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+% ALGORITHMS for LaTeX version 2e
+%
+% Current maintainer: Rogério Brito <rbrito@ime.usp.br>
+% Previous maintainer: Peter Williams <pwil3058@bigpond.net.au>
+%
+% This document file is free software; you can redistribute it and/or
+% modify it under the terms of the GNU Lesser General Public License as
+% published by the Free Software Foundation; either version 2 of the
+% License, or (at your option) any later version.
+%
+% This document file is distributed in the hope that it will be useful, but
+% WITHOUT ANY WARRANTY; without even the implied warranty of
+% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser
+% General Public License for more details.
+%
+% You should have received a copy of the GNU Lesser General Public License
+% along with this document file; if not, write to the Free Software
+% Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307,
+% USA.
+%
+\documentclass{article}
+
+\usepackage[latin1]{inputenc}
+\usepackage[T1]{fontenc}
+\usepackage{lmodern}
+\usepackage[pdfstartview={FitH}]{hyperref}
+\usepackage{algorithm}
+\usepackage{algorithmic}
+
+\title{Algorithms}
+\author{Rogério Brito\\
+ \href{mailto:rbrito@ime.usp.br}{rbrito@ime.usp.br}\thanks{Sincere thanks
+ go to the original maintainer of this package, Peter Williams, and for
+ being kind enough to allow me to continue with his quite useful work.}}
+
+\newcommand{\keyword}[1]{\texttt{#1}}
+\newcommand{\filename}[1]{\texttt{#1}}
+\newcommand{\latcom}[1]{\texttt{$\backslash$#1}}
+
+\setcounter{tocdepth}{2}
+
+\begin{document}
+\maketitle
+\tableofcontents
+%\listofalgorithms
+
+\section{Introduction}
+
+This package provides two environments, \keyword{algorithmic} and
+\keyword{algorithm}, which are designed to be used together but may,
+depending on the necessities of the author, be used separately.
+
+The \keyword{algorithmic} environment provides an environment for
+describing algorithms and the \keyword{algorithm} environment provides a
+``float'' wrapper for algorithms (implemented using \keyword{algorithmic}
+or some other method at the author's option). The reason that two
+environments are provided is to allow the author maximum flexibility.
+
+This work may be distributed and/or modified under the conditions of the
+GNU Lesser General Public License as published by the Free Software
+Foundation (see the file \filename{COPYING} included in this package).
+Currently, this package consists of three files: \filename{algorithm.sty},
+\filename{algorithmic.sty} and \filename{algorithms.tex} (the source of
+this document). This is likely to change in the near future.
+
+\section{The \keyword{algorithmic} Environment}
+\label{sec:algorithmic-envir}
+Within an \keyword{algorithmic} a number of commands for typesetting
+popular algorithmic constructs are available.
+In general, the commands provided can be arbitrarily nested to
+describe quite complex algorithms.
+An optional argument to the \verb+\begin{algorithmic}+ statement can be
+used to turn on line numbering by giving a positive integer indicating the
+required frequency of line numbering.
+For example, \verb+\begin{algorithmic}[5]+ would cause every fifth line to
+be numbered.
+
+\subsection{The Simple Statement}
+
+The simple statement takes the form
+\begin{verbatim}
+\STATE <text>
+\end{verbatim}
+and is used for simple statements, e.g.
+\begin{verbatim}
+\begin{algorithmic}
+\STATE $S \leftarrow 0$
+\end{algorithmic}
+\end{verbatim}
+would produce
+\begin{algorithmic}
+ \STATE $S \leftarrow 0$
+\end{algorithmic}
+and with line numbering selected for every line using
+\begin{verbatim}
+\begin{algorithmic}[1]
+\STATE $S \leftarrow 0$
+\end{algorithmic}
+\end{verbatim}
+would produce
+\begin{algorithmic}[1]
+ \STATE $S \leftarrow 0$
+\end{algorithmic}
+For users of earlier versions of \keyword{algorithmic} this construct is
+a cause of an incompatibility.
+In the earlier version, instead of starting simple statements with the
+\verb+\STATE+
+command, simple statements were entered as free text and terminated with
+\verb+\\+ command.
+Unfortunately, this simpler method failed to survive the modifications
+necessary for statement numbering.
+However, the \verb+\\+ command can still be used to force a line break within
+a simple statement.
+
+\subsection{The \emph{if-then-else} Construct}
+
+The \emph{if-then-else} construct takes the forms.
+\begin{verbatim}
+\IF{<condition>} <text> \ENDIF
+\IF{<condition>} <text1> \ELSE <text2> \ENDIF
+\IF{<condition1>} <text1> \ELSIF{<condition2>} <text2> \ELSE <text3> \ENDIF
+\end{verbatim}
+In the third of these forms there is no limit placed on the number
+of \verb+\ELSIF{<C>}+ that may be used.
+For example,
+\begin{verbatim}
+\begin{algorithmic}
+\IF{some condition is true}
+\STATE do some processing
+\ELSIF{some other condition is true}
+\STATE do some different processing
+\ELSIF{some even more bizarre condition is met}
+\STATE do something else
+\ELSE
+\STATE do the default actions
+\ENDIF
+\end{algorithmic}
+\end{verbatim}
+would produce
+\begin{algorithmic}
+ \IF{some condition is true}
+ \STATE do some processing
+ \ELSIF{some other condition is true}
+ \STATE do some different processing
+ \ELSIF{some even more bizarre condition is met}
+ \STATE do something else
+ \ELSE
+ \STATE do the default actions
+ \ENDIF
+\end{algorithmic}
+with appropriate indentations.
+
+\subsection{The \emph{for} Loop}
+
+The \emph{for} loop takes the forms.
+\begin{verbatim}
+\FOR{<condition>} <text> \ENDFOR
+\FORALL{<condition>} <text> \ENDFOR
+\end{verbatim}
+For example,
+\begin{verbatim}
+\begin{algorithmic}
+\FOR{$i=0$ to $10$}
+\STATE carry out some processing
+\ENDFOR
+\end{algorithmic}
+\end{verbatim}
+produces
+\begin{algorithmic}
+ \FOR{$i=0$ to $10$}
+ \STATE carry out some processing
+ \ENDFOR
+\end{algorithmic}
+and
+\begin{verbatim}
+\begin{algorithmic}[1]
+\FORALL{$i$ such that $0\leq i\leq 10$}
+\STATE carry out some processing
+\ENDFOR
+\end{algorithmic}
+\end{verbatim}
+produces
+\begin{algorithmic}[1]
+ \FORALL{$i$ such that $0\leq i\leq 10$}
+ \STATE carry out some processing
+ \ENDFOR
+\end{algorithmic}
+
+\subsection{The \emph{while} Loop}
+
+The \emph{while} loop takes the form.
+\begin{verbatim}
+\WHILE{<condition>} <text> \ENDWHILE
+\end{verbatim}
+For example,
+\begin{verbatim}
+\begin{algorithmic}
+\WHILE{some condition holds}
+\STATE carry out some processing
+\ENDWHILE
+\end{algorithmic}
+\end{verbatim}
+produces
+\begin{algorithmic}
+ \WHILE{some condition holds}
+ \STATE carry out some processing
+ \ENDWHILE
+\end{algorithmic}
+
+\subsection{The \emph{repeat-until} Loop}
+
+The \emph{repeat-until} loop takes the form.
+\begin{verbatim}
+\REPEAT <text> \UNTIL{<condition>}
+\end{verbatim}
+For example,
+\begin{verbatim}
+\begin{algorithmic}
+\REPEAT
+\STATE carry out some processing
+\UNTIL{some condition is met}
+\end{algorithmic}
+\end{verbatim}
+produces
+\begin{algorithmic}
+ \REPEAT
+ \STATE carry out some processing
+ \UNTIL{some condition is met}
+\end{algorithmic}
+
+\subsection{The Infinite Loop}
+
+The infinite loop takes the form.
+\begin{verbatim}
+\LOOP <text> \ENDLOOP
+\end{verbatim}
+For example,
+\begin{verbatim}
+\begin{algorithmic}
+\LOOP
+\STATE this processing will be repeated forever
+\ENDLOOP
+\end{algorithmic}
+\end{verbatim}
+produces
+\begin{algorithmic}
+ \LOOP
+ \STATE this processing will be repeated forever
+ \ENDLOOP
+\end{algorithmic}
+
+\subsection{The Precondition}
+
+The precondition (that must be met if an algorithm is to correctly
+execute) takes the form:
+\begin{verbatim}
+\REQUIRE <text>
+\end{verbatim}
+For example,
+\begin{verbatim}
+\begin{algorithmic}
+\REQUIRE $x \neq 0$ and $n \geq 0$
+\end{algorithmic}
+\end{verbatim}
+produces
+\begin{algorithmic}
+ \REQUIRE $x \neq 0$ and $n \geq 0$
+\end{algorithmic}
+
+\subsection{The Postcondition}
+
+The postcondition (that must be met after an algorithm has correctly
+executed) takes the form:
+\begin{verbatim}
+\ENSURE <text>
+\end{verbatim}
+For example,
+\begin{verbatim}
+\begin{algorithmic}
+\ENSURE $x \neq 0$ and $n \geq 0$
+\end{algorithmic}
+\end{verbatim}
+produces
+\begin{algorithmic}
+ \ENSURE $x \neq 0$ and $n \geq 0$
+\end{algorithmic}
+
+\subsection{Returning Values}
+
+The \keyword{algorithmic} environment offers a special statement for
+explicitly returning values in algorithms. It has the syntax:
+\begin{verbatim}
+\RETURN <text>
+\end{verbatim}
+For example,
+\begin{verbatim}
+\begin{algorithmic}
+\RETURN $(x+y)/2$
+\end{algorithmic}
+\end{verbatim}
+produces
+\begin{algorithmic}
+ \RETURN $(x+y)/2$
+\end{algorithmic}
+
+\subsection{Printing Messages}
+
+Another feature of the \keyword{algorithmic} environment is that it
+currently provides a standard way of printing values (which is an operation
+used enough to merit its own keyword). It has the syntax:
+\begin{verbatim}
+\PRINT <text>
+\end{verbatim}
+For example,
+\begin{verbatim}
+\begin{algorithmic}
+\PRINT \texttt{``Hello, World!''}
+\end{algorithmic}
+\end{verbatim}
+produces
+\begin{algorithmic}
+ \PRINT \texttt{``Hello, World!''}
+\end{algorithmic}
+
+\subsection{Comments}
+
+Comments may be inserted at most points in an algorithm using the form:
+\begin{verbatim}
+\COMMENT{<text>}
+\end{verbatim}
+For example,
+\begin{verbatim}
+\begin{algorithmic}
+\STATE do something \COMMENT{this is a comment}
+\end{algorithmic}
+\end{verbatim}
+produces
+\begin{algorithmic}
+ \STATE do something \COMMENT{this is a comment}
+\end{algorithmic}
+Because the mechanisms used to build the various algorithmic structures
+make it difficult to use the above mechanism for placing comments at the
+end of the first line of a construct, the commands \verb+\IF+,
+\verb+\ELSIF+, \verb+\ELSE+, \verb+\WHILE+, \verb+\FOR+,
+\verb+\FORALL+, \verb+\REPEAT+
+and \verb+\LOOP+ all take an optional argument which will be treated
+as a comment to be placed at the end of the line on which they appear.
+For example,
+\begin{algorithmic}
+ \REPEAT[this is comment number one]
+ \IF[this is comment number two]{condition one is met}
+ \STATE do something
+ \ELSIF[this is comment number three]{condition two is met}
+ \STATE do something else
+ \ELSE[this is comment number four]
+ \STATE do nothing
+ \ENDIF
+ \UNTIL{hell freezes over}
+\end{algorithmic}
+
+\subsection{An Example}
+
+The following example demonstrates the use of the \keyword{algorithmic}
+environment to describe a complete algorithm. The following input
+\begin{verbatim}
+\begin{algorithmic}
+\REQUIRE $n \geq 0$
+\ENSURE $y = x^n$
+\STATE $y \Leftarrow 1$
+\STATE $X \Leftarrow x$
+\STATE $N \Leftarrow n$
+\WHILE{$N \neq 0$}
+\IF{$N$ is even}
+\STATE $X \Leftarrow X \times X$
+\STATE $N \Leftarrow N / 2$
+\ELSE[$N$ is odd]
+\STATE $y \Leftarrow y \times X$
+\STATE $N \Leftarrow N - 1$
+\ENDIF
+\ENDWHILE
+\end{algorithmic}
+\end{verbatim}
+will produce
+\begin{algorithmic}
+ \REQUIRE $n \geq 0$
+ \ENSURE $y = x^n$
+ \STATE $y \Leftarrow 1$
+ \STATE $X \Leftarrow x$
+ \STATE $N \Leftarrow n$
+ \WHILE{$N \neq 0$}
+ \IF{$N$ is even}
+ \STATE $X \Leftarrow X \times X$
+ \STATE $N \Leftarrow N / 2$
+ \ELSE[$N$ is odd]
+ \STATE $y \Leftarrow y \times X$
+ \STATE $N \Leftarrow N - 1$
+ \ENDIF
+ \ENDWHILE
+\end{algorithmic}
+which is an algorithm for finding the value of a number taken to a
+non-negative power.
+
+\subsection{Options and Customization}
+
+There is a single option, \keyword{noend}\label{kwd:noend} that may be
+invoked when the \texttt{algorithmic} package is loaded. With this option
+invoked the \emph{end} statements are omitted in the output. This allows
+space to be saved in the output document when this is an issue.
+
+\subsubsection{Changing Indentation}
+\label{sec:changing-indentation}
+In the spirit of saving vertical space (which is especially important when
+submitting a paper for a journal, where space is frequently limited for
+authors), the \keyword{algorithmic} environment offers, beginning with the
+version released in 2005-05-08, a way to control the amount of indentation
+that is used by a given algorithm.
+
+The amount of indentation to be used is given by the command
+\begin{verbatim}
+\algsetup{indent=lenght}
+\end{verbatim}
+where \emph{length} is any valid length used by \TeX. The default value of
+the indentation used by the \keyword{algorithmic} environment is $1$ em
+(for ``backward compatibility reasons''), but a value of $2$ em or more is
+recommended, depending on the publication. For example, the snippet
+\begin{verbatim}
+\algsetup{indent=2em}
+\begin{algorithmic}[1]
+ \STATE $a \Leftarrow 1$
+ \IF{$a$ is even}
+ \PRINT ``$a$ is even''
+ \ELSE
+ \PRINT ``$a$ is odd''
+\end{algorithmic}
+\end{verbatim}
+produces
+\algsetup{indent=2em}
+\begin{algorithmic}[1]
+ \STATE $a \Leftarrow 1$
+ \IF{$a$ is even}
+ \PRINT ``$a$ is even''
+ \ELSE
+ \PRINT ``$a$ is odd''
+ \ENDIF
+\end{algorithmic}
+while
+\begin{verbatim}
+\algsetup{indent=5em}
+\begin{algorithmic}[1]
+ \STATE $a \Leftarrow 1$
+ \IF{$a$ is even}
+ \PRINT ``$a$ is even''
+ \ELSE
+ \PRINT ``$a$ is odd''
+\end{algorithmic}
+\end{verbatim}
+would produce
+\algsetup{indent=5em}
+\begin{algorithmic}[1]
+ \STATE $a \Leftarrow 1$
+ \IF{$a$ is even}
+ \PRINT ``$a$ is even''
+ \ELSE
+ \PRINT ``$a$ is odd''
+ \ENDIF
+\end{algorithmic}
+\algsetup{indent=1em}
+
+The intended use of this option is to allow the author to omit the
+\emph{end} (see Section~\ref{kwd:noend} for details) statements without
+loosing readability, by increasing the amount of indentation to a suitable
+level.
+
+\subsubsection{Changing Line Numbering}
+
+As mentioned in Section~\ref{sec:algorithmic-envir} and illustrated in
+Section~\ref{sec:changing-indentation}, \keyword{algorithms} already
+provides you with the possibility of numbering lines.
+
+Starting with the version released in 2005-07-05, you can now change two
+aspects of line numbering: the size of the line numbers (which, by default,
+is \verb+\footnotesize+) and the delimiter used to separate the line number
+from the code (which, by default, is \verb+:+, i.e., a colon).
+
+You can change the size of the line numbers using the command:
+\begin{verbatim}
+\algsetup{linenosize=size}
+\end{verbatim}
+where \emph{size} is any of the various commands provided by \LaTeX\ to
+change the size of the font to be used. Among others, useful values are
+\verb+\tiny+, \verb+\scriptsize+, \verb+\footnotesize+ and \verb+\small+.
+Please see the complete list of sizes in your \LaTeX\ documentation.
+
+As another frequently requested feature, you can change the delimiter used
+with the line numbers by issuing the command:
+\begin{verbatim}
+\algsetup{linenodelimiter=delimiter}
+\end{verbatim}
+where \emph{delimiter} is any ``well-formed'' string, including the empty
+string. With this command, you can change the colon to a period (\verb+.+)
+by issuing the command
+\begin{verbatim}
+\algsetup{linenodelimiter=.}
+\end{verbatim}
+or even omit the delimiter, by specifying the empty string or a space
+(\verb+\ +), whatever seems best for your document.
+
+As an example of such commands, the code produced by
+\begin{verbatim}
+\algsetup{linenosize=\small,
+ linenodelimiter=.}
+\begin{algorithmic}[1]
+ \STATE $i \leftarrow 10$
+ \RETURN $i$
+\end{algorithmic}
+\end{verbatim}
+would be something like
+\algsetup{linenosize=\small,
+ linenodelimiter=.}
+\begin{algorithmic}[1]
+ \STATE $i \leftarrow 10$
+ \RETURN $i$
+\end{algorithmic}
+\algsetup{linenosize=\footnotesize,
+ linenodelimiter=:}
+
+\subsubsection{Customization}
+
+In order to facilitate the use of this package with foreign languages, all
+of the words in the output are produced via redefinable macro commands.
+The default definitions of these macros are:
+\begin{verbatim}
+\newcommand{\algorithmicrequire}{\textbf{Require:}}
+\newcommand{\algorithmicensure}{\textbf{Ensure:}}
+\newcommand{\algorithmicend}{\textbf{end}}
+\newcommand{\algorithmicif}{\textbf{if}}
+\newcommand{\algorithmicthen}{\textbf{then}}
+\newcommand{\algorithmicelse}{\textbf{else}}
+\newcommand{\algorithmicelsif}{\algorithmicelse\ \algorithmicif}
+\newcommand{\algorithmicendif}{\algorithmicend\ \algorithmicif}
+\newcommand{\algorithmicfor}{\textbf{for}}
+\newcommand{\algorithmicforall}{\textbf{for all}}
+\newcommand{\algorithmicdo}{\textbf{do}}
+\newcommand{\algorithmicendfor}{\algorithmicend\ \algorithmicfor}
+\newcommand{\algorithmicwhile}{\textbf{while}}
+\newcommand{\algorithmicendwhile}{\algorithmicend\ \algorithmicwhile}
+\newcommand{\algorithmicloop}{\textbf{loop}}
+\newcommand{\algorithmicendloop}{\algorithmicend\ \algorithmicloop}
+\newcommand{\algorithmicrepeat}{\textbf{repeat}}
+\newcommand{\algorithmicuntil}{\textbf{until}}
+\newcommand{\algorithmicprint}{\textbf{print}}
+\newcommand{\algorithmicreturn}{\textbf{return}}
+\end{verbatim}
+
+In addition, the formatting of comments is implemented via a single
+argument command macro which may also be redefined.
+The default definition is
+\begin{verbatim}
+\newcommand{\algorithmiccomment}[1]{\{#1\}}
+\end{verbatim}
+and another option that may be interesting for users familiar with C-like
+languages is to redefine the comments to be
+\begin{verbatim}
+\renewcommand{\algorithmiccomment}[1]{//#1}
+\end{verbatim}
+
+Comments produced this way would be like this:
+\renewcommand{\algorithmiccomment}[1]{//#1}
+\begin{algorithmic}
+ \STATE $i \leftarrow i +1$ \COMMENT{Increments $i$}
+\end{algorithmic}
+This second way to present comments may become the default in a future
+version of the package.
+
+\section{The \keyword{algorithm} Environment}
+
+\subsection{General}
+\begin{algorithm}
+\caption{Calculate $y = x^n$}
+\label{alg1}
+\begin{algorithmic}
+\REQUIRE $n \geq 0 \vee x \neq 0$
+\ENSURE $y = x^n$
+\STATE $y \Leftarrow 1$
+\IF{$n < 0$}
+\STATE $X \Leftarrow 1 / x$
+\STATE $N \Leftarrow -n$
+\ELSE
+\STATE $X \Leftarrow x$
+\STATE $N \Leftarrow n$
+\ENDIF
+\WHILE{$N \neq 0$}
+\IF{$N$ is even}
+\STATE $X \Leftarrow X \times X$
+\STATE $N \Leftarrow N / 2$
+\ELSE[$N$ is odd]
+\STATE $y \Leftarrow y \times X$
+\STATE $N \Leftarrow N - 1$
+\ENDIF
+\ENDWHILE
+\end{algorithmic}
+\end{algorithm}
+
+When placed within the text without being encapsulated in a floating
+environment \texttt{algorithmic} environments may be split over a page
+boundary greatly detracting from their appearance.
+In addition, it is useful to have algorithms numbered for reference
+and for lists of algorithms to be appended to the list of contents.
+The \texttt{algorithm} environment is meant to address these concerns
+by providing a floating environment for algorithms.
+For example, the input text
+\begin{verbatim}
+\begin{algorithm}
+\caption{Calculate $y = x^n$}
+\label{alg1}
+\begin{algorithmic}
+\REQUIRE $n \geq 0 \vee x \neq 0$
+\ENSURE $y = x^n$
+\STATE $y \Leftarrow 1$
+\IF{$n < 0$}
+\STATE $X \Leftarrow 1 / x$
+\STATE $N \Leftarrow -n$
+\ELSE
+\STATE $X \Leftarrow x$
+\STATE $N \Leftarrow n$
+\ENDIF
+\WHILE{$N \neq 0$}
+\IF{$N$ is even}
+\STATE $X \Leftarrow X \times X$
+\STATE $N \Leftarrow N / 2$
+\ELSE[$N$ is odd]
+\STATE $y \Leftarrow y \times X$
+\STATE $N \Leftarrow N - 1$
+\ENDIF
+\ENDWHILE
+\end{algorithmic}
+\end{algorithm}
+\end{verbatim}
+produces Algorithm~\ref{alg1} which is a slightly modified version of
+the earlier algorithm for determining the value of a number taken to an
+integer power.
+In this case, provided the power may be negative provided the number is
+not zero.
+
+The command \verb+\listofalgorithms+ may be used to produce a list
+of algorithms as part of the table contents as shown at the beginning of
+this document.
+An auxiliary file with a suffix of \texttt{.loa} is produced when this
+feature is used.
+
+\subsection{Options}
+
+The appearance of the typeset algorithm may be changed by use of the
+options: \texttt{plain}, \texttt{boxed} or \texttt{ruled} during the
+loading of the \texttt{algorithm} package.
+The default option is \texttt{ruled}.
+
+The numbering of algorithms can be influenced by providing the name of
+the document component within which numbering should be recommenced.
+The legal values for this option are: \texttt{part}, \texttt{chapter},
+\texttt{section}, \texttt{subsection}, \texttt{subsubsection}
+or \texttt{nothing}.
+The default value is \texttt{nothing} which causes algorithms to be
+numbered sequentially throughout the document.
+
+\subsection{Customization}
+
+In order to facilitate the use of this package with foreign languages,
+methods have been provided to facilitate the necessary modifications.
+
+The title used in the caption within \texttt{algorithm} environment
+can be set by use of the standard \verb+\floatname+ command which is
+provided as part of the \texttt{float} package which was used to
+implement this package.
+For example,
+\begin{verbatim}
+\floatname{algorithm}{Procedure}
+\end{verbatim}
+would cause \textbf{Procedure} to be used instead of \textbf{Algorithm}
+within the caption of algorithms.
+
+In a manner analogous to that available for the built in floating
+environments, the heading used for the list of algorithms may be changed
+by redefining the command \verb+listalgorithmname+.
+The default definition for this command is
+\begin{verbatim}
+\newcommand{\listalgorithmname}{List of Algorithms}
+\end{verbatim}
+
+\section{Labels and References in Algorithms}
+
+With the release of 2005-07-05, now \keyword{algorithmic} accepts labels
+and references to specific lines of a given algorithm, so you don't have to
+hardcode the line numbers yourself when trying to explain what the code
+does in your texts. Thanks to Arnaud Legrand for the suggestion and patch
+for this highly missed feature.
+
+An example of its use is shown in Algorithm~\ref{alg2}.
+\begin{algorithm}[h!]
+\caption{Calculate $y = x^n$}
+\label{alg2}
+\begin{algorithmic}[1]
+\REQUIRE $n \geq 0 \vee x \neq 0$
+\ENSURE $y = x^n$
+\STATE $y \Leftarrow 1$
+\IF{$n < 0$}
+\STATE $X \Leftarrow 1 / x$
+\STATE $N \Leftarrow -n$
+\ELSE
+\STATE $X \Leftarrow x$
+\STATE $N \Leftarrow n$
+\ENDIF
+\WHILE{$N \neq 0$}
+\IF{$N$ is even}\label{alg:n-is-even}
+\STATE $X \Leftarrow X \times X$
+\STATE $N \Leftarrow N / 2$
+\ELSE\label{alg:n-is-odd}
+\STATE $y \Leftarrow y \times X$
+\STATE $N \Leftarrow N - 1$
+\ENDIF
+\ENDWHILE
+\end{algorithmic}
+\end{algorithm}
+See that, in line~\ref{alg:n-is-even}, we deal with the case of $N$ being
+even, while, in line~\ref{alg:n-is-odd}, we give treatment to the case of
+$N$ being odd.
+
+\end{document}