Round {base} | R Documentation

## Rounding of Numbers

### 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`.

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

`round` rounds the values in its first argument to the specified number of decimal places (default 0).

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

`zapsmall` determines a `digits` argument `dr` for calling `round(x, digits = dr)` such that values close to zero (compared with the maximal absolute value) are ‘zapped’, i.e., treated as `0`.

### Usage

    ceiling(x)
    floor(x)
    trunc(x, ...)

    round(x, digits = 0)
    signif(x, digits = 6)
    zapsmall(x, digits = getOption("digits"))

### Arguments

`x` | a numeric vector. A complex vector is allowed for `round`, `signif` and `zapsmall`.
`digits` | integer indicating the precision to be used.
`...` | arguments to be passed to methods.

### Details

All but `zapsmall` are generic functions: methods can be defined for them individually or via the `Math` group generic.

Note that for rounding off a 5, the IEC 60559 standard is expected to be used, ‘go to the even digit’. Therefore `round(0.5)` is `0` and `round(-1.5)` is `-2`. However, this is dependent on OS services and on representation error (since e.g. `0.15` is not represented exactly, the rounding rule applies to the represented number and not to the printed number, and so `round(0.15, 1)` could be either `0.1` or `0.2`).

For `signif` the recognized values of `digits` are `1...22`. Complex numbers are rounded to retain the specified number of digits in the larger of the components. Each element of the vector is rounded individually, unlike printing.

All except `zapsmall` are primitive, but as from R 2.7.0 arguments are matched by name in `round` and `signif` (whereas the default method for `ceiling`, `floor` and `trunc` ignore argument names).

### S4 methods

`ceiling`, `floor` and `trunc` are S4 generic and members of the `Math` group generic. As an S4 generic, `trunc` has only one argument.

`round` and `signif` are S4 generic and members of the `Math2` group generic.

### References

Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth & Brooks/Cole. (Except `zapsmall`.)

Chambers, J. M. (1998) Programming with Data. A Guide to the S Language. Springer. (`zapsmall`.)

### 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)]
    (non.int <- ceiling(x1) != floor(x1))

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

    print   (x2 / 1000, digits=4)
    zapsmall(x2 / 1000, digits=4)
    zapsmall(exp(1i*0:4*pi/2))

[Package base version 2.8.1 Index]