roundQ: Rounding Big Rationals ("bigq") to Decimals
In gmp: Multiple Precision Arithmetic

roundQ

R Documentation

Rounding Big Rationals ("bigq") to Decimals

Description

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).

Usage

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 R's `round`.

Value

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) .

Author(s)

Martin Maechler, ETH Zurich

References

The vignette “Exact Decimal Rounding via Rationals” from CRAN package round,

Wikipedia, Rounding, notably "Round half to even": https://en.wikipedia.org/wiki/Rounding#Round_half_to_even

Examples

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 == <n>.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
}

gmp documentation built on July 9, 2023, 7 p.m.