\Header{Round}{Rounding of Numbers}
\alias{ceiling}{Round}
\alias{floor}{Round}
\alias{round}{Round}
\alias{signif}{Round}
\alias{trunc}{Round}
\alias{trunc.default}{Round}
\alias{zapsmall}{Round}
\keyword{arith}{Round}
\begin{Usage}
\begin{verbatim}
ceiling(x)
floor(x)
round(x, digits = 0)
signif(x, digits = 6)
trunc(x)
zapsmall(x, digits= .Options$digits)
\end{verbatim}
\end{Usage}
\begin{Description}
\texttt{ceiling} takes a single numeric argument \texttt{x} and returns a
numeric vector containing the smallest integers not less than the
corresponding elements of \texttt{x}.

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

\texttt{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,
\emph{``go to the even digit''}.
Therefore \texttt{round(0.5)} is \texttt{0} and \texttt{round(-1.5)} is \texttt{-2}.

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

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

\texttt{zapsmall} determines a \texttt{digits} argument \texttt{dr} for calling
\texttt{round(x, digits = dr)} such that values ``close to zero'' values
are ``zapped'', i.e., treated as \texttt{0}.\end{Description}
\begin{SeeAlso}
\texttt{\Link{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)]
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)

print   (x2 / 1000, digits=4)
zapsmall(x2 / 1000, digits=4)
zapsmall(exp(1i*0:4*pi/2))
\end{ExampleCode}
\end{Examples}

