j=3: ( 0, -8.11173e+306); ( 0, -8.11173e+306); yl+yh= -8.11173e+306 3. after ADD1(M): yl,yh = ( 0, 1.43594e+307); yl+yh= 1.43594e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 4.37469e+306); yl+yh= 4.37469e+306 ebd0(x=1e+307, M=4.49423e+307): M/x = (r=0.561779104644075) * 2^(e=3); i=16, f=1820, fg=f*2^-(e+10)=0.222168 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, -1.50432e+307); yl+yh= -1.50432e+307 j=1: ( 0, -1.50432e+307); ( 0, -1.50432e+307); yl+yh= -1.50432e+307 j=2: ( 0, -1.50432e+307); ( 0, -1.50432e+307); yl+yh= -1.50432e+307 j=3: ( 0, -1.50432e+307); ( 0, -1.50432e+307); yl+yh= -1.50432e+307 3. after ADD1(M): yl,yh = ( 0, 2.98991e+307); yl+yh= 2.98991e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 1.99144e+307); yl+yh= 1.99144e+307 ebd0(x=1e+307, M=8.98847e+307): M/x = (r=0.561779104644075) * 2^(e=4); i=16, f=1820, fg=f*2^-(e+10)=0.111084 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, -2.19747e+307); yl+yh= -2.19747e+307 j=1: ( 0, -2.19747e+307); ( 0, -2.19747e+307); yl+yh= -2.19747e+307 j=2: ( 0, -2.19747e+307); ( 0, -2.19747e+307); yl+yh= -2.19747e+307 j=3: ( 0, -2.19747e+307); ( 0, -2.19747e+307); yl+yh= -2.19747e+307 3. after ADD1(M): yl,yh = ( 0, 6.791e+307); yl+yh= 6.791e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 5.79252e+307); yl+yh= 5.79252e+307 ebd0(x=1e+307, M=1.79769e+308): M/x = (r=0.561779104644075) * 2^(e=5); i=16, f=1820, fg=f*2^-(e+10)=0.055542 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, -2.89061e+307); yl+yh= -2.89061e+307 j=1: ( 0, -2.89061e+307); ( 0, -2.89061e+307); yl+yh= -2.89061e+307 j=2: ( 0, -2.89061e+307); ( 0, -2.89061e+307); yl+yh= -2.89061e+307 j=3: ( 0, -2.89061e+307); ( 0, -2.89061e+307); yl+yh= -2.89061e+307 3. after ADD1(M): yl,yh = ( 0, 1.50863e+308); yl+yh= 1.50863e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.40878e+308); yl+yh= 1.40878e+308 bd0(1e+307, 1.12356e+307): T.series w/ 125 terms -> bd0=7.05759e+304 > stopifnot( all.equal(bd0v.8, bd0v.10, tol=0), + bd0v.8$aeq0, # even tol=0 equality ! + bd0v.8$aeq4 ) > ## ==> 256 bit gives the *same* (asNumeric() - double-prec accuracy) as 1024 bits ! > rm(bd0v.10) > showProc.time() Time (user system elapsed): 1.08 0 1.16 > > p.relE <- function(bd0v, dFac = if(max(np) >= 8e307) 1e10 else 1, + log = "x", type="b") { + stopifnot(length(x <- bd0v$x) == 1 # for now + , is.numeric(x), is.numeric(np <- bd0v$np), length(np) > 1 + , is.numeric(dFac), dFac > 0, length(dFac) == 1 + , is.matrix(relE <- bd0v$relE) + , (k <- ncol(relE)) >= 1 + , sum(iOk <- local({ y <- bd0v$bd0; is.finite(y) & y != 0 })) > 1 + ) + ## */dFac : otherwise triggering axis() error + ## log - axis(), 'at' creation, _LARGE_ range: invalid {xy}axp or par; nint=5 + ## axp[0:1]=(1e+299,1e+308), usr[0:1]=(7.28752e+298,inf); i=9, ni=1 + pc <- 1:k + matplot(np[iOk]/dFac, relE[iOk,], type=type, log=log, pch=pc, col=1+pc, + main = "relative Errors WRT bd0()", + xlim = range(np)/dFac, # show full range + xlab = paste0("np[iOk]", if(dFac != 1) sprintf("/ dFac, dFac=%g",dFac)), + ## could use sfsmisc::pretty10exp(1e10, drop.1=TRUE) + xaxt="n"); sfsmisc::eaxis(1, sub10=3) + mtext(sprintf("bd0(x, np), x = %g", x)) + if(k >= 2) legend("top", colnames(relE), pch=pc, lty=1:2, col=1+pc, bty="n") + rug(np[!iOk]/dFac, col=2) + axis(1, at=x/dFac, quote(x), col=2, col.axis=2, lwd=2, line=-1) + } > > p.relE(bd0v.8) > > ## ==> FIXME: a whole small (extreme) range where bd0() is *better* than ebd0() !!! > with(bd0v.8, cbind(log2.lam = log2(np), np, relE)) ## around 2^[1018, 1021] log2.lam np ebd0 ebd0C bd0 [1,] 990 1.04639512e+298 Inf Inf Inf [2,] 991 2.09279025e+298 Inf Inf Inf [3,] 992 4.18558050e+298 Inf Inf Inf [4,] 993 8.37116099e+298 Inf Inf Inf [5,] 994 1.67423220e+299 6.86757892e-17 6.86757892e-17 6.86757892e-17 [6,] 995 3.34846440e+299 -2.35238299e-17 -2.35238299e-17 -2.35238299e-17 [7,] 996 6.69692879e+299 4.64722904e-18 4.64722904e-18 1.33253210e-16 [8,] 997 1.33938576e+300 3.54540244e-17 3.54540244e-17 3.54540244e-17 [9,] 998 2.67877152e+300 6.92860492e-17 6.92860492e-17 6.92860492e-17 [10,] 999 5.35754304e+300 -4.18896305e-17 -4.18896305e-17 1.06614915e-16 [11,] 1000 1.07150861e+301 -8.56162226e-18 -8.56162226e-18 1.48018542e-16 [12,] 1001 2.14301721e+301 -1.36953500e-16 -1.36953500e-16 2.86310828e-17 [13,] 1002 4.28603443e+301 -1.05258460e-16 -1.05258460e-16 7.04293432e-17 [14,] 1003 8.57206886e+301 -6.93018205e-17 -6.93018205e-17 1.17802186e-16 [15,] 1004 1.71441377e+302 -2.80427243e-17 -2.80427243e-17 -2.80427243e-17 [16,] 1005 3.42882754e+302 2.00343436e-17 2.00343436e-17 2.00343436e-17 [17,] 1006 6.85765509e+302 -1.55120807e-16 -1.55120807e-16 7.72879792e-17 [18,] 1007 1.37153102e+303 2.12684439e-17 2.12684439e-17 2.12684439e-17 [19,] 1008 2.74306203e+303 9.97903931e-17 9.97903931e-17 9.97903931e-17 [20,] 1009 5.48612407e+303 5.66528379e-17 5.66528379e-17 5.66528379e-17 [21,] 1010 1.09722481e+304 -1.34894374e-16 -1.34894374e-16 3.66854779e-17 [22,] 1011 2.19444963e+304 -1.07502043e-16 -1.07502043e-16 -1.07502043e-16 [23,] 1012 4.38889926e+304 -8.55542215e-18 -8.55542215e-18 -8.55542215e-18 [24,] 1013 8.77779851e+304 -1.23783849e-16 -1.23783849e-16 1.42732769e-16 [25,] 1014 1.75555970e+305 -8.86259493e-17 -8.86259493e-17 7.44362002e-17 [26,] 1015 3.51111940e+305 -1.42625857e-16 -1.42625857e-16 6.66390640e-17 [27,] 1016 7.02223881e+305 -2.50440324e-16 -2.50440324e-16 3.85923155e-17 [28,] 1017 1.40444776e+306 -1.78689561e-16 -1.78689561e-16 4.74145469e-17 [29,] 1018 2.80889552e+306 5.78691591e-16 5.78691591e-16 5.78691591e-16 [30,] 1019 5.61779105e+306 1.07238048e-15 1.07238048e-15 -7.29886761e-16 [31,] 1020 1.12355821e+307 1.45877315e-14 1.45877315e-14 -1.87127858e-16 [32,] 1021 2.24711642e+307 1.31354332e-16 1.31354332e-16 1.31354332e-16 [33,] 1022 4.49423284e+307 1.93926546e-16 1.93926546e-16 -5.66261269e-17 [34,] 1023 8.98846567e+307 5.88175211e-17 5.88175211e-17 5.88175211e-17 [35,] 1024 1.79769313e+308 5.63728043e-17 5.63728043e-17 -3.68640546e-16 > > > with(bd0v.8, stopifnot(exprs = { + yhl["yl",] == 0 # which is not really good and should maybe change ! + ## Fixed now : both have 4 x Inf and then are equal {but do Note relE difference above!} + all.equal(ebd0["yh",], bd0, tol = 4 * .Machine$double.eps) + })) Error in eval(substitute(expr), data, enclos = parent.frame()) : ebd0["yh", ] and bd0 are not equal: Mean absolute difference: 1.44431286e+292 Calls: with ... eval -> eval -> stopifnot -> eval -> eval -> stopifnot Execution halted ** running tests for arch 'x64' ... [290s] ERROR Running 'chisq-nonc-ex.R' [44s] Running 'dnbinom-tst.R' [32s] Running 'dnchisq-tst.R' [1s] Running 'hyper-dist-ex.R' [44s] Running 'pnbeta-tst.R' [0s] Running 'pnt-prec.R' [34s] Running 'ppois-ex.R' [2s] Running 'qPoisBinom-ex.R' [0s] Running 'qbeta-dist.R' [15s] Running 'qbeta-tst.R' [1s] Running 'qgamma-ex.R' [20s] Running 'stirlerr-tst.R' [79s] Running 't-nonc-tst.R' [8s] Running 'wienergerm-pchisq-tst.R' [0s] Running 'wienergerm_nchisq.R' [9s] Running the tests in 'tests/stirlerr-tst.R' failed. Complete output: > #### Testing stirlerr(), bd0(), ebd0(), dpois_raw(), ... > #### =============================================== > > require(DPQ) Loading required package: DPQ > for(pkg in c("Rmpfr", "DPQmpfr")) + if(!requireNamespace(pkg)) { + cat("no CRAN package", sQuote(pkg), " ---> no tests here.\n") + q("no") + } Loading required namespace: Rmpfr Loading required namespace: DPQmpfr > require("Rmpfr") Loading required package: Rmpfr Loading required package: gmp Attaching package: 'gmp' The following objects are masked from 'package:base': %*%, apply, crossprod, matrix, tcrossprod C code of R package 'Rmpfr': GMP using 64 bits per limb Attaching package: 'Rmpfr' The following object is masked from 'package:gmp': outer The following object is masked from 'package:DPQ': log1mexp The following objects are masked from 'package:stats': dbinom, dgamma, dnbinom, dnorm, dpois, dt, pnorm The following objects are masked from 'package:base': cbind, pmax, pmin, rbind > > source(system.file(package="Matrix", "test-tools-1.R", mustWork=TRUE)) Loading required package: tools > ## -> showProc.time(), assertError(), relErrV(), ... > > ##' From ..../sfsmisc/R/relErr.R --- version that *keeps* matrix > ## Componentwise aka "Vectorized" relative error: > ## Must not be NA/NaN unless one of the components is ==> deal with {0, Inf, NA} > relErrV <- function(target, current, eps0 = .Machine$double.xmin) { + n <- length(target <- as.vector(target)) + ## assert( is multiple of ) : + lc <- length(current) + if(!n) { + if(!lc) return(numeric()) # everything length 0 + else stop("length(target) == 0 differing from length(current)") + } else if(!lc) + stop("length(current) == 0 differing from length(target)") + ## else n, lc > 0 + if(lc %% n) + stop("length(current) must be a multiple of length(target)") + recycle <- (lc != n) # explicitly recycle + R <- if(recycle) + target[rep(seq_len(n), length.out=lc)] + else + target # (possibly "mpfr") + R[] <- 0 + ## use *absolute* error when target is zero {and deal with NAs}: + t0 <- abs(target) < eps0 & !(na.t <- is.na(target)) + R[t0] <- current[t0] + ## absolute error also when it is infinite, as (-Inf, Inf) would give NaN: + dInf <- is.infinite(E <- current - target) + R[dInf] <- E[dInf] + useRE <- !dInf & !t0 & (na.t | is.na(current) | (current != target)) + R[useRE] <- (current/target)[useRE] - 1 + if(recycle) { # should also work when target is mpfrArray + if(!is.null(d <- dim(current))) + array(R, dim=d, dimnames=dimnames(current)) + else if(!is.null(nm <- names(current)) && is.null(names(R))) # not needed for mpfr + `names<-`(R, nm) + else R + } else R + } > showProc.time() Time (user system elapsed): 1.64 0.09 1.73 > > cutoffs <- c(15,35,80,500) # cut points, n=*, in the above "algorithm" > ## > n <- c(seq(1,15, by=1/4),seq(16, 25, by=1/2), 26:30, seq(32,50, by=2), seq(55,1000, by=5), + 20*c(51:99), 50*(40:80), 150*(27:48), 500*(15:20)) > st.n <- stirlerr(n)# rather use.halves=TRUE, just here , use.halves=FALSE) > plot(st.n ~ n, log="xy", type="b") ## looks good now > nM <- mpfr(n, 2048) > st.nM <- stirlerr(nM, use.halves=FALSE) ## << on purpose > all.equal(asNumeric(st.nM), st.n)# TRUE [1] TRUE > all.equal(st.nM, as(st.n,"mpfr"))# .. difference: 1.05884..............................e-15 [1] "Mean relative difference: 3.76188328836862237848210671840523134669652278507109803395524851619517133525710813038949864253324335258957995946422636705795318842095018082968414294689177210904242078505467469226107840508716759595731520562809445423582080845132783078190770966884357013373423963183831420177657134945428163130092904941631651286987113921371270172713541623773629860605382909440081832156833672439163785232423191743273755440650299060121762088567869522015326743026183287161491630854095774843808440633833644546114257377272716830527815818340327554735024334315571779348383752605170522238377026508187338666733574758200859673498905046382318912316786e-14" > all.equal(roundMpfr(st.nM, 64), as(st.n,"mpfr"), tol=1e-16)# diff.: 1.05884...e-15 [1] "Mean relative difference: 3.761883442465859304959816110162294641769e-14" > > > ## Very revealing plot showing the *relative* approximation error of stirlerr() > > p.stirlerrDev <- function(n, precBits=2048, stnM = stirlerr(mpfr(n, precBits)), abs=FALSE, + ## cut points, n=*, in the stirlerr() algorithm : + cutoffs = c(15,35,80,500), + type = "b", cex = 1, + col = adjustcolor(1, 3/4), colnB = adjustcolor("orange4", 1/3), + log = if(abs) "xy" else "x", + xlim=NULL, ylim = if(abs) c(8e-18, max(abs(N(relE))))) + { + op <- par(las = 1, mgp=c(2, 0.6, 0)) + on.exit(par(op)) + st <- stirlerr(n, cutoffs=cutoffs) + relE <- sfsmisc::relErrV(stnM, st) + N <- asNumeric + form <- if(abs) abs(N(relE)) ~ n else N(relE) ~ n + plot(form, log=log, type=type, cex=cex, col=col, xlim=xlim, ylim=ylim, + ylab = quote(relErrV(stM, st)), axes=FALSE, frame=TRUE, + main = sprintf("stirlerr(n, cutoffs) rel.error [wrt stirlerr(Rmpfr::mpfr(n, %d))]", + precBits)) + sfsmisc::eaxis(1, sub10=3) + sfsmisc::eaxis(2) + mtext(paste("cutoffs =", deparse(cutoffs))) + ylog <- par("ylog") + if(ylog) { + epsC <- c(1,2,4,8)*2^-52 + epsCxp <- expression(epsilon[C],2*epsilon[C], 4*epsilon[C], 8*epsilon[C]) + } else { + epsC <- (-2:2)*2^-52 + epsCxp <- expression(-2*epsilon[C],-epsilon[C], 0, +epsilon[C], +2*epsilon[C]) + } + dy <- diff(par("usr")[3:4]) + if(diff(range(if(ylog) log10(epsC) else epsC)) > dy/50) { + lw <- rep(1/2, 5); lw[if(ylog) 1 else 3] <- 2 + abline( h=epsC, lty=3, lwd=lw) + axis(4, at=epsC, epsCxp, las=2, cex.axis = 3/4, mgp=c(3/4, 1/4, 0), tck=0) + } else ## only x-axis + abline(h=if(ylog) epsC else 0, lty=3, lwd=2) + abline(v = cutoffs, col=colnB) + axis(3, at=cutoffs, col=colnB, col.axis=colnB, + labels = formatC(cutoffs, digits=3, width=1)) + invisible(relE) + } > > do.pdf <- TRUE > do.pdf <- !dev.interactive(orNone = TRUE) > do.pdf [1] TRUE > if(do.pdf) + pdf("stirlerr-relErr_0.pdf", width=8, height=6) > > showProc.time() Time (user system elapsed): 3.79 0.02 3.82 > > p.stirlerrDev(n=n, stnM=st.nM) # default cutoffs= c(15, 40, 85, 600) > ## show the zoom-in region in next plot > yl2 <- 3e-14*c(-1,1) > abline(h = yl2, col=adjustcolor("tomato", 1/4), lwd=3, lty=2) > > if(do.pdf) { + dev.off() ; pdf("stirlerr-relErr_1.pdf", width=8, height=6) + } > > ## drop small n > p.stirlerrDev(n=n, stnM=st.nM, xlim = c(5, max(n))) # default cutoffs= c(15, 40, 85, 600) > abline(h = yl2, col=adjustcolor("tomato", 1/4), lwd=3, lty=2) > > ## The first plot clearly shows we should do better: > ## Current code is switching to less terms too early, loosing up to 2 decimals precision > p.stirlerrDev(n=n, stnM=st.nM, ylim = yl2) > abline(h = yl2, col=adjustcolor("tomato", 1/4), lwd=3, lty=2) > > if(do.pdf) { + dev.off(); pdf("stirlerr-relErr_6-fin.pdf") + } > > showProc.time() Time (user system elapsed): 0.31 0 0.32 > > ### ~19.April 2021: "This is close to *the* solution" (but ...) > cuts <- c(7, 12, 20, 26, 60, 200, 3300) > st. <- stirlerr(n=n, cutoffs = cuts, verbose=TRUE) stirlerr(n, cutoffs = 7,12,20,26,60,200,3300) : case I (n <= 7), using direct formula for n= num [1:25] 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 3.25 ... case II (n > 7 ), 7 cutoffs: ( 7, 12, 20, 26, 60, 200, 3300 ): n in cutoff intervals: (7,12] (12,20] (20,26] (26,60] (60,200] 20 21 11 16 28 (200,3.3e+03] (3.3e+03,Inf] 236 42 > relE <- asNumeric(sfsmisc::relErrV(st.nM, st.)) > head(cbind(n, relE), 20) n relE [1,] 1.00 8.911677e-16 [2,] 1.25 -1.448799e-15 [3,] 1.50 1.594766e-15 [4,] 1.75 4.066938e-15 [5,] 2.00 -1.439463e-15 [6,] 2.25 3.992641e-15 [7,] 2.50 3.122191e-16 [8,] 2.75 1.178175e-14 [9,] 3.00 -6.421491e-15 [10,] 3.25 -1.844078e-14 [11,] 3.50 -2.035730e-15 [12,] 3.75 -1.035142e-14 [13,] 4.00 1.453032e-14 [14,] 4.25 2.251539e-14 [15,] 4.50 -3.369124e-14 [16,] 4.75 -3.534188e-14 [17,] 5.00 3.069955e-14 [18,] 5.25 -5.701343e-14 [19,] 5.50 6.708174e-15 [20,] 5.75 4.460480e-14 > ## nice printout : > print(cbind(n = format(n, drop0trailing = TRUE), + stirlerr= format(st.,scientific=FALSE, digits=4), + relErr = signif(relE, 4)) + , quote=FALSE) n stirlerr relErr [1,] 1 0.081061467 8.912e-16 [2,] 1.25 0.065431967 -1.449e-15 [3,] 1.5 0.054814121 1.595e-15 [4,] 1.75 0.047140611 4.067e-15 [5,] 2 0.041340696 -1.439e-15 [6,] 2.25 0.036805303 3.993e-15 [7,] 2.5 0.033162874 3.122e-16 [8,] 2.75 0.030174082 1.178e-14 [9,] 3 0.027677926 -6.421e-15 [10,] 3.25 0.025562158 -1.844e-14 [11,] 3.5 0.023746164 -2.036e-15 [12,] 3.75 0.022170565 -1.035e-14 [13,] 4 0.020790672 1.453e-14 [14,] 4.25 0.019572208 2.252e-14 [15,] 4.5 0.018488451 -3.369e-14 [16,] 4.75 0.017518259 -3.534e-14 [17,] 5 0.016644691 3.07e-14 [18,] 5.25 0.015854013 -5.701e-14 [19,] 5.5 0.015134973 6.708e-15 [20,] 5.75 0.014478266 4.46e-14 [21,] 6 0.013876129 -6.719e-15 [22,] 6.25 0.013322037 3.135e-15 [23,] 6.5 0.012810465 -3.891e-15 [24,] 6.75 0.012336703 -5.301e-14 [25,] 7 0.011896710 1.774e-14 [26,] 7.25 0.011487003 -3.257e-14 [27,] 7.5 0.011104560 -1.906e-14 [28,] 7.75 0.010746749 -1.141e-14 [29,] 8 0.010411265 -6.86e-15 [30,] 8.25 0.010096084 -4.267e-15 [31,] 8.5 0.009799416 -2.769e-15 [32,] 8.75 0.009519678 -1.653e-15 [33,] 9 0.009255462 -1.131e-15 [34,] 9.25 0.009005511 -8.71e-16 [35,] 9.5 0.008768700 -5.137e-16 [36,] 9.75 0.008544021 -3.593e-16 [37,] 10 0.008330563 -2.639e-16 [38,] 10.25 0.008127509 -1.544e-16 [39,] 10.5 0.007934115 -2.982e-16 [40,] 10.75 0.007749707 -9.565e-17 [41,] 11 0.007573675 -1.415e-16 [42,] 11.25 0.007405461 -1.027e-16 [43,] 11.5 0.007244554 -2.771e-17 [44,] 11.75 0.007090490 -2.427e-17 [45,] 12 0.006942840 -1.174e-16 [46,] 12.25 0.006801213 2.474e-16 [47,] 12.5 0.006665247 7.289e-17 [48,] 12.75 0.006534610 1.485e-16 [49,] 13 0.006408994 1.166e-17 [50,] 13.25 0.006288116 6.312e-17 [51,] 13.5 0.006171712 -6.452e-18 [52,] 13.75 0.006059539 1.379e-17 [53,] 14 0.005951370 -4.032e-17 [54,] 14.25 0.005846995 -2.056e-17 [55,] 14.5 0.005746217 -3.829e-17 [56,] 14.75 0.005648853 -6.556e-17 [57,] 15 0.005554734 -5.734e-17 [58,] 16 0.005207656 5.537e-19 [59,] 16.5 0.005049887 -4.726e-17 [60,] 17 0.004901396 4.783e-17 [61,] 17.5 0.004761387 -1.976e-16 [62,] 18 0.004629154 -3.698e-17 [63,] 18.5 0.004504066 -7.949e-17 [64,] 19 0.004385560 -2.207e-16 [65,] 19.5 0.004273130 -2.281e-17 [66,] 20 0.004166320 -2.273e-17 [67,] 20.5 0.004064718 -8.882e-17 [68,] 21 0.003967954 -1.583e-16 [69,] 21.5 0.003875690 6.289e-19 [70,] 22 0.003787618 -5.73e-18 [71,] 22.5 0.003703460 -9.793e-17 [72,] 23 0.003622960 -1.029e-16 [73,] 23.5 0.003545885 -2.311e-17 [74,] 24 0.003472021 -4.593e-17 [75,] 24.5 0.003401172 -9.158e-18 [76,] 25 0.003333156 2.703e-17 [77,] 26 0.003204970 -1.109e-16 [78,] 27 0.003086279 -7.897e-17 [79,] 28 0.002976064 -9.417e-18 [80,] 29 0.002873449 -2.472e-17 [81,] 30 0.002777675 3.454e-18 [82,] 32 0.002604082 -4.99e-18 [83,] 34 0.002450910 -5.68e-17 [84,] 36 0.002314755 -2.264e-18 [85,] 38 0.002192932 -3.248e-18 [86,] 40 0.002083290 -2.034e-16 [87,] 42 0.001984089 -7.638e-17 [88,] 44 0.001893907 -1.089e-16 [89,] 46 0.001811566 2.649e-17 [90,] 48 0.001736086 -8.297e-17 [91,] 50 0.001666644 4.193e-17 [92,] 55 0.001515135 -1.209e-16 [93,] 60 0.001388876 -1.322e-16 [94,] 65 0.001282041 -6.821e-17 [95,] 70 0.001190468 -2.89e-17 [96,] 75 0.001111105 -4.77e-17 [97,] 80 0.001041661 -1.163e-16 [98,] 85 0.000980388 -5.347e-17 [99,] 90 0.000925922 -3.745e-17 [100,] 95 0.000877190 -8.095e-17 [101,] 100 0.000833331 -1.496e-17 [102,] 105 0.000793648 -8.561e-17 [103,] 110 0.000757574 -2.762e-17 [104,] 115 0.000724636 6.351e-17 [105,] 120 0.000694443 -6.279e-17 [106,] 125 0.000666665 -4.699e-17 [107,] 130 0.000641024 2.201e-17 [108,] 135 0.000617283 -1.11e-17 [109,] 140 0.000595237 -7.067e-17 [110,] 145 0.000574712 -1.006e-16 [111,] 150 0.000555555 -8.214e-17 [112,] 155 0.000537634 -1.397e-16 [113,] 160 0.000520833 -1.717e-16 [114,] 165 0.000505050 -8.529e-17 [115,] 170 0.000490196 -1.66e-17 [116,] 175 0.000476190 -9.022e-17 [117,] 180 0.000462962 2.137e-17 [118,] 185 0.000450450 -8.115e-17 [119,] 190 0.000438596 -1.624e-17 [120,] 195 0.000427350 8.692e-18 [121,] 200 0.000416666 -6.039e-17 [122,] 205 0.000406504 5.003e-17 [123,] 210 0.000396825 -1.129e-17 [124,] 215 0.000387597 -4.967e-17 [125,] 220 0.000378788 1.949e-17 [126,] 225 0.000370370 -1.198e-16 [127,] 230 0.000362319 5.385e-17 [128,] 235 0.000354610 -1.021e-17 [129,] 240 0.000347222 3.399e-17 [130,] 245 0.000340136 -1.682e-16 [131,] 250 0.000333333 -9.091e-19 [132,] 255 0.000326797 -5.987e-18 [133,] 260 0.000320513 -7.05e-17 [134,] 265 0.000314465 -6.944e-17 [135,] 270 0.000308642 -8.838e-17 [136,] 275 0.000303030 -2.459e-17 [137,] 280 0.000297619 5.586e-18 [138,] 285 0.000292398 -1.002e-16 [139,] 290 0.000287356 -4.698e-17 [140,] 295 0.000282486 3.589e-18 [141,] 300 0.000277778 -8.79e-17 [142,] 305 0.000273224 5.592e-17 [143,] 310 0.000268817 -9.722e-17 [144,] 315 0.000264550 -1.114e-16 [145,] 320 0.000260417 9.132e-17 [146,] 325 0.000256410 -3.948e-17 [147,] 330 0.000252525 -4.325e-17 [148,] 335 0.000248756 -9.059e-17 [149,] 340 0.000245098 -1.621e-16 [150,] 345 0.000241546 1.338e-17 [151,] 350 0.000238095 3.486e-17 [152,] 355 0.000234742 -2.086e-17 [153,] 360 0.000231481 -1.147e-16 [154,] 365 0.000228310 3.977e-17 [155,] 370 0.000225225 -4.736e-17 [156,] 375 0.000222222 -5.641e-17 [157,] 380 0.000219298 -9.447e-17 [158,] 385 0.000216450 -7.211e-17 [159,] 390 0.000213675 -6.235e-18 [160,] 395 0.000210970 4.771e-17 [161,] 400 0.000208333 -1.837e-16 [162,] 405 0.000205761 -9.207e-17 [163,] 410 0.000203252 4.984e-17 [164,] 415 0.000200803 2.075e-17 [165,] 420 0.000198413 -1.513e-16 [166,] 425 0.000196078 -1.915e-16 [167,] 430 0.000193798 -1.057e-16 [168,] 435 0.000191571 -7.294e-17 [169,] 440 0.000189394 -9.068e-17 [170,] 445 0.000187266 -1.479e-17 [171,] 450 0.000185185 -1.037e-16 [172,] 455 0.000183150 -4.903e-17 [173,] 460 0.000181159 -1.496e-19 [174,] 465 0.000179211 -8.755e-17 [175,] 470 0.000177305 -9.812e-17 [176,] 475 0.000175439 1.823e-17 [177,] 480 0.000173611 -1.402e-16 [178,] 485 0.000171821 -1.02e-16 [179,] 490 0.000170068 -1.477e-16 [180,] 495 0.000168350 -8.904e-17 [181,] 500 0.000166667 -1.651e-16 [182,] 505 0.000165016 -2.034e-17 [183,] 510 0.000163399 -2.66e-17 [184,] 515 0.000161812 5.707e-17 [185,] 520 0.000160256 -1.283e-16 [186,] 525 0.000158730 -7.213e-17 [187,] 530 0.000157233 2.542e-17 [188,] 535 0.000155763 9.391e-17 [189,] 540 0.000154321 -1.605e-16 [190,] 545 0.000152905 -1.192e-16 [191,] 550 0.000151515 -3.43e-17 [192,] 555 0.000150150 4.472e-17 [193,] 560 0.000148810 -2.576e-17 [194,] 565 0.000147493 1.196e-16 [195,] 570 0.000146199 1.552e-17 [196,] 575 0.000144928 -2.12e-16 [197,] 580 0.000143678 -1.148e-17 [198,] 585 0.000142450 -1.407e-16 [199,] 590 0.000141243 -8.399e-17 [200,] 595 0.000140056 -5.62e-17 [201,] 600 0.000138889 -9.309e-17 [202,] 605 0.000137741 -1.692e-16 [203,] 610 0.000136612 6.936e-17 [204,] 615 0.000135501 -8.611e-17 [205,] 620 0.000134409 3.987e-17 [206,] 625 0.000133333 -4.148e-17 [207,] 630 0.000132275 -1.1e-16 [208,] 635 0.000131234 -6.594e-17 [209,] 640 0.000130208 -2.265e-17 [210,] 645 0.000129199 2.465e-17 [211,] 650 0.000128205 -5.088e-17 [212,] 655 0.000127226 -5.245e-17 [213,] 660 0.000126263 -1.364e-16 [214,] 665 0.000125313 -1.784e-16 [215,] 670 0.000124378 -4.501e-17 [216,] 675 0.000123457 -3.045e-17 [217,] 680 0.000122549 -7.071e-17 [218,] 685 0.000121654 -8.794e-17 [219,] 690 0.000120773 -9.828e-17 [220,] 695 0.000119904 -7.036e-17 [221,] 700 0.000119048 -1.581e-17 [222,] 705 0.000118203 -3.835e-17 [223,] 710 0.000117371 -5.492e-17 [224,] 715 0.000116550 -2.908e-17 [225,] 720 0.000115741 -3.447e-17 [226,] 725 0.000114943 5.42e-17 [227,] 730 0.000114155 -1.388e-16 [228,] 735 0.000113379 -1.045e-16 [229,] 740 0.000112613 -3.46e-17 [230,] 745 0.000111857 1.05e-17 [231,] 750 0.000111111 -3.025e-17 [232,] 755 0.000110375 -1.144e-16 [233,] 760 0.000109649 -2.414e-17 [234,] 765 0.000108932 -7.09e-17 [235,] 770 0.000108225 -4.449e-17 [236,] 775 0.000107527 -1.123e-16 [237,] 780 0.000106838 -3.249e-18 [238,] 785 0.000106157 2.321e-17 [239,] 790 0.000105485 5.064e-17 [240,] 795 0.000104822 -1.233e-16 [241,] 800 0.000104167 -1.748e-16 [242,] 805 0.000103520 -1.378e-16 [243,] 810 0.000102881 -9.075e-17 [244,] 815 0.000102249 -1.586e-16 [245,] 820 0.000101626 -7.227e-17 [246,] 825 0.000101010 -3.838e-17 [247,] 830 0.000100402 -2.964e-17 [248,] 835 0.000099800 -1.876e-16 [249,] 840 0.000099206 -2.759e-17 [250,] 845 0.000098619 -1.536e-16 [251,] 850 0.000098039 -8.679e-17 [252,] 855 0.000097466 -1.494e-16 [253,] 860 0.000096899 -1.483e-16 [254,] 865 0.000096339 2.876e-17 [255,] 870 0.000095785 -3.176e-17 [256,] 875 0.000095238 2.357e-17 [257,] 880 0.000094697 -1.091e-16 [258,] 885 0.000094162 -5.772e-17 [259,] 890 0.000093633 -1.744e-16 [260,] 895 0.000093110 -1.181e-16 [261,] 900 0.000092593 -1.335e-16 [262,] 905 0.000092081 -5.527e-17 [263,] 910 0.000091575 -1.198e-16 [264,] 915 0.000091075 -1.207e-16 [265,] 920 0.000090580 -5.728e-17 [266,] 925 0.000090090 -4.742e-19 [267,] 930 0.000089606 -5.574e-17 [268,] 935 0.000089127 8.545e-17 [269,] 940 0.000088652 -1.068e-16 [270,] 945 0.000088183 -1.4e-17 [271,] 950 0.000087719 -4.414e-17 [272,] 955 0.000087260 -7.53e-17 [273,] 960 0.000086806 -1.683e-16 [274,] 965 0.000086356 3.832e-17 [275,] 970 0.000085911 -7.401e-17 [276,] 975 0.000085470 -5.156e-17 [277,] 980 0.000085034 -7.189e-17 [278,] 985 0.000084602 -6.9e-17 [279,] 990 0.000084175 -6.533e-17 [280,] 995 0.000083752 -1.062e-16 [281,] 1000 0.000083333 4.47e-17 [282,] 1020 0.000081699 -2.043e-16 [283,] 1040 0.000080128 3.465e-17 [284,] 1060 0.000078616 1.744e-17 [285,] 1080 0.000077160 2.023e-19 [286,] 1100 0.000075758 -8.344e-17 [287,] 1120 0.000074405 4.223e-18 [288,] 1140 0.000073099 1.678e-17 [289,] 1160 0.000071839 1.405e-17 [290,] 1180 0.000070621 1.336e-17 [291,] 1200 0.000069444 -3.825e-18 [292,] 1220 0.000068306 -1.316e-16 [293,] 1240 0.000067204 4.497e-17 [294,] 1260 0.000066138 8.852e-17 [295,] 1280 0.000065104 -4.096e-17 [296,] 1300 0.000064103 -1.05e-16 [297,] 1320 0.000063131 -1.565e-17 [298,] 1340 0.000062189 8.636e-17 [299,] 1360 0.000061275 -8.111e-17 [300,] 1380 0.000060386 -4.864e-17 [301,] 1400 0.000059524 -1.377e-16 [302,] 1420 0.000058685 -4.785e-17 [303,] 1440 0.000057870 7.827e-17 [304,] 1460 0.000057078 -3.29e-17 [305,] 1480 0.000056306 -2.93e-17 [306,] 1500 0.000055556 3.087e-17 [307,] 1520 0.000054825 1.479e-17 [308,] 1540 0.000054113 -6.619e-17 [309,] 1560 0.000053419 -6.097e-17 [310,] 1580 0.000052743 -1.745e-16 [311,] 1600 0.000052083 -1.245e-16 [312,] 1620 0.000051440 -3.918e-17 [313,] 1640 0.000050813 -6.98e-17 [314,] 1660 0.000050201 -9.32e-17 [315,] 1680 0.000049603 -6.853e-18 [316,] 1700 0.000049020 -8.787e-17 [317,] 1720 0.000048450 3.516e-17 [318,] 1740 0.000047893 -4.948e-17 [319,] 1760 0.000047348 1.593e-17 [320,] 1780 0.000046816 -6.248e-17 [321,] 1800 0.000046296 5.308e-17 [322,] 1820 0.000045788 -5.345e-17 [323,] 1840 0.000045290 -5.611e-17 [324,] 1860 0.000044803 -1.23e-16 [325,] 1880 0.000044326 -2.026e-17 [326,] 1900 0.000043860 7.87e-17 [327,] 1920 0.000043403 -5.773e-17 [328,] 1940 0.000042955 4.493e-18 [329,] 1960 0.000042517 -4.638e-17 [330,] 1980 0.000042088 -4.982e-17 [331,] 2000 0.000041667 -1.709e-17 [332,] 2050 0.000040650 1.564e-17 [333,] 2100 0.000039683 5.082e-17 [334,] 2150 0.000038760 -5.206e-17 [335,] 2200 0.000037879 3.535e-17 [336,] 2250 0.000037037 -2.37e-17 [337,] 2300 0.000036232 -1.453e-16 [338,] 2350 0.000035461 -1.478e-16 [339,] 2400 0.000034722 7.893e-17 [340,] 2450 0.000034014 1.053e-16 [341,] 2500 0.000033333 -1.249e-16 [342,] 2550 0.000032680 -2.632e-17 [343,] 2600 0.000032051 -3.594e-17 [344,] 2650 0.000031447 -2.662e-17 [345,] 2700 0.000030864 -1.459e-16 [346,] 2750 0.000030303 -1.228e-16 [347,] 2800 0.000029762 2.86e-18 [348,] 2850 0.000029240 1.979e-17 [349,] 2900 0.000028736 -8.976e-18 [350,] 2950 0.000028249 -8.074e-17 [351,] 3000 0.000027778 3.047e-17 [352,] 3050 0.000027322 -8.783e-17 [353,] 3100 0.000026882 -9.946e-17 [354,] 3150 0.000026455 -5.146e-17 [355,] 3200 0.000026042 -3.577e-17 [356,] 3250 0.000025641 -9.052e-17 [357,] 3300 0.000025253 -7.322e-17 [358,] 3350 0.000024876 -1.866e-16 [359,] 3400 0.000024510 -1.21e-17 [360,] 3450 0.000024155 -1.608e-16 [361,] 3500 0.000023810 9.896e-18 [362,] 3550 0.000023474 -1.422e-16 [363,] 3600 0.000023148 -7.342e-17 [364,] 3650 0.000022831 -1.147e-16 [365,] 3700 0.000022523 -1.354e-16 [366,] 3750 0.000022222 -7.032e-17 [367,] 3800 0.000021930 -9.196e-17 [368,] 3850 0.000021645 -1.068e-16 [369,] 3900 0.000021368 -1.001e-16 [370,] 3950 0.000021097 -8.581e-18 [371,] 4000 0.000020833 -8.034e-17 [372,] 4050 0.000020576 -1.234e-16 [373,] 4200 0.000019841 -1.95e-16 [374,] 4350 0.000019157 -1.488e-16 [375,] 4500 0.000018519 -1.747e-16 [376,] 4650 0.000017921 -1.313e-16 [377,] 4800 0.000017361 -7.346e-17 [378,] 4950 0.000016835 -1.846e-16 [379,] 5100 0.000016340 4.508e-18 [380,] 5250 0.000015873 -1.385e-16 [381,] 5400 0.000015432 -9.5e-17 [382,] 5550 0.000015015 -3.488e-17 [383,] 5700 0.000014620 -2.353e-17 [384,] 5850 0.000014245 -3.92e-17 [385,] 6000 0.000013889 -1.174e-16 [386,] 6150 0.000013550 -1.588e-16 [387,] 6300 0.000013228 -2.74e-17 [388,] 6450 0.000012920 -2.363e-17 [389,] 6600 0.000012626 -7.098e-17 [390,] 6750 0.000012346 -8.038e-18 [391,] 6900 0.000012077 -4.655e-17 [392,] 7050 0.000011820 -6.789e-17 [393,] 7200 0.000011574 -4.496e-17 [394,] 7500 0.000011111 -4.884e-17 [395,] 8000 0.000010417 -7.881e-17 [396,] 8500 0.000009804 -9.742e-19 [397,] 9000 0.000009259 -3.391e-18 [398,] 9500 0.000008772 6.364e-17 [399,] 10000 0.000008333 -3.753e-17 > > if(do.pdf) { + dev.off(); pdf("stirlerr-relErr_6-fin-1.pdf") + } > > p.stirlerrDev(n=n, stnM=st.nM, cex=1/4, type="o", cutoffs = cuts) > > if(do.pdf) { dev.off(); pdf("stirlerr-relErr_6-fin-2.pdf") } > > ## zoom in ==> {good for n >= 10} > p.stirlerrDev(n=n, stnM=st.nM, cex=1/4, type="o", ylim = 2e-15*c(-1,1), + cutoffs = cuts)## old default cutoffs = c(15,35, 80, 500) > > if(do.pdf) { dev.off(); pdf("stirlerr-tst_others.pdf") } > > ##-- April 20: we more terms up to S10 in stirlerr() -- more cutoffs > n <- sfsmisc::lseq(1/16, 5000, length=4096) > nM <- mpfr(n, 2048) > st.nM <- stirlerr(nM, use.halves=FALSE) ## << on purpose > > cuts <- c(5.4, 7.5, 8.5, 10.625, 12.125, 20, 26, 60, 200, 3300) > p.stirlerrDev(n=n, stnM=st.nM, cex=1/4, type="o", cutoffs = cuts) > p.stirlerrDev(n=n, stnM=st.nM, cex=1/4, type="o", cutoffs = cuts, abs=TRUE) > ## using exact values sferr_halves[] > lines((0:30)/2, abs(stirlerr((0:30)/2, cutoffs=cuts, verbose=TRUE)/DPQ:::sferr_halves - 1), type="o", col=2,lwd=2) stirlerr(n, cutoffs = 5.4,7.5,8.5,10.62,12.12,20,26,60,200,3300) : case I (n <= 5.4), using direct formula for n= num [1:11] 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 ... case II (n > 5.4 ), 10 cutoffs: ( 5.4, 7.5, 8.5, 10.625, 12.125, 20, 26, 60, 200, 3300 ): n in cutoff intervals: (5.4,7.5] (7.5,8.5] (8.5,10.6] (10.6,12.1] (12.1,20] 5 2 4 3 6 (20,26] (26,60] (60,200] (200,3.3e+03] (3.3e+03,Inf] 0 0 0 0 0 > ## should we e.g., use interpolation spline through sfserr_halves[] for n <= 7.5 > ## -- doing the interpolation on the log(1 - 12*x*stirlerr(x)) vs log2(x) scale -- maybe ? > curve(1-12*x*stirlerr(x, verbose=TRUE), 1/64, 8, log="xy", n=2048) stirlerr(n, scheme = "R3") : case I (n <= 15), using direct formula for n= num [1:2048] 0.0156 0.0157 0.0157 0.0158 0.0158 ... > ## just need "true" values for x = 2^-(6,5,4,3,2) in addition to those we already have at x = 1/2, 1.5, 2, 2.5, ..., 7.5, 8 > > p.stirlerrDev(n=n, stnM=st.nM, cex=1/4, type="o", cutoffs = cuts, ylim=c(-1,1)*4e-14) > p.stirlerrDev(n=n, stnM=st.nM, cex=1/4, type="o", cutoffs = cuts, ylim=c(-1,1)*1e-15) > > st. <- stirlerr(n=n, cutoffs = cuts, verbose=TRUE) stirlerr(n, cutoffs = 5.4,7.5,8.5,10.62,12.12,20,26,60,200,3300) : case I (n <= 5.4), using direct formula for n= num [1:1618] 0.0625 0.0627 0.0628 0.063 0.0632 ... case II (n > 5.4 ), 10 cutoffs: ( 5.4, 7.5, 8.5, 10.625, 12.125, 20, 26, 60, 200, 3300 ): n in cutoff intervals: (5.4,7.5] (7.5,8.5] (8.5,10.6] (10.6,12.1] (12.1,20] 119 45 81 48 182 (20,26] (26,60] (60,200] (200,3.3e+03] (3.3e+03,Inf] 95 303 437 1017 151 > relE <- asNumeric(sfsmisc::relErrV(st.nM, st.)) > head(cbind(n, relE), 20) n relE [1,] 0.06250000 1.145349e-16 [2,] 0.06267255 2.991784e-16 [3,] 0.06284557 -8.156474e-17 [4,] 0.06301908 1.528496e-16 [5,] 0.06319306 9.174643e-17 [6,] 0.06336752 -7.677091e-17 [7,] 0.06354246 5.967122e-17 [8,] 0.06371789 4.722483e-16 [9,] 0.06389380 1.721318e-16 [10,] 0.06407019 3.924397e-16 [11,] 0.06424708 -1.777654e-16 [12,] 0.06442445 5.391117e-16 [13,] 0.06460231 3.499214e-16 [14,] 0.06478066 1.961559e-16 [15,] 0.06495951 -9.756855e-17 [16,] 0.06513885 2.139647e-16 [17,] 0.06531868 1.273413e-16 [18,] 0.06549901 2.265762e-16 [19,] 0.06567984 2.202612e-16 [20,] 0.06586116 2.793055e-16 > ## nice printout : > print(cbind(n = format(n, drop0trailing = TRUE), + stirlerr= format(st.,scientific=FALSE, digits=4), + relErr = signif(asNumeric(sfsmisc::relErrV(st.nM, st.)), 4)) + , quote=FALSE) n stirlerr relErr [1,] 6.250000e-02 0.67018552 1.145e-16 [2,] 6.267255e-02 0.66920260 2.992e-16 [3,] 6.284557e-02 0.66822034 -8.156e-17 [4,] 6.301908e-02 0.66723875 1.528e-16 [5,] 6.319306e-02 0.66625781 9.175e-17 [6,] 6.336752e-02 0.66527753 -7.677e-17 [7,] 6.354246e-02 0.66429792 5.967e-17 [8,] 6.371789e-02 0.66331897 4.722e-16 [9,] 6.389380e-02 0.66234069 1.721e-16 [10,] 6.407019e-02 0.66136307 3.924e-16 [11,] 6.424708e-02 0.66038612 -1.778e-16 [12,] 6.442445e-02 0.65940984 5.391e-16 [13,] 6.460231e-02 0.65843422 3.499e-16 [14,] 6.478066e-02 0.65745927 1.962e-16 [15,] 6.495951e-02 0.65648499 -9.757e-17 [16,] 6.513885e-02 0.65551138 2.14e-16 [17,] 6.531868e-02 0.65453844 1.273e-16 [18,] 6.549901e-02 0.65356617 2.266e-16 [19,] 6.567984e-02 0.65259457 2.203e-16 [20,] 6.586116e-02 0.65162365 2.793e-16 [21,] 6.604299e-02 0.65065339 1.932e-16 [22,] 6.622532e-02 0.64968382 7.097e-16 [23,] 6.640815e-02 0.64871491 -1.901e-17 [24,] 6.659149e-02 0.64774669 -1.838e-16 [25,] 6.677534e-02 0.64677914 -1.391e-16 [26,] 6.695969e-02 0.64581226 -1.213e-16 [27,] 6.714455e-02 0.64484607 2.032e-16 [28,] 6.732992e-02 0.64388055 -1.909e-16 [29,] 6.751580e-02 0.64291571 -2.471e-16 [30,] 6.770220e-02 0.64195156 5.63e-16 [31,] 6.788911e-02 0.64098808 2.884e-16 [32,] 6.807653e-02 0.64002528 3.839e-16 [33,] 6.826448e-02 0.63906317 -1.54e-17 [34,] 6.845294e-02 0.63810174 -1.624e-16 [35,] 6.864192e-02 0.63714099 3.531e-16 [36,] 6.883143e-02 0.63618093 -3.276e-16 [37,] 6.902145e-02 0.63522155 3.731e-16 [38,] 6.921201e-02 0.63426286 1.101e-17 [39,] 6.940309e-02 0.63330486 2.713e-16 [40,] 6.959469e-02 0.63234754 -3.426e-16 [41,] 6.978683e-02 0.63139091 4.905e-16 [42,] 6.997949e-02 0.63043497 4.93e-16 [43,] 7.017269e-02 0.62947972 1.414e-16 [44,] 7.036642e-02 0.62852516 -2.749e-16 [45,] 7.056069e-02 0.62757129 1.261e-16 [46,] 7.075549e-02 0.62661811 1.128e-16 [47,] 7.095083e-02 0.62566562 2.61e-16 [48,] 7.114671e-02 0.62471383 -4.31e-17 [49,] 7.134313e-02 0.62376273 -1.228e-17 [50,] 7.154009e-02 0.62281233 -2.894e-16 [51,] 7.173759e-02 0.62186262 -1.316e-16 [52,] 7.193564e-02 0.62091361 3.339e-16 [53,] 7.213424e-02 0.61996529 -1.485e-16 [54,] 7.233339e-02 0.61901767 -1.836e-16 [55,] 7.253308e-02 0.61807075 2.161e-16 [56,] 7.273333e-02 0.61712453 -2.776e-16 [57,] 7.293413e-02 0.61617901 3.135e-16 [58,] 7.313549e-02 0.61523418 2.281e-16 [59,] 7.333740e-02 0.61429006 5.148e-16 [60,] 7.353986e-02 0.61334664 3.787e-16 [61,] 7.374289e-02 0.61240393 -4.606e-17 [62,] 7.394648e-02 0.61146191 -7.132e-17 [63,] 7.415063e-02 0.61052061 -3.845e-17 [64,] 7.435534e-02 0.60958000 7.328e-17 [65,] 7.456062e-02 0.60864010 -4.679e-17 [66,] 7.476646e-02 0.60770091 2.763e-16 [67,] 7.497288e-02 0.60676242 2.448e-16 [68,] 7.517986e-02 0.60582464 -4.094e-16 [69,] 7.538741e-02 0.60488757 -5.742e-17 [70,] 7.559554e-02 0.60395121 -8.479e-18 [71,] 7.580424e-02 0.60301555 -5.085e-17 [72,] 7.601352e-02 0.60208061 -2.045e-16 [73,] 7.622338e-02 0.60114638 2.466e-16 [74,] 7.643381e-02 0.60021286 1.597e-16 [75,] 7.664483e-02 0.59928005 2.27e-16 [76,] 7.685643e-02 0.59834796 2.224e-16 [77,] 7.706861e-02 0.59741658 2.234e-16 [78,] 7.728138e-02 0.59648591 3.941e-16 [79,] 7.749474e-02 0.59555596 -2.752e-16 [80,] 7.770868e-02 0.59462673 2.58e-16 [81,] 7.792322e-02 0.59369821 -3.991e-16 [82,] 7.813835e-02 0.59277041 -4.779e-17 [83,] 7.835407e-02 0.59184333 2.01e-16 [84,] 7.857039e-02 0.59091696 -1.999e-16 [85,] 7.878730e-02 0.58999132 2.545e-16 [86,] 7.900481e-02 0.58906639 2.109e-16 [87,] 7.922293e-02 0.58814219 2.587e-16 [88,] 7.944165e-02 0.58721871 1.286e-16 [89,] 7.966097e-02 0.58629595 4.991e-17 [90,] 7.988089e-02 0.58537391 5.19e-17 [91,] 8.010142e-02 0.58445260 1.215e-16 [92,] 8.032257e-02 0.58353201 2.674e-16 [93,] 8.054432e-02 0.58261215 4.596e-16 [94,] 8.076668e-02 0.58169301 2.036e-16 [95,] 8.098966e-02 0.58077460 -5.517e-17 [96,] 8.121325e-02 0.57985691 3.031e-16 [97,] 8.143747e-02 0.57893996 2.247e-16 [98,] 8.166230e-02 0.57802373 -1.209e-16 [99,] 8.188775e-02 0.57710823 -3.133e-16 [100,] 8.211382e-02 0.57619346 7.085e-17 [101,] 8.234052e-02 0.57527942 5.045e-16 [102,] 8.256784e-02 0.57436611 4.135e-16 [103,] 8.279579e-02 0.57345354 4.534e-16 [104,] 8.302437e-02 0.57254169 -1.347e-16 [105,] 8.325358e-02 0.57163058 -1.169e-16 [106,] 8.348343e-02 0.57072021 -7.229e-17 [107,] 8.371391e-02 0.56981057 -4.296e-17 [108,] 8.394502e-02 0.56890166 -4.238e-17 [109,] 8.417677e-02 0.56799349 -2.261e-16 [110,] 8.440917e-02 0.56708606 -3.301e-16 [111,] 8.464220e-02 0.56617936 6.372e-17 [112,] 8.487588e-02 0.56527340 -1.561e-16 [113,] 8.511020e-02 0.56436818 7.831e-17 [114,] 8.534517e-02 0.56346370 1.009e-16 [115,] 8.558079e-02 0.56255996 2.427e-16 [116,] 8.581706e-02 0.56165696 4.317e-16 [117,] 8.605398e-02 0.56075470 1.674e-16 [118,] 8.629156e-02 0.55985319 2.699e-16 [119,] 8.652979e-02 0.55895241 1.665e-16 [120,] 8.676868e-02 0.55805238 2.129e-16 [121,] 8.700823e-02 0.55715310 7.248e-17 [122,] 8.724844e-02 0.55625456 -8.757e-17 [123,] 8.748931e-02 0.55535676 3.256e-16 [124,] 8.773085e-02 0.55445971 5.875e-17 [125,] 8.797305e-02 0.55356341 -2.152e-16 [126,] 8.821592e-02 0.55266785 4.052e-16 [127,] 8.845947e-02 0.55177305 3.825e-16 [128,] 8.870368e-02 0.55087899 2.095e-16 [129,] 8.894858e-02 0.54998568 1.539e-16 [130,] 8.919414e-02 0.54909312 3.122e-17 [131,] 8.944039e-02 0.54820131 -1.472e-16 [132,] 8.968731e-02 0.54731025 1.587e-16 [133,] 8.993492e-02 0.54641994 2.053e-16 [134,] 9.018321e-02 0.54553039 -2.944e-17 [135,] 9.043218e-02 0.54464159 2.054e-16 [136,] 9.068184e-02 0.54375355 6.99e-16 [137,] 9.093220e-02 0.54286625 -8.244e-17 [138,] 9.118324e-02 0.54197972 -5.854e-17 [139,] 9.143498e-02 0.54109394 2.166e-16 [140,] 9.168741e-02 0.54020891 4.317e-16 [141,] 9.194053e-02 0.53932465 3.187e-16 [142,] 9.219436e-02 0.53844114 3.107e-16 [143,] 9.244889e-02 0.53755839 -2.692e-16 [144,] 9.270412e-02 0.53667640 2.38e-16 [145,] 9.296005e-02 0.53579517 5.157e-16 [146,] 9.321670e-02 0.53491470 2.769e-16 [147,] 9.347405e-02 0.53403499 -3.111e-16 [148,] 9.373211e-02 0.53315604 1.749e-16 [149,] 9.399088e-02 0.53227785 -1.574e-18 [150,] 9.425037e-02 0.53140043 -4.084e-17 [151,] 9.451057e-02 0.53052377 2.308e-16 [152,] 9.477149e-02 0.52964787 5.167e-16 [153,] 9.503313e-02 0.52877274 4.811e-16 [154,] 9.529550e-02 0.52789838 5.953e-16 [155,] 9.555859e-02 0.52702478 -2.364e-16 [156,] 9.582240e-02 0.52615195 -4.626e-17 [157,] 9.608695e-02 0.52527988 2.243e-16 [158,] 9.635222e-02 0.52440859 4.394e-16 [159,] 9.661823e-02 0.52353806 -1.482e-16 [160,] 9.688497e-02 0.52266830 -6.535e-17 [161,] 9.715245e-02 0.52179931 8.086e-17 [162,] 9.742066e-02 0.52093109 -6.663e-17 [163,] 9.768962e-02 0.52006365 1.22e-17 [164,] 9.795932e-02 0.51919697 2.278e-16 [165,] 9.822976e-02 0.51833107 1.756e-16 [166,] 9.850095e-02 0.51746594 1.17e-16 [167,] 9.877289e-02 0.51660158 -3.462e-16 [168,] 9.904558e-02 0.51573800 -3.34e-19 [169,] 9.931902e-02 0.51487519 -1.887e-16 [170,] 9.959322e-02 0.51401316 3.785e-16 [171,] 9.986817e-02 0.51315190 -1.978e-16 [172,] 1.001439e-01 0.51229142 9.003e-18 [173,] 1.004204e-01 0.51143172 3.844e-17 [174,] 1.006976e-01 0.51057279 5.549e-16 [175,] 1.009756e-01 0.50971465 1.87e-16 [176,] 1.012544e-01 0.50885728 8.696e-17 [177,] 1.015339e-01 0.50800069 -1.527e-17 [178,] 1.018142e-01 0.50714489 2.44e-16 [179,] 1.020953e-01 0.50628986 4.6e-16 [180,] 1.023772e-01 0.50543562 1.701e-16 [181,] 1.026598e-01 0.50458215 -4.438e-17 [182,] 1.029432e-01 0.50372947 -1.238e-16 [183,] 1.032274e-01 0.50287758 -1.12e-16 [184,] 1.035124e-01 0.50202646 3.054e-16 [185,] 1.037982e-01 0.50117613 3.548e-17 [186,] 1.040848e-01 0.50032659 3.856e-16 [187,] 1.043721e-01 0.49947783 -3.677e-16 [188,] 1.046603e-01 0.49862986 2.09e-16 [189,] 1.049492e-01 0.49778268 -7.104e-17 [190,] 1.052389e-01 0.49693628 -1.113e-16 [191,] 1.055295e-01 0.49609067 4.999e-17 [192,] 1.058208e-01 0.49524585 5.613e-17 [193,] 1.061130e-01 0.49440182 1.585e-16 [194,] 1.064059e-01 0.49355858 -8.152e-17 [195,] 1.066997e-01 0.49271612 2.72e-16 [196,] 1.069943e-01 0.49187446 9.096e-17 [197,] 1.072897e-01 0.49103359 5.32e-16 [198,] 1.075859e-01 0.49019352 1.818e-16 [199,] 1.078829e-01 0.48935423 1.09e-16 [200,] 1.081807e-01 0.48851574 4.357e-16 [201,] 1.084794e-01 0.48767804 -2.295e-17 [202,] 1.087789e-01 0.48684114 -5.037e-16 [203,] 1.090792e-01 0.48600503 5.266e-16 [204,] 1.093803e-01 0.48516971 5.865e-17 [205,] 1.096823e-01 0.48433520 3.658e-16 [206,] 1.099851e-01 0.48350148 -1.289e-16 [207,] 1.102887e-01 0.48266855 1.178e-16 [208,] 1.105932e-01 0.48183643 -1.764e-16 [209,] 1.108985e-01 0.48100510 4.886e-16 [210,] 1.112047e-01 0.48017457 -2.404e-16 [211,] 1.115117e-01 0.47934484 3.576e-16 [212,] 1.118196e-01 0.47851591 5.779e-16 [213,] 1.121283e-01 0.47768778 6.892e-16 [214,] 1.124379e-01 0.47686045 -1.894e-16 [215,] 1.127483e-01 0.47603392 7.23e-16 [216,] 1.130595e-01 0.47520820 2.795e-16 [217,] 1.133717e-01 0.47438328 1.907e-16 [218,] 1.136847e-01 0.47355916 -9.933e-17 [219,] 1.139985e-01 0.47273584 3.813e-16 [220,] 1.143132e-01 0.47191333 6.261e-16 [221,] 1.146288e-01 0.47109163 4.288e-16 [222,] 1.149453e-01 0.47027072 3.66e-16 [223,] 1.152626e-01 0.46945063 3.422e-16 [224,] 1.155809e-01 0.46863134 2.525e-16 [225,] 1.158999e-01 0.46781286 2.113e-16 [226,] 1.162199e-01 0.46699518 -3.694e-16 [227,] 1.165408e-01 0.46617832 1.036e-16 [228,] 1.168625e-01 0.46536226 9.654e-17 [229,] 1.171851e-01 0.46454701 6.554e-16 [230,] 1.175087e-01 0.46373257 -2.011e-16 [231,] 1.178331e-01 0.46291894 4.538e-16 [232,] 1.181584e-01 0.46210612 -1.434e-16 [233,] 1.184846e-01 0.46129412 3.875e-16 [234,] 1.188117e-01 0.46048292 1.15e-16 [235,] 1.191397e-01 0.45967254 1.006e-16 [236,] 1.194686e-01 0.45886297 -1.077e-17 [237,] 1.197985e-01 0.45805421 2.434e-16 [238,] 1.201292e-01 0.45724626 3.035e-16 [239,] 1.204609e-01 0.45643913 6.026e-17 [240,] 1.207934e-01 0.45563282 4.367e-16 [241,] 1.211269e-01 0.45482732 3.222e-16 [242,] 1.214613e-01 0.45402263 5.206e-16 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0.12196979 -5.725e-16 [849,] 6.474716e-01 0.12166327 9.603e-16 [850,] 6.492592e-01 0.12135741 1.704e-15 [851,] 6.510516e-01 0.12105222 1.417e-15 [852,] 6.528490e-01 0.12074770 -7.853e-16 [853,] 6.546514e-01 0.12044384 2.015e-15 [854,] 6.564587e-01 0.12014065 9.72e-16 [855,] 6.582711e-01 0.11983812 -3.596e-16 [856,] 6.600884e-01 0.11953625 3.496e-16 [857,] 6.619108e-01 0.11923504 3.423e-16 [858,] 6.637381e-01 0.11893449 -2.594e-16 [859,] 6.655706e-01 0.11863460 1.61e-16 [860,] 6.674081e-01 0.11833537 -8.031e-17 [861,] 6.692506e-01 0.11803680 8.051e-16 [862,] 6.710983e-01 0.11773888 2.753e-16 [863,] 6.729510e-01 0.11744162 1.317e-15 [864,] 6.748089e-01 0.11714502 6.385e-16 [865,] 6.766719e-01 0.11684906 -5.157e-16 [866,] 6.785400e-01 0.11655376 -1.343e-15 [867,] 6.804133e-01 0.11625912 -5.979e-16 [868,] 6.822918e-01 0.11596512 8.118e-17 [869,] 6.841754e-01 0.11567177 -3.39e-16 [870,] 6.860643e-01 0.11537907 -6.429e-16 [871,] 6.879583e-01 0.11508702 5.342e-16 [872,] 6.898576e-01 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8.436552e-01 0.09520595 -1.53e-16 [946,] 8.459843e-01 0.09495975 1.93e-16 [947,] 8.483199e-01 0.09471413 1.525e-16 [948,] 8.506619e-01 0.09446908 3.843e-16 [949,] 8.530104e-01 0.09422460 -1.242e-15 [950,] 8.553654e-01 0.09398069 4.566e-16 [951,] 8.577268e-01 0.09373735 6.964e-16 [952,] 8.600948e-01 0.09349459 1.828e-15 [953,] 8.624694e-01 0.09325239 2.908e-17 [954,] 8.648504e-01 0.09301076 1.052e-16 [955,] 8.672381e-01 0.09276969 1.151e-15 [956,] 8.696323e-01 0.09252919 1.788e-15 [957,] 8.720332e-01 0.09228926 -2.313e-16 [958,] 8.744407e-01 0.09204988 1.27e-15 [959,] 8.768548e-01 0.09181107 1.575e-15 [960,] 8.792756e-01 0.09157283 1.276e-15 [961,] 8.817031e-01 0.09133514 -4.516e-16 [962,] 8.841373e-01 0.09109801 -4.459e-16 [963,] 8.865782e-01 0.09086144 1.391e-15 [964,] 8.890258e-01 0.09062543 8.464e-16 [965,] 8.914802e-01 0.09038997 -1.671e-17 [966,] 8.939414e-01 0.09015508 1.185e-15 [967,] 8.964093e-01 0.08992073 1.511e-15 [968,] 8.988841e-01 0.08968694 1.295e-15 [969,] 9.013657e-01 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1.033e-14 [1436,] 3.266306 0.02543531 1.007e-14 [1437,] 3.275323 0.02536570 -2.071e-14 [1438,] 3.284366 0.02529628 -2.28e-14 [1439,] 3.293433 0.02522704 3.546e-14 [1440,] 3.302526 0.02515799 1.541e-14 [1441,] 3.311643 0.02508913 -4.71e-15 [1442,] 3.320786 0.02502045 7.556e-15 [1443,] 3.329954 0.02495197 3.761e-14 [1444,] 3.339147 0.02488366 -3.022e-14 [1445,] 3.348366 0.02481554 1.302e-16 [1446,] 3.357610 0.02474761 2.837e-14 [1447,] 3.366879 0.02467986 -1.359e-15 [1448,] 3.376174 0.02461229 8.289e-15 [1449,] 3.385495 0.02454491 4.085e-14 [1450,] 3.394842 0.02447770 1.907e-14 [1451,] 3.404214 0.02441069 -1.151e-14 [1452,] 3.413613 0.02434385 -2.512e-14 [1453,] 3.423037 0.02427719 2.098e-14 [1454,] 3.432487 0.02421071 7.161e-15 [1455,] 3.441963 0.02414442 2.726e-16 [1456,] 3.451466 0.02407830 1.797e-14 [1457,] 3.460994 0.02401236 1.308e-14 [1458,] 3.470549 0.02394660 2.285e-14 [1459,] 3.480131 0.02388102 6.119e-15 [1460,] 3.489739 0.02381562 1.185e-14 [1461,] 3.499373 0.02375040 1.861e-14 [1462,] 3.509034 0.02368535 6.512e-15 [1463,] 3.518722 0.02362047 2.206e-15 [1464,] 3.528436 0.02355578 -1.286e-14 [1465,] 3.538177 0.02349126 1.46e-14 [1466,] 3.547945 0.02342691 5.589e-15 [1467,] 3.557740 0.02336274 -1.856e-15 [1468,] 3.567563 0.02329874 -1.84e-14 [1469,] 3.577412 0.02323492 -4.375e-15 [1470,] 3.587288 0.02317127 6.146e-16 [1471,] 3.597192 0.02310779 1.627e-14 [1472,] 3.607123 0.02304448 1.101e-14 [1473,] 3.617081 0.02298135 2.667e-15 [1474,] 3.627067 0.02291839 2.512e-14 [1475,] 3.637081 0.02285560 -2.623e-15 [1476,] 3.647122 0.02279297 1.984e-14 [1477,] 3.657191 0.02273052 1.004e-14 [1478,] 3.667287 0.02266824 1.975e-14 [1479,] 3.677412 0.02260613 2.519e-14 [1480,] 3.687564 0.02254418 1.125e-14 [1481,] 3.697745 0.02248241 1.612e-14 [1482,] 3.707954 0.02242080 1.939e-14 [1483,] 3.718190 0.02235936 6.39e-15 [1484,] 3.728456 0.02229808 -5.704e-15 [1485,] 3.738749 0.02223698 -1.124e-15 [1486,] 3.749071 0.02217604 3.336e-16 [1487,] 3.759421 0.02211526 9.598e-15 [1488,] 3.769800 0.02205465 -5.367e-15 [1489,] 3.780208 0.02199420 2.74e-14 [1490,] 3.790644 0.02193392 -1.146e-14 [1491,] 3.801109 0.02187380 -2.23e-15 [1492,] 3.811603 0.02181385 -3.821e-15 [1493,] 3.822126 0.02175405 3.662e-14 [1494,] 3.832678 0.02169442 5.64e-15 [1495,] 3.843259 0.02163496 3.927e-14 [1496,] 3.853869 0.02157565 -2.651e-15 [1497,] 3.864509 0.02151651 4.793e-15 [1498,] 3.875178 0.02145752 2.738e-14 [1499,] 3.885877 0.02139870 -1.941e-14 [1500,] 3.896605 0.02134003 2.836e-14 [1501,] 3.907362 0.02128153 9.249e-15 [1502,] 3.918150 0.02122318 4.747e-15 [1503,] 3.928967 0.02116500 -6.158e-15 [1504,] 3.939814 0.02110697 -1.438e-14 [1505,] 3.950691 0.02104910 6.346e-15 [1506,] 3.961598 0.02099139 2.29e-14 [1507,] 3.972535 0.02093383 -7.223e-15 [1508,] 3.983502 0.02087643 2.108e-14 [1509,] 3.994499 0.02081919 2.867e-14 [1510,] 4.005527 0.02076210 -4.883e-14 [1511,] 4.016586 0.02070517 -1.666e-14 [1512,] 4.027675 0.02064839 9.445e-15 [1513,] 4.038794 0.02059177 1.831e-14 [1514,] 4.049944 0.02053530 4.412e-15 [1515,] 4.061125 0.02047898 -1.698e-15 [1516,] 4.072337 0.02042282 -1.087e-14 [1517,] 4.083580 0.02036681 1.918e-14 [1518,] 4.094854 0.02031095 1.904e-14 [1519,] 4.106159 0.02025525 -1.039e-14 [1520,] 4.117495 0.02019969 3.497e-14 [1521,] 4.128862 0.02014429 -2.582e-14 [1522,] 4.140261 0.02008904 -1.19e-14 [1523,] 4.151691 0.02003394 1.494e-14 [1524,] 4.163153 0.01997899 1.775e-14 [1525,] 4.174647 0.01992419 -2.469e-14 [1526,] 4.186172 0.01986954 -2.046e-14 [1527,] 4.197729 0.01981503 -2.456e-16 [1528,] 4.209318 0.01976068 2.497e-14 [1529,] 4.220939 0.01970647 5.371e-15 [1530,] 4.232592 0.01965241 4.262e-14 [1531,] 4.244277 0.01959850 -3.061e-14 [1532,] 4.255995 0.01954474 3.803e-14 [1533,] 4.267745 0.01949112 -2.461e-16 [1534,] 4.279527 0.01943765 -4.938e-16 [1535,] 4.291342 0.01938432 -5.43e-15 [1536,] 4.303189 0.01933114 3.69e-14 [1537,] 4.315069 0.01927810 -3.923e-14 [1538,] 4.326982 0.01922521 -8.734e-15 [1539,] 4.338928 0.01917246 1.602e-14 [1540,] 4.350907 0.01911986 -3.715e-14 [1541,] 4.362919 0.01906740 1.897e-14 [1542,] 4.374964 0.01901508 -1.023e-14 [1543,] 4.387042 0.01896291 6.137e-15 [1544,] 4.399153 0.01891087 -2.593e-14 [1545,] 4.411299 0.01885898 -1.777e-14 [1546,] 4.423477 0.01880723 6.362e-15 [1547,] 4.435689 0.01875563 -1.193e-14 [1548,] 4.447935 0.01870416 -1.323e-14 [1549,] 4.460215 0.01865283 -2.371e-14 [1550,] 4.472529 0.01860164 4.416e-14 [1551,] 4.484876 0.01855060 4.305e-14 [1552,] 4.497258 0.01849969 3.001e-14 [1553,] 4.509674 0.01844892 -1.089e-14 [1554,] 4.522124 0.01839829 -3.901e-14 [1555,] 4.534609 0.01834779 5.301e-14 [1556,] 4.547128 0.01829744 -1.24e-14 [1557,] 4.559681 0.01824722 8.416e-15 [1558,] 4.572269 0.01819714 -7.685e-15 [1559,] 4.584892 0.01814719 -3.141e-14 [1560,] 4.597550 0.01809738 3.229e-14 [1561,] 4.610243 0.01804771 8.755e-15 [1562,] 4.622971 0.01799818 3.52e-15 [1563,] 4.635734 0.01794877 1.865e-14 [1564,] 4.648532 0.01789951 1.039e-14 [1565,] 4.661366 0.01785037 -2.598e-15 [1566,] 4.674235 0.01780138 2.082e-14 [1567,] 4.687139 0.01775251 -4.675e-14 [1568,] 4.700079 0.01770378 -4.241e-14 [1569,] 4.713055 0.01765518 4.733e-14 [1570,] 4.726067 0.01760672 -8.142e-15 [1571,] 4.739114 0.01755838 -1.911e-14 [1572,] 4.752198 0.01751018 -2.144e-14 [1573,] 4.765318 0.01746211 -1.522e-14 [1574,] 4.778474 0.01741417 -7.229e-15 [1575,] 4.791666 0.01736636 -2.416e-15 [1576,] 4.804895 0.01731869 -4.541e-14 [1577,] 4.818160 0.01727114 -7.219e-15 [1578,] 4.831462 0.01722372 1.319e-14 [1579,] 4.844800 0.01717643 4.512e-15 [1580,] 4.858176 0.01712927 1.865e-15 [1581,] 4.871588 0.01708224 4.294e-14 [1582,] 4.885037 0.01703534 2.082e-14 [1583,] 4.898524 0.01698857 5.585e-14 [1584,] 4.912047 0.01694192 3.466e-14 [1585,] 4.925608 0.01689541 -1.326e-14 [1586,] 4.939207 0.01684901 3.65e-14 [1587,] 4.952843 0.01680275 -5.954e-14 [1588,] 4.966517 0.01675661 -6.234e-14 [1589,] 4.980228 0.01671060 -3.293e-14 [1590,] 4.993977 0.01666471 -9.287e-15 [1591,] 5.007764 0.01661895 -5.103e-14 [1592,] 5.021590 0.01657331 3.576e-14 [1593,] 5.035453 0.01652780 1.084e-14 [1594,] 5.049355 0.01648242 6.429e-14 [1595,] 5.063295 0.01643715 1.895e-14 [1596,] 5.077274 0.01639201 -1.663e-14 [1597,] 5.091291 0.01634700 -1.755e-14 [1598,] 5.105347 0.01630210 -3.623e-14 [1599,] 5.119441 0.01625733 7.705e-14 [1600,] 5.133575 0.01621269 8.107e-14 [1601,] 5.147748 0.01616816 -5.02e-14 [1602,] 5.161959 0.01612376 -6.217e-14 [1603,] 5.176210 0.01607947 -1.751e-14 [1604,] 5.190501 0.01603531 -1.608e-14 [1605,] 5.204831 0.01599127 -2.249e-14 [1606,] 5.219200 0.01594735 3.152e-14 [1607,] 5.233609 0.01590355 2.939e-14 [1608,] 5.248058 0.01585987 1.076e-14 [1609,] 5.262546 0.01581631 6.705e-14 [1610,] 5.277075 0.01577286 1.029e-14 [1611,] 5.291644 0.01572954 5.312e-14 [1612,] 5.306253 0.01568633 -8.552e-14 [1613,] 5.320902 0.01564325 6.729e-14 [1614,] 5.335592 0.01560028 -1.031e-14 [1615,] 5.350322 0.01555743 -1.604e-14 [1616,] 5.365093 0.01551469 1.058e-13 [1617,] 5.379905 0.01547207 5.09e-14 [1618,] 5.394758 0.01542957 1.946e-14 [1619,] 5.409652 0.01538719 9.621e-14 [1620,] 5.424586 0.01534492 9.065e-14 [1621,] 5.439562 0.01530276 8.538e-14 [1622,] 5.454580 0.01526073 8.059e-14 [1623,] 5.469639 0.01521880 7.582e-14 [1624,] 5.484739 0.01517699 7.153e-14 [1625,] 5.499881 0.01513530 6.751e-14 [1626,] 5.515065 0.01509372 6.365e-14 [1627,] 5.530291 0.01505225 6e-14 [1628,] 5.545559 0.01501090 5.648e-14 [1629,] 5.560869 0.01496966 5.319e-14 [1630,] 5.576221 0.01492853 5.026e-14 [1631,] 5.591616 0.01488752 4.74e-14 [1632,] 5.607053 0.01484662 4.472e-14 [1633,] 5.622533 0.01480583 4.205e-14 [1634,] 5.638055 0.01476515 3.96e-14 [1635,] 5.653621 0.01472458 3.732e-14 [1636,] 5.669229 0.01468412 3.523e-14 [1637,] 5.684881 0.01464378 3.318e-14 [1638,] 5.700575 0.01460354 3.131e-14 [1639,] 5.716313 0.01456342 2.948e-14 [1640,] 5.732095 0.01452340 2.786e-14 [1641,] 5.747920 0.01448350 2.608e-14 [1642,] 5.763788 0.01444370 2.469e-14 [1643,] 5.779701 0.01440401 2.329e-14 [1644,] 5.795657 0.01436443 2.191e-14 [1645,] 5.811658 0.01432496 2.066e-14 [1646,] 5.827702 0.01428560 1.948e-14 [1647,] 5.843791 0.01424634 1.828e-14 [1648,] 5.859925 0.01420720 1.729e-14 [1649,] 5.876103 0.01416816 1.636e-14 [1650,] 5.892325 0.01412922 1.538e-14 [1651,] 5.908593 0.01409040 1.446e-14 [1652,] 5.924905 0.01405167 1.372e-14 [1653,] 5.941262 0.01401306 1.288e-14 [1654,] 5.957665 0.01397455 1.203e-14 [1655,] 5.974112 0.01393615 1.145e-14 [1656,] 5.990605 0.01389785 1.08e-14 [1657,] 6.007144 0.01385966 1.003e-14 [1658,] 6.023729 0.01382157 9.508e-15 [1659,] 6.040359 0.01378358 9.021e-15 [1660,] 6.057035 0.01374570 8.534e-15 [1661,] 6.073757 0.01370793 7.955e-15 [1662,] 6.090525 0.01367025 7.403e-15 [1663,] 6.107340 0.01363268 6.97e-15 [1664,] 6.124201 0.01359522 6.675e-15 [1665,] 6.141108 0.01355785 6.239e-15 [1666,] 6.158062 0.01352059 5.955e-15 [1667,] 6.175063 0.01348343 5.494e-15 [1668,] 6.192111 0.01344637 5.252e-15 [1669,] 6.209206 0.01340941 4.995e-15 [1670,] 6.226348 0.01337256 4.568e-15 [1671,] 6.243538 0.01333580 4.355e-15 [1672,] 6.260775 0.01329915 4.07e-15 [1673,] 6.278060 0.01326259 4.011e-15 [1674,] 6.295392 0.01322614 3.663e-15 [1675,] 6.312772 0.01318979 3.446e-15 [1676,] 6.330200 0.01315353 3.286e-15 [1677,] 6.347676 0.01311738 3.085e-15 [1678,] 6.365201 0.01308132 2.747e-15 [1679,] 6.382774 0.01304537 2.705e-15 [1680,] 6.400395 0.01300951 2.549e-15 [1681,] 6.418065 0.01297375 2.425e-15 [1682,] 6.435784 0.01293809 2.28e-15 [1683,] 6.453552 0.01290252 2.132e-15 [1684,] 6.471368 0.01286705 2.002e-15 [1685,] 6.489234 0.01283168 1.88e-15 [1686,] 6.507150 0.01279641 1.846e-15 [1687,] 6.525114 0.01276124 1.664e-15 [1688,] 6.543129 0.01272616 1.497e-15 [1689,] 6.561193 0.01269117 1.562e-15 [1690,] 6.579307 0.01265628 1.381e-15 [1691,] 6.597471 0.01262149 1.384e-15 [1692,] 6.615685 0.01258680 1.241e-15 [1693,] 6.633949 0.01255219 1.224e-15 [1694,] 6.652264 0.01251769 1.121e-15 [1695,] 6.670629 0.01248328 9.35e-16 [1696,] 6.689046 0.01244896 9.259e-16 [1697,] 6.707512 0.01241473 8.073e-16 [1698,] 6.726030 0.01238060 7.786e-16 [1699,] 6.744599 0.01234657 8.528e-16 [1700,] 6.763220 0.01231262 6.848e-16 [1701,] 6.781891 0.01227877 7.067e-16 [1702,] 6.800615 0.01224502 6.823e-16 [1703,] 6.819390 0.01221135 6.953e-16 [1704,] 6.838216 0.01217778 4.6e-16 [1705,] 6.857095 0.01214430 4.165e-16 [1706,] 6.876026 0.01211091 3.989e-16 [1707,] 6.895009 0.01207761 4.197e-16 [1708,] 6.914045 0.01204441 4.496e-16 [1709,] 6.933133 0.01201129 2.82e-16 [1710,] 6.952274 0.01197827 4.606e-16 [1711,] 6.971467 0.01194533 3.791e-16 [1712,] 6.990714 0.01191249 2.57e-16 [1713,] 7.010014 0.01187974 2.866e-16 [1714,] 7.029367 0.01184708 3.743e-16 [1715,] 7.048773 0.01181450 3.281e-16 [1716,] 7.068233 0.01178202 2.185e-16 [1717,] 7.087747 0.01174962 3.291e-16 [1718,] 7.107315 0.01171732 2.477e-16 [1719,] 7.126936 0.01168510 2.109e-16 [1720,] 7.146612 0.01165297 2.017e-16 [1721,] 7.166342 0.01162093 6.539e-17 [1722,] 7.186127 0.01158897 1.037e-16 [1723,] 7.205966 0.01155711 1.101e-16 [1724,] 7.225860 0.01152533 1.341e-17 [1725,] 7.245809 0.01149364 1.204e-16 [1726,] 7.265813 0.01146203 4.788e-17 [1727,] 7.285872 0.01143052 1.286e-16 [1728,] 7.305987 0.01139909 1.012e-16 [1729,] 7.326157 0.01136774 8.558e-17 [1730,] 7.346383 0.01133648 1.444e-16 [1731,] 7.366665 0.01130531 -1.294e-17 [1732,] 7.387002 0.01127422 8.415e-17 [1733,] 7.407396 0.01124322 5.994e-17 [1734,] 7.427846 0.01121230 3.653e-17 [1735,] 7.448353 0.01118147 1.144e-16 [1736,] 7.468916 0.01115072 8.587e-18 [1737,] 7.489536 0.01112006 1.529e-16 [1738,] 7.510213 0.01108948 -4.146e-16 [1739,] 7.530947 0.01105898 -4.109e-16 [1740,] 7.551738 0.01102857 -4.397e-16 [1741,] 7.572587 0.01099824 -2.923e-16 [1742,] 7.593493 0.01096800 -3.568e-16 [1743,] 7.614457 0.01093783 -3.542e-16 [1744,] 7.635479 0.01090775 -3.314e-16 [1745,] 7.656558 0.01087776 -2.319e-16 [1746,] 7.677696 0.01084784 -1.937e-16 [1747,] 7.698893 0.01081801 -3.779e-16 [1748,] 7.720148 0.01078826 -2.408e-16 [1749,] 7.741461 0.01075859 -3.285e-16 [1750,] 7.762834 0.01072900 -2.45e-16 [1751,] 7.784265 0.01069949 -4.122e-16 [1752,] 7.805756 0.01067007 -1.744e-16 [1753,] 7.827306 0.01064072 -2.245e-16 [1754,] 7.848915 0.01061146 -1.143e-16 [1755,] 7.870584 0.01058228 -1.208e-16 [1756,] 7.892313 0.01055317 -2.098e-16 [1757,] 7.914102 0.01052415 -2.054e-16 [1758,] 7.935951 0.01049520 -1.702e-16 [1759,] 7.957860 0.01046634 -1.869e-16 [1760,] 7.979830 0.01043755 -7.887e-17 [1761,] 8.001861 0.01040885 -1.832e-16 [1762,] 8.023952 0.01038022 -3.025e-16 [1763,] 8.046104 0.01035167 -2.032e-16 [1764,] 8.068318 0.01032320 -7.211e-17 [1765,] 8.090592 0.01029481 -4.149e-17 [1766,] 8.112929 0.01026649 -2.485e-16 [1767,] 8.135327 0.01023825 -3.832e-17 [1768,] 8.157786 0.01021009 -1.914e-16 [1769,] 8.180308 0.01018201 -2.145e-16 [1770,] 8.202892 0.01015401 2.517e-18 [1771,] 8.225538 0.01012608 -7.205e-17 [1772,] 8.248247 0.01009823 -6.848e-17 [1773,] 8.271019 0.01007045 -1.489e-16 [1774,] 8.293853 0.01004275 -2.556e-16 [1775,] 8.316751 0.01001513 -2.442e-16 [1776,] 8.339711 0.00998758 -2.471e-17 [1777,] 8.362735 0.00996011 -2.17e-16 [1778,] 8.385823 0.00993272 -1.558e-16 [1779,] 8.408974 0.00990539 -1.62e-17 [1780,] 8.432189 0.00987815 -1.539e-16 [1781,] 8.455469 0.00985098 -1.104e-16 [1782,] 8.478812 0.00982388 4.677e-17 [1783,] 8.502220 0.00979686 1.204e-16 [1784,] 8.525693 0.00976991 1.811e-16 [1785,] 8.549231 0.00974304 8.497e-17 [1786,] 8.572833 0.00971624 1.501e-16 [1787,] 8.596501 0.00968951 5.23e-17 [1788,] 8.620234 0.00966286 1.735e-16 [1789,] 8.644032 0.00963628 4.978e-17 [1790,] 8.667896 0.00960977 1.398e-17 [1791,] 8.691827 0.00958334 1.379e-16 [1792,] 8.715823 0.00955698 1.98e-16 [1793,] 8.739885 0.00953069 1.847e-16 [1794,] 8.764014 0.00950447 1.555e-16 [1795,] 8.788209 0.00947832 6.017e-17 [1796,] 8.812472 0.00945225 1.039e-16 [1797,] 8.836801 0.00942625 -1.388e-17 [1798,] 8.861197 0.00940032 2.376e-17 [1799,] 8.885661 0.00937446 6.669e-17 [1800,] 8.910192 0.00934867 1.162e-16 [1801,] 8.934791 0.00932296 -1.462e-17 [1802,] 8.959458 0.00929731 5.874e-19 [1803,] 8.984193 0.00927173 -5.881e-17 [1804,] 9.008996 0.00924623 -2.404e-17 [1805,] 9.033868 0.00922079 1.485e-16 [1806,] 9.058809 0.00919543 1.256e-16 [1807,] 9.083818 0.00917013 -3.139e-17 [1808,] 9.108896 0.00914490 8.469e-17 [1809,] 9.134044 0.00911975 -6.71e-19 [1810,] 9.159261 0.00909466 1.242e-17 [1811,] 9.184548 0.00906964 3.433e-18 [1812,] 9.209904 0.00904469 -3.947e-17 [1813,] 9.235330 0.00901980 -4.689e-17 [1814,] 9.260827 0.00899499 1.167e-16 [1815,] 9.286394 0.00897024 5.882e-17 [1816,] 9.312032 0.00894557 1.5e-17 [1817,] 9.337740 0.00892096 -1.168e-16 [1818,] 9.363519 0.00889641 1.749e-17 [1819,] 9.389370 0.00887194 -1.304e-16 [1820,] 9.415292 0.00884753 -3.264e-17 [1821,] 9.441285 0.00882319 -2.846e-17 [1822,] 9.467351 0.00879892 -1.343e-16 [1823,] 9.493488 0.00877471 2.75e-17 [1824,] 9.519697 0.00875057 1.389e-17 [1825,] 9.545979 0.00872650 -9.471e-18 [1826,] 9.572333 0.00870249 -1.314e-17 [1827,] 9.598760 0.00867855 7.487e-17 [1828,] 9.625260 0.00865467 1.187e-17 [1829,] 9.651833 0.00863086 -1.369e-16 [1830,] 9.678480 0.00860711 -3.837e-17 [1831,] 9.705200 0.00858343 -2.653e-17 [1832,] 9.731994 0.00855982 1.415e-16 [1833,] 9.758861 0.00853627 8.007e-17 [1834,] 9.785803 0.00851278 -1.995e-17 [1835,] 9.812820 0.00848936 -8.4e-17 [1836,] 9.839911 0.00846600 -1.04e-17 [1837,] 9.867076 0.00844271 -3.402e-17 [1838,] 9.894317 0.00841948 -1.135e-16 [1839,] 9.921633 0.00839632 -2.318e-17 [1840,] 9.949025 0.00837322 4.748e-17 [1841,] 9.976492 0.00835018 -6.795e-17 [1842,] 1.000403e+01 0.00832721 3.842e-17 [1843,] 1.003165e+01 0.00830430 4.107e-17 [1844,] 1.005935e+01 0.00828145 9.206e-17 [1845,] 1.008712e+01 0.00825866 -1.059e-16 [1846,] 1.011497e+01 0.00823594 -5.163e-17 [1847,] 1.014289e+01 0.00821328 -5.503e-17 [1848,] 1.017090e+01 0.00819068 6.677e-17 [1849,] 1.019897e+01 0.00816814 -1.815e-16 [1850,] 1.022713e+01 0.00814567 7.084e-17 [1851,] 1.025537e+01 0.00812326 -1.878e-17 [1852,] 1.028368e+01 0.00810091 -5.638e-17 [1853,] 1.031207e+01 0.00807862 6.926e-18 [1854,] 1.034054e+01 0.00805639 -9.775e-17 [1855,] 1.036909e+01 0.00803422 -5.051e-17 [1856,] 1.039771e+01 0.00801212 -1.397e-16 [1857,] 1.042642e+01 0.00799007 -1.683e-17 [1858,] 1.045520e+01 0.00796809 8.494e-17 [1859,] 1.048407e+01 0.00794616 -5.612e-17 [1860,] 1.051301e+01 0.00792430 5.178e-17 [1861,] 1.054204e+01 0.00790250 3.639e-17 [1862,] 1.057114e+01 0.00788075 -1.239e-16 [1863,] 1.060033e+01 0.00785907 -5.24e-17 [1864,] 1.062959e+01 0.00783744 -1.61e-16 [1865,] 1.065894e+01 0.00781588 -1.936e-16 [1866,] 1.068836e+01 0.00779437 -1.577e-16 [1867,] 1.071787e+01 0.00777292 2.622e-18 [1868,] 1.074746e+01 0.00775154 -5.205e-17 [1869,] 1.077713e+01 0.00773021 -1.411e-16 [1870,] 1.080689e+01 0.00770894 -1.529e-16 [1871,] 1.083672e+01 0.00768773 -5.368e-17 [1872,] 1.086664e+01 0.00766657 -7.389e-17 [1873,] 1.089664e+01 0.00764548 -1.113e-16 [1874,] 1.092672e+01 0.00762444 -5.381e-17 [1875,] 1.095689e+01 0.00760346 -8.969e-17 [1876,] 1.098714e+01 0.00758254 -4.332e-17 [1877,] 1.101747e+01 0.00756167 -3.428e-17 [1878,] 1.104789e+01 0.00754086 1.961e-17 [1879,] 1.107839e+01 0.00752011 -1.036e-16 [1880,] 1.110897e+01 0.00749942 -6.48e-17 [1881,] 1.113964e+01 0.00747879 -1.48e-16 [1882,] 1.117040e+01 0.00745821 -1.848e-16 [1883,] 1.120124e+01 0.00743768 -4.813e-17 [1884,] 1.123216e+01 0.00741722 -1.039e-16 [1885,] 1.126317e+01 0.00739681 -1.243e-16 [1886,] 1.129426e+01 0.00737645 -1.41e-16 [1887,] 1.132545e+01 0.00735615 -4.483e-17 [1888,] 1.135671e+01 0.00733591 -3.847e-17 [1889,] 1.138807e+01 0.00731573 -1.765e-16 [1890,] 1.141951e+01 0.00729559 -5.919e-17 [1891,] 1.145103e+01 0.00727552 -1.412e-16 [1892,] 1.148265e+01 0.00725550 -1.079e-16 [1893,] 1.151435e+01 0.00723553 -1.41e-16 [1894,] 1.154614e+01 0.00721562 -1.136e-16 [1895,] 1.157801e+01 0.00719577 -1.192e-16 [1896,] 1.160998e+01 0.00717596 4.681e-17 [1897,] 1.164203e+01 0.00715622 -1.651e-16 [1898,] 1.167417e+01 0.00713652 -1.101e-16 [1899,] 1.170640e+01 0.00711689 -8.113e-17 [1900,] 1.173872e+01 0.00709730 -1.512e-16 [1901,] 1.177113e+01 0.00707777 -1.474e-16 [1902,] 1.180362e+01 0.00705829 -9.768e-17 [1903,] 1.183621e+01 0.00703887 -7.933e-17 [1904,] 1.186889e+01 0.00701950 3.457e-17 [1905,] 1.190165e+01 0.00700018 1.787e-17 [1906,] 1.193451e+01 0.00698092 3.691e-17 [1907,] 1.196746e+01 0.00696171 -1.819e-17 [1908,] 1.200050e+01 0.00694255 -1.1e-16 [1909,] 1.203363e+01 0.00692345 2.361e-17 [1910,] 1.206685e+01 0.00690439 4.718e-17 [1911,] 1.210017e+01 0.00688539 -1.019e-16 [1912,] 1.213357e+01 0.00686644 1.179e-16 [1913,] 1.216707e+01 0.00684755 1.086e-16 [1914,] 1.220066e+01 0.00682870 1.867e-16 [1915,] 1.223434e+01 0.00680991 1.018e-16 [1916,] 1.226812e+01 0.00679117 1.738e-16 [1917,] 1.230199e+01 0.00677248 4.797e-17 [1918,] 1.233595e+01 0.00675385 2.418e-17 [1919,] 1.237001e+01 0.00673526 2.535e-17 [1920,] 1.240416e+01 0.00671672 1.171e-16 [1921,] 1.243841e+01 0.00669824 8.973e-17 [1922,] 1.247274e+01 0.00667981 1.108e-16 [1923,] 1.250718e+01 0.00666142 -2.753e-17 [1924,] 1.254171e+01 0.00664309 1.31e-16 [1925,] 1.257633e+01 0.00662481 3.372e-17 [1926,] 1.261105e+01 0.00660658 8.811e-17 [1927,] 1.264587e+01 0.00658840 1.354e-16 [1928,] 1.268078e+01 0.00657026 1.844e-17 [1929,] 1.271579e+01 0.00655218 1.096e-16 [1930,] 1.275090e+01 0.00653415 8.427e-17 [1931,] 1.278610e+01 0.00651617 8.817e-17 [1932,] 1.282140e+01 0.00649824 4.359e-17 [1933,] 1.285680e+01 0.00648035 7.854e-17 [1934,] 1.289229e+01 0.00646252 3.333e-17 [1935,] 1.292788e+01 0.00644473 5.688e-17 [1936,] 1.296357e+01 0.00642700 1.234e-16 [1937,] 1.299936e+01 0.00640931 7.49e-17 [1938,] 1.303525e+01 0.00639167 9.276e-17 [1939,] 1.307124e+01 0.00637408 5.967e-17 [1940,] 1.310733e+01 0.00635654 -1.096e-16 [1941,] 1.314351e+01 0.00633904 -1.116e-17 [1942,] 1.317980e+01 0.00632160 6.359e-17 [1943,] 1.321618e+01 0.00630420 -4.362e-18 [1944,] 1.325267e+01 0.00628685 1.946e-17 [1945,] 1.328926e+01 0.00626955 6.637e-17 [1946,] 1.332595e+01 0.00625229 -5.855e-17 [1947,] 1.336274e+01 0.00623508 5.636e-17 [1948,] 1.339963e+01 0.00621793 -9.854e-17 [1949,] 1.343662e+01 0.00620081 2.668e-17 [1950,] 1.347372e+01 0.00618375 -1.729e-17 [1951,] 1.351092e+01 0.00616673 -3.522e-17 [1952,] 1.354822e+01 0.00614976 -2.041e-17 [1953,] 1.358562e+01 0.00613283 1.176e-17 [1954,] 1.362313e+01 0.00611595 -4.01e-17 [1955,] 1.366074e+01 0.00609912 -8.449e-17 [1956,] 1.369845e+01 0.00608233 6.346e-17 [1957,] 1.373627e+01 0.00606559 1.837e-17 [1958,] 1.377419e+01 0.00604890 -3.592e-17 [1959,] 1.381222e+01 0.00603225 -8.856e-18 [1960,] 1.385035e+01 0.00601565 -6.647e-17 [1961,] 1.388859e+01 0.00599909 3.621e-18 [1962,] 1.392693e+01 0.00598258 -6.722e-17 [1963,] 1.396538e+01 0.00596612 -9.877e-17 [1964,] 1.400394e+01 0.00594970 -2.662e-17 [1965,] 1.404260e+01 0.00593332 2.319e-17 [1966,] 1.408137e+01 0.00591699 -7.307e-17 [1967,] 1.412024e+01 0.00590071 6.137e-17 [1968,] 1.415922e+01 0.00588447 -3.574e-17 [1969,] 1.419832e+01 0.00586827 -3.63e-17 [1970,] 1.423751e+01 0.00585212 -5.372e-17 [1971,] 1.427682e+01 0.00583601 -8.689e-17 [1972,] 1.431624e+01 0.00581995 -4.634e-17 [1973,] 1.435576e+01 0.00580393 -5.897e-17 [1974,] 1.439539e+01 0.00578796 -7.167e-17 [1975,] 1.443513e+01 0.00577203 6.173e-17 [1976,] 1.447499e+01 0.00575614 -4.044e-17 [1977,] 1.451495e+01 0.00574030 2.463e-17 [1978,] 1.455502e+01 0.00572450 -6.677e-17 [1979,] 1.459520e+01 0.00570875 -6.493e-17 [1980,] 1.463550e+01 0.00569303 -3.427e-17 [1981,] 1.467590e+01 0.00567736 -1.003e-17 [1982,] 1.471642e+01 0.00566174 -5.983e-17 [1983,] 1.475705e+01 0.00564616 2.222e-17 [1984,] 1.479779e+01 0.00563062 2.28e-17 [1985,] 1.483864e+01 0.00561512 -1.098e-16 [1986,] 1.487961e+01 0.00559966 -7.868e-18 [1987,] 1.492069e+01 0.00558425 -6.327e-17 [1988,] 1.496188e+01 0.00556888 -1.04e-16 [1989,] 1.500319e+01 0.00555355 2.548e-17 [1990,] 1.504461e+01 0.00553827 -7.335e-17 [1991,] 1.508614e+01 0.00552303 -1.296e-17 [1992,] 1.512779e+01 0.00550782 -3.03e-17 [1993,] 1.516956e+01 0.00549266 7.078e-17 [1994,] 1.521144e+01 0.00547755 -4.144e-18 [1995,] 1.525343e+01 0.00546247 1.816e-18 [1996,] 1.529554e+01 0.00544744 3.829e-17 [1997,] 1.533777e+01 0.00543244 -5.778e-17 [1998,] 1.538011e+01 0.00541749 1.961e-17 [1999,] 1.542257e+01 0.00540258 1.976e-17 [2000,] 1.546515e+01 0.00538771 8.565e-17 [2001,] 1.550785e+01 0.00537288 -5.308e-17 [2002,] 1.555066e+01 0.00535809 -8.871e-17 [2003,] 1.559359e+01 0.00534334 3.356e-17 [2004,] 1.563664e+01 0.00532864 -1.687e-16 [2005,] 1.567981e+01 0.00531397 -9.577e-18 [2006,] 1.572310e+01 0.00529934 -4.947e-17 [2007,] 1.576651e+01 0.00528476 -1.163e-16 [2008,] 1.581004e+01 0.00527021 -2.078e-17 [2009,] 1.585369e+01 0.00525570 4.32e-17 [2010,] 1.589745e+01 0.00524124 1.276e-18 [2011,] 1.594134e+01 0.00522681 8.286e-17 [2012,] 1.598535e+01 0.00521243 4.246e-18 [2013,] 1.602949e+01 0.00519808 -8.425e-17 [2014,] 1.607374e+01 0.00518377 1.77e-17 [2015,] 1.611812e+01 0.00516950 -1.656e-16 [2016,] 1.616261e+01 0.00515527 4.461e-17 [2017,] 1.620724e+01 0.00514108 -9.962e-17 [2018,] 1.625198e+01 0.00512693 -6.854e-17 [2019,] 1.629685e+01 0.00511282 -1.134e-16 [2020,] 1.634184e+01 0.00509875 4.852e-17 [2021,] 1.638696e+01 0.00508472 -5.987e-17 [2022,] 1.643220e+01 0.00507072 -1.361e-16 [2023,] 1.647756e+01 0.00505676 -5.319e-18 [2024,] 1.652305e+01 0.00504284 -1.526e-17 [2025,] 1.656867e+01 0.00502896 4.312e-17 [2026,] 1.661441e+01 0.00501512 -8.638e-17 [2027,] 1.666028e+01 0.00500132 -1.513e-16 [2028,] 1.670628e+01 0.00498755 3.846e-17 [2029,] 1.675240e+01 0.00497382 -9.375e-17 [2030,] 1.679865e+01 0.00496013 5.155e-18 [2031,] 1.684502e+01 0.00494648 -7.903e-17 [2032,] 1.689153e+01 0.00493286 -6.641e-17 [2033,] 1.693816e+01 0.00491929 -5.549e-17 [2034,] 1.698493e+01 0.00490575 -2.278e-18 [2035,] 1.703182e+01 0.00489224 3.901e-17 [2036,] 1.707884e+01 0.00487878 -9.192e-17 [2037,] 1.712599e+01 0.00486535 -4.879e-18 [2038,] 1.717327e+01 0.00485195 9.207e-17 [2039,] 1.722068e+01 0.00483860 -5.966e-17 [2040,] 1.726822e+01 0.00482528 9.654e-17 [2041,] 1.731590e+01 0.00481200 9.568e-17 [2042,] 1.736370e+01 0.00479875 -1.056e-17 [2043,] 1.741164e+01 0.00478554 -7.328e-18 [2044,] 1.745971e+01 0.00477237 -9.762e-17 [2045,] 1.750791e+01 0.00475924 -1.138e-17 [2046,] 1.755625e+01 0.00474614 -1.058e-16 [2047,] 1.760472e+01 0.00473307 -5.018e-17 [2048,] 1.765332e+01 0.00472004 4.424e-17 [2049,] 1.770205e+01 0.00470705 -6.861e-18 [2050,] 1.775093e+01 0.00469409 -5.499e-17 [2051,] 1.779993e+01 0.00468117 4.379e-17 [2052,] 1.784907e+01 0.00466829 -8.447e-17 [2053,] 1.789835e+01 0.00465544 4.407e-17 [2054,] 1.794776e+01 0.00464262 1.823e-17 [2055,] 1.799731e+01 0.00462984 -3.046e-17 [2056,] 1.804700e+01 0.00461710 -7.409e-17 [2057,] 1.809682e+01 0.00460439 -1.609e-17 [2058,] 1.814679e+01 0.00459172 -3.871e-17 [2059,] 1.819688e+01 0.00457908 -1.089e-16 [2060,] 1.824712e+01 0.00456647 -5.247e-17 [2061,] 1.829750e+01 0.00455390 5.46e-17 [2062,] 1.834801e+01 0.00454137 -2.091e-16 [2063,] 1.839867e+01 0.00452887 -2.247e-17 [2064,] 1.844946e+01 0.00451640 -4.334e-17 [2065,] 1.850040e+01 0.00450397 -4.428e-17 [2066,] 1.855147e+01 0.00449157 -5.642e-17 [2067,] 1.860269e+01 0.00447921 -7.311e-17 [2068,] 1.865405e+01 0.00446688 -8.131e-18 [2069,] 1.870555e+01 0.00445458 -1.434e-16 [2070,] 1.875719e+01 0.00444232 -7.461e-17 [2071,] 1.880897e+01 0.00443009 -9.759e-17 [2072,] 1.886090e+01 0.00441790 -1.179e-16 [2073,] 1.891297e+01 0.00440574 -4.526e-17 [2074,] 1.896518e+01 0.00439361 2.184e-19 [2075,] 1.901754e+01 0.00438152 5.326e-17 [2076,] 1.907005e+01 0.00436945 -2.399e-17 [2077,] 1.912269e+01 0.00435743 5.05e-17 [2078,] 1.917549e+01 0.00434543 6.714e-17 [2079,] 1.922843e+01 0.00433347 -2.294e-17 [2080,] 1.928151e+01 0.00432154 -4.095e-17 [2081,] 1.933474e+01 0.00430965 3.615e-18 [2082,] 1.938812e+01 0.00429778 -4.997e-17 [2083,] 1.944165e+01 0.00428595 1.603e-17 [2084,] 1.949532e+01 0.00427415 -1.55e-16 [2085,] 1.954914e+01 0.00426239 2.996e-18 [2086,] 1.960312e+01 0.00425066 -1.804e-16 [2087,] 1.965724e+01 0.00423896 -1.229e-16 [2088,] 1.971150e+01 0.00422729 -6.969e-17 [2089,] 1.976592e+01 0.00421565 -6.985e-17 [2090,] 1.982049e+01 0.00420405 2.186e-17 [2091,] 1.987521e+01 0.00419247 -1.474e-16 [2092,] 1.993008e+01 0.00418093 -1.239e-16 [2093,] 1.998511e+01 0.00416942 -1.582e-16 [2094,] 2.004028e+01 0.00415795 -6.694e-17 [2095,] 2.009561e+01 0.00414650 7.511e-17 [2096,] 2.015109e+01 0.00413509 -6.268e-17 [2097,] 2.020672e+01 0.00412370 1.875e-17 [2098,] 2.026250e+01 0.00411235 -1.766e-17 [2099,] 2.031844e+01 0.00410103 -5.18e-17 [2100,] 2.037454e+01 0.00408974 -1.407e-16 [2101,] 2.043079e+01 0.00407849 -1.125e-16 [2102,] 2.048719e+01 0.00406726 5.148e-17 [2103,] 2.054375e+01 0.00405606 4.047e-17 [2104,] 2.060047e+01 0.00404490 -1.725e-16 [2105,] 2.065734e+01 0.00403376 2.665e-17 [2106,] 2.071437e+01 0.00402266 -1.389e-16 [2107,] 2.077156e+01 0.00401159 -1.57e-17 [2108,] 2.082891e+01 0.00400054 -6.89e-17 [2109,] 2.088641e+01 0.00398953 -1.549e-16 [2110,] 2.094407e+01 0.00397855 -1.169e-16 [2111,] 2.100190e+01 0.00396760 -8.91e-17 [2112,] 2.105988e+01 0.00395667 -1.527e-16 [2113,] 2.111802e+01 0.00394578 5.34e-17 [2114,] 2.117632e+01 0.00393492 -1.643e-16 [2115,] 2.123478e+01 0.00392409 -4.449e-17 [2116,] 2.129341e+01 0.00391329 -4.027e-17 [2117,] 2.135219e+01 0.00390251 4.295e-17 [2118,] 2.141114e+01 0.00389177 -8.417e-17 [2119,] 2.147025e+01 0.00388106 -1.911e-16 [2120,] 2.152953e+01 0.00387037 -9.326e-17 [2121,] 2.158897e+01 0.00385972 -4.279e-17 [2122,] 2.164857e+01 0.00384910 -4.157e-17 [2123,] 2.170834e+01 0.00383850 -6.067e-17 [2124,] 2.176827e+01 0.00382793 -8.553e-17 [2125,] 2.182836e+01 0.00381740 -2.351e-17 [2126,] 2.188863e+01 0.00380689 -9.314e-17 [2127,] 2.194906e+01 0.00379641 -1.359e-16 [2128,] 2.200965e+01 0.00378596 -4.672e-17 [2129,] 2.207042e+01 0.00377554 -6.789e-17 [2130,] 2.213135e+01 0.00376514 6.365e-17 [2131,] 2.219245e+01 0.00375478 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[2155,] 2.371053e+01 0.00351440 -1.547e-16 [2156,] 2.377599e+01 0.00350473 -1.053e-16 [2157,] 2.384163e+01 0.00349508 -4.442e-17 [2158,] 2.390745e+01 0.00348546 2.99e-18 [2159,] 2.397345e+01 0.00347587 -1.129e-16 [2160,] 2.403964e+01 0.00346630 -4.258e-17 [2161,] 2.410601e+01 0.00345675 6.679e-18 [2162,] 2.417256e+01 0.00344724 -2.349e-17 [2163,] 2.423929e+01 0.00343775 2.775e-17 [2164,] 2.430621e+01 0.00342829 -1.131e-16 [2165,] 2.437332e+01 0.00341885 -5.189e-17 [2166,] 2.444061e+01 0.00340944 -1.187e-16 [2167,] 2.450808e+01 0.00340005 -1.377e-16 [2168,] 2.457574e+01 0.00339069 -1.64e-19 [2169,] 2.464359e+01 0.00338136 -8.768e-17 [2170,] 2.471163e+01 0.00337205 -1.403e-17 [2171,] 2.477985e+01 0.00336277 -2.984e-17 [2172,] 2.484826e+01 0.00335351 -8.605e-17 [2173,] 2.491686e+01 0.00334428 -9.324e-18 [2174,] 2.498565e+01 0.00333507 -3.401e-17 [2175,] 2.505463e+01 0.00332589 8.481e-18 [2176,] 2.512380e+01 0.00331673 1.999e-17 [2177,] 2.519316e+01 0.00330760 1.05e-18 [2178,] 2.526271e+01 0.00329850 -2.739e-17 [2179,] 2.533246e+01 0.00328942 -1.365e-16 [2180,] 2.540239e+01 0.00328036 2.648e-17 [2181,] 2.547253e+01 0.00327133 -4.905e-17 [2182,] 2.554285e+01 0.00326233 2.933e-17 [2183,] 2.561337e+01 0.00325334 -1.061e-16 [2184,] 2.568408e+01 0.00324439 -2.654e-17 [2185,] 2.575499e+01 0.00323546 -1.053e-16 [2186,] 2.582609e+01 0.00322655 -8.629e-17 [2187,] 2.589739e+01 0.00321767 -9.268e-17 [2188,] 2.596889e+01 0.00320881 -8.183e-17 [2189,] 2.604058e+01 0.00319998 1.218e-16 [2190,] 2.611247e+01 0.00319117 6.462e-17 [2191,] 2.618456e+01 0.00318238 2.518e-17 [2192,] 2.625685e+01 0.00317362 1.648e-16 [2193,] 2.632934e+01 0.00316488 2.768e-17 [2194,] 2.640203e+01 0.00315617 4.795e-17 [2195,] 2.647492e+01 0.00314748 -1.098e-17 [2196,] 2.654801e+01 0.00313882 1.076e-16 [2197,] 2.662131e+01 0.00313018 1.704e-17 [2198,] 2.669480e+01 0.00312156 4.75e-17 [2199,] 2.676850e+01 0.00311297 1.373e-17 [2200,] 2.684240e+01 0.00310440 4.923e-17 [2201,] 2.691651e+01 0.00309585 1.201e-16 [2202,] 2.699082e+01 0.00308733 6.537e-17 [2203,] 2.706533e+01 0.00307883 -7.665e-18 [2204,] 2.714005e+01 0.00307035 5.204e-17 [2205,] 2.721498e+01 0.00306190 1.153e-16 [2206,] 2.729012e+01 0.00305347 4.451e-17 [2207,] 2.736546e+01 0.00304507 6.581e-18 [2208,] 2.744101e+01 0.00303668 4.644e-17 [2209,] 2.751677e+01 0.00302832 1.103e-17 [2210,] 2.759273e+01 0.00301999 -6.08e-18 [2211,] 2.766891e+01 0.00301167 -8.728e-17 [2212,] 2.774530e+01 0.00300338 1.481e-17 [2213,] 2.782190e+01 0.00299511 2.168e-17 [2214,] 2.789871e+01 0.00298687 3.874e-17 [2215,] 2.797573e+01 0.00297865 -4.506e-17 [2216,] 2.805296e+01 0.00297045 1.053e-16 [2217,] 2.813041e+01 0.00296227 3.741e-17 [2218,] 2.820807e+01 0.00295411 -5.342e-18 [2219,] 2.828595e+01 0.00294598 -4.346e-17 [2220,] 2.836404e+01 0.00293787 5.427e-17 [2221,] 2.844235e+01 0.00292978 -5.033e-17 [2222,] 2.852087e+01 0.00292172 -6.135e-17 [2223,] 2.859961e+01 0.00291367 -1.614e-17 [2224,] 2.867857e+01 0.00290565 5.261e-18 [2225,] 2.875774e+01 0.00289765 -2.021e-17 [2226,] 2.883713e+01 0.00288968 -5.45e-17 [2227,] 2.891675e+01 0.00288172 1.151e-17 [2228,] 2.899658e+01 0.00287379 9.315e-17 [2229,] 2.907663e+01 0.00286588 -7.411e-17 [2230,] 2.915691e+01 0.00285799 -2.017e-17 [2231,] 2.923740e+01 0.00285012 -6.915e-17 [2232,] 2.931812e+01 0.00284227 -2.813e-17 [2233,] 2.939906e+01 0.00283445 -1.071e-16 [2234,] 2.948023e+01 0.00282665 -3.233e-17 [2235,] 2.956161e+01 0.00281886 -2.179e-17 [2236,] 2.964323e+01 0.00281110 -1.217e-16 [2237,] 2.972506e+01 0.00280336 -8.537e-18 [2238,] 2.980713e+01 0.00279565 -4.305e-17 [2239,] 2.988942e+01 0.00278795 -1.258e-16 [2240,] 2.997194e+01 0.00278028 -3.687e-17 [2241,] 3.005468e+01 0.00277262 -3.231e-17 [2242,] 3.013766e+01 0.00276499 -3.671e-17 [2243,] 3.022086e+01 0.00275738 -3.72e-17 [2244,] 3.030429e+01 0.00274979 -6.451e-17 [2245,] 3.038796e+01 0.00274222 -1.17e-17 [2246,] 3.047185e+01 0.00273467 -8.929e-17 [2247,] 3.055598e+01 0.00272714 -1.893e-17 [2248,] 3.064033e+01 0.00271963 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9.753815e+01 0.00085436 -1.161e-16 [2669,] 9.780743e+01 0.00085201 4.357e-17 [2670,] 9.807746e+01 0.00084967 -1.387e-16 [2671,] 9.834823e+01 0.00084733 -9.871e-17 [2672,] 9.861974e+01 0.00084499 -5.674e-17 [2673,] 9.889201e+01 0.00084267 -6.223e-17 [2674,] 9.916503e+01 0.00084035 -4.337e-17 [2675,] 9.943880e+01 0.00083803 -4.542e-17 [2676,] 9.971333e+01 0.00083573 3.655e-17 [2677,] 9.998861e+01 0.00083343 -4.244e-17 [2678,] 1.002647e+02 0.00083113 -1.045e-16 [2679,] 1.005415e+02 0.00082884 -4.965e-17 [2680,] 1.008190e+02 0.00082656 -4.1e-17 [2681,] 1.010974e+02 0.00082429 -1.406e-16 [2682,] 1.013765e+02 0.00082202 -1.046e-16 [2683,] 1.016564e+02 0.00081975 -4.848e-18 [2684,] 1.019370e+02 0.00081750 -2.541e-17 [2685,] 1.022184e+02 0.00081524 -5.97e-17 [2686,] 1.025006e+02 0.00081300 -1.07e-16 [2687,] 1.027836e+02 0.00081076 -7.371e-18 [2688,] 1.030674e+02 0.00080853 4.23e-17 [2689,] 1.033519e+02 0.00080630 2.649e-17 [2690,] 1.036373e+02 0.00080408 8.442e-18 [2691,] 1.039234e+02 0.00080187 3.406e-17 [2692,] 1.042103e+02 0.00079966 3.193e-18 [2693,] 1.044980e+02 0.00079746 2.573e-17 [2694,] 1.047865e+02 0.00079527 2.149e-17 [2695,] 1.050758e+02 0.00079308 -1.885e-16 [2696,] 1.053659e+02 0.00079089 -3.229e-17 [2697,] 1.056568e+02 0.00078872 -1.354e-16 [2698,] 1.059484e+02 0.00078654 4.75e-17 [2699,] 1.062409e+02 0.00078438 2.444e-17 [2700,] 1.065343e+02 0.00078222 -4.53e-17 [2701,] 1.068284e+02 0.00078007 -8.443e-17 [2702,] 1.071233e+02 0.00077792 6.564e-17 [2703,] 1.074190e+02 0.00077578 -6.89e-18 [2704,] 1.077156e+02 0.00077364 -1.185e-16 [2705,] 1.080130e+02 0.00077151 -7.593e-17 [2706,] 1.083112e+02 0.00076939 -1.238e-16 [2707,] 1.086102e+02 0.00076727 -4.686e-18 [2708,] 1.089100e+02 0.00076516 -1.525e-16 [2709,] 1.092107e+02 0.00076305 -7.897e-17 [2710,] 1.095122e+02 0.00076095 -9.176e-17 [2711,] 1.098146e+02 0.00075885 3.402e-17 [2712,] 1.101177e+02 0.00075676 -1.041e-16 [2713,] 1.104218e+02 0.00075468 3.551e-18 [2714,] 1.107266e+02 0.00075260 -3.462e-17 [2715,] 1.110323e+02 0.00075053 -1.103e-16 [2716,] 1.113388e+02 0.00074846 -1.188e-16 [2717,] 1.116462e+02 0.00074640 -8.411e-17 [2718,] 1.119544e+02 0.00074435 -1.47e-16 [2719,] 1.122635e+02 0.00074230 -5.063e-17 [2720,] 1.125735e+02 0.00074026 3.939e-17 [2721,] 1.128842e+02 0.00073822 -9.441e-17 [2722,] 1.131959e+02 0.00073619 -4.98e-17 [2723,] 1.135084e+02 0.00073416 -3.472e-17 [2724,] 1.138218e+02 0.00073214 -3.953e-17 [2725,] 1.141360e+02 0.00073012 -8.064e-17 [2726,] 1.144511e+02 0.00072811 -7.469e-17 [2727,] 1.147671e+02 0.00072611 -3.313e-17 [2728,] 1.150839e+02 0.00072411 -6.93e-17 [2729,] 1.154016e+02 0.00072211 5.692e-17 [2730,] 1.157202e+02 0.00072013 -8.403e-17 [2731,] 1.160397e+02 0.00071814 2.573e-17 [2732,] 1.163601e+02 0.00071617 9.644e-18 [2733,] 1.166813e+02 0.00071419 -1.078e-16 [2734,] 1.170035e+02 0.00071223 7.319e-17 [2735,] 1.173265e+02 0.00071027 -3.375e-17 [2736,] 1.176504e+02 0.00070831 -1.053e-16 [2737,] 1.179752e+02 0.00070636 1.19e-17 [2738,] 1.183009e+02 0.00070442 -1.041e-16 [2739,] 1.186275e+02 0.00070248 3.292e-17 [2740,] 1.189550e+02 0.00070054 -4.631e-17 [2741,] 1.192834e+02 0.00069861 -1.676e-17 [2742,] 1.196127e+02 0.00069669 -8.621e-17 [2743,] 1.199429e+02 0.00069477 -6.539e-17 [2744,] 1.202741e+02 0.00069286 6.118e-17 [2745,] 1.206061e+02 0.00069095 -8.833e-17 [2746,] 1.209391e+02 0.00068905 -1.095e-16 [2747,] 1.212730e+02 0.00068715 -1.846e-16 [2748,] 1.216078e+02 0.00068526 -3.352e-18 [2749,] 1.219435e+02 0.00068337 -6.395e-17 [2750,] 1.222802e+02 0.00068149 -1.311e-16 [2751,] 1.226178e+02 0.00067962 -1.377e-16 [2752,] 1.229563e+02 0.00067775 -1.367e-16 [2753,] 1.232957e+02 0.00067588 -3.297e-17 [2754,] 1.236361e+02 0.00067402 1.641e-17 [2755,] 1.239775e+02 0.00067216 -7.607e-18 [2756,] 1.243197e+02 0.00067031 -1.182e-16 [2757,] 1.246630e+02 0.00066847 -1.174e-16 [2758,] 1.250071e+02 0.00066663 -6.607e-17 [2759,] 1.253522e+02 0.00066479 -8.634e-17 [2760,] 1.256983e+02 0.00066296 -1.242e-16 [2761,] 1.260453e+02 0.00066114 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1.346675e+02 0.00061881 -6.704e-17 [2786,] 1.350393e+02 0.00061710 -1.256e-16 [2787,] 1.354121e+02 0.00061540 -3.502e-17 [2788,] 1.357859e+02 0.00061371 -2.002e-16 [2789,] 1.361608e+02 0.00061202 -4.294e-17 [2790,] 1.365367e+02 0.00061034 -6.517e-17 [2791,] 1.369137e+02 0.00060865 -2.187e-16 [2792,] 1.372917e+02 0.00060698 -1.586e-16 [2793,] 1.376707e+02 0.00060531 -1.188e-16 [2794,] 1.380508e+02 0.00060364 -1.832e-16 [2795,] 1.384319e+02 0.00060198 -1.065e-16 [2796,] 1.388141e+02 0.00060032 -2.072e-17 [2797,] 1.391973e+02 0.00059867 -2.211e-16 [2798,] 1.395816e+02 0.00059702 -9.254e-17 [2799,] 1.399670e+02 0.00059538 -6.101e-17 [2800,] 1.403534e+02 0.00059374 1.43e-17 [2801,] 1.407409e+02 0.00059210 -3.765e-17 [2802,] 1.411294e+02 0.00059047 -1.019e-17 [2803,] 1.415190e+02 0.00058885 -9.172e-17 [2804,] 1.419097e+02 0.00058723 -1.863e-16 [2805,] 1.423015e+02 0.00058561 4.084e-17 [2806,] 1.426944e+02 0.00058400 -3.793e-17 [2807,] 1.430883e+02 0.00058239 -2.75e-17 [2808,] 1.434834e+02 0.00058079 5.319e-17 [2809,] 1.438795e+02 0.00057919 -1.466e-16 [2810,] 1.442767e+02 0.00057759 -1.249e-16 [2811,] 1.446750e+02 0.00057600 -1.498e-16 [2812,] 1.450744e+02 0.00057442 -1.303e-16 [2813,] 1.454749e+02 0.00057284 8.839e-17 [2814,] 1.458766e+02 0.00057126 9.279e-17 [2815,] 1.462793e+02 0.00056969 -8.465e-17 [2816,] 1.466831e+02 0.00056812 -2.124e-17 [2817,] 1.470881e+02 0.00056655 -3.57e-17 [2818,] 1.474942e+02 0.00056499 6.836e-17 [2819,] 1.479014e+02 0.00056344 -1.507e-16 [2820,] 1.483097e+02 0.00056189 3.735e-17 [2821,] 1.487192e+02 0.00056034 8.535e-18 [2822,] 1.491297e+02 0.00055880 -4.513e-17 [2823,] 1.495414e+02 0.00055726 -1.248e-16 [2824,] 1.499543e+02 0.00055572 -7.855e-18 [2825,] 1.503683e+02 0.00055419 -4.281e-17 [2826,] 1.507834e+02 0.00055267 -3.345e-17 [2827,] 1.511997e+02 0.00055115 6.905e-17 [2828,] 1.516171e+02 0.00054963 7.744e-17 [2829,] 1.520357e+02 0.00054812 -1.113e-16 [2830,] 1.524554e+02 0.00054661 -1.255e-16 [2831,] 1.528763e+02 0.00054510 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1.633339e+02 0.00051020 6.654e-17 [2856,] 1.637848e+02 0.00050880 -7.254e-17 [2857,] 1.642370e+02 0.00050740 -8.123e-17 [2858,] 1.646904e+02 0.00050600 -3.608e-17 [2859,] 1.651451e+02 0.00050461 -6.361e-17 [2860,] 1.656010e+02 0.00050322 -1.22e-16 [2861,] 1.660582e+02 0.00050183 -5.553e-17 [2862,] 1.665166e+02 0.00050045 -5.51e-17 [2863,] 1.669764e+02 0.00049907 6.464e-17 [2864,] 1.674373e+02 0.00049770 2.795e-17 [2865,] 1.678996e+02 0.00049633 -1.351e-16 [2866,] 1.683631e+02 0.00049496 3.86e-17 [2867,] 1.688279e+02 0.00049360 -3.305e-17 [2868,] 1.692940e+02 0.00049224 -1.124e-16 [2869,] 1.697614e+02 0.00049088 -1.161e-16 [2870,] 1.702301e+02 0.00048953 -2.685e-17 [2871,] 1.707001e+02 0.00048819 1.435e-17 [2872,] 1.711713e+02 0.00048684 -1.619e-17 [2873,] 1.716439e+02 0.00048550 -8.423e-17 [2874,] 1.721178e+02 0.00048416 -8.609e-17 [2875,] 1.725929e+02 0.00048283 -5.218e-17 [2876,] 1.730694e+02 0.00048150 -1.197e-16 [2877,] 1.735472e+02 0.00048018 -4.316e-17 [2878,] 1.740264e+02 0.00047885 -1.416e-16 [2879,] 1.745068e+02 0.00047754 -1.343e-16 [2880,] 1.749886e+02 0.00047622 -1.457e-17 [2881,] 1.754717e+02 0.00047491 5.566e-17 [2882,] 1.759561e+02 0.00047360 -5.605e-17 [2883,] 1.764419e+02 0.00047230 -5.027e-17 [2884,] 1.769290e+02 0.00047100 2.541e-17 [2885,] 1.774175e+02 0.00046970 -8.852e-17 [2886,] 1.779073e+02 0.00046841 -1.033e-16 [2887,] 1.783984e+02 0.00046712 2.618e-17 [2888,] 1.788910e+02 0.00046583 -1.218e-17 [2889,] 1.793848e+02 0.00046455 2.57e-17 [2890,] 1.798801e+02 0.00046327 -1.319e-16 [2891,] 1.803767e+02 0.00046200 -1.067e-16 [2892,] 1.808747e+02 0.00046072 2.011e-17 [2893,] 1.813740e+02 0.00045946 -1.43e-16 [2894,] 1.818747e+02 0.00045819 -1.412e-17 [2895,] 1.823769e+02 0.00045693 -2.717e-17 [2896,] 1.828804e+02 0.00045567 -6.13e-17 [2897,] 1.833853e+02 0.00045442 -1.365e-16 [2898,] 1.838915e+02 0.00045317 -3.183e-17 [2899,] 1.843992e+02 0.00045192 -2.32e-17 [2900,] 1.849083e+02 0.00045067 -1.09e-16 [2901,] 1.854188e+02 0.00044943 2.536e-17 [2902,] 1.859307e+02 0.00044820 -1.509e-16 [2903,] 1.864440e+02 0.00044696 -6.699e-17 [2904,] 1.869587e+02 0.00044573 7.479e-18 [2905,] 1.874749e+02 0.00044450 2.236e-18 [2906,] 1.879925e+02 0.00044328 -9.405e-17 [2907,] 1.885115e+02 0.00044206 -4.67e-17 [2908,] 1.890319e+02 0.00044084 -1.01e-16 [2909,] 1.895538e+02 0.00043963 -1.635e-16 [2910,] 1.900771e+02 0.00043842 9.679e-18 [2911,] 1.906019e+02 0.00043721 -2.463e-17 [2912,] 1.911281e+02 0.00043601 -7.803e-17 [2913,] 1.916557e+02 0.00043481 5.486e-18 [2914,] 1.921848e+02 0.00043361 -2.5e-17 [2915,] 1.927154e+02 0.00043242 2.865e-17 [2916,] 1.932475e+02 0.00043123 -8.852e-17 [2917,] 1.937810e+02 0.00043004 -8.15e-17 [2918,] 1.943160e+02 0.00042885 1.265e-17 [2919,] 1.948524e+02 0.00042767 -8.503e-17 [2920,] 1.953904e+02 0.00042650 -8.493e-17 [2921,] 1.959298e+02 0.00042532 -1.545e-17 [2922,] 1.964707e+02 0.00042415 -1.534e-17 [2923,] 1.970131e+02 0.00042298 -4.529e-17 [2924,] 1.975570e+02 0.00042182 1.692e-17 [2925,] 1.981024e+02 0.00042066 -1.702e-16 [2926,] 1.986494e+02 0.00041950 6.451e-17 [2927,] 1.991978e+02 0.00041834 -4.227e-17 [2928,] 1.997477e+02 0.00041719 -8.335e-17 [2929,] 2.002992e+02 0.00041604 1.144e-16 [2930,] 2.008522e+02 0.00041490 5.557e-17 [2931,] 2.014067e+02 0.00041376 -6.812e-18 [2932,] 2.019627e+02 0.00041262 8.328e-17 [2933,] 2.025203e+02 0.00041148 7.49e-17 [2934,] 2.030794e+02 0.00041035 -4.426e-17 [2935,] 2.036400e+02 0.00040922 3.744e-17 [2936,] 2.042022e+02 0.00040809 1.562e-16 [2937,] 2.047660e+02 0.00040697 -6.232e-17 [2938,] 2.053313e+02 0.00040585 5.735e-17 [2939,] 2.058982e+02 0.00040473 1.773e-16 [2940,] 2.064666e+02 0.00040362 8.703e-17 [2941,] 2.070366e+02 0.00040250 1.474e-16 [2942,] 2.076082e+02 0.00040140 7.559e-17 [2943,] 2.081814e+02 0.00040029 5.5e-17 [2944,] 2.087561e+02 0.00039919 5.961e-17 [2945,] 2.093324e+02 0.00039809 -8.477e-17 [2946,] 2.099104e+02 0.00039699 -2.378e-17 [2947,] 2.104899e+02 0.00039590 1.137e-16 [2948,] 2.110710e+02 0.00039481 2.425e-18 [2949,] 2.116537e+02 0.00039372 1.648e-17 [2950,] 2.122380e+02 0.00039264 -9.598e-17 [2951,] 2.128240e+02 0.00039156 1.043e-16 [2952,] 2.134115e+02 0.00039048 -6.339e-18 [2953,] 2.140007e+02 0.00038941 7.703e-17 [2954,] 2.145915e+02 0.00038833 1.032e-16 [2955,] 2.151840e+02 0.00038727 1.364e-16 [2956,] 2.157780e+02 0.00038620 -6.379e-17 [2957,] 2.163737e+02 0.00038514 7.119e-17 [2958,] 2.169711e+02 0.00038408 2.173e-17 [2959,] 2.175701e+02 0.00038302 9.425e-18 [2960,] 2.181708e+02 0.00038196 -2.002e-17 [2961,] 2.187731e+02 0.00038091 1.261e-16 [2962,] 2.193771e+02 0.00037986 7.865e-17 [2963,] 2.199827e+02 0.00037882 -3.272e-17 [2964,] 2.205900e+02 0.00037777 5.71e-17 [2965,] 2.211990e+02 0.00037673 -2.395e-17 [2966,] 2.218097e+02 0.00037570 8.566e-17 [2967,] 2.224221e+02 0.00037466 9.883e-17 [2968,] 2.230361e+02 0.00037363 5.203e-17 [2969,] 2.236519e+02 0.00037260 1.101e-17 [2970,] 2.242694e+02 0.00037158 -8.405e-17 [2971,] 2.248885e+02 0.00037055 -1.012e-17 [2972,] 2.255094e+02 0.00036953 5.965e-17 [2973,] 2.261320e+02 0.00036852 -1.362e-17 [2974,] 2.267563e+02 0.00036750 -7.84e-18 [2975,] 2.273823e+02 0.00036649 8.281e-17 [2976,] 2.280100e+02 0.00036548 -2.544e-17 [2977,] 2.286395e+02 0.00036447 -8.031e-18 [2978,] 2.292707e+02 0.00036347 -1.281e-16 [2979,] 2.299037e+02 0.00036247 6.645e-17 [2980,] 2.305384e+02 0.00036147 -7.303e-17 [2981,] 2.311749e+02 0.00036048 -1.339e-17 [2982,] 2.318131e+02 0.00035948 -4.778e-17 [2983,] 2.324531e+02 0.00035850 -8.137e-17 [2984,] 2.330948e+02 0.00035751 -1.089e-16 [2985,] 2.337383e+02 0.00035652 -1.408e-17 [2986,] 2.343836e+02 0.00035554 2.106e-17 [2987,] 2.350307e+02 0.00035456 -3.665e-17 [2988,] 2.356796e+02 0.00035359 -7.411e-17 [2989,] 2.363302e+02 0.00035261 -8.284e-17 [2990,] 2.369827e+02 0.00035164 -8.285e-17 [2991,] 2.376370e+02 0.00035067 -1.029e-16 [2992,] 2.382930e+02 0.00034971 2.841e-17 [2993,] 2.389509e+02 0.00034875 -5.204e-17 [2994,] 2.396106e+02 0.00034779 -1.076e-16 [2995,] 2.402721e+02 0.00034683 -3.36e-17 [2996,] 2.409354e+02 0.00034587 -3.663e-17 [2997,] 2.416006e+02 0.00034492 3.698e-18 [2998,] 2.422676e+02 0.00034397 -1.854e-17 [2999,] 2.429364e+02 0.00034303 -6.268e-17 [3000,] 2.436071e+02 0.00034208 -5.22e-17 [3001,] 2.442797e+02 0.00034114 3.741e-17 [3002,] 2.449541e+02 0.00034020 -9.428e-17 [3003,] 2.456303e+02 0.00033926 -1.251e-17 [3004,] 2.463085e+02 0.00033833 -3.348e-17 [3005,] 2.469885e+02 0.00033740 2.887e-17 [3006,] 2.476703e+02 0.00033647 -5.896e-17 [3007,] 2.483541e+02 0.00033554 -6.896e-17 [3008,] 2.490398e+02 0.00033462 -3.259e-17 [3009,] 2.497273e+02 0.00033370 9.402e-17 [3010,] 2.504167e+02 0.00033278 2.598e-17 [3011,] 2.511081e+02 0.00033186 -9.439e-17 [3012,] 2.518013e+02 0.00033095 -3.64e-17 [3013,] 2.524965e+02 0.00033004 -7.669e-17 [3014,] 2.531936e+02 0.00032913 1.122e-16 [3015,] 2.538926e+02 0.00032822 -8.772e-17 [3016,] 2.545935e+02 0.00032732 -1.098e-16 [3017,] 2.552964e+02 0.00032642 3.69e-17 [3018,] 2.560012e+02 0.00032552 -6.246e-17 [3019,] 2.567080e+02 0.00032462 -4.632e-17 [3020,] 2.574167e+02 0.00032373 3.849e-17 [3021,] 2.581274e+02 0.00032284 9.765e-17 [3022,] 2.588400e+02 0.00032195 -6.194e-17 [3023,] 2.595546e+02 0.00032106 5.816e-17 [3024,] 2.602712e+02 0.00032018 7.125e-17 [3025,] 2.609897e+02 0.00031930 3.951e-17 [3026,] 2.617102e+02 0.00031842 -9.708e-17 [3027,] 2.624328e+02 0.00031754 -1.197e-16 [3028,] 2.631573e+02 0.00031667 3.842e-17 [3029,] 2.638838e+02 0.00031580 -1.073e-17 [3030,] 2.646123e+02 0.00031493 -1.307e-16 [3031,] 2.653429e+02 0.00031406 -4.761e-17 [3032,] 2.660754e+02 0.00031319 -1.81e-16 [3033,] 2.668100e+02 0.00031233 -3.332e-17 [3034,] 2.675466e+02 0.00031147 -5.84e-17 [3035,] 2.682852e+02 0.00031061 -2.396e-17 [3036,] 2.690259e+02 0.00030976 -7.558e-17 [3037,] 2.697686e+02 0.00030891 3.772e-17 [3038,] 2.705134e+02 0.00030806 1.146e-16 [3039,] 2.712602e+02 0.00030721 -5.47e-17 [3040,] 2.720091e+02 0.00030636 5.547e-18 [3041,] 2.727601e+02 0.00030552 1.835e-18 [3042,] 2.735131e+02 0.00030468 -4.651e-17 [3043,] 2.742682e+02 0.00030384 -2.431e-17 [3044,] 2.750254e+02 0.00030300 -1.28e-16 [3045,] 2.757847e+02 0.00030217 6.474e-18 [3046,] 2.765460e+02 0.00030134 -8.83e-18 [3047,] 2.773095e+02 0.00030051 -3.663e-17 [3048,] 2.780751e+02 0.00029968 -1.382e-16 [3049,] 2.788428e+02 0.00029885 2.125e-17 [3050,] 2.796126e+02 0.00029803 -3.38e-17 [3051,] 2.803846e+02 0.00029721 -1.678e-16 [3052,] 2.811587e+02 0.00029639 -1.773e-17 [3053,] 2.819349e+02 0.00029558 -5.007e-17 [3054,] 2.827132e+02 0.00029476 -5.878e-17 [3055,] 2.834937e+02 0.00029395 6.112e-18 [3056,] 2.842764e+02 0.00029314 7.043e-17 [3057,] 2.850612e+02 0.00029233 -1.603e-16 [3058,] 2.858482e+02 0.00029153 -7.767e-17 [3059,] 2.866374e+02 0.00029073 -1.666e-16 [3060,] 2.874287e+02 0.00028993 -1.831e-17 [3061,] 2.882222e+02 0.00028913 -6.988e-17 [3062,] 2.890179e+02 0.00028833 -1.013e-16 [3063,] 2.898159e+02 0.00028754 -3.311e-17 [3064,] 2.906160e+02 0.00028675 -1.263e-16 [3065,] 2.914183e+02 0.00028596 -1.438e-16 [3066,] 2.922228e+02 0.00028517 9.157e-17 [3067,] 2.930296e+02 0.00028439 -5.526e-17 [3068,] 2.938386e+02 0.00028360 8.919e-17 [3069,] 2.946498e+02 0.00028282 -2.728e-17 [3070,] 2.954633e+02 0.00028204 -4.895e-17 [3071,] 2.962790e+02 0.00028127 -1.449e-16 [3072,] 2.970969e+02 0.00028049 -4.763e-17 [3073,] 2.979172e+02 0.00027972 6.71e-17 [3074,] 2.987396e+02 0.00027895 -6.536e-17 [3075,] 2.995644e+02 0.00027818 3.488e-17 [3076,] 3.003914e+02 0.00027742 -1.053e-17 [3077,] 3.012207e+02 0.00027665 -5.712e-17 [3078,] 3.020523e+02 0.00027589 -7.668e-17 [3079,] 3.028862e+02 0.00027513 1.665e-17 [3080,] 3.037224e+02 0.00027437 5.536e-17 [3081,] 3.045609e+02 0.00027362 -1.532e-16 [3082,] 3.054018e+02 0.00027286 -4.959e-17 [3083,] 3.062449e+02 0.00027211 -7.754e-17 [3084,] 3.070904e+02 0.00027136 -1.113e-16 [3085,] 3.079382e+02 0.00027062 -1.182e-16 [3086,] 3.087883e+02 0.00026987 -1.472e-16 [3087,] 3.096408e+02 0.00026913 -3.797e-18 [3088,] 3.104957e+02 0.00026839 -1.209e-16 [3089,] 3.113529e+02 0.00026765 -6.033e-17 [3090,] 3.122125e+02 0.00026691 2.64e-17 [3091,] 3.130744e+02 0.00026618 4.426e-17 [3092,] 3.139387e+02 0.00026544 9.726e-17 [3093,] 3.148054e+02 0.00026471 4.725e-17 [3094,] 3.156745e+02 0.00026398 4.91e-17 [3095,] 3.165460e+02 0.00026326 -8.602e-17 [3096,] 3.174200e+02 0.00026253 6.398e-18 [3097,] 3.182963e+02 0.00026181 -7.652e-17 [3098,] 3.191750e+02 0.00026109 -5.484e-17 [3099,] 3.200562e+02 0.00026037 -1.258e-16 [3100,] 3.209398e+02 0.00025965 2.295e-17 [3101,] 3.218258e+02 0.00025894 1.024e-16 [3102,] 3.227143e+02 0.00025823 4.926e-17 [3103,] 3.236053e+02 0.00025752 -4.786e-17 [3104,] 3.244987e+02 0.00025681 -4.623e-17 [3105,] 3.253945e+02 0.00025610 1.138e-16 [3106,] 3.262929e+02 0.00025539 -1.53e-16 [3107,] 3.271937e+02 0.00025469 -3.162e-17 [3108,] 3.280970e+02 0.00025399 -8.803e-17 [3109,] 3.290028e+02 0.00025329 -4.047e-17 [3110,] 3.299111e+02 0.00025259 -3.968e-17 [3111,] 3.308219e+02 0.00025190 -9.965e-17 [3112,] 3.317352e+02 0.00025120 -9.531e-17 [3113,] 3.326511e+02 0.00025051 -3.367e-17 [3114,] 3.335695e+02 0.00024982 -5.184e-17 [3115,] 3.344904e+02 0.00024914 -3.57e-17 [3116,] 3.354138e+02 0.00024845 9.073e-19 [3117,] 3.363398e+02 0.00024777 1.056e-16 [3118,] 3.372684e+02 0.00024708 -1.103e-16 [3119,] 3.381995e+02 0.00024640 -7.439e-17 [3120,] 3.391332e+02 0.00024572 -1.251e-16 [3121,] 3.400695e+02 0.00024505 -1.61e-16 [3122,] 3.410083e+02 0.00024437 -4.495e-17 [3123,] 3.419498e+02 0.00024370 -9.272e-17 [3124,] 3.428938e+02 0.00024303 -1.393e-17 [3125,] 3.438405e+02 0.00024236 -3.886e-18 [3126,] 3.447897e+02 0.00024169 6.661e-17 [3127,] 3.457416e+02 0.00024103 -8.998e-17 [3128,] 3.466961e+02 0.00024036 -6.72e-17 [3129,] 3.476533e+02 0.00023970 2.197e-17 [3130,] 3.486131e+02 0.00023904 -2.422e-17 [3131,] 3.495755e+02 0.00023838 -4.427e-17 [3132,] 3.505406e+02 0.00023773 -5.503e-17 [3133,] 3.515084e+02 0.00023707 -4.625e-17 [3134,] 3.524788e+02 0.00023642 -3.431e-17 [3135,] 3.534519e+02 0.00023577 2.116e-17 [3136,] 3.544277e+02 0.00023512 -9.155e-17 [3137,] 3.554062e+02 0.00023447 -7.349e-17 [3138,] 3.563874e+02 0.00023383 -7.913e-17 [3139,] 3.573713e+02 0.00023318 1.346e-17 [3140,] 3.583579e+02 0.00023254 -7.706e-17 [3141,] 3.593473e+02 0.00023190 2.197e-17 [3142,] 3.603393e+02 0.00023126 -1.027e-16 [3143,] 3.613342e+02 0.00023063 4.423e-17 [3144,] 3.623317e+02 0.00022999 -8.581e-17 [3145,] 3.633320e+02 0.00022936 2.299e-17 [3146,] 3.643351e+02 0.00022873 -3.696e-17 [3147,] 3.653410e+02 0.00022810 -2.913e-17 [3148,] 3.663496e+02 0.00022747 -2.14e-17 [3149,] 3.673610e+02 0.00022684 4.508e-17 [3150,] 3.683752e+02 0.00022622 3.907e-17 [3151,] 3.693922e+02 0.00022560 6.563e-17 [3152,] 3.704120e+02 0.00022497 -1.702e-17 [3153,] 3.714346e+02 0.00022436 -1.014e-16 [3154,] 3.724601e+02 0.00022374 -6.374e-17 [3155,] 3.734883e+02 0.00022312 -6.3e-17 [3156,] 3.745195e+02 0.00022251 -1.232e-16 [3157,] 3.755534e+02 0.00022189 -1.312e-16 [3158,] 3.765902e+02 0.00022128 -1.686e-17 [3159,] 3.776299e+02 0.00022067 7.184e-17 [3160,] 3.786725e+02 0.00022007 -7.672e-18 [3161,] 3.797179e+02 0.00021946 -4.089e-17 [3162,] 3.807662e+02 0.00021886 -7.667e-17 [3163,] 3.818174e+02 0.00021825 -6.623e-17 [3164,] 3.828715e+02 0.00021765 1.601e-17 [3165,] 3.839285e+02 0.00021705 -1.342e-16 [3166,] 3.849885e+02 0.00021646 -9.454e-17 [3167,] 3.860513e+02 0.00021586 -6.855e-17 [3168,] 3.871171e+02 0.00021527 -1.51e-16 [3169,] 3.881859e+02 0.00021467 -2.663e-17 [3170,] 3.892576e+02 0.00021408 2.853e-17 [3171,] 3.903322e+02 0.00021349 6.447e-17 [3172,] 3.914099e+02 0.00021291 -1.663e-16 [3173,] 3.924904e+02 0.00021232 1.011e-18 [3174,] 3.935740e+02 0.00021173 -2.993e-17 [3175,] 3.946606e+02 0.00021115 2.985e-17 [3176,] 3.957502e+02 0.00021057 6.267e-18 [3177,] 3.968427e+02 0.00020999 -4.186e-17 [3178,] 3.979383e+02 0.00020941 -1.624e-16 [3179,] 3.990369e+02 0.00020884 -7.564e-17 [3180,] 4.001386e+02 0.00020826 -1.039e-16 [3181,] 4.012433e+02 0.00020769 -5.516e-17 [3182,] 4.023510e+02 0.00020712 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[3206,] 4.298740e+02 0.00019386 -4.713e-17 [3207,] 4.310608e+02 0.00019332 -9.108e-17 [3208,] 4.322508e+02 0.00019279 -8.318e-17 [3209,] 4.334442e+02 0.00019226 -1.158e-17 [3210,] 4.346408e+02 0.00019173 -2.501e-17 [3211,] 4.358408e+02 0.00019120 2.143e-17 [3212,] 4.370440e+02 0.00019067 -9.98e-17 [3213,] 4.382506e+02 0.00019015 -1.008e-17 [3214,] 4.394605e+02 0.00018963 -4.925e-17 [3215,] 4.406738e+02 0.00018910 -1.123e-16 [3216,] 4.418904e+02 0.00018858 -5.392e-17 [3217,] 4.431103e+02 0.00018806 -1.288e-17 [3218,] 4.443336e+02 0.00018755 -7.625e-17 [3219,] 4.455603e+02 0.00018703 1.435e-17 [3220,] 4.467904e+02 0.00018652 -1.251e-16 [3221,] 4.480239e+02 0.00018600 -1.209e-16 [3222,] 4.492608e+02 0.00018549 -6.749e-17 [3223,] 4.505011e+02 0.00018498 -1.468e-16 [3224,] 4.517449e+02 0.00018447 -1.7e-16 [3225,] 4.529920e+02 0.00018396 -8.036e-17 [3226,] 4.542426e+02 0.00018346 -6.679e-17 [3227,] 4.554967e+02 0.00018295 -1.824e-16 [3228,] 4.567542e+02 0.00018245 -1.614e-16 [3229,] 4.580152e+02 0.00018194 3.054e-17 [3230,] 4.592797e+02 0.00018144 -2.468e-17 [3231,] 4.605476e+02 0.00018094 2.835e-17 [3232,] 4.618191e+02 0.00018045 -4.072e-17 [3233,] 4.630941e+02 0.00017995 -1.136e-16 [3234,] 4.643726e+02 0.00017945 -1.015e-16 [3235,] 4.656546e+02 0.00017896 -5.394e-17 [3236,] 4.669402e+02 0.00017847 -7.107e-17 [3237,] 4.682293e+02 0.00017798 -1.178e-16 [3238,] 4.695220e+02 0.00017749 2.291e-17 [3239,] 4.708182e+02 0.00017700 -1.252e-16 [3240,] 4.721180e+02 0.00017651 -3.294e-17 [3241,] 4.734214e+02 0.00017602 -7.005e-17 [3242,] 4.747284e+02 0.00017554 -4.084e-17 [3243,] 4.760391e+02 0.00017506 1.074e-17 [3244,] 4.773533e+02 0.00017457 -7.374e-17 [3245,] 4.786712e+02 0.00017409 -9.595e-17 [3246,] 4.799927e+02 0.00017361 -5.068e-17 [3247,] 4.813178e+02 0.00017314 -3.426e-17 [3248,] 4.826466e+02 0.00017266 -5.479e-17 [3249,] 4.839791e+02 0.00017218 -8.043e-17 [3250,] 4.853153e+02 0.00017171 -2.932e-17 [3251,] 4.866551e+02 0.00017124 2.377e-17 [3252,] 4.879986e+02 0.00017077 -4.807e-17 [3253,] 4.893459e+02 0.00017030 -2.771e-17 [3254,] 4.906969e+02 0.00016983 -3.767e-17 [3255,] 4.920516e+02 0.00016936 -4.442e-19 [3256,] 4.934100e+02 0.00016889 6.933e-17 [3257,] 4.947722e+02 0.00016843 2.431e-17 [3258,] 4.961382e+02 0.00016796 -5.991e-17 [3259,] 4.975079e+02 0.00016750 -1.574e-16 [3260,] 4.988814e+02 0.00016704 -3.947e-17 [3261,] 5.002587e+02 0.00016658 9.75e-17 [3262,] 5.016398e+02 0.00016612 -9.109e-17 [3263,] 5.030247e+02 0.00016566 1.603e-17 [3264,] 5.044134e+02 0.00016521 -4.013e-17 [3265,] 5.058060e+02 0.00016475 -1.915e-16 [3266,] 5.072024e+02 0.00016430 -5.446e-19 [3267,] 5.086027e+02 0.00016385 2.557e-17 [3268,] 5.100068e+02 0.00016340 -1.063e-16 [3269,] 5.114148e+02 0.00016295 -2.758e-17 [3270,] 5.128267e+02 0.00016250 -5.037e-17 [3271,] 5.142425e+02 0.00016205 -1.513e-16 [3272,] 5.156622e+02 0.00016160 -4.719e-17 [3273,] 5.170859e+02 0.00016116 8.855e-18 [3274,] 5.185134e+02 0.00016072 -4.955e-17 [3275,] 5.199449e+02 0.00016027 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[3299,] 5.555119e+02 0.00015001 -9.005e-17 [3300,] 5.570456e+02 0.00014960 -2.677e-17 [3301,] 5.585835e+02 0.00014919 -2.084e-16 [3302,] 5.601256e+02 0.00014878 8.569e-17 [3303,] 5.616720e+02 0.00014837 2.664e-17 [3304,] 5.632226e+02 0.00014796 -8.87e-17 [3305,] 5.647775e+02 0.00014755 -1.93e-16 [3306,] 5.663368e+02 0.00014714 -4.502e-17 [3307,] 5.679003e+02 0.00014674 -7.081e-17 [3308,] 5.694681e+02 0.00014634 -3.084e-17 [3309,] 5.710403e+02 0.00014593 3.968e-17 [3310,] 5.726168e+02 0.00014553 -6.351e-17 [3311,] 5.741977e+02 0.00014513 -5.676e-17 [3312,] 5.757829e+02 0.00014473 -5.769e-17 [3313,] 5.773725e+02 0.00014433 -6.75e-17 [3314,] 5.789665e+02 0.00014393 -1.839e-16 [3315,] 5.805649e+02 0.00014354 -9.909e-17 [3316,] 5.821677e+02 0.00014314 -6.814e-17 [3317,] 5.837749e+02 0.00014275 9.751e-17 [3318,] 5.853866e+02 0.00014236 3.841e-17 [3319,] 5.870027e+02 0.00014196 -1.465e-16 [3320,] 5.886233e+02 0.00014157 -1.619e-16 [3321,] 5.902483e+02 0.00014118 -7.966e-17 [3322,] 5.918779e+02 0.00014079 -3.508e-17 [3323,] 5.935119e+02 0.00014041 -5.88e-17 [3324,] 5.951505e+02 0.00014002 -1.832e-16 [3325,] 5.967936e+02 0.00013964 8.993e-17 [3326,] 5.984412e+02 0.00013925 -7.523e-17 [3327,] 6.000933e+02 0.00013887 -3.74e-17 [3328,] 6.017500e+02 0.00013848 -1.474e-16 [3329,] 6.034113e+02 0.00013810 -9.296e-17 [3330,] 6.050772e+02 0.00013772 1.04e-16 [3331,] 6.067477e+02 0.00013734 8.44e-18 [3332,] 6.084228e+02 0.00013697 -1.428e-16 [3333,] 6.101025e+02 0.00013659 -8.462e-17 [3334,] 6.117869e+02 0.00013621 -4.455e-17 [3335,] 6.134759e+02 0.00013584 7.394e-17 [3336,] 6.151695e+02 0.00013546 -1.379e-16 [3337,] 6.168679e+02 0.00013509 -2.754e-17 [3338,] 6.185709e+02 0.00013472 -1.694e-17 [3339,] 6.202786e+02 0.00013435 -1.67e-16 [3340,] 6.219911e+02 0.00013398 -2.097e-16 [3341,] 6.237083e+02 0.00013361 -1.056e-16 [3342,] 6.254302e+02 0.00013324 -1.065e-16 [3343,] 6.271568e+02 0.00013287 -1.399e-16 [3344,] 6.288883e+02 0.00013251 -1.382e-16 [3345,] 6.306245e+02 0.00013214 -3.832e-17 [3346,] 6.323655e+02 0.00013178 -6.244e-17 [3347,] 6.341113e+02 0.00013142 -6.597e-17 [3348,] 6.358620e+02 0.00013106 -1.982e-16 [3349,] 6.376174e+02 0.00013069 -1.727e-17 [3350,] 6.393777e+02 0.00013034 4.899e-17 [3351,] 6.411429e+02 0.00012998 -6.81e-17 [3352,] 6.429130e+02 0.00012962 2.72e-17 [3353,] 6.446879e+02 0.00012926 -9.928e-18 [3354,] 6.464677e+02 0.00012891 -1.923e-16 [3355,] 6.482525e+02 0.00012855 -6.233e-17 [3356,] 6.500422e+02 0.00012820 7.372e-17 [3357,] 6.518368e+02 0.00012784 8.561e-18 [3358,] 6.536364e+02 0.00012749 -5.092e-17 [3359,] 6.554409e+02 0.00012714 4.757e-17 [3360,] 6.572504e+02 0.00012679 -7.467e-17 [3361,] 6.590649e+02 0.00012644 -1.982e-16 [3362,] 6.608845e+02 0.00012609 -3.669e-18 [3363,] 6.627090e+02 0.00012575 -7.063e-17 [3364,] 6.645386e+02 0.00012540 -1.493e-16 [3365,] 6.663732e+02 0.00012506 2.339e-17 [3366,] 6.682130e+02 0.00012471 -1.308e-16 [3367,] 6.700577e+02 0.00012437 7.017e-17 [3368,] 6.719076e+02 0.00012402 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[3392,] 7.178697e+02 0.00011608 5.068e-17 [3393,] 7.198516e+02 0.00011576 -1.328e-16 [3394,] 7.218389e+02 0.00011545 -1.57e-16 [3395,] 7.238317e+02 0.00011513 -1.155e-17 [3396,] 7.258301e+02 0.00011481 -1.291e-16 [3397,] 7.278339e+02 0.00011449 -1.333e-16 [3398,] 7.298433e+02 0.00011418 4.501e-18 [3399,] 7.318582e+02 0.00011387 -7.179e-17 [3400,] 7.338787e+02 0.00011355 -4.703e-17 [3401,] 7.359048e+02 0.00011324 -2.595e-17 [3402,] 7.379365e+02 0.00011293 -9.92e-17 [3403,] 7.399738e+02 0.00011262 -1.134e-16 [3404,] 7.420166e+02 0.00011231 -1.173e-16 [3405,] 7.440652e+02 0.00011200 -1.714e-16 [3406,] 7.461194e+02 0.00011169 6.674e-17 [3407,] 7.481792e+02 0.00011138 -6.101e-17 [3408,] 7.502448e+02 0.00011107 -1.06e-16 [3409,] 7.523161e+02 0.00011077 -7.932e-17 [3410,] 7.543930e+02 0.00011046 4.919e-17 [3411,] 7.564757e+02 0.00011016 -9.229e-17 [3412,] 7.585642e+02 0.00010986 -1.197e-16 [3413,] 7.606584e+02 0.00010955 -2.465e-17 [3414,] 7.627584e+02 0.00010925 -3.703e-17 [3415,] 7.648642e+02 0.00010895 -9.847e-17 [3416,] 7.669758e+02 0.00010865 -5.863e-17 [3417,] 7.690933e+02 0.00010835 -1.222e-16 [3418,] 7.712166e+02 0.00010805 -2.78e-17 [3419,] 7.733457e+02 0.00010776 -8.673e-17 [3420,] 7.754808e+02 0.00010746 -5.867e-17 [3421,] 7.776217e+02 0.00010716 -1.082e-16 [3422,] 7.797685e+02 0.00010687 -5.194e-17 [3423,] 7.819213e+02 0.00010658 -3.261e-17 [3424,] 7.840800e+02 0.00010628 1.818e-17 [3425,] 7.862446e+02 0.00010599 -2.861e-17 [3426,] 7.884153e+02 0.00010570 -3.117e-17 [3427,] 7.905919e+02 0.00010541 -8.395e-17 [3428,] 7.927746e+02 0.00010512 -2.429e-17 [3429,] 7.949632e+02 0.00010483 -1.247e-17 [3430,] 7.971579e+02 0.00010454 -5.918e-17 [3431,] 7.993587e+02 0.00010425 -4.313e-17 [3432,] 8.015656e+02 0.00010396 -1.495e-16 [3433,] 8.037785e+02 0.00010368 -1.156e-17 [3434,] 8.059976e+02 0.00010339 -1.018e-16 [3435,] 8.082227e+02 0.00010311 -4.851e-17 [3436,] 8.104540e+02 0.00010282 -7.258e-17 [3437,] 8.126915e+02 0.00010254 -7.405e-17 [3438,] 8.149352e+02 0.00010226 4.072e-17 [3439,] 8.171850e+02 0.00010198 3.439e-17 [3440,] 8.194411e+02 0.00010170 7.043e-17 [3441,] 8.217034e+02 0.00010142 -6.385e-18 [3442,] 8.239719e+02 0.00010114 5.402e-17 [3443,] 8.262467e+02 0.00010086 -4.516e-17 [3444,] 8.285278e+02 0.00010058 -9.339e-18 [3445,] 8.308152e+02 0.00010030 -4.78e-17 [3446,] 8.331089e+02 0.00010003 1.332e-17 [3447,] 8.354089e+02 0.00009975 6.238e-17 [3448,] 8.377153e+02 0.00009948 -8.603e-17 [3449,] 8.400280e+02 0.00009920 -1.276e-16 [3450,] 8.423471e+02 0.00009893 7.224e-18 [3451,] 8.446726e+02 0.00009866 -9.149e-17 [3452,] 8.470046e+02 0.00009839 -1.192e-16 [3453,] 8.493430e+02 0.00009812 3.696e-17 [3454,] 8.516878e+02 0.00009784 -1.641e-16 [3455,] 8.540391e+02 0.00009758 -1.681e-16 [3456,] 8.563969e+02 0.00009731 -4.664e-17 [3457,] 8.587613e+02 0.00009704 3.416e-17 [3458,] 8.611321e+02 0.00009677 4.015e-17 [3459,] 8.635095e+02 0.00009651 -9.166e-17 [3460,] 8.658934e+02 0.00009624 -5.044e-17 [3461,] 8.682840e+02 0.00009597 -3.161e-17 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9.276793e+02 0.00008983 9.319e-18 [3486,] 9.302404e+02 0.00008958 3.402e-18 [3487,] 9.328086e+02 0.00008934 -4.291e-17 [3488,] 9.353838e+02 0.00008909 -7.383e-17 [3489,] 9.379662e+02 0.00008884 -4.606e-17 [3490,] 9.405557e+02 0.00008860 2.586e-17 [3491,] 9.431524e+02 0.00008836 -2.485e-17 [3492,] 9.457562e+02 0.00008811 5.294e-17 [3493,] 9.483672e+02 0.00008787 -1.099e-16 [3494,] 9.509854e+02 0.00008763 -9.246e-17 [3495,] 9.536109e+02 0.00008739 -8.41e-17 [3496,] 9.562436e+02 0.00008715 7.258e-17 [3497,] 9.588836e+02 0.00008691 -8.784e-17 [3498,] 9.615308e+02 0.00008667 -9.904e-17 [3499,] 9.641854e+02 0.00008643 4.825e-17 [3500,] 9.668473e+02 0.00008619 -1.726e-16 [3501,] 9.695165e+02 0.00008595 -1.128e-16 [3502,] 9.721931e+02 0.00008572 -1.323e-17 [3503,] 9.748772e+02 0.00008548 1.214e-17 [3504,] 9.775686e+02 0.00008525 -1.257e-16 [3505,] 9.802674e+02 0.00008501 -7.217e-17 [3506,] 9.829737e+02 0.00008478 3.875e-17 [3507,] 9.856875e+02 0.00008454 -4.374e-17 [3508,] 9.884087e+02 0.00008431 -1.239e-16 [3509,] 9.911375e+02 0.00008408 4.307e-17 [3510,] 9.938738e+02 0.00008385 -2.654e-17 [3511,] 9.966177e+02 0.00008362 -7.125e-17 [3512,] 9.993691e+02 0.00008339 -1.05e-16 [3513,] 1.002128e+03 0.00008316 1.283e-17 [3514,] 1.004895e+03 0.00008293 -5.225e-17 [3515,] 1.007669e+03 0.00008270 8.561e-18 [3516,] 1.010451e+03 0.00008247 7.41e-17 [3517,] 1.013241e+03 0.00008224 -6.368e-17 [3518,] 1.016038e+03 0.00008202 -1.199e-16 [3519,] 1.018843e+03 0.00008179 -6.802e-17 [3520,] 1.021656e+03 0.00008157 -4.685e-17 [3521,] 1.024476e+03 0.00008134 -9.203e-17 [3522,] 1.027305e+03 0.00008112 -7.811e-17 [3523,] 1.030141e+03 0.00008090 1.843e-17 [3524,] 1.032985e+03 0.00008067 -8.243e-17 [3525,] 1.035837e+03 0.00008045 1.449e-17 [3526,] 1.038696e+03 0.00008023 1.603e-17 [3527,] 1.041564e+03 0.00008001 -1.343e-16 [3528,] 1.044439e+03 0.00007979 -1.936e-17 [3529,] 1.047323e+03 0.00007957 -3.234e-17 [3530,] 1.050214e+03 0.00007935 -3.308e-17 [3531,] 1.053114e+03 0.00007913 2.076e-17 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0.00007406 -4.818e-17 [3556,] 1.128259e+03 0.00007386 -2.69e-17 [3557,] 1.131374e+03 0.00007366 -4.402e-17 [3558,] 1.134497e+03 0.00007345 -9.457e-17 [3559,] 1.137629e+03 0.00007325 2.813e-17 [3560,] 1.140770e+03 0.00007305 2.951e-17 [3561,] 1.143919e+03 0.00007285 -7.519e-17 [3562,] 1.147077e+03 0.00007265 1.254e-17 [3563,] 1.150244e+03 0.00007245 -5.445e-17 [3564,] 1.153420e+03 0.00007225 -5.351e-17 [3565,] 1.156604e+03 0.00007205 -1.232e-16 [3566,] 1.159797e+03 0.00007185 7.292e-17 [3567,] 1.162999e+03 0.00007165 -2.661e-17 [3568,] 1.166210e+03 0.00007146 -9.814e-17 [3569,] 1.169430e+03 0.00007126 3.908e-17 [3570,] 1.172658e+03 0.00007106 -1.007e-16 [3571,] 1.175895e+03 0.00007087 -6.215e-17 [3572,] 1.179142e+03 0.00007067 -1.397e-16 [3573,] 1.182397e+03 0.00007048 -1.648e-16 [3574,] 1.185662e+03 0.00007028 -9.662e-17 [3575,] 1.188935e+03 0.00007009 -1.616e-16 [3576,] 1.192217e+03 0.00006990 6.107e-17 [3577,] 1.195509e+03 0.00006971 -6.574e-17 [3578,] 1.198809e+03 0.00006951 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1.280814e+03 0.00006506 -2.973e-17 [3603,] 1.284350e+03 0.00006488 -9.017e-17 [3604,] 1.287896e+03 0.00006471 -4.654e-17 [3605,] 1.291452e+03 0.00006453 -1.275e-16 [3606,] 1.295017e+03 0.00006435 -7.327e-17 [3607,] 1.298592e+03 0.00006417 -7.18e-17 [3608,] 1.302177e+03 0.00006400 -1.443e-17 [3609,] 1.305772e+03 0.00006382 -5.26e-17 [3610,] 1.309377e+03 0.00006364 -5.119e-17 [3611,] 1.312992e+03 0.00006347 8.597e-18 [3612,] 1.316617e+03 0.00006329 -2.577e-18 [3613,] 1.320252e+03 0.00006312 -1.754e-16 [3614,] 1.323897e+03 0.00006295 -2.514e-18 [3615,] 1.327552e+03 0.00006277 -1.007e-16 [3616,] 1.331217e+03 0.00006260 -4.041e-17 [3617,] 1.334892e+03 0.00006243 -1.074e-16 [3618,] 1.338577e+03 0.00006226 -3.49e-17 [3619,] 1.342273e+03 0.00006208 -1.103e-16 [3620,] 1.345979e+03 0.00006191 -1.983e-16 [3621,] 1.349695e+03 0.00006174 -5.009e-17 [3622,] 1.353421e+03 0.00006157 -5.021e-17 [3623,] 1.357157e+03 0.00006140 -9.781e-17 [3624,] 1.360904e+03 0.00006123 -8.599e-18 [3625,] 1.364661e+03 0.00006107 -1.226e-16 [3626,] 1.368429e+03 0.00006090 1.292e-17 [3627,] 1.372207e+03 0.00006073 -4.177e-17 [3628,] 1.375995e+03 0.00006056 -1.236e-16 [3629,] 1.379794e+03 0.00006040 -7.051e-17 [3630,] 1.383603e+03 0.00006023 -5.291e-17 [3631,] 1.387423e+03 0.00006006 -1.394e-16 [3632,] 1.391253e+03 0.00005990 -1.138e-16 [3633,] 1.395094e+03 0.00005973 1.939e-17 [3634,] 1.398946e+03 0.00005957 -2.074e-17 [3635,] 1.402808e+03 0.00005940 -1.164e-16 [3636,] 1.406681e+03 0.00005924 -1.161e-16 [3637,] 1.410564e+03 0.00005908 7.402e-18 [3638,] 1.414459e+03 0.00005892 -1.71e-17 [3639,] 1.418364e+03 0.00005875 1.1e-17 [3640,] 1.422279e+03 0.00005859 -5.402e-17 [3641,] 1.426206e+03 0.00005843 -6.225e-17 [3642,] 1.430143e+03 0.00005827 -7.527e-17 [3643,] 1.434092e+03 0.00005811 -4.165e-18 [3644,] 1.438051e+03 0.00005795 -1.201e-16 [3645,] 1.442021e+03 0.00005779 -7.807e-17 [3646,] 1.446002e+03 0.00005763 -7.517e-17 [3647,] 1.449994e+03 0.00005747 -5.211e-17 [3648,] 1.453997e+03 0.00005731 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1.553458e+03 0.00005364 -1.398e-16 [3673,] 1.557747e+03 0.00005350 -8.396e-17 [3674,] 1.562048e+03 0.00005335 -8.01e-17 [3675,] 1.566360e+03 0.00005320 3.27e-18 [3676,] 1.570685e+03 0.00005306 -8.454e-17 [3677,] 1.575021e+03 0.00005291 -9.309e-17 [3678,] 1.579369e+03 0.00005276 3.71e-18 [3679,] 1.583729e+03 0.00005262 -1.028e-16 [3680,] 1.588102e+03 0.00005247 -3.304e-17 [3681,] 1.592486e+03 0.00005233 1.414e-17 [3682,] 1.596883e+03 0.00005219 4.96e-17 [3683,] 1.601291e+03 0.00005204 -1.989e-17 [3684,] 1.605712e+03 0.00005190 -1.148e-16 [3685,] 1.610145e+03 0.00005176 -9.93e-17 [3686,] 1.614590e+03 0.00005161 6.555e-17 [3687,] 1.619048e+03 0.00005147 -4.606e-17 [3688,] 1.623518e+03 0.00005133 -1.228e-16 [3689,] 1.628000e+03 0.00005119 -3.384e-17 [3690,] 1.632494e+03 0.00005105 -5.306e-17 [3691,] 1.637001e+03 0.00005091 -5.957e-17 [3692,] 1.641521e+03 0.00005077 -1.269e-16 [3693,] 1.646053e+03 0.00005063 -1.347e-18 [3694,] 1.650597e+03 0.00005049 -6.426e-17 [3695,] 1.655154e+03 0.00005035 -1.485e-17 [3696,] 1.659723e+03 0.00005021 -8.448e-17 [3697,] 1.664305e+03 0.00005007 -8.628e-17 [3698,] 1.668900e+03 0.00004993 1.57e-17 [3699,] 1.673508e+03 0.00004980 -1.264e-16 [3700,] 1.678128e+03 0.00004966 -4.379e-17 [3701,] 1.682761e+03 0.00004952 -1.681e-16 [3702,] 1.687406e+03 0.00004939 -7.267e-17 [3703,] 1.692065e+03 0.00004925 -4.469e-17 [3704,] 1.696736e+03 0.00004911 1.699e-18 [3705,] 1.701421e+03 0.00004898 -8.43e-17 [3706,] 1.706118e+03 0.00004884 1.148e-17 [3707,] 1.710828e+03 0.00004871 5.592e-17 [3708,] 1.715551e+03 0.00004858 -1.781e-16 [3709,] 1.720288e+03 0.00004844 -1.004e-16 [3710,] 1.725037e+03 0.00004831 -7.922e-17 [3711,] 1.729799e+03 0.00004818 -9.019e-17 [3712,] 1.734575e+03 0.00004804 -8.536e-17 [3713,] 1.739364e+03 0.00004791 -1.432e-16 [3714,] 1.744166e+03 0.00004778 -3.821e-17 [3715,] 1.748981e+03 0.00004765 -1.478e-16 [3716,] 1.753809e+03 0.00004752 -7.768e-17 [3717,] 1.758651e+03 0.00004738 -1.376e-16 [3718,] 1.763507e+03 0.00004725 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1.884140e+03 0.00004423 3.756e-17 [3743,] 1.889342e+03 0.00004411 -1.339e-16 [3744,] 1.894558e+03 0.00004399 -5.592e-17 [3745,] 1.899788e+03 0.00004386 -1.816e-16 [3746,] 1.905033e+03 0.00004374 -4.077e-17 [3747,] 1.910292e+03 0.00004362 -1.185e-16 [3748,] 1.915566e+03 0.00004350 8.353e-17 [3749,] 1.920855e+03 0.00004338 -1.96e-17 [3750,] 1.926158e+03 0.00004326 4.506e-17 [3751,] 1.931475e+03 0.00004314 -1.721e-16 [3752,] 1.936808e+03 0.00004303 -4.33e-17 [3753,] 1.942155e+03 0.00004291 -7.382e-17 [3754,] 1.947517e+03 0.00004279 -1.666e-16 [3755,] 1.952893e+03 0.00004267 -8.824e-17 [3756,] 1.958285e+03 0.00004255 -5.414e-17 [3757,] 1.963691e+03 0.00004244 -4.423e-17 [3758,] 1.969112e+03 0.00004232 -7.708e-17 [3759,] 1.974549e+03 0.00004220 -6.857e-17 [3760,] 1.980000e+03 0.00004209 -2.063e-17 [3761,] 1.985466e+03 0.00004197 -5.418e-17 [3762,] 1.990948e+03 0.00004186 2.622e-17 [3763,] 1.996444e+03 0.00004174 5.325e-17 [3764,] 2.001956e+03 0.00004163 2.516e-17 [3765,] 2.007483e+03 0.00004151 -5.529e-17 [3766,] 2.013025e+03 0.00004140 -1.241e-16 [3767,] 2.018583e+03 0.00004128 -1.264e-16 [3768,] 2.024155e+03 0.00004117 -1.83e-16 [3769,] 2.029744e+03 0.00004106 -1.265e-17 [3770,] 2.035347e+03 0.00004094 -1.199e-16 [3771,] 2.040967e+03 0.00004083 3.137e-17 [3772,] 2.046601e+03 0.00004072 6.408e-17 [3773,] 2.052251e+03 0.00004061 -1.794e-16 [3774,] 2.057917e+03 0.00004049 -1.398e-16 [3775,] 2.063599e+03 0.00004038 -1.53e-16 [3776,] 2.069296e+03 0.00004027 -1.067e-16 [3777,] 2.075009e+03 0.00004016 -3.429e-17 [3778,] 2.080737e+03 0.00004005 2.818e-17 [3779,] 2.086482e+03 0.00003994 -3.002e-17 [3780,] 2.092242e+03 0.00003983 -1.098e-16 [3781,] 2.098018e+03 0.00003972 -8.385e-17 [3782,] 2.103810e+03 0.00003961 -1.109e-16 [3783,] 2.109618e+03 0.00003950 -5.542e-17 [3784,] 2.115443e+03 0.00003939 -4.32e-17 [3785,] 2.121283e+03 0.00003928 -4.265e-17 [3786,] 2.127139e+03 0.00003918 -2.706e-17 [3787,] 2.133012e+03 0.00003907 -9.061e-17 [3788,] 2.138901e+03 0.00003896 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[3812,] 2.285213e+03 0.00003647 8.282e-18 [3813,] 2.291522e+03 0.00003637 -1.517e-16 [3814,] 2.297848e+03 0.00003627 4.639e-17 [3815,] 2.304192e+03 0.00003617 -2.149e-16 [3816,] 2.310553e+03 0.00003607 -4.747e-17 [3817,] 2.316932e+03 0.00003597 3.533e-17 [3818,] 2.323329e+03 0.00003587 -6.234e-17 [3819,] 2.329743e+03 0.00003577 -1.657e-16 [3820,] 2.336175e+03 0.00003567 -1.056e-16 [3821,] 2.342624e+03 0.00003557 -7.014e-17 [3822,] 2.349092e+03 0.00003547 4.553e-17 [3823,] 2.355577e+03 0.00003538 -1.434e-16 [3824,] 2.362080e+03 0.00003528 -9.902e-17 [3825,] 2.368602e+03 0.00003518 5.665e-17 [3826,] 2.375141e+03 0.00003509 -3.357e-17 [3827,] 2.381698e+03 0.00003499 -6.653e-17 [3828,] 2.388273e+03 0.00003489 -3.208e-17 [3829,] 2.394867e+03 0.00003480 -1.136e-16 [3830,] 2.401478e+03 0.00003470 8.225e-17 [3831,] 2.408108e+03 0.00003461 -1.761e-16 [3832,] 2.414757e+03 0.00003451 -1.53e-17 [3833,] 2.421423e+03 0.00003442 -7.309e-17 [3834,] 2.428108e+03 0.00003432 -3.593e-18 [3835,] 2.434812e+03 0.00003423 -2.661e-17 [3836,] 2.441534e+03 0.00003413 -4.315e-17 [3837,] 2.448274e+03 0.00003404 -3.709e-18 [3838,] 2.455033e+03 0.00003394 9.43e-17 [3839,] 2.461811e+03 0.00003385 6.451e-17 [3840,] 2.468608e+03 0.00003376 -1.044e-16 [3841,] 2.475423e+03 0.00003366 -1.568e-17 [3842,] 2.482257e+03 0.00003357 3.081e-17 [3843,] 2.489110e+03 0.00003348 -1.407e-16 [3844,] 2.495982e+03 0.00003339 -2.143e-17 [3845,] 2.502872e+03 0.00003330 -1.687e-16 [3846,] 2.509782e+03 0.00003320 -1.942e-16 [3847,] 2.516711e+03 0.00003311 -1.674e-16 [3848,] 2.523659e+03 0.00003302 -3.108e-17 [3849,] 2.530627e+03 0.00003293 -5.116e-18 [3850,] 2.537613e+03 0.00003284 1.024e-16 [3851,] 2.544619e+03 0.00003275 -6.132e-17 [3852,] 2.551644e+03 0.00003266 -2.067e-17 [3853,] 2.558688e+03 0.00003257 -1.49e-16 [3854,] 2.565752e+03 0.00003248 -2.265e-18 [3855,] 2.572836e+03 0.00003239 -1.26e-16 [3856,] 2.579939e+03 0.00003230 -1.5e-16 [3857,] 2.587062e+03 0.00003221 -3.873e-17 [3858,] 2.594204e+03 0.00003212 -1.138e-16 [3859,] 2.601366e+03 0.00003203 2.455e-17 [3860,] 2.608548e+03 0.00003195 -1.328e-16 [3861,] 2.615749e+03 0.00003186 -1.788e-16 [3862,] 2.622971e+03 0.00003177 2.765e-17 [3863,] 2.630212e+03 0.00003168 -1.051e-16 [3864,] 2.637474e+03 0.00003160 -8.401e-17 [3865,] 2.644755e+03 0.00003151 -1.15e-17 [3866,] 2.652057e+03 0.00003142 -1.428e-17 [3867,] 2.659378e+03 0.00003134 -6.852e-17 [3868,] 2.666720e+03 0.00003125 -1.503e-16 [3869,] 2.674082e+03 0.00003116 -1.898e-16 [3870,] 2.681465e+03 0.00003108 -2.05e-16 [3871,] 2.688868e+03 0.00003099 -1.661e-16 [3872,] 2.696291e+03 0.00003091 -1.44e-16 [3873,] 2.703735e+03 0.00003082 -1.424e-16 [3874,] 2.711199e+03 0.00003074 -5.327e-17 [3875,] 2.718684e+03 0.00003065 -4.684e-17 [3876,] 2.726190e+03 0.00003057 -8.534e-17 [3877,] 2.733716e+03 0.00003048 2.874e-17 [3878,] 2.741264e+03 0.00003040 -4.514e-17 [3879,] 2.748832e+03 0.00003032 -4.852e-17 [3880,] 2.756421e+03 0.00003023 -9.1e-17 [3881,] 2.764030e+03 0.00003015 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[3905,] 2.953105e+03 0.00002822 -3.359e-17 [3906,] 2.961258e+03 0.00002814 -1.068e-16 [3907,] 2.969433e+03 0.00002806 -1.376e-16 [3908,] 2.977631e+03 0.00002799 -1.098e-16 [3909,] 2.985852e+03 0.00002791 -8.982e-17 [3910,] 2.994095e+03 0.00002783 -1.466e-16 [3911,] 3.002361e+03 0.00002776 -1.928e-17 [3912,] 3.010650e+03 0.00002768 -5.71e-17 [3913,] 3.018961e+03 0.00002760 -1.69e-17 [3914,] 3.027296e+03 0.00002753 5.728e-17 [3915,] 3.035654e+03 0.00002745 -5.086e-17 [3916,] 3.044034e+03 0.00002738 -9.653e-17 [3917,] 3.052438e+03 0.00002730 -6.01e-17 [3918,] 3.060865e+03 0.00002723 -9.807e-17 [3919,] 3.069316e+03 0.00002715 -7.126e-17 [3920,] 3.077789e+03 0.00002708 -7.521e-17 [3921,] 3.086287e+03 0.00002700 -6.537e-17 [3922,] 3.094807e+03 0.00002693 -3.102e-17 [3923,] 3.103351e+03 0.00002685 8.157e-18 [3924,] 3.111919e+03 0.00002678 -1.65e-16 [3925,] 3.120510e+03 0.00002671 3.413e-17 [3926,] 3.129125e+03 0.00002663 -2.298e-17 [3927,] 3.137764e+03 0.00002656 -3.973e-17 [3928,] 3.146427e+03 0.00002649 -8.173e-17 [3929,] 3.155113e+03 0.00002641 -9.081e-17 [3930,] 3.163824e+03 0.00002634 -6.771e-17 [3931,] 3.172558e+03 0.00002627 -1.732e-16 [3932,] 3.181317e+03 0.00002619 -7.4e-17 [3933,] 3.190100e+03 0.00002612 -1.064e-16 [3934,] 3.198907e+03 0.00002605 -7.915e-17 [3935,] 3.207738e+03 0.00002598 -2.359e-17 [3936,] 3.216594e+03 0.00002591 3.617e-17 [3937,] 3.225475e+03 0.00002584 -5.183e-17 [3938,] 3.234379e+03 0.00002576 2.238e-17 [3939,] 3.243309e+03 0.00002569 -3.87e-17 [3940,] 3.252263e+03 0.00002562 5.682e-17 [3941,] 3.261241e+03 0.00002555 -1.871e-16 [3942,] 3.270245e+03 0.00002548 -7.423e-17 [3943,] 3.279273e+03 0.00002541 4.821e-17 [3944,] 3.288327e+03 0.00002534 -3.775e-17 [3945,] 3.297405e+03 0.00002527 -1.375e-16 [3946,] 3.306508e+03 0.00002520 -1.905e-16 [3947,] 3.315637e+03 0.00002513 -7.664e-17 [3948,] 3.324791e+03 0.00002506 -1.868e-16 [3949,] 3.333970e+03 0.00002500 -7.517e-18 [3950,] 3.343174e+03 0.00002493 -7.008e-18 [3951,] 3.352404e+03 0.00002486 -2.239e-16 [3952,] 3.361659e+03 0.00002479 -2.46e-16 [3953,] 3.370940e+03 0.00002472 -8.345e-17 [3954,] 3.380246e+03 0.00002465 -1.515e-16 [3955,] 3.389578e+03 0.00002459 -2.221e-16 [3956,] 3.398936e+03 0.00002452 -1.989e-16 [3957,] 3.408320e+03 0.00002445 -1.686e-16 [3958,] 3.417729e+03 0.00002438 -2.022e-16 [3959,] 3.427165e+03 0.00002432 -1.277e-16 [3960,] 3.436627e+03 0.00002425 -1.29e-16 [3961,] 3.446114e+03 0.00002418 -8.84e-17 [3962,] 3.455628e+03 0.00002412 -2.065e-16 [3963,] 3.465168e+03 0.00002405 -1.83e-16 [3964,] 3.474735e+03 0.00002398 -8.013e-17 [3965,] 3.484328e+03 0.00002392 -6.687e-17 [3966,] 3.493947e+03 0.00002385 -1.904e-16 [3967,] 3.503593e+03 0.00002379 -1.784e-16 [3968,] 3.513266e+03 0.00002372 -6.836e-17 [3969,] 3.522965e+03 0.00002365 -5.854e-17 [3970,] 3.532691e+03 0.00002359 -7.628e-17 [3971,] 3.542444e+03 0.00002352 -1.713e-16 [3972,] 3.552224e+03 0.00002346 -1.799e-17 [3973,] 3.562031e+03 0.00002339 -5.029e-17 [3974,] 3.571865e+03 0.00002333 -1.563e-16 [3975,] 3.581726e+03 0.00002327 -9.322e-17 [3976,] 3.591614e+03 0.00002320 -3.243e-17 [3977,] 3.601530e+03 0.00002314 -1.165e-16 [3978,] 3.611473e+03 0.00002307 -1.538e-16 [3979,] 3.621444e+03 0.00002301 -1.074e-16 [3980,] 3.631442e+03 0.00002295 -9.083e-17 [3981,] 3.641467e+03 0.00002288 -2.047e-16 [3982,] 3.651520e+03 0.00002282 -9.817e-17 [3983,] 3.661601e+03 0.00002276 -1.738e-16 [3984,] 3.671710e+03 0.00002270 -5.416e-17 [3985,] 3.681847e+03 0.00002263 -7.673e-17 [3986,] 3.692012e+03 0.00002257 -1.504e-16 [3987,] 3.702205e+03 0.00002251 -1.021e-16 [3988,] 3.712425e+03 0.00002245 -1.176e-16 [3989,] 3.722675e+03 0.00002239 -3.748e-17 [3990,] 3.732952e+03 0.00002232 -1.269e-16 [3991,] 3.743258e+03 0.00002226 -9.194e-17 [3992,] 3.753592e+03 0.00002220 -5.19e-17 [3993,] 3.763955e+03 0.00002214 -2.043e-18 [3994,] 3.774346e+03 0.00002208 -1.161e-16 [3995,] 3.784767e+03 0.00002202 -1.667e-16 [3996,] 3.795215e+03 0.00002196 -3.703e-17 [3997,] 3.805693e+03 0.00002190 -2.044e-16 [3998,] 3.816200e+03 0.00002184 -1.83e-16 [3999,] 3.826735e+03 0.00002178 -6.466e-17 [4000,] 3.837300e+03 0.00002172 -1.668e-17 [4001,] 3.847894e+03 0.00002166 -1.121e-16 [4002,] 3.858517e+03 0.00002160 -2.22e-16 [4003,] 3.869170e+03 0.00002154 -1.216e-16 [4004,] 3.879852e+03 0.00002148 -7.758e-17 [4005,] 3.890563e+03 0.00002142 -2.035e-16 [4006,] 3.901304e+03 0.00002136 -8.265e-17 [4007,] 3.912075e+03 0.00002130 -1.707e-16 [4008,] 3.922875e+03 0.00002124 -2.187e-16 [4009,] 3.933705e+03 0.00002118 -1.613e-16 [4010,] 3.944565e+03 0.00002113 -1.033e-16 [4011,] 3.955455e+03 0.00002107 -4.871e-17 [4012,] 3.966375e+03 0.00002101 -8.547e-17 [4013,] 3.977326e+03 0.00002095 -6.591e-17 [4014,] 3.988306e+03 0.00002089 -1.161e-16 [4015,] 3.999317e+03 0.00002084 -2.176e-16 [4016,] 4.010358e+03 0.00002078 -9.896e-17 [4017,] 4.021430e+03 0.00002072 -2.761e-17 [4018,] 4.032532e+03 0.00002067 -2.111e-16 [4019,] 4.043665e+03 0.00002061 -2.239e-16 [4020,] 4.054828e+03 0.00002055 -1.33e-16 [4021,] 4.066023e+03 0.00002050 -1.28e-16 [4022,] 4.077248e+03 0.00002044 -3.278e-17 [4023,] 4.088505e+03 0.00002038 -1.874e-16 [4024,] 4.099792e+03 0.00002033 -1.027e-16 [4025,] 4.111111e+03 0.00002027 -1.565e-16 [4026,] 4.122460e+03 0.00002021 -8.387e-18 [4027,] 4.133842e+03 0.00002016 -1.622e-16 [4028,] 4.145254e+03 0.00002010 -8.65e-17 [4029,] 4.156698e+03 0.00002005 -1.526e-16 [4030,] 4.168174e+03 0.00001999 -3.823e-17 [4031,] 4.179681e+03 0.00001994 -7.698e-17 [4032,] 4.191221e+03 0.00001988 -2.121e-17 [4033,] 4.202792e+03 0.00001983 2.608e-18 [4034,] 4.214394e+03 0.00001977 -6.998e-17 [4035,] 4.226029e+03 0.00001972 -7.092e-18 [4036,] 4.237697e+03 0.00001966 -1.532e-16 [4037,] 4.249396e+03 0.00001961 -1.991e-16 [4038,] 4.261128e+03 0.00001956 -1.183e-16 [4039,] 4.272892e+03 0.00001950 -4.438e-17 [4040,] 4.284688e+03 0.00001945 -1.07e-17 [4041,] 4.296517e+03 0.00001940 -2.231e-17 [4042,] 4.308379e+03 0.00001934 -1.759e-17 [4043,] 4.320273e+03 0.00001929 3.073e-17 [4044,] 4.332200e+03 0.00001924 -1.112e-16 [4045,] 4.344161e+03 0.00001918 -2.853e-17 [4046,] 4.356154e+03 0.00001913 -3.555e-17 [4047,] 4.368180e+03 0.00001908 -2.883e-17 [4048,] 4.380240e+03 0.00001902 -3.857e-17 [4049,] 4.392333e+03 0.00001897 1.474e-17 [4050,] 4.404459e+03 0.00001892 -1.236e-16 [4051,] 4.416619e+03 0.00001887 -3.911e-17 [4052,] 4.428812e+03 0.00001882 -4.843e-17 [4053,] 4.441039e+03 0.00001876 -3.831e-17 [4054,] 4.453299e+03 0.00001871 -4.747e-17 [4055,] 4.465594e+03 0.00001866 5.526e-17 [4056,] 4.477923e+03 0.00001861 6.7e-17 [4057,] 4.490285e+03 0.00001856 -9.339e-17 [4058,] 4.502682e+03 0.00001851 -2.023e-18 [4059,] 4.515113e+03 0.00001846 -1.519e-16 [4060,] 4.527578e+03 0.00001841 -1.627e-16 [4061,] 4.540077e+03 0.00001836 -1.978e-16 [4062,] 4.552611e+03 0.00001830 -1.005e-16 [4063,] 4.565180e+03 0.00001825 -1.556e-16 [4064,] 4.577784e+03 0.00001820 -1.269e-17 [4065,] 4.590422e+03 0.00001815 -8.607e-17 [4066,] 4.603095e+03 0.00001810 -5.355e-17 [4067,] 4.615803e+03 0.00001805 -2.019e-16 [4068,] 4.628546e+03 0.00001800 -2.226e-16 [4069,] 4.641325e+03 0.00001795 -5.26e-17 [4070,] 4.654138e+03 0.00001791 -6.697e-17 [4071,] 4.666987e+03 0.00001786 2.034e-18 [4072,] 4.679872e+03 0.00001781 -1.175e-16 [4073,] 4.692792e+03 0.00001776 6.692e-18 [4074,] 4.705747e+03 0.00001771 -6.696e-17 [4075,] 4.718739e+03 0.00001766 -8.089e-17 [4076,] 4.731766e+03 0.00001761 -8.559e-17 [4077,] 4.744830e+03 0.00001756 -4.276e-17 [4078,] 4.757929e+03 0.00001751 -1.058e-16 [4079,] 4.771065e+03 0.00001747 -4.105e-17 [4080,] 4.784236e+03 0.00001742 -1.158e-16 [4081,] 4.797445e+03 0.00001737 -1.687e-16 [4082,] 4.810689e+03 0.00001732 6.829e-17 [4083,] 4.823970e+03 0.00001727 -6.768e-17 [4084,] 4.837288e+03 0.00001723 -5.583e-18 [4085,] 4.850643e+03 0.00001718 -1.494e-16 [4086,] 4.864034e+03 0.00001713 -1.535e-16 [4087,] 4.877463e+03 0.00001709 -1.776e-16 [4088,] 4.890929e+03 0.00001704 -1.214e-16 [4089,] 4.904431e+03 0.00001699 3.946e-18 [4090,] 4.917971e+03 0.00001694 4.615e-17 [4091,] 4.931549e+03 0.00001690 -5.954e-17 [4092,] 4.945164e+03 0.00001685 -9.589e-19 [4093,] 4.958816e+03 0.00001681 -1.529e-17 [4094,] 4.972506e+03 0.00001676 -6.325e-17 [4095,] 4.986234e+03 0.00001671 -7.555e-17 [4096,] 5.000000e+03 0.00001667 1.57e-17 > > showProc.time() Time (user system elapsed): 46.16 0.19 46.47 > > ## below, 7 "it's okay, but not perfect:" ===> need more terms in stirlerr() __or__ ?? > ## April 20: MM added more terms up to S10 > x <- sfsmisc::lseq(1, 7, length=2048) > system.time(stM <- DPQmpfr::stirlerrM(Rmpfr::mpfr(x,2048))) # 1.52 sec elapsed user system elapsed 22.81 0.00 22.84 > plot(x, stirlerr(x, use.halves=FALSE) - stM, type="l", log="x", main="absolute Error") > plot(x, stirlerr(x, use.halves=FALSE) / stM - 1, type="l", log="x", main="relative Error") > plot(x, abs(stirlerr(x, use.halves=FALSE) / stM - 1), type="l", log="xy",main="|relative Error|") > abline(h=c(1,2,4)*.Machine$double.eps, lty=3) > ## lgammacor() does *NOT* help, as it is *designed* for x >= 10! > lines(x, abs(lgammacor(x, 5) / stM - 1), col=2) > ## maybe look at it for x >= 9 or so ? > ## > ## ==> Need another chebyshev() or rational-approx. for x in [.1, 7] or so !! > > showProc.time() Time (user system elapsed): 23.47 0 23.49 > > > > > ###--------------- bd0() & ebd0() ------------------------------------------------------ > > > ## ebd0 constants: the column sums of "bd0_scale": log(n / 1024) for all these n > ## ---- according to the *comments* in the C code -- so here I test that at least the *sums* are correct > bd0.n <- c(2048,2032,2016,2001,1986,1971,1956,1942,1928,1913,1900,1886,1872,1859, + 1846,1833,1820,1808,1796,1783,1771,1759,1748,1736,1725,1713,1702,1691, + 1680,1670,1659,1649,1638,1628,1618,1608,1598,1589,1579,1570,1560,1551, + 1542,1533,1524,1515,1507,1498,1489,1481,1473,1464,1456,1448,1440,1432, + 1425,1417,1409,1402,1394,1387,1380,1372,1365,1358,1351,1344,1337,1331, + 1324,1317,1311,1304,1298,1291,1285,1279,1273,1266,1260,1254,1248,1242, + 1237,1231,1225,1219,1214,1208,1202,1197,1192,1186,1181,1176,1170,1165, + 1160,1155,1150,1145,1140,1135,1130,1125,1120,1116,1111,1106,1101,1097, + 1092,1088,1083,1079,1074,1070,1066,1061,1057,1053,1049,1044,1040,1036, + 1032,1028,1024) > > stopifnot( + all.equal(bd0.n, + 1024 * exp(colSums(DPQ:::logf_mat))) + ) ## on lynne (64-bit, Fedora 32, 2021) they are even *identical* > identical(bd0.n, 1024 * exp(colSums(DPQ:::logf_mat))) # amazingly to me [1] TRUE > > ## Also, the numbers themselves decrease monotonely, > ## their differences are close to, but *not* monotone: > diff(bd0.n) # -16 -16 -15 -15 -15 -15 -14 -14 -15 -13 -14 ... [1] -16 -16 -15 -15 -15 -15 -14 -14 -15 -13 -14 -14 -13 -13 -13 -13 -12 -12 [19] -13 -12 -12 -11 -12 -11 -12 -11 -11 -11 -10 -11 -10 -11 -10 -10 -10 -10 [37] -9 -10 -9 -10 -9 -9 -9 -9 -9 -8 -9 -9 -8 -8 -9 -8 -8 -8 [55] -8 -7 -8 -8 -7 -8 -7 -7 -8 -7 -7 -7 -7 -7 -6 -7 -7 -6 [73] -7 -6 -7 -6 -6 -6 -7 -6 -6 -6 -6 -5 -6 -6 -6 -5 -6 -6 [91] -5 -5 -6 -5 -5 -6 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -4 -5 [109] -5 -5 -4 -5 -4 -5 -4 -5 -4 -4 -5 -4 -4 -4 -5 -4 -4 -4 [127] -4 -4 > # ^^^^^^^^^^^^^^ (etc) > > if(do.pdf) { dev.off(); pdf("diff-bd0_tab.pdf") } > > plot(diff(bd0.n), type="b") > c2 <- adjustcolor(2, 1/2) > par(new=TRUE) > plot(diff(bd0.n, differences = 2), type="b", col=c2, axes=FALSE, ann=FALSE) > axis(4, at=-1:2, col=c2, col.axis=c2) > > showProc.time() Time (user system elapsed): 0.01 0 0.02 > > ## close to over-/underflow ------- > > ### Large lambda == np == M ------- > > if(do.pdf) { dev.off(); pdf("stirlerr-bd0-ebd0.pdf") } > ##-- FIXME: use functionality from ~/R/MM/NUMERICS/dpq-functions/15628-dpois_raw_accuracy.R > ##-- ----- *or* move to vignette > > LL <- 1e20 > dput(x1 <- 1e20 - 2e11) # 9.99999998e+19 9.99999998e+19 > > (P1 <- dpois (x1, LL)) # was 3.989455e-11; now 5.520993e-98 [1] 5.520993e-98 > (P1m <- Rmpfr::dpois(mpfr(x1, 128), LL)) # 5.52099285934214335003128935..e-98 1 'mpfr' number of precision 128 bits [1] 5.520992859342143350031289352677120249641e-98 > ## However -- the ebd0() version > (P1e <- dpois_raw(x1, LL, version="ebd0_v1")) [1] 5.520993e-98 > ## was 3.989455e-11, but now good! > stopifnot(exprs = { + all.equal(P1 , 5.520992859342e-98, tol=1e-12) + all.equal(P1e, P1, tol=1e-12) + all.equal(P1m, P1, tol=1e-12) + }) > > options(digits=9) > > ## indeed: regular bd0() works "ok" --- but ebd0() does non-sense !! > (bd.1 <- bd0(x1, LL, verbose=2)) bd0(1e+20, 1e+20): T.series w/ 2 terms -> bd0=200 [1] 199.999992 > ## bd0(1e+20, 1e+20): T.series w/ 2 terms -> bd0=200 > ## [1] 200 > (bd.1M <- bd0(x1, mpfr(LL, 128), verbose=2)) bd0(1e+20, 1e+20): T.series w/ 3 terms -> bd0=200 1 'mpfr' number of precision 128 bits [1] 199.9999919413334091607468236761591740489 > ## bd0(1e+20, 1e+20): T.series w/ 3 terms -> bd0=200 > ## ---> 199.9999919413334091607468236761591740489 > asNumeric(bd.1 / bd.1M - 1)# -1.82e-17 -- suggests bd0() is really accurate here [1] -1.8200191e-17 > stopifnot(abs(bd.1 / bd.1M - 1) < 3e-16, + all.equal(199.999991941333, bd.1, tol=1e-14)) > > ebd0(x1, LL, verbose=TRUE)# fixed since June 6, 2021 ebd0(x=1e+20, M=1e+20): M/x = (r=0.500000001) * 2^(e=1); i=0, f=2048, fg=f*2^-(e+10)=1 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = 1.99999996304e-09 1a. before adding -x * log1pmx(.) = -x * -2e-18 = 200 1. after A.(-x*l..): yl,yh = ( -8.05867e-06, 200); yl+yh= 200 ___ fg = 1 ___ skipping further steps [,1] yh 2.00000000e+02 yl -8.05866662e-06 > > showProc.time() Time (user system elapsed): 0.06 0 0.06 > > ### Large x -- small np == M ------------------------------------ > > > mpfrPrec <- 1024 > mpfrPrec <- 256 > > yy <- bd0 (1e307, 10^(-5:1), verbose=TRUE) > yhl <- ebd0 (1e307, 10^(-5:1), verbose=TRUE) ebd0(x=1e+307, M=1e-05): M/x = (r=0.736335108038475) * 2^(e=-1036); i=61, f=1387, fg=f*2^-(e+10)=Inf --> fg = +Inf --> return( +Inf ) ebd0(x=1e+307, M=0.0001): M/x = (r=0.920418885049457) * 2^(e=-1033); i=108, f=1111, fg=f*2^-(e+10)=Inf --> fg = +Inf --> return( +Inf ) ebd0(x=1e+307, M=0.001): M/x = (r=0.575261803155939) * 2^(e=-1029); i=19, f=1783, fg=f*2^-(e+10)=Inf --> fg = +Inf --> return( +Inf ) ebd0(x=1e+307, M=0.01): M/x = (r=0.719077253944928) * 2^(e=-1026); i=56, f=1425, fg=f*2^-(e+10)=Inf --> fg = +Inf --> return( +Inf ) ebd0(x=1e+307, M=0.1): M/x = (r=0.898846567431158) * 2^(e=-1023); i=102, f=1140, fg=f*2^-(e+10)=1.00067e+308 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.107312 -4.72853e-09 -4.29763e-16 5.35114e-24 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = 0.0006690301479688298 1a. before adding -x * log1pmx(.) = -x * -2.23701e-07 = 2.23701e+300 1. after A.(-x*l..): yl,yh = ( 0, 2.23701e+300); yl+yh= 2.23701e+300 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 1.07312e+306); ( NaN, Inf); yl+yh= NaN non-finite yh --> return((yh=Inf, yl=0)) ebd0(x=1e+307, M=1): M/x = (r=0.561779104644474) * 2^(e=-1019); i=16, f=1820, fg=f*2^-(e+10)=9.98475e+306 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419479548646 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( NaN, Inf); yl+yh= NaN non-finite yh --> return((yh=Inf, yl=0)) ebd0(x=1e+307, M=10): M/x = (r=0.702223880805592) * 2^(e=-1016); i=52, f=1456, fg=f*2^-(e+10)=9.98475e+305 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.351976 2.85039e-08 -9.56643e-16 -6.4096e-24 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419479548646 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 3.51978e+306); ( NaN, Inf); yl+yh= NaN non-finite yh --> return((yh=Inf, yl=0)) > yhlC<- ebd0C(1e307, 10^(-5:1)) > stopifnot(yy == Inf, colSums(yhl) == Inf, yhlC == yhl) > yM <- bd0(mpfr(1e307, mpfrPrec), 10^(-5:1)) > roundMpfr(range(yM), 12) ## 7.0363e+309 7.1739e+309 -- *are* larger than DBL_MAX 2 'mpfr' numbers of precision 12 bits [1] 7.0363e+309 7.1739e+309 > > > ### Now *BOTH* x and lambda are large : --------------------------------------- > ## (FIXME?? Small loss for ebd0, see below) <<< ??? > ## is bd0(, *) really accurate ??? > ## it uses it's own convergent series approxmation for |x-np| < .. ???? > > x. <- 1e307 > ebd0(x., 10^(300:308)) [,1] [,2] [,3] [,4] yh 1.51180958e+308 1.28155116e+308 1.05129355e+308 8.21044037e+307 yl 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00 [,5] [,6] [,7] [,8] [,9] yh 5.90875528e+307 3.61517019e+307 1.40258509e+307 0 6.69741491e+307 yl 0.00000000e+00 0.00000000e+00 0.00000000e+00 0 0.00000000e+00 > > stopifnot(is.finite(Llam <- 2^(990:1024 - 1e-12))) > > bd0ver <- function(x, np, mpfrPrec, chkVerb=TRUE, keepMpfr=FALSE) { + stopifnot(length(mpfrPrec <- as.integer(mpfrPrec)) == 1, + !is.na(mpfrPrec), mpfrPrec >= 64, + x >= 0, np >= 0) + yy <- bd0 (x, np) + yhl <- ebd0 (x, np) + yhlC <- ebd0C(x, np) + if(chkVerb) { + yhl. <- ebd0 (x, np, verbose=TRUE) + yhlC. <- ebd0C(x, np, verbose=TRUE) + stopifnot(identical(yhl., yhl), + identical(yhlC., yhlC)) + } + epsC <- .Machine$double.eps + aeq0 <- all.equal(yhl, yhlC, tol = 0) + aeq4 <- all.equal(yhl, yhlC, tol = 4*epsC) + if(!isTRUE(aeq4)) warning("the C and R versions of ebd0() differ:", aeq4) + stopifnot(is.whole(yhl ["yh",]), + is.whole(yhlC["yh",])) + yM <- bd0(mpfr(x, mpfrPrec), + mpfr(np,mpfrPrec), verbose=chkVerb)# more accurate ! (?? always ??) + relE <- relErrV(target = yM, # the mpfr one + cbind(ebd0 = yhl ["yh",] + yhl ["yl",], + ebd0C= yhlC["yh",] + yhlC["yl",], + bd0 = yy)) + relE <- structure(asNumeric(relE), dim=dim(relE), dimnames=dimnames(relE)) + ## return: + list(x=x, np=np, bd0=yy, ebd0=yhl, ebd0C=yhlC, + bd0M=if(keepMpfr) yM, # <- expensive + aeq0=aeq0, aeq4=aeq4, relE = relE) + } > > bd0v.8 <- bd0ver(x., Llam, mpfrPrec = 256) ebd0(x=1e+307, M=1.0464e+298): M/x = (r=0.561779104644075) * 2^(e=-29); i=16, f=1820, fg=f*2^-(e+10)=9.54204e+08 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( NaN, Inf); yl+yh= NaN non-finite yh --> return((yh=Inf, yl=0)) ebd0(x=1e+307, M=2.09279e+298): M/x = (r=0.561779104644075) * 2^(e=-28); i=16, f=1820, fg=f*2^-(e+10)=4.77102e+08 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( NaN, Inf); yl+yh= NaN non-finite yh --> return((yh=Inf, yl=0)) ebd0(x=1e+307, M=4.18558e+298): M/x = (r=0.561779104644075) * 2^(e=-27); i=16, f=1820, fg=f*2^-(e+10)=2.38551e+08 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( NaN, Inf); yl+yh= NaN non-finite yh --> return((yh=Inf, yl=0)) ebd0(x=1e+307, M=8.37116e+298): M/x = (r=0.561779104644075) * 2^(e=-26); i=16, f=1820, fg=f*2^-(e+10)=1.19276e+08 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( NaN, Inf); yl+yh= NaN non-finite yh --> return((yh=Inf, yl=0)) ebd0(x=1e+307, M=1.67423e+299): M/x = (r=0.561779104644075) * 2^(e=-25); i=16, f=1820, fg=f*2^-(e+10)=5.96378e+07 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 1.79038e+308); yl+yh= 1.79038e+308 j=2: ( 0, 1.79038e+308); ( 0, 1.79038e+308); yl+yh= 1.79038e+308 j=3: ( 0, 1.79038e+308); ( 0, 1.79038e+308); yl+yh= 1.79038e+308 j=4: ( 0, 1.79038e+308); ( 0, 1.79038e+308); yl+yh= 1.79038e+308 3. after ADD1(M): yl,yh = ( 0, 1.79038e+308); yl+yh= 1.79038e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.69053e+308); yl+yh= 1.69053e+308 ebd0(x=1e+307, M=3.34846e+299): M/x = (r=0.561779104644075) * 2^(e=-24); i=16, f=1820, fg=f*2^-(e+10)=2.98189e+07 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 1.72107e+308); yl+yh= 1.72107e+308 j=2: ( 0, 1.72107e+308); ( 0, 1.72107e+308); yl+yh= 1.72107e+308 j=3: ( 0, 1.72107e+308); ( 0, 1.72107e+308); yl+yh= 1.72107e+308 j=4: ( 0, 1.72107e+308); ( 0, 1.72107e+308); yl+yh= 1.72107e+308 3. after ADD1(M): yl,yh = ( 0, 1.72107e+308); yl+yh= 1.72107e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.62122e+308); yl+yh= 1.62122e+308 ebd0(x=1e+307, M=6.69693e+299): M/x = (r=0.561779104644075) * 2^(e=-23); i=16, f=1820, fg=f*2^-(e+10)=1.49094e+07 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 1.65175e+308); yl+yh= 1.65175e+308 j=2: ( 0, 1.65175e+308); ( 0, 1.65175e+308); yl+yh= 1.65175e+308 j=3: ( 0, 1.65175e+308); ( 0, 1.65175e+308); yl+yh= 1.65175e+308 j=4: ( 0, 1.65175e+308); ( 0, 1.65175e+308); yl+yh= 1.65175e+308 3. after ADD1(M): yl,yh = ( 0, 1.65175e+308); yl+yh= 1.65175e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.5519e+308); yl+yh= 1.5519e+308 ebd0(x=1e+307, M=1.33939e+300): M/x = (r=0.561779104644075) * 2^(e=-22); i=16, f=1820, fg=f*2^-(e+10)=7.45472e+06 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 1.58244e+308); yl+yh= 1.58244e+308 j=2: ( 0, 1.58244e+308); ( 0, 1.58244e+308); yl+yh= 1.58244e+308 j=3: ( 0, 1.58244e+308); ( 0, 1.58244e+308); yl+yh= 1.58244e+308 j=4: ( 0, 1.58244e+308); ( 0, 1.58244e+308); yl+yh= 1.58244e+308 3. after ADD1(M): yl,yh = ( 0, 1.58244e+308); yl+yh= 1.58244e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.48259e+308); yl+yh= 1.48259e+308 ebd0(x=1e+307, M=2.67877e+300): M/x = (r=0.561779104644075) * 2^(e=-21); i=16, f=1820, fg=f*2^-(e+10)=3.72736e+06 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 1.51312e+308); yl+yh= 1.51312e+308 j=2: ( 0, 1.51312e+308); ( 0, 1.51312e+308); yl+yh= 1.51312e+308 j=3: ( 0, 1.51312e+308); ( 0, 1.51312e+308); yl+yh= 1.51312e+308 j=4: ( 0, 1.51312e+308); ( 0, 1.51312e+308); yl+yh= 1.51312e+308 3. after ADD1(M): yl,yh = ( 0, 1.51312e+308); yl+yh= 1.51312e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.41327e+308); yl+yh= 1.41327e+308 ebd0(x=1e+307, M=5.35754e+300): M/x = (r=0.561779104644075) * 2^(e=-20); i=16, f=1820, fg=f*2^-(e+10)=1.86368e+06 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 1.44381e+308); yl+yh= 1.44381e+308 j=2: ( 0, 1.44381e+308); ( 0, 1.44381e+308); yl+yh= 1.44381e+308 j=3: ( 0, 1.44381e+308); ( 0, 1.44381e+308); yl+yh= 1.44381e+308 j=4: ( 0, 1.44381e+308); ( 0, 1.44381e+308); yl+yh= 1.44381e+308 3. after ADD1(M): yl,yh = ( 0, 1.44381e+308); yl+yh= 1.44381e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.34396e+308); yl+yh= 1.34396e+308 ebd0(x=1e+307, M=1.07151e+301): M/x = (r=0.561779104644075) * 2^(e=-19); i=16, f=1820, fg=f*2^-(e+10)=931840 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 1.37449e+308); yl+yh= 1.37449e+308 j=2: ( 0, 1.37449e+308); ( 0, 1.37449e+308); yl+yh= 1.37449e+308 j=3: ( 0, 1.37449e+308); ( 0, 1.37449e+308); yl+yh= 1.37449e+308 j=4: ( 0, 1.37449e+308); ( 0, 1.37449e+308); yl+yh= 1.37449e+308 3. after ADD1(M): yl,yh = ( 0, 1.37449e+308); yl+yh= 1.37449e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.27464e+308); yl+yh= 1.27464e+308 ebd0(x=1e+307, M=2.14302e+301): M/x = (r=0.561779104644075) * 2^(e=-18); i=16, f=1820, fg=f*2^-(e+10)=465920 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 1.30518e+308); yl+yh= 1.30518e+308 j=2: ( 0, 1.30518e+308); ( 0, 1.30518e+308); yl+yh= 1.30518e+308 j=3: ( 0, 1.30518e+308); ( 0, 1.30518e+308); yl+yh= 1.30518e+308 j=4: ( 0, 1.30518e+308); ( 0, 1.30518e+308); yl+yh= 1.30518e+308 3. after ADD1(M): yl,yh = ( 0, 1.30518e+308); yl+yh= 1.30518e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.20533e+308); yl+yh= 1.20533e+308 ebd0(x=1e+307, M=4.28603e+301): M/x = (r=0.561779104644075) * 2^(e=-17); i=16, f=1820, fg=f*2^-(e+10)=232960 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 1.23586e+308); yl+yh= 1.23586e+308 j=2: ( 0, 1.23586e+308); ( 0, 1.23586e+308); yl+yh= 1.23586e+308 j=3: ( 0, 1.23586e+308); ( 0, 1.23586e+308); yl+yh= 1.23586e+308 j=4: ( 0, 1.23586e+308); ( 0, 1.23586e+308); yl+yh= 1.23586e+308 3. after ADD1(M): yl,yh = ( 0, 1.23586e+308); yl+yh= 1.23586e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.13602e+308); yl+yh= 1.13602e+308 ebd0(x=1e+307, M=8.57207e+301): M/x = (r=0.561779104644075) * 2^(e=-16); i=16, f=1820, fg=f*2^-(e+10)=116480 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 1.16655e+308); yl+yh= 1.16655e+308 j=2: ( 0, 1.16655e+308); ( 0, 1.16655e+308); yl+yh= 1.16655e+308 j=3: ( 0, 1.16655e+308); ( 0, 1.16655e+308); yl+yh= 1.16655e+308 j=4: ( 0, 1.16655e+308); ( 0, 1.16655e+308); yl+yh= 1.16655e+308 3. after ADD1(M): yl,yh = ( 0, 1.16655e+308); yl+yh= 1.16655e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.0667e+308); yl+yh= 1.0667e+308 ebd0(x=1e+307, M=1.71441e+302): M/x = (r=0.561779104644075) * 2^(e=-15); i=16, f=1820, fg=f*2^-(e+10)=58240 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 1.09723e+308); yl+yh= 1.09723e+308 j=2: ( 0, 1.09723e+308); ( 0, 1.09723e+308); yl+yh= 1.09723e+308 j=3: ( 0, 1.09723e+308); ( 0, 1.09723e+308); yl+yh= 1.09723e+308 j=4: ( 0, 1.09723e+308); ( 0, 1.09723e+308); yl+yh= 1.09723e+308 3. after ADD1(M): yl,yh = ( 0, 1.09723e+308); yl+yh= 1.09723e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 9.97387e+307); yl+yh= 9.97387e+307 ebd0(x=1e+307, M=3.42883e+302): M/x = (r=0.561779104644075) * 2^(e=-14); i=16, f=1820, fg=f*2^-(e+10)=29120 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 1.02792e+308); yl+yh= 1.02792e+308 j=2: ( 0, 1.02792e+308); ( 0, 1.02792e+308); yl+yh= 1.02792e+308 j=3: ( 0, 1.02792e+308); ( 0, 1.02792e+308); yl+yh= 1.02792e+308 j=4: ( 0, 1.02792e+308); ( 0, 1.02792e+308); yl+yh= 1.02792e+308 3. after ADD1(M): yl,yh = ( 0, 1.02792e+308); yl+yh= 1.02792e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 9.28074e+307); yl+yh= 9.28074e+307 ebd0(x=1e+307, M=6.85766e+302): M/x = (r=0.561779104644075) * 2^(e=-13); i=16, f=1820, fg=f*2^-(e+10)=14560 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 9.58603e+307); yl+yh= 9.58603e+307 j=2: ( 0, 9.58603e+307); ( 0, 9.58603e+307); yl+yh= 9.58603e+307 j=3: ( 0, 9.58603e+307); ( 0, 9.58603e+307); yl+yh= 9.58603e+307 j=4: ( 0, 9.58603e+307); ( 0, 9.58603e+307); yl+yh= 9.58603e+307 3. after ADD1(M): yl,yh = ( 0, 9.5861e+307); yl+yh= 9.5861e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 8.58763e+307); yl+yh= 8.58763e+307 ebd0(x=1e+307, M=1.37153e+303): M/x = (r=0.561779104644075) * 2^(e=-12); i=16, f=1820, fg=f*2^-(e+10)=7280 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 8.89289e+307); yl+yh= 8.89289e+307 j=2: ( 0, 8.89289e+307); ( 0, 8.89289e+307); yl+yh= 8.89289e+307 j=3: ( 0, 8.89289e+307); ( 0, 8.89289e+307); yl+yh= 8.89289e+307 j=4: ( 0, 8.89289e+307); ( 0, 8.89289e+307); yl+yh= 8.89289e+307 3. after ADD1(M): yl,yh = ( 0, 8.89302e+307); yl+yh= 8.89302e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 7.89455e+307); yl+yh= 7.89455e+307 ebd0(x=1e+307, M=2.74306e+303): M/x = (r=0.561779104644075) * 2^(e=-11); i=16, f=1820, fg=f*2^-(e+10)=3640 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 8.19974e+307); yl+yh= 8.19974e+307 j=2: ( 0, 8.19974e+307); ( 0, 8.19974e+307); yl+yh= 8.19974e+307 j=3: ( 0, 8.19974e+307); ( 0, 8.19974e+307); yl+yh= 8.19974e+307 j=4: ( 0, 8.19974e+307); ( 0, 8.19974e+307); yl+yh= 8.19974e+307 3. after ADD1(M): yl,yh = ( 0, 8.20001e+307); yl+yh= 8.20001e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 7.20154e+307); yl+yh= 7.20154e+307 ebd0(x=1e+307, M=5.48612e+303): M/x = (r=0.561779104644075) * 2^(e=-10); i=16, f=1820, fg=f*2^-(e+10)=1820 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 7.50659e+307); yl+yh= 7.50659e+307 j=2: ( 0, 7.50659e+307); ( 0, 7.50659e+307); yl+yh= 7.50659e+307 j=3: ( 0, 7.50659e+307); ( 0, 7.50659e+307); yl+yh= 7.50659e+307 j=4: ( 0, 7.50659e+307); ( 0, 7.50659e+307); yl+yh= 7.50659e+307 3. after ADD1(M): yl,yh = ( 0, 7.50714e+307); yl+yh= 7.50714e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 6.50867e+307); yl+yh= 6.50867e+307 ebd0(x=1e+307, M=1.09722e+304): M/x = (r=0.561779104644075) * 2^(e=-9); i=16, f=1820, fg=f*2^-(e+10)=910 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 6.81345e+307); yl+yh= 6.81345e+307 j=2: ( 0, 6.81345e+307); ( 0, 6.81345e+307); yl+yh= 6.81345e+307 j=3: ( 0, 6.81345e+307); ( 0, 6.81345e+307); yl+yh= 6.81345e+307 j=4: ( 0, 6.81345e+307); ( 0, 6.81345e+307); yl+yh= 6.81345e+307 3. after ADD1(M): yl,yh = ( 0, 6.81454e+307); yl+yh= 6.81454e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 5.81607e+307); yl+yh= 5.81607e+307 ebd0(x=1e+307, M=2.19445e+304): M/x = (r=0.561779104644075) * 2^(e=-8); i=16, f=1820, fg=f*2^-(e+10)=455 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 6.1203e+307); yl+yh= 6.1203e+307 j=2: ( 0, 6.1203e+307); ( 0, 6.1203e+307); yl+yh= 6.1203e+307 j=3: ( 0, 6.1203e+307); ( 0, 6.1203e+307); yl+yh= 6.1203e+307 j=4: ( 0, 6.1203e+307); ( 0, 6.1203e+307); yl+yh= 6.1203e+307 3. after ADD1(M): yl,yh = ( 0, 6.12249e+307); yl+yh= 6.12249e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 5.12402e+307); yl+yh= 5.12402e+307 ebd0(x=1e+307, M=4.3889e+304): M/x = (r=0.561779104644075) * 2^(e=-7); i=16, f=1820, fg=f*2^-(e+10)=227.5 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 5.42715e+307); yl+yh= 5.42715e+307 j=2: ( 0, 5.42715e+307); ( 0, 5.42715e+307); yl+yh= 5.42715e+307 j=3: ( 0, 5.42715e+307); ( 0, 5.42715e+307); yl+yh= 5.42715e+307 j=4: ( 0, 5.42715e+307); ( 0, 5.42715e+307); yl+yh= 5.42715e+307 3. after ADD1(M): yl,yh = ( 0, 5.43154e+307); yl+yh= 5.43154e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 4.43307e+307); yl+yh= 4.43307e+307 ebd0(x=1e+307, M=8.7778e+304): M/x = (r=0.561779104644075) * 2^(e=-6); i=16, f=1820, fg=f*2^-(e+10)=113.75 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 4.734e+307); yl+yh= 4.734e+307 j=2: ( 0, 4.734e+307); ( 0, 4.734e+307); yl+yh= 4.734e+307 j=3: ( 0, 4.734e+307); ( 0, 4.734e+307); yl+yh= 4.734e+307 j=4: ( 0, 4.734e+307); ( 0, 4.734e+307); yl+yh= 4.734e+307 3. after ADD1(M): yl,yh = ( 0, 4.74278e+307); yl+yh= 4.74278e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 3.74431e+307); yl+yh= 3.74431e+307 ebd0(x=1e+307, M=1.75556e+305): M/x = (r=0.561779104644075) * 2^(e=-5); i=16, f=1820, fg=f*2^-(e+10)=56.875 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 4.04086e+307); yl+yh= 4.04086e+307 j=2: ( 0, 4.04086e+307); ( 0, 4.04086e+307); yl+yh= 4.04086e+307 j=3: ( 0, 4.04086e+307); ( 0, 4.04086e+307); yl+yh= 4.04086e+307 j=4: ( 0, 4.04086e+307); ( 0, 4.04086e+307); yl+yh= 4.04086e+307 3. after ADD1(M): yl,yh = ( 0, 4.05841e+307); yl+yh= 4.05841e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 3.05994e+307); yl+yh= 3.05994e+307 ebd0(x=1e+307, M=3.51112e+305): M/x = (r=0.561779104644075) * 2^(e=-4); i=16, f=1820, fg=f*2^-(e+10)=28.4375 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 3.34771e+307); yl+yh= 3.34771e+307 j=2: ( 0, 3.34771e+307); ( 0, 3.34771e+307); yl+yh= 3.34771e+307 j=3: ( 0, 3.34771e+307); ( 0, 3.34771e+307); yl+yh= 3.34771e+307 j=4: ( 0, 3.34771e+307); ( 0, 3.34771e+307); yl+yh= 3.34771e+307 3. after ADD1(M): yl,yh = ( 0, 3.38282e+307); yl+yh= 3.38282e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 2.38435e+307); yl+yh= 2.38435e+307 ebd0(x=1e+307, M=7.02224e+305): M/x = (r=0.561779104644075) * 2^(e=-3); i=16, f=1820, fg=f*2^-(e+10)=14.2188 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 2.65456e+307); yl+yh= 2.65456e+307 j=2: ( 0, 2.65456e+307); ( 0, 2.65456e+307); yl+yh= 2.65456e+307 j=3: ( 0, 2.65456e+307); ( 0, 2.65456e+307); yl+yh= 2.65456e+307 j=4: ( 0, 2.65456e+307); ( 0, 2.65456e+307); yl+yh= 2.65456e+307 3. after ADD1(M): yl,yh = ( 0, 2.72479e+307); yl+yh= 2.72479e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 1.72631e+307); yl+yh= 1.72631e+307 ebd0(x=1e+307, M=1.40445e+306): M/x = (r=0.561779104644075) * 2^(e=-2); i=16, f=1820, fg=f*2^-(e+10)=7.10938 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 1.96142e+307); yl+yh= 1.96142e+307 j=2: ( 0, 1.96142e+307); ( 0, 1.96142e+307); yl+yh= 1.96142e+307 j=3: ( 0, 1.96142e+307); ( 0, 1.96142e+307); yl+yh= 1.96142e+307 j=4: ( 0, 1.96142e+307); ( 0, 1.96142e+307); yl+yh= 1.96142e+307 3. after ADD1(M): yl,yh = ( 0, 2.10186e+307); yl+yh= 2.10186e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 1.10339e+307); yl+yh= 1.10339e+307 ebd0(x=1e+307, M=2.8089e+306): M/x = (r=0.561779104644075) * 2^(e=-1); i=16, f=1820, fg=f*2^-(e+10)=3.55469 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 1.26827e+307); yl+yh= 1.26827e+307 j=2: ( 0, 1.26827e+307); ( 0, 1.26827e+307); yl+yh= 1.26827e+307 j=3: ( 0, 1.26827e+307); ( 0, 1.26827e+307); yl+yh= 1.26827e+307 j=4: ( 0, 1.26827e+307); ( 0, 1.26827e+307); yl+yh= 1.26827e+307 3. after ADD1(M): yl,yh = ( 0, 1.54916e+307); yl+yh= 1.54916e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 5.50683e+306); yl+yh= 5.50683e+306 ebd0(x=1e+307, M=5.61779e+306): M/x = (r=0.561779104644075) * 2^(e=0); i=16, f=1820, fg=f*2^-(e+10)=1.77734 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 5.75121e+306); yl+yh= 5.75121e+306 j=2: ( 0, 5.75121e+306); ( 0, 5.75121e+306); yl+yh= 5.75121e+306 j=3: ( 0, 5.75121e+306); ( 0, 5.75121e+306); yl+yh= 5.75121e+306 j=4: ( 0, 5.75121e+306); ( 0, 5.75121e+306); yl+yh= 5.75121e+306 3. after ADD1(M): yl,yh = ( 0, 1.1369e+307); yl+yh= 1.1369e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 1.38426e+306); yl+yh= 1.38426e+306 ebd0(x=1e+307, M=1.12356e+307): M/x = (r=0.561779104644075) * 2^(e=1); i=16, f=1820, fg=f*2^-(e+10)=0.888672 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, -1.18026e+306); yl+yh= -1.18026e+306 j=2: ( 0, -1.18026e+306); ( 0, -1.18026e+306); yl+yh= -1.18026e+306 j=3: ( 0, -1.18026e+306); ( 0, -1.18026e+306); yl+yh= -1.18026e+306 j=4: ( 0, -1.18026e+306); ( 0, -1.18026e+306); yl+yh= -1.18026e+306 3. after ADD1(M): yl,yh = ( 0, 1.00553e+307); yl+yh= 1.00553e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 7.05759e+304); yl+yh= 7.05759e+304 ebd0(x=1e+307, M=2.24712e+307): M/x = (r=0.561779104644075) * 2^(e=2); i=16, f=1820, fg=f*2^-(e+10)=0.444336 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, -8.11173e+306); yl+yh= -8.11173e+306 j=2: ( 0, -8.11173e+306); ( 0, -8.11173e+306); yl+yh= -8.11173e+306 j=3: ( 0, -8.11173e+306); ( 0, -8.11173e+306); yl+yh= -8.11173e+306 j=4: ( 0, -8.11173e+306); ( 0, -8.11173e+306); yl+yh= -8.11173e+306 3. after ADD1(M): yl,yh = ( 0, 1.43594e+307); yl+yh= 1.43594e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 4.37469e+306); yl+yh= 4.37469e+306 ebd0(x=1e+307, M=4.49423e+307): M/x = (r=0.561779104644075) * 2^(e=3); i=16, f=1820, fg=f*2^-(e+10)=0.222168 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, -1.50432e+307); yl+yh= -1.50432e+307 j=2: ( 0, -1.50432e+307); ( 0, -1.50432e+307); yl+yh= -1.50432e+307 j=3: ( 0, -1.50432e+307); ( 0, -1.50432e+307); yl+yh= -1.50432e+307 j=4: ( 0, -1.50432e+307); ( 0, -1.50432e+307); yl+yh= -1.50432e+307 3. after ADD1(M): yl,yh = ( 0, 2.98991e+307); yl+yh= 2.98991e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 1.99144e+307); yl+yh= 1.99144e+307 ebd0(x=1e+307, M=8.98847e+307): M/x = (r=0.561779104644075) * 2^(e=4); i=16, f=1820, fg=f*2^-(e+10)=0.111084 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, -2.19747e+307); yl+yh= -2.19747e+307 j=2: ( 0, -2.19747e+307); ( 0, -2.19747e+307); yl+yh= -2.19747e+307 j=3: ( 0, -2.19747e+307); ( 0, -2.19747e+307); yl+yh= -2.19747e+307 j=4: ( 0, -2.19747e+307); ( 0, -2.19747e+307); yl+yh= -2.19747e+307 3. after ADD1(M): yl,yh = ( 0, 6.791e+307); yl+yh= 6.791e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 5.79252e+307); yl+yh= 5.79252e+307 ebd0(x=1e+307, M=1.79769e+308): M/x = (r=0.561779104644075) * 2^(e=5); i=16, f=1820, fg=f*2^-(e+10)=0.055542 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, -2.89061e+307); yl+yh= -2.89061e+307 j=2: ( 0, -2.89061e+307); ( 0, -2.89061e+307); yl+yh= -2.89061e+307 j=3: ( 0, -2.89061e+307); ( 0, -2.89061e+307); yl+yh= -2.89061e+307 j=4: ( 0, -2.89061e+307); ( 0, -2.89061e+307); yl+yh= -2.89061e+307 3. after ADD1(M): yl,yh = ( 0, 1.50863e+308); yl+yh= 1.50863e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.40878e+308); yl+yh= 1.40878e+308 dpq_ebd0(x[1:1], np[1:35], ... ): ebd0(x=1e+307, M=4.18558e+298): M/x = (r=0.561779104644075) * 2^(e=-27); i=16, f=1820, fg=f*2^-(e+10)=2.38551e+08 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( nan, inf); yl+yh= nan non-finite yh --> return((yh=Inf, yl=0)) ebd0(x=1e+307, M=8.37116e+298): M/x = (r=0.561779104644075) * 2^(e=-26); i=16, f=1820, fg=f*2^-(e+10)=1.19276e+08 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( nan, inf); yl+yh= nan non-finite yh --> return((yh=Inf, yl=0)) ebd0(x=1e+307, M=1.67423e+299): M/x = (r=0.561779104644075) * 2^(e=-25); i=16, f=1820, fg=f*2^-(e+10)=5.96378e+07 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 1.79038e+308); yl+yh= 1.79038e+308 j=1: ( 0, 1.79038e+308); ( 0, 1.79038e+308); yl+yh= 1.79038e+308 j=2: ( 0, 1.79038e+308); ( 0, 1.79038e+308); yl+yh= 1.79038e+308 j=3: ( 0, 1.79038e+308); ( 0, 1.79038e+308); yl+yh= 1.79038e+308 3. after ADD1(M): yl,yh = ( 0, 1.79038e+308); yl+yh= 1.79038e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.69053e+308); yl+yh= 1.69053e+308 ebd0(x=1e+307, M=3.34846e+299): M/x = (r=0.561779104644075) * 2^(e=-24); i=16, f=1820, fg=f*2^-(e+10)=2.98189e+07 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 1.72107e+308); yl+yh= 1.72107e+308 j=1: ( 0, 1.72107e+308); ( 0, 1.72107e+308); yl+yh= 1.72107e+308 j=2: ( 0, 1.72107e+308); ( 0, 1.72107e+308); yl+yh= 1.72107e+308 j=3: ( 0, 1.72107e+308); ( 0, 1.72107e+308); yl+yh= 1.72107e+308 3. after ADD1(M): yl,yh = ( 0, 1.72107e+308); yl+yh= 1.72107e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.62122e+308); yl+yh= 1.62122e+308 ebd0(x=1e+307, M=6.69693e+299): M/x = (r=0.561779104644075) * 2^(e=-23); i=16, f=1820, fg=f*2^-(e+10)=1.49094e+07 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 1.65175e+308); yl+yh= 1.65175e+308 j=1: ( 0, 1.65175e+308); ( 0, 1.65175e+308); yl+yh= 1.65175e+308 j=2: ( 0, 1.65175e+308); ( 0, 1.65175e+308); yl+yh= 1.65175e+308 j=3: ( 0, 1.65175e+308); ( 0, 1.65175e+308); yl+yh= 1.65175e+308 3. after ADD1(M): yl,yh = ( 0, 1.65175e+308); yl+yh= 1.65175e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.5519e+308); yl+yh= 1.5519e+308 ebd0(x=1e+307, M=1.33939e+300): M/x = (r=0.561779104644075) * 2^(e=-22); i=16, f=1820, fg=f*2^-(e+10)=7.45472e+06 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 1.58244e+308); yl+yh= 1.58244e+308 j=1: ( 0, 1.58244e+308); ( 0, 1.58244e+308); yl+yh= 1.58244e+308 j=2: ( 0, 1.58244e+308); ( 0, 1.58244e+308); yl+yh= 1.58244e+308 j=3: ( 0, 1.58244e+308); ( 0, 1.58244e+308); yl+yh= 1.58244e+308 3. after ADD1(M): yl,yh = ( 0, 1.58244e+308); yl+yh= 1.58244e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.48259e+308); yl+yh= 1.48259e+308 ebd0(x=1e+307, M=2.67877e+300): M/x = (r=0.561779104644075) * 2^(e=-21); i=16, f=1820, fg=f*2^-(e+10)=3.72736e+06 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 1.51312e+308); yl+yh= 1.51312e+308 j=1: ( 0, 1.51312e+308); ( 0, 1.51312e+308); yl+yh= 1.51312e+308 j=2: ( 0, 1.51312e+308); ( 0, 1.51312e+308); yl+yh= 1.51312e+308 j=3: ( 0, 1.51312e+308); ( 0, 1.51312e+308); yl+yh= 1.51312e+308 3. after ADD1(M): yl,yh = ( 0, 1.51312e+308); yl+yh= 1.51312e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.41327e+308); yl+yh= 1.41327e+308 ebd0(x=1e+307, M=5.35754e+300): M/x = (r=0.561779104644075) * 2^(e=-20); i=16, f=1820, fg=f*2^-(e+10)=1.86368e+06 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 1.44381e+308); yl+yh= 1.44381e+308 j=1: ( 0, 1.44381e+308); ( 0, 1.44381e+308); yl+yh= 1.44381e+308 j=2: ( 0, 1.44381e+308); ( 0, 1.44381e+308); yl+yh= 1.44381e+308 j=3: ( 0, 1.44381e+308); ( 0, 1.44381e+308); yl+yh= 1.44381e+308 3. after ADD1(M): yl,yh = ( 0, 1.44381e+308); yl+yh= 1.44381e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.34396e+308); yl+yh= 1.34396e+308 ebd0(x=1e+307, M=1.07151e+301): M/x = (r=0.561779104644075) * 2^(e=-19); i=16, f=1820, fg=f*2^-(e+10)=931840 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 1.37449e+308); yl+yh= 1.37449e+308 j=1: ( 0, 1.37449e+308); ( 0, 1.37449e+308); yl+yh= 1.37449e+308 j=2: ( 0, 1.37449e+308); ( 0, 1.37449e+308); yl+yh= 1.37449e+308 j=3: ( 0, 1.37449e+308); ( 0, 1.37449e+308); yl+yh= 1.37449e+308 3. after ADD1(M): yl,yh = ( 0, 1.37449e+308); yl+yh= 1.37449e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.27464e+308); yl+yh= 1.27464e+308 ebd0(x=1e+307, M=2.14302e+301): M/x = (r=0.561779104644075) * 2^(e=-18); i=16, f=1820, fg=f*2^-(e+10)=465920 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 1.30518e+308); yl+yh= 1.30518e+308 j=1: ( 0, 1.30518e+308); ( 0, 1.30518e+308); yl+yh= 1.30518e+308 j=2: ( 0, 1.30518e+308); ( 0, 1.30518e+308); yl+yh= 1.30518e+308 j=3: ( 0, 1.30518e+308); ( 0, 1.30518e+308); yl+yh= 1.30518e+308 3. after ADD1(M): yl,yh = ( 0, 1.30518e+308); yl+yh= 1.30518e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.20533e+308); yl+yh= 1.20533e+308 ebd0(x=1e+307, M=4.28603e+301): M/x = (r=0.561779104644075) * 2^(e=-17); i=16, f=1820, fg=f*2^-(e+10)=232960 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 1.23586e+308); yl+yh= 1.23586e+308 j=1: ( 0, 1.23586e+308); ( 0, 1.23586e+308); yl+yh= 1.23586e+308 j=2: ( 0, 1.23586e+308); ( 0, 1.23586e+308); yl+yh= 1.23586e+308 j=3: ( 0, 1.23586e+308); ( 0, 1.23586e+308); yl+yh= 1.23586e+308 3. after ADD1(M): yl,yh = ( 0, 1.23586e+308); yl+yh= 1.23586e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.13602e+308); yl+yh= 1.13602e+308 ebd0(x=1e+307, M=8.57207e+301): M/x = (r=0.561779104644075) * 2^(e=-16); i=16, f=1820, fg=f*2^-(e+10)=116480 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 1.16655e+308); yl+yh= 1.16655e+308 j=1: ( 0, 1.16655e+308); ( 0, 1.16655e+308); yl+yh= 1.16655e+308 j=2: ( 0, 1.16655e+308); ( 0, 1.16655e+308); yl+yh= 1.16655e+308 j=3: ( 0, 1.16655e+308); ( 0, 1.16655e+308); yl+yh= 1.16655e+308 3. after ADD1(M): yl,yh = ( 0, 1.16655e+308); yl+yh= 1.16655e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.0667e+308); yl+yh= 1.0667e+308 ebd0(x=1e+307, M=1.71441e+302): M/x = (r=0.561779104644075) * 2^(e=-15); i=16, f=1820, fg=f*2^-(e+10)=58240 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 1.09723e+308); yl+yh= 1.09723e+308 j=1: ( 0, 1.09723e+308); ( 0, 1.09723e+308); yl+yh= 1.09723e+308 j=2: ( 0, 1.09723e+308); ( 0, 1.09723e+308); yl+yh= 1.09723e+308 j=3: ( 0, 1.09723e+308); ( 0, 1.09723e+308); yl+yh= 1.09723e+308 3. after ADD1(M): yl,yh = ( 0, 1.09723e+308); yl+yh= 1.09723e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 9.97387e+307); yl+yh= 9.97387e+307 ebd0(x=1e+307, M=3.42883e+302): M/x = (r=0.561779104644075) * 2^(e=-14); i=16, f=1820, fg=f*2^-(e+10)=29120 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 1.02792e+308); yl+yh= 1.02792e+308 j=1: ( 0, 1.02792e+308); ( 0, 1.02792e+308); yl+yh= 1.02792e+308 j=2: ( 0, 1.02792e+308); ( 0, 1.02792e+308); yl+yh= 1.02792e+308 j=3: ( 0, 1.02792e+308); ( 0, 1.02792e+308); yl+yh= 1.02792e+308 3. after ADD1(M): yl,yh = ( 0, 1.02792e+308); yl+yh= 1.02792e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 9.28074e+307); yl+yh= 9.28074e+307 ebd0(x=1e+307, M=6.85766e+302): M/x = (r=0.561779104644075) * 2^(e=-13); i=16, f=1820, fg=f*2^-(e+10)=14560 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 9.58603e+307); yl+yh= 9.58603e+307 j=1: ( 0, 9.58603e+307); ( 0, 9.58603e+307); yl+yh= 9.58603e+307 j=2: ( 0, 9.58603e+307); ( 0, 9.58603e+307); yl+yh= 9.58603e+307 j=3: ( 0, 9.58603e+307); ( 0, 9.58603e+307); yl+yh= 9.58603e+307 3. after ADD1(M): yl,yh = ( 0, 9.5861e+307); yl+yh= 9.5861e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 8.58763e+307); yl+yh= 8.58763e+307 ebd0(x=1e+307, M=1.37153e+303): M/x = (r=0.561779104644075) * 2^(e=-12); i=16, f=1820, fg=f*2^-(e+10)=7280 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 8.89289e+307); yl+yh= 8.89289e+307 j=1: ( 0, 8.89289e+307); ( 0, 8.89289e+307); yl+yh= 8.89289e+307 j=2: ( 0, 8.89289e+307); ( 0, 8.89289e+307); yl+yh= 8.89289e+307 j=3: ( 0, 8.89289e+307); ( 0, 8.89289e+307); yl+yh= 8.89289e+307 3. after ADD1(M): yl,yh = ( 0, 8.89302e+307); yl+yh= 8.89302e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 7.89455e+307); yl+yh= 7.89455e+307 ebd0(x=1e+307, M=2.74306e+303): M/x = (r=0.561779104644075) * 2^(e=-11); i=16, f=1820, fg=f*2^-(e+10)=3640 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 8.19974e+307); yl+yh= 8.19974e+307 j=1: ( 0, 8.19974e+307); ( 0, 8.19974e+307); yl+yh= 8.19974e+307 j=2: ( 0, 8.19974e+307); ( 0, 8.19974e+307); yl+yh= 8.19974e+307 j=3: ( 0, 8.19974e+307); ( 0, 8.19974e+307); yl+yh= 8.19974e+307 3. after ADD1(M): yl,yh = ( 0, 8.20001e+307); yl+yh= 8.20001e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 7.20154e+307); yl+yh= 7.20154e+307 ebd0(x=1e+307, M=5.48612e+303): M/x = (r=0.561779104644075) * 2^(e=-10); i=16, f=1820, fg=f*2^-(e+10)=1820 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 7.50659e+307); yl+yh= 7.50659e+307 j=1: ( 0, 7.50659e+307); ( 0, 7.50659e+307); yl+yh= 7.50659e+307 j=2: ( 0, 7.50659e+307); ( 0, 7.50659e+307); yl+yh= 7.50659e+307 j=3: ( 0, 7.50659e+307); ( 0, 7.50659e+307); yl+yh= 7.50659e+307 3. after ADD1(M): yl,yh = ( 0, 7.50714e+307); yl+yh= 7.50714e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 6.50867e+307); yl+yh= 6.50867e+307 ebd0(x=1e+307, M=1.09722e+304): M/x = (r=0.561779104644075) * 2^(e=-9); i=16, f=1820, fg=f*2^-(e+10)=910 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 6.81345e+307); yl+yh= 6.81345e+307 j=1: ( 0, 6.81345e+307); ( 0, 6.81345e+307); yl+yh= 6.81345e+307 j=2: ( 0, 6.81345e+307); ( 0, 6.81345e+307); yl+yh= 6.81345e+307 j=3: ( 0, 6.81345e+307); ( 0, 6.81345e+307); yl+yh= 6.81345e+307 3. after ADD1(M): yl,yh = ( 0, 6.81454e+307); yl+yh= 6.81454e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 5.81607e+307); yl+yh= 5.81607e+307 ebd0(x=1e+307, M=2.19445e+304): M/x = (r=0.561779104644075) * 2^(e=-8); i=16, f=1820, fg=f*2^-(e+10)=455 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 6.1203e+307); yl+yh= 6.1203e+307 j=1: ( 0, 6.1203e+307); ( 0, 6.1203e+307); yl+yh= 6.1203e+307 j=2: ( 0, 6.1203e+307); ( 0, 6.1203e+307); yl+yh= 6.1203e+307 j=3: ( 0, 6.1203e+307); ( 0, 6.1203e+307); yl+yh= 6.1203e+307 3. after ADD1(M): yl,yh = ( 0, 6.12249e+307); yl+yh= 6.12249e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 5.12402e+307); yl+yh= 5.12402e+307 ebd0(x=1e+307, M=4.3889e+304): M/x = (r=0.561779104644075) * 2^(e=-7); i=16, f=1820, fg=f*2^-(e+10)=227.5 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 5.42715e+307); yl+yh= 5.42715e+307 j=1: ( 0, 5.42715e+307); ( 0, 5.42715e+307); yl+yh= 5.42715e+307 j=2: ( 0, 5.42715e+307); ( 0, 5.42715e+307); yl+yh= 5.42715e+307 j=3: ( 0, 5.42715e+307); ( 0, 5.42715e+307); yl+yh= 5.42715e+307 3. after ADD1(M): yl,yh = ( 0, 5.43154e+307); yl+yh= 5.43154e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 4.43307e+307); yl+yh= 4.43307e+307 ebd0(x=1e+307, M=8.7778e+304): M/x = (r=0.561779104644075) * 2^(e=-6); i=16, f=1820, fg=f*2^-(e+10)=113.75 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 4.734e+307); yl+yh= 4.734e+307 j=1: ( 0, 4.734e+307); ( 0, 4.734e+307); yl+yh= 4.734e+307 j=2: ( 0, 4.734e+307); ( 0, 4.734e+307); yl+yh= 4.734e+307 j=3: ( 0, 4.734e+307); ( 0, 4.734e+307); yl+yh= 4.734e+307 3. after ADD1(M): yl,yh = ( 0, 4.74278e+307); yl+yh= 4.74278e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 3.74431e+307); yl+yh= 3.74431e+307 ebd0(x=1e+307, M=1.75556e+305): M/x = (r=0.561779104644075) * 2^(e=-5); i=16, f=1820, fg=f*2^-(e+10)=56.875 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 4.04086e+307); yl+yh= 4.04086e+307 j=1: ( 0, 4.04086e+307); ( 0, 4.04086e+307); yl+yh= 4.04086e+307 j=2: ( 0, 4.04086e+307); ( 0, 4.04086e+307); yl+yh= 4.04086e+307 j=3: ( 0, 4.04086e+307); ( 0, 4.04086e+307); yl+yh= 4.04086e+307 3. after ADD1(M): yl,yh = ( 0, 4.05841e+307); yl+yh= 4.05841e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 3.05994e+307); yl+yh= 3.05994e+307 ebd0(x=1e+307, M=3.51112e+305): M/x = (r=0.561779104644075) * 2^(e=-4); i=16, f=1820, fg=f*2^-(e+10)=28.4375 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 3.34771e+307); yl+yh= 3.34771e+307 j=1: ( 0, 3.34771e+307); ( 0, 3.34771e+307); yl+yh= 3.34771e+307 j=2: ( 0, 3.34771e+307); ( 0, 3.34771e+307); yl+yh= 3.34771e+307 j=3: ( 0, 3.34771e+307); ( 0, 3.34771e+307); yl+yh= 3.34771e+307 3. after ADD1(M): yl,yh = ( 0, 3.38282e+307); yl+yh= 3.38282e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 2.38435e+307); yl+yh= 2.38435e+307 ebd0(x=1e+307, M=7.02224e+305): M/x = (r=0.561779104644075) * 2^(e=-3); i=16, f=1820, fg=f*2^-(e+10)=14.2188 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 2.65456e+307); yl+yh= 2.65456e+307 j=1: ( 0, 2.65456e+307); ( 0, 2.65456e+307); yl+yh= 2.65456e+307 j=2: ( 0, 2.65456e+307); ( 0, 2.65456e+307); yl+yh= 2.65456e+307 j=3: ( 0, 2.65456e+307); ( 0, 2.65456e+307); yl+yh= 2.65456e+307 3. after ADD1(M): yl,yh = ( 0, 2.72479e+307); yl+yh= 2.72479e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 1.72631e+307); yl+yh= 1.72631e+307 ebd0(x=1e+307, M=1.40445e+306): M/x = (r=0.561779104644075) * 2^(e=-2); i=16, f=1820, fg=f*2^-(e+10)=7.10938 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 1.96142e+307); yl+yh= 1.96142e+307 j=1: ( 0, 1.96142e+307); ( 0, 1.96142e+307); yl+yh= 1.96142e+307 j=2: ( 0, 1.96142e+307); ( 0, 1.96142e+307); yl+yh= 1.96142e+307 j=3: ( 0, 1.96142e+307); ( 0, 1.96142e+307); yl+yh= 1.96142e+307 3. after ADD1(M): yl,yh = ( 0, 2.10186e+307); yl+yh= 2.10186e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 1.10339e+307); yl+yh= 1.10339e+307 ebd0(x=1e+307, M=2.8089e+306): M/x = (r=0.561779104644075) * 2^(e=-1); i=16, f=1820, fg=f*2^-(e+10)=3.55469 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 1.26827e+307); yl+yh= 1.26827e+307 j=1: ( 0, 1.26827e+307); ( 0, 1.26827e+307); yl+yh= 1.26827e+307 j=2: ( 0, 1.26827e+307); ( 0, 1.26827e+307); yl+yh= 1.26827e+307 j=3: ( 0, 1.26827e+307); ( 0, 1.26827e+307); yl+yh= 1.26827e+307 3. after ADD1(M): yl,yh = ( 0, 1.54916e+307); yl+yh= 1.54916e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 5.50683e+306); yl+yh= 5.50683e+306 ebd0(x=1e+307, M=5.61779e+306): M/x = (r=0.561779104644075) * 2^(e=0); i=16, f=1820, fg=f*2^-(e+10)=1.77734 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 5.75121e+306); yl+yh= 5.75121e+306 j=1: ( 0, 5.75121e+306); ( 0, 5.75121e+306); yl+yh= 5.75121e+306 j=2: ( 0, 5.75121e+306); ( 0, 5.75121e+306); yl+yh= 5.75121e+306 j=3: ( 0, 5.75121e+306); ( 0, 5.75121e+306); yl+yh= 5.75121e+306 3. after ADD1(M): yl,yh = ( 0, 1.1369e+307); yl+yh= 1.1369e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 1.38426e+306); yl+yh= 1.38426e+306 ebd0(x=1e+307, M=1.12356e+307): M/x = (r=0.561779104644075) * 2^(e=1); i=16, f=1820, fg=f*2^-(e+10)=0.888672 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, -1.18026e+306); yl+yh= -1.18026e+306 j=1: ( 0, -1.18026e+306); ( 0, -1.18026e+306); yl+yh= -1.18026e+306 j=2: ( 0, -1.18026e+306); ( 0, -1.18026e+306); yl+yh= -1.18026e+306 j=3: ( 0, -1.18026e+306); ( 0, -1.18026e+306); yl+yh= -1.18026e+306 3. after ADD1(M): yl,yh = ( 0, 1.00553e+307); yl+yh= 1.00553e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 7.05759e+304); yl+yh= 7.05759e+304 ebd0(x=1e+307, M=2.24712e+307): M/x = (r=0.561779104644075) * 2^(e=2); i=16, f=1820, fg=f*2^-(e+10)=0.444336 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, -8.11173e+306); yl+yh= -8.11173e+306 j=1: ( 0, -8.11173e+306); ( 0, -8.11173e+306); yl+yh= -8.11173e+306 j=2: ( 0, -8.11173e+306); ( 0, -8.11173e+306); yl+yh= -8.11173e+306 j=3: ( 0, -8.11173e+306); ( 0, -8.11173e+306); yl+yh= -8.11173e+306 3. after ADD1(M): yl,yh = ( 0, 1.43594e+307); yl+yh= 1.43594e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 4.37469e+306); yl+yh= 4.37469e+306 ebd0(x=1e+307, M=4.49423e+307): M/x = (r=0.561779104644075) * 2^(e=3); i=16, f=1820, fg=f*2^-(e+10)=0.222168 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, -1.50432e+307); yl+yh= -1.50432e+307 j=1: ( 0, -1.50432e+307); ( 0, -1.50432e+307); yl+yh= -1.50432e+307 j=2: ( 0, -1.50432e+307); ( 0, -1.50432e+307); yl+yh= -1.50432e+307 j=3: ( 0, -1.50432e+307); ( 0, -1.50432e+307); yl+yh= -1.50432e+307 3. after ADD1(M): yl,yh = ( 0, 2.98991e+307); yl+yh= 2.98991e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 1.99144e+307); yl+yh= 1.99144e+307 ebd0(x=1e+307, M=8.98847e+307): M/x = (r=0.561779104644075) * 2^(e=4); i=16, f=1820, fg=f*2^-(e+10)=0.111084 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, -2.19747e+307); yl+yh= -2.19747e+307 j=1: ( 0, -2.19747e+307); ( 0, -2.19747e+307); yl+yh= -2.19747e+307 j=2: ( 0, -2.19747e+307); ( 0, -2.19747e+307); yl+yh= -2.19747e+307 j=3: ( 0, -2.19747e+307); ( 0, -2.19747e+307); yl+yh= -2.19747e+307 3. after ADD1(M): yl,yh = ( 0, 6.791e+307); yl+yh= 6.791e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 5.79252e+307); yl+yh= 5.79252e+307 ebd0(x=1e+307, M=1.79769e+308): M/x = (r=0.561779104644075) * 2^(e=5); i=16, f=1820, fg=f*2^-(e+10)=0.055542 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, -2.89061e+307); yl+yh= -2.89061e+307 j=1: ( 0, -2.89061e+307); ( 0, -2.89061e+307); yl+yh= -2.89061e+307 j=2: ( 0, -2.89061e+307); ( 0, -2.89061e+307); yl+yh= -2.89061e+307 j=3: ( 0, -2.89061e+307); ( 0, -2.89061e+307); yl+yh= -2.89061e+307 3. after ADD1(M): yl,yh = ( 0, 1.50863e+308); yl+yh= 1.50863e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.40878e+308); yl+yh= 1.40878e+308 bd0(1e+307, 1.12356e+307): T.series w/ 32 terms -> bd0=7.05759e+304 > bd0v.10 <- bd0ver(x., Llam, mpfrPrec = 1024) ebd0(x=1e+307, M=1.0464e+298): M/x = (r=0.561779104644075) * 2^(e=-29); i=16, f=1820, fg=f*2^-(e+10)=9.54204e+08 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( NaN, Inf); yl+yh= NaN non-finite yh --> return((yh=Inf, yl=0)) ebd0(x=1e+307, M=2.09279e+298): M/x = (r=0.561779104644075) * 2^(e=-28); i=16, f=1820, fg=f*2^-(e+10)=4.77102e+08 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( NaN, Inf); yl+yh= NaN non-finite yh --> return((yh=Inf, yl=0)) ebd0(x=1e+307, M=4.18558e+298): M/x = (r=0.561779104644075) * 2^(e=-27); i=16, f=1820, fg=f*2^-(e+10)=2.38551e+08 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( NaN, Inf); yl+yh= NaN non-finite yh --> return((yh=Inf, yl=0)) ebd0(x=1e+307, M=8.37116e+298): M/x = (r=0.561779104644075) * 2^(e=-26); i=16, f=1820, fg=f*2^-(e+10)=1.19276e+08 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( NaN, Inf); yl+yh= NaN non-finite yh --> return((yh=Inf, yl=0)) ebd0(x=1e+307, M=1.67423e+299): M/x = (r=0.561779104644075) * 2^(e=-25); i=16, f=1820, fg=f*2^-(e+10)=5.96378e+07 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 1.79038e+308); yl+yh= 1.79038e+308 j=2: ( 0, 1.79038e+308); ( 0, 1.79038e+308); yl+yh= 1.79038e+308 j=3: ( 0, 1.79038e+308); ( 0, 1.79038e+308); yl+yh= 1.79038e+308 j=4: ( 0, 1.79038e+308); ( 0, 1.79038e+308); yl+yh= 1.79038e+308 3. after ADD1(M): yl,yh = ( 0, 1.79038e+308); yl+yh= 1.79038e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.69053e+308); yl+yh= 1.69053e+308 ebd0(x=1e+307, M=3.34846e+299): M/x = (r=0.561779104644075) * 2^(e=-24); i=16, f=1820, fg=f*2^-(e+10)=2.98189e+07 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 1.72107e+308); yl+yh= 1.72107e+308 j=2: ( 0, 1.72107e+308); ( 0, 1.72107e+308); yl+yh= 1.72107e+308 j=3: ( 0, 1.72107e+308); ( 0, 1.72107e+308); yl+yh= 1.72107e+308 j=4: ( 0, 1.72107e+308); ( 0, 1.72107e+308); yl+yh= 1.72107e+308 3. after ADD1(M): yl,yh = ( 0, 1.72107e+308); yl+yh= 1.72107e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.62122e+308); yl+yh= 1.62122e+308 ebd0(x=1e+307, M=6.69693e+299): M/x = (r=0.561779104644075) * 2^(e=-23); i=16, f=1820, fg=f*2^-(e+10)=1.49094e+07 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 1.65175e+308); yl+yh= 1.65175e+308 j=2: ( 0, 1.65175e+308); ( 0, 1.65175e+308); yl+yh= 1.65175e+308 j=3: ( 0, 1.65175e+308); ( 0, 1.65175e+308); yl+yh= 1.65175e+308 j=4: ( 0, 1.65175e+308); ( 0, 1.65175e+308); yl+yh= 1.65175e+308 3. after ADD1(M): yl,yh = ( 0, 1.65175e+308); yl+yh= 1.65175e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.5519e+308); yl+yh= 1.5519e+308 ebd0(x=1e+307, M=1.33939e+300): M/x = (r=0.561779104644075) * 2^(e=-22); i=16, f=1820, fg=f*2^-(e+10)=7.45472e+06 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 1.58244e+308); yl+yh= 1.58244e+308 j=2: ( 0, 1.58244e+308); ( 0, 1.58244e+308); yl+yh= 1.58244e+308 j=3: ( 0, 1.58244e+308); ( 0, 1.58244e+308); yl+yh= 1.58244e+308 j=4: ( 0, 1.58244e+308); ( 0, 1.58244e+308); yl+yh= 1.58244e+308 3. after ADD1(M): yl,yh = ( 0, 1.58244e+308); yl+yh= 1.58244e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.48259e+308); yl+yh= 1.48259e+308 ebd0(x=1e+307, M=2.67877e+300): M/x = (r=0.561779104644075) * 2^(e=-21); i=16, f=1820, fg=f*2^-(e+10)=3.72736e+06 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 1.51312e+308); yl+yh= 1.51312e+308 j=2: ( 0, 1.51312e+308); ( 0, 1.51312e+308); yl+yh= 1.51312e+308 j=3: ( 0, 1.51312e+308); ( 0, 1.51312e+308); yl+yh= 1.51312e+308 j=4: ( 0, 1.51312e+308); ( 0, 1.51312e+308); yl+yh= 1.51312e+308 3. after ADD1(M): yl,yh = ( 0, 1.51312e+308); yl+yh= 1.51312e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.41327e+308); yl+yh= 1.41327e+308 ebd0(x=1e+307, M=5.35754e+300): M/x = (r=0.561779104644075) * 2^(e=-20); i=16, f=1820, fg=f*2^-(e+10)=1.86368e+06 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 1.44381e+308); yl+yh= 1.44381e+308 j=2: ( 0, 1.44381e+308); ( 0, 1.44381e+308); yl+yh= 1.44381e+308 j=3: ( 0, 1.44381e+308); ( 0, 1.44381e+308); yl+yh= 1.44381e+308 j=4: ( 0, 1.44381e+308); ( 0, 1.44381e+308); yl+yh= 1.44381e+308 3. after ADD1(M): yl,yh = ( 0, 1.44381e+308); yl+yh= 1.44381e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.34396e+308); yl+yh= 1.34396e+308 ebd0(x=1e+307, M=1.07151e+301): M/x = (r=0.561779104644075) * 2^(e=-19); i=16, f=1820, fg=f*2^-(e+10)=931840 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 1.37449e+308); yl+yh= 1.37449e+308 j=2: ( 0, 1.37449e+308); ( 0, 1.37449e+308); yl+yh= 1.37449e+308 j=3: ( 0, 1.37449e+308); ( 0, 1.37449e+308); yl+yh= 1.37449e+308 j=4: ( 0, 1.37449e+308); ( 0, 1.37449e+308); yl+yh= 1.37449e+308 3. after ADD1(M): yl,yh = ( 0, 1.37449e+308); yl+yh= 1.37449e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.27464e+308); yl+yh= 1.27464e+308 ebd0(x=1e+307, M=2.14302e+301): M/x = (r=0.561779104644075) * 2^(e=-18); i=16, f=1820, fg=f*2^-(e+10)=465920 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 1.30518e+308); yl+yh= 1.30518e+308 j=2: ( 0, 1.30518e+308); ( 0, 1.30518e+308); yl+yh= 1.30518e+308 j=3: ( 0, 1.30518e+308); ( 0, 1.30518e+308); yl+yh= 1.30518e+308 j=4: ( 0, 1.30518e+308); ( 0, 1.30518e+308); yl+yh= 1.30518e+308 3. after ADD1(M): yl,yh = ( 0, 1.30518e+308); yl+yh= 1.30518e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.20533e+308); yl+yh= 1.20533e+308 ebd0(x=1e+307, M=4.28603e+301): M/x = (r=0.561779104644075) * 2^(e=-17); i=16, f=1820, fg=f*2^-(e+10)=232960 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 1.23586e+308); yl+yh= 1.23586e+308 j=2: ( 0, 1.23586e+308); ( 0, 1.23586e+308); yl+yh= 1.23586e+308 j=3: ( 0, 1.23586e+308); ( 0, 1.23586e+308); yl+yh= 1.23586e+308 j=4: ( 0, 1.23586e+308); ( 0, 1.23586e+308); yl+yh= 1.23586e+308 3. after ADD1(M): yl,yh = ( 0, 1.23586e+308); yl+yh= 1.23586e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.13602e+308); yl+yh= 1.13602e+308 ebd0(x=1e+307, M=8.57207e+301): M/x = (r=0.561779104644075) * 2^(e=-16); i=16, f=1820, fg=f*2^-(e+10)=116480 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 1.16655e+308); yl+yh= 1.16655e+308 j=2: ( 0, 1.16655e+308); ( 0, 1.16655e+308); yl+yh= 1.16655e+308 j=3: ( 0, 1.16655e+308); ( 0, 1.16655e+308); yl+yh= 1.16655e+308 j=4: ( 0, 1.16655e+308); ( 0, 1.16655e+308); yl+yh= 1.16655e+308 3. after ADD1(M): yl,yh = ( 0, 1.16655e+308); yl+yh= 1.16655e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.0667e+308); yl+yh= 1.0667e+308 ebd0(x=1e+307, M=1.71441e+302): M/x = (r=0.561779104644075) * 2^(e=-15); i=16, f=1820, fg=f*2^-(e+10)=58240 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 1.09723e+308); yl+yh= 1.09723e+308 j=2: ( 0, 1.09723e+308); ( 0, 1.09723e+308); yl+yh= 1.09723e+308 j=3: ( 0, 1.09723e+308); ( 0, 1.09723e+308); yl+yh= 1.09723e+308 j=4: ( 0, 1.09723e+308); ( 0, 1.09723e+308); yl+yh= 1.09723e+308 3. after ADD1(M): yl,yh = ( 0, 1.09723e+308); yl+yh= 1.09723e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 9.97387e+307); yl+yh= 9.97387e+307 ebd0(x=1e+307, M=3.42883e+302): M/x = (r=0.561779104644075) * 2^(e=-14); i=16, f=1820, fg=f*2^-(e+10)=29120 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 1.02792e+308); yl+yh= 1.02792e+308 j=2: ( 0, 1.02792e+308); ( 0, 1.02792e+308); yl+yh= 1.02792e+308 j=3: ( 0, 1.02792e+308); ( 0, 1.02792e+308); yl+yh= 1.02792e+308 j=4: ( 0, 1.02792e+308); ( 0, 1.02792e+308); yl+yh= 1.02792e+308 3. after ADD1(M): yl,yh = ( 0, 1.02792e+308); yl+yh= 1.02792e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 9.28074e+307); yl+yh= 9.28074e+307 ebd0(x=1e+307, M=6.85766e+302): M/x = (r=0.561779104644075) * 2^(e=-13); i=16, f=1820, fg=f*2^-(e+10)=14560 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 9.58603e+307); yl+yh= 9.58603e+307 j=2: ( 0, 9.58603e+307); ( 0, 9.58603e+307); yl+yh= 9.58603e+307 j=3: ( 0, 9.58603e+307); ( 0, 9.58603e+307); yl+yh= 9.58603e+307 j=4: ( 0, 9.58603e+307); ( 0, 9.58603e+307); yl+yh= 9.58603e+307 3. after ADD1(M): yl,yh = ( 0, 9.5861e+307); yl+yh= 9.5861e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 8.58763e+307); yl+yh= 8.58763e+307 ebd0(x=1e+307, M=1.37153e+303): M/x = (r=0.561779104644075) * 2^(e=-12); i=16, f=1820, fg=f*2^-(e+10)=7280 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 8.89289e+307); yl+yh= 8.89289e+307 j=2: ( 0, 8.89289e+307); ( 0, 8.89289e+307); yl+yh= 8.89289e+307 j=3: ( 0, 8.89289e+307); ( 0, 8.89289e+307); yl+yh= 8.89289e+307 j=4: ( 0, 8.89289e+307); ( 0, 8.89289e+307); yl+yh= 8.89289e+307 3. after ADD1(M): yl,yh = ( 0, 8.89302e+307); yl+yh= 8.89302e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 7.89455e+307); yl+yh= 7.89455e+307 ebd0(x=1e+307, M=2.74306e+303): M/x = (r=0.561779104644075) * 2^(e=-11); i=16, f=1820, fg=f*2^-(e+10)=3640 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 8.19974e+307); yl+yh= 8.19974e+307 j=2: ( 0, 8.19974e+307); ( 0, 8.19974e+307); yl+yh= 8.19974e+307 j=3: ( 0, 8.19974e+307); ( 0, 8.19974e+307); yl+yh= 8.19974e+307 j=4: ( 0, 8.19974e+307); ( 0, 8.19974e+307); yl+yh= 8.19974e+307 3. after ADD1(M): yl,yh = ( 0, 8.20001e+307); yl+yh= 8.20001e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 7.20154e+307); yl+yh= 7.20154e+307 ebd0(x=1e+307, M=5.48612e+303): M/x = (r=0.561779104644075) * 2^(e=-10); i=16, f=1820, fg=f*2^-(e+10)=1820 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 7.50659e+307); yl+yh= 7.50659e+307 j=2: ( 0, 7.50659e+307); ( 0, 7.50659e+307); yl+yh= 7.50659e+307 j=3: ( 0, 7.50659e+307); ( 0, 7.50659e+307); yl+yh= 7.50659e+307 j=4: ( 0, 7.50659e+307); ( 0, 7.50659e+307); yl+yh= 7.50659e+307 3. after ADD1(M): yl,yh = ( 0, 7.50714e+307); yl+yh= 7.50714e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 6.50867e+307); yl+yh= 6.50867e+307 ebd0(x=1e+307, M=1.09722e+304): M/x = (r=0.561779104644075) * 2^(e=-9); i=16, f=1820, fg=f*2^-(e+10)=910 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 6.81345e+307); yl+yh= 6.81345e+307 j=2: ( 0, 6.81345e+307); ( 0, 6.81345e+307); yl+yh= 6.81345e+307 j=3: ( 0, 6.81345e+307); ( 0, 6.81345e+307); yl+yh= 6.81345e+307 j=4: ( 0, 6.81345e+307); ( 0, 6.81345e+307); yl+yh= 6.81345e+307 3. after ADD1(M): yl,yh = ( 0, 6.81454e+307); yl+yh= 6.81454e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 5.81607e+307); yl+yh= 5.81607e+307 ebd0(x=1e+307, M=2.19445e+304): M/x = (r=0.561779104644075) * 2^(e=-8); i=16, f=1820, fg=f*2^-(e+10)=455 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 6.1203e+307); yl+yh= 6.1203e+307 j=2: ( 0, 6.1203e+307); ( 0, 6.1203e+307); yl+yh= 6.1203e+307 j=3: ( 0, 6.1203e+307); ( 0, 6.1203e+307); yl+yh= 6.1203e+307 j=4: ( 0, 6.1203e+307); ( 0, 6.1203e+307); yl+yh= 6.1203e+307 3. after ADD1(M): yl,yh = ( 0, 6.12249e+307); yl+yh= 6.12249e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 5.12402e+307); yl+yh= 5.12402e+307 ebd0(x=1e+307, M=4.3889e+304): M/x = (r=0.561779104644075) * 2^(e=-7); i=16, f=1820, fg=f*2^-(e+10)=227.5 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 5.42715e+307); yl+yh= 5.42715e+307 j=2: ( 0, 5.42715e+307); ( 0, 5.42715e+307); yl+yh= 5.42715e+307 j=3: ( 0, 5.42715e+307); ( 0, 5.42715e+307); yl+yh= 5.42715e+307 j=4: ( 0, 5.42715e+307); ( 0, 5.42715e+307); yl+yh= 5.42715e+307 3. after ADD1(M): yl,yh = ( 0, 5.43154e+307); yl+yh= 5.43154e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 4.43307e+307); yl+yh= 4.43307e+307 ebd0(x=1e+307, M=8.7778e+304): M/x = (r=0.561779104644075) * 2^(e=-6); i=16, f=1820, fg=f*2^-(e+10)=113.75 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 4.734e+307); yl+yh= 4.734e+307 j=2: ( 0, 4.734e+307); ( 0, 4.734e+307); yl+yh= 4.734e+307 j=3: ( 0, 4.734e+307); ( 0, 4.734e+307); yl+yh= 4.734e+307 j=4: ( 0, 4.734e+307); ( 0, 4.734e+307); yl+yh= 4.734e+307 3. after ADD1(M): yl,yh = ( 0, 4.74278e+307); yl+yh= 4.74278e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 3.74431e+307); yl+yh= 3.74431e+307 ebd0(x=1e+307, M=1.75556e+305): M/x = (r=0.561779104644075) * 2^(e=-5); i=16, f=1820, fg=f*2^-(e+10)=56.875 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 4.04086e+307); yl+yh= 4.04086e+307 j=2: ( 0, 4.04086e+307); ( 0, 4.04086e+307); yl+yh= 4.04086e+307 j=3: ( 0, 4.04086e+307); ( 0, 4.04086e+307); yl+yh= 4.04086e+307 j=4: ( 0, 4.04086e+307); ( 0, 4.04086e+307); yl+yh= 4.04086e+307 3. after ADD1(M): yl,yh = ( 0, 4.05841e+307); yl+yh= 4.05841e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 3.05994e+307); yl+yh= 3.05994e+307 ebd0(x=1e+307, M=3.51112e+305): M/x = (r=0.561779104644075) * 2^(e=-4); i=16, f=1820, fg=f*2^-(e+10)=28.4375 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 3.34771e+307); yl+yh= 3.34771e+307 j=2: ( 0, 3.34771e+307); ( 0, 3.34771e+307); yl+yh= 3.34771e+307 j=3: ( 0, 3.34771e+307); ( 0, 3.34771e+307); yl+yh= 3.34771e+307 j=4: ( 0, 3.34771e+307); ( 0, 3.34771e+307); yl+yh= 3.34771e+307 3. after ADD1(M): yl,yh = ( 0, 3.38282e+307); yl+yh= 3.38282e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 2.38435e+307); yl+yh= 2.38435e+307 ebd0(x=1e+307, M=7.02224e+305): M/x = (r=0.561779104644075) * 2^(e=-3); i=16, f=1820, fg=f*2^-(e+10)=14.2188 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 2.65456e+307); yl+yh= 2.65456e+307 j=2: ( 0, 2.65456e+307); ( 0, 2.65456e+307); yl+yh= 2.65456e+307 j=3: ( 0, 2.65456e+307); ( 0, 2.65456e+307); yl+yh= 2.65456e+307 j=4: ( 0, 2.65456e+307); ( 0, 2.65456e+307); yl+yh= 2.65456e+307 3. after ADD1(M): yl,yh = ( 0, 2.72479e+307); yl+yh= 2.72479e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 1.72631e+307); yl+yh= 1.72631e+307 ebd0(x=1e+307, M=1.40445e+306): M/x = (r=0.561779104644075) * 2^(e=-2); i=16, f=1820, fg=f*2^-(e+10)=7.10938 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 1.96142e+307); yl+yh= 1.96142e+307 j=2: ( 0, 1.96142e+307); ( 0, 1.96142e+307); yl+yh= 1.96142e+307 j=3: ( 0, 1.96142e+307); ( 0, 1.96142e+307); yl+yh= 1.96142e+307 j=4: ( 0, 1.96142e+307); ( 0, 1.96142e+307); yl+yh= 1.96142e+307 3. after ADD1(M): yl,yh = ( 0, 2.10186e+307); yl+yh= 2.10186e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 1.10339e+307); yl+yh= 1.10339e+307 ebd0(x=1e+307, M=2.8089e+306): M/x = (r=0.561779104644075) * 2^(e=-1); i=16, f=1820, fg=f*2^-(e+10)=3.55469 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 1.26827e+307); yl+yh= 1.26827e+307 j=2: ( 0, 1.26827e+307); ( 0, 1.26827e+307); yl+yh= 1.26827e+307 j=3: ( 0, 1.26827e+307); ( 0, 1.26827e+307); yl+yh= 1.26827e+307 j=4: ( 0, 1.26827e+307); ( 0, 1.26827e+307); yl+yh= 1.26827e+307 3. after ADD1(M): yl,yh = ( 0, 1.54916e+307); yl+yh= 1.54916e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 5.50683e+306); yl+yh= 5.50683e+306 ebd0(x=1e+307, M=5.61779e+306): M/x = (r=0.561779104644075) * 2^(e=0); i=16, f=1820, fg=f*2^-(e+10)=1.77734 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, 5.75121e+306); yl+yh= 5.75121e+306 j=2: ( 0, 5.75121e+306); ( 0, 5.75121e+306); yl+yh= 5.75121e+306 j=3: ( 0, 5.75121e+306); ( 0, 5.75121e+306); yl+yh= 5.75121e+306 j=4: ( 0, 5.75121e+306); ( 0, 5.75121e+306); yl+yh= 5.75121e+306 3. after ADD1(M): yl,yh = ( 0, 1.1369e+307); yl+yh= 1.1369e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 1.38426e+306); yl+yh= 1.38426e+306 ebd0(x=1e+307, M=1.12356e+307): M/x = (r=0.561779104644075) * 2^(e=1); i=16, f=1820, fg=f*2^-(e+10)=0.888672 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, -1.18026e+306); yl+yh= -1.18026e+306 j=2: ( 0, -1.18026e+306); ( 0, -1.18026e+306); yl+yh= -1.18026e+306 j=3: ( 0, -1.18026e+306); ( 0, -1.18026e+306); yl+yh= -1.18026e+306 j=4: ( 0, -1.18026e+306); ( 0, -1.18026e+306); yl+yh= -1.18026e+306 3. after ADD1(M): yl,yh = ( 0, 1.00553e+307); yl+yh= 1.00553e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 7.05759e+304); yl+yh= 7.05759e+304 ebd0(x=1e+307, M=2.24712e+307): M/x = (r=0.561779104644075) * 2^(e=2); i=16, f=1820, fg=f*2^-(e+10)=0.444336 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, -8.11173e+306); yl+yh= -8.11173e+306 j=2: ( 0, -8.11173e+306); ( 0, -8.11173e+306); yl+yh= -8.11173e+306 j=3: ( 0, -8.11173e+306); ( 0, -8.11173e+306); yl+yh= -8.11173e+306 j=4: ( 0, -8.11173e+306); ( 0, -8.11173e+306); yl+yh= -8.11173e+306 3. after ADD1(M): yl,yh = ( 0, 1.43594e+307); yl+yh= 1.43594e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 4.37469e+306); yl+yh= 4.37469e+306 ebd0(x=1e+307, M=4.49423e+307): M/x = (r=0.561779104644075) * 2^(e=3); i=16, f=1820, fg=f*2^-(e+10)=0.222168 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, -1.50432e+307); yl+yh= -1.50432e+307 j=2: ( 0, -1.50432e+307); ( 0, -1.50432e+307); yl+yh= -1.50432e+307 j=3: ( 0, -1.50432e+307); ( 0, -1.50432e+307); yl+yh= -1.50432e+307 j=4: ( 0, -1.50432e+307); ( 0, -1.50432e+307); yl+yh= -1.50432e+307 3. after ADD1(M): yl,yh = ( 0, 2.98991e+307); yl+yh= 2.98991e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 1.99144e+307); yl+yh= 1.99144e+307 ebd0(x=1e+307, M=8.98847e+307): M/x = (r=0.561779104644075) * 2^(e=4); i=16, f=1820, fg=f*2^-(e+10)=0.111084 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, -2.19747e+307); yl+yh= -2.19747e+307 j=2: ( 0, -2.19747e+307); ( 0, -2.19747e+307); yl+yh= -2.19747e+307 j=3: ( 0, -2.19747e+307); ( 0, -2.19747e+307); yl+yh= -2.19747e+307 j=4: ( 0, -2.19747e+307); ( 0, -2.19747e+307); yl+yh= -2.19747e+307 3. after ADD1(M): yl,yh = ( 0, 6.791e+307); yl+yh= 6.791e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 5.79252e+307); yl+yh= 5.79252e+307 ebd0(x=1e+307, M=1.79769e+308): M/x = (r=0.561779104644075) * 2^(e=5); i=16, f=1820, fg=f*2^-(e+10)=0.055542 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*b[0,j]), j=1:4: j=1: ( 0, 5.75121e+306); ( 0, -2.89061e+307); yl+yh= -2.89061e+307 j=2: ( 0, -2.89061e+307); ( 0, -2.89061e+307); yl+yh= -2.89061e+307 j=3: ( 0, -2.89061e+307); ( 0, -2.89061e+307); yl+yh= -2.89061e+307 j=4: ( 0, -2.89061e+307); ( 0, -2.89061e+307); yl+yh= -2.89061e+307 3. after ADD1(M): yl,yh = ( 0, 1.50863e+308); yl+yh= 1.50863e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.40878e+308); yl+yh= 1.40878e+308 dpq_ebd0(x[1:1], np[1:35], ... ): ebd0(x=1e+307, M=4.18558e+298): M/x = (r=0.561779104644075) * 2^(e=-27); i=16, f=1820, fg=f*2^-(e+10)=2.38551e+08 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( nan, inf); yl+yh= nan non-finite yh --> return((yh=Inf, yl=0)) ebd0(x=1e+307, M=8.37116e+298): M/x = (r=0.561779104644075) * 2^(e=-26); i=16, f=1820, fg=f*2^-(e+10)=1.19276e+08 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( nan, inf); yl+yh= nan non-finite yh --> return((yh=Inf, yl=0)) ebd0(x=1e+307, M=1.67423e+299): M/x = (r=0.561779104644075) * 2^(e=-25); i=16, f=1820, fg=f*2^-(e+10)=5.96378e+07 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 1.79038e+308); yl+yh= 1.79038e+308 j=1: ( 0, 1.79038e+308); ( 0, 1.79038e+308); yl+yh= 1.79038e+308 j=2: ( 0, 1.79038e+308); ( 0, 1.79038e+308); yl+yh= 1.79038e+308 j=3: ( 0, 1.79038e+308); ( 0, 1.79038e+308); yl+yh= 1.79038e+308 3. after ADD1(M): yl,yh = ( 0, 1.79038e+308); yl+yh= 1.79038e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.69053e+308); yl+yh= 1.69053e+308 ebd0(x=1e+307, M=3.34846e+299): M/x = (r=0.561779104644075) * 2^(e=-24); i=16, f=1820, fg=f*2^-(e+10)=2.98189e+07 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 1.72107e+308); yl+yh= 1.72107e+308 j=1: ( 0, 1.72107e+308); ( 0, 1.72107e+308); yl+yh= 1.72107e+308 j=2: ( 0, 1.72107e+308); ( 0, 1.72107e+308); yl+yh= 1.72107e+308 j=3: ( 0, 1.72107e+308); ( 0, 1.72107e+308); yl+yh= 1.72107e+308 3. after ADD1(M): yl,yh = ( 0, 1.72107e+308); yl+yh= 1.72107e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.62122e+308); yl+yh= 1.62122e+308 ebd0(x=1e+307, M=6.69693e+299): M/x = (r=0.561779104644075) * 2^(e=-23); i=16, f=1820, fg=f*2^-(e+10)=1.49094e+07 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 1.65175e+308); yl+yh= 1.65175e+308 j=1: ( 0, 1.65175e+308); ( 0, 1.65175e+308); yl+yh= 1.65175e+308 j=2: ( 0, 1.65175e+308); ( 0, 1.65175e+308); yl+yh= 1.65175e+308 j=3: ( 0, 1.65175e+308); ( 0, 1.65175e+308); yl+yh= 1.65175e+308 3. after ADD1(M): yl,yh = ( 0, 1.65175e+308); yl+yh= 1.65175e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.5519e+308); yl+yh= 1.5519e+308 ebd0(x=1e+307, M=1.33939e+300): M/x = (r=0.561779104644075) * 2^(e=-22); i=16, f=1820, fg=f*2^-(e+10)=7.45472e+06 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 1.58244e+308); yl+yh= 1.58244e+308 j=1: ( 0, 1.58244e+308); ( 0, 1.58244e+308); yl+yh= 1.58244e+308 j=2: ( 0, 1.58244e+308); ( 0, 1.58244e+308); yl+yh= 1.58244e+308 j=3: ( 0, 1.58244e+308); ( 0, 1.58244e+308); yl+yh= 1.58244e+308 3. after ADD1(M): yl,yh = ( 0, 1.58244e+308); yl+yh= 1.58244e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.48259e+308); yl+yh= 1.48259e+308 ebd0(x=1e+307, M=2.67877e+300): M/x = (r=0.561779104644075) * 2^(e=-21); i=16, f=1820, fg=f*2^-(e+10)=3.72736e+06 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 1.51312e+308); yl+yh= 1.51312e+308 j=1: ( 0, 1.51312e+308); ( 0, 1.51312e+308); yl+yh= 1.51312e+308 j=2: ( 0, 1.51312e+308); ( 0, 1.51312e+308); yl+yh= 1.51312e+308 j=3: ( 0, 1.51312e+308); ( 0, 1.51312e+308); yl+yh= 1.51312e+308 3. after ADD1(M): yl,yh = ( 0, 1.51312e+308); yl+yh= 1.51312e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.41327e+308); yl+yh= 1.41327e+308 ebd0(x=1e+307, M=5.35754e+300): M/x = (r=0.561779104644075) * 2^(e=-20); i=16, f=1820, fg=f*2^-(e+10)=1.86368e+06 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 1.44381e+308); yl+yh= 1.44381e+308 j=1: ( 0, 1.44381e+308); ( 0, 1.44381e+308); yl+yh= 1.44381e+308 j=2: ( 0, 1.44381e+308); ( 0, 1.44381e+308); yl+yh= 1.44381e+308 j=3: ( 0, 1.44381e+308); ( 0, 1.44381e+308); yl+yh= 1.44381e+308 3. after ADD1(M): yl,yh = ( 0, 1.44381e+308); yl+yh= 1.44381e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.34396e+308); yl+yh= 1.34396e+308 ebd0(x=1e+307, M=1.07151e+301): M/x = (r=0.561779104644075) * 2^(e=-19); i=16, f=1820, fg=f*2^-(e+10)=931840 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 1.37449e+308); yl+yh= 1.37449e+308 j=1: ( 0, 1.37449e+308); ( 0, 1.37449e+308); yl+yh= 1.37449e+308 j=2: ( 0, 1.37449e+308); ( 0, 1.37449e+308); yl+yh= 1.37449e+308 j=3: ( 0, 1.37449e+308); ( 0, 1.37449e+308); yl+yh= 1.37449e+308 3. after ADD1(M): yl,yh = ( 0, 1.37449e+308); yl+yh= 1.37449e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.27464e+308); yl+yh= 1.27464e+308 ebd0(x=1e+307, M=2.14302e+301): M/x = (r=0.561779104644075) * 2^(e=-18); i=16, f=1820, fg=f*2^-(e+10)=465920 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 1.30518e+308); yl+yh= 1.30518e+308 j=1: ( 0, 1.30518e+308); ( 0, 1.30518e+308); yl+yh= 1.30518e+308 j=2: ( 0, 1.30518e+308); ( 0, 1.30518e+308); yl+yh= 1.30518e+308 j=3: ( 0, 1.30518e+308); ( 0, 1.30518e+308); yl+yh= 1.30518e+308 3. after ADD1(M): yl,yh = ( 0, 1.30518e+308); yl+yh= 1.30518e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.20533e+308); yl+yh= 1.20533e+308 ebd0(x=1e+307, M=4.28603e+301): M/x = (r=0.561779104644075) * 2^(e=-17); i=16, f=1820, fg=f*2^-(e+10)=232960 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 1.23586e+308); yl+yh= 1.23586e+308 j=1: ( 0, 1.23586e+308); ( 0, 1.23586e+308); yl+yh= 1.23586e+308 j=2: ( 0, 1.23586e+308); ( 0, 1.23586e+308); yl+yh= 1.23586e+308 j=3: ( 0, 1.23586e+308); ( 0, 1.23586e+308); yl+yh= 1.23586e+308 3. after ADD1(M): yl,yh = ( 0, 1.23586e+308); yl+yh= 1.23586e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.13602e+308); yl+yh= 1.13602e+308 ebd0(x=1e+307, M=8.57207e+301): M/x = (r=0.561779104644075) * 2^(e=-16); i=16, f=1820, fg=f*2^-(e+10)=116480 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 1.16655e+308); yl+yh= 1.16655e+308 j=1: ( 0, 1.16655e+308); ( 0, 1.16655e+308); yl+yh= 1.16655e+308 j=2: ( 0, 1.16655e+308); ( 0, 1.16655e+308); yl+yh= 1.16655e+308 j=3: ( 0, 1.16655e+308); ( 0, 1.16655e+308); yl+yh= 1.16655e+308 3. after ADD1(M): yl,yh = ( 0, 1.16655e+308); yl+yh= 1.16655e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.0667e+308); yl+yh= 1.0667e+308 ebd0(x=1e+307, M=1.71441e+302): M/x = (r=0.561779104644075) * 2^(e=-15); i=16, f=1820, fg=f*2^-(e+10)=58240 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 1.09723e+308); yl+yh= 1.09723e+308 j=1: ( 0, 1.09723e+308); ( 0, 1.09723e+308); yl+yh= 1.09723e+308 j=2: ( 0, 1.09723e+308); ( 0, 1.09723e+308); yl+yh= 1.09723e+308 j=3: ( 0, 1.09723e+308); ( 0, 1.09723e+308); yl+yh= 1.09723e+308 3. after ADD1(M): yl,yh = ( 0, 1.09723e+308); yl+yh= 1.09723e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 9.97387e+307); yl+yh= 9.97387e+307 ebd0(x=1e+307, M=3.42883e+302): M/x = (r=0.561779104644075) * 2^(e=-14); i=16, f=1820, fg=f*2^-(e+10)=29120 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 1.02792e+308); yl+yh= 1.02792e+308 j=1: ( 0, 1.02792e+308); ( 0, 1.02792e+308); yl+yh= 1.02792e+308 j=2: ( 0, 1.02792e+308); ( 0, 1.02792e+308); yl+yh= 1.02792e+308 j=3: ( 0, 1.02792e+308); ( 0, 1.02792e+308); yl+yh= 1.02792e+308 3. after ADD1(M): yl,yh = ( 0, 1.02792e+308); yl+yh= 1.02792e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 9.28074e+307); yl+yh= 9.28074e+307 ebd0(x=1e+307, M=6.85766e+302): M/x = (r=0.561779104644075) * 2^(e=-13); i=16, f=1820, fg=f*2^-(e+10)=14560 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 9.58603e+307); yl+yh= 9.58603e+307 j=1: ( 0, 9.58603e+307); ( 0, 9.58603e+307); yl+yh= 9.58603e+307 j=2: ( 0, 9.58603e+307); ( 0, 9.58603e+307); yl+yh= 9.58603e+307 j=3: ( 0, 9.58603e+307); ( 0, 9.58603e+307); yl+yh= 9.58603e+307 3. after ADD1(M): yl,yh = ( 0, 9.5861e+307); yl+yh= 9.5861e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 8.58763e+307); yl+yh= 8.58763e+307 ebd0(x=1e+307, M=1.37153e+303): M/x = (r=0.561779104644075) * 2^(e=-12); i=16, f=1820, fg=f*2^-(e+10)=7280 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 8.89289e+307); yl+yh= 8.89289e+307 j=1: ( 0, 8.89289e+307); ( 0, 8.89289e+307); yl+yh= 8.89289e+307 j=2: ( 0, 8.89289e+307); ( 0, 8.89289e+307); yl+yh= 8.89289e+307 j=3: ( 0, 8.89289e+307); ( 0, 8.89289e+307); yl+yh= 8.89289e+307 3. after ADD1(M): yl,yh = ( 0, 8.89302e+307); yl+yh= 8.89302e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 7.89455e+307); yl+yh= 7.89455e+307 ebd0(x=1e+307, M=2.74306e+303): M/x = (r=0.561779104644075) * 2^(e=-11); i=16, f=1820, fg=f*2^-(e+10)=3640 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 8.19974e+307); yl+yh= 8.19974e+307 j=1: ( 0, 8.19974e+307); ( 0, 8.19974e+307); yl+yh= 8.19974e+307 j=2: ( 0, 8.19974e+307); ( 0, 8.19974e+307); yl+yh= 8.19974e+307 j=3: ( 0, 8.19974e+307); ( 0, 8.19974e+307); yl+yh= 8.19974e+307 3. after ADD1(M): yl,yh = ( 0, 8.20001e+307); yl+yh= 8.20001e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 7.20154e+307); yl+yh= 7.20154e+307 ebd0(x=1e+307, M=5.48612e+303): M/x = (r=0.561779104644075) * 2^(e=-10); i=16, f=1820, fg=f*2^-(e+10)=1820 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 7.50659e+307); yl+yh= 7.50659e+307 j=1: ( 0, 7.50659e+307); ( 0, 7.50659e+307); yl+yh= 7.50659e+307 j=2: ( 0, 7.50659e+307); ( 0, 7.50659e+307); yl+yh= 7.50659e+307 j=3: ( 0, 7.50659e+307); ( 0, 7.50659e+307); yl+yh= 7.50659e+307 3. after ADD1(M): yl,yh = ( 0, 7.50714e+307); yl+yh= 7.50714e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 6.50867e+307); yl+yh= 6.50867e+307 ebd0(x=1e+307, M=1.09722e+304): M/x = (r=0.561779104644075) * 2^(e=-9); i=16, f=1820, fg=f*2^-(e+10)=910 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 6.81345e+307); yl+yh= 6.81345e+307 j=1: ( 0, 6.81345e+307); ( 0, 6.81345e+307); yl+yh= 6.81345e+307 j=2: ( 0, 6.81345e+307); ( 0, 6.81345e+307); yl+yh= 6.81345e+307 j=3: ( 0, 6.81345e+307); ( 0, 6.81345e+307); yl+yh= 6.81345e+307 3. after ADD1(M): yl,yh = ( 0, 6.81454e+307); yl+yh= 6.81454e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 5.81607e+307); yl+yh= 5.81607e+307 ebd0(x=1e+307, M=2.19445e+304): M/x = (r=0.561779104644075) * 2^(e=-8); i=16, f=1820, fg=f*2^-(e+10)=455 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 6.1203e+307); yl+yh= 6.1203e+307 j=1: ( 0, 6.1203e+307); ( 0, 6.1203e+307); yl+yh= 6.1203e+307 j=2: ( 0, 6.1203e+307); ( 0, 6.1203e+307); yl+yh= 6.1203e+307 j=3: ( 0, 6.1203e+307); ( 0, 6.1203e+307); yl+yh= 6.1203e+307 3. after ADD1(M): yl,yh = ( 0, 6.12249e+307); yl+yh= 6.12249e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 5.12402e+307); yl+yh= 5.12402e+307 ebd0(x=1e+307, M=4.3889e+304): M/x = (r=0.561779104644075) * 2^(e=-7); i=16, f=1820, fg=f*2^-(e+10)=227.5 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 5.42715e+307); yl+yh= 5.42715e+307 j=1: ( 0, 5.42715e+307); ( 0, 5.42715e+307); yl+yh= 5.42715e+307 j=2: ( 0, 5.42715e+307); ( 0, 5.42715e+307); yl+yh= 5.42715e+307 j=3: ( 0, 5.42715e+307); ( 0, 5.42715e+307); yl+yh= 5.42715e+307 3. after ADD1(M): yl,yh = ( 0, 5.43154e+307); yl+yh= 5.43154e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 4.43307e+307); yl+yh= 4.43307e+307 ebd0(x=1e+307, M=8.7778e+304): M/x = (r=0.561779104644075) * 2^(e=-6); i=16, f=1820, fg=f*2^-(e+10)=113.75 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 4.734e+307); yl+yh= 4.734e+307 j=1: ( 0, 4.734e+307); ( 0, 4.734e+307); yl+yh= 4.734e+307 j=2: ( 0, 4.734e+307); ( 0, 4.734e+307); yl+yh= 4.734e+307 j=3: ( 0, 4.734e+307); ( 0, 4.734e+307); yl+yh= 4.734e+307 3. after ADD1(M): yl,yh = ( 0, 4.74278e+307); yl+yh= 4.74278e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 3.74431e+307); yl+yh= 3.74431e+307 ebd0(x=1e+307, M=1.75556e+305): M/x = (r=0.561779104644075) * 2^(e=-5); i=16, f=1820, fg=f*2^-(e+10)=56.875 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 4.04086e+307); yl+yh= 4.04086e+307 j=1: ( 0, 4.04086e+307); ( 0, 4.04086e+307); yl+yh= 4.04086e+307 j=2: ( 0, 4.04086e+307); ( 0, 4.04086e+307); yl+yh= 4.04086e+307 j=3: ( 0, 4.04086e+307); ( 0, 4.04086e+307); yl+yh= 4.04086e+307 3. after ADD1(M): yl,yh = ( 0, 4.05841e+307); yl+yh= 4.05841e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 3.05994e+307); yl+yh= 3.05994e+307 ebd0(x=1e+307, M=3.51112e+305): M/x = (r=0.561779104644075) * 2^(e=-4); i=16, f=1820, fg=f*2^-(e+10)=28.4375 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 3.34771e+307); yl+yh= 3.34771e+307 j=1: ( 0, 3.34771e+307); ( 0, 3.34771e+307); yl+yh= 3.34771e+307 j=2: ( 0, 3.34771e+307); ( 0, 3.34771e+307); yl+yh= 3.34771e+307 j=3: ( 0, 3.34771e+307); ( 0, 3.34771e+307); yl+yh= 3.34771e+307 3. after ADD1(M): yl,yh = ( 0, 3.38282e+307); yl+yh= 3.38282e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 2.38435e+307); yl+yh= 2.38435e+307 ebd0(x=1e+307, M=7.02224e+305): M/x = (r=0.561779104644075) * 2^(e=-3); i=16, f=1820, fg=f*2^-(e+10)=14.2188 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 2.65456e+307); yl+yh= 2.65456e+307 j=1: ( 0, 2.65456e+307); ( 0, 2.65456e+307); yl+yh= 2.65456e+307 j=2: ( 0, 2.65456e+307); ( 0, 2.65456e+307); yl+yh= 2.65456e+307 j=3: ( 0, 2.65456e+307); ( 0, 2.65456e+307); yl+yh= 2.65456e+307 3. after ADD1(M): yl,yh = ( 0, 2.72479e+307); yl+yh= 2.72479e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 1.72631e+307); yl+yh= 1.72631e+307 ebd0(x=1e+307, M=1.40445e+306): M/x = (r=0.561779104644075) * 2^(e=-2); i=16, f=1820, fg=f*2^-(e+10)=7.10938 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 1.96142e+307); yl+yh= 1.96142e+307 j=1: ( 0, 1.96142e+307); ( 0, 1.96142e+307); yl+yh= 1.96142e+307 j=2: ( 0, 1.96142e+307); ( 0, 1.96142e+307); yl+yh= 1.96142e+307 j=3: ( 0, 1.96142e+307); ( 0, 1.96142e+307); yl+yh= 1.96142e+307 3. after ADD1(M): yl,yh = ( 0, 2.10186e+307); yl+yh= 2.10186e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 1.10339e+307); yl+yh= 1.10339e+307 ebd0(x=1e+307, M=2.8089e+306): M/x = (r=0.561779104644075) * 2^(e=-1); i=16, f=1820, fg=f*2^-(e+10)=3.55469 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 1.26827e+307); yl+yh= 1.26827e+307 j=1: ( 0, 1.26827e+307); ( 0, 1.26827e+307); yl+yh= 1.26827e+307 j=2: ( 0, 1.26827e+307); ( 0, 1.26827e+307); yl+yh= 1.26827e+307 j=3: ( 0, 1.26827e+307); ( 0, 1.26827e+307); yl+yh= 1.26827e+307 3. after ADD1(M): yl,yh = ( 0, 1.54916e+307); yl+yh= 1.54916e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 5.50683e+306); yl+yh= 5.50683e+306 ebd0(x=1e+307, M=5.61779e+306): M/x = (r=0.561779104644075) * 2^(e=0); i=16, f=1820, fg=f*2^-(e+10)=1.77734 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, 5.75121e+306); yl+yh= 5.75121e+306 j=1: ( 0, 5.75121e+306); ( 0, 5.75121e+306); yl+yh= 5.75121e+306 j=2: ( 0, 5.75121e+306); ( 0, 5.75121e+306); yl+yh= 5.75121e+306 j=3: ( 0, 5.75121e+306); ( 0, 5.75121e+306); yl+yh= 5.75121e+306 3. after ADD1(M): yl,yh = ( 0, 1.1369e+307); yl+yh= 1.1369e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 1.38426e+306); yl+yh= 1.38426e+306 ebd0(x=1e+307, M=1.12356e+307): M/x = (r=0.561779104644075) * 2^(e=1); i=16, f=1820, fg=f*2^-(e+10)=0.888672 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, -1.18026e+306); yl+yh= -1.18026e+306 j=1: ( 0, -1.18026e+306); ( 0, -1.18026e+306); yl+yh= -1.18026e+306 j=2: ( 0, -1.18026e+306); ( 0, -1.18026e+306); yl+yh= -1.18026e+306 j=3: ( 0, -1.18026e+306); ( 0, -1.18026e+306); yl+yh= -1.18026e+306 3. after ADD1(M): yl,yh = ( 0, 1.00553e+307); yl+yh= 1.00553e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 7.05759e+304); yl+yh= 7.05759e+304 ebd0(x=1e+307, M=2.24712e+307): M/x = (r=0.561779104644075) * 2^(e=2); i=16, f=1820, fg=f*2^-(e+10)=0.444336 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, -8.11173e+306); yl+yh= -8.11173e+306 j=1: ( 0, -8.11173e+306); ( 0, -8.11173e+306); yl+yh= -8.11173e+306 j=2: ( 0, -8.11173e+306); ( 0, -8.11173e+306); yl+yh= -8.11173e+306 j=3: ( 0, -8.11173e+306); ( 0, -8.11173e+306); yl+yh= -8.11173e+306 3. after ADD1(M): yl,yh = ( 0, 1.43594e+307); yl+yh= 1.43594e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 4.37469e+306); yl+yh= 4.37469e+306 ebd0(x=1e+307, M=4.49423e+307): M/x = (r=0.561779104644075) * 2^(e=3); i=16, f=1820, fg=f*2^-(e+10)=0.222168 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, -1.50432e+307); yl+yh= -1.50432e+307 j=1: ( 0, -1.50432e+307); ( 0, -1.50432e+307); yl+yh= -1.50432e+307 j=2: ( 0, -1.50432e+307); ( 0, -1.50432e+307); yl+yh= -1.50432e+307 j=3: ( 0, -1.50432e+307); ( 0, -1.50432e+307); yl+yh= -1.50432e+307 3. after ADD1(M): yl,yh = ( 0, 2.98991e+307); yl+yh= 2.98991e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 1.99144e+307); yl+yh= 1.99144e+307 ebd0(x=1e+307, M=8.98847e+307): M/x = (r=0.561779104644075) * 2^(e=4); i=16, f=1820, fg=f*2^-(e+10)=0.111084 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, -2.19747e+307); yl+yh= -2.19747e+307 j=1: ( 0, -2.19747e+307); ( 0, -2.19747e+307); yl+yh= -2.19747e+307 j=2: ( 0, -2.19747e+307); ( 0, -2.19747e+307); yl+yh= -2.19747e+307 j=3: ( 0, -2.19747e+307); ( 0, -2.19747e+307); yl+yh= -2.19747e+307 3. after ADD1(M): yl,yh = ( 0, 6.791e+307); yl+yh= 6.791e+307 4. after ADD1(- M*fg): yl,yh = ( 0, 5.79252e+307); yl+yh= 5.79252e+307 ebd0(x=1e+307, M=1.79769e+308): M/x = (r=0.561779104644075) * 2^(e=5); i=16, f=1820, fg=f*2^-(e+10)=0.055542 bd0_sc[0][0..3]= (0.693147 -1.90465e-09 -8.78318e-17 3.06184e-24 ) i -> bd0_sc[i][0..3]= (0.57512 2.24238e-09 -2.20452e-17 4.07854e-25 ) small(?) (M*fg-x)/x = (M*fg)/x - 1 = -0.001525419480256795 1a. before adding -x * log1pmx(.) = -x * -1.16464e-06 = 1.16464e+301 1. after A.(-x*l..): yl,yh = ( 0, 1.16464e+301); yl+yh= 1.16464e+301 2: A(x*b[i,j]) and A(-x*e*b[0,j]), j=1:4: j=0: ( 0, 5.75121e+306); ( 0, -2.89061e+307); yl+yh= -2.89061e+307 j=1: ( 0, -2.89061e+307); ( 0, -2.89061e+307); yl+yh= -2.89061e+307 j=2: ( 0, -2.89061e+307); ( 0, -2.89061e+307); yl+yh= -2.89061e+307 j=3: ( 0, -2.89061e+307); ( 0, -2.89061e+307); yl+yh= -2.89061e+307 3. after ADD1(M): yl,yh = ( 0, 1.50863e+308); yl+yh= 1.50863e+308 4. after ADD1(- M*fg): yl,yh = ( 0, 1.40878e+308); yl+yh= 1.40878e+308 bd0(1e+307, 1.12356e+307): T.series w/ 125 terms -> bd0=7.05759e+304 > stopifnot( all.equal(bd0v.8, bd0v.10, tol=0), + bd0v.8$aeq0, # even tol=0 equality ! + bd0v.8$aeq4 ) > ## ==> 256 bit gives the *same* (asNumeric() - double-prec accuracy) as 1024 bits ! > rm(bd0v.10) > showProc.time() Time (user system elapsed): 1.2 0.03 1.23 > > p.relE <- function(bd0v, dFac = if(max(np) >= 8e307) 1e10 else 1, + log = "x", type="b") { + stopifnot(length(x <- bd0v$x) == 1 # for now + , is.numeric(x), is.numeric(np <- bd0v$np), length(np) > 1 + , is.numeric(dFac), dFac > 0, length(dFac) == 1 + , is.matrix(relE <- bd0v$relE) + , (k <- ncol(relE)) >= 1 + , sum(iOk <- local({ y <- bd0v$bd0; is.finite(y) & y != 0 })) > 1 + ) + ## */dFac : otherwise triggering axis() error + ## log - axis(), 'at' creation, _LARGE_ range: invalid {xy}axp or par; nint=5 + ## axp[0:1]=(1e+299,1e+308), usr[0:1]=(7.28752e+298,inf); i=9, ni=1 + pc <- 1:k + matplot(np[iOk]/dFac, relE[iOk,], type=type, log=log, pch=pc, col=1+pc, + main = "relative Errors WRT bd0()", + xlim = range(np)/dFac, # show full range + xlab = paste0("np[iOk]", if(dFac != 1) sprintf("/ dFac, dFac=%g",dFac)), + ## could use sfsmisc::pretty10exp(1e10, drop.1=TRUE) + xaxt="n"); sfsmisc::eaxis(1, sub10=3) + mtext(sprintf("bd0(x, np), x = %g", x)) + if(k >= 2) legend("top", colnames(relE), pch=pc, lty=1:2, col=1+pc, bty="n") + rug(np[!iOk]/dFac, col=2) + axis(1, at=x/dFac, quote(x), col=2, col.axis=2, lwd=2, line=-1) + } > > p.relE(bd0v.8) > > ## ==> FIXME: a whole small (extreme) range where bd0() is *better* than ebd0() !!! > with(bd0v.8, cbind(log2.lam = log2(np), np, relE)) ## around 2^[1018, 1021] log2.lam np ebd0 ebd0C bd0 [1,] 990 1.04639512e+298 Inf Inf Inf [2,] 991 2.09279025e+298 Inf Inf Inf [3,] 992 4.18558050e+298 Inf Inf Inf [4,] 993 8.37116099e+298 Inf Inf Inf [5,] 994 1.67423220e+299 6.86757892e-17 6.86757892e-17 6.86757892e-17 [6,] 995 3.34846440e+299 -2.35238299e-17 -2.35238299e-17 -2.35238299e-17 [7,] 996 6.69692879e+299 4.64722904e-18 4.64722904e-18 1.33253210e-16 [8,] 997 1.33938576e+300 3.54540244e-17 3.54540244e-17 3.54540244e-17 [9,] 998 2.67877152e+300 6.92860492e-17 6.92860492e-17 6.92860492e-17 [10,] 999 5.35754304e+300 -4.18896305e-17 -4.18896305e-17 1.06614915e-16 [11,] 1000 1.07150861e+301 -8.56162226e-18 -8.56162226e-18 1.48018542e-16 [12,] 1001 2.14301721e+301 -1.36953500e-16 -1.36953500e-16 2.86310828e-17 [13,] 1002 4.28603443e+301 -1.05258460e-16 -1.05258460e-16 7.04293432e-17 [14,] 1003 8.57206886e+301 -6.93018205e-17 -6.93018205e-17 1.17802186e-16 [15,] 1004 1.71441377e+302 -2.80427243e-17 -2.80427243e-17 -2.80427243e-17 [16,] 1005 3.42882754e+302 2.00343436e-17 2.00343436e-17 2.00343436e-17 [17,] 1006 6.85765509e+302 -1.55120807e-16 -1.55120807e-16 7.72879792e-17 [18,] 1007 1.37153102e+303 2.12684439e-17 2.12684439e-17 2.12684439e-17 [19,] 1008 2.74306203e+303 9.97903931e-17 9.97903931e-17 9.97903931e-17 [20,] 1009 5.48612407e+303 5.66528379e-17 5.66528379e-17 5.66528379e-17 [21,] 1010 1.09722481e+304 -1.34894374e-16 -1.34894374e-16 3.66854779e-17 [22,] 1011 2.19444963e+304 -1.07502043e-16 -1.07502043e-16 -1.07502043e-16 [23,] 1012 4.38889926e+304 -8.55542215e-18 -8.55542215e-18 -8.55542215e-18 [24,] 1013 8.77779851e+304 -1.23783849e-16 -1.23783849e-16 1.42732769e-16 [25,] 1014 1.75555970e+305 -8.86259493e-17 -8.86259493e-17 7.44362002e-17 [26,] 1015 3.51111940e+305 -1.42625857e-16 -1.42625857e-16 6.66390640e-17 [27,] 1016 7.02223881e+305 -2.50440324e-16 -2.50440324e-16 3.85923155e-17 [28,] 1017 1.40444776e+306 -1.78689561e-16 -1.78689561e-16 4.74145469e-17 [29,] 1018 2.80889552e+306 5.78691591e-16 5.78691591e-16 5.78691591e-16 [30,] 1019 5.61779105e+306 1.07238048e-15 1.07238048e-15 -7.29886761e-16 [31,] 1020 1.12355821e+307 1.45877315e-14 1.45877315e-14 -1.87127858e-16 [32,] 1021 2.24711642e+307 1.31354332e-16 1.31354332e-16 1.31354332e-16 [33,] 1022 4.49423284e+307 1.93926546e-16 1.93926546e-16 -5.66261269e-17 [34,] 1023 8.98846567e+307 5.88175211e-17 5.88175211e-17 5.88175211e-17 [35,] 1024 1.79769313e+308 5.63728043e-17 5.63728043e-17 -3.68640546e-16 > > > with(bd0v.8, stopifnot(exprs = { + yhl["yl",] == 0 # which is not really good and should maybe change ! + ## Fixed now : both have 4 x Inf and then are equal {but do Note relE difference above!} + all.equal(ebd0["yh",], bd0, tol = 4 * .Machine$double.eps) + })) Error in eval(substitute(expr), data, enclos = parent.frame()) : ebd0["yh", ] and bd0 are not equal: Mean absolute difference: 1.44431286e+292 Calls: with ... eval -> eval -> stopifnot -> eval -> eval -> stopifnot Execution halted * checking for unstated dependencies in vignettes ... OK * checking package vignettes in 'inst/doc' ... OK * checking re-building of vignette outputs ... [32s] OK * checking PDF version of manual ... OK * DONE Status: 2 ERRORs