path: root/Master/texmf-dist/source/latex/lcg/lcg.dtx

% \iffalse
% File: lcg.dtx
%% Copyright (C) 2001 Erich Janka (janka@utanet.at)
%%
%% This package may be distributed  and/or modified under the terms of the
%% LaTeX Project Public License, as described in lppl.txt in the base
%% LaTeX distribution, either version 1.2 or (at your option)
%% any later version.
%% The latest version of this license is in
%%    http://www.latex-project.org/lppl.txt
%%
%% This program consits of the files lcg.dtx and lcg.ins
%
%<lcg>\NeedsTeXFormat{LaTeX2e}
%<lcg>\ProvidesPackage{lcg}[2001/03/03 v1.0 generating random numbers]
%<lcg>\RequirePackage{keyval}
%
%<*driver>
\documentclass{ltxdoc}
\usepackage[first=10, last=20]{lcg}
\begin{document}
  \GetFileInfo{lcg.sty}
  \title{The \texttt{lcg} package}
  \author{Erich Janka\\ \texttt{janka@utanet.at}}
  \date{2001/03/03 (v1.0)}
  \maketitle
  \DocInput{lcg.dtx}
\end{document}
%
%</driver>
% \fi
%
% \iffalse
%<*lcg>
% \fi
%
% \newcommand{\mod}{\;\;\mbox{mod}\;\;}
% \newcommand{\key}[1]{\meta{#1}}
% \newcommand{\cntr}[1]{\texttt{#1}}
%
% \begin{abstract}
%
% This Package contains macros to generate (pseudo) random numbers
% with \LaTeX\ by a simple linear congruential generator.
% The user can specify a range of integers
% containing the generated random numbers.
%
% To pass options to the package, the \meta{key}=\meta{value}
% scheme of the \texttt{keyval} package is used.
%
% If no options are specified, random numbers will be
% generated in the interval from $1$ to $2^{31}-1 \;\;(= 2147483647)$.
% Let $S$ be the smallest and $L$ the largest number of the specified range,
% then the following inequalities must hold  because of
% limitations of \LaTeX:
%
% $$  -2^{31}+1 \leq S \leq L \leq  2^{31}-1   \qquad\mbox{and}\qquad
%     L-S \leq  2^{31}-2 $$
%
% The generated random numbers will be stored in a \LaTeX\
% counter definable by the user.
% \end{abstract}
%
% \section{User Interface}
%
% The \texttt{lcg} package is loaded with\\[1ex]
% \hspace*{2ex}\cmd{\usepackage\oarg{list of options}\{lcg\}}.\\[1ex]
% The optional Argument is a comma separated list of entries of
% the kind \key{key}=\key{value} or \key{key}. In the second case
% the key will be set to a standard value.
% For example the line\\[1ex]
% \hspace*{2ex}\cmd{\usepackage[first=10, last=20]\{lcg\}}\\[1ex]
% loads the package and generates the \LaTeX\ counter \cntr{rand}
% which will hold pseudo random numbers from $10$ to $20$.
% All available keys and their standard values are introduced below.
% \begin{macro}{\rand}
% Each call of the command \cmd{\rand} will write a new random number
% to the counter provided by the user with the key \key{counter} or
% to the standard counter of this package---\cntr{rand}. Now
% it's possible to do whatever can be done with counters. The command
% evokes a linear congruential random number generator described below.
% \end{macro}
% \begin{macro}{\reinitrand}
% The command \cmd{\reinitrand}\oarg{list of options} has
% one optional argument which is identical to the argument of
% \cmd{\usepackage},
% i.~e. the same keys in the comma separated list are allowed.
% The effect is that specified keys will be set and all others
% will be reset to their standard values.
% \end{macro}
% \begin{macro}{\chgrand}
% The syntax of the command \cmd{\chgrand} is identical to \cmd{\reinitrand}.
% The difference is that \cmd{\chgrand} will set the specified keys but
% won't effect any other key.
% \end{macro}
%
% \subsection{The Options}
%
% This section deals with the list of all available keys
% and their standard values.
% \begin{macro}{counter}
% This key sets the name of the \LaTeX\ counter where
% the random numbers will be stored.
% If the counter already exists (maybe somebody likes
% random page numbers), \LaTeX\ will prompt a
% warning and will use it. If the counter doesn't exist,
% it will be defined by this package and set to $0$.\\
% \textbf{Standard value:} rand
% \end{macro}
% \begin{macro}{first}
% This key sets the left boarder of the range within
% random numbers will be generated.
% Its value can be any number from $-2^{31}+1$ to $2^{31}-1$,
% as long as it is not greater than the value of the key \key{last}
% and the difference to the value of \key{last} doesn't exceed
% $2^{31}-2$.\\
% \textbf{Standard value:} $1$
% \end{macro}
% \begin{macro}{last}
% This key sets the right boarder of the range within
% random numbers will be generated. Its value can be any
% number from $-2^{31}+1$ to $2^{31}-1$,
% as long as it is not less than the value of the key \key{first}
% and the difference to the value of \key{first} doesn't exceed
% $2^{31}-2$.\\
% \textbf{Standard value:} $2^{31}-1$
% \end{macro}
% \begin{macro}{seed}
% The value of this key is the starting value
% for the algorithm generating the random numbers
% and must be within the range $1$ to $2^{31}-1$.
% If the value is smaller than $1$,
% the random number generator will
% be initialized with the time, the page number and
% the actual line of the file. This key allows
% reproduction of the sequences of random numbers.\\
% \textbf{Standard value:} $0$
% \end{macro}
% \begin{macro}{quiet}
% When using the \texttt{lcg} package it sends some lines of
% information to the screen and the \texttt{log}-file:
% \begin{itemize}
%   \setlength{\itemsep}{-3pt}
%   \item[--] The name of the counter holding the generated random numbers
%   \item[--] The lower bound of the range of random numbers
%   \item[--] The upper bound of the range of random numbers
%   \item[--] The initial value of the random number generator
% \end{itemize}
% To supress this output this key
% can be used. If the value starts with the letter \emph{y}, \emph{Y},
% \emph{j} or \emph{J}
% there will be no output whereas words beginning
% with the letters \emph{n} or \emph{N} won't supress it.\\
% \textbf{Standard value:} $y$
% \end{macro}
%
% \section{Example}
%
% This documentation loaded the package with:
% \begin{verbatim}
%   \usepackage[first=10, last=20]{lcg}\end{verbatim}
% The lines
% \begin{verbatim}
%   \rand\arabic{rand} \rand\arabic{rand} \rand\arabic{rand}
%   \rand\arabic{rand} \rand\arabic{rand} \rand\arabic{rand}
%   \rand\arabic{rand} \rand\arabic{rand} \rand\arabic{rand}\end{verbatim}
% generate these numbers (all between 10 and 20):
% \rand\arabic{rand} \rand\arabic{rand} \rand\arabic{rand}
% \rand\arabic{rand} \rand\arabic{rand} \rand\arabic{rand}
% \rand\arabic{rand} \rand\arabic{rand} \rand\arabic{rand}
%
% Now the counter \cntr{die} should simulate a die and hold
% random numbers from $1$ to $6$. In addition it is demonstrated
% how to switch off the output to the screen and to the \texttt{log}-file.
% This can achieved with one of the following lines:
% \begin{verbatim}
%   \reinitrand[last=6, counter=die, quiet]\end{verbatim}
% \reinitrand[last=6, counter=die]
% After that, the numbers
% \rand\arabic{die} \rand\arabic{die} \rand\arabic{die}
% \rand\arabic{die} \rand\arabic{die} \rand\arabic{die}.
% are a product of:
% \begin{verbatim}
%   \rand\arabic{die} \rand\arabic{die} \rand\arabic{die}
%   \rand\arabic{die} \rand\arabic{die} \rand\arabic{die}\end{verbatim}
% As one can see, the key \meta{first} has been reset to $1$. 
%
% The following lines  will change the range to $-6$ to $+6$
% without modifying any other option:
% \begin{verbatim}   \chgrand[first=-6]\end{verbatim} \chgrand[first=-6]
% Here the numbers
% \rand\arabic{die} \rand\arabic{die} \rand\arabic{die}
% \rand\arabic{die} \rand\arabic{die} \rand\arabic{die}
% are stored in a user defined counter and brought to paper
% by:
% \begin{verbatim}
%   \rand\arabic{die} \rand\arabic{die} \rand{arabic}{die}
%   \rand\arabic{die} \rand\arabic{die} \rand\arabic{die}\end{verbatim}
%
% At last, random numbers between $1$ and $12$ will
% be generated and stored in the standard counter \cntr{rand}.
% The seed will be set to $1234$. There will also be a warning because
% the name of the counter is set to \texttt{rand} which was already
% defined when calling the package:
% \begin{verbatim}   \reinitrand[last=12, seed=1234]\end{verbatim}
% \reinitrand[last=12, seed=1234]
% \begin{verbatim}
%   \rand\Roman{rand} \rand\Roman{rand} \rand\Roman{rand} \end{verbatim}
% These lines produce:  \rand\Roman{rand} \rand\Roman{rand} \rand\Roman{rand}.
% When using other formats than \texttt{arabic} for printing,
% the desired numbers might not appear on the screen
% because these formats don't support the full range of $2^{31}-1$.
%
%
% \section{The Linear Congruential Generator}
%
% The linear congruential generator used produces
% a sequence of numbers $I_j$ in the range from
% $1$ to $m$ by following rule:
% $$ I_{j+1} =   a I_j \mod m  $$
% where $I_0$ is set to a arbitrary starting value (called ``seed'').
% The quality of this generator depends on the choice of the
% parameters $a$ and $m$.
% Another problem is that when implementing the algorithm as above,
% the multiplication might leave the range \LaTeX\ can deal with.
% The solution is Schrage's method [\textsc{W.~Press} et~al.
% \emph{Numerical Recipies in \texttt{C}}\@.
% 2nd edition. Cambridge University Press 1992] which allows
% to perform the multiplications without leaving the given range.
% This is done by introducing two variables $r$ and $q$:
%  $$
%    m = a q + r  \qquad\mbox{with}\qquad
%    q = \left[m/a\right]\quad\mbox{and}\quad r = m \mod a
%  $$
% where $[\,\cdot\,]$ denotes the integer part of the argument.
% If $z$ is an integer and $0 \leq r < q$ and $0 < z < m-1$,
% then the following (in)equalities hold:
% \begin{eqnarray*}
%  &  0 \leq a \cdot (z \mod q) \leq m-1\\
%  &  0 \leq \left[m/a\right] \leq m-1\\
%  &  a z \mod m = \left\{
%       \begin{array}{ll} a \cdot (z \mod q ) -
%           \left[z/q\right] & \mbox{if the term is } \leq 0\\
%               a \cdot (z \mod q ) -
%           \left[z/q\right] + m & \mbox{otherwise}
%       \end{array}\right.
% \end{eqnarray*}
%
% To exploit the whole possible range and guarantee good performance,
% $a$ and $m$ are set as follows:
% $a = 7^5  \; = 16807$ and $m  = 2^{31}-1 \; = 2147483647$ and
% this gives $q=127773$ and $r=2836$.
%
%
% \section{The Code}
%
% \subsection{Checking for possible conflicts}
%
% The following lines check if the commands provided by
% this package are already defined:
%
%    \begin{macrocode}
\@ifundefined{rand}{}
       {\PackageWarning{lcg}{Command `rand' already defined}}
\@ifundefined{r@ndcountername}{}
       {\PackageWarning{lcg}{Command `r@ndcountername'
         already defined}}
%    \end{macrocode}
% Checking internal commands:
%    \begin{macrocode}
\@ifundefined{r@nd}{}
       {\PackageWarning{lcg}{Command `r@nd' already defined}}
\@ifundefined{initr@nd}{}
       {\PackageWarning{lcg}{Command `initr@nd' already defined}}
\@ifundefined{cutr@nger@nd}{}
       {\PackageWarning{lcg}{Command `cutr@nger@nd' already defined}}
\@ifundefined{@rderr@nd}{}
       {\PackageWarning{lcg}{Command `@rderr@nd' already defined}}
\@ifundefined{ProcessOptionsWithKVr@nd}{}
       {\PackageWarning{lcg}{Command `ProcessOptionsWithKVr@nd'
         already defined}}%
\@ifundefined{qui@t}{}
       {\PackageWarning{lcg}{Command `qui@t' already defined}}
\@ifundefined{firstletterr@nd}{}
       {\PackageWarning{lcg}{Command `firstletterr@nd' already defined}}
       %    \end{macrocode}
% Checking the used counters:
%    \begin{macrocode}
\@ifundefined{c@f@rst}{}
       {\PackageWarning{lcg}{Counter `f@rst' already defined}}
\@ifundefined{c@l@st}{}
       {\PackageWarning{lcg}{Counter `l@st' already defined}}
\@ifundefined{c@cr@nd}{}
       {\PackageWarning{lcg}{Counter `cr@nd' already defined}}
\@ifundefined{f@rst}{}
       {\PackageWarning{lcg}{Existing command `f@rst' conflicts
         with counter `f@rst'}}
\@ifundefined{l@st}{}
       {\PackageWarning{lcg}{Existing command `l@st' conflicts
         with counter `l@st'}}
\@ifundefined{cr@nd}{}
       {\PackageWarning{lcg}{Existing command `cr@nd' conflicts
         with counter `cr@nd'}}
%    \end{macrocode}
%
%
% \subsection{Macros for (re)initialization}
%
% \begin{macro}{init}
%  Set starting values for the parameters and counters
%  to standard values or according to the provides keys
%    \begin{macrocode}
\def\initr@nd{%
   \def\r@ndcountername{rand}%
   \newcount \f@rst
   \newcount \l@st
   \newcount \cr@nd
   \pr@keysr@nd%
   \ProcessOptionsWithKVr@nd{Init}%
   \p@stkeysr@nd%
   \@utputr@nd%
}  % end of \def\initr@nd
%    \end{macrocode}
% \end{macro}
% \begin{macro}{reinit}
%  Sets the provided keys and resets all other options.
%    \begin{macrocode}
\def\reinitrand{\@ifnextchar[\@reinitr@nd{\@reinitr@nd[]}}%
\def\@reinitr@nd[#1]{%
    \pr@keysr@nd%
    \setkeys{Init}{#1}%
    \p@stkeysr@nd%
    \@utputr@nd%
}%    end of \def\reinitrand
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{chgrand}
%  Sets the provided keys and doesn't change any other option.
%    \begin{macrocode}
\def\chgrand{\@ifnextchar[\@chgr@nd{\@chgr@nd[]}}
\def\@chgr@nd[#1]{%
    \@tempcnta = \z@
    \@tempcntb = \z@
    \setkeys{Init}{#1}%
    \p@stkeysr@nd%
    \@utputr@nd%
}  % end of \def\chgrand
%    \end{macrocode}
% \end{macro}
%
%
% \subsection{The keys}
%
% \begin{macro}{use keys}
% The following lines are from the \texttt{geometry} package
% written by \textsc{Hideo Umeki} (who borrowed it from the
% \texttt{hyperref}  package written by \textsc{Sebastian Rahtz}).
% It enables the usage of the \meta{key}=\meta{value} scheme of the
% keyval package.
%
%    \begin{macrocode}
\def\ProcessOptionsWithKVr@nd#1{%
  \let\@tempa\@empty
  \@for\CurrentOption:=\@classoptionslist\do{%
    \@ifundefined{KV@#1@\CurrentOption}%
    {}{\edef\@tempa{\@tempa,\CurrentOption,}}}
  \edef\@tempa{%
    \noexpand\setkeys{#1}{\@tempa\@ptionlist{\@currname.\@currext}}}
  \@tempa
  \AtEndOfPackage{\let\@unprocessedoptions\relax}}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{first}
%    \begin{macrocode}
\define@key{Init}{first}[1]{\f@rst = #1}
%    \end{macrocode}
% \end{macro}
% \begin{macro}{last}
%    \begin{macrocode}
\define@key{Init}{last}[2147483647]{\l@st = #1}
%    \end{macrocode}
% \end{macro}
% \begin{macro}{counter}
%    \begin{macrocode}
\define@key{Init}{counter}[rand]{\def\r@ndcountername{#1}}
%    \end{macrocode}
% \end{macro}
% \begin{macro}{seed}
%    \begin{macrocode}
\define@key{Init}{seed}[\z@]{% seed for random number generator
   \ifnum #1 < \z@%
      \PackageWarning{lcg}{Seed should be > 0 --
              Seed will be initialized with the actual time}%
      \cr@nd = \z@%
   \else%
      \cr@nd = #1
      \typeout{Random number generator initialized to #1}%
   \fi%
}
%    \end{macrocode}
% \end{macro}
% \begin{macro}{quiet}
%    \begin{macrocode}
\define@key{Init}{quiet}[y]{
   \def\qui@t{\expandafter\firstletterr@nd #1\delimiter}
   \if\qui@t y    % nothing to do
   \else\if\qui@t Y \def\qui@t{y}
   \else\if\qui@t j \def\qui@t{y}
   \else\if\qui@t J \def\qui@t{y}
   \else\if\qui@t n \def\qui@t{n}
   \else\if\qui@t N \def\qui@t{n}
   \else 
      \PackageWarning{lcg}{Value of key <quiet> must be <y> or <n>}
      \def\qui@t{y}
   \fi\fi\fi\fi\fi\fi
}
%    \end{macrocode}
% \end{macro}
%
% \subsection{Macros called by other macros}
%
% \begin{macro}{pr@keys}
% The command \cmd{\pr@keysr@nd} is used to define and initialize
% all parameters (counters) needed by this package (before
% the keys are evaluated).
% Random numbers will be generated from $\mathtt{f@rst}$ to
% $\mathtt{f@rst} + \mathtt{l@st} - 1$,
% \cntr{cr@nd} will hold the random numbers
% (full range: $1$ to $2^{31}-1$) and \cntr{rand}
% will hold the random numbers (user defined range).
% The counters are also initialized to standard values.
% If the counter \cntr{cr@nd} equals zero, the seed will be
% initialized according to the actual time by the command \cmd{\r@nd}:
%
%    \begin{macrocode}
\def\pr@keysr@nd{%
    \f@rst = \@ne        % 1
    \l@st = 2147483647   % 2147483647
    \cr@nd  = \z@        % 0
    \@tempcnta = \z@
    \@tempcntb = \z@
    \def\r@ndcountername{rand}%
    \def\qui@t{n}
} % end of newcommand\def\pr@keysr@nd
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{p@stkeys}
% The command \cmd{\p@stkeysr@nd} is executed after the
% keys are evaluated as last step of the initialization.
% The setting of the counter \cntr{l@st} depends on weather
% the key \key{last} is set or not.
% and the counter (user defined or standard name) is created.
%    \begin{macrocode}
\def\p@stkeysr@nd{%
   \@rderr@nd%                  last < first  -> swap
   \cutr@nger@nd%               range too big -> cut
   \@ifundefined{c@\r@ndcountername}{\newcounter{\r@ndcountername}}%
   {%
      \PackageWarning{lcg}{Using an already existing
           counter \r@ndcountername}%
   }%
\setcounter{\r@ndcountername}{0}%
} % end of \def\p@stkeysr@nd
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{firstletter}
% This macro is used to determine the first letter of the value
% of the key \key{quiet}.
%    \begin{macrocode}
\def\firstletterr@nd#1#2\delimiter{#1}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{@utput}
% Output to log-file/screen
%    \begin{macrocode}
\def\@utputr@nd{%
   \if\qui@t y
      % do nothing
   \else
     \typeout{Smallest possible random number: \the\f@rst}%
     \typeout{Largest possible random number:  \the\l@st}%
     \typeout{The pseudo random numbers will be stored
      in the LaTeX counter `\r@ndcountername'}%
   \fi
}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{@rder}
% If the value of the key \key{last} is less than
% the value of \key{first},  they will be exchanged.
%    \begin{macrocode}
\def\@rderr@nd{%
   \ifnum \l@st < \f@rst%
       \PackageWarning{lcg}{Key `last' less than key `first'
               -- swapped}%
       \@tempcnta = \f@rst
       \f@rst = \l@st
       \l@st = \@tempcnta
   \fi%
}%   end of \def\@rderr@nd
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{cutr@nge}
% If the given range of random numbers exceeds the possibilities
% of \LaTeX\ (the limit is $2^{31}-1$), then the value of the \TeX-counter
% \cntr{@tempcnta} will be less than zero and the right border will be adjusted.
%    \begin{macrocode}
\def\cutr@nger@nd{%
   \@tempcntb =  -2147483646   % -2^31 + 2
   \@tempcnta = \f@rst
   \advance \@tempcntb \l@st
   \multiply \@tempcntb \m@ne
   \advance \@tempcnta \@tempcntb
   \ifnum \@tempcnta < \z@%
      \PackageWarning{lcg}{Range contains too many numbers
                     -- right border reset to largest possible value}%
      \advance \l@st \@tempcnta
   \fi%

}%   end of \checkr@ange
%    \end{macrocode}
% \end{macro}
%
%
% \subsection{Macros for random number generation}
%
% \begin{macro}{rand}
% The command \cmd{\rand} calls the internal command
% \cmd{\r@nd} which stores s random number (full range)
% within the counter \cntr{cr@nd}.
% If the condition
% $$
% \mathtt{cr@nd} \leq (\mathtt{l@st}-\mathtt{f@rst}+1)
% \cdot \frac{2^{31}-1}{\mathtt{l@st}-\mathtt{f@rst}+1}
% $$
% holds,  \cntr{cr@nd} will be transformed
% to the given range:
% $$
%  \mathtt{f@rst}+ \mathtt{cr@nd} - (\mathtt{l@st}-\mathtt{f@rst}+1)
%  \cdot \frac{\mathtt{cr@nd}}{\mathtt{l@st}-\mathtt{f@rst}+1}
% $$
% and the result stored in the corresponding counter
% and otherwise \cmd{\rand} calls itself till the condition
% is satisfied. It's important
% to notice that the result of the division of two integers is
% again an integer (the fraction part is lost)!
%
%    \begin{macrocode}
\def\rand{%
   \r@nd%
   \@tempcnta
   \@tempcntb
   \@tempcnta = \f@rst
   \@tempcntb = \l@st
   \multiply \@tempcnta \m@ne
   \advance \@tempcntb \@tempcnta
   \advance \@tempcntb \@ne         %l@st-f@rst+1
   \@tempcnta = 2147483647
   \divide \@tempcnta \@tempcntb
   \multiply \@tempcnta \@tempcntb
   \ifnum \cr@nd > \@tempcnta
      \rand%
   \else
      \setcounter{\r@ndcountername}{\cr@nd}%
      \@tempcnta = \cr@nd
      \divide \@tempcnta \@tempcntb
      \multiply \@tempcnta \@tempcntb
      \multiply \@tempcnta \m@ne
      \addtocounter{\r@ndcountername}{\@tempcnta}%
      \addtocounter{\r@ndcountername}{\f@rst}%
   \fi
} % end of \rand
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{r@nd}
% The command \cmd{\r@nd} generates pseudo random numbers within
% the range  $1$ to $2^{31}-1$ Schrage's method and stores them
% in the counter  \cntr{cr@nd}:
%
%    \begin{macrocode}
\def\r@nd{%
   \ifnum \cr@nd < \@ne%       then  ... initialize generator
      \cr@nd = \the\time
      \advance \cr@nd  \inputlineno
      \multiply \cr@nd  \thepage
      \advance \cr@nd \the\year
      \multiply \cr@nd \the\month
      \multiply \cr@nd \the\day
      \advance \cr@nd \inputlineno
      \if\qui@t y
      \else
         \typeout{Random number generator initialized to \the\cr@nd}%
      \fi
      \r@nd%
   \else                         %  else ... generate new number
      \@tempcnta = \cr@nd
      \divide \@tempcnta  127773    % \@tempcnta = floor(z/q)
      \@tempcntb = \@tempcnta       % \@tempcntb = floor(z/q)
      \multiply \@tempcnta  -2836   % \@tempcnta = -r*floor(z/q)
      \multiply \@tempcntb -127773  % \@tempcntb = -q*floor(z/q)
      \advance \cr@nd \@tempcntb    % cr@nd = z mod q
      \multiply \cr@nd 16807        % cr@nd = a * (z mod q)
      \advance \cr@nd \@tempcnta    % cr@nd = a*z mod m
      \ifnum \cr@nd < \z@%
         \advance \cr@nd 2147483647 % cr@nd = (a*z mod m) > 0
      \fi
   \fi
}%        end of \r@nd
%    \end{macrocode}
% \end{macro}
%
%
% \subsection{Initialization}
%
%    \begin{macrocode}
\initr@nd      % initialize the package
%    \end{macrocode}
%
% \iffalse
%</lcg>
% \fi