## Rounding of Numbers

## Usage

    ceiling(x)
    floor(x)
    round(x, digits = 0)
    signif(x, digits = 6)
    trunc(x)

## Description

`ceiling` takes a single numeric argument `x` and returns a numeric vector containing the smallest integers not less than the corresponding elements of `x`.

`floor` takes a single numeric argument `x` and returns a numeric vector containing the largest integers not greater than the corresponding elements of `x`.

`round` rounds the values in its first argument to the specified number of decimal places (default 0). Note that for rounding off a 5, the IEEE standard is used, ``go to the even digit''. Therefore `round(0.5)` is `0` and `round(-1.5)` is `-2`.

`signif` rounds the values in its first argument to the specified number of significant digits.

`trunc` takes a single numeric argument `x` and returns a numeric vector containing the integers by truncating the values in `x` toward `0`.

## See Also

`as.integer`.

## Examples

    round(.5 + -2:4) # IEEE rounding: -2  0  0  2  2  4  4
    ( x1 <- seq(-2, 4, by = .5) )
    round(x1)#-- IEEE rounding !
    x1[trunc(x1) != floor(x1)]
    x1[round(x1) != floor(x1 + .5)]
    all(trunc(x1) == as.integer(x1))# TRUE
    non.int <- ceiling(x1) != floor(x1)
    all(non.int == (ceiling(x1) != trunc(x1) | trunc(x1) != floor(x1)))
    # TRUE
    all((signif(x1, 1) != round(x1,1)) == (non.int & abs(x1)>1)) # TRUE

    x2 <- pi * 100^(-1:3)
    round(x2, 3)
    signif(x2, 3)

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