% \iffalse meta-comment
%
% qrcode.ins
% Copyright 2014 by Anders O.F. Hendrickson (anders.hendrickson@snc.edu)
%
% This work may be distributed and/or modified under the
% conditions of the LaTeX Project Public License, either version 1.3
% of this license or (at your option) any later version.
% The latest version of this license is in
%   http://www.latex-project.org/lppl.txt
% and version 1.3 or later is part of all distributions of LaTeX
% version 2005/12/01 or later.
%
% This work has the LPPL maintenance status `maintained'.
% 
% The Current Maintainer of this work is Anders O.F. Hendrickson.
%
% This work consists of the files qrcode.dtx and qrcode.ins
% and the derived file qrcode.sty.
%
% \fi
%
% \iffalse
%<*driver>
\ProvidesFile{qrcode.dtx}
%</driver>
%<package>\NeedsTeXFormat{LaTeX2e}[1999/12/01]
%<package>\ProvidesPackage{qrcode}
%<*package>
    [2015/01/08 v1.51 QR code generation]
%</package>
%
%<*driver>
\documentclass{ltxdoc}
\usepackage{hyperref}
\usepackage[nolinks]{qrcode}
\EnableCrossrefs         
\CodelineIndex
\OnlyDescription
\RecordChanges
\begin{document}
  \DocInput{qrcode.dtx}
  \PrintChanges
  %\PrintIndex
\end{document}
%</driver>
% \fi
%
% \CheckSum{0}
%
% \CharacterTable
%  {Upper-case    \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
%   Lower-case    \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
%   Digits        \0\1\2\3\4\5\6\7\8\9
%   Exclamation   \!     Double quote  \"     Hash (number) \#
%   Dollar        \$     Percent       \%     Ampersand     \&
%   Acute accent  \'     Left paren    \(     Right paren   \)
%   Asterisk      \*     Plus          \+     Comma         \,
%   Minus         \-     Point         \.     Solidus       \/
%   Colon         \:     Semicolon     \;     Less than     \<
%   Equals        \=     Greater than  \>     Question mark \?
%   Commercial at \@     Left bracket  \[     Backslash     \\
%   Right bracket \]     Circumflex    \^     Underscore    \_
%   Grave accent  \`     Left brace    \{     Vertical bar  \|
%   Right brace   \}     Tilde         \~}
%
%
% \changes{v1.0}{2014/09/26}{Initial version}
% \changes{v1.5}{2015/01/08}{Added support for new lines and hyperlinks.}
% \changes{v1.51}{2015/01/14}{Bug fix.}
%
% \GetFileInfo{qrcode.sty}
%
% \DoNotIndex{\newcommand,\newenvironment,\def}
% 
% \def\F{F}
%
% \title{The \textsf{qrcode} package: \\
%        \makebox[0pt][r]{\raisebox{-0.3\height}[0pt][0pt]{\qrcode[hyperlink,tight]{http://ctan.org/pkg/qrcode}}\rule{0.75in}{0pt}}Quick Response code \\
%        generation in \LaTeX\thanks{This document
%   corresponds to \textsf{qrcode}~\fileversion, dated \filedate.}}
% \author{Anders Hendrickson\\ St.~Norbert College, De~Pere, WI, USA \\ \texttt{anders.hendrickson@snc.edu}}
% \date{January 8, 2015}
%
% \maketitle
%
%
% \section{Introduction}
%
% The proliferation of smartphones and tablets has led to the widespread
% use of Quick Response (QR) codes, which encode numeric, alphanumeric, kanji,
% or binary information into a square matrix of black and white pixels called modules.
% Although QR codes can encode any information up to almost three kilobytes,
% their most common use is as physical hyperlinks: a mobile device scans
% a printed QR code, decodes a URL, and automatically points a browser to that location.
% 
% It is natural to want to include QR codes in certain \LaTeX\ documents;
% for example, one may want to direct the reader of a printed page to 
% related interactive content online.
% Before now, the only \LaTeX\ package for producing QR codes was the
% immensely flexible {\tt pst-barcode}.  As that package relies on 
% {\tt pstricks}, however, it can be difficult to integrate with 
% a pdf\LaTeX\ workflow,\footnote{%
% The {\tt auto-pst-pdf} or {\tt pstool} packages can make this possible
%    by automatically running
%    \LaTeX${}\rightarrow \tt dvips \rightarrow ps2pdf \rightarrow pdfcrop$ 
%    for each barcode generated in {\tt pstricks}, 
%    so long as the user is able and willing to enable {\tt\string\write18}
%    in {\tt pdflatex} and install Perl.
%    Judging by questions on {\tt tex.stackexchange.com} and {\tt latexcommunity.org},
%    this is a significant hurdle for some users.
%    Moreover, according to {\tt http://tex.stackexchange.com/questions/72876/}
%    this workflow may have trouble if the QR code is in a header.}
% and a pdf\LaTeX\ user may not want the extra overhead just to produce a QR code.
% If one wants to avoid {\tt pstricks}, a Lua\TeX\ solution was proposed at
% {\tt http://tex.stackexchange.com/questions/89649/},
% and a plain\TeX\ solution can be found at 
% {\catcode`\~=12\tt http://ktiml.mff.cuni.cz/~maj/QRcode.TeX},
% but until now no \LaTeX\ package had been available that did not call on outside machinery.
% 
% The {\tt qrcode} package, in contrast, implements the QR code algorithm using 
% only \TeX\ and \LaTeX\ commands, so it should work with any \LaTeX\ workflow.
% Because it draws the squares constituting a QR code using the \TeX\ primitive 
% |\rule|, there is no need to load any graphics package whatsoever.
% For a user who merely wants a QR code, this is the simplest solution.
% 
% \section{Usage}\label{sect:usage}
%
%
% \DescribeMacro{\qrcode}
% The package provides just one command, |\qrcode|, with the following syntax:
% \begin{center}
% |\qrcode|\oarg{options}\marg{text to be encoded}
% \end{center}
% For example, |\qrcode[hyperlink,height=0.5in]{http://www.ctan.org}| produces
% \begin{center}
%   \qrcode[hyperlink,height=0.5in]{http://www.ctan.org}
% \end{center}
% Although the most common use of QR codes is as URLs,
% the \meta{text to be encoded} can be almost any typed text.
% The few exceptions to this are described in section \ref{sect:specialcharacters}.
%
% \subsection{Package Options}
% 
% \DescribeMacro{nolinks}
% When the |hyperref| package is loaded,
% by default |\qrcode| assumes its argument is a URL
% and makes the QR code produced a hyperlink to that URL.
% This default behavior may be changed by invoking the |nolinks| package option.
% For example, most of the QR codes in this document are not in fact URLs, 
% so this documentation was typeset with |\usepackage[nolinks]{qrcode}|.
% The |hyperlinks| option is an antonym to |nolinks| and is the default.
% These options have no effect if hyperref is not loaded.
% 
% \DescribeMacro{draft}
% \DescribeMacro{final}
% Creating QR codes for short URLs takes relatively little time.\footnote{On 
%           this author's laptop, even a 60-character URL (version 4, level M) adds 
%           only about 0.7 seconds of compilation time.}
% Because \TeX\ was designed for typesetting, not for extensive computations,
% however, if many small QR codes or a single large one are required,
% the time spent can be quite noticeable.  To save compilation
% time while working on a large document, calling the |draft| option 
% causes the package not to compute QR codes, but merely to insert placeholder
% symbols with no data.  The |final| option is an antonym to |draft|
% and is the default.
% \begin{quote}
%   \begin{tabular}{p{1.25in}p{3.5in}}
%     {\qrcode[draft,version=15]{http://www.tug.org}}
%     &
%     \begin{minipage}{3in}
%       \tt 
%       |\documentclass{article}| \\
%       |\usepackage[draft]{qrcode}| \\
%       |\begin{document}| \\
%       |  \qrcode[version=15]{Dummy code}| \\
%       |\end{document}|
%     \end{minipage}
%   \end{tabular}
% \end{quote}
% The placeholder symbol produced in {\tt draft} mode will have the same size
% and dimensions as the actual QR code.
%
% To conserve processing time, when |\qrcode| computes the binary matrix representing
% a QR code, it saves that binary data as a string of 1's and 0's
% both in a macro and in the {\tt .aux} file.
% Thus if the same QR code is desired later in the document, or upon the next
% run of \LaTeX, the QR symbol can be redrawn immediately from the saved binary data.
%
% \DescribeMacro{forget}
% There may be times when this is not desired; testing of this package is the chief
% example, but one might also have reason to believe that the {\tt .aux} file 
% contains bad data.
% Invoking the |forget| package option causes |\qrcode| to calculate
% every QR code anew, even if a QR code for that \meta{text to be encoded}, level,
% and version
% was read from the {\tt .aux} file or was already computed earlier in the document.
%
% \subsection{Options}
% \DescribeMacro{\qrset}
% Several options affect the appearance and encoding of the QR code;
% {\tt qrcode} uses the {\tt xkeyval} package to handle the setting
% and processing of key-value pairs.
% The following options may either be given as optional arguments
% to |\qrcode| or changed within a \TeX-grouping using the
% macro |\qrset|.
% \begin{quote}
%   \begin{tabular}{p{6cm}p{2in}}
%     \qrcode{ABCD}
%     {\qrset{height=1cm}%
%      \qrcode{EFGH}}
%     \qrcode{IJKL}
%     &
%     \begin{minipage}{3in}
%       |\qrcode{ABCD}| \\
%       |{\qrset{height=1cm}%| \\
%       | \qrcode{EFGH}}| \\
%       |\qrcode{IJKL}|
%     \end{minipage}
%   \end{tabular}
% \end{quote}
%
% \DescribeMacro{height}
% The |height=|\meta{dimen} key sets the printed height (and width) of the 
% QR code.  The default value is {\tt 2cm}.
% \begin{quote}
%   \begin{tabular}{p{2in}p{2in}}
%   \qrcode{ABCD} \qrcode[height=1cm]{ABCD}
%   & |\qrcode{ABCD}| |\qrcode[height=1cm]{ABCD}|
% \end{tabular}
% \end{quote}
% 
% \DescribeMacro{level}
% The QR code specification (ISO 18004:2006) includes four 
% levels of encoding: Low, Medium, Quality, and High, in
% increasing order of error-correction capabaility.  
% In general, for a given text a higher error-correction
% level requires more bits of information in the QR code.
% The key |level=|\meta{level specification}
% selects the minimum acceptable level.
% The \meta{level specification} may be |L|, |M|, |Q|, or |H|;
% the default is |M|.
% It may happen that the smallest QR code able to encode
% the specified text at the desired level
% is in fact large enough to provide a higher level of 
% error-correction.  If so, {\tt qrcode} automatically upgrades to the higher
% error-correction level, and a message is printed in the log file.
% 
% \DescribeMacro{version}
% QR codes range in size from $21\times 21$ modules (``version 1'') 
% to $177\times 177$ modules (``version 40''), in steps of 4 modules.  
% The package automatically selects the smallest version large enough to encode
% the specified text at the desired error-correction level.
% Nevertheless, there might be occasions when a specific version is required;
% for example, perhaps a set of QR codes should have the same dimensions for 
% aesthetic reasons, even though some encode shorter texts than others.
% For this reason, the key |version=|\meta{version specification} allows the user
% to specify a minimum version number, from 1 through 40, for the QR code.
% Setting |version=0| means ``as small as possible''; this is the default.
% If the desired version is not large enough to encode the text, the version
% will automatically be increased to accommodate the text, and a message will
% be placed in the log file.
% \begin{quote}
%   \begin{tabular}{p{5.2cm}p{3in}}
%     \raggedright
%     \qrcode{ABCD}
%     \qrcode[version=5]{ABCD} 
%     \medskip \\
%     \qrcode[version=10]{ABCD}
%     \qrcode[version=20]{ABCD}
%     &
%     \begin{minipage}{3in}
%       |\qrcode{ABCD}| \\
%       |\qrcode[version=5]{ABCD}| \\
%       |\medskip \\| \\
%       |\qrcode[version=10]{ABCD}| \\
%       |\qrcode[version=20]{ABCD}|
%     \end{minipage}
%   \end{tabular}
% \end{quote}
%
% 
% \DescribeMacro{tight}
% \DescribeMacro{padding}
% The QR specification states that a QR code should be surrounded by white\-space
% of a width equal to that of four modules.  In many applications, a document
% author is likely to provide sufficient spacing anyway (e.g., by placing the 
% QR code in a {\tt center} environment, header, or |\marginpar|), so by 
% default the |qrcode| package adds no spacing.  If the option |padding| is 
% specified, however, the QR code will automatically be surrounded with 4 modules'
% worth of white\-space. The key |tight| is an antonym of |padding|; the default is |tight|.
% 
% \DescribeMacro{link}
% \DescribeMacro{nolink}
% \DescribeMacro{\qrcode*}
% As described above, if the |hyperref| package is loaded,
% then the QR codes produced in a PDF document can be made 
% into hyperlinks to their text.  The default behavior 
% can be controlled with the options |nolinks| and |hyperlinks|,
% but this default can be overridden for individual QR codes by invoking
% the options |link| or |nolink|. 
% Moreover, the starred version of the macro, |\qrcode*|, is a shorthand 
% equivalent to |\qrcode[nolink]|.
% \begin{quote}
%   \begin{tabular}{p{5.2cm}p{3in}}
%     \raggedright
%     \qrset{link, height=1.5cm}
%     \qrcode{http://www.ctan.org}
%     \qrcode[nolink]{This is not a URL.}
%     \qrcode*{Neither is this.} 
%     &
%     \begin{minipage}{3in}
%       |\qrset{link, height=1.5cm}| \\
%       |\qrcode{http://www.ctan.org}| \\
%       |\qrcode[nolink]{This is not a URL.}| \\
%       |\qrcode*{Neither is this.}|
%     \end{minipage}
%   \end{tabular}
% \end{quote}
% 
% \subsection{Special characters}\label{sect:specialcharacters}
% Many URLs can be processed by \TeX\ with no hiccups,
% but not infrequently a URL may contain the symbols |%|, |#|,
% |~|, |_|, and |&|.  Moreover, QR codes need not just contain
% URL's, so a user may wish to encode text containing |^|, |$|, or spaces.
% The |qrcode| package offers two ways of coping with these special characters.
% 
% First, the |\qrcode| command itself processes its \meta{text to be encoded} 
% in a limited verbatim mode.  The following characters will be encoded into
% the QR code as typed:
% \begin{center}
%   |#| |$| |&| |^| |_| |~| |%| {\tt\char32}
% \end{center}
% and line breaks as well.\footnote{Technically, when the input character 
% {\tt\char`\^\char`\^M} (CR, charcode 13) is encountered,
% the character {\tt\char`\^\char`\^J} (LF, charcode 10) is placed into the QR code.}
% Conspicuously absent from this list are |\|, |{|, and |}|.
% This is intentional, so that macros may be used within |\qrcode|
% to generate the \meta{text to be encoded} automatically.
% If these characters are desired, they may be obtained by ``escaping'' them
% with an extra backslash.
% \begin{quote}
%   \begin{tabular}{p{2in}p{3in}}
%   \qrset{height=1.5cm}%
%   \qrcode{We can include #$&^_~%.}
%   \def\foo{bar}%
%   \qrcode{Set the \foo\ high.}
%   \qrcode{We must escape \\emph\{this\}.}
%   & \begin{minipage}{3in}
%     |\qrset{height=1.5cm}%| \\
%     |\qrcode{We can include #$&^_~%.}| \\
%     |\def\foo{bar}%| \\
%     |\qrcode{Set the \foo\ high.}| \\
%     |\qrcode{We must escape \\emph\{this\}.}|
%     \end{minipage}
% \end{tabular}
% \end{quote}
% 
% As with all verbatim modes, however, because \TeX\ irrevocably sets catcodes 
% when it first encounters characters, this will not work if the |\qrcode| macro
% is contained in another macro.  If you call |\qrcode| inside an
% |\fbox| or a |\marginpar|, for example, and if your URL contains one of those
% special characters, you will either encounter error messages or (worse, because
% it is undetectable to the naked eye) have the wrong QR code typeset.
% In this scenario, you can still include any of the characters
% |#$&^_~%|{\tt\char32}|\{}|
% by escaping them with an extra backslash;
% so long as they eventually pass unexpanded to |\qrcode|,
% they will produce the correct QR code.
% A line break may be obtained with |\?|.
% \begin{quote}
%   \begin{tabular}{p{1.5cm}p{2in}}
%     \fbox{\qrcode[height=1cm]{\#\$\&\^\_\~\?\%\ \\\{\}}} 
%     & |\fbox{qrcode[height=1cm]{\#\$\&\^\_\~\?\%\ \\\{\}}}| 
%   \end{tabular}
% \end{quote}
% 
% \section{Limitations and Cautions}
%
% \begin{itemize}
%   \item The QR specification includes modes for encoding numeric, alphanumeric,
%         or Kanji data more efficiently.  This package does not (yet) offer
%         those options.
%   \item The QR specification offers ways to string lengthy data across multiple
%         QR codes.  This package does not implement that possibility.
% \end{itemize}
% 
% \StopEventually{}
% 
% \section{Implementation}
% \subsection{Key handling and options}
%    \begin{macrocode}
%%PACKAGE LOADING
\RequirePackage{xcolor}%
\RequirePackage{xkeyval}%

%%INITIAL CODE
\newif\ifqr@draft@mode
\newif\ifqr@forget@mode

%%DECLARATION OF OPTIONS
\define@boolkey{qr}[qr@]{draft}[true]{\ifqr@draft\qr@draft@modetrue\else\qr@draft@modefalse\fi}%
\define@boolkey{qr}[qr@]{final}[true]{\ifqr@final\qr@draft@modefalse\else\qr@draft@modetrue\fi}%
\define@boolkey{qr}[qr@]{forget}[true]{\ifqr@forget\qr@forget@modetrue\else\qr@forget@modefalse\fi}%
\define@boolkey{qr}[qr@]{hyperlink}[true]{}% %This creates \ifqr@hyperlink.
\define@boolkey{qr}[qr@]{hyperlinks}[true]{\ifqr@hyperlinks\qr@hyperlinktrue\else\qr@hyperlinkfalse\fi}%
\define@boolkey{qr}[qr@]{link}[true]{\ifqr@link\qr@hyperlinktrue\else\qr@hyperlinkfalse\fi}%
\define@boolkey{qr}[qr@]{nolink}[true]{\ifqr@nolink\qr@hyperlinkfalse\else\qr@hyperlinktrue\fi}% %Make nolink an antonym.
\define@boolkey{qr}[qr@]{links}[true]{\ifqr@links\qr@hyperlinktrue\else\qr@hyperlinkfalse\fi}%
\define@boolkey{qr}[qr@]{nolinks}[true]{\ifqr@nolinks\qr@hyperlinkfalse\else\qr@hyperlinktrue\fi}% %Make nolinks an antonym.

%%EXECUTION OF OPTIONS
\qr@draft@modefalse
\qr@forget@modefalse
\qr@hyperlinktrue

\ProcessOptionsX<qr>

%    \end{macrocode}
% \subsection{Utilities}
%    \begin{macrocode}
%COUNTERS
\newcounter{qr@i}%
\newcounter{qr@j}%
\newcount\qr@a
\newcount\qr@b
\newcount\qr@c

%BASICS
\let\xa=\expandafter

%This is for messages.
\newlinechar=`\^^J


%Tests
\def\qr@relax{\relax}%

%Manipulating macros
\def\qr@preface@macro#1#2{%
  % #1 = macro name
  % #2 = text to add to front of macro
  \def\qr@tempb{#2}%
  \xa\xa\xa\def\xa\xa\xa#1\xa\xa\xa{\xa\qr@tempb #1}%
}%

\def\qr@g@preface@macro#1#2{%
  % #1 = macro to be appended to
  % #2 = code to add
  \edef\qr@tempb{#2}%
  \xa\xa\xa\gdef\xa\xa\xa#1\xa\xa\xa{\xa\qr@tempb#1}%
}


\def\qr@getstringlength#1{%
  \bgroup
    \qr@a=0%
    \xdef\qr@thestring{#1}%
    \xa\qr@stringlength@recursive\xa(\qr@thestring\relax\relax)%
    \xdef\qr@stringlength{\the\qr@a}%
  \egroup
}%

\def\qr@stringlength@recursive(#1#2){%
  \def\qr@testi{#1}%
  \ifx\qr@testi\qr@relax
    %we are done.
    \let\qr@next=\relax%
  \else 
    \advance\qr@a by 1%
    \def\qr@next{\qr@stringlength@recursive(#2)}%
  \fi
  \qr@next
}%
%    \end{macrocode}
% \subsubsection{For-loop macro}
% We implement a macro |\qr@for| with the syntax
% \begin{center}
% |\qr@for| \meta{control sequence}=\meta{number} to \meta{number} by \meta{number} \marg{loop body}
% \end{center}
% The \meta{control sequence} becomes the loop variable,
% which is a \TeX\ counter.
% For example, |\qr@for \i=1 to 8 by 2 {\fbox{\number\i}}|
% produces {\makeatletter\qr@for \i=1 to 8 by 2 {\fbox{\number\i}}}.
%    \begin{macrocode}
%The \qr@for@depth counter measures the depth of our loop. 
%The outermost loop has depth zero.
\newcount\qr@for@depth%
\newcount\qr@for@maxdepth%
\qr@for@depth=0%
\qr@for@maxdepth=0%
%These counters are used in the qr@for loop.
\newcount\qr@for@start%
\newcount\qr@for@end%
\newcount\qr@for@step%
%Now a macro to get a new count for every depth as needed.
\def\qr@allocate@new@for@counter{%
  \global\advance\qr@for@maxdepth by 1%
  \newcount\qr@newforcount%
  \xa\global\xa\let\csname qr@for@var@\the\qr@for@maxdepth\endcsname=\qr@newforcount%
}%

\newif\ifqr@loopshouldrun
%The extra # in the following definition makes sure #4 scoops up everything up to the next opening brace.
%This is needed so the step can include more than one character without being enclosed in braces itself.
\def\qr@for #1=#2to#3by#4#{%
  \qr@for@int{#1}{#2}{#3}{#4}%
}%
\long\def\qr@for@int#1#2#3#4#5{%
  \bgroup
    %Because we're working within a TeX group, 
    %any values of \qr@for@start, \qr@for@end, and \qr@for@step from an outer loop
    %will be restored after the \egroup.
    %
    %For the \qr@for@var itself, however, we need a different counter,
    %because the user's text within the loop might need to access the variable from the outer loop.
    \advance\qr@for@depth by 1\relax% This is a local change.
    \ifnum\qr@for@depth>\qr@for@maxdepth%
      %This is the first time we have gone to this depth of nesting!
      %We should only be over by one.
      \qr@allocate@new@for@counter%
    \fi
%    \showthe\qr@for@depth%
    \xa\let\xa\qr@for@var\xa=\csname qr@for@var@\the\qr@for@depth\endcsname%
    %Now \qr@for@var points to the same register as \qr@for@var@3 or something.
    %The next line lets the user-level variable (e.g., \i or \j) point to the same count register.
    \let#1=\qr@for@var%
    %Now establish the looping parameters.
    \edef\qr@for@start@text{#2}%
    \edef\qr@for@end@text{#3}%
    \edef\qr@for@step@text{#4}%
    \def\qr@for@body{\bgroup #5\egroup}%
    \xa\qr@for@start\qr@for@start@text\relax%
    \xa\qr@for@end  \qr@for@end@text\relax%
    \xa\qr@for@step \qr@for@step@text\relax%
    %
    %Next, test whether the loop should run at all.
    % * "\qr@for \i = 1 to 0 by 1" should fail.
    % * "\qr@for \i = 3 to 5 by -1" should fail.
    % * "\qr@for \i = 6 to 2 by 1" should fail.
    % * "\qr@for \i = 4 to 4 by -1" should run.
    % * "\qr@for \i = 4 to 4 by 1" should run.
    % * "\qr@for \i = 5 to 7 by 0" should fail.
    %The loop should fail if (step)=0 or if (step) and (end-start) have opposite signs.
    %The loop will fail if (step=0) or (step)*(end-start)<0.
    % TODO: "\qr@for \i = 5 to 5 by 0" should run (just one iteration).
    \qr@loopshouldruntrue
    \ifnum\qr@for@step=0\relax
      \qr@loopshouldrunfalse
    \fi
    \qr@a=\qr@for@end%
    \advance\qr@a by -\qr@for@start%
    \multiply\qr@a by \qr@for@step%
    \ifnum\qr@a<0\relax
      \qr@loopshouldrunfalse
    \fi
    \ifqr@loopshouldrun
      \qr@for@var=\qr@for@start%
      \ifnum\qr@for@step>0\relax
        \def\qr@for@recursive{%
          \qr@for@body%
          \advance\qr@for@var by \qr@for@step%
          \ifnum\qr@for@var>\qr@for@end%
            \let\qr@for@next=\relax%
          \else%
            \let\qr@for@next=\qr@for@recursive%
          \fi%
          \qr@for@next%
        }%
      \else
        \def\qr@for@recursive{%
          \qr@for@body%
          \advance\qr@for@var by \qr@for@step%
          \ifnum\qr@for@var<\qr@for@end%
            \let\qr@for@next=\relax%
          \else%
            \let\qr@for@next=\qr@for@recursive%
          \fi%
          \qr@for@next%
        }%
      \fi
      \qr@for@recursive%
    \fi
  \egroup
}%
%    \end{macrocode}
% \subsubsection{Base conversions}
%    \begin{macrocode}
\def\qr@padatfront#1#2{%
  % #1 = macro containing text to pad
  % #2 = desired number of characters
  % Pads a number with initial zeros.
  \qr@getstringlength{#1}%
  \qr@a=\qr@stringlength\relax%
  \advance\qr@a by 1\relax%
  \qr@for \i = \qr@a to #2 by 1\relax%
    {\qr@g@preface@macro{#1}{0}}%
}


\qr@a=-1\relax%
\def\qr@savehexsymbols(#1#2){%
  \advance\qr@a by 1\relax%
  \xa\def\csname qr@hexchar@\the\qr@a\endcsname{#1}%
  \xa\edef\csname qr@hextodecimal@#1\endcsname{\the\qr@a}%
  \ifnum\qr@a=15\relax
    %Done.
    \let\qr@next=\relax%
  \else
    \def\qr@next{\qr@savehexsymbols(#2)}%
  \fi%
  \qr@next%
}%
\qr@savehexsymbols(0123456789abcdef\relax\relax)%


\def\qr@decimaltobase#1#2#3{%
  % #1 = macro to store result
  % #2 = decimal representation of a positive integer
  % #3 = new base
  \bgroup
    \edef\qr@newbase{#3}%
    \gdef\qr@base@result{}%
    \qr@a=#2\relax%
    \qr@decimaltobase@recursive%
    \xdef#1{\qr@base@result}%
  \egroup
}
\def\qr@decimaltobase@recursive{%
  \qr@b=\qr@a%
  \divide\qr@b by \qr@newbase\relax
  \multiply\qr@b by -\qr@newbase\relax
  \advance\qr@b by \qr@a\relax%
  \divide\qr@a by \qr@newbase\relax%
  \ifnum\qr@b<10\relax
    \edef\qr@newdigit{\the\qr@b}%
  \else
    \edef\qr@newdigit{\csname qr@hexchar@\the\qr@b\endcsname}%
  \fi
  \edef\qr@argument{{\noexpand\qr@base@result}{\qr@newdigit}}%
  \xa\qr@g@preface@macro\qr@argument%
  \ifnum\qr@a=0\relax
    \relax
  \else
    \xa\qr@decimaltobase@recursive
  \fi
}

\newcommand\qr@decimaltohex[3][0]{%
  % #1 (opt.) = number of hex digits to create
  % #2 = macro to store result
  % #3 = decimal digits to convert
  \qr@decimaltobase{#2}{#3}{16}%
  \qr@padatfront{#2}{#1}%
}


\newcommand\qr@decimaltobinary[3][0]{%
  % #1 (opt.) = number of bits to create
  % #2 = macro to store result
  % #3 = decimal digits to convert
  \qr@decimaltobase{#2}{#3}{2}%
  \qr@padatfront{#2}{#1}%
}

\qr@for \i = 0 to 15 by 1%
  {%
   \qr@decimaltohex[1]{\qr@hexchar}{\the\i}%
   \qr@decimaltobinary[4]{\qr@bits}{\the\i}%
   \xa\xdef\csname qr@b2h@\qr@bits\endcsname{\qr@hexchar}%
   \xa\xdef\csname qr@h2b@\qr@hexchar\endcsname{\qr@bits}%
  }%



\newcommand\qr@binarytohex[3][\relax]{%
  % #1 (optional) = # digits desired
  % #2 = macro to save to
  % #3 = binary string (must be multiple of 4 bits)
  \def\qr@test@i{#1}%
  \ifx\qr@test@i\qr@relax%
    %No argument specified
    \def\qr@desireddigits{0}%
  \else
    \def\qr@desireddigits{#1}%
  \fi
  \gdef\qr@base@result{}%
  \edef\qr@argument{(#3\relax\relax\relax\relax\relax)}%
  \xa\qr@binarytohex@int\qr@argument%
  \qr@padatfront{\qr@base@result}{\qr@desireddigits}%
  \xdef#2{\qr@base@result}%
}
\def\qr@binarytohex@int(#1#2#3#4#5){%
  % #1#2#3#4 = 4 bits
  % #5 = remainder, including \relax\relax\relax\relax\relax terminator
  \def\qr@test@i{#1}%
  \ifx\qr@test@i\qr@relax%
    %Done.
    \def\qr@next{\relax}%
  \else%
    \xdef\qr@base@result{\qr@base@result\csname qr@b2h@#1#2#3#4\endcsname}%
    \def\qr@next{\qr@binarytohex@int(#5)}%
  \fi%
  \qr@next%
}

\newcommand\qr@hextobinary[3][\relax]{%
  % #1 (optional) = # bits desired
  % #2 = macro to save to
  % #3 = hexadecimal string
  \bgroup
  \def\qr@test@i{#1}%
  \ifx\qr@test@i\qr@relax%
    %No argument specified
    \def\qr@desireddigits{0}%
  \else
    \def\qr@desireddigits{#1}%
  \fi
  \gdef\qr@base@result{}%
  \edef\qr@argument{(#3\relax\relax)}%
  \xa\qr@hextobinary@int\qr@argument%
  \qr@padatfront{\qr@base@result}{\qr@desireddigits}%
  \xdef#2{\qr@base@result}%
  \egroup
}
\def\qr@hextobinary@int(#1#2){%
  % #1 = hexadecimal character
  % #2 = remainder, including \relax\relax terminator
  \def\qr@test@@i{#1}%
  \ifx\qr@test@@i\qr@relax%
    %Done.
    \def\qr@next{\relax}%
  \else%
    \xdef\qr@base@result{\qr@base@result\csname qr@h2b@#1\endcsname}%
    \def\qr@next{\qr@hextobinary@int(#2)}%
  \fi%
  \qr@next%
}

\def\qr@hextodecimal#1#2{%
  \edef\qr@argument{#2}%
  \xa\qr@a\xa=\xa\number\xa"\qr@argument\relax%
  \edef#1{\the\qr@a}%
}

\def\qr@hextodecimal#1#2{%
  % #1 = macro to store result
  % #2 = hexadecimal representation of a positive integer
  \bgroup
    \qr@a=0\relax%
    \edef\qr@argument{(#2\relax)}%
    \xa\qr@hextodecimal@recursive\qr@argument%
    \xdef#1{\the\qr@a}%
  \egroup
}
\def\qr@hextodecimal@recursive(#1#2){%
  % #1 = first hex char
  % #2 = remainder
  \advance \qr@a by \csname qr@hextodecimal@#1\endcsname\relax%
  \edef\qr@testii{#2}%
  \ifx\qr@testii\qr@relax%
    %Done.
    \let\qr@next=\relax%
  \else
    %There's at least one more digit.
    \multiply\qr@a by 16\relax
    \edef\qr@next{\noexpand\qr@hextodecimal@recursive(#2)}%
  \fi%
  \qr@next%
}
%    \end{macrocode}
% \subsubsection{Catcode setup}
%    \begin{macrocode}
%The following catcode trickery creates special characters
%with catcode 12 (other) for use in our verbatim handling.
{\catcode`\ =12\relax\gdef\qr@otherspace{ }}%
{\catcode`\%=12\relax\gdef\qr@otherpercent{%}}%
{\catcode`\#=12\relax\gdef\qr@otherpound{#}}%
{\catcode`\|=0\relax|catcode`|\=12|relax|gdef|qr@otherbackslash{\}}%
{\catcode`\^^J=12\relax\gdef\qr@otherlf{^^J}}%
\bgroup
 \catcode`\<=1\relax
 \catcode`\>=2\relax
 \catcode`\{=12\relax\gdef\qr@otherleftbrace<{>%
 \catcode`\}=12\relax\gdef\qr@otherrightbrace<}>%
\egroup%
{\catcode`\&=12\relax\gdef\qr@otherampersand{&}}%
{\catcode`\~=12\relax\gdef\qr@othertilde{~}}%
{\catcode`\^=12\relax\gdef\qr@othercaret{^}}%
{\catcode`\_=12\relax\gdef\qr@otherunderscore{_}}%
{\catcode`\$=12\relax\gdef\qr@otherdollar{$}}%

%Line feeds require some special handling.  \TeX\ reads a line feed in the input 
%as |^^M| (carriage return, character code 13), but it should be encoded in a
%QR code as |^^J| (line feed, character code 10).
%To do this, we make |^^M| an active character and a synonym for a |^^J| with catcode 12.
%Note that the macro |\qr@verbatimlinefeeds| must itself be processed with |^^M| active.
{\catcode`\^^M=13\relax\gdef\qr@verbatimlinefeeds{\let^^M=\qr@otherlf}}
\def\qr@verbatimcatcodes{%
  \catcode`\#=12\relax
  \catcode`\$=12\relax
  \catcode`\&=12\relax
  \catcode`\^=12\relax
  \catcode`\_=12\relax
  \catcode`\~=12\relax
  \catcode`\%=12\relax
  \catcode`\ =12\relax
  \catcode`\^^M=13\relax\qr@verbatimlinefeeds}%

\def\qr@setescapedspecials{%
  \let\ =\qr@otherspace%
  \let\%=\qr@otherpercent%
  \let\#=\qr@otherpound%
  \let\&=\qr@otherampersand%
  \let\^=\qr@othercaret%
  \let\_=\qr@otherunderscore%
  \let\~=\qr@othertilde%
  \let\$=\qr@otherdollar%
  \let\\=\qr@otherbackslash%
  \let\{=\qr@otherleftbrace%
  \let\}=\qr@otherrightbrace%
  \let\?=\qr@otherlf%
}%
%    \end{macrocode}
% \subsection{Plotting}
%    \begin{macrocode}
\def\qr@creatematrix#1{%
  \xa\gdef\csname #1\endcsname##1##2{%
    \csname #1@##1@##2\endcsname
  }%
}%


\def\qr@storetomatrix#1#2#3#4{%
  % #1 = matrix name
  % #2 = row number
  % #3 = column number
  % #4 = value of matrix entry
  \xa\gdef\csname #1@#2@#3\endcsname{#4}%
}%

\def\qr@estoretomatrix#1#2#3#4{%
  % This version performs exactly one expansion on #4.
  % #1 = matrix name
  % #2 = row number
  % #3 = column number
  % #4 = value of matrix
  \xa\xa\xa\gdef\xa\xa\csname #1@#2@#3\endcsname\xa{#4}%
}%

\def\qr@matrixentry#1#2#3{%
  % #1 = matrix name
  % #2 = row number
  % #3 = column number
  \csname #1@#2@#3\endcsname%
}%



\def\qr@createsquareblankmatrix#1#2{%
  \qr@creatematrix{#1}%
  \xa\gdef\csname #1@numrows\endcsname{#2}%
  \xa\gdef\csname #1@numcols\endcsname{#2}%
  \qr@for \i = 1 to #2 by 1%
    {\qr@for \j = 1 to #2 by 1%
      {\qr@storetomatrix{#1}{\the\i}{\the\j}{\qr@blank}}}%
}%

\def\qr@numberofrowsinmatrix#1{%
  \csname #1@numrows\endcsname%
}%

\def\qr@numberofcolsinmatrix#1{%
  \csname #1@numcols\endcsname%
}%

\def\qr@setnumberofrows#1#2{%
  \xa\xdef\csname #1@numrows\endcsname{#2}%
}%

\def\qr@setnumberofcols#1#2{%
  \xa\xdef\csname #1@numcols\endcsname{#2}%
}%

\newlength\qr@desiredheight
\setlength\qr@desiredheight{2cm}%
\newlength\qr@modulesize
\newlength\qr@minipagewidth

\def\qr@printmatrix#1{%
  \def\qr@black{\rule{\qr@modulesize}{\qr@modulesize}}%
  \def\qr@white{\rule{\qr@modulesize}{0pt}}%
  \def\qr@black@fixed{\rule{\qr@modulesize}{\qr@modulesize}}%
  \def\qr@white@fixed{\rule{\qr@modulesize}{0pt}}%
  \def\qr@black@format{\rule{\qr@modulesize}{\qr@modulesize}}%
  \def\qr@white@format{\rule{\qr@modulesize}{0pt}}%
  %Set module size
  \setlength{\qr@modulesize}{\qr@desiredheight}%
  \divide\qr@modulesize by \qr@size\relax%
  %
  \setlength{\qr@minipagewidth}{\qr@modulesize}%
  \multiply\qr@minipagewidth by \qr@size\relax%
  \ifqr@tight
  \else
    \advance\qr@minipagewidth by 8\qr@modulesize%
  \fi
  \begin{minipage}{\qr@minipagewidth}%
    \baselineskip=\qr@modulesize%
    \ifqr@tight\else\rule{0pt}{4\qr@modulesize}\par\fi% %Blank space at top.
    \qr@for \i = 1 to \qr@numberofrowsinmatrix{#1} by 1%
      {\ifqr@tight\else\rule{4\qr@modulesize}{0pt}\fi% %Blank space at left.
       \qr@for \j = 1 to \qr@numberofcolsinmatrix{#1} by 1%
         {\qr@matrixentry{#1}{\the\i}{\the\j}}%
       \par}%
    \ifqr@tight\else\rule{0pt}{4\qr@modulesize}\par\fi%
  \end{minipage}%
}%

\def\qr@printsavedbinarymatrix#1{%
  \edef\qr@binarystring{#1\relax\relax}%
  %Set module size
  \setlength{\qr@modulesize}{\qr@desiredheight}%
  \divide\qr@modulesize by \qr@size\relax%
  %
  \setlength{\qr@minipagewidth}{\qr@modulesize}%
  \multiply\qr@minipagewidth by \qr@size\relax%
  \ifqr@tight
  \else
    \advance\qr@minipagewidth by 8\qr@modulesize%
  \fi
  \begin{minipage}{\qr@minipagewidth}%
    \baselineskip=\qr@modulesize%
    \ifqr@tight\else\rule{0pt}{4\qr@modulesize}\par\fi% %Blank space at top.
    \qr@for \i = 1 to \qr@size by 1%
      {\ifqr@tight\else\rule{4\qr@modulesize}{0pt}\fi% %Blank space at left.
       \qr@for \j = 1 to \qr@size by 1%
         {\edef\qr@theargument{(\qr@binarystring)}%
          \xa\qr@printsavedbinarymatrix@int\qr@theargument
         }%
       \par}%
    \ifqr@tight\else\rule{0pt}{4\qr@modulesize}\par\fi%
  \end{minipage}%
}%

\def\qr@printsavedbinarymatrix@int(#1#2){%
  % #1 = first bit, either 1 or 0.
  % #2 = remainder of string, terminating with \relax\relax
  % There's no need to check for EOF here, because
  % we'll only call this n^2 times.
  \ifcase #1\relax
    \rule{\qr@modulesize}{0pt}% % 0: white square
  \or
    \rule{\qr@modulesize}{\qr@modulesize}% % 1: black square
  \fi
  \xdef\qr@binarystring{#2}%
}%

\def\qr@createliteralmatrix#1#2#3{%
  % #1 = matrix name
  % #2 = m, the number of rows and columns in the square matrix
  % #3 = a string of m^2 tokens to be written into the matrix
  \qr@creatematrix{#1}%
  \xa\xdef\csname #1@numrows\endcsname{#2}%
  \xa\xdef\csname #1@numcols\endcsname{#2}%
  \gdef\qr@literalmatrix@tokens{#3}%
  \qr@for \i = 1 to #2 by 1%
    {\qr@for \j = 1 to #2 by 1%
      {\xa\qr@createliteralmatrix@int\xa(\qr@literalmatrix@tokens)%
       \qr@estoretomatrix{#1}{\the\i}{\the\j}{\qr@entrytext}%
      }%
    }%
}
\def\qr@createliteralmatrix@int(#1#2){%
  \def\qr@entrytext{#1}%
  \gdef\qr@literalmatrix@tokens{#2}%
}


\qr@createliteralmatrix{finderpattern}{8}{%
  \qr@black@fixed\qr@black@fixed\qr@black@fixed\qr@black@fixed\qr@black@fixed\qr@black@fixed\qr@black@fixed\qr@white@fixed%
  \qr@black@fixed\qr@white@fixed\qr@white@fixed\qr@white@fixed\qr@white@fixed\qr@white@fixed\qr@black@fixed\qr@white@fixed%
  \qr@black@fixed\qr@white@fixed\qr@black@fixed\qr@black@fixed\qr@black@fixed\qr@white@fixed\qr@black@fixed\qr@white@fixed%
  \qr@black@fixed\qr@white@fixed\qr@black@fixed\qr@black@fixed\qr@black@fixed\qr@white@fixed\qr@black@fixed\qr@white@fixed%
  \qr@black@fixed\qr@white@fixed\qr@black@fixed\qr@black@fixed\qr@black@fixed\qr@white@fixed\qr@black@fixed\qr@white@fixed%
  \qr@black@fixed\qr@white@fixed\qr@white@fixed\qr@white@fixed\qr@white@fixed\qr@white@fixed\qr@black@fixed\qr@white@fixed%
  \qr@black@fixed\qr@black@fixed\qr@black@fixed\qr@black@fixed\qr@black@fixed\qr@black@fixed\qr@black@fixed\qr@white@fixed%
  \qr@white@fixed\qr@white@fixed\qr@white@fixed\qr@white@fixed\qr@white@fixed\qr@white@fixed\qr@white@fixed\qr@white@fixed%
}%

\qr@createliteralmatrix{alignmentpattern}{5}{%
  \qr@black@fixed\qr@black@fixed\qr@black@fixed\qr@black@fixed\qr@black@fixed%
  \qr@black@fixed\qr@white@fixed\qr@white@fixed\qr@white@fixed\qr@black@fixed%
  \qr@black@fixed\qr@white@fixed\qr@black@fixed\qr@white@fixed\qr@black@fixed%
  \qr@black@fixed\qr@white@fixed\qr@white@fixed\qr@white@fixed\qr@black@fixed%
  \qr@black@fixed\qr@black@fixed\qr@black@fixed\qr@black@fixed\qr@black@fixed%
}%




\def\qr@copymatrixentry#1#2#3#4#5#6{%
  % Copy the (#2,#3) entry of matrix #1
  % to the (#5,#6) position of matrix #4.
  \xa\xa\xa\global%
  \xa\xa\xa\let\xa\xa\csname #4@#5@#6\endcsname%
                     \csname #1@#2@#3\endcsname% 
}%

\def\qr@createduplicatematrix#1#2{%
  % #1 = name of copy
  % #2 = original matrix to be copied
  \qr@creatematrix{#1}%
  \qr@for \i = 1 to \qr@numberofrowsinmatrix{#2} by 1%
    {\qr@for \j = 1 to \qr@numberofcolsinmatrix{#2} by 1%
      {\qr@copymatrixentry{#2}{\the\i}{\the\j}{#1}{\the\i}{\the\j}%
      }%
    }%
  \qr@setnumberofrows{#1}{\qr@numberofrowsinmatrix{#2}}%
  \qr@setnumberofcols{#1}{\qr@numberofcolsinmatrix{#2}}%
}%

\def\qr@placefinderpattern@int#1#2#3#4#5{%
  % Work on matrix #1.
  % Start in position (#2, #3) -- should be a corner
  % #4 indicates horizontal direction (1=right, -1=left)
  % #5 indicates vertical direction (1=down, -1=up)
  %
  % In this code, \sourcei and \sourcej are TeX counts working through the finderpattern matrix,
  % and i and j are LaTeX counters indicating positions in the big matrix.
  \setcounter{qr@i}{#2}%
  \qr@for \sourcei=1 to 8 by 1%
    {\setcounter{qr@j}{#3}%
     \qr@for \sourcej=1 to 8 by 1%
       {\qr@copymatrixentry{finderpattern}{\the\sourcei}{\the\sourcej}%
                        {#1}{\theqr@i}{\theqr@j}%
        \addtocounter{qr@j}{#5}%
       }%
     \addtocounter{qr@i}{#4}%
    }%
}%

\def\qr@placefinderpatterns#1{%
  % #1=matrix name
  \qr@placefinderpattern@int{#1}{1}{1}{1}{1}%
  \qr@placefinderpattern@int{#1}{\qr@numberofrowsinmatrix{#1}}{1}{-1}{1}%
  \qr@placefinderpattern@int{#1}{1}{\qr@numberofcolsinmatrix{#1}}{1}{-1}%
}%

\def\qr@placetimingpatterns#1{%
  %Set \qr@endingcol to n-8.
  \qr@a=\qr@size\relax%
  \advance\qr@a by -8\relax%
  \edef\qr@endingcol{\the\qr@a}%
  \qr@for \j = 9 to \qr@endingcol by 1%
    {\ifodd\j\relax%
       \qr@storetomatrix{#1}{7}{\the\j}{\qr@black@fixed}%
       \qr@storetomatrix{#1}{\the\j}{7}{\qr@black@fixed}%
     \else%
       \qr@storetomatrix{#1}{7}{\the\j}{\qr@white@fixed}%
       \qr@storetomatrix{#1}{\the\j}{7}{\qr@white@fixed}%
     \fi%
    }%
}%

\def\qr@placealignmentpattern@int#1#2#3{%
  % Work on matrix #1.
  % Write an alignment pattern into the matrix, centered on (#2,#3).
  \qr@a=#2\relax%
  \advance\qr@a by -2\relax%
  \qr@b=#3\relax%
  \advance\qr@b by -2\relax%
  \setcounter{qr@i}{\the\qr@a}%
  \qr@for \i=1 to 5 by 1%
    {\setcounter{qr@j}{\the\qr@b}%
     \qr@for \j=1 to 5 by 1%
      {\qr@copymatrixentry{alignmentpattern}{\the\i}{\the\j}%
                       {#1}{\theqr@i}{\theqr@j}%
       \stepcounter{qr@j}%
      }%
     \stepcounter{qr@i}%
    }% 
}%

\newif\ifqr@incorner%
\def\qr@placealignmentpatterns#1{%
  %There are k^2-3 alignment patterns,
  %arranged in a (k x k) grid within the matrix.
  %They begin in row 7, column 7,
  %except that the ones in the NW, NE, and SW corners
  %are omitted because of the finder patterns.
  %Recall that 
  %  * \qr@k stores k,
  %  * \qr@alignment@firstskip stores how far between the 1st and 2nd row/col, &
  %  * \qr@alignment@generalskip stores how far between each subsequent row/col.
  \xa\ifnum\qr@k>0\relax
    %There will be at least one alignment pattern.
    %N.B. k cannot equal 1.
    \xa\ifnum\qr@k=2\relax
      % 2*2-3 = exactly 1 alignment pattern.
      \qr@a=7\relax
      \advance\qr@a by \qr@alignment@firstskip\relax
      \xdef\qr@target@ii{\the\qr@a}%
      \qr@placealignmentpattern@int{#1}{\qr@target@ii}{\qr@target@ii}%
    \else
      % k is at least 3, so the following loops should be safe.
      \xdef\qr@target@ii{7}%
      \qr@for \ii = 1 to \qr@k by 1%
        {\ifcase\ii\relax%
           \relax% \ii should never equal 0.
         \or
           \xdef\qr@target@ii{7}% If \ii = 1, we start in row 7.
         \or
           %If \ii = 2, we add the firstskip.
           \qr@a=\qr@target@ii\relax%
           \advance\qr@a by \qr@alignment@firstskip\relax%
           \xdef\qr@target@ii{\the\qr@a}%
         \else
           %If \ii>2, we add the generalskip.
           \qr@a=\qr@target@ii\relax%
           \advance\qr@a by \qr@alignment@generalskip\relax%
           \xdef\qr@target@ii{\the\qr@a}%
         \fi
         \qr@for \jj = 1 to \qr@k by 1%
           {\ifcase\jj\relax%
              \relax% \jj should never equal 0.
            \or
              \xdef\qr@target@jj{7}% If \jj=1, we start in row 7.
            \or
              %If \jj=2, we add the firstskip.
              \qr@a=\qr@target@jj\relax%
              \advance\qr@a by \qr@alignment@firstskip%
              \xdef\qr@target@jj{\the\qr@a}%
            \else
              %If \jj>2, we add the generalskip.
              \qr@a=\qr@target@jj\relax%
              \advance\qr@a by \qr@alignment@generalskip%
              \xdef\qr@target@jj{\the\qr@a}%
            \fi
            \qr@incornerfalse%
            \ifnum\ii=1\relax
              \ifnum\jj=1\relax
                \qr@incornertrue
              \else
                \ifnum\qr@k=\jj\relax
                  \qr@incornertrue
                \fi
              \fi
            \else
              \xa\ifnum\qr@k=\ii\relax
                \ifnum\jj=1\relax
                  \qr@incornertrue
                \fi
              \fi
            \fi
            \ifqr@incorner
              \relax
            \else
              \qr@placealignmentpattern@int{#1}{\qr@target@ii}{\qr@target@jj}%
            \fi
           }% ends \qr@for \jj
        }% ends \qr@for \ii
    \fi
  \fi
}%

\def\qr@placedummyformatpatterns#1{%
  \qr@for \j = 1 to 9 by 1%
    {\ifnum\j=7\relax%
     \else%
       \qr@storetomatrix{#1}{9}{\the\j}{\qr@format@square}%
       \qr@storetomatrix{#1}{\the\j}{9}{\qr@format@square}%
     \fi%
    }%
  \setcounter{qr@j}{\qr@size}%
  \qr@for \j = 1 to 8 by 1%
    {\qr@storetomatrix{#1}{9}{\theqr@j}{\qr@format@square}%
     \qr@storetomatrix{#1}{\theqr@j}{9}{\qr@format@square}%
     \addtocounter{qr@j}{-1}%
    }%
  %Now go back and change the \qr@format@square in (n-8,9) to \qr@black@fixed.
  \addtocounter{qr@j}{1}%
  \qr@storetomatrix{#1}{\theqr@j}{9}{\qr@black@fixed}%
}%

\def\qr@placedummyversionpatterns#1{%
  \xa\ifnum\qr@version>6\relax
    %Must include version information.
    \global\c@qr@i=\qr@size%
    \global\advance\c@qr@i by -10\relax%
    \qr@for \i = 1 to 3 by 1%
      {\qr@for \j = 1 to 6 by 1%
        {\qr@storetomatrix{#1}{\theqr@i}{\the\j}{\qr@format@square}%
         \qr@storetomatrix{#1}{\the\j}{\theqr@i}{\qr@format@square}%
        }%
       \stepcounter{qr@i}%
      }%
  \fi
}%

\def\qr@writebit(#1#2)#3{%
  % #3 = matrix name
  % (qr@i,qr@j) = position to write in (LaTeX counters)
  % #1 = bit to be written
  % #2 = remaining bits plus '\relax' as an end-of-file marker
  \edef\qr@datatowrite{#2}%
  \ifnum#1=1
    \qr@storetomatrix{#3}{\theqr@i}{\theqr@j}{\qr@black}%
  \else
    \qr@storetomatrix{#3}{\theqr@i}{\theqr@j}{\qr@white}%
  \fi
}%

\newif\ifqr@rightcol
\newif\ifqr@goingup

\def\qr@writedata@hex#1#2{%
  % #1 = name of a matrix that has been prepared with finder patterns, timing patterns, etc.
  % #2 = a string consisting of bytes to write into the matrix, in two-char hex format.
  \setcounter{qr@i}{\qr@numberofrowsinmatrix{#1}}%
  \setcounter{qr@j}{\qr@numberofcolsinmatrix{#1}}%
  \qr@rightcoltrue%
  \qr@goinguptrue%
  \edef\qr@argument{{#1}(#2\relax\relax\relax)}%
  \xa\qr@writedata@hex@recursive\qr@argument%
}%

\def\qr@writedata@hex@recursive#1(#2#3#4){%
  % #1 = name of a matrix that has been prepared with finder patterns, timing patterns, etc.
  % (qr@i,qr@j) = position to write in LaTeX counters
  % #2#3#4 contains the hex codes of the bytes to be written, plus \relax\relax\relax
  % as an end-of-file marker
  \edef\qr@testii{#2}%
  \ifx\qr@testii\qr@relax%
    % #2 is \relax, so there is nothing more to write.
    \relax
    \let\qr@next=\relax
  \else
    % #2 is not \relax, so there is another byte to write.
    \qr@hextobinary[8]{\bytetowrite}{#2#3}%
    \xdef\qr@datatowrite{\bytetowrite\relax}% %Add terminating "\relax"
    \qr@writedata@recursive{#1}% %This function actually writes the 8 bits.
    \edef\qr@argument{{#1}(#4)}%
    \xa\def\xa\qr@next\xa{\xa\qr@writedata@hex@recursive\qr@argument}% %Call self to write the next bit.
  \fi
  \qr@next
}%

\def\qr@writedata#1#2{%
  % #1 = name of a matrix that has been prepared with finder patterns, timing patterns, etc.
  % #2 = a string consisting of 0's and 1's to write into the matrix.
  \setcounter{qr@i}{\qr@numberofrowsinmatrix{#1}}%
  \setcounter{qr@j}{\qr@numberofcolsinmatrix{#1}}%
  \qr@rightcoltrue
  \qr@goinguptrue
  \edef\qr@datatowrite{#2\relax}%
  \qr@writedata@recursive{#1}%
}%

\def\qr@@blank{\qr@blank}%

\def\qr@writedata@recursive#1{%
  % #1 = matrix name
  % (qr@i,qr@j) = position to write in (LaTeX counters)
  % \qr@datatowrite contains the bits to be written, plus '\relax' as an end-of-file marker
  \xa\let\xa\squarevalue\csname #1@\theqr@i @\theqr@j\endcsname%
  \ifx\squarevalue\qr@@blank
    %Square is blank, so write data in it.
    \xa\qr@writebit\xa(\qr@datatowrite){#1}%
    %The \qr@writebit macro not only writes the first bit of \qr@datatowrite into the matrix,
    %but also removes the bit from the 'bitstream' of \qr@datatowrite.
  \fi
  %Now adjust our position in the matrix.
  \ifqr@rightcol
    %From the right-hand half of the two-bit column, we always move left.  Easy peasy.
    \addtocounter{qr@j}{-1}%
    \qr@rightcolfalse
  \else
    %If we're in the left-hand column, things are harder.
    \ifqr@goingup
      %First, suppose we're going upwards.
      \ifnum\c@qr@i>1\relax%
        %If we're not in the first row, things are easy.
        %We move one to the right and one up.
        \addtocounter{qr@j}{1}%
        \addtocounter{qr@i}{-1}%
        \qr@rightcoltrue
      \else
        %If we are in the first row, then we move to the left,
        %and we are now in the right-hand column on a downward pass.
        \addtocounter{qr@j}{-1}%
        \qr@goingupfalse
        \qr@rightcoltrue
      \fi
    \else
      %Now, suppose we're going downwards.
      \xa\ifnum\qr@size>\c@qr@i\relax%
        %If we're not yet in the bottom row, things are easy.
        %We move one to the right and one down.
        \addtocounter{qr@j}{1}%
        \addtocounter{qr@i}{1}%
        \qr@rightcoltrue
      \else
        %If we are in the bottom row, then we move to the left,
        %and we are now in the right-hand column on an upward pass.
        \addtocounter{qr@j}{-1}%
        \qr@rightcoltrue
        \qr@goinguptrue
      \fi
    \fi
    %One problem: what if we just moved into the 7th column?
    %Das ist verboten.
    %If we just moved (left) into the 7th column, we should move on into the 6th column.
    \ifnum\c@qr@j=7\relax%
      \setcounter{qr@j}{6}%
    \fi
  \fi
  %Now check whether there are any more bits to write.
  \ifx\qr@datatowrite\qr@relax
    % \qr@datatowrite is just `\relax', so we're done.
    \let\qr@next=\relax
    \relax
  \else
    % Write some more!
    \def\qr@next{\qr@writedata@recursive{#1}}%
  \fi
  \qr@next
}%

\def\qr@writeremainderbits#1{%
  % #1 = name of a matrix that has been prepared and partly filled.
  % (qr@i,qr@j) = position to write in LaTeX counters
  \xa\ifnum\qr@numremainderbits>0\relax
    \def\qr@datatowrite{}%
    \qr@for \i = 1 to \qr@numremainderbits by 1%
      {\g@addto@macro{\qr@datatowrite}{0}}%
    \g@addto@macro{\qr@datatowrite}{\relax}% terminator
    \qr@writedata@recursive{#1}%
  \fi
}%

\newif\ifqr@cellinmask

\def\qr@setmaskingfunction#1{%
  % #1 = 1 decimal digit for the mask. (I see no reason to use the 3-bit binary code.) 
  % The current position is (\themaski,\themaskj), with indexing starting at 0.
  \edef\qr@maskselection{#1}%
  \xa\ifcase\qr@maskselection\relax
    %Case 0: checkerboard
    \def\qr@parsemaskingfunction{%
      % Compute mod(\themaski+\themaskj,2)%
      \qr@a=\c@maski%
      \advance\qr@a by \c@maskj%
      \qr@b=\qr@a%
      \divide\qr@b by 2%
      \multiply\qr@b by 2%
      \advance\qr@a by -\qr@b%
      \edef\qr@maskfunctionresult{\the\qr@a}%
    }%
  \or
    %Case 1: horizontal stripes
    \def\qr@parsemaskingfunction{%
      % Compute mod(\themaski,2)%
      \ifodd\c@maski\relax%
        \def\qr@maskfunctionresult{1}%
      \else%
        \def\qr@maskfunctionresult{0}%
      \fi%
    }%
  \or
    %Case 2: vertical stripes
    \def\qr@parsemaskingfunction{%
      % Compute mod(\themaskj,3)%
      \qr@a=\c@maskj%
      \divide\qr@a by 3%
      \multiply\qr@a by 3%
      \advance\qr@a by -\c@maskj%
      \edef\qr@maskfunctionresult{\the\qr@a}%
    }%
  \or
    %Case 3: diagonal stripes
    \def\qr@parsemaskingfunction{%
      % Compute mod(\themaski+\themaskj,3)%
      \qr@a=\c@maski%
      \advance\qr@a by \c@maskj%
      \qr@b=\qr@a%
      \divide\qr@b by 3%
      \multiply\qr@b by 3%
      \advance\qr@b by -\qr@a%
      \edef\qr@maskfunctionresult{\the\qr@b}%
    }%
  \or
    %Case 4: wide checkerboard
    \def\qr@parsemaskingfunction{%
      % Compute mod(floor(\themaski/2) + floor(\themaskj/3),2) %
      \qr@a=\c@maski%
      \divide\qr@a by 2%
      \qr@b=\c@maskj%
      \divide\qr@b by 3%
      \advance\qr@a by \qr@b%
      \qr@b=\qr@a%
      \divide\qr@a by 2%
      \multiply\qr@a by 2%
      \advance\qr@a by -\qr@b%
      \edef\qr@maskfunctionresult{\the\qr@a}%
    }%
  \or
    %Case 5: quilt
    \def\qr@parsemaskingfunction{%
      % Compute mod(\themaski*\themaskj,2) + mod(\themaski*\themaskj,3) %
      \qr@a=\c@maski%
      \multiply\qr@a by \c@maskj%
      \qr@b=\qr@a%
      \qr@c=\qr@a%
      \divide\qr@a by 2%
      \multiply\qr@a by 2%
      \advance\qr@a by -\qr@c% (result will be -mod(i*j,2), which is negative.)
      \divide\qr@b by 3%
      \multiply\qr@b by 3%
      \advance\qr@b by -\qr@c% (result will be -mod(i*j,3), which is negative.)
      \advance\qr@a by \qr@b% (result is negative of what's in the spec.)
      \edef\qr@maskfunctionresult{\the\qr@a}%
    }%
  \or
    %Case 6: arrows
    \def\qr@parsemaskingfunction{%
      % Compute mod( mod(\themaski*\themaskj,2) + mod(\themaski*\themaskj,3) , 2 ) %
      \qr@a=\c@maski%
      \multiply\qr@a by \c@maskj%
      \qr@b=\qr@a%
      \qr@c=\qr@a%
      \multiply\qr@c by 2% % \qr@c equals 2*i*j.
      \divide\qr@a by 2%
      \multiply\qr@a by 2%
      \advance\qr@c by -\qr@a% Now \qr@c equals i*j + mod(i*j,2).
      \divide\qr@b by 3%
      \multiply\qr@b by 3%
      \advance\qr@c by -\qr@b% (Now \qr@c equals mod(i*j,2) + mod(i*j,3).
      \qr@a=\qr@c%
      \divide\qr@a by 2%
      \multiply\qr@a by 2%
      \advance\qr@c by-\qr@a%
      \edef\qr@maskfunctionresult{\the\qr@c}%
    }%
  \or
    %Case 7: shotgun
    \def\qr@parsemaskingfunction{%
      % Compute mod( mod(\themaski+\themaskj,2) + mod(\themaski*\themaskj,3) , 2 ) %
      \qr@a=\c@maski%
      \advance\qr@a by \c@maskj% %So \qr@a = i+j
      \qr@b=\c@maski%
      \multiply\qr@b by \c@maskj% %So \qr@b = i*j
      \qr@c=\qr@a%
      \advance\qr@c by \qr@b% So \qr@c = i+j+i*j
      \divide\qr@a by 2%
      \multiply\qr@a by 2%
      \advance\qr@c by -\qr@a% So \qr@c = mod(i+j,2) + i*j
      \divide\qr@b by 3%
      \multiply\qr@b by 3%
      \advance\qr@c by -\qr@b% So \qr@c = mod(i+j,2) + mod(i*j,3)
      \qr@a=\qr@c%
      \divide\qr@c by 2%
      \multiply\qr@c by 2%
      \advance\qr@a by -\qr@c%
      \edef\qr@maskfunctionresult{\the\qr@a}%
    }%
  \fi
}%


\def\qr@checkifcellisinmask{%
  % The current position is (\i,\j), in TeX counts,
  % but the LaTeX counters (maski,maskj) should contain
  % the current position with indexing starting at 0.
  % That is, maski = \i-1 and maskj = \j-1.
  % 
  % \qr@parsemaskingfunction must have been set by a call to \qr@setmaskingfunction
  \qr@parsemaskingfunction
  \xa\ifnum\qr@maskfunctionresult=0\relax
    \qr@cellinmasktrue
  \else
    \qr@cellinmaskfalse
  \fi
}%

\newcounter{maski}%
\newcounter{maskj}%

\def\qr@applymask#1#2#3{%
  % #1 = name of a matrix that should be filled out completely
  %      except for the format and/or version information.
  % #2 = name of a new matrix to contain the masked version
  % #3 = 1 decimal digit naming the mask
  \qr@createduplicatematrix{#2}{#1}%
  \qr@setmaskingfunction{#3}%
  \setcounter{maski}{-1}%
  \qr@for \i = 1 to \qr@size by 1%
    {\stepcounter{maski}%
     \setcounter{maskj}{-1}%
     \qr@for \j = 1 to \qr@size by 1%
     {\stepcounter{maskj}%
      \qr@checkifcellisinmask
      \ifqr@cellinmask
        \qr@checkifcurrentcellcontainsdata{#2}%
        \ifqr@currentcellcontainsdata
          \qr@flipcurrentcell{#2}%
        \fi
      \fi
      }%
    }%
}%

\newif\ifqr@currentcellcontainsdata
\qr@currentcellcontainsdatafalse

\def\qr@@white{\qr@white}%
\def\qr@@black{\qr@black}%

\def\qr@checkifcurrentcellcontainsdata#1{%
  % #1 = name of matrix
  \qr@currentcellcontainsdatafalse
  \xa\ifx\csname #1@\the\i @\the\j\endcsname\qr@@white
    \qr@currentcellcontainsdatatrue
  \fi
  \xa\ifx\csname #1@\the\i @\the\j\endcsname\qr@@black
    \qr@currentcellcontainsdatatrue
  \fi
}%

\def\qr@flipped@black{\qr@black}%
\def\qr@flipped@white{\qr@white}%

\def\qr@flipcurrentcell#1{%
  % #1 = name of matrix
  % (\i, \j) = current position, in TeX counts.
  % This assumes the cell contains data, either black or white!
  \xa\ifx\csname #1@\the\i @\the\j\endcsname\qr@@white
    \qr@storetomatrix{#1}{\the\i}{\the\j}{\qr@flipped@black}%
  \else
    \qr@storetomatrix{#1}{\the\i}{\the\j}{\qr@flipped@white}%
  \fi
}%

\def\qr@chooseandapplybestmask#1{%
  % #1 = name of a matrix that should be filled out completely
  %      except for the format and/or version information.
  % This function applies all eight masks in succession,
  % calculates their penalties, and remembers the best.
  % The number indicating which mask was used is saved in \qr@mask@selected.
  \qr@createduplicatematrix{originalmatrix}{#1}%
  \message{<Applying Mask 0...}%
  \qr@applymask{originalmatrix}{#1}{0}%
  \message{done. Calculating penalty...}%
  \qr@evaluatemaskpenalty{#1}%
  \xdef\qr@currentbestpenalty{\qr@penalty}%
  \message{penalty is \qr@penalty>^^J}%
  \gdef\qr@currentbestmask{0}%
  \qr@for \i = 1 to 7 by 1%
    {\message{<Applying Mask \the\i...}%
     \qr@applymask{originalmatrix}{currentmasked}{\the\i}%
     \message{done. Calculating penalty...}%
     \qr@evaluatemaskpenalty{currentmasked}%
     \message{penalty is \qr@penalty>^^J}%
     \xa\xa\xa\ifnum\xa\qr@penalty\xa<\qr@currentbestpenalty\relax
       %We found a better mask.
       \xdef\qr@currentbestmask{\the\i}%
       \qr@createduplicatematrix{#1}{currentmasked}%
       \xdef\qr@currentbestpenalty{\qr@penalty}%
     \fi
    }%
  \xdef\qr@mask@selected{\qr@currentbestmask}%
  \message{<Selected Mask \qr@mask@selected>^^J}%
}%


\def\qr@Ni{3}%
\def\qr@Nii{3}%
\def\qr@Niii{40}%
\def\qr@Niv{10}%
\def\qr@fiveones{11111}%
\def\qr@fivezeros{11111}%
\def\qr@twoones{11}%
\def\qr@twozeros{00}%
\def\qr@finderA{00001011101}%
\def\qr@finderB{10111010000}%
\def\qr@finderB@three{1011101000}%
\def\qr@finderB@two{101110100}%
\def\qr@finderB@one{10111010}%
\def\qr@finderB@zero{1011101}%
\newif\ifqr@stringoffive
\def\qr@addpenaltyiii{%
  \addtocounter{penaltyiii}{\qr@Niii}%
}%
\newcounter{totalones}%
\newcounter{penaltyi}%
\newcounter{penaltyii}%
\newcounter{penaltyiii}%
\newcounter{penaltyiv}%
\def\qr@evaluatemaskpenalty#1{%
  % #1 = name of a matrix that we will test for the penalty
  % according to the specs.
  \setcounter{penaltyi}{0}%
  \setcounter{penaltyii}{0}%
  \setcounter{penaltyiii}{0}%
  \setcounter{penaltyiv}{0}%
  \bgroup%localize the meanings we give to the symbols
    \def\qr@black{1}\def\qr@white{0}%
    \def\qr@black@fixed{1}\def\qr@white@fixed{0}%
    \def\qr@format@square{0}% This is not stated in the specs, but seems
                            % to be the standard implementation.
    \def\qr@blank{0}% These would be any bits at the end.
    %
    \setcounter{totalones}{0}%
    \qr@for \i=1 to \qr@size by 1%
      {\def\qr@lastfive{z}% %The z is a dummy, that will be removed before any testing.
       \qr@stringoffivefalse
       \def\qr@lasttwo@thisrow{z}% %The z is a dummy.
       \def\qr@lasttwo@nextrow{z}% %The z is a dummy.
       \def\qr@lastnine{z0000}% %The 0000 stands for the white space to the left. The z is a dummy.
       \def\qr@ignore@finderB@at{0}%
       \qr@for \j=1 to \qr@size by 1%
         {\edef\qr@newbit{\qr@matrixentry{#1}{\the\i}{\the\j}}%
          %
          % LASTFIVE CODE FOR PENALTY 1
          % First, add the new bit to the end.
          \xa\g@addto@macro\xa\qr@lastfive\xa{\qr@newbit}%
          \ifnum\j<5\relax% 
            %Not yet on the 5th entry.
            %Don't do any testing.
          \else
            % 5th entry or later.
            % Remove the old one, and then test.
            \qr@removefirsttoken\qr@lastfive%
            \ifx\qr@lastfive\qr@fiveones%
              \ifqr@stringoffive%
                %This is a continuation of a previous block of five or more 1's.
                \stepcounter{penaltyi}%
              \else
                %This is a new string of five 1's.
                \addtocounter{penaltyi}{\qr@Ni}%
                \global\qr@stringoffivetrue
              \fi
            \else
              \ifx\qr@lastfive\qr@fivezeros%
                \ifqr@stringoffive
                  %This is a continuation of a previous block of five or more 0's.
                  \stepcounter{penaltyi}%
                \else
                  %This is a new string of five 0's.
                  \addtocounter{penaltyi}{\qr@Ni}%
                  \global\qr@stringoffivetrue
                \fi
              \else
                %This is not a string of five 1's or five 0's.
                \global\qr@stringoffivefalse
              \fi
            \fi
          \fi
          %
          % 2x2 BLOCKS FOR PENALTY 2
          % Every 2x2 block of all 1's counts for \qr@Nii penalty points.
          % We do not need to run this test in the last row.
          \xa\ifnum\xa\i\xa<\qr@size\relax
            \xa\g@addto@macro\xa\qr@lasttwo@thisrow\xa{\qr@newbit}%
            %Compute \qr@iplusone
            \qr@a=\i\relax%
            \advance\qr@a by 1%
            \edef\qr@iplusone{\the\qr@a}%
            %
            \edef\qr@nextrowbit{\qr@matrixentry{#1}{\qr@iplusone}{\the\j}}%
            \xa\g@addto@macro\xa\qr@lasttwo@nextrow\xa{\qr@nextrowbit}%
            \ifnum\j<2\relax%
              %Still in the first column; no check.
            \else
              %Second column or later.  Remove the old bits, and then test.
              \qr@removefirsttoken\qr@lasttwo@thisrow
              \qr@removefirsttoken\qr@lasttwo@nextrow
              \ifx\qr@lasttwo@thisrow\qr@twoones
                \ifx\qr@lasttwo@nextrow\qr@twoones
                  \addtocounter{penaltyii}{\qr@Nii}%
                \fi
              \else
                \ifx\qr@lasttwo@thisrow\qr@twozeros
                  \ifx\qr@lasttwo@nextrow\qr@twozeros
                    \addtocounter{penaltyii}{\qr@Nii}%
                  \fi
                \fi
              \fi
            \fi
          \fi
          %
          % LASTNINE CODE FOR PENALTY 3
          % First, add the new bit to the end.
          \xa\g@addto@macro\xa\qr@lastnine\xa{\qr@newbit}%
          \ifnum\j<7\relax% 
            %Not yet on the 7th entry.
            %Don't do any testing.
          \else
            % 7th entry or later.
            % Remove the old one, and then test.
            \qr@removefirsttoken\qr@lastnine
            \xa\ifnum\qr@size=\j\relax%
              % Last column.  Any of the following should count:
              %     1011101 (\qr@finderB@zero)
              %    10111010 (\qr@finderB@one)
              %   101110100 (\qr@finderB@two)
              %  1011101000 (\qr@finderB@three)
              % 10111010000 (\qr@finderB)
              \ifx\qr@lastnine\qr@finderB
                \qr@addpenaltyiii
              \else
                \qr@removefirsttoken\qr@lastnine
                \ifx\qr@lastnine\qr@finderB@three
                  \qr@addpenaltyiii
                \else
                  \qr@removefirsttoken\qr@lastnine
                  \ifx\qr@lastnine\qr@finderB@two
                    \qr@addpenaltyiii
                  \else
                    \qr@removefirsttoken\qr@lastnine
                    \ifx\qr@lastnine\qr@finderB@one
                      \qr@addpenaltyiii
                    \else
                      \qr@removefirsttoken\qr@lastnine
                      \ifx\qr@lastnine\qr@finderB@zero
                        \qr@addpenaltyiii
                      \fi
                    \fi
                  \fi
                \fi
              \fi
            \else
              \ifx\qr@lastnine\qr@finderA% %Matches 0000 1011101
                \qr@addpenaltyiii
                %Also, we record our discovery, so that we can't count this pattern again
                %if it shows up four columns later as 1011101 0000.
                %
                %Set \qr@ignore@finderB@at to \j+4.
                \qr@a=\j\relax%
                \advance\qr@a by 4%
                \xdef\qr@ignore@finderB@at{\the\qr@a}%
              \else
                \ifx\qr@lastfive\qr@finderB% %Matches 1011101 0000.
                  \xa\ifnum\qr@ignore@finderB@at=\j\relax
                    %This pattern was *not* counted already earlier.
                    \qr@addpenaltyiii
                  \fi
                \fi
              \fi
            \fi
          \fi
          %
          %COUNT 1's FOR PENALTY 4
          \xa\ifnum\qr@newbit=1\relax%
            \stepcounter{totalones}%
          \fi
         }% end of j-loop
      }% end of i-loop
    %
    %NOW WE ALSO NEED TO RUN DOWN THE COLUMNS TO FINISH CALCULATING PENALTIES 1 AND 3.
    \qr@for \j=1 to \qr@size by 1%
      {\def\qr@lastfive{z}% %The z is a dummy, that will be removed before any testing.
       \qr@stringoffivefalse
       \def\qr@lastnine{z0000}% %The 0000 stands for the white space to the left. The z is a dummy.
       \def\qr@ignore@finderB@at{0}%
       \qr@for \i=1 to \qr@size by 1%
         {\edef\qr@newbit{\qr@matrixentry{#1}{\the\i}{\the\j}}%
          %
          % LASTFIVE CODE FOR PENALTY 1
          % First, add the new bit to the end.
          \xa\g@addto@macro\xa\qr@lastfive\xa{\qr@newbit}%
          \ifnum\i<5\relax% 
            %Not yet on the 5th entry.
            %Don't do any testing.
          \else
            % 5th entry or later.
            % Remove the old one, and then test.
            \qr@removefirsttoken\qr@lastfive%
            \ifx\qr@lastfive\qr@fiveones%
              \ifqr@stringoffive%
                %This is a continuation of a previous block of five or more 1's.
                \stepcounter{penaltyi}%
              \else
                %This is a new string of five 1's.
                \addtocounter{penaltyi}{\qr@Ni}%
                \global\qr@stringoffivetrue
              \fi
            \else
              \ifx\qr@lastfive\qr@fivezeros%
                \ifqr@stringoffive
                  %This is a continuation of a previous block of five or more 0's.
                  \stepcounter{penaltyi}%
                \else
                  %This is a new string of five 0's.
                  \addtocounter{penaltyi}{\qr@Ni}%
                  \global\qr@stringoffivetrue
                \fi
              \else
                %This is not a string of five 1's or five 0's.
                \global\qr@stringoffivefalse
              \fi
            \fi
          \fi
          %
          % HAPPILY, WE DON'T NEED TO CALCULATE PENALTY 2 AGAIN.
          %
          % LASTNINE CODE FOR PENALTY 3
          % First, add the new bit to the end.
          \xa\g@addto@macro\xa\qr@lastnine\xa{\qr@newbit}%
          \ifnum\i<7\relax% 
            %Not yet on the 7th entry.
            %Don't do any testing.
          \else
            % 7th entry or later.
            % Remove the old one, and then test.
            \qr@removefirsttoken\qr@lastnine
            \xa\ifnum\qr@size=\i\relax%
              % Last column.  Any of the following should count:
              %     1011101 (\qr@finderB@zero)
              %    10111010 (\qr@finderB@one)
              %   101110100 (\qr@finderB@two)
              %  1011101000 (\qr@finderB@three)
              % 10111010000 (\qr@finderB)
              \ifx\qr@lastnine\qr@finderB
                \qr@addpenaltyiii
              \else
                \qr@removefirsttoken\qr@lastnine
                \ifx\qr@lastnine\qr@finderB@three
                  \qr@addpenaltyiii
                \else
                  \qr@removefirsttoken\qr@lastnine
                  \ifx\qr@lastnine\qr@finderB@two
                    \qr@addpenaltyiii
                  \else
                    \qr@removefirsttoken\qr@lastnine
                    \ifx\qr@lastnine\qr@finderB@one
                      \qr@addpenaltyiii
                    \else
                      \qr@removefirsttoken\qr@lastnine
                      \ifx\qr@lastnine\qr@finderB@zero
                        \qr@addpenaltyiii
                      \fi
                    \fi
                  \fi
                \fi
              \fi
            \else
              \ifx\qr@lastnine\qr@finderA% %Matches 0000 1011101
                \qr@addpenaltyiii
                %Also, we record our discovery, so that we can't count this pattern again
                %if it shows up four columns later as 1011101 0000.
                %
                %Set \qr@ignore@finderB@at to \i+4.
                \qr@a=\i\relax%
                \advance\qr@a by 4%
                \xdef\qr@ignore@finderB@at{\the\qr@a}%
              \else
                \ifx\qr@lastfive\qr@finderB% %Matches 1011101 0000.
                  \xa\ifnum\qr@ignore@finderB@at=\i\relax
                    %This pattern was *not* counted already earlier.
                    \qr@addpenaltyiii
                  \fi
                \fi
              \fi
            \fi
          \fi
          %
         }% end of i-loop
      }% end of j-loop
  \egroup%
  %
  %CALCULATE PENALTY 4
  %According to the spec, penalty #4 is computed as
  % floor( |(i/n^2)-0.5|/0.05 )
  % where i is the total number of 1's in the matrix.
  % This is equal to abs(20*i-10n^2) div n^2.
  %
  \qr@a=\c@totalones\relax
  \multiply\qr@a by 20\relax
  \qr@b=\qr@size\relax
  \multiply\qr@b by \qr@size\relax
  \qr@c=10\relax
  \multiply\qr@c by \qr@b\relax
  \advance\qr@a by -\qr@c\relax
  \ifnum\qr@a<0\relax
    \multiply\qr@a by -1\relax
  \fi
  \divide\qr@a by \qr@b\relax
  \setcounter{penaltyiv}{\the\qr@a}%
  %
  %CALCULATE TOTAL PENALTY
  \qr@a=\thepenaltyi\relax%
  \advance\qr@a by \thepenaltyii\relax%
  \advance\qr@a by \thepenaltyiii\relax%
  \advance\qr@a by \thepenaltyiv\relax%
  \edef\qr@penalty{\the\qr@a}%
}%

\def\qr@removefirsttoken#1{%
  %Removes the first token from the macro named in #1.
  \edef\qr@argument{(#1)}%
  \xa\qr@removefirsttoken@int\qr@argument%
  \xdef#1{\qr@removefirsttoken@result}%
}%
\def\qr@removefirsttoken@int(#1#2){%
  \def\qr@removefirsttoken@result{#2}%
}%

\def\qr@writeformatstring#1#2{%
  % #1 = matrix name
  % #2 = binary string representing the encoded and masked format information
  \setcounter{qr@i}{9}%
  \setcounter{qr@j}{1}%
  \edef\qr@argument{{#1}(#2\relax)}%
  \xa\qr@writeformatA@recursive\qr@argument
  %
  \setcounter{qr@i}{\qr@numberofrowsinmatrix{#1}}%
  \setcounter{qr@j}{9}%
  \xa\qr@writeformatB@recursive\qr@argument
}%

\def\qr@writeformatA@recursive#1(#2#3){%
  % #1 = matrix name
  % #2 = first bit of string
  % #3 = rest of bitstream
  % (qr@i,qr@j) = current (valid) position to write (in LaTeX counters)
  \ifnum#2=1\relax
    \qr@storetomatrix{#1}{\theqr@i}{\theqr@j}{\qr@black@format}%
  \else
    \qr@storetomatrix{#1}{\theqr@i}{\theqr@j}{\qr@white@format}%
  \fi
  % Now the tricky part--moving \i and \j to their next positions.
  \ifnum\c@qr@j<9\relax
    %If we're not yet in column 9, move right.
    \stepcounter{qr@j}%
    \ifnum\c@qr@j=7\relax
      %But we skip column 7!
      \stepcounter{qr@j}%
    \fi
  \else
    %If we're in column 9, we move up.
    \addtocounter{qr@i}{-1}%
    \ifnum\c@qr@i=7\relax
      %But we skip row 7!
      \addtocounter{qr@i}{-1}%
    \fi
  \fi
  %N.B. that at the end of time, this will leave us at invalid position (0,9).
  %That makes for an easy test to know when we are done.
  \ifnum\c@qr@i<1
    \let\qr@next=\relax
  \else
    \def\qr@next{\qr@writeformatA@recursive{#1}(#3)}%
  \fi
  \qr@next
}%

\def\qr@writeformatB@recursive#1(#2#3){%
  % #1 = matrix name
  % #2 = first bit of string
  % #3 = rest of bitstream
  % (qr@i,qr@j) = current (valid) position to write (in LaTeX counters)
  \ifnum#2=1\relax
    \qr@storetomatrix{#1}{\theqr@i}{\theqr@j}{\qr@black@format}%
  \else
    \qr@storetomatrix{#1}{\theqr@i}{\theqr@j}{\qr@white@format}%
  \fi
  % Now the tricky part--moving counters i and j to their next positions.
  \qr@a=\qr@size%
  \advance\qr@a by -6\relax%
  \ifnum\qr@a<\c@qr@i\relax
    %If we're not yet in row n-6, move up.
    \addtocounter{qr@i}{-1}%
  \else
    \ifnum\qr@a=\c@qr@i\relax
      %If we're actually in row n-6, we jump to position (9,n-7).
      \setcounter{qr@i}{9}%
      %Set counter j equal to \qr@size-7.
      \global\c@qr@j=\qr@size\relax%
      \global\advance\c@qr@j by -7\relax%
    \else
      %Otherwise, we must be in row 9.
      %In this case, we move right.
      \stepcounter{qr@j}%
    \fi
  \fi
  %N.B. that at the end of time, this will leave us at invalid position (9,n+1).
  %That makes for an easy test to know when we are done.
  \xa\ifnum\qr@size<\c@qr@j\relax
    \let\qr@next=\relax
  \else
    \def\qr@next{\qr@writeformatB@recursive{#1}(#3)}%
  \fi
  \qr@next
}%

\def\qr@writeversionstring#1#2{%
  % #1 = matrix name
  % #2 = binary string representing the encoded version information
  %
  % Plot the encoded version string into the matrix.
  % This is only done for versions 7 and higher.
  \xa\ifnum\qr@version>6\relax
    %Move to position (n-8,6).
    \setcounter{qr@i}{\qr@size}\relax%
    \addtocounter{qr@i}{-8}\relax%
    \setcounter{qr@j}{6}%
    \edef\qr@argument{{#1}(#2\relax)}%
    \xa\qr@writeversion@recursive\qr@argument
  \fi
}%

\def\qr@writeversion@recursive#1(#2#3){%
  % #1 = matrix name
  % #2 = first bit of string
  % #3 = rest of bitstream
  % (qr@i,qr@j) = current (valid) position to write (in LaTeX counters)
  %
  % The version information is stored symmetrically in the matrix
  % In two transposed regions, so we can write both at the same time.
  % In the comments, we describe what happens in the lower-left region,
  % not the upper-right.
  % 
  %Set \qr@topline equal to n-10.
  \qr@a=\qr@size\relax%
  \advance\qr@a by -10\relax%
  \edef\qr@topline{\the\qr@a}%
  %
  \ifnum#2=1\relax
    \qr@storetomatrix{#1}{\theqr@i}{\theqr@j}{\qr@black@format}%
    \qr@storetomatrix{#1}{\theqr@j}{\theqr@i}{\qr@black@format}%
  \else
    \qr@storetomatrix{#1}{\theqr@i}{\theqr@j}{\qr@white@format}%
    \qr@storetomatrix{#1}{\theqr@j}{\theqr@i}{\qr@white@format}%
  \fi
  % Now the tricky part--moving counters i and j to their next positions.
  \addtocounter{qr@i}{-1}%
  \xa\ifnum\qr@topline>\c@qr@i\relax
    %We've overshot the top of the region.
    %We need to move left one column and down three.
    \addtocounter{qr@j}{-1}%
    \addtocounter{qr@i}{3}%
  \fi
  %N.B. that at the end of time, this will leave us at invalid position (n-8,0).
  %That makes for an easy test to know when we are done.
  \ifnum\c@qr@j<1\relax
    \let\qr@next=\relax
  \else
    \def\qr@next{\qr@writeversion@recursive{#1}(#3)}%
  \fi
  \qr@next
}%
%    \end{macrocode}
% 
% \subsection{Encoding and error correction}
%    \begin{macrocode}
\newcounter{qr@hexchars}%

\def\qr@string@binarytohex#1{%
  \qr@binarytohex{\qr@hex@result}{#1}%
}%

\def\qr@encode@binary#1{%
  % #1 = string of ascii characters, to be converted into bitstream
  %
  % We do this one entirely in hex, rather than binary, because we can.
  \edef\qr@plaintext{#1}%
  %
  %First, the mode indicator.
  \def\qr@codetext{4}% %This means `binary'
  %
  %Next, the character count.
  \qr@getstringlength{\qr@plaintext}%
  %Set \qr@charactercountlengthinhex to \qr@charactercountbits@byte/4%
  \qr@a=\qr@charactercountbits@byte\relax%
  \divide \qr@a by 4\relax%
  \edef\qr@charactercountlengthinhex{\the\qr@a}%
  \qr@decimaltohex[\qr@charactercountlengthinhex]{\qr@charactercount}{\qr@stringlength}%
  \xa\g@addto@macro\xa\qr@codetext\xa{\qr@charactercount}%
  %
  %Now comes the actual data.
  \edef\qr@argument{(,\qr@plaintext\relax\relax\relax)}%
  \xa\qr@encode@ascii@recursive\qr@argument%
  %
  %Now the terminator.
  \g@addto@macro\qr@codetext{0}% %This is '0000' in binary.
  %
  %There is no need to pad bits to make a multiple of 8,
  %because the data length is already 4 + 8 + 8n + 4.
  %
  %Now add padding codewords if needed.
  \setcounter{qr@hexchars}{0}%
  \qr@getstringlength{\qr@codetext}%
  \setcounter{qr@hexchars}{\qr@stringlength}%
  %Set \qr@numpaddingcodewords equal to \qr@totaldatacodewords - qr@hexchars/2.
  \qr@a=-\c@qr@hexchars\relax
  \divide\qr@a by 2\relax
  \advance\qr@a by \qr@totaldatacodewords\relax
  \edef\qr@numpaddingcodewords{\the\qr@a}%
  %
  \xa\ifnum\qr@numpaddingcodewords<0%
    \edef\ds{ERROR: Too much data!  Over by \qr@numpaddingcodewords bytes.}\show\ds%
  \fi%
  \xa\ifnum\qr@numpaddingcodewords>0%
    \qr@for \i = 2 to \qr@numpaddingcodewords by 2%
      {\g@addto@macro{\qr@codetext}{ec11}}%
    \xa\ifodd\qr@numpaddingcodewords\relax%
      \g@addto@macro{\qr@codetext}{ec}%
    \fi%
  \fi%
}%

\def\qr@encode@ascii@recursive(#1,#2#3){%
  % #1 = hex codes translated so far
  % #2 = next plaintext character to translate
  % #3 = remainder of plaintext
  \edef\qr@testii{#2}%
  \ifx\qr@testii\qr@relax%
    % All done!
    \g@addto@macro\qr@codetext{#1}%
  \else%
    % Another character to translate.
    \edef\qr@asciicode{\number`#2}%
    \qr@decimaltohex[2]{\qr@newhexcodes}{\qr@asciicode}%
    \edef\qr@argument{(#1\qr@newhexcodes,#3)}%
    %\show\qr@argument
    \xa\qr@encode@ascii@recursive\qr@argument%
  \fi%
}%

\def\qr@splitcodetextintoblocks{%
  \setcounter{qr@i}{0}%
  \qr@for \j = 1 to \qr@numshortblocks by 1%
    {\stepcounter{qr@i}%
     \qr@splitoffblock{\qr@codetext}{\theqr@i}{\qr@shortblock@size}%
    }%
  \xa\ifnum\qr@numlongblocks>0\relax%
    \qr@for \j = 1 to \qr@numlongblocks by 1%
      {\stepcounter{qr@i}%
       \qr@splitoffblock{\qr@codetext}{\theqr@i}{\qr@longblock@size}%
      }%
  \fi%
}%

\def\qr@splitoffblock#1#2#3{%
  % #1 = current codetext in hexadecimal
  % #2 = number to use in csname "\datablock@#2".
  % #3 = number of bytes to split off
  \message{<Splitting off block #2>}%
  \xa\gdef\csname datablock@#2\endcsname{}% %This line is important!
  \qr@for \i = 1 to #3 by 1%
    {\edef\qr@argument{{#2}(#1)}%
     \xa\qr@splitoffblock@int\qr@argument%
    }%
}%

\def\qr@splitoffblock@int#1(#2#3#4){%
  % #1 = number to use in csname "\datablock@#1".
  % #2#3 = next byte to split off
  % #4 = remaining text
  %
  % We add the next byte to "\datablock@#1",
  % and we remove it from the codetext.
  \xa\xdef\csname datablock@#1\endcsname{\csname datablock@#1\endcsname#2#3}%
  \xdef\qr@codetext{#4}%
}%

\def\qr@createerrorblocks{%
  \qr@for \ii = 1 to \qr@numblocks by 1%
    {\message{<Making error block \the\ii>}%
     \FX@generate@errorbytes{\csname datablock@\the\ii\endcsname}{\qr@num@eccodewords}%
     \xa\xdef\csname errorblock@\the\ii\endcsname{\FX@errorbytes}%
    }%
}%

\def\qr@interleave{%
  \setcounter{qr@i}{0}%
  \def\qr@interleaved@text{}%
  \message{<Interleaving datablocks of length \qr@shortblock@size\ and \qr@longblock@size: }%
  \qr@for \ii = 1 to \qr@shortblock@size by 1%
    {\qr@for \jj = 1 to \qr@numblocks by 1%
      {\qr@writefromblock{datablock}{\the\jj}%
      }%
     \message{\the\ii,}%
    }%
  %The long blocks are numbered \qr@numshortblocks+1, \qr@numshortblocks+2, ..., \qr@numblocks.
  \qr@a=\qr@numshortblocks\relax%
  \advance\qr@a by 1\relax%
  \qr@for \jj = \qr@a to \qr@numblocks by 1%
      {\qr@writefromblock{datablock}{\the\jj}}%
  \xa\ifnum\qr@numlongblocks>0\relax%
    \message{\qr@longblock@size.>}%
  \else
    \message{.>}%
  \fi
  \message{<Interleaving errorblocks of length \qr@num@eccodewords: }%
  \qr@for \ii = 1 to \qr@num@eccodewords by 1%
    {\message{\the\ii,}%
     \qr@for \jj = 1 to \qr@numblocks by 1%
      {\qr@writefromblock{errorblock}{\the\jj}%
      }%
    }%
  \message{.><Interleaving complete.>}%
}%

\def\qr@writefromblock#1#2{%
  % #1 = either 'datablock' or 'errorblock'
  % #2 = block number, in {1,...,\qr@numblocks}%
  \edef\qr@argument{(\csname #1@#2\endcsname\relax\relax\relax)}%
  \xa\qr@writefromblock@int\qr@argument
  \xa\xdef\csname #1@#2\endcsname{\qr@writefromblock@remainder}%
}%

\def\qr@writefromblock@int(#1#2#3){%
  % #1#2 = first byte (in hex) of text, which will be written to \qr@interleaved@text
  % #3 = remainder, including \relax\relax\relax terminator.
  \g@addto@macro{\qr@interleaved@text}{#1#2}%
  \qr@writefromblock@intint(#3)%
}%

\def\qr@writefromblock@intint(#1\relax\relax\relax){%
  \xdef\qr@writefromblock@remainder{#1}%
}%
%    \end{macrocode}
% 
% \subsection{Encoding format and version information}
%    \begin{macrocode}
\let\xa=\expandafter
\makeatletter

\def\qr@preface@macro#1#2{%
  % #1 = macro name
  % #2 = text to add to front of macro
  \def\qr@tempb{#2}%
  \xa\xa\xa\gdef\xa\xa\xa#1\xa\xa\xa{\xa\qr@tempb #1}%
}%

\newif\ifqr@leadingcoeff
\def\qr@testleadingcoeff(#1#2){%
  % Tests whether the leading digit of #1#2 is 1.
  \ifnum#1=1\relax
    \qr@leadingcoefftrue
  \else
    \qr@leadingcoefffalse
  \fi
}%

\def\qr@polynomialdivide#1#2{%
  \edef\qr@numerator{#1}%
  \edef\qr@denominator{#2}%
  \qr@divisiondonefalse%
  \xa\xa\xa\qr@oneroundofdivision\xa\xa\xa{\xa\qr@numerator\xa}\xa{\qr@denominator}%
}%

\def\@qr@empty{}%
\def\qr@oneroundofdivision#1#2{%
  % #1 = f(x), of degree n
  % #2 = g(x), of degree m
  % Obtains a new polynomial h(x), congruent to f(x) modulo g(x),
  % but of degree at most n-1.
  % 
  % If leading coefficient of f(x) is 1, subtracts off g(x) * x^(n-m).
  % If leading coefficient of f(x) is 0, strips off that leading zero.
  %
  \qr@testleadingcoeff(#1)%
  \ifqr@leadingcoeff
    \qr@xorbitstrings{#1}{#2}%
    \ifqr@xorfailed
      %If xor failed, that means our #1 was already the remainder!
      \qr@divisiondonetrue
      \edef\qr@theremainder{#1}%
    \else
      %xor succeeded. We need to recurse.
      \xa\xa\xa\edef\xa\xa\xa\qr@numerator\xa\xa\xa{\xa\qr@stripleadingzero\xa(\qr@xorresult)}%
    \fi
  \else
    \xa\def\xa\qr@numerator\xa{\qr@stripleadingzero(#1)}%
    \ifx\qr@numerator\@qr@empty
      \qr@divisiondonetrue
      \def\qr@theremainder{0}%
    \fi
  \fi
  \ifqr@divisiondone
    \relax
  \else
    \xa\qr@oneroundofdivision\xa{\qr@numerator}{#2}%
  \fi
}%

\def\qr@stripleadingzero(0#1){#1}%Strips off a leading zero.

\newif\ifqr@xorfailed% This flag will trigger when #2 is longer than #1.

\def\qr@xorbitstrings#1#2{%
 % #1 = bitstring
 % #2 = bitstring no longer than #1
 \qr@xorfailedfalse
 \edef\qr@argument{(,#1\relax\relax)(#2\relax\relax)}%
 \xa\qr@xorbitstrings@recursive\qr@argument
 %\qr@xorbitstrings@recursive(,#1\relax\relax)(#2\relax\relax)%
}%

\def\qr@xorbitstrings@recursive(#1,#2#3)(#4#5){%
 % #1#2#3 is the first bitstring, xor'ed up through #1.
 % #4#5 is the remaining portion of the second bitstring.
 \def\qr@testii{#2}%
 \def\qr@testiv{#4}%
 \ifx\qr@testii\qr@relax
   % #1 contains the whole string.
   % Now if #4 is also \relax, that means the two strings started off with equal lengths.
   % If, however, #4 is not \relax, that means the second string was longer than the first, a problem.
   \ifx\qr@testiv\qr@relax
     %No problem.  We are done.
     \qr@xorbit@saveresult(#1#2#3)%
   \else
     %Problem!  The second string was longer than the first.
     \qr@xorfailedtrue
     \def\qr@xorresult{}%
   \fi
 \else
   % There is still a bit to manipulate in #2.
   % Check whether #4 contains anything.
   \ifx\qr@testiv\qr@relax
     % No, #4 is empty.  We are done. "#2#3" contains the remainder of the first string,
     % which we append untouched and then strip off the two \relax-es.
     \qr@xorbit@saveresult(#1#2#3)%
   \else
     % Yes, #4 still has something to XOR. Do the task.
     \ifnum#2=#4\relax
       \qr@xorbitstrings@recursive(#1%
                                 0,#3)(#5)%
     \else
       \qr@xorbitstrings@recursive(#1%
                                 1,#3)(#5)%
     \fi
   \fi
 \fi
}%

\def\qr@xorbit@saveresult(#1\relax\relax){%
  %Strips off the extra '\relax'es at the end.
  \def\qr@xorresult{#1}%
}%

\newif\ifqr@divisiondone

\def\qr@BCHcode#1{%
  \edef\qr@formatinfo{#1}%
  \def\qr@formatinfopadded{\qr@formatinfo 0000000000}%
  \def\qr@divisor{10100110111}%
  \qr@divisiondonefalse
  \qr@polynomialdivide{\qr@formatinfopadded}{\qr@divisor}%
  %
  \qr@getstringlength{\qr@theremainder}%
  %Run loop from stringlength+1 to 10.
  \qr@a=\qr@stringlength\relax%
  \advance\qr@a by 1\relax%
  \qr@for \i = \qr@a to 10 by 1%
    {\qr@preface@macro{\qr@theremainder}{0}%
     \xdef\qr@theremainder{\qr@theremainder}%
    }%
  \edef\qr@BCHresult{\qr@formatinfo\qr@theremainder}%
}%

\def\qr@formatmask{101010000010010}%

\def\qr@encodeandmaskformat#1{%
  \qr@BCHcode{#1}%
  \qr@xorbitstrings{\qr@BCHresult}{\qr@formatmask}%
  \edef\qr@format@bitstring{\qr@xorresult}%
}%

\def\qr@Golaycode#1{%
  % #1 = 6-bit version number
  \edef\qr@versioninfo{#1}%
  \def\qr@versioninfopadded{\qr@versioninfo 000000000000}% %Append 12 zeros.
  \def\qr@divisor{1111100100101}%
  \qr@divisiondonefalse
  \qr@polynomialdivide{\qr@versioninfopadded}{\qr@divisor}%
  %
  \qr@getstringlength{\qr@theremainder}%
  %Run loop from stringlength+1 to 12.
  \qr@a=\qr@stringlength\relax%
  \advance\qr@a by 1\relax%
  \qr@for \i = \qr@a to 12 by 1%
    {\qr@preface@macro{\qr@theremainder}{0}%
     \xdef\qr@theremainder{\qr@theremainder}%
    }%
  \edef\qr@Golayresult{\qr@versioninfo\qr@theremainder}%
}%
%    \end{macrocode}
% 
% \subsection{Error correction}
% The error-correction code is defined over $\F_{256}=GF(256)$,
% the finite field of order $256$.
% The QR specification encodes this field as $\F_2[X]/(X^8+X^4+X^3+X^2+1)$;
% in other words, each field element is an 8-bit binary string representing
% an integer between 0 and 255.
% 
% We represent these 8-bit strings as two hexadecimal characters;
% for example, {\tt 5a} represents {\tt 01011010}.
% Because addition is done by xor-ing the bitstrings,
% we can define addition on hexadecimal characters.
% Since there are only $16^2$ possibilities,
% we create a lookup table.
%    \begin{macrocode}
\def\F@result{}%

\def\qr@xorbitstring#1#2#3{%
  % #1 = new macro to receive result
  % #2, #3 = bitstrings to xor.  The second can be shorter than the first.
  \def\qr@xor@result{}%
  \edef\qr@argument{(#2\relax\relax)(#3\relax\relax)}%
  \xa\qr@xorbitstring@recursive\qr@argument%
  \edef#1{\qr@xor@result}%
}%
\def\qr@xorbitstring@recursive(#1#2)(#3#4){%
  \edef\qr@testi{#1}%
  \ifx\qr@testi\qr@relax%
    %Done.
    \let\qr@next=\relax%
  \else
    \if#1#3\relax
      \g@addto@macro{\qr@xor@result}{0}%
    \else
      \g@addto@macro{\qr@xor@result}{1}%
    \fi
    \edef\qr@next{\noexpand\qr@xorbitstring@recursive(#2)(#4)}%
  \fi
  \qr@next
}

\def\F@addchar@raw#1#2{%
  %Add two hexadecimal digits using bitwise xor
  \qr@hextobinary[4]{\qr@summandA}{#1}%
  \qr@hextobinary[4]{\qr@summandB}{#2}%
  \qr@xorbitstring{\F@result}{\qr@summandA}{\qr@summandB}%
  \qr@binarytohex[1]{\F@result}{\F@result}%
}%

\def\qr@canceltwos#1{%
  \edef\qr@argument{(#1\relax\relax)}%
  \xa\qr@canceltwos@int\qr@argument%
}%

\def\qr@canceltwos@int(#1#2){%
  \xa\qr@canceltwos@recursion(,#1#2)%
}%

\def\qr@canceltwos@recursion(#1,#2#3){%
  \def\qr@testii{#2}%
  \ifx\qr@testii\qr@relax
    %Cancelling complete.
    \qr@striptworelaxes(#1#2#3)%
    %Now \F@result contains the answer.
  \else
    \relax
    \ifnum#2=2\relax
      \qr@canceltwos@recursion(#10,#3)%
    \else
      \qr@canceltwos@recursion(#1#2,#3)%
    \fi
  \fi
}%

\def\qr@striptworelaxes(#1\relax\relax){%
  \gdef\F@result{#1}%
}%

\qr@for \i = 0 to 15 by 1%
  {\qr@decimaltohex[1]{\qr@tempa}{\the\i}%
   \qr@for \j = 0 to 15 by 1%
    {\qr@decimaltohex[1]{\qr@tempb}{\the\j}%
     \F@addchar@raw\qr@tempa\qr@tempb
     \xa\xdef\csname F@addchar@\qr@tempa\qr@tempb\endcsname{\F@result}%
    }%
  }%

\def\F@addchar#1#2{%
  \xa\def\xa\F@result\xa{\csname F@addchar@#1#2\endcsname}%
}%

\def\F@addstrings#1#2{%
  \edef\qr@argument{(,#1\relax\relax)(#2\relax\relax)}%
  \xa\F@addstrings@recursion\qr@argument%
}%

\def\F@addstrings@recursion(#1,#2#3)(#4#5){%
  %Adds two hexadecimal strings, bitwise, from left to right.
  %The second string is allowed to be shorter than the first.
  \def\qr@testii{#2}%
  \def\qr@testiv{#4}%
  \ifx\qr@testii\qr@relax
    %The entire string has been processed.
    \gdef\F@result{#1}%
  \else
    \ifx\qr@testiv\qr@relax
      %The second string is over.
      \qr@striptworelaxes(#1#2#3)%
      %Now \F@result contains the answer.
    \else
      %We continue to add.
      \F@addchar{#2}{#4}%
      \edef\qr@argument{(#1\F@result,#3)(#5)}%
      \xa\F@addstrings@recursion\qr@argument%
    \fi
  \fi
}%
%    \end{macrocode}
% Now we handle multiplication.
% Our approach to multiplying $a,b\in\F_{256}$
% is to take discrete logarithms (with 2 as our base),
% add the logarithms, and then take the antilog.
% We first create a log table.
%    \begin{macrocode}
\gdef\F@stripleadingzero(0#1){\edef\F@result{#1}}%

\setcounter{qr@i}{0}%
\def\qr@poweroftwo{1}%
\qr@for \i = 1 to 254 by 1%
  {\stepcounter{qr@i}%
   \qr@a=\qr@poweroftwo\relax
   \multiply\qr@a by 2\relax
   \edef\qr@poweroftwo{\the\qr@a}%
   %\show\qr@poweroftwo
   \qr@decimaltohex[2]{\qr@poweroftwo@hex}{\qr@poweroftwo}%
   \xa\ifnum\qr@poweroftwo>255\relax
     %We need to bitwise add the polynomial represented by 100011101, i.e. 0x11d.
     \F@addstrings{\qr@poweroftwo@hex}{11d}%               %Now it should start with 0.
     \xa\F@stripleadingzero\xa(\F@result)%              %Now it should be two hex digits.
     \edef\qr@poweroftwo@hex{\F@result}%                   %Save the hex version.
     \qr@hextodecimal{\qr@poweroftwo}{\F@result}%
   \fi
   \xdef\qr@poweroftwo{\qr@poweroftwo}%
   \xa\xdef\csname F@twotothe@\theqr@i\endcsname{\qr@poweroftwo@hex}%
   \xa\xdef\csname F@logtwo@\qr@poweroftwo@hex\endcsname{\theqr@i}%
  }%
\xa\xdef\csname F@twotothe@0\endcsname{01}%
\xa\xdef\csname F@logtwo@01\endcsname{0}%

\def\F@twotothe#1{%
  \xa\xdef\xa\F@result\xa{\csname F@twotothe@#1\endcsname}%
}%
\def\F@logtwo#1{%
  \xa\xdef\xa\F@result\xa{\csname F@logtwo@#1\endcsname}%
}%

\def\qr@zerozero{00}%

\def\F@multiply#1#2{%
  % #1 and #2 are two elements of F_256,
  % given as two-character hexadecimal strings.
  % Multiply them within F_256, and place the answer in \F@result
  \edef\qr@argA{#1}%
  \edef\qr@argB{#2}%
  \ifx\qr@argA\qr@zerozero
    \def\F@result{00}%
  \else
    \ifx\qr@argB\qr@zerozero
      \def\F@result{00}%
    \else
      \xa\F@logtwo\xa{\qr@argA}%
        \edef\qr@logA{\F@result}%
      \xa\F@logtwo\xa{\qr@argB}%
        \edef\qr@logB{\F@result}%
      \xa\qr@a\xa=\qr@logA\relax%  \qr@a = \qr@logA
      \xa\advance\xa\qr@a\qr@logB\relax% \advance \qr@a by \qr@logB
      \ifnum\qr@a>254\relax%
        \advance\qr@a by -255\relax%
      \fi%
      \xa\F@twotothe\xa{\the\qr@a}%
      % Now \F@result contains the product, as desired.
    \fi
  \fi
}%


\def\F@multiply#1#2{%
  % #1 and #2 are two elements of F_256,
  % given as two-character hexadecimal strings.
  % Multiply them within F_256, and place the answer in \F@result
  \edef\qr@argA{#1}%
  \edef\qr@argB{#2}%
  \ifx\qr@argA\qr@zerozero
    \def\F@result{00}%
  \else
    \ifx\qr@argB\qr@zerozero
      \def\F@result{00}%
    \else
      \xa\F@logtwo\xa{\qr@argA}%
        \edef\qr@logA{\F@result}%
      \xa\F@logtwo\xa{\qr@argB}%
        \edef\qr@logB{\F@result}%
      \xa\qr@a\xa=\qr@logA\relax%  \qr@a = \qr@logA
      \xa\advance\xa\qr@a\qr@logB\relax% \advance \qr@a by \qr@logB
      \ifnum\qr@a>254\relax%
        \advance\qr@a by -255\relax%
      \fi%
      \xa\F@twotothe\xa{\the\qr@a}%
      % Now \F@result contains the product, as desired.
    \fi
  \fi
}%
%    \end{macrocode}
% Having developed $\F_{256}$, we now turn to the real task.
% Each byte of data is read as an element of $\F_{256}$,
% and a sequence of bytes corresponds a polynomial in
% $\F_{256}[X]$.
% The Reed-Solomon code takes that codeword $f(X)\in \F_{256}[X]$
% of degree $k$, divides $f(X)\cdot X^\ell$ by a fixed
% polynomial,
% and keeps the remainder $r(X)$ as the error-correction word.
% We therefore must implement polynomial division over $\F_{256}$.
%    \begin{macrocode}
%These polynomials are represented as sequences of coefficients,
%from highest power to lowest,
%with each coefficient represented by two hexadecimal characters.

\def\FX@getstringlength#1{%
  %Count number of two-character coefficients
  \setcounter{qr@i}{0}%
  \xdef\qr@argument{(#1\relax\relax\relax)}%
  \xa\FX@stringlength@recursive\qr@argument%
  \xdef\stringresult{\arabic{qr@i}}%
}%

\def\FX@stringlength@recursive(#1#2#3){%
  \def\qr@testi{#1}%
  \ifx\qr@testi\qr@relax
    %we are done.
  \else 
    \stepcounter{qr@i}%
    %\showthe\c@qr@i
    \qr@stringlength@recursive(#3)%
  \fi
}%

\newif\ifFX@leadingcoeff@zero
\def\FX@testleadingcoeff(#1#2#3){%
  % Tests whether the leading coefficient of the hex-string #1#2#3 is '00'.
  \edef\FX@leadingcoefficient{#1#2}%
  \FX@leadingcoeff@zerofalse
  \ifx\FX@leadingcoefficient\qr@zerozero
    \FX@leadingcoeff@zerotrue
  \fi
}%

\newif\ifFX@divisiondone

\newcounter{qr@divisionsremaining} %Keep track of how many divisions to go!
\def\FX@polynomialdivide#1#2{%
  \edef\FX@numerator{#1}%
  \edef\FX@denominator{#2}%
  \qr@getstringlength\FX@numerator%
  \setcounter{qr@divisionsremaining}{\qr@stringlength}%
  \qr@getstringlength\FX@denominator%
  \addtocounter{qr@divisionsremaining}{-\qr@stringlength}%
  \addtocounter{qr@divisionsremaining}{2}%
  \divide\c@qr@divisionsremaining by 2\relax% %2 hex chars per number
  \FX@divisiondonefalse%
  \xa\xa\xa\FX@polynomialdivide@recursive\xa\xa\xa{\xa\FX@numerator\xa}\xa{\FX@denominator}%
}%

\def\FX@polynomialdivide@recursive#1#2{%
  % #1 = f(x), of degree n
  % #2 = g(x), of degree m
  % Obtains a new polynomial h(x), congruent to f(x) modulo g(x),
  % but of degree at most n-1.
  % 
  % If leading coefficient of f(x) is 0, strips off that leading zero.
  % If leading coefficient of f(x) is a, subtracts off a * g(x) * x^(n-m).
  % N.B. we assume g is monic.
  %
  \FX@testleadingcoeff(#1)%
  \ifFX@leadingcoeff@zero%
    %Leading coefficient is zero, so remove it.
    \xa\def\xa\FX@numerator\xa{\FX@stripleadingzero(#1)}%
  \else%
    %Leading coefficient is nonzero, and contained in \FX@leadingcoefficient
    \FX@subtractphase{#1}{#2}{\FX@leadingcoefficient}%
    \ifFX@subtract@failed%
      %If subtraction failed, that means our #1 was already the remainder!
      \FX@divisiondonetrue%
      \edef\qr@theremainder{#1}%
    \else%
      %xor succeeded. We need to recurse.
      \xa\xa\xa\edef\xa\xa\xa\FX@numerator\xa\xa\xa{\xa\FX@stripleadingzero\xa(\FX@subtraction@result)}%
    \fi%
  \fi%
  \addtocounter{qr@divisionsremaining}{-1}%
  \ifnum\c@qr@divisionsremaining=0\relax
    %Division is done!
    \FX@divisiondonetrue%
    \edef\qr@theremainder{\FX@numerator}%
    \relax%
  \else%
    \xa\FX@polynomialdivide@recursive\xa{\FX@numerator}{#2}%
  \fi%
}%

\def\FX@stripleadingzero(00#1){#1}%Strips off a single leading zero of F_256.

\newif\ifFX@subtract@failed% This flag will trigger when #2 is longer than #1.

\def\FX@subtractphase#1#2#3{%
 % #1 = bitstring
 % #2 = bitstring no longer than #1
 % #3 = leading coefficient
 \FX@subtract@failedfalse%
 \edef\qr@argument{(,#1\relax\relax\relax)(#2\relax\relax\relax)(#3)}%
 \xa\FX@subtract@recursive\qr@argument%
}%

\def\FX@subtract@recursive(#1,#2#3#4)(#5#6#7)(#8){%
 % This is a recursive way to compute f(x) - a*g(x)*x^k.
 % #1#2#3#4 is the first bitstring, subtracted up through #1.
 %          Thus #2#3 constitutes the next two-character coefficient.
 % #5#6#7 is the remaining portion of the second bitstring.
 %          Thus #5#6 constitutes the next two-character coefficient
 % #8 is the element a of F_256.  It should contain two characters.
 \def\qr@testii{#2}%
 \def\qr@testv{#5}%
 \ifx\qr@testii\qr@relax
   % #1 contains the whole string.
   % Now if #5 is also \relax, that means the two strings started off with equal lengths.
   % If, however, #5 is not \relax, that means the second string was longer than the first, a problem.
   \ifx\qr@testv\qr@relax
     %No problem.  We are done.
     \FX@subtract@saveresult(#1#2#3#4)% %We keep the #2#3#4 to be sure we have all three relax-es to strip off.
   \else
     %Problem!  The second string was longer than the first.
     %This usually indicates the end of the long division process.
     \FX@subtract@failedtrue
     \def\FX@subtraction@result{}%
   \fi
 \else
   % There is still a coefficient to manipulate in #2#3.
   % Check whether #5 contains anything.
   \ifx\qr@testv\qr@relax
     % No, #5 is empty.  We are done. "#2#3#4" contains the remainder of the first string,
     % which we append untouched and then strip off the three \relax-es.
     \FX@subtract@saveresult(#1#2#3#4)%
   \else
     % Yes, #5#6 still has something to XOR. Do the task.
     \F@multiply{#5#6}{#8}% Multiply by the factor 'a'.
     \F@addstrings{#2#3}{\F@result}% Subtract.  (We're in characteristic two, so adding works.)
     \edef\qr@argument{(#1\F@result,#4)(#7)(#8)}%
     \xa\FX@subtract@recursive\qr@argument%
   \fi
 \fi
}%

\def\FX@subtract@saveresult(#1\relax\relax\relax){%
  %Strips off the three extra '\relax'es at the end.
  \def\FX@subtraction@result{#1}%
}%

\def\FX@creategeneratorpolynomial#1{%
  % #1 = n, the number of error codewords desired.
  % We need to create \prod_{j=0}^{n-1} (x-2^j).
  \edef\FX@generator@degree{#1}%
  \def\FX@generatorpolynomial{01}% Initially, set it equal to 1.
  \setcounter{qr@i}{0}%
  \FX@creategenerator@recursive%
  %The result is now stored in \FX@generatorpolynomial
}%

\def\FX@creategenerator@recursive{%
  % \c@qr@i contains the current value of i.
  % \FX@generatorpolynomial contains the current polynomial f(x),
  %   which should be a degree-i polynomial
  %   equal to \prod_{j=0}^{i-1} (x-2^j).
  %   (If i=0, then \FX@generatorpolynomial should be 01.)
  % This recursion step should multiply the existing polynomial by (x-2^i),
  % increment i by 1, and check whether we're done or not.
  \edef\qr@summandA{\FX@generatorpolynomial 00}% This is f(x) * x
  \edef\qr@summandB{00\FX@generatorpolynomial}% This is f(x), with a 0x^{i+1} in front.
  \F@twotothe{\theqr@i}%
  \edef\qr@theconstant{\F@result}%
  \FX@subtractphase{\qr@summandA}{\qr@summandB}{\qr@theconstant}%
     %This calculates \qr@summandA + \qr@theconstant * \qr@summandB
     %and stores the result in \FX@subtraction@result
  \edef\FX@generatorpolynomial{\FX@subtraction@result}%
  \stepcounter{qr@i}%
  \xa\ifnum\FX@generator@degree=\c@qr@i\relax%
    %We just multiplied by (x-2^{n-1}), so we're done.
    \relax%
  \else%
    %We need to do this again!
    \xa%
    \FX@creategenerator@recursive%
  \fi%
}%

\def\FX@generate@errorbytes#1#2{%
  % #1 = datastream in hex
  % #2 = number of error correction bytes requested
  \edef\qr@numerrorbytes{#2}%
  \xa\FX@creategeneratorpolynomial\xa{\qr@numerrorbytes}%
  \edef\FX@numerator{#1}%
  \qr@for \i = 1 to \qr@numerrorbytes by 1%
    {\g@addto@macro\FX@numerator{00}}% %One error byte means two hex codes.
  \FX@polynomialdivide{\FX@numerator}{\FX@generatorpolynomial}%
  \edef\FX@errorbytes{\qr@theremainder}%
}%
%    \end{macrocode}
% 
% \subsection{Version handling}
%    \begin{macrocode}
\newif\ifqr@versionmodules

\def\qr@level@char#1{%
    \xa\ifcase#1
      M\or L\or H\or Q\fi}%
      
\newif\ifqr@versiongoodenough
\def\qr@choose@best@version#1{%
  % \qr@desiredversion = user-requested version
  % \qr@desiredlevel = user-requested error-correction level
  \edef\qr@plaintext{#1}%
  \qr@getstringlength{\qr@plaintext}%
  %
  %Run double loop over levels and versions, looking for 
  %the smallest version that can contain our data,
  %and then choosing the best error-correcting level at that version,
  %subject to the level being at least as good as the user desires.
  \global\qr@versiongoodenoughfalse%
  \gdef\qr@bestversion{0}%
  \gdef\qr@bestlevel{0}%
  \ifnum\qr@desiredversion=0\relax
    \qr@a=1\relax
  \else
    \qr@a=\qr@desiredversion\relax
  \fi
  \qr@for \i=\qr@a to 40 by 1
    {\edef\qr@version{\the\i}%
     \global\qr@versiongoodenoughfalse
     \qr@for \j=0 to 3 by 1%
      {%First, we map {0,1,2,3} to {1,0,4,3}, so that we loop through {M,L,H,Q} 
       %in order of increasing error-correction capabilities.
       \qr@a = \j\relax
       \divide \qr@a by 2\relax
       \multiply \qr@a by 4\relax
       \advance \qr@a by 1\relax
       \advance \qr@a by -\j\relax
       \edef\qr@level{\the\qr@a}%
       \ifnum\qr@desiredlevel=\qr@a\relax
         \global\qr@versiongoodenoughtrue
       \fi
       \ifqr@versiongoodenough
         \qr@calculate@capacity{\qr@version}{\qr@level}%
         \xa\xa\xa\ifnum\xa\qr@truecapacity\xa<\qr@stringlength\relax
           %Too short
           \relax
         \else
           %Long enough!
           \xdef\qr@bestversion{\qr@version}%
           \xdef\qr@bestlevel{\qr@level}%
           \global\i=40%
         \fi
       \fi
      }%
     }%
  \edef\qr@version{\qr@bestversion}%
  \edef\qr@level{\qr@bestlevel}%
  \xa\ifnum\qr@desiredversion>0\relax
    \ifx\qr@bestversion\qr@desiredversion\relax
      %No change from desired version.
    \else
      %Version was increased
      \message{<Requested QR version '\qr@desiredversion' is too small for desired text.}%
      \message{Version increased to '\qr@bestversion' to fit text.>^^J}%
    \fi
  \fi
  \ifx\qr@bestlevel\qr@desiredlevel\relax
    %No change in level.
  \else
    \message{<Error-correction level increased from \qr@level@char{\qr@desiredlevel}}%
    \message{to \qr@level@char{\qr@bestlevel} at no cost.>^^J}%
  \fi
}%

\def\qr@calculate@capacity#1#2{%
  \edef\qr@version{#1}%
  \edef\qr@level{#2}%
  %Calculate \qr@size, the number of modules per side.
  % The formula is 4\qr@version+17.
  \qr@a=\qr@version\relax%
  \multiply\qr@a by 4\relax%
  \advance\qr@a by 17\relax%
  \edef\qr@size{\the\qr@a}%
  %
  % Calculate \qr@k, which governs the number of alignment patterns.
  % The alignment patterns lie in a kxk square, except for 3 that are replaced by finding patterns.
  % The formula is 2 + floor( \qr@version / 7 ), except that k=0 for version 1.
  \xa\ifnum\qr@version=1\relax%
    \def\qr@k{0}%
  \else%
    \qr@a=\qr@version\relax
    \divide \qr@a by 7\relax
    \advance\qr@a by 2\relax
    \edef\qr@k{\the\qr@a}%
  \fi%
  %
  %Calculate number of function pattern modules.
  %This consists of the three 8x8 finder patterns, the two timing strips, and the (k^2-3) 5x5 alignment patterns.
  %The formula is 160+2n+25(k^2-3)-10(k-2), unless k=0 in which case we just have 160+2n.
  \qr@a=\qr@size\relax
  \multiply\qr@a by 2\relax
  \advance\qr@a by 160\relax
  \xa\ifnum\qr@k=0\relax\else
    %\qr@k is nonzero, hence at least 2, so we continue to add 25(k^2-3)-10(k-2).
    \qr@b=\qr@k\relax
    \multiply\qr@b by \qr@k\relax
    \advance\qr@b by -3\relax
    \multiply\qr@b by 25\relax
    \advance\qr@a by \qr@b\relax
    \qr@b=\qr@k\relax
    \advance\qr@b by -2\relax
    \multiply\qr@b by 10\relax
    \advance\qr@a by -\qr@b\relax
  \fi
  \edef\qr@numfunctionpatternmodules{\the\qr@a}%
  %
  %Calculate the number of version modules, either 36 or 0.
  \xa\ifnum\qr@version>6\relax
    \qr@versionmodulestrue
    \def\qr@numversionmodules{36}%
  \else
    \qr@versionmodulesfalse
    \def\qr@numversionmodules{0}%
  \fi
  %
  %Now calculate the codeword capacity and remainder bits.
  %Take n^2 modules, subtract all those dedicated to finder patterns etc., format information, and version information,
  %and what's left is the number of bits we can play with.
  %The number of complete bytes is \qr@numdatacodewords;
  %the leftover bits are \qr@numremainderbits.
  \qr@a=\qr@size\relax
  \multiply \qr@a by \qr@size\relax
  \advance \qr@a by -\qr@numfunctionpatternmodules\relax
  \advance \qr@a by -31\relax% % There are 31 format modules.
  \advance \qr@a by -\qr@numversionmodules\relax
  \qr@b=\qr@a\relax
  \divide \qr@a by 8\relax
  \edef\qr@numdatacodewords{\the\qr@a}%
  \multiply\qr@a by 8\relax
  \advance \qr@b by -\qr@a\relax
  \edef\qr@numremainderbits{\the\qr@b}%
  %
  %The size of the character count indicator also varies by version.
  %There are only two options, so hardcoding seems easier than expressing these functionally.
  \xa\ifnum\qr@version<10\relax
    \def\qr@charactercountbytes@byte{1}%
    \def\qr@charactercountbits@byte{8}%
  \else
    \def\qr@charactercountbytes@byte{2}%
    \def\qr@charactercountbits@byte{16}%
  \fi
  %
  %Now we call on the table, from the QR specification,
  %of how many blocks to divide the message into, and how many error bytes each block gets.
  %This affects the true capacity for data, which we store into \qr@totaldatacodewords.
  % The following macro sets \qr@numblocks and \qr@num@eccodewords
  % based on Table 9 of the QR specification.
  \qr@settableix
  \qr@a = -\qr@numblocks\relax
  \multiply \qr@a by \qr@num@eccodewords\relax
  \advance\qr@a by \qr@numdatacodewords\relax
  \edef\qr@totaldatacodewords{\the\qr@a}%
  \advance\qr@a by -\qr@charactercountbytes@byte\relax%Subtract character count
  \advance\qr@a by -1\relax% Subtract 1 byte for the 4-bit mode indicator and the 4-bit terminator at the end.
  \edef\qr@truecapacity{\the\qr@a}%
}


\def\qr@setversion#1#2{%
  % #1 = version number, an integer between 1 and 40 inclusive.
  % #2 = error-correction level, as an integer between 0 and 3 inclusive.
  %      0 = 00 = M
  %      1 = 01 = L
  %      2 = 10 = H
  %      3 = 11 = Q
  % This macro calculates and sets a variety of global macros and/or counters
  % storing version information that is used later in construction the QR code.
  % Thus \qr@setversion should be called every time!
  %
  \edef\qr@version{#1}%
  \edef\qr@level{#2}%
  %
  \qr@calculate@capacity{\qr@version}{\qr@level}%
  %The capacity-check code sets the following:
  % * \qr@size
  % * \qr@k
  % * \ifqr@versionmodules
  % * \qr@numversionmodules
  % * \qr@numdatacodewords
  % * \qr@numremainderbits
  % * \qr@charactercountbits@byte
  % * \qr@charactercountbytes@byte
  % * \qr@numblocks (via \qr@settableix)
  % * \qr@num@eccodewords (via \qr@settableix)
  % * \qr@totaldatacodewords
  %
  % The alignment patterns' square is 7 modules in from each edge.
  % They are spaced "as evenly as possible" with an even number of modules between each row/column,
  % unevenness in division being accommodated by making the first such gap smaller.
  % The formula seems to be
  %    general distance = 2*round((n-13)/(k-1)/2+0.25)
  %                     = 2*floor((n-13)/(k-1)/2+0.75)
  %                     = 2*floor( (2*(n-13)/(k-1)+3) / 4 )
  %                     = (((2*(n-13)) div (k-1) + 3 ) div 4 ) * 2
  %    first distance = leftovers
  % The 0.25 is to accommodate version 32, which is the only time we round down.
  % Otherwise a simple 2*ceiling((n-13)/(k-1)/2) would have sufficed.
  %
  \qr@a = \qr@size\relax
  \advance\qr@a by -13\relax
  \multiply\qr@a by 2\relax
  \qr@b = \qr@k\relax
  \advance \qr@b by -1\relax
  \divide\qr@a by \qr@b\relax
  \advance\qr@a by 3\relax
  \divide\qr@a by 4\relax
  \multiply\qr@a by 2\relax
  \edef\qr@alignment@generalskip{\the\qr@a}%
  %
  %Now set \qr@alignment@firstskip to (\qr@size-13)-(\qr@k-2)*\qr@alignment@generalskip %
  \qr@a = \qr@k\relax
  \advance\qr@a by -2\relax
  \multiply\qr@a by -\qr@alignment@generalskip\relax
  \advance\qr@a by \qr@size\relax
  \advance\qr@a by -13\relax
  \edef\qr@alignment@firstskip{\the\qr@a}%
  %
  %
  %
  % Our \qr@totaldatacodewords bytes of data are broken up as evenly as possible 
  % into \qr@numblocks datablocks; some may be one byte longer than others. 
  % We set \qr@shortblock@size to floor(\qr@totaldatacodewords / \qr@numblocks)
  % and \qr@numlongblocks to mod(\qr@totaldatacodewords , \qr@numblocks).
  \qr@a=\qr@totaldatacodewords\relax
  \divide\qr@a by \qr@numblocks\relax
  \edef\qr@shortblock@size{\the\qr@a}%
  \multiply\qr@a by -\qr@numblocks\relax
  \advance\qr@a by \qr@totaldatacodewords\relax
  \edef\qr@numlongblocks{\the\qr@a}%
  %
  %Set \qr@longblock@size to \qr@shortblock@size+1.
  \qr@a=\qr@shortblock@size\relax
  \advance\qr@a by 1\relax
  \edef\qr@longblock@size{\the\qr@a}%
  %
  %Set \qr@numshortblocks to \qr@numblocks - \qr@numlongblocks
  \qr@b=\qr@numblocks\relax
  \advance\qr@b by -\qr@numlongblocks\relax
  \edef\qr@numshortblocks{\the\qr@b}%
}%

\def\qr@settableix@int(#1,#2){%
  \edef\qr@numblocks{#1}%
  \edef\qr@num@eccodewords{#2}%
}%

\def\qr@settableix{%
\xa\ifcase\qr@level\relax
  %00: Level 'M', medium error correction
  \edef\qr@tempdata{(%
    \ifcase\qr@version\relax
      \relax %There is no version 0.
    \or1,10%
    \or1,16%
    \or1,26%
    \or2,18%
    \or2,24%
    \or4,16%
    \or4,18%
    \or4,22%
    \or5,22%
    \or5,26%
    \or5,30%
    \or8,22%
    \or9,22%
    \or9,24%
    \or10,24%
    \or10,28%
    \or11,28%
    \or13,26%
    \or14,26%
    \or16,26%
    \or17,26%
    \or17,28%
    \or18,28%
    \or20,28%
    \or21,28%
    \or23,28%
    \or25,28%
    \or26,28%
    \or28,28%
    \or29,28%
    \or31,28%
    \or33,28%
    \or35,28%
    \or37,28%
    \or38,28%
    \or40,28%
    \or43,28%
    \or45,28%
    \or47,28%
    \or49,28%
  \fi)}%
\or
  %01: Level 'L', low error correction
  \edef\qr@tempdata{%
  (\ifcase\qr@version\relax
    \relax %There is no version 0.
  \or 1,7%
  \or 1,10%
  \or 1,15%
  \or 1,20%
  \or 1,26%
  \or 2,18%
  \or 2,20%
  \or 2,24%
  \or 2,30%
  \or 4,18%
  \or 4,20%
  \or 4,24%
  \or 4,26%
  \or 4,30%
  \or 6,22%
  \or 6,24%
  \or 6,28%
  \or 6,30%
  \or 7,28%
  \or 8,28%
  \or 8,28%
  \or 9,28%
  \or 9,30%
  \or 10,30%
  \or 12,26%
  \or 12,28%
  \or 12,30%
  \or 13,30%
  \or 14,30%
  \or 15,30%
  \or 16,30%
  \or 17,30%
  \or 18,30%
  \or 19,30%
  \or 19,30%
  \or 20,30%
  \or 21,30%
  \or 22,30%
  \or 24,30%
  \or 25,30%
  \fi)}%
\or
  %10: Level 'H', high error correction
  \edef\qr@tempdata{(%
    \ifcase\qr@version\relax
      \relax %There is no version 0.
    \or1,17%
    \or1,28%
    \or2,22%
    \or4,16%
    \or4,22%
    \or4,28%
    \or5,26%
    \or6,26%
    \or8,24%
    \or8,28%
    \or11,24%
    \or11,28%
    \or16,22%
    \or16,24%
    \or18,24%
    \or16,30%
    \or19,28%
    \or21,28%
    \or25,26%
    \or25,28%
    \or25,30%
    \or34,24%
    \or30,30%
    \or32,30%
    \or35,30%
    \or37,30%
    \or40,30%
    \or42,30%
    \or45,30%
    \or48,30%
    \or51,30%
    \or54,30%
    \or57,30%
    \or60,30%
    \or63,30%
    \or66,30%
    \or70,30%
    \or74,30%
    \or77,30%
    \or81,30%
  \fi)}%
\or
  %11: Level 'Q', quality error correction
  \edef\qr@tempdata{(%
    \ifcase\qr@version\relax
      \relax %There is no version 0.
    \or1,13%
    \or1,22%
    \or2,18%
    \or2,26%
    \or4,18%
    \or4,24%
    \or6,18%
    \or6,22%
    \or8,20%
    \or8,24%
    \or8,28%
    \or10,26%
    \or12,24%
    \or16,20%
    \or12,30%
    \or17,24%
    \or16,28%
    \or18,28%
    \or21,26%
    \or20,30%
    \or23,28%
    \or23,30%
    \or25,30%
    \or27,30%
    \or29,30%
    \or34,28%
    \or34,30%
    \or35,30%
    \or38,30%
    \or40,30%
    \or43,30%
    \or45,30%
    \or48,30%
    \or51,30%
    \or53,30%
    \or56,30%
    \or59,30%
    \or62,30%
    \or65,30%
    \or68,30%
    \fi)}%
\fi
\xa\qr@settableix@int\qr@tempdata
}%
%    \end{macrocode}
% \subsection{More key handling}
%    \begin{macrocode}
\define@key{qr}{version}{\edef\qr@desiredversion{#1}}%
\define@key{qr}{level}{\qr@setlevel{#1}}%
\define@key{qr}{height}{\qr@setheight{#1}}%
\define@boolkey{qr}[qr@]{tight}[true]{}% %This creates \ifqr@tight and initializes it to true.
\define@boolkey{qr}[qr@]{padding}[true]{\ifqr@padding\qr@tightfalse\else\qr@tighttrue\fi}% %Define 'padding' as antonym to 'tight'

\def\@qr@M{M}\def\@qr@z{0}%
\def\@qr@L{L}\def\@qr@i{1}%
\def\@qr@H{H}\def\@qr@ii{2}%
\def\@qr@Q{Q}\def\@qr@iii{3}%
\def\qr@setlevel#1{%
  \edef\qr@level@selected{#1}%
  \ifx\qr@level@selected\@qr@M
    \edef\qr@desiredlevel{0}%
  \fi
  \ifx\qr@level@selected\@qr@L
    \edef\qr@desiredlevel{1}%
  \fi
  \ifx\qr@level@selected\@qr@H
    \edef\qr@desiredlevel{2}%
  \fi
  \ifx\qr@level@selected\@qr@Q
    \edef\qr@desiredlevel{3}%
  \fi
  \ifx\qr@level@selected\@qr@z
    \edef\qr@desiredlevel{0}%
  \fi
  \ifx\qr@level@selected\@qr@i
    \edef\qr@desiredlevel{1}%
  \fi
  \ifx\qr@level@selected\@qr@ii
    \edef\qr@desiredlevel{2}%
  \fi
  \ifx\qr@level@selected\@qr@iii
    \edef\qr@desiredlevel{3}%
  \fi
}%

\def\qr@setheight#1{%
  \setlength{\qr@desiredheight}{#1}%
}%

\newcommand\qrset[1]{%
  \setkeys{qr}{#1}%
}

%SET DEFAULTS
\qrset{version=0, level=0, tight}
%    \end{macrocode}
% \subsection{Main user functions}
% At last we are ready to define the main user functions.
% Some care is needed to ensure
% that the \meta{text to be encoded} is read with the appropriate catcodes,
% and that any escaped special characters are converted to the intended
% characters with category code 12 (other).
%    \begin{macrocode}
\newif\ifqr@starinvoked%
\def\qrcode{\@ifstar\qrcode@star\qrcode@nostar}%
\def\qrcode@star{\qr@starinvokedtrue\qrcode@i}%
\def\qrcode@nostar{\qr@starinvokedfalse\qrcode@i}%

\newcommand\qrcode@i[1][]{%
  \begingroup%
    \ifqr@starinvoked%
      \qr@hyperlinkfalse%
    \fi%
    \setkeys{qr}{#1}%
    \bgroup\qr@verbatimcatcodes\qr@setescapedspecials\qrcode@in}%

\def\qrcode@in#1{\xdef\qr@texttoencode{#1}\egroup\qrcode@int\endgroup}%

\def\qrcode@hyperwrapper@hyperref{\href{\qr@texttoencode}}%
\def\qrcode@hyperwrapper@nohyperref{\relax}%

\AtBeginDocument{%
  \@ifpackageloaded{hyperref}%
    {\global\let\qrcode@hyperwrapper=\qrcode@hyperwrapper@hyperref}%
    {\global\let\qrcode@hyperwrapper=\qrcode@hyperwrapper@nohyperref}%
}%

\def\qrcode@int{%
  \message{^^J^^J<QR code requested for "\qr@texttoencode" in version 
           \qr@desiredversion-\qr@level@char{\qr@desiredlevel}.>^^J}%
  %First, choose the version and level.
  %Recall that \qr@choose@best@version sets \qr@version and \qr@level.
  \xa\qr@choose@best@version\xa{\qr@texttoencode}%
  \qr@setversion{\qr@version}{\qr@level}%
  %
  \ifqr@hyperlink%
    \let\qrcode@wrapper=\qrcode@hyperwrapper%
  \else%
    \let\qrcode@wrapper=\relax%
  \fi%
  %
  %Next, check whether we have already encoded this text at this version 
  %and level.
  \qrcode@wrapper{%
    \xa\ifx\csname qr@savedbinarymatrix@\qr@texttoencode @\qr@version @\qr@level\endcsname
           \relax%
      %This text has not yet been encoded.
      \qrcode@int@new%
    \else
      %This text has already been encoded!
      \ifqr@forget@mode
        %In 'forget' mode, we deliberately recalculate anyway.
        \qrcode@int@new%
      \else
        \qrcode@int@remember%
      \fi
    \fi%
  }%
}%

\def\qrcode@int@new{%
  \qr@createsquareblankmatrix{newqr}{\qr@size}%
  \qr@placefinderpatterns{newqr}%
  \qr@placetimingpatterns{newqr}%
  \qr@placealignmentpatterns{newqr}%
  \qr@placedummyformatpatterns{newqr}%
  \qr@placedummyversionpatterns{newqr}%
  \ifqr@draft@mode
    \message{<Inserting dummy QR code in draft mode for "\qr@texttoencode" in 
              version \qr@version-\qr@level@char{\qr@level}.>^^J}%
    \relax% Draft mode---don't load any data or do any work.  Also don't save!
    \def\qr@format@square{\qr@black}%
    \def\qr@blank{\qr@white}%
    \fboxsep=-\fboxrule%
    \fbox{\qr@printmatrix{newqr}}%
  \else
    \message{<Calculating QR code for "\qr@texttoencode" in 
              version \qr@version-\qr@level@char{\qr@level}.>^^J}%
    \xa\qr@encode@binary\xa{\qr@texttoencode}%
    \qr@splitcodetextintoblocks
    \qr@createerrorblocks
    \qr@interleave
    \message{<Writing data...}%
    \qr@writedata@hex{newqr}{\qr@interleaved@text}%
    \message{done.>^^J}%
    \qr@writeremainderbits{newqr}%
    \qr@chooseandapplybestmask{newqr}%
    \qr@decimaltobinary[2]{\qr@level@binary}{\qr@level}%
    \qr@decimaltobinary[3]{\qr@mask@binary}{\qr@mask@selected}%
    \edef\qr@formatstring{\qr@level@binary\qr@mask@binary}%
    \message{<Encoding and writing format string...}%
    \xa\qr@encodeandmaskformat\xa{\qr@formatstring}%
    \qr@writeformatstring{newqr}{\qr@format@bitstring}%
    \message{done.>^^J}%
    \message{<Encoding and writing version information...}%
    \qr@decimaltobinary[6]{\qr@version@binary}{\qr@version}%
    \qr@Golaycode{\qr@version@binary}%
    \qr@writeversionstring{newqr}{\qr@Golayresult}%
    \message{done.>^^J}%
    \message{<Saving QR code to memory...}%
    \qr@matrixtobinary{newqr}%
    %
    %Now save the binary version into TeX's memory for later use in this document.
    \xa\xdef\csname qr@savedbinarymatrix@\qr@texttoencode @\qr@version @\qr@level\endcsname 
            {\qr@binarymatrix@result}%
    \message{done.>^^J}%
    %
    %Also save the binary version into the aux file, for use in later runs.
    \message{<Writing QR code to aux file...}%
    \qr@writebinarymatrixtoauxfile{\qr@binarymatrix@result}%
    \message{done.>^^J}%
    \message{<Printing matrix...}%
    \qr@printmatrix{newqr}%
    \message{done.>^^J}%
  \fi
  \message{^^J}%
}%
\def\qrcode@int@remember{%
  %This text has already been encoded,
  %so we just copy it from the saved binary string.
  \message{<Copying the QR code for "\qr@texttoencode" in version \qr@version-\qr@level@char{\qr@level} as previously calculated.>^^J}%
  \xa\qr@printsavedbinarymatrix\xa{\csname qr@savedbinarymatrix@\qr@texttoencode @\qr@version @\qr@level\endcsname}%
  %
  % Now this still might need to be written to the aux file.
  % 
  \xa\ifx\csname qr@savedflag@\qr@texttoencode @\qr@version @\qr@level\endcsname\@qr@TRUE
    %Okay, this has already been written to aux file.
    %Do nothing.
    \relax%
  \else%
    %This has NOT been written to the aux file yet.
    %We need to do so now.
    \xa\qr@writebinarymatrixtoauxfile\xa{\csname qr@savedbinarymatrix@\qr@texttoencode @\qr@version @\qr@level\endcsname}%
  \fi%
}%

\def\qr@matrixtobinary#1{%
  \def\qr@binarymatrix@result{}%
  \bgroup
    \def\qr@black{1}%
    \def\qr@white{0}%
    \def\qr@blank{0}%
    \def\qr@black@fixed{1}%
    \def\qr@white@fixed{0}%
    \def\qr@black@format{1}%
    \def\qr@white@format{0}%
    %      
    \qr@for \i = 1 to \qr@size by 1%
      {\qr@for \j = 1 to \qr@size by 1%
        {\edef\qr@theentry{\qr@matrixentry{#1}{\the\i}{\the\j}}%
         \xa\g@addto@macro\xa\qr@binarymatrix@result\xa{\qr@theentry}%
        }%
      }%
  \egroup%
}%

\def\qr@sanitize@output#1{%
  %Read through ASCII text '#1' and escape backslashes and braces
  \def\qr@sanitized@result{}%
  \edef\qr@argument{(#1\relax\relax\relax)}%
  \xa\qr@sanitize@output@int\qr@argument%
}

\def\qr@sanitize@output@int(#1#2){%
  % #1 = first character
  % #2 = rest of output, including terminator
  \edef\qr@testi{#1}%
  \ifx\qr@testi\qr@relax
    % Done.
    \let\qr@next=\relax
  \else
    \ifx\qr@testi\qr@otherrightbrace
      \edef\qr@sanitized@result{\qr@sanitized@result\qr@otherbackslash}%
      \else\ifx\qr@testi\qr@otherleftbrace
        \edef\qr@sanitized@result{\qr@sanitized@result\qr@otherbackslash}%
        \else\ifx\qr@testi\qr@otherbackslash
          \edef\qr@sanitized@result{\qr@sanitized@result\qr@otherbackslash}%
        \fi
      \fi
    \fi
    \edef\qr@sanitized@result{\qr@sanitized@result#1}%
    \def\qr@next{\qr@sanitize@output@int(#2)}%
  \fi
  \qr@next
}

\def\@qr@TRUE{TRUE}%
\def\qr@writebinarymatrixtoauxfile#1{%
  \qr@sanitize@output{\qr@texttoencode}%
  \edef\qr@theargument{{\qr@sanitized@result}{\qr@version}{\qr@level}{#1}}%
  \xa\write\xa\@auxout\xa{\xa\string\xa\qr@savematrix\qr@theargument}%
  %
  % Now set a flag, so we don't write this again.
  \xa\gdef\csname qr@savedflag@\qr@texttoencode @\qr@version @\qr@level\endcsname{TRUE}%
}%

\gdef\qr@dummyqrsavedefinition{}%
\begingroup
  \catcode`\#=12\relax
  \catcode`\<=1\relax
  \catcode`\{=12\relax
  \catcode`\>=2\relax
  \catcode`\}=12\relax
  \catcode`\|=0\relax
  \catcode`\\=12|relax
  |gdef|qr@dummyqrsavedefinition<%
    \ifx\qr@savematrix\@undefined%
      \def\qr@savematrix{\begingroup\let\do\@makeother\dospecials\catcode`\{=1\catcode`\}=2\relax
                         \qr@savematrix@int}%
      \def\qr@savematrix@int#1#2#3#4{\endgroup}%
    \fi%
  >
|endgroup

\edef\qr@argument{(\qr@dummyqrsavedefinition)}%
\xa\write\xa\@auxout\xa{\qr@dummyqrsavedefinition}%

\def\qr@savematrix{\bgroup\qr@verbatimcatcodes\qr@setescapedspecials\qr@savematrix@int}%

\def\qr@savematrix@int#1{\xdef\qr@savedmatrix@name{#1}\egroup\qr@savematrix@int@int}%

\def\qr@savematrix@int@int#1#2#3{%
  % \qr@savedmatrix@name = encoded text
  % #1 = version
  % #2 = level
  % #3 = binary text
  \def\ds{<Reading QR code for "\qr@savedmatrix@name" at level #1-\qr@level@char{#2} from aux file.>^^J}\xa\message\xa{\ds}%
  {\let\%=\qr@otherpercent
   \xa\gdef\csname qr@savedbinarymatrix@\qr@savedmatrix@name @#1@#2\endcsname{#3}%
  }%
}%
%    \end{macrocode}
%
% \Finale
\endinput