# Rounding Big Rationals ("bigq") to Decimals Rounding big rationals (of class `"bigq"`, see `as.bigq()`) to decimal `digits` is strictly based on a (optionally choosable) definition of rounding to integer, i.e., `digits = 0`, the default method of which we provide as `round0()`. The users typically just call `round(x, digits)` as elsewhere, and the `round()` method will call `round(x, digits, round0=round0)`. ```r round0(x) roundQ(x, digits = 0, r0 = round0) ## S3 method for class 'bigq' round(x, digits = 0) ``` ## Arguments - `x`: vector of big rationals, i.e., of `class` `"bigq"`. - `digits`: integer number of decimal digits to round to. - `r0`: a `function` of one argument which implements a version of `round(x, digits=0)`. The default for `roundQ()` is to use our `round0()` which implements round to even , as base 's `round`. ## Returns `round0()` returns a vector of big integers, i.e., `"bigz"` classed. `roundQ(x, digits, round0)` returns a vector of big rationals, `"bigq"`, as `x`. `round.bigq` is very simply defined as `function(x, digits) roundQ(x, digits)` . ## References The vignette _Exact Decimal Rounding via Rationals_ from CRAN package [list("round")](https://CRAN.R-project.org/package=round), Wikipedia, Rounding, notably "Round half to even": [https://en.wikipedia.org/wiki/Rounding#Round_half_to_even](https://en.wikipedia.org/wiki/Rounding#Round_half_to_even) ## Author(s) Martin Maechler, ETH Zurich ## See Also `round` for (double precision) numbers in base ; `roundX` from CRAN package [list("round")](https://CRAN.R-project.org/package=round). ## Examples ```r qq <- as.bigq((-21:31), 10) noquote(cbind(as.character(qq), asNumeric(qq))) round0(qq) # Big Integer ("bigz") ## corresponds to R's own "round to even" : stopifnot(round0(qq) == round(asNumeric(qq))) round(qq) # == round(qq, 0): the same as round0(qq) *but* Big Rational ("bigq") halfs <- as.bigq(1,2) + -5:12 ## round0() is simply round0 <- function (x) { nU <- as.bigz.bigq(xU <- x + as.bigq(1, 2)) # traditional round: .5 rounded up if(any(I <- is.whole.bigq(xU))) { # I <==> x == .5 : "hard case" I[I] <- .mod.bigz(nU[I], 2L) == 1L # rounded up is odd ==> round *down* nU[I] <- nU[I] - 1L } nU } ## 's' for simple: rounding as you learned in school: round0s <- function(x) as.bigz.bigq(x + as.bigq(1, 2)) cbind(halfs, round0s(halfs), round0(halfs)) ## roundQ() is simply roundQ <- function(x, digits = 0, r0 = round0) { ## round(x * 10^d) / 10^d -- vectorizing in both (x, digits) p10 <- as.bigz(10) ^ digits # class: if(all(digits >= 0)) "bigz" else "bigq" r0(x * p10) / p10 } ```

roundQ function