`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.

```
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.

`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.`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.`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.\ifelse{latex}{\out{~}}{ } `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.

`as.integer`

.
```
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)
```

Run the code above in your browser using DataLab