%\iffalse
%<*copyright>
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Rangen.sty package, 2016-02-19 %%
%% Copyright (C) 1999-2016 D. P. Story %%
%% dpstory@uakron.edu %%
%% %%
%% This program can redistributed and/or modified under %%
%% the terms of the LaTeX Project Public License %%
%% Distributed from CTAN archives in directory %%
%% macros/latex/base/lppl.txt; either version 1 of the %%
%% License, or (at your option) any later version. %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%</copyright>
%<package>\NeedsTeXFormat{LaTeX2e}[1997/12/01]
%<package>\ProvidesPackage{rangen}
%<package> [2014/10/17 v1.4 Rangen: Generate Random Questions (dps)]
%<*driver>
\documentclass{ltxdoc}
\usepackage[colorlinks,hyperindex]{hyperref}
%\pdfstringdefDisableCommands{\let\\\textbackslash}
%\EnableCrossrefs \CodelineIndex
\begin{document}
\GetFileInfo{rangen.sty}
% \settowidth{\oddsidemargin}{0pt}%
% \setlength{\evensidemargin}{0pt}
% \setlength{\marginparsep}{0pt}
% \setlength{\marginparwidth}{0pt}
% \setlength\textwidth{6in}
% \hoffset=.5in
% \hsize = 6in
\title{\textsf{Rangen}\texorpdfstring{\\}{:} Random Generation of Integer, Rational, and Real Numbers with
Applications to the \texttt{exercise}, \texttt{quiz}, and \texttt{shortquiz} environments of \textsf{Exerquiz}}
\author{D. P. Story\\
Email: \texttt{dpstory@uakron.edu}}
\date{processed \today}
\maketitle
\tableofcontents
\let\Email\texttt
\DocInput{rangen.dtx}
\PrintIndex
\end{document}
%</driver>
% \fi
% \MakeShortVerb{|}
% \StopEventually{}
%
% \DoNotIndex{\def,\edef,\gdef,\xdef,\global,\long,\let}
% \DoNotIndex{\expandafter,\string,\the,\ifx,\else,\fi}
% \DoNotIndex{\csname,\endcsname,\relax,\begingroup,\endgroup}
% \DoNotIndex{\DeclareTextCommand,\DeclareTextCompositeCommand}
% \DoNotIndex{\space,\@empty,\special}
%
% \begin{macrocode}
%<*package>
% \end{macrocode}
% \section{Introduction}
%
% This package provides some commands for creating randomly generated integers, rational,
% and real numbers. There are options for specifying constraints on the generation of the numbers.
% Companion JavaScript functions are developed to use these random numbers as part of a
% question in a \texttt{shortquiz} or \texttt{quiz}. The syntax of this package can be used
% to pose number-related questions, the JavaScript can be used to create the answer to the
% question based on a formula. You'll have to see it to believe it.
%
% \section{The Main Code}
%
% \subsection{Declare Options}
%
% This package has one option, other options are passed to the really nice \textsf{lcg} Package,
% by Erich Janka (\texttt{janka@utanet.at}).
% \begin{macrocode}
\newcount\seedCnt
\DeclareOption{testmode}{%
\InputIfFileExists{\jobname.seed}{}{\def\thisseed{1}}%
\PassOptionsToPackage{seed=\thisseed}{lcg}%
\AtEndOfPackage{\reseedEachRun}%
}
\def\reseedEachRun{%
\seedCnt=\thisseed
\advance\seedCnt1\relax
\newwrite \rngWrite
\immediate\openout\rngWrite \jobname.seed
\immediate\write\rngWrite{\string\def\string\thisseed{\the\seedCnt}}
\immediate\closeout\rngWrite
}
\def\RNG@Dec{.}
\DeclareOption*{\PassOptionsToPackage{\CurrentOption}{lcg}}
\ProcessOptions
\RequirePackage{lcg}[2008/09/10]
% \end{macrocode}
% Save the seed value so we can reproduce the same pseudo-random number sequence.
% \begin{macrocode}
\edef\rng@saveSeed{\the\cr@nd}
% \end{macrocode}
% There are three data types: Integer, Rational, and Real. The following macros
% gives each of these types a numerical value, 0, 1 and 2, respectively.
% \begin{macrocode}
\newcount\loopCnt
\def\maxLoopLimit{10}
\def\typeCodeForz{0}
\def\typeCodeForq{1}
\def\typeCodeForr{2}
% \end{macrocode}
% Some scratch count registers
% \begin{macrocode}
\newcount\rng@cnta
\newcount\rng@cntb
% \end{macrocode}
% A random variable is specified using a control sequence, e.g. \cs{a}. The following macro
% extracts the underlying name of the command, e.g. \verb+\@gtVarName{\a}+ expands to \texttt{a},
% and returns the name as the expansion of the macro \cs{@varName}.
% \begin{macrocode}
\def\@getVarName#1{%
\edef\@varName{\expandafter\@gobble\string#1}%
}
% \end{macrocode}
% The command \cs{@getVarType} takes one argument, a random variable, e.g., \cs{a}. This
% command defines a macro \cs{varType} which expands to the data type the random variable is.
% \begin{macrocode}
\def\@getVarType#1{%
\@getVarName{#1}\edef\varType{\csname typeof@\@varName\endcsname}}
% \end{macrocode}
% \subsection{GCD and Rational Reduction Commands}
% \begin{macro}{\gcd}
% Here we use Euclid's Algorithm to find the greatest common divisor of two integers.
% \begin{macrocode}
\def\gcd#1#2{{% #1 = a, #2 = b
\ifnum#2=0 \edef\next{#1}\else
\@tempcnta=#1 \@tempcntb=#2 \divide\@tempcnta by\@tempcntb
\multiply\@tempcnta by\@tempcntb % q*b
\@tempcntb=#1
\advance\@tempcntb by-\@tempcnta % remainder in \@tempcntb
\ifnum\@tempcntb=0
\@tempcnta=#2
\ifnum\@tempcnta < 0 \@tempcnta=-\@tempcnta\fi
\xdef\gcd@next{\noexpand%
\def\noexpand\thegcd{\the\@tempcnta}}%
\else
\xdef\gcd@next{\noexpand\gcd{#2}{\the\@tempcntb}}%
\fi
\fi}\gcd@next
}
% \end{macrocode}
% \end{macro}
% \begin{macro}{\lcm}
% Now compute the least common multiple
% \begin{macrocode}
\def\lcm#1#2{% #1 = a, #2 = b
\gcd{#1}{#2}%
{\@tempcnta=#1
\multiply\@tempcnta by#2
\divide\@tempcnta by\thegcd
\xdef\thelcm{\the\@tempcnta}}%
}
% \end{macrocode}
% \end{macro}
% \begin{macro}{\amodb}
% Modular arithmetic \texttt{a mod b}, returns its results
% as a macro \cs{retnmod}.
% \begin{macrocode}
\def\amodb#1#2{% #1 = a, #2 = b
{\@tempcnta=#1
\divide\@tempcnta by#2
\multiply\@tempcnta by#2
\@tempcntb=#1
\advance\@tempcntb by-\@tempcnta
\xdef\retnmod{\the\@tempcntb}}%
}
% \end{macrocode}
% \end{macro}
% \begin{macro}{\reduceFrac}
% Reduce a fraction to lowest terms. The first argument is the numerator and the second
% argument is the denominator. This command computes the \texttt{gcd} of the two integers,
% divides each by the \texttt{gcd}, and returns the results in the two scratch count
% registers \cs{@tempcnta} and \cs{@tempcntb}.
% \begin{macrocode}
\newcommand\reduceFrac[2]
{%
\gcd{#1}{#2}{\@tempcnta=#1 \divide\@tempcnta by\thegcd
\@tempcntb=#2 \divide\@tempcntb by\thegcd
\ifnum\@tempcntb<0\relax
% \end{macrocode}
% Always have the denominator as positive.
% \begin{macrocode}
\@tempcntb=-\@tempcntb
\@tempcnta=-\@tempcnta
\fi
\xdef\rfNumer{\the\@tempcnta}\xdef\rfDenom{\the\@tempcntb}}%
}
% \end{macrocode}
% \end{macro}
% \begin{macro}{\convertRatTo}
% Converts a fraction \texttt{a/b} (\texttt{\#1/\#2}) to a denominator of \texttt{\#3}. Will return
% new numerator in \cs{rnd@Cnta} register. This will be exact if
% \texttt{\#2} divides \texttt{\#3}.
% \begin{macrocode}
\def\convertRatTo#1#2#3{{%
\@tempcnta=#3
\multiply\@tempcnta by#1
\divide\@tempcnta by#2
\xdef\rng@retn@num{\the\@tempcnta}%
}}
% \end{macrocode}
% \end{macro}
% \begin{macro}{\RNGadd}
% This is the support for rational arithmetic (addition and subtraction).
% Adds two rational numbers, \texttt{\#1} and \texttt{\#2} together. These two rational numbers must have been defined
% already, possibly by \cs{defineQ}. Usage: \verb+\RNGadd\a\b+. This macro returns a rational number:
% the numerator in the \cs{rfNumer} command, and the denominator in the \cs{rfDenom} command.
% For example,
%\begin{verbatim}
%\defineQ\a{1}{3}\defineQ\b{3}{5}\RNGadd\a\b
%\makeatletter
%The sum of $\frac{\nOf\a}{\dOf\a} + \frac{\nOf\b}{\dOf\b}
% = \frac{\rfNumer}{\rfDenom}$
%\makeatother
%\end{verbatim}
%This code typesets as $\frac{1}{3}+\frac{3}{5}=\frac{14}{15}$.
% \begin{macrocode}
\newcommand\RNGadd[2]{%
\rng@cnta=\nOf#1 \multiply\rng@cnta by\dOf#2
\rng@cntb=\nOf#2 \multiply\rng@cntb by\dOf#1
\advance\rng@cnta by\the\rng@cntb
\rng@cntb=\dOf#1 \multiply\rng@cntb by\dOf#2
\reduceFrac{\the\rng@cnta}{\the\rng@cntb}
}
% \end{macrocode}
% \end{macro}
% This is a simple macro for detecting if the argument \texttt{\#1}
% is a macro or not. Used when interval definitions of the
% \cs{RandomZ/Q/R} macros.
% \begin{macrocode}
\def\rng@isControl#1{\@ifundefined{\expandafter\@gobble\string#1}%
{\let\rng@isC@ntrol=0}{\let\rng@isC@ntrol=1}}
% \end{macrocode}
% This command determines if its argument has an \texttt{*}
% prefixed or post-fixed to its argument.
% If \cs{rng@isStariii} equals \texttt{*}, then an \texttt{*} exists.
% \begin{itemize}
% \item If there is no \texttt{*}, then the argument is \texttt{\#1}
% \item \cs{rng@isStariii} equals \texttt{*}, there is \texttt{*},
% If the argument has the form \cs{*a}, then \cs{rng@isStari} is \cs{@empty}
% and the argument, stripped of the \texttt{*}, is given as \cs{rng@isStarii}
% \item \cs{rng@isStariii} equals \texttt{*}, there is \texttt{*},
% If the argument has the form \cs{a*}, then \cs{rng@isStarii} is \cs{@empty}
% and the argument, stripped of the \texttt{*}, is given as \cs{rng@isStari}
%\end{itemize}
% \begin{macrocode}
\def\rng@existStar#1{\rng@existSt@r#1**\@nil}
\def\rng@existSt@r#1*#2*#3\@nil{\def\rng@isStari{#1}%
\def\rng@isStarii{#2}\def\rng@isStariii{#3}%
}
\def\rng@NameEndpoint#1{%
\ifx\rng@isStari\@empty
\edef#1{\expandafter\noexpand\rng@isStarii}%
\else\ifx\rng@isStarii\@empty
\edef#1{\expandafter\noexpand\rng@isStari}%
\fi\fi
}
% \end{macrocode}
% \subsection{Define an Integer and a Rational}
% \begin{macro}{\defineZ}
% Define a integer for use in other macros.
% \begin{macrocode}
\newcommand\defineZ[2]
{%
\@getVarName#1\relax
\expandafter\def\csname typeof@\@varName\endcsname{0}%
\expandafter\edef\csname n@\@varName\endcsname{#2}%
\expandafter\edef\csname d@\@varName\endcsname{1}%
\edef\display@TeXfmt{#2}\edef\inline@TeXfmt{#2}%
\ifnum#2=1\relax\rng@makeOneFmtDefns
\else\ifnum#2=-1\relax\rng@makeMinusOneFmtDefns
\else\rng@makeOtherFmtDefns\fi\fi
\expandafter\let\csname\@varName*\endcsname\display@TeXfmt
\expandafter\let\csname\@varName!\endcsname\inline@TeXfmt
\expandafter\edef\csname\@varName\endcsname{#2}%
}
% \end{macrocode}
% \end{macro}
% \begin{macro}{\defineQ}
% The following macro defines a rational number. Usage
% \verb+\defineQ\a{1}{2}+. This defines the rational number 1/2 and
% gives it a name, \cs{a}.
% \begin{macrocode}
\newcommand\defineQ[3]
{%
\@getVarName#1\relax
\expandafter\def\csname typeof@\@varName\endcsname{1}%
\expandafter\edef\csname n@\@varName\endcsname{#2}%
\expandafter\edef\csname d@\@varName\endcsname{#3}%
\edef\display@TeXfmt{\frac{#2}{#3}}\edef\inline@TeXfmt{#2/#3}%
\ifnum#2=#3\relax\rng@makeOneFmtDefns
\else\ifnum#2=-#3\relax\rng@makeMinusOneFmtDefns
\else\rng@makeOtherFmtDefns\fi\fi
\expandafter\let\csname\@varName*\endcsname\display@TeXfmt
\expandafter\let\csname\@varName!\endcsname\inline@TeXfmt
\expandafter\edef\csname\@varName\endcsname{#2/#3}%
\simplifyCurrentQ
}
% \end{macrocode}
% \end{macro}
% \begin{macro}{\defineR}
% This macro computes: (1) \cs{rng@intpart}; (2) \cs{rng@fracpart};
% (3) \cs{rndnDec} (the number of decimals of the fractional part);
% (4) \cs{rndPower} (the power of ten determined by \cs{rndnDec}).
% \begin{macrocode}
\newcommand{\defineR}[2]{%
\@getVarName{#1}\RNGparseDec{#2}%
\expandafter\def\csname typeof@\@varName\endcsname{2}%
\reduceFrac{\rng@intpart\rng@fracpart}{\rndPower}%
\expandafter\edef\csname n@\@varName\endcsname{\rfNumer}%
\expandafter\edef\csname d@\@varName\endcsname{\rfDenom}%
\edef\display@TeXfmt{#2}\edef\inline@TeXfmt{#2}%
\ifnum\rfNumer=1\relax\rng@makeOneFmtDefns
\else\ifnum\rfNumer=-1\relax\rng@makeMinusOneFmtDefns
\else\rng@makeOtherFmtDefns\fi\fi
\expandafter\let\csname\@varName*\endcsname\display@TeXfmt
\expandafter\let\csname\@varName!\endcsname\inline@TeXfmt
\expandafter\edef\csname\@varName\endcsname{#2}%
\simplifyCurrentR
}
\newcommand{\simplifyCurrentR}{%
\ifnum\csname d@\@varName\endcsname=1
\expandafter\defineZ
\csname\@varName\endcsname{\csname n@\@varName\endcsname}\fi
}
% \end{macrocode}
% \end{macro}
% \begin{macrocode}
\def\rng@makeOneFmtDefns{%
% inline
\expandafter\def\csname\@varName!e\endcsname{}%
\expandafter\def\csname\@varName!c\endcsname{}%
% display
\expandafter\def\csname\@varName*e\endcsname{}%
\expandafter\def\csname\@varName*c\endcsname{}%
}
\def\rng@makeMinusOneFmtDefns{%
% inline
\expandafter\def\csname\@varName!e\endcsname{-1}%
\expandafter\def\csname\@varName!c\endcsname{-}%
% display
\expandafter\def\csname\@varName*e\endcsname{-1}%
\expandafter\def\csname\@varName*c\endcsname{-}%
}
\def\rng@makeOtherFmtDefns{%
% inline
\expandafter\let\csname\@varName!e\endcsname\inline@TeXfmt
\expandafter\let\csname\@varName!c\endcsname\inline@TeXfmt
% display
\expandafter\let\csname\@varName*e\endcsname\display@TeXfmt
\expandafter\let\csname\@varName*c\endcsname\display@TeXfmt
}
% \end{macrocode}
%
% \subsection{Parse a Number}
%
% \subsubsection{Parsing a Rational}
%
% \begin{macro}{\RNGparseRat}
% \begin{macrocode}
\def\RNGparseRat#1{\expandafter\@chkslash#1//\@nil}
\def\@chkslash#1/#2/#3\@nil{%
\def\rng@num{#1}\def\rng@denom{#2}%
\def\rng@parseQ@iii{#3}%
\ifx\rng@denom\@empty\def\rng@denom{1}\fi
}
% \end{macrocode}
% \end{macro}
%
% \subsubsection{Parsing a Real}
%
% \begin{macro}{\RNGparseDec}
% The argument \texttt{\#1} is a decimal number (or integer)
% This macro computes: (1) \cs{rng@intpart}; (2) \cs{rng@fracpart};
% (3) \cs{rndnDec} (the number of decimals of the fractional part);
% (4) \cs{rndPower} (the power of ten determined by \cs{rndnDec}).
% These variables will be overwritten the next time this command
% is executed.
% \begin{macrocode}
\newcommand{\RNGparseDec}[1]{\edef\parse@argi{#1}%
\expandafter\@chkdec\parse@argi..\@nil}
\def\@chkdec#1.#2.#3\@nil{%
\def\rng@intpart{#1}\def\rng@fracpart{#2}%
\def\rng@parseR@iii{#3}\rng@getnDec}
\def\rng@getnDec{%
\begingroup
\ifx\rng@fracpart\@empty\gdef\rndnDec{0}\gdef\rndPower{1}\else
\count0=0\relax\count2=1\relax
\expandafter\cntNumDec\rng@fracpart\end\fi
\endgroup}
\def\cntNumDec#1#2\end{%
\advance\count0by1
\def\rng@arg{#2}%
\ifx\rng@arg\@empty
\xdef\rndnDec{\the\count0}%
\xdef\rndPower{1\@nameuse{rng@tz\the\count0}}%
\let\rng@next\relax
\else
\def\rng@next{\cntNumDec#2\end}%
\fi\rng@next
}
% \end{macrocode}
% \end{macro}
% \begin{macro}{\nDivisionsPowerOfTen}
% This is a control of how many nodes to create in an interval
% of real numbers, as defined by \cs{RandomR}. The argument is
% an integer between 1 and 4 inclusive.
% \begin{macrocode}
\newcommand{\nDivisionsPowerOfTen}[1]{%
\begingroup
\count0=#1\relax
\ifnum\count0>4\relax
\PackageError{rangen}{Number of subdivisions too large}%
{Reduce the argument of \string\nDivisionsPowerOfTen.}%
\else
\ifnum\count0<1\relax
\PackageError{rangen}{Number of subdivisions too large}%
{Increase the argument of \string\nDivisionsPowerOfTen.}%
\fi\fi
\xdef\RNGpowerOfTen{1\@nameuse{rng@tz#1}}%
\endgroup
}
\nDivisionsPowerOfTen{2}
% \end{macrocode}
% \end{macro}
%\subsection{Creating Random Things}
%\subsubsection{Random Integer}
% \begin{macro}{\RandomZ}
% Randomly generates an integer in the specified range of values.
%\begin{verbatim}
%[#1] Optional parameter to modify the variable.
% #2 The random variable being defined, e.g., \a
% #3 lower limit of random integer
% #4 upper limit of random integer
%\end{verbatim}
% \begin{macrocode}
\newcommand\RandomZ[4][]
{%
\def\rng@ne@values{}%
\setkeys{rangen}{ne,#1}%
% \end{macrocode}
% Now see if there is an \texttt{*}, and get un-stripped
% argument.
%
% The \cs{rng@isControl} lets \cs{rng@isC@ntrol} to 0 if the arg is undefined,
% and lets \cs{rng@isC@ntrol} to 1 if it is defined.
% Check the left endpoint:
% \begin{macrocode}
\let\rng@CtrlLEP=0\let\rng@CtrlUEP=0%
\let\rng@makeLEPStrict=0\let\rng@makeUEPStrict=0%
% \end{macrocode}
% \paragraph*{Left endpoint.}
% \begin{macrocode}
\rng@existStar{#3}\rng@NameEndpoint{\rng@LEP}%
\if\rng@isStariii*\edef\tmp@exp{%
\noexpand\rng@isControl{\expandafter\noexpand\rng@LEP}}\tmp@exp
\if\rng@isC@ntrol1% a control sequence
\let\rng@CtrlLEP=1\let\rng@makeLEPStrict=1%
% \end{macrocode}
% The LEP is a control sequence with a star, we need to increment the value
% of \cs{rng@LEP} to the next largest integer.
% \begin{macrocode}
\edef\tmp@exp{\noexpand%
\@getVarType{\expandafter\noexpand\rng@LEP}}\tmp@exp
\ifcase\varType % integer
\rng@cnta=\rng@LEP
\or % rational
\rng@dima=\expandafter\nOf\rng@LEP pt
\divide\rng@dima by\expandafter\dOf\rng@LEP
\defineR{\rng@LEP}{\strip@pt\rng@dima}%
\RNGparseDec{\rng@LEP}%
\rng@cnta=\rng@intpart
\or % real
\defineR{\rng@LEP}{\rng@LEP}%
\RNGparseDec{\rng@LEP}%
\rng@cnta=\rng@intpart
\fi
\advance\rng@cnta by1\relax
\defineZ{\rng@LEP}{\the\rng@cnta}%
\else
% \end{macrocode}
% Not a control sequence but has a star
% \begin{macrocode}
\defineZ{\rng@LEP}{\rng@LEP}%
\fi
\else
% \end{macrocode}
% No star, control sequence or not?
% \begin{macrocode}
\rng@isControl{#3}%
\if\rng@isC@ntrol1% control sequence
\let\rng@CtrlLEP=1%
\def\rng@LEP{#3}%
\@getVarType{#3}%
\ifcase\varType % integer
\defineZ{\rng@LEP}{#3}%
\or % rational
\rng@dima=\nOf{#3}pt
\divide\rng@dima by\dOf{#3}%
\defineR{\rng@LEP}{\strip@pt\rng@dima}%
\RNGparseDec{\rng@LEP}%
\defineZ{\rng@LEP}{\rng@intpart}%
\or % real
\defineR{\rng@LEP}{\rng@LEP}%
\RNGparseDec{\rng@LEP}%
\defineZ{\rng@LEP}{\rng@intpart}%
\fi
\else
% \end{macrocode}
% A number, no star
% \begin{macrocode}
\defineZ{\rng@LEP}{#3}%
\fi
\fi
% \end{macrocode}
% \paragraph*{Right endpoint.}
% \begin{macrocode}
\rng@existStar{#4}\rng@NameEndpoint{\rng@UEP}%
\if\rng@isStariii*\edef\tmp@exp{%
\noexpand\rng@isControl{\expandafter\noexpand\rng@UEP}}\tmp@exp
\if\rng@isC@ntrol1% a control sequence
\let\rng@CtrlUEP=1\let\rng@makeUEPStrict=1%
% \end{macrocode}
% The UEP is a control sequence with a star, we need to increment the value
% of \cs{rng@UEP} to the next largest integer.
% \begin{macrocode}
\edef\tmp@exp{\noexpand%
\@getVarType{\expandafter\noexpand\rng@UEP}}\tmp@exp
\ifcase\varType % integer
\rng@cnta=\rng@UEP
\or % rational
\rng@dima=\expandafter\nOf\rng@UEP pt
\divide\rng@dima by\expandafter\dOf\rng@UEP
\defineR{\rng@UEP}{\strip@pt\rng@dima}%
\RNGparseDec{\rng@UEP}%
\rng@cnta=\rng@intpart
\or % real
\defineR{\rng@UEP}{\rng@UEP}%
\RNGparseDec{\rng@UEP}%
\rng@cnta=\rng@intpart
\fi
\advance\rng@cnta by-1\relax
\defineZ{\rng@UEP}{\the\rng@cnta}%
\else
% \end{macrocode}
% Not a control sequence but has a star
% \begin{macrocode}
\defineZ{\rng@UEP}{\rng@UEP}%
\fi
\else
% \end{macrocode}
% No star, control sequence or not?
% \begin{macrocode}
\rng@isControl{#4}%
\if\rng@isC@ntrol1% control sequence
\let\rng@CtrlUEP=1%
\def\rng@UEP{#4}%
\@getVarType{#4}%
\ifcase\varType % integer
\defineZ{\rng@UEP}{#4}%
\or % rational
\rng@dima=\nOf{#4}pt
\divide\rng@dima by\dOf{#4}%
\defineR{\rng@UEP}{\strip@pt\rng@dima}%
\RNGparseDec{\rng@UEP}%
\defineZ{\rng@UEP}{\rng@intpart}%
\or % real
\defineR{\rng@UEP}{\rng@UEP}%
\RNGparseDec{\rng@UEP}%
\defineZ{\rng@UEP}{\rng@intpart}%
\fi
\else
% \end{macrocode}
% A number, no star, assume it is an integer
% \begin{macrocode}
\defineZ{\rng@UEP}{#4}%
\fi
\fi
% \end{macrocode}
% \textbf{To Do.} Check if LEP is less than UEP, if not, notify user.
% Save the random variable, e.g., \cs{a}
% \begin{macrocode}
\def\@currentName{#2}%
% \end{macrocode}
% Record the variable type
% \begin{macrocode}
\@getVarName{#2}%
\expandafter\def\csname typeof@\@varName\endcsname{0}%
% \end{macrocode}
% Save the range of this variable
% \begin{macrocode}
\expandafter\edef\csname first@\@varName\endcsname{\rng@LEP}%
\expandafter\edef\csname last@\@varName\endcsname{\rng@UEP}%
% \end{macrocode}
% Now get a value for the variable using \cs{rand}, defined in \texttt{lcg}
% \begin{macrocode}
\rng@chgrand[first=\rng@LEP,last=\rng@UEP]\rand
% \end{macrocode}
% Now define the integer.
% \begin{macrocode}
\defineZ{#2}{\arabic{rand}}%
% \end{macrocode}
% \paragraph*{Constraints}
% We have a random Z, we now try to satisfy the \texttt{ne} condition.
%
% The macro \cs{rangen@ne} can be of the form \verb!{1,3,4,5}!. We try to
% satisfy all the conditions specified by \cs{rangen@ne}
% \begin{macrocode}
\ifx\rangen@ne\@empty\else\loopCnt=0\relax
% \end{macrocode}
% We will try a total number of \cs{maxLoopLimit} to meet the required
% conditions.
% \begin{macrocode}
\@whilenum\loopCnt<\maxLoopLimit\do{%
% \end{macrocode}
% Set \cs{rng@cnta=1}, if \cs{rng@cnta} is still 1 at the end of this
% loop, the condition is satisfied.
% conditions.
% \begin{macrocode}
\rng@cnta=1\relax
% \end{macrocode}
% We use a \cs{@for} loop to run through all the NE values
% \begin{macrocode}
\@for\ne@@tmp:=\rangen@ne\do{%
% \end{macrocode}
% If the current RV is equal to the current NE value, we fail, so we
% ``and'' a zero into the \cs{rng@cnta} register.
% \begin{macrocode}
\ifnum\value{rand}=\ne@@tmp\relax
\multiply\rng@cnta0\relax
\else
% \end{macrocode}
% \dots otherwise, we ``and'' a one.
% \begin{macrocode}
\multiply\rng@cnta1\relax
\fi
}%
% \end{macrocode}
% If \cs{rng@cnt} is still equal to 1, all conditions have been met,
% in this case we set \verb!\loopCnt=\maxLoopLimit! so we can exit the outer loop.
% \begin{macrocode}
\ifnum\rng@cnta=1\relax % all conditions met
\loopCnt=\maxLoopLimit
\else % if \rng@cnta \ne 1, try again
% \end{macrocode}
% Otherwise, we increment the loop, see if we have gone the limit, if
% not, loop back with a new random choice.
% \begin{macrocode}
\advance\loopCnt1\relax
\ifnum\loopCnt=\maxLoopLimit
\PackageWarning{rangen}{Not all conditions met
after \maxLoopLimit\space tries}%
\else
\rng@chgrand[first=\rng@LEP,last=\rng@UEP]\rand
\fi
\fi
}%
\fi
% \end{macrocode}
% Whether we fail or succeed, we'll go with the last RV. Hopefully, the
% author is aware of the log file, and re-compile, possibly with a
% wider range for the variable, or with a larger value of \cs{maxLoopLimit}.
%
% \begin{macrocode}
\defineZ{#2}{\arabic{rand}}%
}
% \end{macrocode}
% \end{macro}
% \begin{macrocode}
\def\updateZ#1#2{%
\@getVarName#1\relax
\expandafter\edef\csname\@varName\endcsname{#2}%
\expandafter\edef\csname n@\@varName\endcsname{#2}%
\expandafter\edef\csname d@\@varName\endcsname{1}%
}
% \end{macrocode}
%\subsubsection{Random Rational}
% \begin{macro}{\RandomQ}
% Randomly generate a rational number. The parameters for \cs{RandomQ} are
%\begin{verbatim}
%[#1] Optional parameter to modify the variable.
% #2 The random variable being defined, e.g., \a
%[#3] maximum denominator permitted (optional)
% #4 rational number for lower endpoint of range
% #5 rational number for upper endpoint of range
%\end{verbatim}
% Here, it is assume that the first rational number is less than the second. This macro
% will randomly generate a rational number between rat1 and rat2, with a maximum denominator
% specified in \texttt{\#3}.
%
% \medskip\noindent\textbf{Note: }To allow for random endpoints, if one or both are real numbers, we convert
% them to rational numbers in \cs{@RandomQ}.
%
% We begin by getting the first two parameters:
%\begin{verbatim}
%[#1] Optional parameter to modify the variable.
% #2 The random variable being defined, e.g., \a
%\end{verbatim}
% \begin{macrocode}
\newcommand{\RandomQ}[2][]
{%
\setkeys{rangen}{ne,#1}%
\def\rq@currentName{#2}%
\@RandomQ
}
% \end{macrocode}
% We use \cs{@RandomQ} to get the last three parameters of \cs{RandomQ}.
% If the endpoints are not rational, they are converted to rationals.
%\begin{verbatim}
%[#1] maximum denominator permitted (optional)
% #2 rational number for lower endpoint of range
% #3 rational number for upper endpoint of range
%\end{verbatim}
% \begin{macrocode}
\newcommand{\@RandomQ}[3][]
{%
% \end{macrocode}
% Now see if there is an \texttt{*}, and get un-stripped
% argument.
%
% The \cs{rng@isControl} lets \cs{rng@isC@ntrol} to 0 if the arg is undefined,
% and lets \cs{rng@isC@ntrol} to 1 if it is defined.
% Check the left endpoint:
% \begin{macrocode}
\let\rng@CtrlLEP=0\let\rng@CtrlUEP=0%
\let\rng@makeLEPStrict=0\let\rng@makeUEPStrict=0%
% \end{macrocode}
% \paragraph*{Left endpoint}
% \begin{macrocode}
\rng@existStar{#2}\rng@NameEndpoint{\rng@LEP}%
\if\rng@isStariii*\edef\tmp@exp{\noexpand%
\rng@isControl{\expandafter\noexpand\rng@LEP}}\tmp@exp
\if\rng@isC@ntrol1% a control sequence
\let\rng@CtrlLEP=1\let\rng@makeLEPStrict=1%
% \end{macrocode}
% The LEP is a control sequence we get its type and convert to rational
% \begin{macrocode}
\edef\tmp@exp{\noexpand%
\@getVarType{\expandafter\noexpand\rng@LEP}}\tmp@exp
\ifcase\varType % integer
\defineQ{\rng@LEP}{\rng@LEP}{1}%
\or % rational
\edef\tmp@exp{\noexpand%
\defineQ{\noexpand\rng@LEP}{\expandafter\nOf\rng@LEP}%
{\expandafter\dOf\rng@LEP}}\tmp@exp
\or % real
\defineR{\rng@LEP}{\rng@LEP}%
\RNGparseDec{\rng@LEP}%
\defineQ{\rng@LEP}{\rng@intpart}{\rng@fracpart}%
\fi
\else
% \end{macrocode}
% Not a control sequence but has a star, a number, we assume rational
% \begin{macrocode}
\RNGparseRat{\rng@LEP}%
\defineQ{\rng@UEP}{\rng@intpart}{\rng@fracpart}%
\fi
\else
% \end{macrocode}
% No star, is it a control sequence or not?
% \begin{macrocode}
\rng@isControl{#2}%
\if\rng@isC@ntrol1% a control sequence
\@getVarType{#2}%
\ifcase\varType % integer
\defineQ{\rng@LEP}{#2}{1}%
\or % rational
\defineQ{\rng@LEP}{\nOf{#2}}{\dOf{#2}}%
\or % real
\defineR{\rng@LEP}{#2}%
\RNGparseDec{\rng@LEP}%
\defineQ{\rng@LEP}{\rng@intpart}{\rng@fracpart}%
\fi
\else % a number, required to be rational
\RNGparseRat{#2}%
\defineQ{\rng@LEP}{\rng@num}{\rng@denom}%
\fi
\fi
% \end{macrocode}
% \paragraph*{Right endpoint}
% \begin{macrocode}
\rng@existStar{#3}\rng@NameEndpoint{\rng@UEP}%%
\if\rng@isStariii*%
\edef\tmp@exp{\noexpand%
\rng@isControl{\expandafter\noexpand\rng@UEP}}\tmp@exp
\if\rng@isC@ntrol1% a control sequence
\let\rng@CtrlUEP=1\let\rng@makeUEPStrict=1%
% \end{macrocode}
% The UEP is a control sequence we get its type and convert to rational
% \begin{macrocode}
\edef\tmp@exp{\noexpand%
\@getVarType{\expandafter\noexpand\rng@UEP}}\tmp@exp
\ifcase\varType % integer
\defineQ{\rng@UEP}{\rng@UEP}{1}%
\or % rational
\edef\tmp@exp{\noexpand%
\defineQ{\noexpand\rng@UEP}{\expandafter\nOf\rng@UEP}%
{\expandafter\dOf\rng@UEP}}\tmp@exp
\or % real
\defineR{\rng@UEP}{\rng@UEP}%
\RNGparseDec{\rng@UEP}%
\defineQ{\rng@UEP}{\rng@intpart}{\rng@fracpart}%
\fi
\else
% \end{macrocode}
% Not a control sequence but has a star, a number, we assume rational
% \begin{macrocode}
\RNGparseRat{\rng@UEP}%
\defineQ{\rng@UEP}{\rng@intpart}{\rng@fracpart}%
\fi
\else
% \end{macrocode}
% No star, is it a control sequence or not?
% \begin{macrocode}
\rng@isControl{#3}%
\if\rng@isC@ntrol1% a control sequence
\@getVarType{#3}%
\ifcase\varType % integer
\defineQ{\rng@UEP}{#3}{1}%
\or % rational
\defineQ{\rng@UEP}{\nOf{#3}}{\dOf{#3}}%
\or % real
\defineR{\rng@UEP}{#3}%
\RNGparseDec{\rng@UEP}%
\defineQ{\rng@UEP}{\rng@intpart}{\rng@fracpart}%
\fi
\else % a number, required to be rational
\RNGparseRat{#3}%
\defineQ{\rng@UEP}{\rng@num}{\rng@denom}%
\fi
\fi
\@@RandomQ{#1}{\nOf{\rng@LEP}}{\dOf{\rng@LEP}}%
{\nOf{\rng@UEP}}{\dOf{\rng@UEP}}%
}
% \end{macrocode}
% Once all the parameters have been acquired, and
% any needed conversions are made, we call \cs{@@RandomQ} which
% actually generates the random rational.
%\begin{verbatim}
% #1 maximum denominator permitted
% #2 numerator of first rational
% #3 denominator of first rational
% #4 numerator of second rational
% #5 denominator of second rational
%\end{verbatim}
% \begin{macrocode}
\newcommand{\@@RandomQ}[5]
{%
% \end{macrocode}
% Now take parameters \texttt{\#2}--\texttt{\#5}, and make into two rationals
% \begin{macrocode}
\updateQ\@rqi{#2}{#3}\updateQ\@rqii{#4}{#5}%
% \end{macrocode}
% Find least common multiple between \texttt{\#3}, \texttt{\#5} and \texttt{\#1}
% \begin{macrocode}
\lcm{#3}{#5}\edef\@thelcm{\thelcm}%
\def\@maxDenom{#1}%
\ifx\@maxDenom\@empty\edef\@maxDenom{\@thelcm}\else
\lcm{\@thelcm}{#1}\edef\@thelcm{\thelcm}\fi
% \end{macrocode}
% Now convert all rationals to have a denominator of \cs{@thelcm}
% \begin{macrocode}
\convertRatTo{\nOf\@rqi}{\dOf\@rqi}{\@thelcm}%
\updateQ\@@rqi{\rng@retn@num}{\@thelcm}%
\convertRatTo{\nOf\@rqii}{\dOf\@rqii}{\@thelcm}%
\updateQ\@@rqii{\rng@retn@num}{\@thelcm}%
% \end{macrocode}
% get divisor
% \begin{macrocode}
\rng@cnta=\@thelcm \divide\rng@cnta by\@maxDenom
\edef\@divisor{\the\rng@cnta}%
% \end{macrocode}
% Round up lower limit
% \begin{macrocode}
\rng@cnta=\nOf\@@rqi
\divide\rng@cnta by\@divisor
\advance\rng@cnta by1
% \end{macrocode}
% Round down the upper limit
% \begin{macrocode}
\rng@cntb=\nOf\@@rqii\divide\rng@cntb by\@divisor
% \end{macrocode}
% If a strict inequality is requested, we creep in a little.
% \begin{macrocode}
\if\rng@makeLEPStrict1\advance\rng@cnta1\relax\fi
\if\rng@makeUEPStrict1\advance\rng@cntb-1\relax\fi
% \end{macrocode}
% construct numerator
% \begin{macrocode}
\expandafter\@getVarName\rq@currentName
\let\save@varName\@varName
\expandafter\edef\csname first@n@\@varName\endcsname{\the\rng@cnta}%
\expandafter\edef\csname last@n@\@varName\endcsname{\the\rng@cntb}%
\expandafter\edef\csname first@d@\@varName\endcsname{\@maxDenom}%
\expandafter\edef\csname last@d@\@varName\endcsname{\@maxDenom}%
\edef\rng@LEP{\csname first@n@\@varName\endcsname}%
\edef\rng@UEP{\csname last@n@\@varName\endcsname}%
%\typeout{\@varName: first=\rng@LEP,last=\rng@UEP}%
\rng@chgrand[first=\rng@LEP,last=\rng@UEP]\rand
% \end{macrocode}
% Record the random variable name, e.g., \cs{a}, ...
% \begin{macrocode}
\let\@currentName\rq@currentName
\expandafter\@getVarName\rq@currentName
\expandafter\defineQ\@currentName{\arabic{rand}}{\@maxDenom}%
\simplifyCurrentQ
\expandafter\defineQ\@currentName{\expandafter\nOf\@currentName}%
{\expandafter\dOf\@currentName}%
% \end{macrocode}
%
% \paragraph*{Constraints}
%
% We now attempt to satisfy the NE constraints.
% \begin{macrocode}
\ifx\rangen@ne\@empty\else\loopCnt=0\relax
\@whilenum\loopCnt<\maxLoopLimit\do{%
\rng@cnta=1\relax
\@for\ne@@tmp:=\rangen@ne\do{%
% \end{macrocode}
% Define a rational by the name of \cs{cmp@Name}, then make it have
% the same denominator as \cs{@currentName}.
% \begin{macrocode}
\let\save@currentName\rq@currentName
\RNGparseRat{\ne@@tmp}%
\defineQ{\cmp@Name}{\rng@num}{\rng@denom}%
\let\@varName\save@varName
\syncronizeQs{\@varName}%
\ifnum\csname n@\@varName\endcsname=\n@cmp@Name
\multiply\rng@cnta0\relax
\else
\multiply\rng@cnta1\relax
\fi
}%
\ifnum\rng@cnta=1\relax % all conditions met
\loopCnt=\maxLoopLimit
\else % if \rng@cnta \ne 1, try again
\advance\loopCnt1\relax
\ifnum\loopCnt=\maxLoopLimit
\PackageWarning{rangen}{Not all conditions met
after \maxLoopLimit\space tries}%
\else
\rng@chgrand[first=\rng@LEP,last=\rng@UEP]\rand
\expandafter\@getVarName\rq@currentName
\expandafter\defineQ\@currentName{\arabic{rand}}%
{\@maxDenom}%
\fi
\fi
}%
\fi
\simplifyCurrentQ
\expandafter\defineQ\@currentName{\expandafter\nOf\@currentName}%
{\expandafter\dOf\@currentName}%
% \end{macrocode}
% If the denominator is equal to 1, let's change the data type to an integer.
% \begin{macrocode}
\let\@currentName\rq@currentName
\expandafter\@getVarName\rq@currentName
\ifnum\csname d@\@varName\endcsname=1\relax\expandafter
\defineZ\@currentName{\expandafter\nOf\@currentName}%
\fi
\simplifyCurrentQ
}
% \end{macrocode}
% \end{macro}
% \begin{macro}{\updateQ}
% Updates the value of a rational number, its numerator and denominator
% without changing any of the format macros.
% \begin{macrocode}
\newcommand\updateQ[3]
{%
\@getVarName#1\relax
\expandafter\edef\csname\@varName\endcsname{#2/#3}%
\expandafter\edef\csname n@\@varName\endcsname{#2}%
\expandafter\edef\csname d@\@varName\endcsname{#3}%
}
% \end{macrocode}
% \end{macro}
% A macro for performing routine adjustments on a rational number.
% \begin{macrocode}
\def\simplifyCurrentQ
{%
% \end{macrocode}
% Reduce fraction: Reduce the fraction to its lowest terms.
% \begin{macrocode}
\reduceFrac{\csname n@\@varName\endcsname}%
{\csname d@\@varName\endcsname}%
% \end{macrocode}
% \cs{reduceFrac} returns results in \cs{@tempcnta} and \cs{@tempcntb}, now
% update the numerator and denominator
% \begin{macrocode}
\expandafter\edef\csname n@\@varName\endcsname{\rfNumer}%
\expandafter\edef\csname d@\@varName\endcsname{\rfDenom}%
% \end{macrocode}
% If the numerator is zero, then zero out \cs{@varName} and special format
% \begin{macrocode}
\ifnum\csname n@\@varName\endcsname=0
\expandafter\edef\csname\@varName\endcsname{0}%
\edef\display@TeXfmt{0}\edef\inline@TeXfmt{0}%
\else
% \end{macrocode}
% If numerator equals denominator, just replace by 1
% \begin{macrocode}
\ifnum\csname n@\@varName\endcsname=\csname d@\@varName\endcsname
\expandafter\defineZ\csname\@varName\endcsname{1}%
\else
% \end{macrocode}
% If numerator equals -denominator, just replace by -1
% \begin{macrocode}
\ifnum\csname n@\@varName\endcsname
=-\csname d@\@varName\endcsname
\expandafter\defineZ\csname\@varName\endcsname{-1}%
\else
% \end{macrocode}
% If denominator equals 1, modify value; otherwise, ok.
% \begin{macrocode}
\ifnum\csname d@\@varName\endcsname=1
\expandafter\defineZ\csname\@varName\endcsname
{\csname n@\@varName\endcsname}%
\else
\expandafter\edef\csname \@varName\endcsname{%
\csname n@\@varName\endcsname/%
\csname d@\@varName\endcsname}%
\edef\display@TeXfmt{%
\frac{\csname n@\@varName\endcsname}
{\csname d@\@varName\endcsname}}%
\edef\inline@TeXfmt{%
\csname n@\@varName\endcsname/%
\csname d@\@varName\endcsname}%
\expandafter\let
\csname\@varName*\endcsname\display@TeXfmt
\fi
\fi
\fi
\fi
}
% \end{macrocode}
% \begin{macro}{\nOf}
% \begin{macro}{\dOf}
% \begin{macro}{\iOf}
% \begin{macro}{\typeOf}
% User access to numerator and denominator of random variables.
% \begin{macrocode}
\newcommand\nOf[1]{\csname n@\expandafter\@gobble\string#1\endcsname}
\newcommand\dOf[1]{\csname d@\expandafter\@gobble\string#1\endcsname}
% \end{macrocode}
% For a variable created by \cs{RandomL}, the index of the number chosen (1-based)
% can be accessed through the \cs{iOf} command.
% \begin{macrocode}
\newcommand{\iOf}[1]{\csname i@\expandafter\@gobble\string#1\endcsname}
% \end{macrocode}
% Get the type of a RV, \cs{ifnum}\cs{typeOf}\cs{a}=0 (integer), 1 (rational), 2 (real),
% 3 (literal, created by \cs{RandomP}).
% \begin{macrocode}
\newcommand\typeOf[1]{%
\csname typeof@\expandafter\@gobble\string#1\endcsname}
% \end{macrocode}
% \end{macro}
% \end{macro}
% \end{macro}
% \end{macro}
%
%\subsubsection{Random Real}
%
% We attempt to generate a random real number, in a given interval of real numbers.
%
% The following are some data and switches used by \cs{RandomReal}.
% \begin{macrocode}
\newif\iftrailingzeros\trailingzerosfalse
\@namedef{rng@tz1}{0}
\@namedef{rng@tz2}{00}
\@namedef{rng@tz3}{000}
\@namedef{rng@tz4}{0000}
\@namedef{rng@tz5}{00000}
\@namedef{rng@tz6}{000000}
\@namedef{rng@tz7}{0000000}
\@namedef{rng@tz8}{00000000}
\def\rng@true{true}\def\rng@false{false}
\newdimen\rng@dima
\newdimen\rng@dimb
\newdimen\rng@dimc
% \end{macrocode}
% \begin{macro}{\RandomR}
% Create a real number at random within the given interval. For example,
%\begin{verbatim}
% \RandomR[<key-values>]{\a}{3.45}{6.45}
%\end{verbatim}
% \begin{macro}{round}
% \begin{macro}{showzeros}
% The key-value pairs recognized by \cs{RandomZ|Q|R}.
% \begin{macrocode}
\define@key{rangen}{ne}[]{\edef\rangen@ne{#1}}
\define@key{rangen}{round}[]{\def\rangen@round{#1}}
\define@key{rangen}{showzeros}[]{\def\rangen@showzeros{#1}%
\ifx\rangen@showzeros\@empty\global\trailingzerostrue\else
\ifx\rangen@showzeros\rng@true\global\trailingzerostrue\else
\global\trailingzerosfalse\fi\fi}
\define@key{rangen}{index}[]{\edef\rangen@index{#1}}
% \end{macrocode}
% \end{macro}
% \end{macro}
%\begin{verbatim}
%[#1] = options
% #2 = name of real to correct
% #3 = lower endpoint of interval
% #4 = upper endpoint of interval
%\end{verbatim}
% \begin{macrocode}
\newcommand{\RandomR}[4][]{%
\setkeys{rangen}{ne,round,showzeros=false,#1}%
% \end{macrocode}
% Now see if there is an \texttt{*}, and get un-stripped
% argument.
%
% The \cs{rng@isControl} lets \cs{rng@isC@ntrol} to 0 if the arg is undefined,
% and lets \cs{rng@isC@ntrol} to 1 if it is defined.
% Check the left endpoint:
% \begin{macrocode}
\let\rng@CtrlLEP=0\let\rng@CtrlUEP=0%
\let\rng@makeLEPStrict=0\let\rng@makeUEPStrict=0%
\def\rng@lcg@first{0}\edef\rng@lcg@last{\RNGpowerOfTen}%
% \end{macrocode}
% \paragraph{Left endpoint.} Check the left endpoint:
% \begin{macrocode}
\rng@existStar{#3}\rng@NameEndpoint{\rng@LEP}%
\if\rng@isStariii*\edef\tmp@exp{\noexpand%
\rng@isControl{\expandafter\noexpand\rng@LEP}}\tmp@exp
\if\rng@isC@ntrol1% a control sequence
\let\rng@CtrlLEP=1\let\rng@makeLEPStrict=1%
\def\rng@lcg@first{1}%
% \end{macrocode}
% The LEP is a control sequence with a star. Convert LEP to a real
% number as needed.
% \begin{macrocode}
\edef\tmp@exp{\noexpand%
\@getVarType{\expandafter\noexpand\rng@LEP}}\tmp@exp
\ifcase\varType % integer
\defineR{\rng@LEP}{\rng@LEP\RNG@Dec}%
\or % rational
\rng@dima=\expandafter\nOf\rng@LEP pt
\divide\rng@dima by\expandafter\dOf\rng@LEP
\defineR{\rng@LEP}{\strip@pt\rng@dima}%
\or % real
\defineR{\rng@LEP}{\rng@LEP}%
\fi
% \end{macrocode}
% Not a control sequence, but has a star
% \begin{macrocode}
\else
\defineR{\rng@LEP}{\rng@LEP}%
\fi
\else
% \end{macrocode}
% No star, control sequence or not?
% \begin{macrocode}
\rng@isControl{#3}%
\if\rng@isC@ntrol1% control sequence
\let\rng@CtrlLEP=1\def\rng@LEP{#3}%
\@getVarType{#3}%
\ifcase\varType % integer
\defineR{\rng@LEP}{\rng@LEP\RNG@Dec}%
\or % rational
\rng@dima=\nOf{#3}pt
\divide\rng@dima by\dOf{#3}%
\defineR{\rng@LEP}{\strip@pt\rng@dima}%
\or % real
\defineR{\rng@LEP}{\rng@LEP}%
\fi
\else
% \end{macrocode}
% A number, no star, number is required to be real
% \begin{macrocode}
\defineR{\rng@LEP}{#3}%
\fi
\fi
% \end{macrocode}
% \paragraph{Right endpoint.} Check the right endpoint:
% \begin{macrocode}
\rng@existStar{#4}\rng@NameEndpoint{\rng@UEP}%
\if\rng@isStariii*\edef\tmp@exp{\noexpand%
\rng@isControl{\expandafter\noexpand\rng@UEP}}\tmp@exp
\if\rng@isC@ntrol1% a control sequence
\let\rng@CtrlUEP=1\let\rng@makeUEPStrict=1%
\rng@cnta=\rng@lcg@last\advance\rng@cnta-1\relax
\edef\rng@lcg@last{\the\rng@cnta}%
% \end{macrocode}
% The UEP is a control sequence with a star. Convert UEP to a real
% number as needed.
% \begin{macrocode}
\edef\tmp@exp{\noexpand%
\@getVarType{\expandafter\noexpand\rng@UEP}}\tmp@exp
\ifcase\varType % integer
\defineR{\rng@UEP}{\rng@UEP\RNG@Dec}%
\or % rational
\rng@dima=\expandafter\nOf\rng@UEP pt
\divide\rng@dima by\expandafter\dOf\rng@UEP
\defineR{\rng@UEP}{\strip@pt\rng@dima}%
\or % real
\defineR{\rng@UEP}{\rng@UEP}%
\fi
% \end{macrocode}
% Not a control sequence, but has a star
% \begin{macrocode}
\else
\defineR{\rng@UEP}{\rng@UEP}%
\fi
\else
% \end{macrocode}
% No star, control sequence or not?
% \begin{macrocode}
\rng@isControl{#4}%
\if\rng@isC@ntrol1% control sequence
\let\rng@CtrlUEP=1\def\rng@UEP{#4}%
\@getVarType{#4}%
\ifcase\varType % integer
\defineR{\rng@UEP}{\rng@UEP\RNG@Dec}%
\or % rational
\rng@dima=\nOf{#4}pt
\divide\rng@dima by\dOf{#4}%
\defineR{\rng@UEP}{\strip@pt\rng@dima}%
\or % real
\defineR{\rng@UEP}{\rng@UEP}%
\fi
\else
% \end{macrocode}
% A number, no star, number is required to be real
% \begin{macrocode}
\defineR{\rng@UEP}{#4}%
\fi
\fi
% \end{macrocode}
% Prepare to generate the random real
% \begin{macrocode}
\def\@currentName{#2}\@getVarName{#2}%
% \end{macrocode}
% Save upper and lower endpoints where they are expected to be.
% \begin{macrocode}
\expandafter\edef\csname first@\@varName\endcsname{\rng@LEP}%
\expandafter\edef\csname last@\@varName\endcsname{\rng@UEP}%
% \end{macrocode}
% Get a random real, and declare it to be a real number using \cs{defineR}.
% \begin{macrocode}
\rng@getRandomR
\defineR{#2}{\strip@pt\rng@dima}%
% \end{macrocode}
% Round and remove trailing zeros.
% \begin{macrocode}
\ifx\rangen@round\@empty\else
\RNGround{#2}{#2}{\rangen@round}%
\rng@dima=#2pt\relax
\defineR{#2}{\strip@pt\rng@dima}%
\fi
% \end{macrocode}
% \paragraph{Constraints.} Let's try to apply constraints. We only allow one constraint.
% \begin{macrocode}
\ifx\rangen@ne\@empty\else\loopCnt=0\relax
\@whilenum\loopCnt<\maxLoopLimit\do{%
\rng@cnta=1\relax
\@for\ne@@tmp:=\rangen@ne\do{%
\rng@dima=#2pt
\ifdim\rng@dima=\ne@@tmp pt\relax
\multiply\rng@cnta0\relax\else
\multiply\rng@cnta1\relax\fi
}%
\ifnum\rng@cnta=1\relax % all conditions met
\loopCnt=\maxLoopLimit
\else % if \rng@cnta \ne 1, try again
\advance\loopCnt1\relax
\ifnum\loopCnt=\maxLoopLimit
\PackageWarning{rangen}{Not all conditions met
after \maxLoopLimit\space tries}%
\else
\rng@getRandomR
\defineR{#2}{\strip@pt\rng@dima}%
% \end{macrocode}
% Round and remove trailing zeros.
% \begin{macrocode}
\ifx\rangen@round\@empty\else
\RNGround{#2}{#2}{\rangen@round}%
\rng@dima=#2pt\relax
\defineR{#2}{\strip@pt\rng@dima}%
\fi
\fi
\fi
}%
\fi
% \end{macrocode}
% \paragraph{Formatting.} Begin formatting of the real, keys recognized are
% \texttt{round} and \texttt{showzeros}.
% \begin{macrocode}
\rnd@ProcessRealFormat{#2}%
% \end{macrocode}
% We declare our number.
% \begin{macrocode}
\def\@currentName{#2}%
\defineR{#2}{#2}%
}
% \end{macrocode}
% Get a new random real and return it in the \cs{rng@dima}
% \begin{macrocode}
\def\rng@getRandomR{%
% \end{macrocode}
% Put the endpoints in dimension registers so we can subtract them.
% \begin{macrocode}
\rng@dima=\rng@LEP pt
\rng@dimb=\rng@UEP pt
% \end{macrocode}
% Compute the difference between upper and lower, then strip off the \texttt{pt},
% to make it a decimal number.
% \begin{macrocode}
\advance\rng@dimb-\rng@dima
% \edef\r@getDiff{\strip@pt\rng@dimb}%
% \end{macrocode}
% Get a random integer from the interval 0 to \cs{RNGpowerOfTen}.
% the default value of the latter command is 100, and it can be changed
% using \cs{nDivisionsPowerOfTen}. The idea is to divide the interval
% from the lower bound to the upper bound into \cs{RNGpowerOfTen} nodes,
% and we choose one of these nodes are random.
%
% If the endpoints where strict, then we changed \cs{rng@lcg@first}
% from 0 to 1 (if the lower endpoint is strict); and changed
% \cs{rng@lcg@last} from \cs{RNGpowerOfTen} to \texttt{\string\RNGpowerOfTen-1}
% (if the upper end point is strict).
% \begin{macrocode}
\rng@chgrand[first=\rng@lcg@first,last=\rng@lcg@last]\rand
% \end{macrocode}
% Divide the length of the interval by \cs{RNGpowerOfTen},
% and store the result in \cs{rng@dimb}, then multiply
% that by \verb!\arabic{rand}!.
% \begin{macrocode}
\divide\rng@dimb by\RNGpowerOfTen\relax
\rng@dimb=\arabic{rand}\rng@dimb
% \end{macrocode}
% Finally, the left-end point is still in \cs{rng@dima}
% we add the result in \cs{rng@dimb} to \cs{rng@dima}
% to compute our random rational.
% \begin{macrocode}
\advance\rng@dima by\rng@dimb
}
\def\rnd@ProcessRealFormat#1{%
\ifx\rangen@round\@empty
\rng@dima=#1pt\relax
\defineR{#1}{\strip@pt\rng@dima}%
\else
\RNGround{#1}{#1}{\rangen@round}%
\rng@dima=#1pt\relax
\defineR{#1}{\strip@pt\rng@dima}%
\iftrailingzeros
{\RNGparseDec{#1}\count0=\decPls\relax
\advance\count0-\rndnDec\relax
\ifnum\count0>0\relax\xdef#1{%
\rng@intpart\RNG@Dec\rng@fracpart%
\@nameuse{rng@tz\the\count0}}%
\fi}%
\defineR{#1}{#1}%
\fi
\fi
}
% \end{macrocode}
% \end{macro}
%
% \subsubsection{Random Sign}
% \begin{macro}{\RandomS}
% We randomly generate a \texttt{+} or \texttt{-} sign
% for addition and subtraction. The first optional argument
% is a rational number between 0 and 1. The default is \texttt{1/2}.
% This number represents the probably of a \texttt{+} sign.
% \begin{macrocode}
\newcommand{\RandomS}[2][1/2]{%
\RNGparseRat{#1}%
\ifnum\rng@num<0\relax
\PackageError{rangen}{A positive numerator is required}%
{The rational number must be between 0 and 1}\fi
\ifnum\rng@denom<0\relax
\PackageError{rangen}{A positive denominator is required}%
{The rational number must be between 0 and 1}\fi
\ifnum\rng@num>\rng@denom\relax
\PackageError{rangen}{The rational must be between 0 and 1}%
{The rational number must be between 0 and 1}\fi
\rng@chgrand[first=1,last=\rng@denom]\rand
\@getVarName{#2}%
\ifnum\value{rand}>\rng@num\relax\def#2{-}%
\rng@makeMinusOneFmtDefns
\def\display@TeXfmt{-}\def\inline@TeXfmt{-}%
\else\def#2{+}\rng@makeOneFmtDefns
\def\display@TeXfmt{}\def\inline@TeXfmt{}\fi
\expandafter\let\csname\@varName*\endcsname\display@TeXfmt
\expandafter\let\csname\@varName!\endcsname\inline@TeXfmt
}
% \end{macrocode}
% \end{macro}
%
% \subsubsection{Random Number from a List}
%
% \begin{macro}{\RandomL}
% Select a number of any type from a comma-delimited list.
%\begin{verbatim}
% \RandomL[key-values]{\RV}{<comma-delimited list>}
%\end{verbatim}
% Currently, the only key recognized is the \texttt{index} key.
% If the \texttt{index} key is specified, the number whose index is specified
% is retrieved from the list.
% \begin{macrocode}
\newcommand{\RandomL}[3][]{%
\let\rangen@index\@empty
\setkeys{rangen}{#1}%
\rng@cnta=0\relax\@for\@@tmp:=#3\do{%
\advance\rng@cnta1\relax}\edef\n@rng@listItems{\the\rng@cnta}%
\ifx\rangen@index\@empty
\rng@chgrand[first=1,last=\n@rng@listItems]\rand
\else
\rng@cnta=\rangen@index
\advance\rng@cnta-1\relax
\amodb{\rng@cnta}{\n@rng@listItems}%
\rng@cnta=\retnmod
\advance\rng@cnta1\relax
\value{rand}=\rng@cnta
\fi
\@getVarName{#2}%
\expandafter\edef\csname i@\@varName\endcsname{\arabic{rand}}%
\rng@cnta=0\relax\@for\@@tmp:=#3\do{%
\advance\rng@cnta1\relax\ifnum\rng@cnta=\arabic{rand}%
\edef\rng@choice{\@@tmp}\fi}%
\def\@currentName{#2}%
% \end{macrocode}
% Now, determine the type of this choice, and make appropriate
% data type definition.
% \begin{macrocode}
\RNGparseDec{\rng@choice}%
\if\rng@parseR@iii\RNG@Dec\defineR{#2}{\rng@choice}%
\else\RNGparseRat{\rng@choice}%
\if\rng@parseQ@iii/\defineQ{#2}{\rng@num}{\rng@denom}%
\else\defineZ{#2}{\rng@choice}\fi\fi
}
% \end{macrocode}
% \end{macro}
% \subsubsection{Random Problem from a List}
%
% \begin{macro}{\RandomP}
% Select a literal from a comma-delimited list of literals.
%\begin{verbatim}
% \RandomP[key-values]{\RV}{<comma-delimited list>}
%\end{verbatim}
% Currently, the only key recognized is the \texttt{index} key.
% If the \texttt{index} key is specified, the number whose index is specified
% is retrieved from the list.
% \begin{macrocode}
\newcommand{\RandomP}[3][]{%
\let\rangen@index\@empty
\setkeys{rangen}{#1}%
\rng@cnta=0\relax\@for\@@tmp:=#3\do{%
\advance\rng@cnta1\relax}\edef\n@rng@listItems{\the\rng@cnta}%
\ifx\rangen@index\@empty
\rng@chgrand[first=1,last=\n@rng@listItems]\rand
\else
\rng@cnta=\rangen@index
\advance\rng@cnta-1\relax
\amodb{\rng@cnta}{\n@rng@listItems}%
\rng@cnta=\retnmod
\advance\rng@cnta1\relax
\value{rand}=\rng@cnta
\fi
\@getVarName{#2}%
\expandafter\edef\csname i@\@varName\endcsname{\arabic{rand}}%
\rng@cnta=0\relax\@for\@@tmp:=#3\do{%
\advance\rng@cnta1\relax\ifnum\rng@cnta=\arabic{rand}%
\rng@toks=\expandafter{\@@tmp}\edef#2{\the\rng@toks}%
\expandafter\def\csname typeof@\@varName\endcsname{3}\fi}%
}
% \end{macrocode}
% \end{macro}
%
% \subsubsection{Random Index}
%
% \begin{macro}{\RandomI}
% This command creates an implied list of \verb!{1, 2, 3,...,n}!,
% and randomly selects a number from this list. The result is
% defined as an integer, and held in the macro \texttt{\#1}.
%\begin{verbatim}
% \Random{\i}{n} --> select \i from {1, 2, 3,...,n} at random
%\end{verbatim}
%A random index, \cs{i}, created by \cs{RandomI}, can be used
%in the \cs{RandomL} command; for example,
%\begin{verbatim}
% \RandomL[index=\i]{\a}{17,\rPI,3/4,\rE,88,1/2}
%\end{verbatim}
%The value of \cs{a} is determined by the index \cs{i}.
% \begin{macrocode}
\newcommand{\RandomI}[2]{%
\rng@chgrand[first=1,last=#2]\rand
\defineZ{#1}{\arabic{rand}}%
\expandafter\edef\csname i@\@varName\endcsname{\arabic{rand}}%
}
% \end{macrocode}
% \end{macro}
%
% \subsection{Some Constants}
%
% \begin{macro}{\zZero}
% \begin{macro}{\zOne}
% \begin{macro}{\zMinusOne}
% \begin{macro}{\rPI}
% \begin{macro}{\rE}
% Define three convenience integers corresponding to $0$, $1$, and $-1$.
% \begin{macrocode}
\defineZ{\zZero}{0}
\defineZ{\zOne}{1}
\defineZ{\zMinusOne}{-1}
\defineR{\rPI}{3.1415927}
\defineR{\rE}{2.7182818}
% \end{macrocode}
% \end{macro}
% \end{macro}
% \end{macro}
% \end{macro}
% \end{macro}
%
% This macro takes \cs{@varName} and \cs{cmp@Name} and converts to the same common
% denominator. This makes it easy to make comparisons between two rational numbers.
% \begin{macrocode}
\def\syncronizeQs#1{\edef\sync@arg{#1}%
\lcm{\csname d@\sync@arg\endcsname}{\d@cmp@Name}%
\edef\@thelcm{\thelcm}%
\convertRatTo{\n@cmp@Name}{\d@cmp@Name}{\@thelcm}%
\updateQ\cmp@Name{\rng@retn@num}{\@thelcm}%
\convertRatTo{\csname n@\sync@arg\endcsname}%
{\csname d@\sync@arg\endcsname}{\@thelcm}\expandafter
\defineQ\csname\sync@arg\endcsname{\rng@retn@num}{\@thelcm}%
}
% \end{macrocode}
% \subsection{Formatting Commands}
% \begin{macro}{\ds}
% \begin{macro}{\eds}
% \begin{macro}{\cds}
% Displays an alternate representation (\textbf display\textbf style) of the random variable. Usage \cs{ds}\cs{a}.
% This displays the contents of \cs{display@TeXfmt} for this variable. The value of \cs{display@TeXfmt}
% is effected by the formatting commands above.
%
% For a rational number \cs{a}, the expression \cs{ds}\cs{a} expands either to the special format representation, or
% to a rational of the form $\frac{p}{q}$.
% \begin{macrocode}
\newcommand\ds[1]{%
\expandafter\csname\expandafter\@gobble\string#1*\endcsname
}
\newcommand\eds[1]{%
\expandafter\csname\expandafter\@gobble\string#1*e\endcsname
}
\newcommand\cds[1]{%
\expandafter\csname\expandafter\@gobble\string#1*c\endcsname
}
% \end{macrocode}
% \end{macro}
% \end{macro}
% \end{macro}
% \begin{macro}{\fmt}
% \begin{macro}{\efmt}
% \begin{macro}{\cfmt}
% Displays a special format for the random variable. Usage \cs{ds}\cs{a}.
% This displays the contents of \cs{display@TeXfmt} for this variable.
% Same as \cs{ds}, but does not display a display style if there is not
% special formatting.
%
% For a rational number \cs{a}, the expression \cs{ds}\cs{a} expands either to the special format representation, or
% to a rational of the form $p/q$.
% \begin{macrocode}
\newcommand\fmt[1]{%
\expandafter\csname\expandafter\@gobble\string#1!\endcsname
}
\newcommand\efmt[1]{%
\expandafter\csname\expandafter\@gobble\string#1!e\endcsname
}
\newcommand\cfmt[1]{%
\expandafter\csname\expandafter\@gobble\string#1!c\endcsname
}
% \end{macrocode}
% \end{macro}
% \end{macro}
% \end{macro}
% \begin{macro}{\js}
% Used within \cs{CorrAnsButton} to get a more precise expansion of a variable. Used with variables
% that have been defined using \cs{defineDepVar}. When you say \verb+\js\m+, for example,
% the \cs{eval@JSfmt} is expanded.
% \par\medskip\noindent
% \textbf{Usage:} \verb+\CorrAnsButton*{y = \js\m\space x }+
% \begin{macrocode}
\newcommand\js[1]{%
\expandafter\csname\expandafter\@gobble\string#1!*\endcsname
}
% \end{macrocode}
% \end{macro}
%
% \subsection{Commands specialized to Reals}
% \begin{macro}{\RNGround}
% Round \texttt{\#1} to \texttt{\#3} decimal places, and leave result in \texttt{\#2}.
% \begin{macrocode}
\def\RNGround#1#2#3{%
\begingroup
\def\rng@ctrlName{#1}%
\def\rng@sourceName{#2}%
\def\rng@nDecPl{#3}%
\RNGparseDec{#2}%
\ifnum\rndnDec<#3\relax
\xdef\theseDigits{\rng@fracpart}%
\let\rng@next\relax
\else
\count0=0\relax
\gdef\theseDigits{}%
\def\rng@next{\expandafter\@rng@round\rng@fracpart\end}%
\fi
\rng@next
\xdef\decPls{\@ifundefined{save@rng@nDecPl}%
{\rng@nDecPl}{\save@rng@nDecPl}}%
\ifx\theseDigits\@empty
\xdef#1{\rng@intpart}\else
\xdef#1{\rng@intpart\RNG@Dec\theseDigits}\fi
\endgroup
}
\def\@rng@round#1{%
\ifx#1\end\let\rng@next\relax
\else
\ifnum\rng@nDecPl=0\relax
\ifnum#1>4\relax
\count0=\rng@intpart\relax
\ifnum\rng@intpart<0\relax
\advance\count0by-1\relax
\else
\advance\count0by1\relax
\fi
\xdef\rng@intpart{\the\count0}%
\fi
\gdef\theseDigits{}%
\let\rng@next\rng@gobbletoend
\else
\advance\count0by1\relax
\ifnum\count0=\rng@nDecPl\relax
\def\rng@next{\@@rng@round#1}%
\else
\xdef\theseDigits{\theseDigits#1}%
\let\rng@next\@rng@round
\fi
\fi
\fi
\rng@next
}
\def\rng@gobbletoend#1\end{}
\def\@@rng@round#1#2{%
\ifx#2\end%
\xdef\theseDigits{\theseDigits#1}%
\let\rng@next\relax
\else
\ifnum#2>4\relax\count2=#1\relax
\ifnum\count2=9\relax
\count0=\rng@nDecPl\relax
\ifnum\count0=1\relax
\count0=\rng@intpart\relax
\ifnum\rng@intpart<0\relax
\advance\count0by-1\relax
\else
\advance\count0by1\relax
\fi
\xdef\rng@intpart{\the\count0}%
\let\rng@next\rng@gobbletoend
\else
\advance\count0by-1\relax\expandafter
\xdef\rng@sourceName{%
\rng@intpart\RNG@Dec\theseDigits#1}%
\edef\save@rng@nDecPl{\rng@nDecPl}%
\edef\rng@next{\noexpand\RNGround{%
\expandafter\noexpand\rng@ctrlName}%
{\expandafter\noexpand\rng@sourceName}%
{\the\count0}\noexpand\rng@gobbletoend}%
\fi
\else
\advance\count2by1\relax
\xdef\theseDigits{\theseDigits\the\count2}%
\let\rng@next\rng@gobbletoend
\fi
\else % \ifnum#2<=4
\xdef\theseDigits{\theseDigits#1}%
\let\rng@next\rng@gobbletoend
\fi
\fi
\rng@next
}
% \end{macrocode}
% \end{macro}
% Used with \cs{CorrAnsButton} and \texttt{rngCorrAnsButton}, like so,
%\begin{verbatim}
% \CorrAnsButton{rEval(\strAns)}*{rngCorrAnsButton\RNGprintf{\%.2f}}
%\end{verbatim}
% \begin{macrocode}
\def\RNGprintf#1{("#1",\@gobble}
% \end{macrocode}
%
% \subsection{User Defined Dependent Variables for JavaScript}
% \begin{macro}{\defineDepQJS}
% Define a rational as a function of other integers. This macro defines
% \cs{fmt} and \cs{ds} for the variable, but its primary use it
% for \cs{js}. This command is aimed at the JavaScript side of things
%\begin{verbatim}
%#1 = name of rational to be defined, e.g., \a
%#2 = numerator
%#3 = denominator
%#4 = \js expression for #1
%\end{verbatim}
% Usage:
%\begin{verbatim}
% \defineDepQJS{\m}{\d-\b}{\c-\a}
% {rFrac(rEval(\nOf\m)/rEval(\dOf\m))}
% ...
% \CorrAnsButton{y = \js\m\space x}*{rngCorrAnsButton}%
%\end{verbatim}
% The above example would calculate equation of the line passing through
% the two points \verb!P(\a,\b)! and \verb!Q(\c,\d)!. The code is used
% in the \cs{CorrAnsButton} to have the answer appear.
% \begin{macrocode}
\newcommand\defineDepQJS[4]{%
\@getVarName#1
\expandafter\edef\csname\@varName\endcsname{(#2)/(#3)}%
\expandafter\edef\csname n@\@varName\endcsname{(#2)}%
\expandafter\edef\csname d@\@varName\endcsname{(#3)}%
\edef\display@TeXfmt{\csname\@varName\endcsname}%
\edef\inline@TeXfmt{\csname\@varName\endcsname}%
\def\dv@argiv{#4}\ifx\dv@argiv\@empty
\edef\eval@JSfmt{\csname\@varName\endcsname}\else
\edef\eval@JSfmt{#4}\fi
\expandafter\let\csname\@varName!*\endcsname\eval@JSfmt
}
% \end{macrocode}
% \end{macro}
%
% \subsection{Writing RVs to Solution Files}
% \begin{macrocode}
\def\rng@writeCurrentSeed#1{\immediate\write#1{\string\makeatletter
\string\global\string\cr@nd=\the\cr@nd\string\relax
\string\makeatother}}
% \end{macrocode}
% Token register to hold the verbatim contents of the \texttt{writeRVsTo} environment.
% \begin{macrocode}
\newtoks\rng@toks
\def\wrv@ex@solns{exercises}%
\def\wrv@ex@quiz{quizzes}%
% \end{macrocode}
% \begin{environment}{writeRVsTo}
% This environment takes its environment contents and writes it to
% two files, one file is \cs{jobname\_rvs.cut} which is input back
% into the source file immediately. The second parameter
% accepts the string \texttt{exercises} or \texttt{quizzes}, or a write
% handle to write to an auxiliary file. The environment was designed for
% use with the \texttt{exercise}, \texttt{quiz}, and \texttt{shortquiz} environments
% of \textsf{exerquiz}.
% \begin{macrocode}
\newenvironment{writeRVsTo}[2][]
{%
\def\wrv@argii{#2}%
\ifx\wrv@argii\wrv@ex@quiz\let\wrv@out\quiz@solns
\else\ifx\wrv@argii\wrv@ex@solns\let\wrv@out\ex@solns\else
\let\wrv@out#2\fi\fi
\rng@writeCurrentSeed\wrv@out
\rng@toks={}%
\def\verbatim@processline{%
\xdef\rng@temp{\the\rng@toks\the\verbatim@line}%
\global\rng@toks=\expandafter{\rng@temp}}%
\let\do\@makeother\dospecials\catcode`\^^M\active
#1%
\verbatim@start
}{ \immediate\write\wrv@out{\the\rng@toks}%
\newwrite\rng@writeRVs
\immediate\openout\rng@writeRVs\jobname_rvs.cut
\immediate\write\rng@writeRVs{\the\rng@toks}%
\immediate\closeout\rng@writeRVs
\aftergroup\rng@Input@RVs
}
% \end{macrocode}
% \end{environment}
% After the \texttt{writeRVsTo} environment writes the RVs to
% \cs{jobname\_rvs.cut}. The environment executes
% \cs{rng@Input@RVs} to input the file back into the source file.
% \begin{macrocode}
\def\rng@Input@RVs{\InputIfFileExists{\jobname_rvs.cut}{}{}}
% \end{macrocode}
% \subsection{Redefine lcg Package Macro}
% \begin{macrocode}
\def\rng@p@stkeysr@nd{%
\@rderr@nd% last < first -> swap
\cutr@nger@nd% range too big -> cut
} % end of \def\p@stkeysr@nd
\def\rng@chgrand{\@ifnextchar[\rng@chgr@nd{\rng@chgr@nd[]}}
\def\rng@chgr@nd[#1]{%
\@tempcnta=\z@
\@tempcntb=\z@
\setkeys{Init}{#1}%
\rng@p@stkeysr@nd%
\@utputr@nd%
} % end of \def\rng@chgrand
% \end{macrocode}
% \subsection{DLJS Support}
% \begin{macrocode}
\begin{insDLJS}[partialExpand]{partial}{Rangen}
var partre = /rEval|rFrac/;
% \end{macrocode}
% The arguments for this function take two forms
% (1) \texttt{fieldname}, \texttt{theanswer} (the default); (2)
% \texttt{theformat}, \texttt{fieldname}, \texttt{theanswer}. The later case
% is created by using the \cs{RNGprintf} command that inserts allows the
% document author to insert a \texttt{printf} formatting template. For example,
%\begin{verbatim}
% \CorrAnsButton{rEval(\strAns)}*{rngCorrAnsButton\RNGprintf{\%.4f}}
%\end{verbatim}
% \begin{macrocode}
function rngCorrAnsButton()
{
var theprecision,fieldname,theanswer;
if (arguments.length==4) {
var theformat=arguments[0];
var fieldname=arguments[1];
var theanswer=arguments[2];
var thequiz=arguments[3];
} else {
var fieldname=arguments[0];
var theanswer=arguments[1];
var thequiz=arguments[2];
}
theanswer = partialExpand(0,theanswer);
if (arguments.length==4)
theanswer=util.printf(theformat,eval(theanswer));
DisplayAnswer(fieldname,theanswer,thequiz);
}
% \end{macrocode}
% The JavaScript function \texttt{partialExpand} searches through \texttt{Ans} in search of
% \texttt{rEval} and \texttt{rFrac}. It calls itself recursively to search for the inner most
% appearances of these two functions. It evaluates these two functions starting with the inner
% most and working its way outward.
% \begin{macrocode}
function partialExpand(level,Ans)
{
Ans = correctPlusMinus(Ans)
level += 1;
\db console.println("Enter level = " + level +": Ans: " + Ans);\db%
var n=0, m, bP, eP, subExp;
while ( true ) {
\db console.println("Searching a level " + level);\db%
try { m = Ans.match(partre); }
catch (e) { break; }
if ( m != null ) {
bP = m.index + m[0].length;
eP = FindBalP(Ans, bP, true);
\db console.println("bP = " + bP + " : eP = " + eP);\db%
var subExp = Ans.substring(bP+1, eP);
\db console.println("Found \'" + subExp%
+ "\' at level = " + level);\db%
% subExp = partialExpand(level, subExp);
// n = beginning of "rEval",
// eP = beginning of balanced parens,
// bP = end of balanced parens
Ans = Ans.substring(0, m.index)
+ eval(m[0]+"(level,subExp)") + Ans.substring(eP+1);
\db console.println("level = " + level%
+": New Ans: " + Ans);\db %
} else {
if ( level == 1 ) {
\db console.println("Level 1 break");\db %
break;
}
}
}
\db console.println("Return Ans: " + Ans);\db%
Ans = correctPlusMinus(Ans);
return Ans;
}
% \end{macrocode}
% Evaluates the value of \texttt{Ans}.
% \begin{macrocode}
function rEval(level, Ans)
{
level += 1;
\db console.println("Enter rEval: level = "%
+ level +": Ans: " + Ans);\db%
var n=0, m, bP, eP, subExp;
while ( true )
{
\db console.println("Searching a level " + level);\db%
try { m = Ans.match(partre); }
catch (e) { break; }
if ( m != null ) {
bP = m.index + m[0].length;
eP = FindBalP(Ans, bP, true);
\db console.println("bP = " + bP + " : eP = " + eP);\db%
var subExp = Ans.substring(bP+1, eP);
\db console.println("Found \'" + subExp%
+ "\' at level = " + level);\db%
// n = beginning of "rEval",
// eP = beginning of balanced parens,
// bP = end of balanced parens
Ans = Ans.substring(0, m.index)
+eval(m[0]+"(level,subExp)")+Ans.substring(eP+1);
\db console.println("level = "%
+ level +": New Ans: " + Ans);\db %
} else {
Ans = ParseInput(Ans);
\db console.println("Ready to eval at level = "%
+ level + ": Ans = " + Ans);\db%
with(Math) { Ans = eval( Ans ) };
\db console.println("After eval at level = "%
+ level + ": Ans = " + Ans);\db%
break;
}
}
\db console.println("Return Ans: " + Ans);\db%
return Ans;
}
% \end{macrocode}
% Evaluates an rational number by evaluating the value of the numerator and denominator separately.
% \begin{macrocode}
function rFrac(level, Ans)
{
level += 1;
\db console.println("Enter rFrac level = "%
+ level +": Ans: " + Ans);\db%
var n=0, m, bP, eP, subExp;
while ( true ) {
\db console.println("Searching a level " + level);\db%
try { m = Ans.match(partre); }
catch (e) { break; }
if ( m != null ) {
bP = m.index + m[0].length;
eP = FindBalP(Ans, bP, true);
\db console.println("bP = "%
+ bP + " : eP = " + eP);\db%
var subExp = Ans.substring(bP+1, eP);
\db console.println("Found \'" + subExp%
+ "\' at level = " + level);\db%
// n = beginning of "rEval",
// eP = beginning of balanced parens,
// bP = end of balanced parens
Ans = Ans.substring(0, m.index)
+ eval(m[0]+"(level,subExp)") + Ans.substring(eP+1);
\db console.println("level = " + level%
+": New Ans: " + Ans);\db %
} else {
var numDenom = Ans.split("/");
numDenom[0] = eval(numDenom[0]);
numDenom[1] = eval(numDenom[1]);
var g = gcd(numDenom[0], numDenom[1]);
numDenom[0] /= g;
numDenom[1] /= g;
if ( numDenom[1] == 1)
Ans = numDenom[0];
else
Ans = numDenom.join("/");
\db console.println("Reduce: " + numDenom.join("/"));\db%
break;
}
}
\db console.println("Return Ans: " + Ans);\db%
return Ans;
}
function correctPlusMinus(Ans)
{
Ans = "" + Ans;
Ans = Ans.replace(/\s*([\+-])\s*\1\s*/g, " + ");
Ans = Ans.replace(/\s*\+\s*-\s*/g, " - ");
% Ans = Ans.replace(/\s*\+\s*\+\s*/g, " + ");
% Ans = Ans.replace(/\s*-\s*-\s*/g, " + ");
Ans = Ans.replace(/\s*-\s*\+\s*/g, " - ");
return Ans;
}
function gcd(a,b)
{
var x = a, y = b, r;
while (true)
{
r = x \% y;
if ( r == 0 ) break;
x = y;
y = r;
}
return Math.abs(y);
}
function lcm (a,b) { return (a*b)/gcd(a,b); }
\end{insDLJS}
%</package>
% \end{macrocode}
\endinput