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-rw-r--r--Master/texmf-dist/doc/latex/qrcode/README49
-rw-r--r--Master/texmf-dist/doc/latex/qrcode/qrcode.pdfbin0 -> 250696 bytes
-rw-r--r--Master/texmf-dist/source/latex/qrcode/qrcode.dtx3466
-rw-r--r--Master/texmf-dist/source/latex/qrcode/qrcode.ins57
-rw-r--r--Master/texmf-dist/tex/latex/qrcode/qrcode.sty3023
-rwxr-xr-xMaster/tlpkg/bin/tlpkg-ctan-check2
-rw-r--r--Master/tlpkg/tlpsrc/collection-pictures.tlpsrc1
-rw-r--r--Master/tlpkg/tlpsrc/qrcode.tlpsrc0
8 files changed, 6597 insertions, 1 deletions
diff --git a/Master/texmf-dist/doc/latex/qrcode/README b/Master/texmf-dist/doc/latex/qrcode/README
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@@ -0,0 +1,49 @@
+==============================================================================
+
+The `qrcode' package v1.0
+Copyright (C) 2014 Anders Hendrickson (anders.hendrickson@snc.edu)
+
+This package generates Quick Response (QR) codes in
+LaTeX without the need for pstricks or any other graphics
+packages.
+
+Changes:
+- 2014/09/26 Initial version
+
+==============================================================================
+
+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 consists of the files:
+README (this file)
+qrcode.dtx
+qrcode.ins
+ and the derived file:
+qrcode.sty
+
+ The distribution consists of the files:
+README (this file)
+qrcode.dtx
+qrcode.ins
+qrcode.pdf (the user manual)
+
+-----------------------------------------------------------------
+
+ To install the package:
+- run: latex qrcode.ins (which will generate qrcode.sty)
+- Move qrcode.sty to a location where LaTeX will find it (typically
+ in a local texmf tree at tex/latex/qrcode) and refresh the
+ file database. See the FAQ on CTAN at help/uk-tex-faq or
+ http://www.tug.ac.uk/faq for more information on this.
+ To process the user manual
+- run: pdflatex qrcode.dtx
+- run: pdflatex qrcode.dtx
diff --git a/Master/texmf-dist/doc/latex/qrcode/qrcode.pdf b/Master/texmf-dist/doc/latex/qrcode/qrcode.pdf
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index 00000000000..c366b880e46
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/qrcode/qrcode.pdf
Binary files differ
diff --git a/Master/texmf-dist/source/latex/qrcode/qrcode.dtx b/Master/texmf-dist/source/latex/qrcode/qrcode.dtx
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index 00000000000..b7a8afa4f79
--- /dev/null
+++ b/Master/texmf-dist/source/latex/qrcode/qrcode.dtx
@@ -0,0 +1,3466 @@
+% \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>
+ [2014/09/26 v1.0 QR code generation]
+%</package>
+%
+%<*driver>
+\documentclass{ltxdoc}
+\usepackage{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}
+%
+% \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[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{September 26, 2014}
+%
+% \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[height=0.5in]{http://www.ctan.org}| produces
+% \begin{center}
+% \qrcode[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{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|.
+%
+%
+% \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}
+% 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.
+% \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}%
+
+%%EXECUTION OF OPTIONS
+\qr@draft@modefalse
+\qr@forget@modefalse
+
+\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\@relax{\relax}%
+
+%Manipulating macros
+\def\preface@macro#1#2{%
+ % #1 = macro name
+ % #2 = text to add to front of macro
+ \def\tempb{#2}%
+ \xa\xa\xa\def\xa\xa\xa#1\xa\xa\xa{\xa\tempb #1}%
+}%
+
+\def\g@preface@macro#1#2{%
+ % #1 = macro to be appended to
+ % #2 = code to add
+ \edef\codeA{#2}%
+ \xa\xa\xa\gdef\xa\xa\xa#1\xa\xa\xa{\xa\codeA#1}%
+}
+
+
+\def\qr@getstringlength#1{%
+ \bgroup
+ \qr@a=0%
+ \xdef\thestring{#1}%
+ \xa\qr@stringlength@recursive\xa(\thestring\relax\relax)%
+ \xdef\qr@stringlength{\the\qr@a}%
+ \egroup
+}%
+
+\def\qr@stringlength@recursive(#1#2){%
+ \def\testi{#1}%
+ \ifx\testi\@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%
+ {\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\newdigit{\the\qr@b}%
+ \else
+ \edef\newdigit{\csname qr@hexchar@\the\qr@b\endcsname}%
+ \fi
+ \edef\qr@argument{{\noexpand\qr@base@result}{\newdigit}}%
+ \xa\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\test@i{#1}%
+ \ifx\test@i\@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\test@i{#1}%
+ \ifx\test@i\@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\test@i{#1}%
+ \ifx\test@i\@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\test@@i{#1}%
+ \ifx\test@@i\@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\testii{#2}%
+ \ifx\testii\@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{\}}%
+\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{$}}%
+
+\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}%
+
+\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%
+}%
+% \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}{\@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\@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\theargument{(\qr@binarystring)}%
+ \xa\qr@printsavedbinarymatrix@int\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 \endingcol to n-8.
+ \qr@a=\qr@size\relax%
+ \advance\qr@a by -8\relax%
+ \edef\endingcol{\the\qr@a}%
+ \qr@for \j = 9 to \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}{\@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\testii{#2}%
+ \ifx\testii\@relax%
+ % #2 is \relax, so there is nothing more to write.
+ \relax
+ \let\go=\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\go\xa{\xa\qr@writedata@hex@recursive\qr@argument}% %Call self to write the next bit.
+ \fi
+ \go
+}%
+
+\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\@@blank{\@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\@@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\@relax
+ % \qr@datatowrite is just `\relax', so we're done.
+ \let\nexttoken=\relax
+ \relax
+ \else
+ % Write some more!
+ \def\nexttoken{\qr@writedata@recursive{#1}}%
+ \fi
+ \nexttoken
+}%
+
+\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\maskselection{#1}%
+ \xa\ifcase\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\@@white{\@white}%
+\def\@@black{\qr@black}%
+
+\def\qr@checkifcurrentcellcontainsdata#1{%
+ % #1 = name of matrix
+ \qr@currentcellcontainsdatafalse
+ \xa\ifx\csname #1@\the\i @\the\j\endcsname\@@white
+ \qr@currentcellcontainsdatatrue
+ \fi
+ \xa\ifx\csname #1@\the\i @\the\j\endcsname\@@black
+ \qr@currentcellcontainsdatatrue
+ \fi
+}%
+
+\def\qr@flipped@black{\qr@black}%
+\def\qr@flipped@white{\@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\@@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\currentbestpenalty{\qr@penalty}%
+ \message{penalty is \qr@penalty>^^J}%
+ \gdef\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<\currentbestpenalty\relax
+ %We found a better mask.
+ \xdef\currentbestmask{\the\i}%
+ \qr@createduplicatematrix{#1}{currentmasked}%
+ \xdef\currentbestpenalty{\qr@penalty}%
+ \fi
+ }%
+ \xdef\qr@mask@selected{\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\@fiveones{11111}%
+\def\@fivezeros{11111}%
+\def\@twoones{11}%
+\def\@twozeros{00}%
+\def\@finderA{00001011101}%
+\def\@finderB{10111010000}%
+\def\@finderB@three{1011101000}%
+\def\@finderB@two{101110100}%
+\def\@finderB@one{10111010}%
+\def\@finderB@zero{1011101}%
+\newif\ifstringoffive
+\def\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\@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\@blank{0}% These would be any bits at the end.
+ %
+ \setcounter{totalones}{0}%
+ \qr@for \i=1 to \qr@size by 1%
+ {\def\lastfive{z}% %The z is a dummy, that will be removed before any testing.
+ \stringoffivefalse
+ \def\lasttwo@thisrow{z}% %The z is a dummy.
+ \def\lasttwo@nextrow{z}% %The z is a dummy.
+ \def\lastnine{z0000}% %The 0000 stands for the white space to the left. The z is a dummy.
+ \def\ignore@finderB@at{0}%
+ \qr@for \j=1 to \qr@size by 1%
+ {\edef\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\lastfive\xa{\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.
+ \removefirsttoken\lastfive%
+ \ifx\lastfive\@fiveones%
+ \ifstringoffive%
+ %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\stringoffivetrue
+ \fi
+ \else
+ \ifx\lastfive\@fivezeros%
+ \ifstringoffive
+ %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\stringoffivetrue
+ \fi
+ \else
+ %This is not a string of five 1's or five 0's.
+ \global\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\lasttwo@thisrow\xa{\newbit}%
+ %Compute \iplusone
+ \qr@a=\i\relax%
+ \advance\qr@a by 1%
+ \edef\iplusone{\the\qr@a}%
+ %
+ \edef\nextrowbit{\qr@matrixentry{#1}{\iplusone}{\the\j}}%
+ \xa\g@addto@macro\xa\lasttwo@nextrow\xa{\nextrowbit}%
+ \ifnum\j<2\relax%
+ %Still in the first column; no check.
+ \else
+ %Second column or later. Remove the old bits, and then test.
+ \removefirsttoken\lasttwo@thisrow
+ \removefirsttoken\lasttwo@nextrow
+ \ifx\lasttwo@thisrow\@twoones
+ \ifx\lasttwo@nextrow\@twoones
+ \addtocounter{penaltyii}{\qr@Nii}%
+ \fi
+ \else
+ \ifx\lasttwo@thisrow\@twozeros
+ \ifx\lasttwo@nextrow\@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\lastnine\xa{\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.
+ \removefirsttoken\lastnine
+ \xa\ifnum\qr@size=\j\relax%
+ % Last column. Any of the following should count:
+ % 1011101 (\@finderB@zero)
+ % 10111010 (\@finderB@one)
+ % 101110100 (\@finderB@two)
+ % 1011101000 (\@finderB@three)
+ % 10111010000 (\@finderB)
+ \ifx\lastnine\@finderB
+ \addpenaltyiii
+ \else
+ \removefirsttoken\lastnine
+ \ifx\lastnine\@finderB@three
+ \addpenaltyiii
+ \else
+ \removefirsttoken\lastnine
+ \ifx\lastnine\@finderB@two
+ \addpenaltyiii
+ \else
+ \removefirsttoken\lastnine
+ \ifx\lastnine\@finderB@one
+ \addpenaltyiii
+ \else
+ \removefirsttoken\lastnine
+ \ifx\lastnine\@finderB@zero
+ \addpenaltyiii
+ \fi
+ \fi
+ \fi
+ \fi
+ \fi
+ \else
+ \ifx\lastnine\@finderA% %Matches 0000 1011101
+ \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 \ignore@finderB@at to \j+4.
+ \qr@a=\j\relax%
+ \advance\qr@a by 4%
+ \xdef\ignore@finderB@at{\the\qr@a}%
+ \else
+ \ifx\lastfive\@finderB% %Matches 1011101 0000.
+ \xa\ifnum\ignore@finderB@at=\j\relax
+ %This pattern was *not* counted already earlier.
+ \addpenaltyiii
+ \fi
+ \fi
+ \fi
+ \fi
+ \fi
+ %
+ %COUNT 1's FOR PENALTY 4
+ \xa\ifnum\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\lastfive{z}% %The z is a dummy, that will be removed before any testing.
+ \stringoffivefalse
+ \def\lastnine{z0000}% %The 0000 stands for the white space to the left. The z is a dummy.
+ \def\ignore@finderB@at{0}%
+ \qr@for \i=1 to \qr@size by 1%
+ {\edef\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\lastfive\xa{\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.
+ \removefirsttoken\lastfive%
+ \ifx\lastfive\@fiveones%
+ \ifstringoffive%
+ %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\stringoffivetrue
+ \fi
+ \else
+ \ifx\lastfive\@fivezeros%
+ \ifstringoffive
+ %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\stringoffivetrue
+ \fi
+ \else
+ %This is not a string of five 1's or five 0's.
+ \global\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\lastnine\xa{\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.
+ \removefirsttoken\lastnine
+ \xa\ifnum\qr@size=\i\relax%
+ % Last column. Any of the following should count:
+ % 1011101 (\@finderB@zero)
+ % 10111010 (\@finderB@one)
+ % 101110100 (\@finderB@two)
+ % 1011101000 (\@finderB@three)
+ % 10111010000 (\@finderB)
+ \ifx\lastnine\@finderB
+ \addpenaltyiii
+ \else
+ \removefirsttoken\lastnine
+ \ifx\lastnine\@finderB@three
+ \addpenaltyiii
+ \else
+ \removefirsttoken\lastnine
+ \ifx\lastnine\@finderB@two
+ \addpenaltyiii
+ \else
+ \removefirsttoken\lastnine
+ \ifx\lastnine\@finderB@one
+ \addpenaltyiii
+ \else
+ \removefirsttoken\lastnine
+ \ifx\lastnine\@finderB@zero
+ \addpenaltyiii
+ \fi
+ \fi
+ \fi
+ \fi
+ \fi
+ \else
+ \ifx\lastnine\@finderA% %Matches 0000 1011101
+ \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 \ignore@finderB@at to \i+4.
+ \qr@a=\i\relax%
+ \advance\qr@a by 4%
+ \xdef\ignore@finderB@at{\the\qr@a}%
+ \else
+ \ifx\lastfive\@finderB% %Matches 1011101 0000.
+ \xa\ifnum\ignore@finderB@at=\i\relax
+ %This pattern was *not* counted already earlier.
+ \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\removefirsttoken#1{%
+ %Removes the first token from the macro named in #1.
+ \edef\qr@argument{(#1)}%
+ \xa\removefirsttoken@int\qr@argument%
+ \xdef#1{\removefirsttoken@result}%
+}%
+\def\removefirsttoken@int(#1#2){%
+ \def\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)
+ \def\formattowrite{#3}%
+ \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\nexttoken=\relax
+ \else
+ \def\nexttoken{\qr@writeformatA@recursive{#1}(#3)}%
+ \fi
+ \nexttoken
+}%
+
+\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)
+ \def\formattowrite{#3}%
+ \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\nexttoken=\relax
+ \else
+ \def\nexttoken{\qr@writeformatB@recursive{#1}(#3)}%
+ \fi
+ \nexttoken
+}%
+
+\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.
+ %
+ \def\versiontowrite{#3}%
+ %
+ %Set \topline equal to n-10.
+ \qr@a=\qr@size\relax%
+ \advance\qr@a by -10\relax%
+ \edef\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\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\nexttoken=\relax
+ \else
+ \def\nexttoken{\qr@writeversion@recursive{#1}(#3)}%
+ \fi
+ \nexttoken
+}%
+% \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\plaintext{#1}%
+ %
+ %First, the mode indicator.
+ \def\qr@codetext{4}% %This means `binary'
+ %
+ %Next, the character count.
+ \qr@getstringlength{\plaintext}%
+ %Set \charactercountlengthinhex to \qr@charactercountbits@byte/4%
+ \qr@a=\qr@charactercountbits@byte\relax%
+ \divide \qr@a by 4\relax%
+ \edef\charactercountlengthinhex{\the\qr@a}%
+ \qr@decimaltohex[\charactercountlengthinhex]{\charactercount}{\qr@stringlength}%
+ \xa\g@addto@macro\xa\qr@codetext\xa{\charactercount}%
+ %
+ %Now comes the actual data.
+ \edef\qr@argument{(,\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 - 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\testii{#2}%
+ \ifx\testii\@relax%
+ % All done!
+ \g@addto@macro\qr@codetext{#1}%
+ \else%
+ % Another character to translate.
+ \edef\asciicode{\number`#2}%
+ \qr@decimaltohex[2]{\newhexcodes}{\asciicode}%
+ \edef\qr@argument{(#1\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\preface@macro#1#2{%
+ % #1 = macro name
+ % #2 = text to add to front of macro
+ \def\tempb{#2}%
+ \xa\xa\xa\gdef\xa\xa\xa#1\xa\xa\xa{\xa\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\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(\xorresult)}%
+ \fi
+ \else
+ \xa\def\xa\qr@numerator\xa{\qr@stripleadingzero(#1)}%
+ \ifx\qr@numerator\@qr@empty
+ \qr@divisiondonetrue
+ \def\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\testii{#2}%
+ \def\testiv{#4}%
+ \ifx\testii\@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\testiv\@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\xorresult{}%
+ \fi
+ \else
+ % There is still a bit to manipulate in #2.
+ % Check whether #4 contains anything.
+ \ifx\testiv\@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\xorresult{#1}%
+}%
+
+\newif\ifqr@divisiondone
+\def\dodivision#1#2{%
+ \qr@divisiondonefalse
+ \dodivision@recursive{#1}{#2}%
+}%
+
+\def\BCHcode#1{%
+ \edef\formatinfo{#1}%
+ \def\formatinfopadded{\formatinfo 0000000000}%
+ \def\qr@divisor{10100110111}%
+ \qr@divisiondonefalse
+ \qr@polynomialdivide{\formatinfopadded}{\qr@divisor}%
+ %
+ \qr@getstringlength{\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%
+ {\preface@macro{\theremainder}{0}%
+ \xdef\theremainder{\theremainder}%
+ }%
+ \edef\BCHresult{\formatinfo\theremainder}%
+}%
+
+\def\qr@formatmask{101010000010010}%
+
+\def\qr@encodeandmaskformat#1{%
+ \BCHcode{#1}%
+ \qr@xorbitstrings{\BCHresult}{\qr@formatmask}%
+ \edef\qr@format@bitstring{\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{\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%
+ {\preface@macro{\theremainder}{0}%
+ \xdef\theremainder{\theremainder}%
+ }%
+ \edef\Golayresult{\qr@versioninfo\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\testi{#1}%
+ \ifx\testi\@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]{\summandA}{#1}%
+ \qr@hextobinary[4]{\summandB}{#2}%
+ \qr@xorbitstring{\F@result}{\summandA}{\summandB}%
+ \qr@binarytohex[1]{\F@result}{\F@result}%
+}%
+
+\def\canceltwos#1{%
+ \edef\qr@argument{(#1\relax\relax)}%
+ \xa\canceltwos@int\qr@argument%
+}%
+
+\def\canceltwos@int(#1#2){%
+ \xa\canceltwos@recursion(,#1#2)%
+}%
+
+\def\canceltwos@recursion(#1,#2#3){%
+ \def\testii{#2}%
+ \ifx\testii\@relax
+ %Cancelling complete.
+ \striptworelaxes(#1#2#3)%
+ %Now \F@result contains the answer.
+ \else
+ \relax
+ \ifnum#2=2\relax
+ \canceltwos@recursion(#10,#3)%
+ \else
+ \canceltwos@recursion(#1#2,#3)%
+ \fi
+ \fi
+}%
+
+\def\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\testii{#2}%
+ \def\testiv{#4}%
+ \ifx\testii\@relax
+ %The entire string has been processed.
+ \gdef\F@result{#1}%
+ \else
+ \ifx\testiv\@relax
+ %The second string is over.
+ \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\poweroftwo{1}%
+\qr@for \i = 1 to 254 by 1%
+ {\stepcounter{qr@i}%
+ \qr@a=\poweroftwo\relax
+ \multiply\qr@a by 2\relax
+ \edef\poweroftwo{\the\qr@a}%
+ %\show\poweroftwo
+ \qr@decimaltohex[2]{\poweroftwo@hex}{\poweroftwo}%
+ \xa\ifnum\poweroftwo>255\relax
+ %We need to bitwise add the polynomial represented by 100011101, i.e. 0x11d.
+ \F@addstrings{\poweroftwo@hex}{11d}% %Now it should start with 0.
+ \xa\F@stripleadingzero\xa(\F@result)% %Now it should be two hex digits.
+ \edef\poweroftwo@hex{\F@result}% %Save the hex version.
+ \qr@hextodecimal{\poweroftwo}{\F@result}%
+ \fi
+ \xdef\poweroftwo{\poweroftwo}%
+ \xa\xdef\csname F@twotothe@\theqr@i\endcsname{\poweroftwo@hex}%
+ \xa\xdef\csname F@logtwo@\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\@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\argA{#1}%
+ \edef\argB{#2}%
+ \ifx\argA\@zerozero
+ \def\F@result{00}%
+ \else
+ \ifx\argB\@zerozero
+ \def\F@result{00}%
+ \else
+ \xa\F@logtwo\xa{\argA}%
+ \edef\logA{\F@result}%
+ \xa\F@logtwo\xa{\argB}%
+ \edef\logB{\F@result}%
+ \xa\qr@a\xa=\logA\relax% \qr@a = \logA
+ \xa\advance\xa\qr@a\logB\relax% \advance \qr@a by \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\argA{#1}%
+ \edef\argB{#2}%
+ \ifx\argA\@zerozero
+ \def\F@result{00}%
+ \else
+ \ifx\argB\@zerozero
+ \def\F@result{00}%
+ \else
+ \xa\F@logtwo\xa{\argA}%
+ \edef\logA{\F@result}%
+ \xa\F@logtwo\xa{\argB}%
+ \edef\logB{\F@result}%
+ \xa\qr@a\xa=\logA\relax% \qr@a = \logA
+ \xa\advance\xa\qr@a\logB\relax% \advance \qr@a by \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\testi{#1}%
+ \ifx\testi\@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\@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\denominator{#2}%
+ \qr@getstringlength\FX@numerator%
+ \setcounter{qr@divisionsremaining}{\qr@stringlength}%
+ \qr@getstringlength\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{\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\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\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\testii{#2}%
+ \def\testv{#5}%
+ \ifx\testii\@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\testv\@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\testv\@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\summandA{\FX@generatorpolynomial 00}% This is f(x) * x
+ \edef\summandB{00\FX@generatorpolynomial}% This is f(x), with a 0x^{i+1} in front.
+ \F@twotothe{\theqr@i}%
+ \edef\theconstant{\F@result}%
+ \FX@subtractphase{\summandA}{\summandB}{\theconstant}%
+ %This calculates \summandA + \theconstant * \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\numerrorbytes{#2}%
+ \xa\FX@creategeneratorpolynomial\xa{\numerrorbytes}%
+ \edef\FX@numerator{#1}%
+ \qr@for \i = 1 to \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{\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 \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\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\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\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\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\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 false.
+\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}
+\newcommand\qrcode[1][]{%
+ \begingroup%
+ \setkeys{qr}{#1}%
+ \bgroup\qr@verbatimcatcodes\qr@setescapedspecials\qrcode@i}%
+
+\def\qrcode@i#1{\xdef\qr@texttoencode{#1}\egroup\qrcode@int\endgroup}%
+
+\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}%
+ %
+ %Next, check whether we have already encoded this text at this version
+ %and level.
+ \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\@blank{\@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]{\level@binary}{\qr@level}%
+ \qr@decimaltobinary[3]{\mask@binary}{\qr@mask@selected}%
+ \edef\formatstring{\level@binary\mask@binary}%
+ \message{<Encoding and writing format string...}%
+ \xa\qr@encodeandmaskformat\xa{\formatstring}%
+ \qr@writeformatstring{newqr}{\qr@format@bitstring}%
+ \message{done.>^^J}%
+ \message{<Encoding and writing version information...}%
+ \qr@decimaltobinary[6]{\version@binary}{\qr@version}%
+ \qr@Golaycode{\version@binary}%
+ \qr@writeversionstring{newqr}{\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\@white{0}%
+ \def\@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\theentry{\qr@matrixentry{#1}{\the\i}{\the\j}}%
+ \xa\g@addto@macro\xa\qr@binarymatrix@result\xa{\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\testi{#1}%
+ \ifx\testi\@relax
+ % Done.
+ \let\qr@next=\relax
+ \else
+ \ifx\testi\qr@otherrightbrace
+ \edef\qr@sanitized@result{\qr@sanitized@result\qr@otherbackslash}%
+ \else\ifx\testi\qr@otherleftbrace
+ \edef\qr@sanitized@result{\qr@sanitized@result\qr@otherbackslash}%
+ \else\ifx\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\theargument{{\qr@sanitized@result}{\qr@version}{\qr@level}{#1}}%
+ \xa\write\xa\@auxout\xa{\xa\string\xa\qr@savematrix\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\dummyqrsavedefinition{}%
+\begingroup
+ \catcode`\#=12\relax
+ \catcode`\<=1\relax
+ \catcode`\{=12\relax
+ \catcode`\>=2\relax
+ \catcode`\}=12\relax
+ \catcode`\|=0\relax
+ \catcode`\\=12|relax
+ |gdef|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{(\dummyqrsavedefinition)}%
+\xa\write\xa\@auxout\xa{\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
diff --git a/Master/texmf-dist/source/latex/qrcode/qrcode.ins b/Master/texmf-dist/source/latex/qrcode/qrcode.ins
new file mode 100644
index 00000000000..b50f77ae891
--- /dev/null
+++ b/Master/texmf-dist/source/latex/qrcode/qrcode.ins
@@ -0,0 +1,57 @@
+%% qrcode.ins
+%% Copyright 2014 by Anders O.F. Hendrickson
+%%
+%% 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.
+
+\input docstrip.tex
+\keepsilent
+
+\usedir{tex/latex/qrcode}
+
+\preamble
+
+This is a generated file.
+
+Copyright (C) 2014 by Anders Hendrickson <ahendric@cord.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.
+
+\endpreamble
+
+\generate{\file{qrcode.sty}{\from{qrcode.dtx}{package}}}
+
+\obeyspaces
+\Msg{*************************************************************}
+\Msg{* *}
+\Msg{* To finish the installation you have to move the following *}
+\Msg{* file into a directory searched by TeX: *}
+\Msg{* *}
+\Msg{* qrcode.sty *}
+\Msg{* *}
+\Msg{* To produce the documentation run the file qrcode.dtx *}
+\Msg{* through LaTeX. *}
+\Msg{* *}
+\Msg{* Happy TeXing! *}
+\Msg{* *}
+\Msg{*************************************************************}
+
+\endbatchfile
diff --git a/Master/texmf-dist/tex/latex/qrcode/qrcode.sty b/Master/texmf-dist/tex/latex/qrcode/qrcode.sty
new file mode 100644
index 00000000000..71504c64504
--- /dev/null
+++ b/Master/texmf-dist/tex/latex/qrcode/qrcode.sty
@@ -0,0 +1,3023 @@
+%%
+%% This is file `qrcode.sty',
+%% generated with the docstrip utility.
+%%
+%% The original source files were:
+%%
+%% qrcode.dtx (with options: `package')
+%%
+%% This is a generated file.
+%%
+%% Copyright (C) 2014 by Anders Hendrickson <ahendric@cord.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.
+%%
+\NeedsTeXFormat{LaTeX2e}[1999/12/01]
+\ProvidesPackage{qrcode}
+ [2014/09/26 v1.0 QR code generation]
+%%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}%
+
+%%EXECUTION OF OPTIONS
+\qr@draft@modefalse
+\qr@forget@modefalse
+
+\ProcessOptionsX<qr>
+
+\newcounter{qr@i}%
+\newcounter{qr@j}%
+\newcount\qr@a
+\newcount\qr@b
+\newcount\qr@c
+
+\let\xa=\expandafter
+
+\newlinechar=`\^^J
+
+\def\@relax{\relax}%
+
+\def\preface@macro#1#2{%
+ % #1 = macro name
+ % #2 = text to add to front of macro
+ \def\tempb{#2}%
+ \xa\xa\xa\def\xa\xa\xa#1\xa\xa\xa{\xa\tempb #1}%
+}%
+
+\def\g@preface@macro#1#2{%
+ % #1 = macro to be appended to
+ % #2 = code to add
+ \edef\codeA{#2}%
+ \xa\xa\xa\gdef\xa\xa\xa#1\xa\xa\xa{\xa\codeA#1}%
+}
+
+\def\qr@getstringlength#1{%
+ \bgroup
+ \qr@a=0%
+ \xdef\thestring{#1}%
+ \xa\qr@stringlength@recursive\xa(\thestring\relax\relax)%
+ \xdef\qr@stringlength{\the\qr@a}%
+ \egroup
+}%
+
+\def\qr@stringlength@recursive(#1#2){%
+ \def\testi{#1}%
+ \ifx\testi\@relax
+ %we are done.
+ \let\qr@next=\relax%
+ \else
+ \advance\qr@a by 1%
+ \def\qr@next{\qr@stringlength@recursive(#2)}%
+ \fi
+ \qr@next
+}%
+\newcount\qr@for@depth%
+\newcount\qr@for@maxdepth%
+\qr@for@depth=0%
+\qr@for@maxdepth=0%
+\newcount\qr@for@start%
+\newcount\qr@for@end%
+\newcount\qr@for@step%
+\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
+\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
+ \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
+}%
+\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%
+ {\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\newdigit{\the\qr@b}%
+ \else
+ \edef\newdigit{\csname qr@hexchar@\the\qr@b\endcsname}%
+ \fi
+ \edef\qr@argument{{\noexpand\qr@base@result}{\newdigit}}%
+ \xa\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\test@i{#1}%
+ \ifx\test@i\@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\test@i{#1}%
+ \ifx\test@i\@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\test@i{#1}%
+ \ifx\test@i\@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\test@@i{#1}%
+ \ifx\test@@i\@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\testii{#2}%
+ \ifx\testii\@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%
+}
+{\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{\}}%
+\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{$}}%
+
+\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}%
+
+\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%
+}%
+\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}{\@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\@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\theargument{(\qr@binarystring)}%
+ \xa\qr@printsavedbinarymatrix@int\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 \endingcol to n-8.
+ \qr@a=\qr@size\relax%
+ \advance\qr@a by -8\relax%
+ \edef\endingcol{\the\qr@a}%
+ \qr@for \j = 9 to \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}{\@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\testii{#2}%
+ \ifx\testii\@relax%
+ % #2 is \relax, so there is nothing more to write.
+ \relax
+ \let\go=\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\go\xa{\xa\qr@writedata@hex@recursive\qr@argument}% %Call self to write the next bit.
+ \fi
+ \go
+}%
+
+\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\@@blank{\@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\@@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\@relax
+ % \qr@datatowrite is just `\relax', so we're done.
+ \let\nexttoken=\relax
+ \relax
+ \else
+ % Write some more!
+ \def\nexttoken{\qr@writedata@recursive{#1}}%
+ \fi
+ \nexttoken
+}%
+
+\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\maskselection{#1}%
+ \xa\ifcase\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\@@white{\@white}%
+\def\@@black{\qr@black}%
+
+\def\qr@checkifcurrentcellcontainsdata#1{%
+ % #1 = name of matrix
+ \qr@currentcellcontainsdatafalse
+ \xa\ifx\csname #1@\the\i @\the\j\endcsname\@@white
+ \qr@currentcellcontainsdatatrue
+ \fi
+ \xa\ifx\csname #1@\the\i @\the\j\endcsname\@@black
+ \qr@currentcellcontainsdatatrue
+ \fi
+}%
+
+\def\qr@flipped@black{\qr@black}%
+\def\qr@flipped@white{\@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\@@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\currentbestpenalty{\qr@penalty}%
+ \message{penalty is \qr@penalty>^^J}%
+ \gdef\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<\currentbestpenalty\relax
+ %We found a better mask.
+ \xdef\currentbestmask{\the\i}%
+ \qr@createduplicatematrix{#1}{currentmasked}%
+ \xdef\currentbestpenalty{\qr@penalty}%
+ \fi
+ }%
+ \xdef\qr@mask@selected{\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\@fiveones{11111}%
+\def\@fivezeros{11111}%
+\def\@twoones{11}%
+\def\@twozeros{00}%
+\def\@finderA{00001011101}%
+\def\@finderB{10111010000}%
+\def\@finderB@three{1011101000}%
+\def\@finderB@two{101110100}%
+\def\@finderB@one{10111010}%
+\def\@finderB@zero{1011101}%
+\newif\ifstringoffive
+\def\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\@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\@blank{0}% These would be any bits at the end.
+ %
+ \setcounter{totalones}{0}%
+ \qr@for \i=1 to \qr@size by 1%
+ {\def\lastfive{z}% %The z is a dummy, that will be removed before any testing.
+ \stringoffivefalse
+ \def\lasttwo@thisrow{z}% %The z is a dummy.
+ \def\lasttwo@nextrow{z}% %The z is a dummy.
+ \def\lastnine{z0000}% %The 0000 stands for the white space to the left. The z is a dummy.
+ \def\ignore@finderB@at{0}%
+ \qr@for \j=1 to \qr@size by 1%
+ {\edef\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\lastfive\xa{\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.
+ \removefirsttoken\lastfive%
+ \ifx\lastfive\@fiveones%
+ \ifstringoffive%
+ %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\stringoffivetrue
+ \fi
+ \else
+ \ifx\lastfive\@fivezeros%
+ \ifstringoffive
+ %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\stringoffivetrue
+ \fi
+ \else
+ %This is not a string of five 1's or five 0's.
+ \global\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\lasttwo@thisrow\xa{\newbit}%
+ %Compute \iplusone
+ \qr@a=\i\relax%
+ \advance\qr@a by 1%
+ \edef\iplusone{\the\qr@a}%
+ %
+ \edef\nextrowbit{\qr@matrixentry{#1}{\iplusone}{\the\j}}%
+ \xa\g@addto@macro\xa\lasttwo@nextrow\xa{\nextrowbit}%
+ \ifnum\j<2\relax%
+ %Still in the first column; no check.
+ \else
+ %Second column or later. Remove the old bits, and then test.
+ \removefirsttoken\lasttwo@thisrow
+ \removefirsttoken\lasttwo@nextrow
+ \ifx\lasttwo@thisrow\@twoones
+ \ifx\lasttwo@nextrow\@twoones
+ \addtocounter{penaltyii}{\qr@Nii}%
+ \fi
+ \else
+ \ifx\lasttwo@thisrow\@twozeros
+ \ifx\lasttwo@nextrow\@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\lastnine\xa{\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.
+ \removefirsttoken\lastnine
+ \xa\ifnum\qr@size=\j\relax%
+ % Last column. Any of the following should count:
+ % 1011101 (\@finderB@zero)
+ % 10111010 (\@finderB@one)
+ % 101110100 (\@finderB@two)
+ % 1011101000 (\@finderB@three)
+ % 10111010000 (\@finderB)
+ \ifx\lastnine\@finderB
+ \addpenaltyiii
+ \else
+ \removefirsttoken\lastnine
+ \ifx\lastnine\@finderB@three
+ \addpenaltyiii
+ \else
+ \removefirsttoken\lastnine
+ \ifx\lastnine\@finderB@two
+ \addpenaltyiii
+ \else
+ \removefirsttoken\lastnine
+ \ifx\lastnine\@finderB@one
+ \addpenaltyiii
+ \else
+ \removefirsttoken\lastnine
+ \ifx\lastnine\@finderB@zero
+ \addpenaltyiii
+ \fi
+ \fi
+ \fi
+ \fi
+ \fi
+ \else
+ \ifx\lastnine\@finderA% %Matches 0000 1011101
+ \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 \ignore@finderB@at to \j+4.
+ \qr@a=\j\relax%
+ \advance\qr@a by 4%
+ \xdef\ignore@finderB@at{\the\qr@a}%
+ \else
+ \ifx\lastfive\@finderB% %Matches 1011101 0000.
+ \xa\ifnum\ignore@finderB@at=\j\relax
+ %This pattern was *not* counted already earlier.
+ \addpenaltyiii
+ \fi
+ \fi
+ \fi
+ \fi
+ \fi
+ %
+ %COUNT 1's FOR PENALTY 4
+ \xa\ifnum\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\lastfive{z}% %The z is a dummy, that will be removed before any testing.
+ \stringoffivefalse
+ \def\lastnine{z0000}% %The 0000 stands for the white space to the left. The z is a dummy.
+ \def\ignore@finderB@at{0}%
+ \qr@for \i=1 to \qr@size by 1%
+ {\edef\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\lastfive\xa{\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.
+ \removefirsttoken\lastfive%
+ \ifx\lastfive\@fiveones%
+ \ifstringoffive%
+ %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\stringoffivetrue
+ \fi
+ \else
+ \ifx\lastfive\@fivezeros%
+ \ifstringoffive
+ %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\stringoffivetrue
+ \fi
+ \else
+ %This is not a string of five 1's or five 0's.
+ \global\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\lastnine\xa{\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.
+ \removefirsttoken\lastnine
+ \xa\ifnum\qr@size=\i\relax%
+ % Last column. Any of the following should count:
+ % 1011101 (\@finderB@zero)
+ % 10111010 (\@finderB@one)
+ % 101110100 (\@finderB@two)
+ % 1011101000 (\@finderB@three)
+ % 10111010000 (\@finderB)
+ \ifx\lastnine\@finderB
+ \addpenaltyiii
+ \else
+ \removefirsttoken\lastnine
+ \ifx\lastnine\@finderB@three
+ \addpenaltyiii
+ \else
+ \removefirsttoken\lastnine
+ \ifx\lastnine\@finderB@two
+ \addpenaltyiii
+ \else
+ \removefirsttoken\lastnine
+ \ifx\lastnine\@finderB@one
+ \addpenaltyiii
+ \else
+ \removefirsttoken\lastnine
+ \ifx\lastnine\@finderB@zero
+ \addpenaltyiii
+ \fi
+ \fi
+ \fi
+ \fi
+ \fi
+ \else
+ \ifx\lastnine\@finderA% %Matches 0000 1011101
+ \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 \ignore@finderB@at to \i+4.
+ \qr@a=\i\relax%
+ \advance\qr@a by 4%
+ \xdef\ignore@finderB@at{\the\qr@a}%
+ \else
+ \ifx\lastfive\@finderB% %Matches 1011101 0000.
+ \xa\ifnum\ignore@finderB@at=\i\relax
+ %This pattern was *not* counted already earlier.
+ \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\removefirsttoken#1{%
+ %Removes the first token from the macro named in #1.
+ \edef\qr@argument{(#1)}%
+ \xa\removefirsttoken@int\qr@argument%
+ \xdef#1{\removefirsttoken@result}%
+}%
+\def\removefirsttoken@int(#1#2){%
+ \def\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)
+ \def\formattowrite{#3}%
+ \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\nexttoken=\relax
+ \else
+ \def\nexttoken{\qr@writeformatA@recursive{#1}(#3)}%
+ \fi
+ \nexttoken
+}%
+
+\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)
+ \def\formattowrite{#3}%
+ \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\nexttoken=\relax
+ \else
+ \def\nexttoken{\qr@writeformatB@recursive{#1}(#3)}%
+ \fi
+ \nexttoken
+}%
+
+\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.
+ %
+ \def\versiontowrite{#3}%
+ %
+ %Set \topline equal to n-10.
+ \qr@a=\qr@size\relax%
+ \advance\qr@a by -10\relax%
+ \edef\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\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\nexttoken=\relax
+ \else
+ \def\nexttoken{\qr@writeversion@recursive{#1}(#3)}%
+ \fi
+ \nexttoken
+}%
+\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\plaintext{#1}%
+ %
+ %First, the mode indicator.
+ \def\qr@codetext{4}% %This means `binary'
+ %
+ %Next, the character count.
+ \qr@getstringlength{\plaintext}%
+ %Set \charactercountlengthinhex to \qr@charactercountbits@byte/4%
+ \qr@a=\qr@charactercountbits@byte\relax%
+ \divide \qr@a by 4\relax%
+ \edef\charactercountlengthinhex{\the\qr@a}%
+ \qr@decimaltohex[\charactercountlengthinhex]{\charactercount}{\qr@stringlength}%
+ \xa\g@addto@macro\xa\qr@codetext\xa{\charactercount}%
+ %
+ %Now comes the actual data.
+ \edef\qr@argument{(,\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 - 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\testii{#2}%
+ \ifx\testii\@relax%
+ % All done!
+ \g@addto@macro\qr@codetext{#1}%
+ \else%
+ % Another character to translate.
+ \edef\asciicode{\number`#2}%
+ \qr@decimaltohex[2]{\newhexcodes}{\asciicode}%
+ \edef\qr@argument{(#1\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}%
+}%
+\let\xa=\expandafter
+\makeatletter
+
+\def\preface@macro#1#2{%
+ % #1 = macro name
+ % #2 = text to add to front of macro
+ \def\tempb{#2}%
+ \xa\xa\xa\gdef\xa\xa\xa#1\xa\xa\xa{\xa\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\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(\xorresult)}%
+ \fi
+ \else
+ \xa\def\xa\qr@numerator\xa{\qr@stripleadingzero(#1)}%
+ \ifx\qr@numerator\@qr@empty
+ \qr@divisiondonetrue
+ \def\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\testii{#2}%
+ \def\testiv{#4}%
+ \ifx\testii\@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\testiv\@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\xorresult{}%
+ \fi
+ \else
+ % There is still a bit to manipulate in #2.
+ % Check whether #4 contains anything.
+ \ifx\testiv\@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\xorresult{#1}%
+}%
+
+\newif\ifqr@divisiondone
+\def\dodivision#1#2{%
+ \qr@divisiondonefalse
+ \dodivision@recursive{#1}{#2}%
+}%
+
+\def\BCHcode#1{%
+ \edef\formatinfo{#1}%
+ \def\formatinfopadded{\formatinfo 0000000000}%
+ \def\qr@divisor{10100110111}%
+ \qr@divisiondonefalse
+ \qr@polynomialdivide{\formatinfopadded}{\qr@divisor}%
+ %
+ \qr@getstringlength{\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%
+ {\preface@macro{\theremainder}{0}%
+ \xdef\theremainder{\theremainder}%
+ }%
+ \edef\BCHresult{\formatinfo\theremainder}%
+}%
+
+\def\qr@formatmask{101010000010010}%
+
+\def\qr@encodeandmaskformat#1{%
+ \BCHcode{#1}%
+ \qr@xorbitstrings{\BCHresult}{\qr@formatmask}%
+ \edef\qr@format@bitstring{\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{\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%
+ {\preface@macro{\theremainder}{0}%
+ \xdef\theremainder{\theremainder}%
+ }%
+ \edef\Golayresult{\qr@versioninfo\theremainder}%
+}%
+\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\testi{#1}%
+ \ifx\testi\@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]{\summandA}{#1}%
+ \qr@hextobinary[4]{\summandB}{#2}%
+ \qr@xorbitstring{\F@result}{\summandA}{\summandB}%
+ \qr@binarytohex[1]{\F@result}{\F@result}%
+}%
+
+\def\canceltwos#1{%
+ \edef\qr@argument{(#1\relax\relax)}%
+ \xa\canceltwos@int\qr@argument%
+}%
+
+\def\canceltwos@int(#1#2){%
+ \xa\canceltwos@recursion(,#1#2)%
+}%
+
+\def\canceltwos@recursion(#1,#2#3){%
+ \def\testii{#2}%
+ \ifx\testii\@relax
+ %Cancelling complete.
+ \striptworelaxes(#1#2#3)%
+ %Now \F@result contains the answer.
+ \else
+ \relax
+ \ifnum#2=2\relax
+ \canceltwos@recursion(#10,#3)%
+ \else
+ \canceltwos@recursion(#1#2,#3)%
+ \fi
+ \fi
+}%
+
+\def\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\testii{#2}%
+ \def\testiv{#4}%
+ \ifx\testii\@relax
+ %The entire string has been processed.
+ \gdef\F@result{#1}%
+ \else
+ \ifx\testiv\@relax
+ %The second string is over.
+ \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
+}%
+\gdef\F@stripleadingzero(0#1){\edef\F@result{#1}}%
+
+\setcounter{qr@i}{0}%
+\def\poweroftwo{1}%
+\qr@for \i = 1 to 254 by 1%
+ {\stepcounter{qr@i}%
+ \qr@a=\poweroftwo\relax
+ \multiply\qr@a by 2\relax
+ \edef\poweroftwo{\the\qr@a}%
+ %\show\poweroftwo
+ \qr@decimaltohex[2]{\poweroftwo@hex}{\poweroftwo}%
+ \xa\ifnum\poweroftwo>255\relax
+ %We need to bitwise add the polynomial represented by 100011101, i.e. 0x11d.
+ \F@addstrings{\poweroftwo@hex}{11d}% %Now it should start with 0.
+ \xa\F@stripleadingzero\xa(\F@result)% %Now it should be two hex digits.
+ \edef\poweroftwo@hex{\F@result}% %Save the hex version.
+ \qr@hextodecimal{\poweroftwo}{\F@result}%
+ \fi
+ \xdef\poweroftwo{\poweroftwo}%
+ \xa\xdef\csname F@twotothe@\theqr@i\endcsname{\poweroftwo@hex}%
+ \xa\xdef\csname F@logtwo@\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\@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\argA{#1}%
+ \edef\argB{#2}%
+ \ifx\argA\@zerozero
+ \def\F@result{00}%
+ \else
+ \ifx\argB\@zerozero
+ \def\F@result{00}%
+ \else
+ \xa\F@logtwo\xa{\argA}%
+ \edef\logA{\F@result}%
+ \xa\F@logtwo\xa{\argB}%
+ \edef\logB{\F@result}%
+ \xa\qr@a\xa=\logA\relax% \qr@a = \logA
+ \xa\advance\xa\qr@a\logB\relax% \advance \qr@a by \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\argA{#1}%
+ \edef\argB{#2}%
+ \ifx\argA\@zerozero
+ \def\F@result{00}%
+ \else
+ \ifx\argB\@zerozero
+ \def\F@result{00}%
+ \else
+ \xa\F@logtwo\xa{\argA}%
+ \edef\logA{\F@result}%
+ \xa\F@logtwo\xa{\argB}%
+ \edef\logB{\F@result}%
+ \xa\qr@a\xa=\logA\relax% \qr@a = \logA
+ \xa\advance\xa\qr@a\logB\relax% \advance \qr@a by \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\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\testi{#1}%
+ \ifx\testi\@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\@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\denominator{#2}%
+ \qr@getstringlength\FX@numerator%
+ \setcounter{qr@divisionsremaining}{\qr@stringlength}%
+ \qr@getstringlength\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{\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\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\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\testii{#2}%
+ \def\testv{#5}%
+ \ifx\testii\@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\testv\@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\testv\@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\summandA{\FX@generatorpolynomial 00}% This is f(x) * x
+ \edef\summandB{00\FX@generatorpolynomial}% This is f(x), with a 0x^{i+1} in front.
+ \F@twotothe{\theqr@i}%
+ \edef\theconstant{\F@result}%
+ \FX@subtractphase{\summandA}{\summandB}{\theconstant}%
+ %This calculates \summandA + \theconstant * \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\numerrorbytes{#2}%
+ \xa\FX@creategeneratorpolynomial\xa{\numerrorbytes}%
+ \edef\FX@numerator{#1}%
+ \qr@for \i = 1 to \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{\theremainder}%
+}%
+\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 \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\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\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\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\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\tempdata
+}%
+\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 false.
+\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}%
+}
+
+\qrset{version=0, level=0, tight}
+\newcommand\qrcode[1][]{%
+ \begingroup%
+ \setkeys{qr}{#1}%
+ \bgroup\qr@verbatimcatcodes\qr@setescapedspecials\qrcode@i}%
+
+\def\qrcode@i#1{\xdef\qr@texttoencode{#1}\egroup\qrcode@int\endgroup}%
+
+\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}%
+ %
+ %Next, check whether we have already encoded this text at this version
+ %and level.
+ \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\@blank{\@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]{\level@binary}{\qr@level}%
+ \qr@decimaltobinary[3]{\mask@binary}{\qr@mask@selected}%
+ \edef\formatstring{\level@binary\mask@binary}%
+ \message{<Encoding and writing format string...}%
+ \xa\qr@encodeandmaskformat\xa{\formatstring}%
+ \qr@writeformatstring{newqr}{\qr@format@bitstring}%
+ \message{done.>^^J}%
+ \message{<Encoding and writing version information...}%
+ \qr@decimaltobinary[6]{\version@binary}{\qr@version}%
+ \qr@Golaycode{\version@binary}%
+ \qr@writeversionstring{newqr}{\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\@white{0}%
+ \def\@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\theentry{\qr@matrixentry{#1}{\the\i}{\the\j}}%
+ \xa\g@addto@macro\xa\qr@binarymatrix@result\xa{\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\testi{#1}%
+ \ifx\testi\@relax
+ % Done.
+ \let\qr@next=\relax
+ \else
+ \ifx\testi\qr@otherrightbrace
+ \edef\qr@sanitized@result{\qr@sanitized@result\qr@otherbackslash}%
+ \else\ifx\testi\qr@otherleftbrace
+ \edef\qr@sanitized@result{\qr@sanitized@result\qr@otherbackslash}%
+ \else\ifx\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\theargument{{\qr@sanitized@result}{\qr@version}{\qr@level}{#1}}%
+ \xa\write\xa\@auxout\xa{\xa\string\xa\qr@savematrix\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\dummyqrsavedefinition{}%
+\begingroup
+ \catcode`\#=12\relax
+ \catcode`\<=1\relax
+ \catcode`\{=12\relax
+ \catcode`\>=2\relax
+ \catcode`\}=12\relax
+ \catcode`\|=0\relax
+ \catcode`\\=12|relax
+ |gdef|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{(\dummyqrsavedefinition)}%
+\xa\write\xa\@auxout\xa{\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}%
+ }%
+}%
+\endinput
+%%
+%% End of file `qrcode.sty'.
diff --git a/Master/tlpkg/bin/tlpkg-ctan-check b/Master/tlpkg/bin/tlpkg-ctan-check
index cf091690c78..3ea2383da25 100755
--- a/Master/tlpkg/bin/tlpkg-ctan-check
+++ b/Master/tlpkg/bin/tlpkg-ctan-check
@@ -417,7 +417,7 @@ my @TLP_working = qw(
pxchfon pxcjkcat pxfonts pxgreeks pxjahyper
pxpgfmark pxrubrica pxtxalfa pygmentex python pythontex
quattrocento qcircuit qcm
- qobitree qstest qsymbols qtree quotchap quoting quotmark
+ qobitree qrcode qstest qsymbols qtree quotchap quoting quotmark
r_und_s raleway ran_toks randbild randomwalk randtext
rccol rcs rcs-multi rcsinfo
readarray realboxes realscripts rec-thy recipe recipecard recycle rectopma
diff --git a/Master/tlpkg/tlpsrc/collection-pictures.tlpsrc b/Master/tlpkg/tlpsrc/collection-pictures.tlpsrc
index 7812f20c9b9..ce44e352ccd 100644
--- a/Master/tlpkg/tlpsrc/collection-pictures.tlpsrc
+++ b/Master/tlpkg/tlpsrc/collection-pictures.tlpsrc
@@ -85,6 +85,7 @@ depend prerex
depend productbox
depend pxpgfmark
depend qcircuit
+depend qrcode
depend randbild
depend randomwalk
depend reotex
diff --git a/Master/tlpkg/tlpsrc/qrcode.tlpsrc b/Master/tlpkg/tlpsrc/qrcode.tlpsrc
new file mode 100644
index 00000000000..e69de29bb2d
--- /dev/null
+++ b/Master/tlpkg/tlpsrc/qrcode.tlpsrc
generated by cgit v1.2.3 (git 2.39.1) at 2024-11-02 06:08:23 +0000