# wch/r-source

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 ###---- ALL tests here should return TRUE ! ### ### '##P': This lines give not 'T' but relevant ``Print output'' ### Meps <- .Machine \$ double.eps options(rErr.eps = 1e-30) rErr <- function(approx, true, eps = .Options\$rErr.eps) { if(is.null(eps)) { eps <- 1e-30; options(rErr.eps = eps) } ifelse(Mod(true) >= eps, 1 - approx / true, # relative error true - approx) # absolute error (e.g. when true=0) } is.infinite(.Machine\$double.base ^ .Machine\$double.max.exp)# overflow abs(1- .Machine\$double.xmin * 10^(-.Machine\$double.min.exp*log10(2)))/Meps < 1e3 ##P (1- .Machine\$double.xmin * 10^(-.Machine\$double.min.exp*log10(2)))/Meps log10(.Machine\$double.xmax) / log10(2) == .Machine\$double.max.exp log10(.Machine\$double.xmin) / log10(2) == .Machine\$double.min.exp ## Real Trig.: cos(0) == 1 sin(3*pi/2) == cos(pi) x <- rnorm(99) all( sin(-x) == - sin(x)) all( cos(-x) == cos(x)) x <- 1:99/100 all(abs(1 - x / asin(sin(x))) <= Meps) all(abs(1 - x / atan(tan(x))) <= Meps) ## Complex Trig.: abs(Im(cos(acos(1i))) - 1) < 2*Meps abs(Im(sin(asin(1i))) - 1) < 2*Meps ##P (1 - Im(sin(asin(Ii))))/Meps ##P (1 - Im(cos(acos(Ii))))/Meps abs(Im(asin(sin(1i))) - 1) < 2*Meps cos(1i) == cos(-1i)# i.e. Im(acos(*)) gives + or - 1i: abs(abs(Im(acos(cos(1i)))) - 1) < 4*Meps .Random.seed <- c(0, 629, 6137, 22167) # want reproducible output Isi <- Im(sin(asin(1i + rnorm(100)))) all(abs(Isi-1) < 100* Meps) ##P table(2*abs(Isi-1) / Meps) Isi <- Im(cos(acos(1i + rnorm(100)))) all(abs(Isi-1) < 100* Meps) ##P table(2*abs(Isi-1) / Meps) Isi <- Im(atan(tan(1i + rnorm(100)))) #-- tan(atan(..)) does NOT work (Math!) all(abs(Isi-1) < 100* Meps) ##P table(2*abs(Isi-1) / Meps) ## gamma(): abs(gamma(1/2)^2 - pi) < 4* Meps r <- rlnorm(5000) all(abs(rErr(gamma(r+1), r*gamma(r))) < 500 * Meps) n <- 10; all( gamma(1:n) == cumprod(c(1,1:(n-1)))) n <- 20; all(abs(rErr( gamma(1:n), cumprod(c(1,1:(n-1))))) < 100*Meps) n <- 120; all(abs(rErr( gamma(1:n), cumprod(c(1,1:(n-1))))) < 1000*Meps) n <- 10000;all(abs(rErr(lgamma(1:n),cumsum(log(c(1,1:(n-1)))))) < 100*Meps) ## fft(): ok <- TRUE ##test EXTENSIVELY: for(N in 1:100) { cat(".") for(n in c(1:30, 1000:1050)) { x <- rnorm(n) er <- Mod(rErr(fft(fft(x), inverse = TRUE)/n, x*(1+0i))) n.ok <- all(er < 1e-8) & quantile(er, 0.95, names=FALSE) < 10000*Meps if(!n.ok) cat("\nn=",n,": quantile(rErr, c(.95,1)) =", formatC(quantile(er, prob= c(.95,1))),"\n") ok <- ok & n.ok } cat("\n") ##test EXTENSIVELY: } ok
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