reverxii (6nov21)

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+{\def\x{plain}\expandafter}\ifx\fmtname\x
+  \errmessage{Use LaTeX for the documentation reverxii.dtx.  Play with reverxii.tex}
+\fi
+\documentclass{article}
+\usepackage{shortvrb,verbatim}
+\MakeShortVerb|
+\title{\texttt{reverxii}\\
+  Playing Reversi in \TeX{}}
+\author{Bruno Le Floch}
+\date{November 6, 2021}
+\newcommand{\cs}[1]{\texttt{\char`\\ #1}}
+\newcommand{\meta}[1]{$\langle \mathit{#1}\rangle$}
+\newcommand{\enquote}[1]{``#1''}
+\begin{document}
+\maketitle
+
+\begin{abstract}
+  \texttt{reverxii.tex} is a $983$ character long \TeX{} program which
+  lets you play Reversi against your favorite typestting engine.  To
+  play, run plain \TeX{} or \LaTeX{} (either the dvi or the pdf
+  engines), on the command line, on the file \texttt{reverxii.tex}. In
+  most distributions, this can mean running \texttt{tex reverxii.tex} in
+  a terminal.  To typeset the documentation, run \LaTeX{} on
+  \texttt{reverxii.dtx}, with any engine (\emph{e.g.}, \texttt{pdflatex
+    reverxii.dtx}).
+\end{abstract}
+
+\section{The code}
+
+Line breaks can be removed, and the stripped down code takes $983$
+characters.
+{\small \verbatiminput{reverxii.tex}}
+In fact, the first line and |\ifx\>\:1\fi| are only used to support
+\LaTeX{} and can be removed for plain \TeX{}.  This reduces the code down to $938$ characters.
+
+To play a two-player game, change |1=P| to |0=P| near the end:
+this changes the computer player from $0$ to $1$, hence disabling it.
+
+\section{Explanation}
+
+\subsection{Some comments}
+
+The name \texttt{reverxii.tex} is of course a reference to the infamous
+\texttt{xii.tex}, also on CTAN, which typesets the lyrics of the
+\textit{Twelve days of Christmas} using code that very few can understand.
+In my case, I aimed for the shortest possible code, rather than the
+most obfuscated. In particular, I did not assign weird catcodes
+other than making most characters active.
+
+Since I was aiming for short code, the text presented to the player
+is concise, but hopefully enough to leave the game understandable
+and usable. Despite aiming for short code, I thought it would be
+neat to typeset a record of the game as it goes: after all, \TeX{}
+is a typesetting program. This used up around $38$ characters, putting
+me above the $900$ character line.
+
+One technique used to make the code shorter is to rename any primitive
+used more than once into a single active character. Also, counters
+holding the information about the board are accessed directly by number.
+
+A careful reader would notice that changing one of the remaining
+one-character control sequences to active characters (|$| is still %$
+unused) would gain one character. I didn't do it, because it messes
+up the code-highlighting of my editor |:)|. Of course, I chose the
+control sequences which are not active characters to be those appearing
+the least, only twice each.
+
+\subsubsection{On with the code!}
+
+In \LaTeXe{}, detected by comparing the spaces |\>| and~|\:| (only one
+of them is defined in plain \TeX{}), load a document class.
+\begin{verbatim}
+\ifx\>\:\documentclass{report}\fi
+\end{verbatim}
+We do not need \cs{begin}|{document}| because the text is eventually
+typeset inside an \cs{halign} table, which means \cs{everypar} (and its
+usual error) is never called.
+
+First set up the page dimensions. This would not be enough for pdf output.
+\begin{verbatim}
+\vsize5cm
+\hsize3cm
+\end{verbatim}
+
+Since plain \TeX{} does not provide the \cs{typeout} command, we are
+using \cs{message}, hence need to setup a new line character. It is
+arbitrarily chosen to be |*|, which will be made active and \cs{let}
+to \cs{cr}.
+\begin{verbatim}
+\newlinechar`*
+\end{verbatim}
+
+Then a first loop to make many characters active. The loop ends when
+reaching the trailing brace group: there we make spaces active, then
+redefine |~| for the next loop. We still have an annoying |13~| in the
+input stream. Introduce a short-hand for count registers whose number
+starts with |1| (or in fact |11| in \LaTeX{} given the test
+|\ifx\>\:1\fi|, see later for why we do this).  Then remove |13| by
+setting |\count11| to |213| (this counter is used for allocation later
+on). The next loop is triggered by the |~| which we left.
+\begin{verbatim}
+\def~#1{\catcode`#113~}
+~IJKLMNOPQRSTUVWXYZjqz@.[|](/+^'";:?,_)!*
+{ 13\def~#1#2{\let#1#2~}\def+{\count\ifx\>\:1\fi1}+1=2}
+\end{verbatim}
+
+At this stage, |~| is defined to take two arguments, \cs{let} the
+first to the second, and repeat. As announced |*| becomes \cs{cr},
+so that it will be a new line both in messages and in alignments.
+We try to keep a relatively consistent naming scheme: opening
+conditionals are left delimiters, \cs{or} and \cs{else} are
+middle delimiters, and \cs{fi} is a right bracket. Other primitives
+which are used a lot are also given short names. The loop ends by
+redefining |~| to \cs{def}.
+\begin{verbatim}
+*\cr
+[\ifnum
+(\ifcase
+|\or
+/\else
+]\fi
+N\number
+@\advance
+X\expandafter
+!\global
+?\message
+~\def
+\end{verbatim}
+
+It is time to allocate counters. Unfortunately, \cs{newcount} is
+\cs{outer} in plain \TeX{}, so it is unpractical to use.  We have
+defined |+| to be |\count1| in plain and |\count11| in \LaTeX{}.  This
+will eventually let us access a table of $8\times 8$ counters |+11| to
+|+88|, which are thus |\count111| to |\count188| in plain, and
+|\count1111| to |\count1188| in \LaTeX{}.  This is needed because plain
+\TeX{} without e\TeX{} extensions only has $256$ counters, while
+\LaTeX{} \emph{uses} some of these counters already so we must use the
+higher counters provided by the e\TeX{} extensions, always available in
+\LaTeX{}.  The following text explains the plain \TeX{} case; in the
+other case just replace |\count1| by |\count11|.
+
+We have set |+1|,
+\emph{aka.} |\count11| to $213$, and will allocate counters
+starting from that number upwards. Repeatedly advance |+1|
+by $1$ and define the next character to be the counter number |+1|,
+then repeat. As always, the loop is interrupted by making it
+redefine the looping macro |.| to be a counter. We use the trailing
+dot to assign it the value $-1$, then assign a couple of counters:
+starting player, other player, and the initial position:
+the squares in rows and columns $4$ and $5$ are initially
+filled in a cross pattern.
+\begin{verbatim}
+.#1{@+1 1\countdef#1+1.}.IJKLPQRSTUVWYZ.-1P1T2+44P+55P+45T+54T
+\end{verbatim}
+Let us summarize which counters are used where:
+\begin{itemize}
+\item [P] is the current player ($1$ for |-| or $2$ for |0|);
+\item [T] is the other player;
+\item [Q] is the row number;
+\item [J] is the column number;
+\item [S] is the step size in the row direction;
+\item [K] is the step size in the column direction;
+\item [R] is the score difference, positive when $0$ is winning;
+\item [V] is used when computing the value of placing a piece at
+  the position (|Q|,|J|);
+\item [W] is the value of the best possible move according to the AI,
+  also used to end the game if neither player can move;
+\item [U] is the row number of the best move;
+\item [L] is the column number of the best move;
+\item [Y] is a boolean, true ($0$) most of the time,
+  it has to do with when we flip or not, but I don't
+  understand it now, help welcome;
+\item [Z] is a temporary counter, used locally to compute
+  how much a given cell matters (\emph{i.e.} corners are important),
+  and used globally as a boolean to indicate whether to flip pieces
+  or not.
+\end{itemize}
+
+The board is stored in counters |1|\meta{row}\meta{column}.
+An empty square is has the value $0$, a square for player |-|
+has value $1$, and player |0| corresponds to the value $2$.
+The macro |j| retrieves that value, assuming that the row and
+column numbers are stored as |Q| and |J|, and returns |.|,
+that is, $-1$, if outside the board. Recall that |[| is \cs{ifnum},
+|/| is \cs{else}, and |]| is \cs{fi}. When |Q| and |J| are
+within bounds, the value is retrieved by |^| as
+|\count1|\meta{row}\meta{column}. Note that |j| and |^| are
+only safe to use on the left-hand side of an \cs{ifnum} test
+(because of expansion issues), and that |^| can be used
+on the left-hand side of an assignment.
+\begin{verbatim}
+~j{[0<Q[9>Q[0<J[9>J^/.]/.]/.]/.]}
+~^{+NQNJ}
+\end{verbatim}
+
+We often need to loop over numbers from $1$ to $8$; here is a macro.
+\begin{verbatim}
+~:#1{#11#12#13#14#15#16#17#18}
+\end{verbatim}
+
+The macros to print the board, both to the dvi and to the console.
+|M| spews its argument as a \cs{message} (|?|), and directly typeset.
+This is used rather directly to print the first and last lines (|'|),
+which are simply alignment cells containing each number from $1$ to $8$,
+with some care given to spaces and new lines.
+The |_| macro receives a digit and the corresponding capital letter
+as arguments, and outputs that row of the board. First place the
+letter on the left of the board, then loop from $1$ to $8$,
+typesetting and \cs{message}ing a space, |-| or |0|, depending on
+the value of the relevant count register. Note the two spaces
+in the definition: the first ends the counter's number, the second
+is typeset (in plain \TeX{}, active spaces expand to a normal space).
+\begin{verbatim}
+~M#1{?{#1}#1}
+~'{M :{&M}&M{*}}
+~_#1#2{M#2:{\B#1}&M#2&M{*}}
+~\B#1#2{&M{(+#1#2  |-|0]}}
+\end{verbatim}
+
+The input is done by |q|, which queries the user until they give
+a correct input, so that |Q| and |J| are in the range $[1,8]$.
+Prompt the user with a small \cs{message}, giving an example
+of what move he could do (only true at the start, but the hope
+is that the player will understand what the input format is).
+The code that follows is similar to \LaTeXe{}'s \cs{@onelevel@sanitize}.
+We extract the two first characters from the the \cs{meaning}
+of the user's input (remember, |X| is \cs{expandafter}),
+as |#2| and |#3| of \cs{D}. Grab the character code of each,
+relative to the characters |@| (row) or |0| (column).
+The closing parenthesis is where most of the work is done.
+It sets |V| to the value of placing a piece in the cell
+$(|Q|,|J|)$, zero if the move does not flip any of the opponent's
+pieces, or if the cell is outside the board. After performing
+that calculation, if |V| is zero, the move was not valid,
+and we query the user again.
+\begin{verbatim}
+~q{?{Row and column? e.g. E6*}\read.to\EX\D\meaning\E  ;}
+~\D#1->#2#3#4;{Q`#2@Q-`@J`#3@J-`0)(V?{Invalid move #2#3.}q]}
+\end{verbatim}
+
+So\ldots{} how do we compute the \enquote{value} of a move?
+It is automatically invalid if |j| does not return $0$:
+either the cell is occupied, or it is outside the board.
+Then for each of the $8$ directions around the cell,
+we count the number of pieces that are flipped in that
+direction. The direction is stored as two counters,
+|S| and |K|, each $\pm 1$ or $0$. We call |,| a first
+time to test whether flipping should happen in that direction,
+and, if it is (as indicated by the global value of |Z|),
+call it again to actually flip. The call to |,| must happen
+within a group, because it directly changes the row and column
+numbers |Q| and |J|, following which cell is being queried.
+\begin{verbatim}
+~){V0 (jS1z1z0z.S0z1z.S.z1z0z.]}
+~z#1{{K#1Z1{Y1,}(Z,]}}
+\end{verbatim}
+
+The macro |,| is recursive. At each step, move $(|Q|,|J|)$
+in the direction $(|S|,|K|)$. Then, if that cell (|j|)
+contains a piece belonging to the other player (|T|),
+do some stuff |(Y!^P!;2]O| and repeat. What is it that
+we do? Well, if the condition |Y| is met (I don't remember
+how that works), we set the current cell to belong to the
+player, globally, and change the score difference by $2$
+(see |;|), also globally. Then, we compute with |O| the value
+corresponding to the cell that we might be flipping (see |O|).
+
+Otherwise (|/|), if the cell (|j|) contains a piece from the
+current player (|P|), it means we have reached the end of a
+run of the form \meta{initial cell} \meta{opponent's pieces}
+\meta{own piece}, hence the \meta{opponent's pieces} should
+count as flipped if we place our piece in the \meta{initial
+  cell}. Until there, all changes to |V| were local, returning
+to the old value at the end of the group that |,| is contained
+in. Since the run in that direction was successful, we escape
+the value of |V| from the group with |\global V=V|. Under
+some conditions, we set the boolean |Z| to true, globally (|!Z0|),
+which triggers a second call to |,| with different setting,
+and actually flips the opponent's pieces.
+\begin{verbatim}
+~,{@QS@JK[j=T(Y!^P!;2]O,/[j=P!VV(I(Y/!Z0]]]]}
+\end{verbatim}
+
+I moved those |O| and |"| guys a little bit in this explanation,
+but not in the original implemenation, because it is hard
+to sync. We assign weights to each of the $64$ cells:
+\begin{center}
+  \halign{&\hfil#\hfil\cr
+    9 & 1 & 6 & 6 & 6 & 6 & 1 & 9 \cr
+    1 & 1 & 2 & 2 & 2 & 2 & 1 & 1 \cr
+    6 & 2 & 4 & 4 & 4 & 4 & 2 & 6 \cr
+    6 & 2 & 4 & 4 & 4 & 4 & 2 & 6 \cr
+    6 & 2 & 4 & 4 & 4 & 4 & 2 & 6 \cr
+    6 & 2 & 4 & 4 & 4 & 4 & 2 & 6 \cr
+    1 & 1 & 2 & 2 & 2 & 2 & 1 & 1 \cr
+    9 & 1 & 6 & 6 & 6 & 6 & 1 & 9 \cr}
+\end{center}
+All weights are positive, so that every move which flips a piece
+ends up with a positive overall value. The AI would be better if
+the places next to corners had a negative weight, but I would have
+too much code to rewrite for that to work. We really have three
+types of rows and three types of columns. Converting from |Q|
+or |J| is done by |"|, then we assemble the two as a number
+in the range $[0,8]$, and use another \cs{ifcase} construction
+to produce the weights.
+\begin{verbatim}
+~O{Z"Q\multiplyZ3@Z"J@V(Z9|1|6|1|1|2|6|2|4] }
+~"#1{(#1|0|1|2|2|2|2|1|0]}
+\end{verbatim}
+
+The counter |R| keeps track of the score difference,
+and is updated with |;2| (when flipping a piece) or |;1| (when
+adding a piece). The counter |R| should be \cs{advance}d (|@|)
+by a positive amount when the current player |P| is player |0|,
+and a negative amount for player |-|.
+\begin{verbatim}
+~;{@R(P|-]}
+\end{verbatim}
+
+After printing the board, we go through every cell and find the
+one with the highest value. The macro \cs{A}, does one row, hence
+|\:\A| does all the rows. Store the argument as the row number |Q|,
+then loop over columns. After setting the column number |J| to
+its argument, \cs{C} calls |)|, which as explained above computes
+the value of placing a piece there, throws away that case if it flips
+nothing, otherwise also counts the weight of the current cell. Then
+update the best value |W| and the best row |U| and column |L| if
+the new |V| is larger than |W|.
+\begin{verbatim}
+~\A#1{Q#1:\C}
+~\C#1{J#1)[0<VO[V>WWVUQLJ]]}
+\end{verbatim}
+
+We won't need |~| as \cs{def} anymore, so we reuse it as the main command.
+\begin{itemize}
+\item First exchange the players: set |P| equal to |T|, but first expand
+  the value of |P| after |T| to set that as well.
+\item Secondly, open an alignment, with a repeating preamble adding a space
+  at its end. Then message a new-line (we should be using |?| rather than
+  |M| here, I think) to keep a clean output. Afterwards, print the top line
+  with |'|, the eight lines of the bulk with |_|, and the bottom line,
+  which happens to end with |?{*}*|, \emph{i.e.}, ends with \cs{cr}:
+  we can thus close the alignment, and cause \TeX{} to output the page.
+\item After printing, it is time to check whether there is a move or not.
+  We don't want to flip pieces at this stage, hence set the boolean |I|
+  to false ($1$). And we reset the best value to $0$, unless it was
+  already $0$ (which means that the previous player had no available
+  move), in which case we set it to $-1$. Then loop over rows, finding
+  the best value (see \cs{A}). Reset the boolean |I| to be true.
+\item If a move was found in the previous step ($|W|>0$), either
+  use it if the player is the AI, or query the user. The various
+  booleans are set up in such a way as to do the flipping, so
+  calling |)| does it. Then also put a player's piece in the current
+  cell |^|, and increase the score difference by $1$.
+\item Finally, if neither player could move, declare the game ended,
+  give the score, and \cs{dump} the run (not \cs{end} because we want to
+  support both plain \TeX{} and \LaTeX{}). Otherwise, repeat.
+\end{itemize}
+Of course, after defining |~|, we call it. Let's play!
+\begin{verbatim}
+~~{
+  PXTXTNP
+  \halign{&## *M{*}'_1A_2B_3C_4D_5E_6F_7G_8H'}\vfil\break
+  I1 W(W./0] :\AI0
+  [0<W
+    [1=PQUJL/q]
+    )
+    ^P;1
+  ]
+  [.=W
+    ?{(RTie/ Player [0>R-/0] wins by N[0>R-]R].}
+    X\dump
+  ]
+  ~
+}
+~
+\end{verbatim}
+
+\end{document}
\ No newline at end of file