\HeaderA{Round}{Rounding of Numbers}{Round}
\aliasA{ceiling}{Round}{ceiling}
\aliasA{floor}{Round}{floor}
\aliasA{round}{Round}{round}
\aliasA{signif}{Round}{signif}
\aliasA{trunc}{Round}{trunc}
\aliasA{zapsmall}{Round}{zapsmall}
\keyword{arith}{Round}
\begin{Description}\relax
\code{ceiling} takes a single numeric argument \code{x} and returns a
numeric vector containing the smallest integers not less than the
corresponding elements of \code{x}.

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

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

\code{round} rounds the values in its first argument to the specified
number of decimal places (default 0).

\code{signif} rounds the values in its first argument to the specified
number of significant digits.

\code{zapsmall} determines a \code{digits} argument \code{dr} for
calling \code{round(x, digits = dr)} such that values close to
zero (compared with the maximal absolute value) are \sQuote{zapped},
i.e., treated as \code{0}.
\end{Description}
\begin{Usage}
\begin{verbatim}
ceiling(x)
floor(x)
trunc(x, ...)

round(x, digits = 0)
signif(x, digits = 6)
zapsmall(x, digits = getOption("digits"))
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{x}] a numeric vector.  A complex vector is allowed for
\code{round}, \code{signif} and \code{zapsmall}.
\item[\code{digits}] integer indicating the precision to be used.
\item[\code{...}] arguments to be passed to methods.
\end{ldescription}
\end{Arguments}
\begin{Details}\relax
All but \code{zapsmall} are generic functions: methods can be
defined for them individually or via the
\code{\LinkA{Math}{Math}} group generic.

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

For \code{signif} the recognized values of \code{digits} are
\code{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 \code{zapsmall} are primitive, so positional argument
matching is used for the default methods of \code{round} and
\code{signif}.
\end{Details}
\begin{Section}{S4 methods}
\code{ceiling}, \code{floor} and \code{trunc} are S4 generic and
members of the \code{\LinkA{Math}{Math}} group
generic.  As an S4 generic, \code{trunc} has only one argument.

\code{round} and \code{signif} are S4 generic and members of the
\code{\LinkA{Math2}{Math2}} group generic.
\end{Section}
\begin{References}\relax
Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988)
\emph{The New S Language}.
Wadsworth \& Brooks/Cole. (Except \code{zapsmall}.)

Chambers, J. M. (1998)
\emph{Programming with Data. A Guide to the S Language}.
Springer. (\code{zapsmall}.)
\end{References}
\begin{SeeAlso}\relax
\code{\LinkA{as.integer}{as.integer}}.
\end{SeeAlso}
\begin{Examples}
\begin{ExampleCode}
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))
\end{ExampleCode}
\end{Examples}

