`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). See ‘Details’ about
“round to even” when rounding off a 5.

`signif`

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

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

x

a numeric vector. Or, for `round`

and `signif`

, a
complex vector.

digits

integer indicating the number of decimal places
(`round`

) or significant digits (`signif`

) to be used.
Negative values are allowed (see ‘Details’).

…

arguments to be passed to methods.

These are all (internally) S4 generic.

`ceiling`

, `floor`

and `trunc`

are members of the
`Math`

group generic. As an S4
generic, `trunc`

has only one argument.

`round`

and `signif`

are members of the
`Math2`

group generic.

The realities of computer arithmetic can cause unexpected results,
especially with `floor`

and `ceiling`

. For example, we
‘know’ that `floor(log(x, base = 8))`

for `x = 8`

is
`1`

, but `0`

has been seen on an R platform. It is
normally necessary to use a tolerance.

These 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 (see also
‘IEEE 754’) 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`

).

Rounding to a negative number of digits means rounding to a power of
ten, so for example `round(x, digits = -2)`

rounds to the nearest
hundred.

For `signif`

the recognized values of `digits`

are
`1...22`

, and non-missing values are rounded to the nearest
integer in that range. 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.

These are all primitive functions.

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

The ISO/IEC/IEEE 60559:2011 standard is available for money from https://www.iso.org.

The IEEE 745:2008 standard is more openly documented, e.g, at https://en.wikipedia.org/wiki/IEEE_754.

# NOT RUN { round(.5 + -2:4) # IEEE / IEC rounding: -2 0 0 2 2 4 4 ## (this is *good* behaviour -- do *NOT* report it as bug !) ( x1 <- seq(-2, 4, by = .5) ) round(x1) #-- IEEE / IEC 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) # }