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+% This program is copyright (C) 1982 by D. E. Knuth; all rights are reserved.
+% Copying of this file is authorized only if (1) you are D. E. Knuth, or if
+% (2) you make absolutely no changes to your copy. (The WEB system provides
+% for alterations via an auxiliary file; the master file should stay intact.)
+% See Appendix H of the WEB manual for hints on how to install this program.
+% And see Appendix A of the TRIP manual for details about how to validate it.
+
+% TeX is a trademark of the American Mathematical Society.
+% METAFONT is a trademark of Addison-Wesley Publishing Company.
+
+% Version 0 was released in September 1982 after it passed a variety of tests.
+% Version 1 was released in November 1983 after thorough testing.
+% Version 1.1 fixed ``disappearing font identifiers'' et alia (July 1984).
+% Version 1.2 allowed `0' in response to an error, et alia (October 1984).
+% Version 1.3 made memory allocation more flexible and local (November 1984).
+% Version 1.4 fixed accents right after line breaks, et alia (April 1985).
+% Version 1.5 fixed \the\toks after other expansion in \edefs (August 1985).
+% Version 2.0 (almost identical to 1.5) corresponds to "Volume B" (April 1986).
+% Version 2.1 corrected anomalies in discretionary breaks (January 1987).
+% Version 2.2 corrected "(Please type...)" with null \endlinechar (April 1987).
+% Version 2.3 avoided incomplete page in premature termination (August 1987).
+% Version 2.4 fixed \noaligned rules in indented displays (August 1987).
+% Version 2.5 saved cur_order when expanding tokens (September 1987).
+% Version 2.6 added 10sp slop when shipping leaders (November 1987).
+% Version 2.7 improved rounding of negative-width characters (November 1987).
+% Version 2.8 fixed weird bug if no \patterns are used (December 1987).
+% Version 2.9 made \csname\endcsname's "relax" local (December 1987).
+% Version 2.91 fixed \outer\def\a0{}\a\a bug (April 1988).
+% Version 2.92 fixed \patterns, also file names with complex macros (May 1988).
+% Version 2.93 fixed negative halving in allocator when mem_min<0 (June 1988).
+% Version 2.94 kept open_log_file from calling fatal_error (November 1988).
+% Version 2.95 solved that problem a better way (December 1988).
+% Version 2.96 corrected bug in "Infinite shrinkage" recovery (January 1989).
+% Version 2.97 corrected blunder in creating 2.95 (February 1989).
+% Version 2.98 omitted save_for_after at outer level (March 1989).
+% Version 2.99 caught $$\begingroup\halign..$$ (June 1989).
+% Version 2.991 caught .5\ifdim.6... (June 1989).
+% Version 2.992 introduced major changes for 8-bit extensions (September 1989).
+% Version 2.993 fixed a save_stack synchronization bug et alia (December 1989).
+% Version 3.0 fixed unusual displays; was more \output robust (March 1990).
+% Version 3.1 fixed nullfont, disabled \write{\the\prevgraf} (September 1990).
+% Version 3.14 fixed unprintable font names and corrected typos (March 1991).
+% Version 3.141 more of same; reconstituted ligatures better (March 1992).
+% Version 3.1415 preserved nonexplicit kerns, tidied up (February 1993).
+% Version 3.14159 allowed fontmemsize to change; bulletproofing (March 1995).
+% Version 3.141592 fixed \xleaders, glueset, weird alignments (December 2002).
+
+% A reward of $327.68 will be paid to the first finder of any remaining bug.
+
+% Although considerable effort has been expended to make the TeX program
+% correct and reliable, no warranty is implied; the author disclaims any
+% obligation or liability for damages, including but not limited to
+% special, indirect, or consequential damages arising out of or in
+% connection with the use or performance of this software. This work has
+% been a ``labor of love'' and the author hopes that users enjoy it.
+
+% Here is TeX material that gets inserted after \input webmac
+\def\hang{\hangindent 3em\noindent\ignorespaces}
+\def\hangg#1 {\hang\hbox{#1 }}
+\def\textindent#1{\hangindent2.5em\noindent\hbox to2.5em{\hss#1 }\ignorespaces}
+\font\ninerm=cmr9
+\let\mc=\ninerm % medium caps for names like SAIL
+\def\PASCAL{Pascal}
+\def\ph{\hbox{Pascal-H}}
+\def\pct!{{\char`\%}} % percent sign in ordinary text
+\font\logo=logo10 % font used for the METAFONT logo
+\def\MF{{\logo META}\-{\logo FONT}}
+\def\<#1>{$\langle#1\rangle$}
+\def\section{\mathhexbox278}
+
+\def\(#1){} % this is used to make section names sort themselves better
+\def\9#1{} % this is used for sort keys in the index via @@:sort key}{entry@@>
+
+\outer\def\N#1. \[#2]#3.{\MN#1.\vfil\eject % begin starred section
+ \def\rhead{PART #2:\uppercase{#3}} % define running headline
+ \message{*\modno} % progress report
+ \edef\next{\write\cont{\Z{\?#2]#3}{\modno}{\the\pageno}}}\next
+ \ifon\startsection{\bf\ignorespaces#3.\quad}\ignorespaces}
+\let\?=\relax % we want to be able to \write a \?
+
+\def\title{\TeX82}
+\def\topofcontents{\hsize 5.5in
+ \vglue 0pt plus 1fil minus 1.5in
+ \def\?##1]{\hbox to 1in{\hfil##1.\ }}
+ }
+\def\botofcontents{\vskip 0pt plus 1fil minus 1.5in}
+\pageno=3
+\def\glob{13} % this should be the section number of "<Global...>"
+\def\gglob{20, 26} % this should be the next two sections of "<Global...>"
+
+@* \[1] Introduction.
+This is \TeX, a document compiler intended to produce typesetting of high
+quality.
+The \PASCAL\ program that follows is the definition of \TeX82, a standard
+@:PASCAL}{\PASCAL@>
+@!@:TeX82}{\TeX82@>
+version of \TeX\ that is designed to be highly portable so that identical output
+will be obtainable on a great variety of computers.
+
+The main purpose of the following program is to explain the algorithms of \TeX\
+as clearly as possible. As a result, the program will not necessarily be very
+efficient when a particular \PASCAL\ compiler has translated it into a
+particular machine language. However, the program has been written so that it
+can be tuned to run efficiently in a wide variety of operating environments
+by making comparatively few changes. Such flexibility is possible because
+the documentation that follows is written in the \.{WEB} language, which is
+at a higher level than \PASCAL; the preprocessing step that converts \.{WEB}
+to \PASCAL\ is able to introduce most of the necessary refinements.
+Semi-automatic translation to other languages is also feasible, because the
+program below does not make extensive use of features that are peculiar to
+\PASCAL.
+
+A large piece of software like \TeX\ has inherent complexity that cannot
+be reduced below a certain level of difficulty, although each individual
+part is fairly simple by itself. The \.{WEB} language is intended to make
+the algorithms as readable as possible, by reflecting the way the
+individual program pieces fit together and by providing the
+cross-references that connect different parts. Detailed comments about
+what is going on, and about why things were done in certain ways, have
+been liberally sprinkled throughout the program. These comments explain
+features of the implementation, but they rarely attempt to explain the
+\TeX\ language itself, since the reader is supposed to be familiar with
+{\sl The \TeX book}.
+@.WEB@>
+@:TeXbook}{\sl The \TeX book@>
+
+@ The present implementation has a long ancestry, beginning in the summer
+of~1977, when Michael~F. Plass and Frank~M. Liang designed and coded
+a prototype
+@^Plass, Michael Frederick@>
+@^Liang, Franklin Mark@>
+@^Knuth, Donald Ervin@>
+based on some specifications that the author had made in May of that year.
+This original proto\TeX\ included macro definitions and elementary
+manipulations on boxes and glue, but it did not have line-breaking,
+page-breaking, mathematical formulas, alignment routines, error recovery,
+or the present semantic nest; furthermore,
+it used character lists instead of token lists, so that a control sequence
+like \.{\\halign} was represented by a list of seven characters. A
+complete version of \TeX\ was designed and coded by the author in late
+1977 and early 1978; that program, like its prototype, was written in the
+{\mc SAIL} language, for which an excellent debugging system was
+available. Preliminary plans to convert the {\mc SAIL} code into a form
+somewhat like the present ``web'' were developed by Luis Trabb~Pardo and
+the author at the beginning of 1979, and a complete implementation was
+created by Ignacio~A. Zabala in 1979 and 1980. The \TeX82 program, which
+@^Zabala Salelles, Ignacio Andr\'es@>
+was written by the author during the latter part of 1981 and the early
+part of 1982, also incorporates ideas from the 1979 implementation of
+@^Guibas, Leonidas Ioannis@>
+@^Sedgewick, Robert@>
+@^Wyatt, Douglas Kirk@>
+\TeX\ in {\mc MESA} that was written by Leonidas Guibas, Robert Sedgewick,
+and Douglas Wyatt at the Xerox Palo Alto Research Center. Several hundred
+refinements were introduced into \TeX82 based on the experiences gained with
+the original implementations, so that essentially every part of the system
+has been substantially improved. After the appearance of ``Version 0'' in
+September 1982, this program benefited greatly from the comments of
+many other people, notably David~R. Fuchs and Howard~W. Trickey.
+A final revision in September 1989 extended the input character set to
+eight-bit codes and introduced the ability to hyphenate words from
+different languages, based on some ideas of Michael~J. Ferguson.
+@^Fuchs, David Raymond@>
+@^Trickey, Howard Wellington@>
+@^Ferguson, Michael John@>
+
+No doubt there still is plenty of room for improvement, but the author
+is firmly committed to keeping \TeX82 ``frozen'' from now on; stability
+and reliability are to be its main virtues.
+
+On the other hand, the \.{WEB} description can be extended without changing
+the core of \TeX82 itself, and the program has been designed so that such
+extensions are not extremely difficult to make.
+The |banner| string defined here should be changed whenever \TeX\
+undergoes any modifications, so that it will be clear which version of
+\TeX\ might be the guilty party when a problem arises.
+@^extensions to \TeX@>
+@^system dependencies@>
+
+If this program is changed, the resulting system should not be called
+`\TeX'; the official name `\TeX' by itself is reserved
+for software systems that are fully compatible with each other.
+A special test suite called the ``\.{TRIP} test'' is available for
+helping to determine whether a particular implementation deserves to be
+known as `\TeX' [cf.~Stanford Computer Science report CS1027,
+November 1984].
+
+@d banner=='This is TeX, Version 3.141592' {printed when \TeX\ starts}
+
+@ Different \PASCAL s have slightly different conventions, and the present
+@!@:PASCAL H}{\ph@>
+program expresses \TeX\ in terms of the \PASCAL\ that was
+available to the author in 1982. Constructions that apply to
+this particular compiler, which we shall call \ph, should help the
+reader see how to make an appropriate interface for other systems
+if necessary. (\ph\ is Charles Hedrick's modification of a compiler
+@^Hedrick, Charles Locke@>
+for the DECsystem-10 that was originally developed at the University of
+Hamburg; cf.\ {\sl SOFTWARE---Practice \AM\ Experience \bf6} (1976),
+29--42. The \TeX\ program below is intended to be adaptable, without
+extensive changes, to most other versions of \PASCAL, so it does not fully
+use the admirable features of \ph. Indeed, a conscious effort has been
+made here to avoid using several idiosyncratic features of standard
+\PASCAL\ itself, so that most of the code can be translated mechanically
+into other high-level languages. For example, the `\&{with}' and `\\{new}'
+features are not used, nor are pointer types, set types, or enumerated
+scalar types; there are no `\&{var}' parameters, except in the case of files;
+there are no tag fields on variant records; there are no assignments
+|real:=integer|; no procedures are declared local to other procedures.)
+
+The portions of this program that involve system-dependent code, where
+changes might be necessary because of differences between \PASCAL\ compilers
+and/or differences between
+operating systems, can be identified by looking at the sections whose
+numbers are listed under `system dependencies' in the index. Furthermore,
+the index entries for `dirty \PASCAL' list all places where the restrictions
+of \PASCAL\ have not been followed perfectly, for one reason or another.
+@!@^system dependencies@>
+@!@^dirty \PASCAL@>
+
+Incidentally, \PASCAL's standard |round| function can be problematical,
+because it disagrees with the IEEE floating-point standard.
+Many implementors have
+therefore chosen to substitute their own home-grown rounding procedure.
+
+@ The program begins with a normal \PASCAL\ program heading, whose
+components will be filled in later, using the conventions of \.{WEB}.
+@.WEB@>
+For example, the portion of the program called `\X\glob:Global
+variables\X' below will be replaced by a sequence of variable declarations
+that starts in $\section\glob$ of this documentation. In this way, we are able
+to define each individual global variable when we are prepared to
+understand what it means; we do not have to define all of the globals at
+once. Cross references in $\section\glob$, where it says ``See also
+sections \gglob, \dots,'' also make it possible to look at the set of
+all global variables, if desired. Similar remarks apply to the other
+portions of the program heading.
+
+Actually the heading shown here is not quite normal: The |program| line
+does not mention any |output| file, because \ph\ would ask the \TeX\ user
+to specify a file name if |output| were specified here.
+@^system dependencies@>
+
+@d mtype==t@&y@&p@&e {this is a \.{WEB} coding trick:}
+@f mtype==type {`\&{mtype}' will be equivalent to `\&{type}'}
+@f type==true {but `|type|' will not be treated as a reserved word}
+
+@p @t\4@>@<Compiler directives@>@/
+program TEX; {all file names are defined dynamically}
+label @<Labels in the outer block@>@/
+const @<Constants in the outer block@>@/
+mtype @<Types in the outer block@>@/
+var @<Global variables@>@/
+@#
+procedure initialize; {this procedure gets things started properly}
+ var @<Local variables for initialization@>@/
+ begin @<Initialize whatever \TeX\ might access@>@;
+ end;@#
+@t\4@>@<Basic printing procedures@>@/
+@t\4@>@<Error handling procedures@>@/
+
+@ The overall \TeX\ program begins with the heading just shown, after which
+comes a bunch of procedure declarations and function declarations.
+Finally we will get to the main program, which begins with the
+comment `|start_here|'. If you want to skip down to the
+main program now, you can look up `|start_here|' in the index.
+But the author suggests that the best way to understand this program
+is to follow pretty much the order of \TeX's components as they appear in the
+\.{WEB} description you are now reading, since the present ordering is
+intended to combine the advantages of the ``bottom up'' and ``top down''
+approaches to the problem of understanding a somewhat complicated system.
+
+@ Three labels must be declared in the main program, so we give them
+symbolic names.
+
+@d start_of_TEX=1 {go here when \TeX's variables are initialized}
+@d end_of_TEX=9998 {go here to close files and terminate gracefully}
+@d final_end=9999 {this label marks the ending of the program}
+
+@<Labels in the out...@>=
+start_of_TEX@t\hskip-2pt@>, end_of_TEX@t\hskip-2pt@>,@,final_end;
+ {key control points}
+
+@ Some of the code below is intended to be used only when diagnosing the
+strange behavior that sometimes occurs when \TeX\ is being installed or
+when system wizards are fooling around with \TeX\ without quite knowing
+what they are doing. Such code will not normally be compiled; it is
+delimited by the codewords `$|debug|\ldots|gubed|$', with apologies
+to people who wish to preserve the purity of English.
+
+Similarly, there is some conditional code delimited by
+`$|stat|\ldots|tats|$' that is intended for use when statistics are to be
+kept about \TeX's memory usage. The |stat| $\ldots$ |tats| code also
+implements diagnostic information for \.{\\tracingparagraphs} and
+\.{\\tracingpages}.
+@^debugging@>
+
+@d debug==@{ {change this to `$\\{debug}\equiv\null$' when debugging}
+@d gubed==@t@>@} {change this to `$\\{gubed}\equiv\null$' when debugging}
+@f debug==begin
+@f gubed==end
+@#
+@d stat==@{ {change this to `$\\{stat}\equiv\null$' when gathering
+ usage statistics}
+@d tats==@t@>@} {change this to `$\\{tats}\equiv\null$' when gathering
+ usage statistics}
+@f stat==begin
+@f tats==end
+
+@ This program has two important variations: (1) There is a long and slow
+version called \.{INITEX}, which does the extra calculations needed to
+@.INITEX@>
+initialize \TeX's internal tables; and (2)~there is a shorter and faster
+production version, which cuts the initialization to a bare minimum.
+Parts of the program that are needed in (1) but not in (2) are delimited by
+the codewords `$|init|\ldots|tini|$'.
+
+@d init== {change this to `$\\{init}\equiv\.{@@\{}$' in the production version}
+@d tini== {change this to `$\\{tini}\equiv\.{@@\}}$' in the production version}
+@f init==begin
+@f tini==end
+
+@<Initialize whatever...@>=
+@<Set initial values of key variables@>@/
+@!init @<Initialize table entries (done by \.{INITEX} only)@>@;@+tini
+
+@ If the first character of a \PASCAL\ comment is a dollar sign,
+\ph\ treats the comment as a list of ``compiler directives'' that will
+affect the translation of this program into machine language. The
+directives shown below specify full checking and inclusion of the \PASCAL\
+debugger when \TeX\ is being debugged, but they cause range checking and other
+redundant code to be eliminated when the production system is being generated.
+Arithmetic overflow will be detected in all cases.
+@^system dependencies@>
+@^Overflow in arithmetic@>
+
+@<Compiler directives@>=
+@{@&$C-,A+,D-@} {no range check, catch arithmetic overflow, no debug overhead}
+@!debug @{@&$C+,D+@}@+ gubed {but turn everything on when debugging}
+
+@ This \TeX\ implementation conforms to the rules of the {\sl Pascal User
+@:PASCAL}{\PASCAL@>
+@^system dependencies@>
+Manual} published by Jensen and Wirth in 1975, except where system-dependent
+@^Wirth, Niklaus@>
+@^Jensen, Kathleen@>
+code is necessary to make a useful system program, and except in another
+respect where such conformity would unnecessarily obscure the meaning
+and clutter up the code: We assume that |case| statements may include a
+default case that applies if no matching label is found. Thus, we shall use
+constructions like
+$$\vbox{\halign{\ignorespaces#\hfil\cr
+|case x of|\cr
+1: $\langle\,$code for $x=1\,\rangle$;\cr
+3: $\langle\,$code for $x=3\,\rangle$;\cr
+|othercases| $\langle\,$code for |x<>1| and |x<>3|$\,\rangle$\cr
+|endcases|\cr}}$$
+since most \PASCAL\ compilers have plugged this hole in the language by
+incorporating some sort of default mechanism. For example, the \ph\
+compiler allows `|others|:' as a default label, and other \PASCAL s allow
+syntaxes like `\&{else}' or `\&{otherwise}' or `\\{otherwise}:', etc. The
+definitions of |othercases| and |endcases| should be changed to agree with
+local conventions. Note that no semicolon appears before |endcases| in
+this program, so the definition of |endcases| should include a semicolon
+if the compiler wants one. (Of course, if no default mechanism is
+available, the |case| statements of \TeX\ will have to be laboriously
+extended by listing all remaining cases. People who are stuck with such
+\PASCAL s have, in fact, done this, successfully but not happily!)
+
+@d othercases == others: {default for cases not listed explicitly}
+@d endcases == @+end {follows the default case in an extended |case| statement}
+@f othercases == else
+@f endcases == end
+
+@ The following parameters can be changed at compile time to extend or
+reduce \TeX's capacity. They may have different values in \.{INITEX} and
+in production versions of \TeX.
+@.INITEX@>
+@^system dependencies@>
+
+@<Constants...@>=
+@!mem_max=30000; {greatest index in \TeX's internal |mem| array;
+ must be strictly less than |max_halfword|;
+ must be equal to |mem_top| in \.{INITEX}, otherwise |>=mem_top|}
+@!mem_min=0; {smallest index in \TeX's internal |mem| array;
+ must be |min_halfword| or more;
+ must be equal to |mem_bot| in \.{INITEX}, otherwise |<=mem_bot|}
+@!buf_size=500; {maximum number of characters simultaneously present in
+ current lines of open files and in control sequences between
+ \.{\\csname} and \.{\\endcsname}; must not exceed |max_halfword|}
+@!error_line=72; {width of context lines on terminal error messages}
+@!half_error_line=42; {width of first lines of contexts in terminal
+ error messages; should be between 30 and |error_line-15|}
+@!max_print_line=79; {width of longest text lines output; should be at least 60}
+@!stack_size=200; {maximum number of simultaneous input sources}
+@!max_in_open=6; {maximum number of input files and error insertions that
+ can be going on simultaneously}
+@!font_max=75; {maximum internal font number; must not exceed |max_quarterword|
+ and must be at most |font_base+256|}
+@!font_mem_size=20000; {number of words of |font_info| for all fonts}
+@!param_size=60; {maximum number of simultaneous macro parameters}
+@!nest_size=40; {maximum number of semantic levels simultaneously active}
+@!max_strings=3000; {maximum number of strings; must not exceed |max_halfword|}
+@!string_vacancies=8000; {the minimum number of characters that should be
+ available for the user's control sequences and font names,
+ after \TeX's own error messages are stored}
+@!pool_size=32000; {maximum number of characters in strings, including all
+ error messages and help texts, and the names of all fonts and
+ control sequences; must exceed |string_vacancies| by the total
+ length of \TeX's own strings, which is currently about 23000}
+@!save_size=600; {space for saving values outside of current group; must be
+ at most |max_halfword|}
+@!trie_size=8000; {space for hyphenation patterns; should be larger for
+ \.{INITEX} than it is in production versions of \TeX}
+@!trie_op_size=500; {space for ``opcodes'' in the hyphenation patterns}
+@!dvi_buf_size=800; {size of the output buffer; must be a multiple of 8}
+@!file_name_size=40; {file names shouldn't be longer than this}
+@!pool_name='TeXformats:TEX.POOL ';
+ {string of length |file_name_size|; tells where the string pool appears}
+@.TeXformats@>
+
+@ Like the preceding parameters, the following quantities can be changed
+at compile time to extend or reduce \TeX's capacity. But if they are changed,
+it is necessary to rerun the initialization program \.{INITEX}
+@.INITEX@>
+to generate new tables for the production \TeX\ program.
+One can't simply make helter-skelter changes to the following constants,
+since certain rather complex initialization
+numbers are computed from them. They are defined here using
+\.{WEB} macros, instead of being put into \PASCAL's |const| list, in order to
+emphasize this distinction.
+
+@d mem_bot=0 {smallest index in the |mem| array dumped by \.{INITEX};
+ must not be less than |mem_min|}
+@d mem_top==30000 {largest index in the |mem| array dumped by \.{INITEX};
+ must be substantially larger than |mem_bot|
+ and not greater than |mem_max|}
+@d font_base=0 {smallest internal font number; must not be less
+ than |min_quarterword|}
+@d hash_size=2100 {maximum number of control sequences; it should be at most
+ about |(mem_max-mem_min)/10|}
+@d hash_prime=1777 {a prime number equal to about 85\pct! of |hash_size|}
+@d hyph_size=307 {another prime; the number of \.{\\hyphenation} exceptions}
+@^system dependencies@>
+
+@ In case somebody has inadvertently made bad settings of the ``constants,''
+\TeX\ checks them using a global variable called |bad|.
+
+This is the first of many sections of \TeX\ where global variables are
+defined.
+
+@<Glob...@>=
+@!bad:integer; {is some ``constant'' wrong?}
+
+@ Later on we will say `\ignorespaces|if mem_max>=max_halfword then bad:=14|',
+or something similar. (We can't do that until |max_halfword| has been defined.)
+
+@<Check the ``constant'' values for consistency@>=
+bad:=0;
+if (half_error_line<30)or(half_error_line>error_line-15) then bad:=1;
+if max_print_line<60 then bad:=2;
+if dvi_buf_size mod 8<>0 then bad:=3;
+if mem_bot+1100>mem_top then bad:=4;
+if hash_prime>hash_size then bad:=5;
+if max_in_open>=128 then bad:=6;
+if mem_top<256+11 then bad:=7; {we will want |null_list>255|}
+
+@ Labels are given symbolic names by the following definitions, so that
+occasional |goto| statements will be meaningful. We insert the label
+`|exit|' just before the `\ignorespaces|end|\unskip' of a procedure in
+which we have used the `|return|' statement defined below; the label
+`|restart|' is occasionally used at the very beginning of a procedure; and
+the label `|reswitch|' is occasionally used just prior to a |case|
+statement in which some cases change the conditions and we wish to branch
+to the newly applicable case. Loops that are set up with the |loop|
+construction defined below are commonly exited by going to `|done|' or to
+`|found|' or to `|not_found|', and they are sometimes repeated by going to
+`|continue|'. If two or more parts of a subroutine start differently but
+end up the same, the shared code may be gathered together at
+`|common_ending|'.
+
+Incidentally, this program never declares a label that isn't actually used,
+because some fussy \PASCAL\ compilers will complain about redundant labels.
+
+@d exit=10 {go here to leave a procedure}
+@d restart=20 {go here to start a procedure again}
+@d reswitch=21 {go here to start a case statement again}
+@d continue=22 {go here to resume a loop}
+@d done=30 {go here to exit a loop}
+@d done1=31 {like |done|, when there is more than one loop}
+@d done2=32 {for exiting the second loop in a long block}
+@d done3=33 {for exiting the third loop in a very long block}
+@d done4=34 {for exiting the fourth loop in an extremely long block}
+@d done5=35 {for exiting the fifth loop in an immense block}
+@d done6=36 {for exiting the sixth loop in a block}
+@d found=40 {go here when you've found it}
+@d found1=41 {like |found|, when there's more than one per routine}
+@d found2=42 {like |found|, when there's more than two per routine}
+@d not_found=45 {go here when you've found nothing}
+@d common_ending=50 {go here when you want to merge with another branch}
+
+@ Here are some macros for common programming idioms.
+
+@d incr(#) == #:=#+1 {increase a variable by unity}
+@d decr(#) == #:=#-1 {decrease a variable by unity}
+@d negate(#) == #:=-# {change the sign of a variable}
+@d loop == @+ while true do@+ {repeat over and over until a |goto| happens}
+@f loop == xclause
+ {\.{WEB}'s |xclause| acts like `\ignorespaces|while true do|\unskip'}
+@d do_nothing == {empty statement}
+@d return == goto exit {terminate a procedure call}
+@f return == nil
+@d empty=0 {symbolic name for a null constant}
+
+@* \[2] The character set.
+In order to make \TeX\ readily portable to a wide variety of
+computers, all of its input text is converted to an internal eight-bit
+code that includes standard ASCII, the ``American Standard Code for
+Information Interchange.'' This conversion is done immediately when each
+character is read in. Conversely, characters are converted from ASCII to
+the user's external representation just before they are output to a
+text file.
+
+Such an internal code is relevant to users of \TeX\ primarily because it
+governs the positions of characters in the fonts. For example, the
+character `\.A' has ASCII code $65=@'101$, and when \TeX\ typesets
+this letter it specifies character number 65 in the current font.
+If that font actually has `\.A' in a different position, \TeX\ doesn't
+know what the real position is; the program that does the actual printing from
+\TeX's device-independent files is responsible for converting from ASCII to
+a particular font encoding.
+@^ASCII code@>
+
+\TeX's internal code also defines the value of constants
+that begin with a reverse apostrophe; and it provides an index to the
+\.{\\catcode}, \.{\\mathcode}, \.{\\uccode}, \.{\\lccode}, and \.{\\delcode}
+tables.
+
+@ Characters of text that have been converted to \TeX's internal form
+are said to be of type |ASCII_code|, which is a subrange of the integers.
+
+@<Types...@>=
+@!ASCII_code=0..255; {eight-bit numbers}
+
+@ The original \PASCAL\ compiler was designed in the late 60s, when six-bit
+character sets were common, so it did not make provision for lowercase
+letters. Nowadays, of course, we need to deal with both capital and small
+letters in a convenient way, especially in a program for typesetting;
+so the present specification of \TeX\ has been written under the assumption
+that the \PASCAL\ compiler and run-time system permit the use of text files
+with more than 64 distinguishable characters. More precisely, we assume that
+the character set contains at least the letters and symbols associated
+with ASCII codes @'40 through @'176; all of these characters are now
+available on most computer terminals.
+
+Since we are dealing with more characters than were present in the first
+\PASCAL\ compilers, we have to decide what to call the associated data
+type. Some \PASCAL s use the original name |char| for the
+characters in text files, even though there now are more than 64 such
+characters, while other \PASCAL s consider |char| to be a 64-element
+subrange of a larger data type that has some other name.
+
+In order to accommodate this difference, we shall use the name |text_char|
+to stand for the data type of the characters that are converted to and
+from |ASCII_code| when they are input and output. We shall also assume
+that |text_char| consists of the elements |chr(first_text_char)| through
+|chr(last_text_char)|, inclusive. The following definitions should be
+adjusted if necessary.
+@^system dependencies@>
+
+@d text_char == char {the data type of characters in text files}
+@d first_text_char=0 {ordinal number of the smallest element of |text_char|}
+@d last_text_char=255 {ordinal number of the largest element of |text_char|}
+
+@<Local variables for init...@>=
+@!i:integer;
+
+@ The \TeX\ processor converts between ASCII code and
+the user's external character set by means of arrays |xord| and |xchr|
+that are analogous to \PASCAL's |ord| and |chr| functions.
+
+@<Glob...@>=
+@!xord: array [text_char] of ASCII_code;
+ {specifies conversion of input characters}
+@!xchr: array [ASCII_code] of text_char;
+ {specifies conversion of output characters}
+
+@ Since we are assuming that our \PASCAL\ system is able to read and
+write the visible characters of standard ASCII (although not
+necessarily using the ASCII codes to represent them), the following
+assignment statements initialize the standard part of the |xchr| array
+properly, without needing any system-dependent changes. On the other
+hand, it is possible to implement \TeX\ with less complete character
+sets, and in such cases it will be necessary to change something here.
+@^system dependencies@>
+
+@<Set init...@>=
+xchr[@'40]:=' ';
+xchr[@'41]:='!';
+xchr[@'42]:='"';
+xchr[@'43]:='#';
+xchr[@'44]:='$';
+xchr[@'45]:='%';
+xchr[@'46]:='&';
+xchr[@'47]:='''';@/
+xchr[@'50]:='(';
+xchr[@'51]:=')';
+xchr[@'52]:='*';
+xchr[@'53]:='+';
+xchr[@'54]:=',';
+xchr[@'55]:='-';
+xchr[@'56]:='.';
+xchr[@'57]:='/';@/
+xchr[@'60]:='0';
+xchr[@'61]:='1';
+xchr[@'62]:='2';
+xchr[@'63]:='3';
+xchr[@'64]:='4';
+xchr[@'65]:='5';
+xchr[@'66]:='6';
+xchr[@'67]:='7';@/
+xchr[@'70]:='8';
+xchr[@'71]:='9';
+xchr[@'72]:=':';
+xchr[@'73]:=';';
+xchr[@'74]:='<';
+xchr[@'75]:='=';
+xchr[@'76]:='>';
+xchr[@'77]:='?';@/
+xchr[@'100]:='@@';
+xchr[@'101]:='A';
+xchr[@'102]:='B';
+xchr[@'103]:='C';
+xchr[@'104]:='D';
+xchr[@'105]:='E';
+xchr[@'106]:='F';
+xchr[@'107]:='G';@/
+xchr[@'110]:='H';
+xchr[@'111]:='I';
+xchr[@'112]:='J';
+xchr[@'113]:='K';
+xchr[@'114]:='L';
+xchr[@'115]:='M';
+xchr[@'116]:='N';
+xchr[@'117]:='O';@/
+xchr[@'120]:='P';
+xchr[@'121]:='Q';
+xchr[@'122]:='R';
+xchr[@'123]:='S';
+xchr[@'124]:='T';
+xchr[@'125]:='U';
+xchr[@'126]:='V';
+xchr[@'127]:='W';@/
+xchr[@'130]:='X';
+xchr[@'131]:='Y';
+xchr[@'132]:='Z';
+xchr[@'133]:='[';
+xchr[@'134]:='\';
+xchr[@'135]:=']';
+xchr[@'136]:='^';
+xchr[@'137]:='_';@/
+xchr[@'140]:='`';
+xchr[@'141]:='a';
+xchr[@'142]:='b';
+xchr[@'143]:='c';
+xchr[@'144]:='d';
+xchr[@'145]:='e';
+xchr[@'146]:='f';
+xchr[@'147]:='g';@/
+xchr[@'150]:='h';
+xchr[@'151]:='i';
+xchr[@'152]:='j';
+xchr[@'153]:='k';
+xchr[@'154]:='l';
+xchr[@'155]:='m';
+xchr[@'156]:='n';
+xchr[@'157]:='o';@/
+xchr[@'160]:='p';
+xchr[@'161]:='q';
+xchr[@'162]:='r';
+xchr[@'163]:='s';
+xchr[@'164]:='t';
+xchr[@'165]:='u';
+xchr[@'166]:='v';
+xchr[@'167]:='w';@/
+xchr[@'170]:='x';
+xchr[@'171]:='y';
+xchr[@'172]:='z';
+xchr[@'173]:='{';
+xchr[@'174]:='|';
+xchr[@'175]:='}';
+xchr[@'176]:='~';@/
+
+@ Some of the ASCII codes without visible characters have been given symbolic
+names in this program because they are used with a special meaning.
+
+@d null_code=@'0 {ASCII code that might disappear}
+@d carriage_return=@'15 {ASCII code used at end of line}
+@d invalid_code=@'177 {ASCII code that many systems prohibit in text files}
+
+@ The ASCII code is ``standard'' only to a certain extent, since many
+computer installations have found it advantageous to have ready access
+to more than 94 printing characters. Appendix~C of {\sl The \TeX book\/}
+gives a complete specification of the intended correspondence between
+characters and \TeX's internal representation.
+@:TeXbook}{\sl The \TeX book@>
+
+If \TeX\ is being used
+on a garden-variety \PASCAL\ for which only standard ASCII
+codes will appear in the input and output files, it doesn't really matter
+what codes are specified in |xchr[0..@'37]|, but the safest policy is to
+blank everything out by using the code shown below.
+
+However, other settings of |xchr| will make \TeX\ more friendly on
+computers that have an extended character set, so that users can type things
+like `\.^^Z' instead of `\.{\\ne}'. People with extended character sets can
+assign codes arbitrarily, giving an |xchr| equivalent to whatever
+characters the users of \TeX\ are allowed to have in their input files.
+It is best to make the codes correspond to the intended interpretations as
+shown in Appendix~C whenever possible; but this is not necessary. For
+example, in countries with an alphabet of more than 26 letters, it is
+usually best to map the additional letters into codes less than~@'40.
+To get the most ``permissive'' character set, change |' '| on the
+right of these assignment statements to |chr(i)|.
+@^character set dependencies@>
+@^system dependencies@>
+
+@<Set init...@>=
+for i:=0 to @'37 do xchr[i]:=' ';
+for i:=@'177 to @'377 do xchr[i]:=' ';
+
+@ The following system-independent code makes the |xord| array contain a
+suitable inverse to the information in |xchr|. Note that if |xchr[i]=xchr[j]|
+where |i<j<@'177|, the value of |xord[xchr[i]]| will turn out to be
+|j| or more; hence, standard ASCII code numbers will be used instead of
+codes below @'40 in case there is a coincidence.
+
+@<Set init...@>=
+for i:=first_text_char to last_text_char do xord[chr(i)]:=invalid_code;
+for i:=@'200 to @'377 do xord[xchr[i]]:=i;
+for i:=0 to @'176 do xord[xchr[i]]:=i;
+
+@* \[3] Input and output.
+The bane of portability is the fact that different operating systems treat
+input and output quite differently, perhaps because computer scientists
+have not given sufficient attention to this problem. People have felt somehow
+that input and output are not part of ``real'' programming. Well, it is true
+that some kinds of programming are more fun than others. With existing
+input/output conventions being so diverse and so messy, the only sources of
+joy in such parts of the code are the rare occasions when one can find a
+way to make the program a little less bad than it might have been. We have
+two choices, either to attack I/O now and get it over with, or to postpone
+I/O until near the end. Neither prospect is very attractive, so let's
+get it over with.
+
+The basic operations we need to do are (1)~inputting and outputting of
+text, to or from a file or the user's terminal; (2)~inputting and
+outputting of eight-bit bytes, to or from a file; (3)~instructing the
+operating system to initiate (``open'') or to terminate (``close'') input or
+output from a specified file; (4)~testing whether the end of an input
+file has been reached.
+
+\TeX\ needs to deal with two kinds of files.
+We shall use the term |alpha_file| for a file that contains textual data,
+and the term |byte_file| for a file that contains eight-bit binary information.
+These two types turn out to be the same on many computers, but
+sometimes there is a significant distinction, so we shall be careful to
+distinguish between them. Standard protocols for transferring
+such files from computer to computer, via high-speed networks, are
+now becoming available to more and more communities of users.
+
+The program actually makes use also of a third kind of file, called a
+|word_file|, when dumping and reloading base information for its own
+initialization. We shall define a word file later; but it will be possible
+for us to specify simple operations on word files before they are defined.
+
+@<Types...@>=
+@!eight_bits=0..255; {unsigned one-byte quantity}
+@!alpha_file=packed file of text_char; {files that contain textual data}
+@!byte_file=packed file of eight_bits; {files that contain binary data}
+
+@ Most of what we need to do with respect to input and output can be handled
+by the I/O facilities that are standard in \PASCAL, i.e., the routines
+called |get|, |put|, |eof|, and so on. But
+standard \PASCAL\ does not allow file variables to be associated with file
+names that are determined at run time, so it cannot be used to implement
+\TeX; some sort of extension to \PASCAL's ordinary |reset| and |rewrite|
+is crucial for our purposes. We shall assume that |name_of_file| is a variable
+of an appropriate type such that the \PASCAL\ run-time system being used to
+implement \TeX\ can open a file whose external name is specified by
+|name_of_file|.
+@^system dependencies@>
+
+@<Glob...@>=
+@!name_of_file:packed array[1..file_name_size] of char;@;@/
+ {on some systems this may be a \&{record} variable}
+@!name_length:0..file_name_size;@/{this many characters are actually
+ relevant in |name_of_file| (the rest are blank)}
+
+@ The \ph\ compiler with which the present version of \TeX\ was prepared has
+extended the rules of \PASCAL\ in a very convenient way. To open file~|f|,
+we can write
+$$\vbox{\halign{#\hfil\qquad&#\hfil\cr
+|reset(f,@t\\{name}@>,'/O')|&for input;\cr
+|rewrite(f,@t\\{name}@>,'/O')|&for output.\cr}}$$
+The `\\{name}' parameter, which is of type `{\bf packed array
+$[\langle\\{any}\rangle]$ of \\{char}}', stands for the name of
+the external file that is being opened for input or output.
+Blank spaces that might appear in \\{name} are ignored.
+
+The `\.{/O}' parameter tells the operating system not to issue its own
+error messages if something goes wrong. If a file of the specified name
+cannot be found, or if such a file cannot be opened for some other reason
+(e.g., someone may already be trying to write the same file), we will have
+|@!erstat(f)<>0| after an unsuccessful |reset| or |rewrite|. This allows
+\TeX\ to undertake appropriate corrective action.
+@:PASCAL H}{\ph@>
+@^system dependencies@>
+
+\TeX's file-opening procedures return |false| if no file identified by
+|name_of_file| could be opened.
+
+@d reset_OK(#)==erstat(#)=0
+@d rewrite_OK(#)==erstat(#)=0
+
+@p function a_open_in(var f:alpha_file):boolean;
+ {open a text file for input}
+begin reset(f,name_of_file,'/O'); a_open_in:=reset_OK(f);
+end;
+@#
+function a_open_out(var f:alpha_file):boolean;
+ {open a text file for output}
+begin rewrite(f,name_of_file,'/O'); a_open_out:=rewrite_OK(f);
+end;
+@#
+function b_open_in(var f:byte_file):boolean;
+ {open a binary file for input}
+begin reset(f,name_of_file,'/O'); b_open_in:=reset_OK(f);
+end;
+@#
+function b_open_out(var f:byte_file):boolean;
+ {open a binary file for output}
+begin rewrite(f,name_of_file,'/O'); b_open_out:=rewrite_OK(f);
+end;
+@#
+function w_open_in(var f:word_file):boolean;
+ {open a word file for input}
+begin reset(f,name_of_file,'/O'); w_open_in:=reset_OK(f);
+end;
+@#
+function w_open_out(var f:word_file):boolean;
+ {open a word file for output}
+begin rewrite(f,name_of_file,'/O'); w_open_out:=rewrite_OK(f);
+end;
+
+@ Files can be closed with the \ph\ routine `|close(f)|', which
+@^system dependencies@>
+should be used when all input or output with respect to |f| has been completed.
+This makes |f| available to be opened again, if desired; and if |f| was used for
+output, the |close| operation makes the corresponding external file appear
+on the user's area, ready to be read.
+
+These procedures should not generate error messages if a file is
+being closed before it has been successfully opened.
+
+@p procedure a_close(var f:alpha_file); {close a text file}
+begin close(f);
+end;
+@#
+procedure b_close(var f:byte_file); {close a binary file}
+begin close(f);
+end;
+@#
+procedure w_close(var f:word_file); {close a word file}
+begin close(f);
+end;
+
+@ Binary input and output are done with \PASCAL's ordinary |get| and |put|
+procedures, so we don't have to make any other special arrangements for
+binary~I/O. Text output is also easy to do with standard \PASCAL\ routines.
+The treatment of text input is more difficult, however, because
+of the necessary translation to |ASCII_code| values.
+\TeX's conventions should be efficient, and they should
+blend nicely with the user's operating environment.
+
+@ Input from text files is read one line at a time, using a routine called
+|input_ln|. This function is defined in terms of global variables called
+|buffer|, |first|, and |last| that will be described in detail later; for
+now, it suffices for us to know that |buffer| is an array of |ASCII_code|
+values, and that |first| and |last| are indices into this array
+representing the beginning and ending of a line of text.
+
+@<Glob...@>=
+@!buffer:array[0..buf_size] of ASCII_code; {lines of characters being read}
+@!first:0..buf_size; {the first unused position in |buffer|}
+@!last:0..buf_size; {end of the line just input to |buffer|}
+@!max_buf_stack:0..buf_size; {largest index used in |buffer|}
+
+@ The |input_ln| function brings the next line of input from the specified
+file into available positions of the buffer array and returns the value
+|true|, unless the file has already been entirely read, in which case it
+returns |false| and sets |last:=first|. In general, the |ASCII_code|
+numbers that represent the next line of the file are input into
+|buffer[first]|, |buffer[first+1]|, \dots, |buffer[last-1]|; and the
+global variable |last| is set equal to |first| plus the length of the
+line. Trailing blanks are removed from the line; thus, either |last=first|
+(in which case the line was entirely blank) or |buffer[last-1]<>" "|.
+
+An overflow error is given, however, if the normal actions of |input_ln|
+would make |last>=buf_size|; this is done so that other parts of \TeX\
+can safely look at the contents of |buffer[last+1]| without overstepping
+the bounds of the |buffer| array. Upon entry to |input_ln|, the condition
+|first<buf_size| will always hold, so that there is always room for an
+``empty'' line.
+
+The variable |max_buf_stack|, which is used to keep track of how large
+the |buf_size| parameter must be to accommodate the present job, is
+also kept up to date by |input_ln|.
+
+If the |bypass_eoln| parameter is |true|, |input_ln| will do a |get|
+before looking at the first character of the line; this skips over
+an |eoln| that was in |f^|. The procedure does not do a |get| when it
+reaches the end of the line; therefore it can be used to acquire input
+from the user's terminal as well as from ordinary text files.
+
+Standard \PASCAL\ says that a file should have |eoln| immediately
+before |eof|, but \TeX\ needs only a weaker restriction: If |eof|
+occurs in the middle of a line, the system function |eoln| should return
+a |true| result (even though |f^| will be undefined).
+
+Since the inner loop of |input_ln| is part of \TeX's ``inner loop''---each
+character of input comes in at this place---it is wise to reduce system
+overhead by making use of special routines that read in an entire array
+of characters at once, if such routines are available. The following
+code uses standard \PASCAL\ to illustrate what needs to be done, but
+finer tuning is often possible at well-developed \PASCAL\ sites.
+@^inner loop@>
+
+@p function input_ln(var f:alpha_file;@!bypass_eoln:boolean):boolean;
+ {inputs the next line or returns |false|}
+var last_nonblank:0..buf_size; {|last| with trailing blanks removed}
+begin if bypass_eoln then if not eof(f) then get(f);
+ {input the first character of the line into |f^|}
+last:=first; {cf.\ Matthew 19\thinspace:\thinspace30}
+if eof(f) then input_ln:=false
+else begin last_nonblank:=first;
+ while not eoln(f) do
+ begin if last>=max_buf_stack then
+ begin max_buf_stack:=last+1;
+ if max_buf_stack=buf_size then
+ @<Report overflow of the input buffer, and abort@>;
+ end;
+ buffer[last]:=xord[f^]; get(f); incr(last);
+ if buffer[last-1]<>" " then last_nonblank:=last;
+ end;
+ last:=last_nonblank; input_ln:=true;
+ end;
+end;
+
+@ The user's terminal acts essentially like other files of text, except
+that it is used both for input and for output. When the terminal is
+considered an input file, the file variable is called |term_in|, and when it
+is considered an output file the file variable is |term_out|.
+@^system dependencies@>
+
+@<Glob...@>=
+@!term_in:alpha_file; {the terminal as an input file}
+@!term_out:alpha_file; {the terminal as an output file}
+
+@ Here is how to open the terminal files
+in \ph. The `\.{/I}' switch suppresses the first |get|.
+@^system dependencies@>
+
+@d t_open_in==reset(term_in,'TTY:','/O/I') {open the terminal for text input}
+@d t_open_out==rewrite(term_out,'TTY:','/O') {open the terminal for text output}
+
+@ Sometimes it is necessary to synchronize the input/output mixture that
+happens on the user's terminal, and three system-dependent
+procedures are used for this
+purpose. The first of these, |update_terminal|, is called when we want
+to make sure that everything we have output to the terminal so far has
+actually left the computer's internal buffers and been sent.
+The second, |clear_terminal|, is called when we wish to cancel any
+input that the user may have typed ahead (since we are about to
+issue an unexpected error message). The third, |wake_up_terminal|,
+is supposed to revive the terminal if the user has disabled it by
+some instruction to the operating system. The following macros show how
+these operations can be specified in \ph:
+@^system dependencies@>
+
+@d update_terminal == break(term_out) {empty the terminal output buffer}
+@d clear_terminal == break_in(term_in,true) {clear the terminal input buffer}
+@d wake_up_terminal == do_nothing {cancel the user's cancellation of output}
+
+@ We need a special routine to read the first line of \TeX\ input from
+the user's terminal. This line is different because it is read before we
+have opened the transcript file; there is sort of a ``chicken and
+egg'' problem here. If the user types `\.{\\input paper}' on the first
+line, or if some macro invoked by that line does such an \.{\\input},
+the transcript file will be named `\.{paper.log}'; but if no \.{\\input}
+commands are performed during the first line of terminal input, the transcript
+file will acquire its default name `\.{texput.log}'. (The transcript file
+will not contain error messages generated by the first line before the
+first \.{\\input} command.)
+@.texput@>
+
+The first line is even more special if we are lucky enough to have an operating
+system that treats \TeX\ differently from a run-of-the-mill \PASCAL\ object
+program. It's nice to let the user start running a \TeX\ job by typing
+a command line like `\.{tex paper}'; in such a case, \TeX\ will operate
+as if the first line of input were `\.{paper}', i.e., the first line will
+consist of the remainder of the command line, after the part that invoked
+\TeX.
+
+The first line is special also because it may be read before \TeX\ has
+input a format file. In such cases, normal error messages cannot yet
+be given. The following code uses concepts that will be explained later.
+(If the \PASCAL\ compiler does not support non-local |@!goto|\unskip, the
+@^system dependencies@>
+statement `|goto final_end|' should be replaced by something that
+quietly terminates the program.)
+
+@<Report overflow of the input buffer, and abort@>=
+if format_ident=0 then
+ begin write_ln(term_out,'Buffer size exceeded!'); goto final_end;
+@.Buffer size exceeded@>
+ end
+else begin cur_input.loc_field:=first; cur_input.limit_field:=last-1;
+ overflow("buffer size",buf_size);
+@:TeX capacity exceeded buffer size}{\quad buffer size@>
+ end
+
+@ Different systems have different ways to get started. But regardless of
+what conventions are adopted, the routine that initializes the terminal
+should satisfy the following specifications:
+
+\yskip\textindent{1)}It should open file |term_in| for input from the
+ terminal. (The file |term_out| will already be open for output to the
+ terminal.)
+
+\textindent{2)}If the user has given a command line, this line should be
+ considered the first line of terminal input. Otherwise the
+ user should be prompted with `\.{**}', and the first line of input
+ should be whatever is typed in response.
+
+\textindent{3)}The first line of input, which might or might not be a
+ command line, should appear in locations |first| to |last-1| of the
+ |buffer| array.
+
+\textindent{4)}The global variable |loc| should be set so that the
+ character to be read next by \TeX\ is in |buffer[loc]|. This
+ character should not be blank, and we should have |loc<last|.
+
+\yskip\noindent(It may be necessary to prompt the user several times
+before a non-blank line comes in. The prompt is `\.{**}' instead of the
+later `\.*' because the meaning is slightly different: `\.{\\input}' need
+not be typed immediately after~`\.{**}'.)
+
+@d loc==cur_input.loc_field {location of first unread character in |buffer|}
+
+@ The following program does the required initialization
+without retrieving a possible command line.
+It should be clear how to modify this routine to deal with command lines,
+if the system permits them.
+@^system dependencies@>
+
+@p function init_terminal:boolean; {gets the terminal input started}
+label exit;
+begin t_open_in;
+loop@+begin wake_up_terminal; write(term_out,'**'); update_terminal;
+@.**@>
+ if not input_ln(term_in,true) then {this shouldn't happen}
+ begin write_ln(term_out);
+ write(term_out,'! End of file on the terminal... why?');
+@.End of file on the terminal@>
+ init_terminal:=false; return;
+ end;
+ loc:=first;
+ while (loc<last)and(buffer[loc]=" ") do incr(loc);
+ if loc<last then
+ begin init_terminal:=true;
+ return; {return unless the line was all blank}
+ end;
+ write_ln(term_out,'Please type the name of your input file.');
+ end;
+exit:end;
+
+@* \[4] String handling.
+Control sequence names and diagnostic messages are variable-length strings
+of eight-bit characters. Since \PASCAL\ does not have a well-developed string
+mechanism, \TeX\ does all of its string processing by homegrown methods.
+
+Elaborate facilities for dynamic strings are not needed, so all of the
+necessary operations can be handled with a simple data structure.
+The array |str_pool| contains all of the (eight-bit) ASCII codes in all
+of the strings, and the array |str_start| contains indices of the starting
+points of each string. Strings are referred to by integer numbers, so that
+string number |s| comprises the characters |str_pool[j]| for
+|str_start[s]<=j<str_start[s+1]|. Additional integer variables
+|pool_ptr| and |str_ptr| indicate the number of entries used so far
+in |str_pool| and |str_start|, respectively; locations
+|str_pool[pool_ptr]| and |str_start[str_ptr]| are
+ready for the next string to be allocated.
+
+String numbers 0 to 255 are reserved for strings that correspond to single
+ASCII characters. This is in accordance with the conventions of \.{WEB},
+@.WEB@>
+which converts single-character strings into the ASCII code number of the
+single character involved, while it converts other strings into integers
+and builds a string pool file. Thus, when the string constant \.{"."} appears
+in the program below, \.{WEB} converts it into the integer 46, which is the
+ASCII code for a period, while \.{WEB} will convert a string like \.{"hello"}
+into some integer greater than~255. String number 46 will presumably be the
+single character `\..'; but some ASCII codes have no standard visible
+representation, and \TeX\ sometimes needs to be able to print an arbitrary
+ASCII character, so the first 256 strings are used to specify exactly what
+should be printed for each of the 256 possibilities.
+
+Elements of the |str_pool| array must be ASCII codes that can actually
+be printed; i.e., they must have an |xchr| equivalent in the local
+character set. (This restriction applies only to preloaded strings,
+not to those generated dynamically by the user.)
+
+Some \PASCAL\ compilers won't pack integers into a single byte unless the
+integers lie in the range |-128..127|. To accommodate such systems
+we access the string pool only via macros that can easily be redefined.
+
+@d si(#) == # {convert from |ASCII_code| to |packed_ASCII_code|}
+@d so(#) == # {convert from |packed_ASCII_code| to |ASCII_code|}
+
+@<Types...@>=
+@!pool_pointer = 0..pool_size; {for variables that point into |str_pool|}
+@!str_number = 0..max_strings; {for variables that point into |str_start|}
+@!packed_ASCII_code = 0..255; {elements of |str_pool| array}
+
+@ @<Glob...@>=
+@!str_pool:packed array[pool_pointer] of packed_ASCII_code; {the characters}
+@!str_start : array[str_number] of pool_pointer; {the starting pointers}
+@!pool_ptr : pool_pointer; {first unused position in |str_pool|}
+@!str_ptr : str_number; {number of the current string being created}
+@!init_pool_ptr : pool_pointer; {the starting value of |pool_ptr|}
+@!init_str_ptr : str_number; {the starting value of |str_ptr|}
+
+@ Several of the elementary string operations are performed using \.{WEB}
+macros instead of \PASCAL\ procedures, because many of the
+operations are done quite frequently and we want to avoid the
+overhead of procedure calls. For example, here is
+a simple macro that computes the length of a string.
+@.WEB@>
+
+@d length(#)==(str_start[#+1]-str_start[#]) {the number of characters
+ in string number \#}
+
+@ The length of the current string is called |cur_length|:
+
+@d cur_length == (pool_ptr - str_start[str_ptr])
+
+@ Strings are created by appending character codes to |str_pool|.
+The |append_char| macro, defined here, does not check to see if the
+value of |pool_ptr| has gotten too high; this test is supposed to be
+made before |append_char| is used. There is also a |flush_char|
+macro, which erases the last character appended.
+
+To test if there is room to append |l| more characters to |str_pool|,
+we shall write |str_room(l)|, which aborts \TeX\ and gives an
+apologetic error message if there isn't enough room.
+
+@d append_char(#) == {put |ASCII_code| \# at the end of |str_pool|}
+begin str_pool[pool_ptr]:=si(#); incr(pool_ptr);
+end
+@d flush_char == decr(pool_ptr) {forget the last character in the pool}
+@d str_room(#) == {make sure that the pool hasn't overflowed}
+ begin if pool_ptr+# > pool_size then
+ overflow("pool size",pool_size-init_pool_ptr);
+@:TeX capacity exceeded pool size}{\quad pool size@>
+ end
+
+@ Once a sequence of characters has been appended to |str_pool|, it
+officially becomes a string when the function |make_string| is called.
+This function returns the identification number of the new string as its
+value.
+
+@p function make_string : str_number; {current string enters the pool}
+begin if str_ptr=max_strings then
+ overflow("number of strings",max_strings-init_str_ptr);
+@:TeX capacity exceeded number of strings}{\quad number of strings@>
+incr(str_ptr); str_start[str_ptr]:=pool_ptr;
+make_string:=str_ptr-1;
+end;
+
+@ To destroy the most recently made string, we say |flush_string|.
+
+@d flush_string==begin decr(str_ptr); pool_ptr:=str_start[str_ptr];
+ end
+
+@ The following subroutine compares string |s| with another string of the
+same length that appears in |buffer| starting at position |k|;
+the result is |true| if and only if the strings are equal.
+Empirical tests indicate that |str_eq_buf| is used in such a way that
+it tends to return |true| about 80 percent of the time.
+
+@p function str_eq_buf(@!s:str_number;@!k:integer):boolean;
+ {test equality of strings}
+label not_found; {loop exit}
+var j: pool_pointer; {running index}
+@!result: boolean; {result of comparison}
+begin j:=str_start[s];
+while j<str_start[s+1] do
+ begin if so(str_pool[j])<>buffer[k] then
+ begin result:=false; goto not_found;
+ end;
+ incr(j); incr(k);
+ end;
+result:=true;
+not_found: str_eq_buf:=result;
+end;
+
+@ Here is a similar routine, but it compares two strings in the string pool,
+and it does not assume that they have the same length.
+
+@p function str_eq_str(@!s,@!t:str_number):boolean;
+ {test equality of strings}
+label not_found; {loop exit}
+var j,@!k: pool_pointer; {running indices}
+@!result: boolean; {result of comparison}
+begin result:=false;
+if length(s)<>length(t) then goto not_found;
+j:=str_start[s]; k:=str_start[t];
+while j<str_start[s+1] do
+ begin if str_pool[j]<>str_pool[k] then goto not_found;
+ incr(j); incr(k);
+ end;
+result:=true;
+not_found: str_eq_str:=result;
+end;
+
+@ The initial values of |str_pool|, |str_start|, |pool_ptr|,
+and |str_ptr| are computed by the \.{INITEX} program, based in part
+on the information that \.{WEB} has output while processing \TeX.
+@.INITEX@>
+@^string pool@>
+
+@p @!init function get_strings_started:boolean; {initializes the string pool,
+ but returns |false| if something goes wrong}
+label done,exit;
+var k,@!l:0..255; {small indices or counters}
+@!m,@!n:text_char; {characters input from |pool_file|}
+@!g:str_number; {garbage}
+@!a:integer; {accumulator for check sum}
+@!c:boolean; {check sum has been checked}
+begin pool_ptr:=0; str_ptr:=0; str_start[0]:=0;
+@<Make the first 256 strings@>;
+@<Read the other strings from the \.{TEX.POOL} file and return |true|,
+ or give an error message and return |false|@>;
+exit:end;
+tini
+
+@ @d app_lc_hex(#)==l:=#;
+ if l<10 then append_char(l+"0")@+else append_char(l-10+"a")
+
+@<Make the first 256...@>=
+for k:=0 to 255 do
+ begin if (@<Character |k| cannot be printed@>) then
+ begin append_char("^"); append_char("^");
+ if k<@'100 then append_char(k+@'100)
+ else if k<@'200 then append_char(k-@'100)
+ else begin app_lc_hex(k div 16); app_lc_hex(k mod 16);
+ end;
+ end
+ else append_char(k);
+ g:=make_string;
+ end
+
+@ The first 128 strings will contain 95 standard ASCII characters, and the
+other 33 characters will be printed in three-symbol form like `\.{\^\^A}'
+unless a system-dependent change is made here. Installations that have
+an extended character set, where for example |xchr[@'32]=@t\.{\'^^Z\'}@>|,
+would like string @'32 to be the single character @'32 instead of the
+three characters @'136, @'136, @'132 (\.{\^\^Z}). On the other hand,
+even people with an extended character set will want to represent string
+@'15 by \.{\^\^M}, since @'15 is |carriage_return|; the idea is to
+produce visible strings instead of tabs or line-feeds or carriage-returns
+or bell-rings or characters that are treated anomalously in text files.
+
+Unprintable characters of codes 128--255 are, similarly, rendered
+\.{\^\^80}--\.{\^\^ff}.
+
+The boolean expression defined here should be |true| unless \TeX\
+internal code number~|k| corresponds to a non-troublesome visible
+symbol in the local character set. An appropriate formula for the
+extended character set recommended in {\sl The \TeX book\/} would, for
+example, be `|k in [0,@'10..@'12,@'14,@'15,@'33,@'177..@'377]|'.
+If character |k| cannot be printed, and |k<@'200|, then character |k+@'100| or
+|k-@'100| must be printable; moreover, ASCII codes |[@'41..@'46,
+@'60..@'71, @'141..@'146, @'160..@'171]| must be printable.
+Thus, at least 80 printable characters are needed.
+@:TeXbook}{\sl The \TeX book@>
+@^character set dependencies@>
+@^system dependencies@>
+
+@<Character |k| cannot be printed@>=
+ (k<" ")or(k>"~")
+
+@ When the \.{WEB} system program called \.{TANGLE} processes the \.{TEX.WEB}
+description that you are now reading, it outputs the \PASCAL\ program
+\.{TEX.PAS} and also a string pool file called \.{TEX.POOL}. The \.{INITEX}
+@.WEB@>@.INITEX@>
+program reads the latter file, where each string appears as a two-digit decimal
+length followed by the string itself, and the information is recorded in
+\TeX's string memory.
+
+@<Glob...@>=
+@!init @!pool_file:alpha_file; {the string-pool file output by \.{TANGLE}}
+tini
+
+@ @d bad_pool(#)==begin wake_up_terminal; write_ln(term_out,#);
+ a_close(pool_file); get_strings_started:=false; return;
+ end
+@<Read the other strings...@>=
+name_of_file:=pool_name; {we needn't set |name_length|}
+if a_open_in(pool_file) then
+ begin c:=false;
+ repeat @<Read one string, but return |false| if the
+ string memory space is getting too tight for comfort@>;
+ until c;
+ a_close(pool_file); get_strings_started:=true;
+ end
+else bad_pool('! I can''t read TEX.POOL.')
+@.I can't read TEX.POOL@>
+
+@ @<Read one string...@>=
+begin if eof(pool_file) then bad_pool('! TEX.POOL has no check sum.');
+@.TEX.POOL has no check sum@>
+read(pool_file,m,n); {read two digits of string length}
+if m='*' then @<Check the pool check sum@>
+else begin if (xord[m]<"0")or(xord[m]>"9")or@|
+ (xord[n]<"0")or(xord[n]>"9") then
+ bad_pool('! TEX.POOL line doesn''t begin with two digits.');
+@.TEX.POOL line doesn't...@>
+ l:=xord[m]*10+xord[n]-"0"*11; {compute the length}
+ if pool_ptr+l+string_vacancies>pool_size then
+ bad_pool('! You have to increase POOLSIZE.');
+@.You have to increase POOLSIZE@>
+ for k:=1 to l do
+ begin if eoln(pool_file) then m:=' '@+else read(pool_file,m);
+ append_char(xord[m]);
+ end;
+ read_ln(pool_file); g:=make_string;
+ end;
+end
+
+@ The \.{WEB} operation \.{@@\$} denotes the value that should be at the
+end of this \.{TEX.POOL} file; any other value means that the wrong pool
+file has been loaded.
+@^check sum@>
+
+@<Check the pool check sum@>=
+begin a:=0; k:=1;
+loop@+ begin if (xord[n]<"0")or(xord[n]>"9") then
+ bad_pool('! TEX.POOL check sum doesn''t have nine digits.');
+@.TEX.POOL check sum...@>
+ a:=10*a+xord[n]-"0";
+ if k=9 then goto done;
+ incr(k); read(pool_file,n);
+ end;
+done: if a<>@$ then bad_pool('! TEX.POOL doesn''t match; TANGLE me again.');
+@.TEX.POOL doesn't match@>
+c:=true;
+end
+
+@* \[5] On-line and off-line printing.
+Messages that are sent to a user's terminal and to the transcript-log file
+are produced by several `|print|' procedures. These procedures will
+direct their output to a variety of places, based on the setting of
+the global variable |selector|, which has the following possible
+values:
+
+\yskip
+\hang |term_and_log|, the normal setting, prints on the terminal and on the
+ transcript file.
+
+\hang |log_only|, prints only on the transcript file.
+
+\hang |term_only|, prints only on the terminal.
+
+\hang |no_print|, doesn't print at all. This is used only in rare cases
+ before the transcript file is open.
+
+\hang |pseudo|, puts output into a cyclic buffer that is used
+ by the |show_context| routine; when we get to that routine we shall discuss
+ the reasoning behind this curious mode.
+
+\hang |new_string|, appends the output to the current string in the
+ string pool.
+
+\hang 0 to 15, prints on one of the sixteen files for \.{\\write} output.
+
+\yskip
+\noindent The symbolic names `|term_and_log|', etc., have been assigned
+numeric codes that satisfy the convenient relations |no_print+1=term_only|,
+|no_print+2=log_only|, |term_only+2=log_only+1=term_and_log|.
+
+Three additional global variables, |tally| and |term_offset| and
+|file_offset|, record the number of characters that have been printed
+since they were most recently cleared to zero. We use |tally| to record
+the length of (possibly very long) stretches of printing; |term_offset|
+and |file_offset|, on the other hand, keep track of how many characters
+have appeared so far on the current line that has been output to the
+terminal or to the transcript file, respectively.
+
+@d no_print=16 {|selector| setting that makes data disappear}
+@d term_only=17 {printing is destined for the terminal only}
+@d log_only=18 {printing is destined for the transcript file only}
+@d term_and_log=19 {normal |selector| setting}
+@d pseudo=20 {special |selector| setting for |show_context|}
+@d new_string=21 {printing is deflected to the string pool}
+@d max_selector=21 {highest selector setting}
+
+@<Glob...@>=
+@!log_file : alpha_file; {transcript of \TeX\ session}
+@!selector : 0..max_selector; {where to print a message}
+@!dig : array[0..22] of 0..15; {digits in a number being output}
+@!tally : integer; {the number of characters recently printed}
+@!term_offset : 0..max_print_line;
+ {the number of characters on the current terminal line}
+@!file_offset : 0..max_print_line;
+ {the number of characters on the current file line}
+@!trick_buf:array[0..error_line] of ASCII_code; {circular buffer for
+ pseudoprinting}
+@!trick_count: integer; {threshold for pseudoprinting, explained later}
+@!first_count: integer; {another variable for pseudoprinting}
+
+@ @<Initialize the output routines@>=
+selector:=term_only; tally:=0; term_offset:=0; file_offset:=0;
+
+@ Macro abbreviations for output to the terminal and to the log file are
+defined here for convenience. Some systems need special conventions
+for terminal output, and it is possible to adhere to those conventions
+by changing |wterm|, |wterm_ln|, and |wterm_cr| in this section.
+@^system dependencies@>
+
+@d wterm(#)==write(term_out,#)
+@d wterm_ln(#)==write_ln(term_out,#)
+@d wterm_cr==write_ln(term_out)
+@d wlog(#)==write(log_file,#)
+@d wlog_ln(#)==write_ln(log_file,#)
+@d wlog_cr==write_ln(log_file)
+
+@ To end a line of text output, we call |print_ln|.
+
+@<Basic print...@>=
+procedure print_ln; {prints an end-of-line}
+begin case selector of
+term_and_log: begin wterm_cr; wlog_cr;
+ term_offset:=0; file_offset:=0;
+ end;
+log_only: begin wlog_cr; file_offset:=0;
+ end;
+term_only: begin wterm_cr; term_offset:=0;
+ end;
+no_print,pseudo,new_string: do_nothing;
+othercases write_ln(write_file[selector])
+endcases;@/
+end; {|tally| is not affected}
+
+@ The |print_char| procedure sends one character to the desired destination,
+using the |xchr| array to map it into an external character compatible with
+|input_ln|. All printing comes through |print_ln| or |print_char|.
+
+@<Basic printing...@>=
+procedure print_char(@!s:ASCII_code); {prints a single character}
+label exit;
+begin if @<Character |s| is the current new-line character@> then
+ if selector<pseudo then
+ begin print_ln; return;
+ end;
+case selector of
+term_and_log: begin wterm(xchr[s]); wlog(xchr[s]);
+ incr(term_offset); incr(file_offset);
+ if term_offset=max_print_line then
+ begin wterm_cr; term_offset:=0;
+ end;
+ if file_offset=max_print_line then
+ begin wlog_cr; file_offset:=0;
+ end;
+ end;
+log_only: begin wlog(xchr[s]); incr(file_offset);
+ if file_offset=max_print_line then print_ln;
+ end;
+term_only: begin wterm(xchr[s]); incr(term_offset);
+ if term_offset=max_print_line then print_ln;
+ end;
+no_print: do_nothing;
+pseudo: if tally<trick_count then trick_buf[tally mod error_line]:=s;
+new_string: begin if pool_ptr<pool_size then append_char(s);
+ end; {we drop characters if the string space is full}
+othercases write(write_file[selector],xchr[s])
+endcases;@/
+incr(tally);
+exit:end;
+
+@ An entire string is output by calling |print|. Note that if we are outputting
+the single standard ASCII character \.c, we could call |print("c")|, since
+|"c"=99| is the number of a single-character string, as explained above. But
+|print_char("c")| is quicker, so \TeX\ goes directly to the |print_char|
+routine when it knows that this is safe. (The present implementation
+assumes that it is always safe to print a visible ASCII character.)
+@^system dependencies@>
+
+@<Basic print...@>=
+procedure print(@!s:integer); {prints string |s|}
+label exit;
+var j:pool_pointer; {current character code position}
+@!nl:integer; {new-line character to restore}
+begin if s>=str_ptr then s:="???" {this can't happen}
+@.???@>
+else if s<256 then
+ if s<0 then s:="???" {can't happen}
+ else begin if selector>pseudo then
+ begin print_char(s); return; {internal strings are not expanded}
+ end;
+ if (@<Character |s| is the current new-line character@>) then
+ if selector<pseudo then
+ begin print_ln; return;
+ end;
+ nl:=new_line_char; new_line_char:=-1;
+ {temporarily disable new-line character}
+ j:=str_start[s];
+ while j<str_start[s+1] do
+ begin print_char(so(str_pool[j])); incr(j);
+ end;
+ new_line_char:=nl; return;
+ end;
+j:=str_start[s];
+while j<str_start[s+1] do
+ begin print_char(so(str_pool[j])); incr(j);
+ end;
+exit:end;
+
+@ Control sequence names, file names, and strings constructed with
+\.{\\string} might contain |ASCII_code| values that can't
+be printed using |print_char|. Therefore we use |slow_print| for them:
+
+@<Basic print...@>=
+procedure slow_print(@!s:integer); {prints string |s|}
+var j:pool_pointer; {current character code position}
+begin if (s>=str_ptr) or (s<256) then print(s)
+else begin j:=str_start[s];
+ while j<str_start[s+1] do
+ begin print(so(str_pool[j])); incr(j);
+ end;
+ end;
+end;
+
+@ Here is the very first thing that \TeX\ prints: a headline that identifies
+the version number and format package. The |term_offset| variable is temporarily
+incorrect, but the discrepancy is not serious since we assume that the banner
+and format identifier together will occupy at most |max_print_line|
+character positions.
+
+@<Initialize the output...@>=
+wterm(banner);
+if format_ident=0 then wterm_ln(' (no format preloaded)')
+else begin slow_print(format_ident); print_ln;
+ end;
+update_terminal;
+
+@ The procedure |print_nl| is like |print|, but it makes sure that the
+string appears at the beginning of a new line.
+
+@<Basic print...@>=
+procedure print_nl(@!s:str_number); {prints string |s| at beginning of line}
+begin if ((term_offset>0)and(odd(selector)))or@|
+ ((file_offset>0)and(selector>=log_only)) then print_ln;
+print(s);
+end;
+
+@ The procedure |print_esc| prints a string that is preceded by
+the user's escape character (which is usually a backslash).
+
+@<Basic print...@>=
+procedure print_esc(@!s:str_number); {prints escape character, then |s|}
+var c:integer; {the escape character code}
+begin @<Set variable |c| to the current escape character@>;
+if c>=0 then if c<256 then print(c);
+slow_print(s);
+end;
+
+@ An array of digits in the range |0..15| is printed by |print_the_digs|.
+
+@<Basic print...@>=
+procedure print_the_digs(@!k:eight_bits);
+ {prints |dig[k-1]|$\,\ldots\,$|dig[0]|}
+begin while k>0 do
+ begin decr(k);
+ if dig[k]<10 then print_char("0"+dig[k])
+ else print_char("A"-10+dig[k]);
+ end;
+end;
+
+@ The following procedure, which prints out the decimal representation of a
+given integer |n|, has been written carefully so that it works properly
+if |n=0| or if |(-n)| would cause overflow. It does not apply |mod| or |div|
+to negative arguments, since such operations are not implemented consistently
+by all \PASCAL\ compilers.
+
+@<Basic print...@>=
+procedure print_int(@!n:integer); {prints an integer in decimal form}
+var k:0..23; {index to current digit; we assume that $|n|<10^{23}$}
+@!m:integer; {used to negate |n| in possibly dangerous cases}
+begin k:=0;
+if n<0 then
+ begin print_char("-");
+ if n>-100000000 then negate(n)
+ else begin m:=-1-n; n:=m div 10; m:=(m mod 10)+1; k:=1;
+ if m<10 then dig[0]:=m
+ else begin dig[0]:=0; incr(n);
+ end;
+ end;
+ end;
+repeat dig[k]:=n mod 10; n:=n div 10; incr(k);
+until n=0;
+print_the_digs(k);
+end;
+
+@ Here is a trivial procedure to print two digits; it is usually called with
+a parameter in the range |0<=n<=99|.
+
+@p procedure print_two(@!n:integer); {prints two least significant digits}
+begin n:=abs(n) mod 100; print_char("0"+(n div 10));
+print_char("0"+(n mod 10));
+end;
+
+@ Hexadecimal printing of nonnegative integers is accomplished by |print_hex|.
+
+@p procedure print_hex(@!n:integer);
+ {prints a positive integer in hexadecimal form}
+var k:0..22; {index to current digit; we assume that $0\L n<16^{22}$}
+begin k:=0; print_char("""");
+repeat dig[k]:=n mod 16; n:=n div 16; incr(k);
+until n=0;
+print_the_digs(k);
+end;
+
+@ Old versions of \TeX\ needed a procedure called |print_ASCII| whose function
+is now subsumed by |print|. We retain the old name here as a possible aid to
+future software arch\ae ologists.
+
+@d print_ASCII == print
+
+@ Roman numerals are produced by the |print_roman_int| routine. Readers
+who like puzzles might enjoy trying to figure out how this tricky code
+works; therefore no explanation will be given. Notice that 1990 yields
+\.{mcmxc}, not \.{mxm}.
+
+@p procedure print_roman_int(@!n:integer);
+label exit;
+var j,@!k: pool_pointer; {mysterious indices into |str_pool|}
+@!u,@!v: nonnegative_integer; {mysterious numbers}
+begin j:=str_start["m2d5c2l5x2v5i"]; v:=1000;
+loop@+ begin while n>=v do
+ begin print_char(so(str_pool[j])); n:=n-v;
+ end;
+ if n<=0 then return; {nonpositive input produces no output}
+ k:=j+2; u:=v div (so(str_pool[k-1])-"0");
+ if str_pool[k-1]=si("2") then
+ begin k:=k+2; u:=u div (so(str_pool[k-1])-"0");
+ end;
+ if n+u>=v then
+ begin print_char(so(str_pool[k])); n:=n+u;
+ end
+ else begin j:=j+2; v:=v div (so(str_pool[j-1])-"0");
+ end;
+ end;
+exit:end;
+
+@ The |print| subroutine will not print a string that is still being
+created. The following procedure will.
+
+@p procedure print_current_string; {prints a yet-unmade string}
+var j:pool_pointer; {points to current character code}
+begin j:=str_start[str_ptr];
+while j<pool_ptr do
+ begin print_char(so(str_pool[j])); incr(j);
+ end;
+end;
+
+@ Here is a procedure that asks the user to type a line of input,
+assuming that the |selector| setting is either |term_only| or |term_and_log|.
+The input is placed into locations |first| through |last-1| of the
+|buffer| array, and echoed on the transcript file if appropriate.
+
+This procedure is never called when |interaction<scroll_mode|.
+
+@d prompt_input(#)==begin wake_up_terminal; print(#); term_input;
+ end {prints a string and gets a line of input}
+
+@p procedure term_input; {gets a line from the terminal}
+var k:0..buf_size; {index into |buffer|}
+begin update_terminal; {now the user sees the prompt for sure}
+if not input_ln(term_in,true) then fatal_error("End of file on the terminal!");
+@.End of file on the terminal@>
+term_offset:=0; {the user's line ended with \<\rm return>}
+decr(selector); {prepare to echo the input}
+if last<>first then for k:=first to last-1 do print(buffer[k]);
+print_ln; incr(selector); {restore previous status}
+end;
+
+@* \[6] Reporting errors.
+When something anomalous is detected, \TeX\ typically does something like this:
+$$\vbox{\halign{#\hfil\cr
+|print_err("Something anomalous has been detected");|\cr
+|help3("This is the first line of my offer to help.")|\cr
+|("This is the second line. I'm trying to")|\cr
+|("explain the best way for you to proceed.");|\cr
+|error;|\cr}}$$
+A two-line help message would be given using |help2|, etc.; these informal
+helps should use simple vocabulary that complements the words used in the
+official error message that was printed. (Outside the U.S.A., the help
+messages should preferably be translated into the local vernacular. Each
+line of help is at most 60 characters long, in the present implementation,
+so that |max_print_line| will not be exceeded.)
+
+The |print_err| procedure supplies a `\.!' before the official message,
+and makes sure that the terminal is awake if a stop is going to occur.
+The |error| procedure supplies a `\..' after the official message, then it
+shows the location of the error; and if |interaction=error_stop_mode|,
+it also enters into a dialog with the user, during which time the help
+message may be printed.
+@^system dependencies@>
+
+@ The global variable |interaction| has four settings, representing increasing
+amounts of user interaction:
+
+@d batch_mode=0 {omits all stops and omits terminal output}
+@d nonstop_mode=1 {omits all stops}
+@d scroll_mode=2 {omits error stops}
+@d error_stop_mode=3 {stops at every opportunity to interact}
+@d print_err(#)==begin if interaction=error_stop_mode then wake_up_terminal;
+ print_nl("! "); print(#);
+ end
+
+@<Glob...@>=
+@!interaction:batch_mode..error_stop_mode; {current level of interaction}
+
+@ @<Set init...@>=interaction:=error_stop_mode;
+
+@ \TeX\ is careful not to call |error| when the print |selector| setting
+might be unusual. The only possible values of |selector| at the time of
+error messages are
+
+\yskip\hang|no_print| (when |interaction=batch_mode|
+ and |log_file| not yet open);
+
+\hang|term_only| (when |interaction>batch_mode| and |log_file| not yet open);
+
+\hang|log_only| (when |interaction=batch_mode| and |log_file| is open);
+
+\hang|term_and_log| (when |interaction>batch_mode| and |log_file| is open).
+
+@<Initialize the print |selector| based on |interaction|@>=
+if interaction=batch_mode then selector:=no_print@+else selector:=term_only
+
+@ A global variable |deletions_allowed| is set |false| if the |get_next|
+routine is active when |error| is called; this ensures that |get_next|
+and related routines like |get_token| will never be called recursively.
+A similar interlock is provided by |set_box_allowed|.
+@^recursion@>
+
+The global variable |history| records the worst level of error that
+has been detected. It has four possible values: |spotless|, |warning_issued|,
+|error_message_issued|, and |fatal_error_stop|.
+
+Another global variable, |error_count|, is increased by one when an
+|error| occurs without an interactive dialog, and it is reset to zero at
+the end of every paragraph. If |error_count| reaches 100, \TeX\ decides
+that there is no point in continuing further.
+
+@d spotless=0 {|history| value when nothing has been amiss yet}
+@d warning_issued=1 {|history| value when |begin_diagnostic| has been called}
+@d error_message_issued=2 {|history| value when |error| has been called}
+@d fatal_error_stop=3 {|history| value when termination was premature}
+
+@<Glob...@>=
+@!deletions_allowed:boolean; {is it safe for |error| to call |get_token|?}
+@!set_box_allowed:boolean; {is it safe to do a \.{\\setbox} assignment?}
+@!history:spotless..fatal_error_stop; {has the source input been clean so far?}
+@!error_count:-1..100; {the number of scrolled errors since the
+ last paragraph ended}
+
+@ The value of |history| is initially |fatal_error_stop|, but it will
+be changed to |spotless| if \TeX\ survives the initialization process.
+
+@<Set init...@>=
+deletions_allowed:=true; set_box_allowed:=true;
+error_count:=0; {|history| is initialized elsewhere}
+
+@ Since errors can be detected almost anywhere in \TeX, we want to declare the
+error procedures near the beginning of the program. But the error procedures
+in turn use some other procedures, which need to be declared |forward|
+before we get to |error| itself.
+
+It is possible for |error| to be called recursively if some error arises
+when |get_token| is being used to delete a token, and/or if some fatal error
+occurs while \TeX\ is trying to fix a non-fatal one. But such recursion
+@^recursion@>
+is never more than two levels deep.
+
+@<Error handling...@>=
+procedure@?normalize_selector; forward;@t\2@>@/
+procedure@?get_token; forward;@t\2@>@/
+procedure@?term_input; forward;@t\2@>@/
+procedure@?show_context; forward;@t\2@>@/
+procedure@?begin_file_reading; forward;@t\2@>@/
+procedure@?open_log_file; forward;@t\2@>@/
+procedure@?close_files_and_terminate; forward;@t\2@>@/
+procedure@?clear_for_error_prompt; forward;@t\2@>@/
+procedure@?give_err_help; forward;@t\2@>@/
+@t\4\hskip-\fontdimen2\font@>@;@+@!debug@+procedure@?debug_help;
+ forward;@;@+gubed
+
+@ Individual lines of help are recorded in the array |help_line|, which
+contains entries in positions |0..(help_ptr-1)|. They should be printed
+in reverse order, i.e., with |help_line[0]| appearing last.
+
+@d hlp1(#)==help_line[0]:=#;@+end
+@d hlp2(#)==help_line[1]:=#; hlp1
+@d hlp3(#)==help_line[2]:=#; hlp2
+@d hlp4(#)==help_line[3]:=#; hlp3
+@d hlp5(#)==help_line[4]:=#; hlp4
+@d hlp6(#)==help_line[5]:=#; hlp5
+@d help0==help_ptr:=0 {sometimes there might be no help}
+@d help1==@+begin help_ptr:=1; hlp1 {use this with one help line}
+@d help2==@+begin help_ptr:=2; hlp2 {use this with two help lines}
+@d help3==@+begin help_ptr:=3; hlp3 {use this with three help lines}
+@d help4==@+begin help_ptr:=4; hlp4 {use this with four help lines}
+@d help5==@+begin help_ptr:=5; hlp5 {use this with five help lines}
+@d help6==@+begin help_ptr:=6; hlp6 {use this with six help lines}
+
+@<Glob...@>=
+@!help_line:array[0..5] of str_number; {helps for the next |error|}
+@!help_ptr:0..6; {the number of help lines present}
+@!use_err_help:boolean; {should the |err_help| list be shown?}
+
+@ @<Set init...@>=
+help_ptr:=0; use_err_help:=false;
+
+@ The |jump_out| procedure just cuts across all active procedure levels and
+goes to |end_of_TEX|. This is the only nontrivial |@!goto| statement in the
+whole program. It is used when there is no recovery from a particular error.
+
+Some \PASCAL\ compilers do not implement non-local |goto| statements.
+@^system dependencies@>
+In such cases the body of |jump_out| should simply be
+`|close_files_and_terminate|;\thinspace' followed by a call on some system
+procedure that quietly terminates the program.
+
+@<Error hand...@>=
+procedure jump_out;
+begin goto end_of_TEX;
+end;
+
+@ Here now is the general |error| routine.
+
+@<Error hand...@>=
+procedure error; {completes the job of error reporting}
+label continue,exit;
+var c:ASCII_code; {what the user types}
+@!s1,@!s2,@!s3,@!s4:integer;
+ {used to save global variables when deleting tokens}
+begin if history<error_message_issued then history:=error_message_issued;
+print_char("."); show_context;
+if interaction=error_stop_mode then @<Get user's advice and |return|@>;
+incr(error_count);
+if error_count=100 then
+ begin print_nl("(That makes 100 errors; please try again.)");
+@.That makes 100 errors...@>
+ history:=fatal_error_stop; jump_out;
+ end;
+@<Put help message on the transcript file@>;
+exit:end;
+
+@ @<Get user's advice...@>=
+loop@+begin continue: clear_for_error_prompt; prompt_input("? ");
+@.?\relax@>
+ if last=first then return;
+ c:=buffer[first];
+ if c>="a" then c:=c+"A"-"a"; {convert to uppercase}
+ @<Interpret code |c| and |return| if done@>;
+ end
+
+@ It is desirable to provide an `\.E' option here that gives the user
+an easy way to return from \TeX\ to the system editor, with the offending
+line ready to be edited. But such an extension requires some system
+wizardry, so the present implementation simply types out the name of the
+file that should be
+edited and the relevant line number.
+@^system dependencies@>
+
+There is a secret `\.D' option available when the debugging routines haven't
+been commented~out.
+@^debugging@>
+
+@<Interpret code |c| and |return| if done@>=
+case c of
+"0","1","2","3","4","5","6","7","8","9": if deletions_allowed then
+ @<Delete \(c)|c-"0"| tokens and |goto continue|@>;
+@t\4\4@>@;@+@!debug "D": begin debug_help; goto continue;@+end;@+gubed@/
+"E": if base_ptr>0 then
+ begin print_nl("You want to edit file ");
+@.You want to edit file x@>
+ slow_print(input_stack[base_ptr].name_field);
+ print(" at line "); print_int(line);
+ interaction:=scroll_mode; jump_out;
+ end;
+"H": @<Print the help information and |goto continue|@>;
+"I":@<Introduce new material from the terminal and |return|@>;
+"Q","R","S":@<Change the interaction level and |return|@>;
+"X":begin interaction:=scroll_mode; jump_out;
+ end;
+othercases do_nothing
+endcases;@/
+@<Print the menu of available options@>
+
+@ @<Print the menu...@>=
+begin print("Type <return> to proceed, S to scroll future error messages,");@/
+@.Type <return> to proceed...@>
+print_nl("R to run without stopping, Q to run quietly,");@/
+print_nl("I to insert something, ");
+if base_ptr>0 then print("E to edit your file,");
+if deletions_allowed then
+ print_nl("1 or ... or 9 to ignore the next 1 to 9 tokens of input,");
+print_nl("H for help, X to quit.");
+end
+
+@ Here the author of \TeX\ apologizes for making use of the numerical
+relation between |"Q"|, |"R"|, |"S"|, and the desired interaction settings
+|batch_mode|, |nonstop_mode|, |scroll_mode|.
+@^Knuth, Donald Ervin@>
+
+@<Change the interaction...@>=
+begin error_count:=0; interaction:=batch_mode+c-"Q";
+print("OK, entering ");
+case c of
+"Q":begin print_esc("batchmode"); decr(selector);
+ end;
+"R":print_esc("nonstopmode");
+"S":print_esc("scrollmode");
+end; {there are no other cases}
+print("..."); print_ln; update_terminal; return;
+end
+
+@ When the following code is executed, |buffer[(first+1)..(last-1)]| may
+contain the material inserted by the user; otherwise another prompt will
+be given. In order to understand this part of the program fully, you need
+to be familiar with \TeX's input stacks.
+
+@<Introduce new material...@>=
+begin begin_file_reading; {enter a new syntactic level for terminal input}
+{now |state=mid_line|, so an initial blank space will count as a blank}
+if last>first+1 then
+ begin loc:=first+1; buffer[first]:=" ";
+ end
+else begin prompt_input("insert>"); loc:=first;
+@.insert>@>
+ end;
+first:=last;
+cur_input.limit_field:=last-1; {no |end_line_char| ends this line}
+return;
+end
+
+@ We allow deletion of up to 99 tokens at a time.
+
+@<Delete \(c)|c-"0"| tokens...@>=
+begin s1:=cur_tok; s2:=cur_cmd; s3:=cur_chr; s4:=align_state;
+align_state:=1000000; OK_to_interrupt:=false;
+if (last>first+1) and (buffer[first+1]>="0")and(buffer[first+1]<="9") then
+ c:=c*10+buffer[first+1]-"0"*11
+else c:=c-"0";
+while c>0 do
+ begin get_token; {one-level recursive call of |error| is possible}
+ decr(c);
+ end;
+cur_tok:=s1; cur_cmd:=s2; cur_chr:=s3; align_state:=s4; OK_to_interrupt:=true;
+help2("I have just deleted some text, as you asked.")@/
+("You can now delete more, or insert, or whatever.");
+show_context; goto continue;
+end
+
+@ @<Print the help info...@>=
+begin if use_err_help then
+ begin give_err_help; use_err_help:=false;
+ end
+else begin if help_ptr=0 then
+ help2("Sorry, I don't know how to help in this situation.")@/
+ @t\kern1em@>("Maybe you should try asking a human?");
+ repeat decr(help_ptr); print(help_line[help_ptr]); print_ln;
+ until help_ptr=0;
+ end;
+help4("Sorry, I already gave what help I could...")@/
+ ("Maybe you should try asking a human?")@/
+ ("An error might have occurred before I noticed any problems.")@/
+ ("``If all else fails, read the instructions.''");@/
+goto continue;
+end
+
+@ @<Put help message on the transcript file@>=
+if interaction>batch_mode then decr(selector); {avoid terminal output}
+if use_err_help then
+ begin print_ln; give_err_help;
+ end
+else while help_ptr>0 do
+ begin decr(help_ptr); print_nl(help_line[help_ptr]);
+ end;
+print_ln;
+if interaction>batch_mode then incr(selector); {re-enable terminal output}
+print_ln
+
+@ A dozen or so error messages end with a parenthesized integer, so we
+save a teeny bit of program space by declaring the following procedure:
+
+@p procedure int_error(@!n:integer);
+begin print(" ("); print_int(n); print_char(")"); error;
+end;
+
+@ In anomalous cases, the print selector might be in an unknown state;
+the following subroutine is called to fix things just enough to keep
+running a bit longer.
+
+@p procedure normalize_selector;
+begin if log_opened then selector:=term_and_log
+else selector:=term_only;
+if job_name=0 then open_log_file;
+if interaction=batch_mode then decr(selector);
+end;
+
+@ The following procedure prints \TeX's last words before dying.
+
+@d succumb==begin if interaction=error_stop_mode then
+ interaction:=scroll_mode; {no more interaction}
+ if log_opened then error;
+ @!debug if interaction>batch_mode then debug_help;@+gubed@;@/
+ history:=fatal_error_stop; jump_out; {irrecoverable error}
+ end
+
+@<Error hand...@>=
+procedure fatal_error(@!s:str_number); {prints |s|, and that's it}
+begin normalize_selector;@/
+print_err("Emergency stop"); help1(s); succumb;
+@.Emergency stop@>
+end;
+
+@ Here is the most dreaded error message.
+
+@<Error hand...@>=
+procedure overflow(@!s:str_number;@!n:integer); {stop due to finiteness}
+begin normalize_selector;
+print_err("TeX capacity exceeded, sorry [");
+@.TeX capacity exceeded ...@>
+print(s); print_char("="); print_int(n); print_char("]");
+help2("If you really absolutely need more capacity,")@/
+ ("you can ask a wizard to enlarge me.");
+succumb;
+end;
+
+@ The program might sometime run completely amok, at which point there is
+no choice but to stop. If no previous error has been detected, that's bad
+news; a message is printed that is really intended for the \TeX\
+maintenance person instead of the user (unless the user has been
+particularly diabolical). The index entries for `this can't happen' may
+help to pinpoint the problem.
+@^dry rot@>
+
+@<Error hand...@>=
+procedure confusion(@!s:str_number);
+ {consistency check violated; |s| tells where}
+begin normalize_selector;
+if history<error_message_issued then
+ begin print_err("This can't happen ("); print(s); print_char(")");
+@.This can't happen@>
+ help1("I'm broken. Please show this to someone who can fix can fix");
+ end
+else begin print_err("I can't go on meeting you like this");
+@.I can't go on...@>
+ help2("One of your faux pas seems to have wounded me deeply...")@/
+ ("in fact, I'm barely conscious. Please fix it and try again.");
+ end;
+succumb;
+end;
+
+@ Users occasionally want to interrupt \TeX\ while it's running.
+If the \PASCAL\ runtime system allows this, one can implement
+a routine that sets the global variable |interrupt| to some nonzero value
+when such an interrupt is signalled. Otherwise there is probably at least
+a way to make |interrupt| nonzero using the \PASCAL\ debugger.
+@^system dependencies@>
+@^debugging@>
+
+@d check_interrupt==begin if interrupt<>0 then pause_for_instructions;
+ end
+
+@<Global...@>=
+@!interrupt:integer; {should \TeX\ pause for instructions?}
+@!OK_to_interrupt:boolean; {should interrupts be observed?}
+
+@ @<Set init...@>=
+interrupt:=0; OK_to_interrupt:=true;
+
+@ When an interrupt has been detected, the program goes into its
+highest interaction level and lets the user have nearly the full flexibility of
+the |error| routine. \TeX\ checks for interrupts only at times when it is
+safe to do this.
+
+@p procedure pause_for_instructions;
+begin if OK_to_interrupt then
+ begin interaction:=error_stop_mode;
+ if (selector=log_only)or(selector=no_print) then
+ incr(selector);
+ print_err("Interruption");
+@.Interruption@>
+ help3("You rang?")@/
+ ("Try to insert some instructions for me (e.g.,`I\showlists'),")@/
+ ("unless you just want to quit by typing `X'.");
+ deletions_allowed:=false; error; deletions_allowed:=true;
+ interrupt:=0;
+ end;
+end;
+
+@* \[7] Arithmetic with scaled dimensions.
+The principal computations performed by \TeX\ are done entirely in terms of
+integers less than $2^{31}$ in magnitude; and divisions are done only when both
+dividend and divisor are nonnegative. Thus, the arithmetic specified in this
+program can be carried out in exactly the same way on a wide variety of
+computers, including some small ones. Why? Because the arithmetic
+calculations need to be spelled out precisely in order to guarantee that
+\TeX\ will produce identical output on different machines. If some
+quantities were rounded differently in different implementations, we would
+find that line breaks and even page breaks might occur in different places.
+Hence the arithmetic of \TeX\ has been designed with care, and systems that
+claim to be implementations of \TeX82 should follow precisely the
+@:TeX82}{\TeX82@>
+calculations as they appear in the present program.
+
+(Actually there are three places where \TeX\ uses |div| with a possibly negative
+numerator. These are harmless; see |div| in the index. Also if the user
+sets the \.{\\time} or the \.{\\year} to a negative value, some diagnostic
+information will involve negative-numerator division. The same remarks
+apply for |mod| as well as for |div|.)
+
+@ Here is a routine that calculates half of an integer, using an
+unambiguous convention with respect to signed odd numbers.
+
+@p function half(@!x:integer):integer;
+begin if odd(x) then half:=(x+1) div 2
+else half:=x @!div 2;
+end;
+
+@ Fixed-point arithmetic is done on {\sl scaled integers\/} that are multiples
+of $2^{-16}$. In other words, a binary point is assumed to be sixteen bit
+positions from the right end of a binary computer word.
+
+@d unity == @'200000 {$2^{16}$, represents 1.00000}
+@d two == @'400000 {$2^{17}$, represents 2.00000}
+
+@<Types...@>=
+@!scaled = integer; {this type is used for scaled integers}
+@!nonnegative_integer=0..@'17777777777; {$0\L x<2^{31}$}
+@!small_number=0..63; {this type is self-explanatory}
+
+@ The following function is used to create a scaled integer from a given decimal
+fraction $(.d_0d_1\ldots d_{k-1})$, where |0<=k<=17|. The digit $d_i$ is
+given in |dig[i]|, and the calculation produces a correctly rounded result.
+
+@p function round_decimals(@!k:small_number) : scaled;
+ {converts a decimal fraction}
+var a:integer; {the accumulator}
+begin a:=0;
+while k>0 do
+ begin decr(k); a:=(a+dig[k]*two) div 10;
+ end;
+round_decimals:=(a+1) div 2;
+end;
+
+@ Conversely, here is a procedure analogous to |print_int|. If the output
+of this procedure is subsequently read by \TeX\ and converted by the
+|round_decimals| routine above, it turns out that the original value will
+be reproduced exactly; the ``simplest'' such decimal number is output,
+but there is always at least one digit following the decimal point.
+
+The invariant relation in the \&{repeat} loop is that a sequence of
+decimal digits yet to be printed will yield the original number if and only if
+they form a fraction~$f$ in the range $s-\delta\L10\cdot2^{16}f<s$.
+We can stop if and only if $f=0$ satisfies this condition; the loop will
+terminate before $s$ can possibly become zero.
+
+@p procedure print_scaled(@!s:scaled); {prints scaled real, rounded to five
+ digits}
+var delta:scaled; {amount of allowable inaccuracy}
+begin if s<0 then
+ begin print_char("-"); negate(s); {print the sign, if negative}
+ end;
+print_int(s div unity); {print the integer part}
+print_char(".");
+s:=10*(s mod unity)+5; delta:=10;
+repeat if delta>unity then s:=s+@'100000-50000; {round the last digit}
+print_char("0"+(s div unity)); s:=10*(s mod unity); delta:=delta*10;
+until s<=delta;
+end;
+
+@ Physical sizes that a \TeX\ user specifies for portions of documents are
+represented internally as scaled points. Thus, if we define an `sp' (scaled
+@^sp@>
+point) as a unit equal to $2^{-16}$ printer's points, every dimension
+inside of \TeX\ is an integer number of sp. There are exactly
+4,736,286.72 sp per inch. Users are not allowed to specify dimensions
+larger than $2^{30}-1$ sp, which is a distance of about 18.892 feet (5.7583
+meters); two such quantities can be added without overflow on a 32-bit
+computer.
+
+The present implementation of \TeX\ does not check for overflow when
+@^Overflow in arithmetic@>
+dimensions are added or subtracted. This could be done by inserting a
+few dozen tests of the form `\ignorespaces|if x>=@'10000000000 then
+@t\\{report\_overflow}@>|', but the chance of overflow is so remote that
+such tests do not seem worthwhile.
+
+\TeX\ needs to do only a few arithmetic operations on scaled quantities,
+other than addition and subtraction, and the following subroutines do most of
+the work. A single computation might use several subroutine calls, and it is
+desirable to avoid producing multiple error messages in case of arithmetic
+overflow; so the routines set the global variable |arith_error| to |true|
+instead of reporting errors directly to the user. Another global variable,
+|remainder|, holds the remainder after a division.
+
+@<Glob...@>=
+@!arith_error:boolean; {has arithmetic overflow occurred recently?}
+@!remainder:scaled; {amount subtracted to get an exact division}
+
+@ The first arithmetical subroutine we need computes $nx+y$, where |x|
+and~|y| are |scaled| and |n| is an integer. We will also use it to
+multiply integers.
+
+@d nx_plus_y(#)==mult_and_add(#,@'7777777777)
+@d mult_integers(#)==mult_and_add(#,0,@'17777777777)
+
+@p function mult_and_add(@!n:integer;@!x,@!y,@!max_answer:scaled):scaled;
+begin if n<0 then
+ begin negate(x); negate(n);
+ end;
+if n=0 then mult_and_add:=y
+else if ((x<=(max_answer-y) div n)and(-x<=(max_answer+y) div n)) then
+ mult_and_add:=n*x+y
+else begin arith_error:=true; mult_and_add:=0;
+ end;
+end;
+
+@ We also need to divide scaled dimensions by integers.
+
+@p function x_over_n(@!x:scaled;@!n:integer):scaled;
+var negative:boolean; {should |remainder| be negated?}
+begin negative:=false;
+if n=0 then
+ begin arith_error:=true; x_over_n:=0; remainder:=x;
+ end
+else begin if n<0 then
+ begin negate(x); negate(n); negative:=true;
+ end;
+ if x>=0 then
+ begin x_over_n:=x div n; remainder:=x mod n;
+ end
+ else begin x_over_n:=-((-x) div n); remainder:=-((-x) mod n);
+ end;
+ end;
+if negative then negate(remainder);
+end;
+
+@ Then comes the multiplication of a scaled number by a fraction |n/d|,
+where |n| and |d| are nonnegative integers |<=@t$2^{16}$@>| and |d| is
+positive. It would be too dangerous to multiply by~|n| and then divide
+by~|d|, in separate operations, since overflow might well occur; and it
+would be too inaccurate to divide by |d| and then multiply by |n|. Hence
+this subroutine simulates 1.5-precision arithmetic.
+
+@p function xn_over_d(@!x:scaled; @!n,@!d:integer):scaled;
+var positive:boolean; {was |x>=0|?}
+@!t,@!u,@!v:nonnegative_integer; {intermediate quantities}
+begin if x>=0 then positive:=true
+else begin negate(x); positive:=false;
+ end;
+t:=(x mod @'100000)*n;
+u:=(x div @'100000)*n+(t div @'100000);
+v:=(u mod d)*@'100000 + (t mod @'100000);
+if u div d>=@'100000 then arith_error:=true
+else u:=@'100000*(u div d) + (v div d);
+if positive then
+ begin xn_over_d:=u; remainder:=v mod d;
+ end
+else begin xn_over_d:=-u; remainder:=-(v mod d);
+ end;
+end;
+
+@ The next subroutine is used to compute the ``badness'' of glue, when a
+total~|t| is supposed to be made from amounts that sum to~|s|. According
+to {\sl The \TeX book}, the badness of this situation is $100(t/s)^3$;
+however, badness is simply a heuristic, so we need not squeeze out the
+last drop of accuracy when computing it. All we really want is an
+approximation that has similar properties.
+@:TeXbook}{\sl The \TeX book@>
+
+The actual method used to compute the badness is easier to read from the
+program than to describe in words. It produces an integer value that is a
+reasonably close approximation to $100(t/s)^3$, and all implementations
+of \TeX\ should use precisely this method. Any badness of $2^{13}$ or more is
+treated as infinitely bad, and represented by 10000.
+
+It is not difficult to prove that $$\hbox{|badness(t+1,s)>=badness(t,s)
+>=badness(t,s+1)|}.$$ The badness function defined here is capable of
+computing at most 1095 distinct values, but that is plenty.
+
+@d inf_bad = 10000 {infinitely bad value}
+
+@p function badness(@!t,@!s:scaled):halfword; {compute badness, given |t>=0|}
+var r:integer; {approximation to $\alpha t/s$, where $\alpha^3\approx
+ 100\cdot2^{18}$}
+begin if t=0 then badness:=0
+else if s<=0 then badness:=inf_bad
+else begin if t<=7230584 then r:=(t*297) div s {$297^3=99.94\times2^{18}$}
+ else if s>=1663497 then r:=t div (s div 297)
+ else r:=t;
+ if r>1290 then badness:=inf_bad {$1290^3<2^{31}<1291^3$}
+ else badness:=(r*r*r+@'400000) div @'1000000;
+ end; {that was $r^3/2^{18}$, rounded to the nearest integer}
+end;
+
+@ When \TeX\ ``packages'' a list into a box, it needs to calculate the
+proportionality ratio by which the glue inside the box should stretch
+or shrink. This calculation does not affect \TeX's decision making,
+so the precise details of rounding, etc., in the glue calculation are not
+of critical importance for the consistency of results on different computers.
+
+We shall use the type |glue_ratio| for such proportionality ratios.
+A glue ratio should take the same amount of memory as an
+|integer| (usually 32 bits) if it is to blend smoothly with \TeX's
+other data structures. Thus |glue_ratio| should be equivalent to
+|short_real| in some implementations of \PASCAL. Alternatively,
+it is possible to deal with glue ratios using nothing but fixed-point
+arithmetic; see {\sl TUGboat \bf3},1 (March 1982), 10--27. (But the
+routines cited there must be modified to allow negative glue ratios.)
+@^system dependencies@>
+
+@d set_glue_ratio_zero(#) == #:=0.0 {store the representation of zero ratio}
+@d set_glue_ratio_one(#) == #:=1.0 {store the representation of unit ratio}
+@d float(#) == # {convert from |glue_ratio| to type |real|}
+@d unfloat(#) == # {convert from |real| to type |glue_ratio|}
+@d float_constant(#) == #.0 {convert |integer| constant to |real|}
+
+@<Types...@>=
+@!glue_ratio=real; {one-word representation of a glue expansion factor}
+
+@* \[8] Packed data.
+In order to make efficient use of storage space, \TeX\ bases its major data
+structures on a |memory_word|, which contains either a (signed) integer,
+possibly scaled, or a (signed) |glue_ratio|, or a small number of
+fields that are one half or one quarter of the size used for storing
+integers.
+
+If |x| is a variable of type |memory_word|, it contains up to four
+fields that can be referred to as follows:
+$$\vbox{\halign{\hfil#&#\hfil&#\hfil\cr
+|x|&.|int|&(an |integer|)\cr
+|x|&.|sc|\qquad&(a |scaled| integer)\cr
+|x|&.|gr|&(a |glue_ratio|)\cr
+|x.hh.lh|, |x.hh|&.|rh|&(two halfword fields)\cr
+|x.hh.b0|, |x.hh.b1|, |x.hh|&.|rh|&(two quarterword fields, one halfword
+ field)\cr
+|x.qqqq.b0|, |x.qqqq.b1|, |x.qqqq|&.|b2|, |x.qqqq.b3|\hskip-100pt
+ &\qquad\qquad\qquad(four quarterword fields)\cr}}$$
+This is somewhat cumbersome to write, and not very readable either, but
+macros will be used to make the notation shorter and more transparent.
+The \PASCAL\ code below gives a formal definition of |memory_word| and
+its subsidiary types, using packed variant records. \TeX\ makes no
+assumptions about the relative positions of the fields within a word.
+
+Since we are assuming 32-bit integers, a halfword must contain at least
+16 bits, and a quarterword must contain at least 8 bits.
+@^system dependencies@>
+But it doesn't hurt to have more bits; for example, with enough 36-bit
+words you might be able to have |mem_max| as large as 262142, which is
+eight times as much memory as anybody had during the first four years of
+\TeX's existence.
+
+N.B.: Valuable memory space will be dreadfully wasted unless \TeX\ is compiled
+by a \PASCAL\ that packs all of the |memory_word| variants into
+the space of a single integer. This means, for example, that |glue_ratio|
+words should be |short_real| instead of |real| on some computers. Some
+\PASCAL\ compilers will pack an integer whose subrange is `|0..255|' into
+an eight-bit field, but others insist on allocating space for an additional
+sign bit; on such systems you can get 256 values into a quarterword only
+if the subrange is `|-128..127|'.
+
+The present implementation tries to accommodate as many variations as possible,
+so it makes few assumptions. If integers having the subrange
+`|min_quarterword..max_quarterword|' can be packed into a quarterword,
+and if integers having the subrange `|min_halfword..max_halfword|'
+can be packed into a halfword, everything should work satisfactorily.
+
+It is usually most efficient to have |min_quarterword=min_halfword=0|,
+so one should try to achieve this unless it causes a severe problem.
+The values defined here are recommended for most 32-bit computers.
+
+@d min_quarterword=0 {smallest allowable value in a |quarterword|}
+@d max_quarterword=255 {largest allowable value in a |quarterword|}
+@d min_halfword==0 {smallest allowable value in a |halfword|}
+@d max_halfword==65535 {largest allowable value in a |halfword|}
+
+@ Here are the inequalities that the quarterword and halfword values
+must satisfy (or rather, the inequalities that they mustn't satisfy):
+
+@<Check the ``constant''...@>=
+init if (mem_min<>mem_bot)or(mem_max<>mem_top) then bad:=10;@+tini@;@/
+if (mem_min>mem_bot)or(mem_max<mem_top) then bad:=10;
+if (min_quarterword>0)or(max_quarterword<127) then bad:=11;
+if (min_halfword>0)or(max_halfword<32767) then bad:=12;
+if (min_quarterword<min_halfword)or@|
+ (max_quarterword>max_halfword) then bad:=13;
+if (mem_min<min_halfword)or(mem_max>=max_halfword)or@|
+ (mem_bot-mem_min>max_halfword+1) then bad:=14;
+if (font_base<min_quarterword)or(font_max>max_quarterword) then bad:=15;
+if font_max>font_base+256 then bad:=16;
+if (save_size>max_halfword)or(max_strings>max_halfword) then bad:=17;
+if buf_size>max_halfword then bad:=18;
+if max_quarterword-min_quarterword<255 then bad:=19;
+
+@ The operation of adding or subtracting |min_quarterword| occurs quite
+frequently in \TeX, so it is convenient to abbreviate this operation
+by using the macros |qi| and |qo| for input and output to and from
+quarterword format.
+
+The inner loop of \TeX\ will run faster with respect to compilers
+that don't optimize expressions like `|x+0|' and `|x-0|', if these
+macros are simplified in the obvious way when |min_quarterword=0|.
+@^inner loop@>@^system dependencies@>
+
+@d qi(#)==#+min_quarterword
+ {to put an |eight_bits| item into a quarterword}
+@d qo(#)==#-min_quarterword
+ {to take an |eight_bits| item out of a quarterword}
+@d hi(#)==#+min_halfword
+ {to put a sixteen-bit item into a halfword}
+@d ho(#)==#-min_halfword
+ {to take a sixteen-bit item from a halfword}
+
+@ The reader should study the following definitions closely:
+@^system dependencies@>
+
+@d sc==int {|scaled| data is equivalent to |integer|}
+
+@<Types...@>=
+@!quarterword = min_quarterword..max_quarterword; {1/4 of a word}
+@!halfword=min_halfword..max_halfword; {1/2 of a word}
+@!two_choices = 1..2; {used when there are two variants in a record}
+@!four_choices = 1..4; {used when there are four variants in a record}
+@!two_halves = packed record@;@/
+ @!rh:halfword;
+ case two_choices of
+ 1: (@!lh:halfword);
+ 2: (@!b0:quarterword; @!b1:quarterword);
+ end;
+@!four_quarters = packed record@;@/
+ @!b0:quarterword;
+ @!b1:quarterword;
+ @!b2:quarterword;
+ @!b3:quarterword;
+ end;
+@!memory_word = record@;@/
+ case four_choices of
+ 1: (@!int:integer);
+ 2: (@!gr:glue_ratio);
+ 3: (@!hh:two_halves);
+ 4: (@!qqqq:four_quarters);
+ end;
+@!word_file = file of memory_word;
+
+@ When debugging, we may want to print a |memory_word| without knowing
+what type it is; so we print it in all modes.
+@^dirty \PASCAL@>@^debugging@>
+
+@p @!debug procedure print_word(@!w:memory_word);
+ {prints |w| in all ways}
+begin print_int(w.int); print_char(" ");@/
+print_scaled(w.sc); print_char(" ");@/
+print_scaled(round(unity*float(w.gr))); print_ln;@/
+@^real multiplication@>
+print_int(w.hh.lh); print_char("="); print_int(w.hh.b0); print_char(":");
+print_int(w.hh.b1); print_char(";"); print_int(w.hh.rh); print_char(" ");@/
+print_int(w.qqqq.b0); print_char(":"); print_int(w.qqqq.b1); print_char(":");
+print_int(w.qqqq.b2); print_char(":"); print_int(w.qqqq.b3);
+end;
+gubed
+
+@* \[9] Dynamic memory allocation.
+The \TeX\ system does nearly all of its own memory allocation, so that it
+can readily be transported into environments that do not have automatic
+facilities for strings, garbage collection, etc., and so that it can be in
+control of what error messages the user receives. The dynamic storage
+requirements of \TeX\ are handled by providing a large array |mem| in
+which consecutive blocks of words are used as nodes by the \TeX\ routines.
+
+Pointer variables are indices into this array, or into another array
+called |eqtb| that will be explained later. A pointer variable might
+also be a special flag that lies outside the bounds of |mem|, so we
+allow pointers to assume any |halfword| value. The minimum halfword
+value represents a null pointer. \TeX\ does not assume that |mem[null]| exists.
+
+@d pointer==halfword {a flag or a location in |mem| or |eqtb|}
+@d null==min_halfword {the null pointer}
+
+@<Glob...@>=
+@!temp_ptr:pointer; {a pointer variable for occasional emergency use}
+
+@ The |mem| array is divided into two regions that are allocated separately,
+but the dividing line between these two regions is not fixed; they grow
+together until finding their ``natural'' size in a particular job.
+Locations less than or equal to |lo_mem_max| are used for storing
+variable-length records consisting of two or more words each. This region
+is maintained using an algorithm similar to the one described in exercise
+2.5--19 of {\sl The Art of Computer Programming}. However, no size field
+appears in the allocated nodes; the program is responsible for knowing the
+relevant size when a node is freed. Locations greater than or equal to
+|hi_mem_min| are used for storing one-word records; a conventional
+\.{AVAIL} stack is used for allocation in this region.
+
+Locations of |mem| between |mem_bot| and |mem_top| may be dumped as part
+of preloaded format files, by the \.{INITEX} preprocessor.
+@.INITEX@>
+Production versions of \TeX\ may extend the memory at both ends in order to
+provide more space; locations between |mem_min| and |mem_bot| are always
+used for variable-size nodes, and locations between |mem_top| and |mem_max|
+are always used for single-word nodes.
+
+The key pointers that govern |mem| allocation have a prescribed order:
+$$\advance\thickmuskip-2mu
+\hbox{|null<=mem_min<=mem_bot<lo_mem_max<
+ hi_mem_min<mem_top<=mem_end<=mem_max|.}$$
+
+Empirical tests show that the present implementation of \TeX\ tends to
+spend about 9\pct! of its running time allocating nodes, and about 6\pct!
+deallocating them after their use.
+
+@<Glob...@>=
+@!mem : array[mem_min..mem_max] of memory_word; {the big dynamic storage area}
+@!lo_mem_max : pointer; {the largest location of variable-size memory in use}
+@!hi_mem_min : pointer; {the smallest location of one-word memory in use}
+
+@ In order to study the memory requirements of particular applications, it
+is possible to prepare a version of \TeX\ that keeps track of current and
+maximum memory usage. When code between the delimiters |@!stat| $\ldots$
+|tats| is not ``commented out,'' \TeX\ will run a bit slower but it will
+report these statistics when |tracing_stats| is sufficiently large.
+
+@<Glob...@>=
+@!var_used, @!dyn_used : integer; {how much memory is in use}
+
+@ Let's consider the one-word memory region first, since it's the
+simplest. The pointer variable |mem_end| holds the highest-numbered location
+of |mem| that has ever been used. The free locations of |mem| that
+occur between |hi_mem_min| and |mem_end|, inclusive, are of type
+|two_halves|, and we write |info(p)| and |link(p)| for the |lh|
+and |rh| fields of |mem[p]| when it is of this type. The single-word
+free locations form a linked list
+$$|avail|,\;\hbox{|link(avail)|},\;\hbox{|link(link(avail))|},\;\ldots$$
+terminated by |null|.
+
+@d link(#) == mem[#].hh.rh {the |link| field of a memory word}
+@d info(#) == mem[#].hh.lh {the |info| field of a memory word}
+
+@<Glob...@>=
+@!avail : pointer; {head of the list of available one-word nodes}
+@!mem_end : pointer; {the last one-word node used in |mem|}
+
+@ If memory is exhausted, it might mean that the user has forgotten
+a right brace. We will define some procedures later that try to help
+pinpoint the trouble.
+
+@p @<Declare the procedure called |show_token_list|@>@/
+@<Declare the procedure called |runaway|@>
+
+@ The function |get_avail| returns a pointer to a new one-word node whose
+|link| field is null. However, \TeX\ will halt if there is no more room left.
+@^inner loop@>
+
+If the available-space list is empty, i.e., if |avail=null|,
+we try first to increase |mem_end|. If that cannot be done, i.e., if
+|mem_end=mem_max|, we try to decrease |hi_mem_min|. If that cannot be
+done, i.e., if |hi_mem_min=lo_mem_max+1|, we have to quit.
+
+@p function get_avail : pointer; {single-word node allocation}
+var p:pointer; {the new node being got}
+begin p:=avail; {get top location in the |avail| stack}
+if p<>null then avail:=link(avail) {and pop it off}
+else if mem_end<mem_max then {or go into virgin territory}
+ begin incr(mem_end); p:=mem_end;
+ end
+else begin decr(hi_mem_min); p:=hi_mem_min;
+ if hi_mem_min<=lo_mem_max then
+ begin runaway; {if memory is exhausted, display possible runaway text}
+ overflow("main memory size",mem_max+1-mem_min);
+ {quit; all one-word nodes are busy}
+@:TeX capacity exceeded main memory size}{\quad main memory size@>
+ end;
+ end;
+link(p):=null; {provide an oft-desired initialization of the new node}
+@!stat incr(dyn_used);@+tats@;{maintain statistics}
+get_avail:=p;
+end;
+
+@ Conversely, a one-word node is recycled by calling |free_avail|.
+This routine is part of \TeX's ``inner loop,'' so we want it to be fast.
+@^inner loop@>
+
+@d free_avail(#)== {single-word node liberation}
+ begin link(#):=avail; avail:=#;
+ @!stat decr(dyn_used);@+tats@/
+ end
+
+@ There's also a |fast_get_avail| routine, which saves the procedure-call
+overhead at the expense of extra programming. This routine is used in
+the places that would otherwise account for the most calls of |get_avail|.
+@^inner loop@>
+
+@d fast_get_avail(#)==@t@>@;@/
+ begin #:=avail; {avoid |get_avail| if possible, to save time}
+ if #=null then #:=get_avail
+ else begin avail:=link(#); link(#):=null;
+ @!stat incr(dyn_used);@+tats@/
+ end;
+ end
+
+@ The procedure |flush_list(p)| frees an entire linked list of
+one-word nodes that starts at position |p|.
+@^inner loop@>
+
+@p procedure flush_list(@!p:pointer); {makes list of single-word nodes
+ available}
+var @!q,@!r:pointer; {list traversers}
+begin if p<>null then
+ begin r:=p;
+ repeat q:=r; r:=link(r); @!stat decr(dyn_used);@+tats@/
+ until r=null; {now |q| is the last node on the list}
+ link(q):=avail; avail:=p;
+ end;
+end;
+
+@ The available-space list that keeps track of the variable-size portion
+of |mem| is a nonempty, doubly-linked circular list of empty nodes,
+pointed to by the roving pointer |rover|.
+
+Each empty node has size 2 or more; the first word contains the special
+value |max_halfword| in its |link| field and the size in its |info| field;
+the second word contains the two pointers for double linking.
+
+Each nonempty node also has size 2 or more. Its first word is of type
+|two_halves|\kern-1pt, and its |link| field is never equal to |max_halfword|.
+Otherwise there is complete flexibility with respect to the contents
+of its other fields and its other words.
+
+(We require |mem_max<max_halfword| because terrible things can happen
+when |max_halfword| appears in the |link| field of a nonempty node.)
+
+@d empty_flag == max_halfword {the |link| of an empty variable-size node}
+@d is_empty(#) == (link(#)=empty_flag) {tests for empty node}
+@d node_size == info {the size field in empty variable-size nodes}
+@d llink(#) == info(#+1) {left link in doubly-linked list of empty nodes}
+@d rlink(#) == link(#+1) {right link in doubly-linked list of empty nodes}
+
+@<Glob...@>=
+@!rover : pointer; {points to some node in the list of empties}
+
+@ A call to |get_node| with argument |s| returns a pointer to a new node
+of size~|s|, which must be 2~or more. The |link| field of the first word
+of this new node is set to null. An overflow stop occurs if no suitable
+space exists.
+
+If |get_node| is called with $s=2^{30}$, it simply merges adjacent free
+areas and returns the value |max_halfword|.
+
+@p function get_node(@!s:integer):pointer; {variable-size node allocation}
+label found,exit,restart;
+var p:pointer; {the node currently under inspection}
+@!q:pointer; {the node physically after node |p|}
+@!r:integer; {the newly allocated node, or a candidate for this honor}
+@!t:integer; {temporary register}
+begin restart: p:=rover; {start at some free node in the ring}
+repeat @<Try to allocate within node |p| and its physical successors,
+ and |goto found| if allocation was possible@>;
+@^inner loop@>
+p:=rlink(p); {move to the next node in the ring}
+until p=rover; {repeat until the whole list has been traversed}
+if s=@'10000000000 then
+ begin get_node:=max_halfword; return;
+ end;
+if lo_mem_max+2<hi_mem_min then if lo_mem_max+2<=mem_bot+max_halfword then
+ @<Grow more variable-size memory and |goto restart|@>;
+overflow("main memory size",mem_max+1-mem_min);
+ {sorry, nothing satisfactory is left}
+@:TeX capacity exceeded main memory size}{\quad main memory size@>
+found: link(r):=null; {this node is now nonempty}
+@!stat var_used:=var_used+s; {maintain usage statistics}
+tats@;@/
+get_node:=r;
+exit:end;
+
+@ The lower part of |mem| grows by 1000 words at a time, unless
+we are very close to going under. When it grows, we simply link
+a new node into the available-space list. This method of controlled
+growth helps to keep the |mem| usage consecutive when \TeX\ is
+implemented on ``virtual memory'' systems.
+@^virtual memory@>
+
+@<Grow more variable-size memory and |goto restart|@>=
+begin if hi_mem_min-lo_mem_max>=1998 then t:=lo_mem_max+1000
+else t:=lo_mem_max+1+(hi_mem_min-lo_mem_max) div 2;
+ {|lo_mem_max+2<=t<hi_mem_min|}
+p:=llink(rover); q:=lo_mem_max; rlink(p):=q; llink(rover):=q;@/
+if t>mem_bot+max_halfword then t:=mem_bot+max_halfword;
+rlink(q):=rover; llink(q):=p; link(q):=empty_flag; node_size(q):=t-lo_mem_max;@/
+lo_mem_max:=t; link(lo_mem_max):=null; info(lo_mem_max):=null;
+rover:=q; goto restart;
+end
+
+@ Empirical tests show that the routine in this section performs a
+node-merging operation about 0.75 times per allocation, on the average,
+after which it finds that |r>p+1| about 95\pct! of the time.
+
+@<Try to allocate...@>=
+q:=p+node_size(p); {find the physical successor}
+@^inner loop@>
+while is_empty(q) do {merge node |p| with node |q|}
+ begin t:=rlink(q);
+ if q=rover then rover:=t;
+ llink(t):=llink(q); rlink(llink(q)):=t;@/
+ q:=q+node_size(q);
+ end;
+r:=q-s;
+if r>p+1 then @<Allocate from the top of node |p| and |goto found|@>;
+if r=p then if rlink(p)<>p then
+ @<Allocate entire node |p| and |goto found|@>;
+node_size(p):=q-p {reset the size in case it grew}
+
+@ @<Allocate from the top...@>=
+begin node_size(p):=r-p; {store the remaining size}
+@^inner loop@>
+rover:=p; {start searching here next time}
+goto found;
+end
+
+@ Here we delete node |p| from the ring, and let |rover| rove around.
+
+@<Allocate entire...@>=
+begin rover:=rlink(p); t:=llink(p);
+llink(rover):=t; rlink(t):=rover;
+goto found;
+end
+
+@ Conversely, when some variable-size node |p| of size |s| is no longer needed,
+the operation |free_node(p,s)| will make its words available, by inserting
+|p| as a new empty node just before where |rover| now points.
+@^inner loop@>
+
+@p procedure free_node(@!p:pointer; @!s:halfword); {variable-size node
+ liberation}
+var q:pointer; {|llink(rover)|}
+begin node_size(p):=s; link(p):=empty_flag;
+q:=llink(rover); llink(p):=q; rlink(p):=rover; {set both links}
+llink(rover):=p; rlink(q):=p; {insert |p| into the ring}
+@!stat var_used:=var_used-s;@+tats@;{maintain statistics}
+end;
+
+@ Just before \.{INITEX} writes out the memory, it sorts the doubly linked
+available space list. The list is probably very short at such times, so a
+simple insertion sort is used. The smallest available location will be
+pointed to by |rover|, the next-smallest by |rlink(rover)|, etc.
+
+@p @!init procedure sort_avail; {sorts the available variable-size nodes
+ by location}
+var p,@!q,@!r: pointer; {indices into |mem|}
+@!old_rover:pointer; {initial |rover| setting}
+begin p:=get_node(@'10000000000); {merge adjacent free areas}
+p:=rlink(rover); rlink(rover):=max_halfword; old_rover:=rover;
+while p<>old_rover do @<Sort \(p)|p| into the list starting at |rover|
+ and advance |p| to |rlink(p)|@>;
+p:=rover;
+while rlink(p)<>max_halfword do
+ begin llink(rlink(p)):=p; p:=rlink(p);
+ end;
+rlink(p):=rover; llink(rover):=p;
+end;
+tini
+
+@ The following |while| loop is guaranteed to
+terminate, since the list that starts at
+|rover| ends with |max_halfword| during the sorting procedure.
+
+@<Sort \(p)|p|...@>=
+if p<rover then
+ begin q:=p; p:=rlink(q); rlink(q):=rover; rover:=q;
+ end
+else begin q:=rover;
+ while rlink(q)<p do q:=rlink(q);
+ r:=rlink(p); rlink(p):=rlink(q); rlink(q):=p; p:=r;
+ end
+
+@* \[10] Data structures for boxes and their friends.
+From the computer's standpoint, \TeX's chief mission is to create
+horizontal and vertical lists. We shall now investigate how the elements
+of these lists are represented internally as nodes in the dynamic memory.
+
+A horizontal or vertical list is linked together by |link| fields in
+the first word of each node. Individual nodes represent boxes, glue,
+penalties, or special things like discretionary hyphens; because of this
+variety, some nodes are longer than others, and we must distinguish different
+kinds of nodes. We do this by putting a `|type|' field in the first word,
+together with the link and an optional `|subtype|'.
+
+@d type(#) == mem[#].hh.b0 {identifies what kind of node this is}
+@d subtype(#) == mem[#].hh.b1 {secondary identification in some cases}
+
+@ A |@!char_node|, which represents a single character, is the most important
+kind of node because it accounts for the vast majority of all boxes.
+Special precautions are therefore taken to ensure that a |char_node| does
+not take up much memory space. Every such node is one word long, and in fact
+it is identifiable by this property, since other kinds of nodes have at least
+two words, and they appear in |mem| locations less than |hi_mem_min|.
+This makes it possible to omit the |type| field in a |char_node|, leaving
+us room for two bytes that identify a |font| and a |character| within
+that font.
+
+Note that the format of a |char_node| allows for up to 256 different
+fonts and up to 256 characters per font; but most implementations will
+probably limit the total number of fonts to fewer than 75 per job,
+and most fonts will stick to characters whose codes are
+less than 128 (since higher codes
+are more difficult to access on most keyboards).
+
+Extensions of \TeX\ intended for oriental languages will need even more
+than $256\times256$ possible characters, when we consider different sizes
+@^oriental characters@>@^Chinese characters@>@^Japanese characters@>
+and styles of type. It is suggested that Chinese and Japanese fonts be
+handled by representing such characters in two consecutive |char_node|
+entries: The first of these has |font=font_base|, and its |link| points
+to the second;
+the second identifies the font and the character dimensions.
+The saving feature about oriental characters is that most of them have
+the same box dimensions. The |character| field of the first |char_node|
+is a ``\\{charext}'' that distinguishes between graphic symbols whose
+dimensions are identical for typesetting purposes. (See the \MF\ manual.)
+Such an extension of \TeX\ would not be difficult; further details are
+left to the reader.
+
+In order to make sure that the |character| code fits in a quarterword,
+\TeX\ adds the quantity |min_quarterword| to the actual code.
+
+Character nodes appear only in horizontal lists, never in vertical lists.
+
+@d is_char_node(#) == (#>=hi_mem_min)
+ {does the argument point to a |char_node|?}
+@d font == type {the font code in a |char_node|}
+@d character == subtype {the character code in a |char_node|}
+
+@ An |hlist_node| stands for a box that was made from a horizontal list.
+Each |hlist_node| is seven words long, and contains the following fields
+(in addition to the mandatory |type| and |link|, which we shall not
+mention explicitly when discussing the other node types): The |height| and
+|width| and |depth| are scaled integers denoting the dimensions of the
+box. There is also a |shift_amount| field, a scaled integer indicating
+how much this box should be lowered (if it appears in a horizontal list),
+or how much it should be moved to the right (if it appears in a vertical
+list). There is a |list_ptr| field, which points to the beginning of the
+list from which this box was fabricated; if |list_ptr| is |null|, the box
+is empty. Finally, there are three fields that represent the setting of
+the glue: |glue_set(p)| is a word of type |glue_ratio| that represents
+the proportionality constant for glue setting; |glue_sign(p)| is
+|stretching| or |shrinking| or |normal| depending on whether or not the
+glue should stretch or shrink or remain rigid; and |glue_order(p)|
+specifies the order of infinity to which glue setting applies (|normal|,
+|fil|, |fill|, or |filll|). The |subtype| field is not used.
+
+@d hlist_node=0 {|type| of hlist nodes}
+@d box_node_size=7 {number of words to allocate for a box node}
+@d width_offset=1 {position of |width| field in a box node}
+@d depth_offset=2 {position of |depth| field in a box node}
+@d height_offset=3 {position of |height| field in a box node}
+@d width(#) == mem[#+width_offset].sc {width of the box, in sp}
+@d depth(#) == mem[#+depth_offset].sc {depth of the box, in sp}
+@d height(#) == mem[#+height_offset].sc {height of the box, in sp}
+@d shift_amount(#) == mem[#+4].sc {repositioning distance, in sp}
+@d list_offset=5 {position of |list_ptr| field in a box node}
+@d list_ptr(#) == link(#+list_offset) {beginning of the list inside the box}
+@d glue_order(#) == subtype(#+list_offset) {applicable order of infinity}
+@d glue_sign(#) == type(#+list_offset) {stretching or shrinking}
+@d normal=0 {the most common case when several cases are named}
+@d stretching = 1 {glue setting applies to the stretch components}
+@d shrinking = 2 {glue setting applies to the shrink components}
+@d glue_offset = 6 {position of |glue_set| in a box node}
+@d glue_set(#) == mem[#+glue_offset].gr
+ {a word of type |glue_ratio| for glue setting}
+
+@ The |new_null_box| function returns a pointer to an |hlist_node| in
+which all subfields have the values corresponding to `\.{\\hbox\{\}}'.
+The |subtype| field is set to |min_quarterword|, since that's the desired
+|span_count| value if this |hlist_node| is changed to an |unset_node|.
+
+@p function new_null_box:pointer; {creates a new box node}
+var p:pointer; {the new node}
+begin p:=get_node(box_node_size); type(p):=hlist_node;
+subtype(p):=min_quarterword;
+width(p):=0; depth(p):=0; height(p):=0; shift_amount(p):=0; list_ptr(p):=null;
+glue_sign(p):=normal; glue_order(p):=normal; set_glue_ratio_zero(glue_set(p));
+new_null_box:=p;
+end;
+
+@ A |vlist_node| is like an |hlist_node| in all respects except that it
+contains a vertical list.
+
+@d vlist_node=1 {|type| of vlist nodes}
+
+@ A |rule_node| stands for a solid black rectangle; it has |width|,
+|depth|, and |height| fields just as in an |hlist_node|. However, if
+any of these dimensions is $-2^{30}$, the actual value will be determined
+by running the rule up to the boundary of the innermost enclosing box.
+This is called a ``running dimension.'' The |width| is never running in
+an hlist; the |height| and |depth| are never running in a~vlist.
+
+@d rule_node=2 {|type| of rule nodes}
+@d rule_node_size=4 {number of words to allocate for a rule node}
+@d null_flag==-@'10000000000 {$-2^{30}$, signifies a missing item}
+@d is_running(#) == (#=null_flag) {tests for a running dimension}
+
+@ A new rule node is delivered by the |new_rule| function. It
+makes all the dimensions ``running,'' so you have to change the
+ones that are not allowed to run.
+
+@p function new_rule:pointer;
+var p:pointer; {the new node}
+begin p:=get_node(rule_node_size); type(p):=rule_node;
+subtype(p):=0; {the |subtype| is not used}
+width(p):=null_flag; depth(p):=null_flag; height(p):=null_flag;
+new_rule:=p;
+end;
+
+@ Insertions are represented by |ins_node| records, where the |subtype|
+indicates the corresponding box number. For example, `\.{\\insert 250}'
+leads to an |ins_node| whose |subtype| is |250+min_quarterword|.
+The |height| field of an |ins_node| is slightly misnamed; it actually holds
+the natural height plus depth of the vertical list being inserted.
+The |depth| field holds the |split_max_depth| to be used in case this
+insertion is split, and the |split_top_ptr| points to the corresponding
+|split_top_skip|. The |float_cost| field holds the |floating_penalty| that
+will be used if this insertion floats to a subsequent page after a
+split insertion of the same class. There is one more field, the
+|ins_ptr|, which points to the beginning of the vlist for the insertion.
+
+@d ins_node=3 {|type| of insertion nodes}
+@d ins_node_size=5 {number of words to allocate for an insertion}
+@d float_cost(#)==mem[#+1].int {the |floating_penalty| to be used}
+@d ins_ptr(#)==info(#+4) {the vertical list to be inserted}
+@d split_top_ptr(#)==link(#+4) {the |split_top_skip| to be used}
+
+@ A |mark_node| has a |mark_ptr| field that points to the reference count
+of a token list that contains the user's \.{\\mark} text.
+This field occupies a full word instead of a halfword, because
+there's nothing to put in the other halfword; it is easier in \PASCAL\ to
+use the full word than to risk leaving garbage in the unused half.
+
+@d mark_node=4 {|type| of a mark node}
+@d small_node_size=2 {number of words to allocate for most node types}
+@d mark_ptr(#)==mem[#+1].int {head of the token list for a mark}
+
+@ An |adjust_node|, which occurs only in horizontal lists,
+specifies material that will be moved out into the surrounding
+vertical list; i.e., it is used to implement \TeX's `\.{\\vadjust}'
+operation. The |adjust_ptr| field points to the vlist containing this
+material.
+
+@d adjust_node=5 {|type| of an adjust node}
+@d adjust_ptr==mark_ptr {vertical list to be moved out of horizontal list}
+
+@ A |ligature_node|, which occurs only in horizontal lists, specifies
+a character that was fabricated from the interaction of two or more
+actual characters. The second word of the node, which is called the
+|lig_char| word, contains |font| and |character| fields just as in a
+|char_node|. The characters that generated the ligature have not been
+forgotten, since they are needed for diagnostic messages and for
+hyphenation; the |lig_ptr| field points to a linked list of character
+nodes for all original characters that have been deleted. (This list
+might be empty if the characters that generated the ligature were
+retained in other nodes.)
+
+The |subtype| field is 0, plus 2 and/or 1 if the original source of the
+ligature included implicit left and/or right boundaries.
+
+@d ligature_node=6 {|type| of a ligature node}
+@d lig_char(#)==#+1 {the word where the ligature is to be found}
+@d lig_ptr(#)==link(lig_char(#)) {the list of characters}
+
+@ The |new_ligature| function creates a ligature node having given
+contents of the |font|, |character|, and |lig_ptr| fields. We also have
+a |new_lig_item| function, which returns a two-word node having a given
+|character| field. Such nodes are used for temporary processing as ligatures
+are being created.
+
+@p function new_ligature(@!f,@!c:quarterword; @!q:pointer):pointer;
+var p:pointer; {the new node}
+begin p:=get_node(small_node_size); type(p):=ligature_node;
+font(lig_char(p)):=f; character(lig_char(p)):=c; lig_ptr(p):=q;
+subtype(p):=0; new_ligature:=p;
+end;
+@#
+function new_lig_item(@!c:quarterword):pointer;
+var p:pointer; {the new node}
+begin p:=get_node(small_node_size); character(p):=c; lig_ptr(p):=null;
+new_lig_item:=p;
+end;
+
+@ A |disc_node|, which occurs only in horizontal lists, specifies a
+``dis\-cretion\-ary'' line break. If such a break occurs at node |p|, the text
+that starts at |pre_break(p)| will precede the break, the text that starts at
+|post_break(p)| will follow the break, and text that appears in the next
+|replace_count(p)| nodes will be ignored. For example, an ordinary
+discretionary hyphen, indicated by `\.{\\-}', yields a |disc_node| with
+|pre_break| pointing to a |char_node| containing a hyphen, |post_break=null|,
+and |replace_count=0|. All three of the discretionary texts must be
+lists that consist entirely of character, kern, box, rule, and ligature nodes.
+
+If |pre_break(p)=null|, the |ex_hyphen_penalty| will be charged for this
+break. Otherwise the |hyphen_penalty| will be charged. The texts will
+actually be substituted into the list by the line-breaking algorithm if it
+decides to make the break, and the discretionary node will disappear at
+that time; thus, the output routine sees only discretionaries that were
+not chosen.
+
+@d disc_node=7 {|type| of a discretionary node}
+@d replace_count==subtype {how many subsequent nodes to replace}
+@d pre_break==llink {text that precedes a discretionary break}
+@d post_break==rlink {text that follows a discretionary break}
+
+@p function new_disc:pointer; {creates an empty |disc_node|}
+var p:pointer; {the new node}
+begin p:=get_node(small_node_size); type(p):=disc_node;
+replace_count(p):=0; pre_break(p):=null; post_break(p):=null;
+new_disc:=p;
+end;
+
+@ A |whatsit_node| is a wild card reserved for extensions to \TeX. The
+|subtype| field in its first word says what `\\{whatsit}' it is, and
+implicitly determines the node size (which must be 2 or more) and the
+format of the remaining words. When a |whatsit_node| is encountered
+in a list, special actions are invoked; knowledgeable people who are
+careful not to mess up the rest of \TeX\ are able to make \TeX\ do new
+things by adding code at the end of the program. For example, there
+might be a `\TeX nicolor' extension to specify different colors of ink,
+@^extensions to \TeX@>
+and the whatsit node might contain the desired parameters.
+
+The present implementation of \TeX\ treats the features associated with
+`\.{\\write}' and `\.{\\special}' as if they were extensions, in order to
+illustrate how such routines might be coded. We shall defer further
+discussion of extensions until the end of this program.
+
+@d whatsit_node=8 {|type| of special extension nodes}
+
+@ A |math_node|, which occurs only in horizontal lists, appears before and
+after mathematical formulas. The |subtype| field is |before| before the
+formula and |after| after it. There is a |width| field, which represents
+the amount of surrounding space inserted by \.{\\mathsurround}.
+
+@d math_node=9 {|type| of a math node}
+@d before=0 {|subtype| for math node that introduces a formula}
+@d after=1 {|subtype| for math node that winds up a formula}
+
+@p function new_math(@!w:scaled;@!s:small_number):pointer;
+var p:pointer; {the new node}
+begin p:=get_node(small_node_size); type(p):=math_node;
+subtype(p):=s; width(p):=w; new_math:=p;
+end;
+
+@ \TeX\ makes use of the fact that |hlist_node|, |vlist_node|,
+|rule_node|, |ins_node|, |mark_node|, |adjust_node|, |ligature_node|,
+|disc_node|, |whatsit_node|, and |math_node| are at the low end of the
+type codes, by permitting a break at glue in a list if and only if the
+|type| of the previous node is less than |math_node|. Furthermore, a
+node is discarded after a break if its type is |math_node| or~more.
+
+@d precedes_break(#)==(type(#)<math_node)
+@d non_discardable(#)==(type(#)<math_node)
+
+@ A |glue_node| represents glue in a list. However, it is really only
+a pointer to a separate glue specification, since \TeX\ makes use of the
+fact that many essentially identical nodes of glue are usually present.
+If |p| points to a |glue_node|, |glue_ptr(p)| points to
+another packet of words that specify the stretch and shrink components, etc.
+
+Glue nodes also serve to represent leaders; the |subtype| is used to
+distinguish between ordinary glue (which is called |normal|) and the three
+kinds of leaders (which are called |a_leaders|, |c_leaders|, and |x_leaders|).
+The |leader_ptr| field points to a rule node or to a box node containing the
+leaders; it is set to |null| in ordinary glue nodes.
+
+Many kinds of glue are computed from \TeX's ``skip'' parameters, and
+it is helpful to know which parameter has led to a particular glue node.
+Therefore the |subtype| is set to indicate the source of glue, whenever
+it originated as a parameter. We will be defining symbolic names for the
+parameter numbers later (e.g., |line_skip_code=0|, |baseline_skip_code=1|,
+etc.); it suffices for now to say that the |subtype| of parametric glue
+will be the same as the parameter number, plus~one.
+
+In math formulas there are two more possibilities for the |subtype| in a
+glue node: |mu_glue| denotes an \.{\\mskip} (where the units are scaled \.{mu}
+instead of scaled \.{pt}); and |cond_math_glue| denotes the `\.{\\nonscript}'
+feature that cancels the glue node immediately following if it appears
+in a subscript.
+
+@d glue_node=10 {|type| of node that points to a glue specification}
+@d cond_math_glue=98 {special |subtype| to suppress glue in the next node}
+@d mu_glue=99 {|subtype| for math glue}
+@d a_leaders=100 {|subtype| for aligned leaders}
+@d c_leaders=101 {|subtype| for centered leaders}
+@d x_leaders=102 {|subtype| for expanded leaders}
+@d glue_ptr==llink {pointer to a glue specification}
+@d leader_ptr==rlink {pointer to box or rule node for leaders}
+
+@ A glue specification has a halfword reference count in its first word,
+@^reference counts@>
+representing |null| plus the number of glue nodes that point to it (less one).
+Note that the reference count appears in the same position as
+the |link| field in list nodes; this is the field that is initialized
+to |null| when a node is allocated, and it is also the field that is flagged
+by |empty_flag| in empty nodes.
+
+Glue specifications also contain three |scaled| fields, for the |width|,
+|stretch|, and |shrink| dimensions. Finally, there are two one-byte
+fields called |stretch_order| and |shrink_order|; these contain the
+orders of infinity (|normal|, |fil|, |fill|, or |filll|)
+corresponding to the stretch and shrink values.
+
+@d glue_spec_size=4 {number of words to allocate for a glue specification}
+@d glue_ref_count(#) == link(#) {reference count of a glue specification}
+@d stretch(#) == mem[#+2].sc {the stretchability of this glob of glue}
+@d shrink(#) == mem[#+3].sc {the shrinkability of this glob of glue}
+@d stretch_order == type {order of infinity for stretching}
+@d shrink_order == subtype {order of infinity for shrinking}
+@d fil=1 {first-order infinity}
+@d fill=2 {second-order infinity}
+@d filll=3 {third-order infinity}
+
+@<Types...@>=
+@!glue_ord=normal..filll; {infinity to the 0, 1, 2, or 3 power}
+
+@ Here is a function that returns a pointer to a copy of a glue spec.
+The reference count in the copy is |null|, because there is assumed
+to be exactly one reference to the new specification.
+
+@p function new_spec(@!p:pointer):pointer; {duplicates a glue specification}
+var q:pointer; {the new spec}
+begin q:=get_node(glue_spec_size);@/
+mem[q]:=mem[p]; glue_ref_count(q):=null;@/
+width(q):=width(p); stretch(q):=stretch(p); shrink(q):=shrink(p);
+new_spec:=q;
+end;
+
+@ And here's a function that creates a glue node for a given parameter
+identified by its code number; for example,
+|new_param_glue(line_skip_code)| returns a pointer to a glue node for the
+current \.{\\lineskip}.
+
+@p function new_param_glue(@!n:small_number):pointer;
+var p:pointer; {the new node}
+@!q:pointer; {the glue specification}
+begin p:=get_node(small_node_size); type(p):=glue_node; subtype(p):=n+1;
+leader_ptr(p):=null;@/
+q:=@<Current |mem| equivalent of glue parameter number |n|@>@t@>;
+glue_ptr(p):=q; incr(glue_ref_count(q));
+new_param_glue:=p;
+end;
+
+@ Glue nodes that are more or less anonymous are created by |new_glue|,
+whose argument points to a glue specification.
+
+@p function new_glue(@!q:pointer):pointer;
+var p:pointer; {the new node}
+begin p:=get_node(small_node_size); type(p):=glue_node; subtype(p):=normal;
+leader_ptr(p):=null; glue_ptr(p):=q; incr(glue_ref_count(q));
+new_glue:=p;
+end;
+
+@ Still another subroutine is needed: this one is sort of a combination
+of |new_param_glue| and |new_glue|. It creates a glue node for one of
+the current glue parameters, but it makes a fresh copy of the glue
+specification, since that specification will probably be subject to change,
+while the parameter will stay put. The global variable |temp_ptr| is
+set to the address of the new spec.
+
+@p function new_skip_param(@!n:small_number):pointer;
+var p:pointer; {the new node}
+begin temp_ptr:=new_spec(@<Current |mem| equivalent of glue parameter...@>);
+p:=new_glue(temp_ptr); glue_ref_count(temp_ptr):=null; subtype(p):=n+1;
+new_skip_param:=p;
+end;
+
+@ A |kern_node| has a |width| field to specify a (normally negative)
+amount of spacing. This spacing correction appears in horizontal lists
+between letters like A and V when the font designer said that it looks
+better to move them closer together or further apart. A kern node can
+also appear in a vertical list, when its `|width|' denotes additional
+spacing in the vertical direction. The |subtype| is either |normal| (for
+kerns inserted from font information or math mode calculations) or |explicit|
+(for kerns inserted from \.{\\kern} and \.{\\/} commands) or |acc_kern|
+(for kerns inserted from non-math accents) or |mu_glue| (for kerns
+inserted from \.{\\mkern} specifications in math formulas).
+
+@d kern_node=11 {|type| of a kern node}
+@d explicit=1 {|subtype| of kern nodes from \.{\\kern} and \.{\\/}}
+@d acc_kern=2 {|subtype| of kern nodes from accents}
+
+@ The |new_kern| function creates a kern node having a given width.
+
+@p function new_kern(@!w:scaled):pointer;
+var p:pointer; {the new node}
+begin p:=get_node(small_node_size); type(p):=kern_node;
+subtype(p):=normal;
+width(p):=w;
+new_kern:=p;
+end;
+
+@ A |penalty_node| specifies the penalty associated with line or page
+breaking, in its |penalty| field. This field is a fullword integer, but
+the full range of integer values is not used: Any penalty |>=10000| is
+treated as infinity, and no break will be allowed for such high values.
+Similarly, any penalty |<=-10000| is treated as negative infinity, and a
+break will be forced.
+
+@d penalty_node=12 {|type| of a penalty node}
+@d inf_penalty=inf_bad {``infinite'' penalty value}
+@d eject_penalty=-inf_penalty {``negatively infinite'' penalty value}
+@d penalty(#) == mem[#+1].int {the added cost of breaking a list here}
+
+@ Anyone who has been reading the last few sections of the program will
+be able to guess what comes next.
+
+@p function new_penalty(@!m:integer):pointer;
+var p:pointer; {the new node}
+begin p:=get_node(small_node_size); type(p):=penalty_node;
+subtype(p):=0; {the |subtype| is not used}
+penalty(p):=m; new_penalty:=p;
+end;
+
+@ You might think that we have introduced enough node types by now. Well,
+almost, but there is one more: An |unset_node| has nearly the same format
+as an |hlist_node| or |vlist_node|; it is used for entries in \.{\\halign}
+or \.{\\valign} that are not yet in their final form, since the box
+dimensions are their ``natural'' sizes before any glue adjustment has been
+made. The |glue_set| word is not present; instead, we have a |glue_stretch|
+field, which contains the total stretch of order |glue_order| that is
+present in the hlist or vlist being boxed.
+Similarly, the |shift_amount| field is replaced by a |glue_shrink| field,
+containing the total shrink of order |glue_sign| that is present.
+The |subtype| field is called |span_count|; an unset box typically
+contains the data for |qo(span_count)+1| columns.
+Unset nodes will be changed to box nodes when alignment is completed.
+
+@d unset_node=13 {|type| for an unset node}
+@d glue_stretch(#)==mem[#+glue_offset].sc {total stretch in an unset node}
+@d glue_shrink==shift_amount {total shrink in an unset node}
+@d span_count==subtype {indicates the number of spanned columns}
+
+@ In fact, there are still more types coming. When we get to math formula
+processing we will see that a |style_node| has |type=14|; and a number
+of larger type codes will also be defined, for use in math mode only.
+
+@ Warning: If any changes are made to these data structure layouts, such as
+changing any of the node sizes or even reordering the words of nodes,
+the |copy_node_list| procedure and the memory initialization code
+below may have to be changed. Such potentially dangerous parts of the
+program are listed in the index under `data structure assumptions'.
+@!@^data structure assumptions@>
+However, other references to the nodes are made symbolically in terms of
+the \.{WEB} macro definitions above, so that format changes will leave
+\TeX's other algorithms intact.
+@^system dependencies@>
+
+@* \[11] Memory layout.
+Some areas of |mem| are dedicated to fixed usage, since static allocation is
+more efficient than dynamic allocation when we can get away with it. For
+example, locations |mem_bot| to |mem_bot+3| are always used to store the
+specification for glue that is `\.{0pt plus 0pt minus 0pt}'. The
+following macro definitions accomplish the static allocation by giving
+symbolic names to the fixed positions. Static variable-size nodes appear
+in locations |mem_bot| through |lo_mem_stat_max|, and static single-word nodes
+appear in locations |hi_mem_stat_min| through |mem_top|, inclusive. It is
+harmless to let |lig_trick| and |garbage| share the same location of |mem|.
+
+@d zero_glue==mem_bot {specification for \.{0pt plus 0pt minus 0pt}}
+@d fil_glue==zero_glue+glue_spec_size {\.{0pt plus 1fil minus 0pt}}
+@d fill_glue==fil_glue+glue_spec_size {\.{0pt plus 1fill minus 0pt}}
+@d ss_glue==fill_glue+glue_spec_size {\.{0pt plus 1fil minus 1fil}}
+@d fil_neg_glue==ss_glue+glue_spec_size {\.{0pt plus -1fil minus 0pt}}
+@d lo_mem_stat_max==fil_neg_glue+glue_spec_size-1 {largest statically
+ allocated word in the variable-size |mem|}
+@#
+@d page_ins_head==mem_top {list of insertion data for current page}
+@d contrib_head==mem_top-1 {vlist of items not yet on current page}
+@d page_head==mem_top-2 {vlist for current page}
+@d temp_head==mem_top-3 {head of a temporary list of some kind}
+@d hold_head==mem_top-4 {head of a temporary list of another kind}
+@d adjust_head==mem_top-5 {head of adjustment list returned by |hpack|}
+@d active==mem_top-7 {head of active list in |line_break|, needs two words}
+@d align_head==mem_top-8 {head of preamble list for alignments}
+@d end_span==mem_top-9 {tail of spanned-width lists}
+@d omit_template==mem_top-10 {a constant token list}
+@d null_list==mem_top-11 {permanently empty list}
+@d lig_trick==mem_top-12 {a ligature masquerading as a |char_node|}
+@d garbage==mem_top-12 {used for scrap information}
+@d backup_head==mem_top-13 {head of token list built by |scan_keyword|}
+@d hi_mem_stat_min==mem_top-13 {smallest statically allocated word in
+ the one-word |mem|}
+@d hi_mem_stat_usage=14 {the number of one-word nodes always present}
+
+@ The following code gets |mem| off to a good start, when \TeX\ is
+initializing itself the slow~way.
+
+@<Local variables for init...@>=
+@!k:integer; {index into |mem|, |eqtb|, etc.}
+
+@ @<Initialize table entries...@>=
+for k:=mem_bot+1 to lo_mem_stat_max do mem[k].sc:=0;
+ {all glue dimensions are zeroed}
+@^data structure assumptions@>
+k:=mem_bot;@+while k<=lo_mem_stat_max do
+ {set first words of glue specifications}
+ begin glue_ref_count(k):=null+1;
+ stretch_order(k):=normal; shrink_order(k):=normal;
+ k:=k+glue_spec_size;
+ end;
+stretch(fil_glue):=unity; stretch_order(fil_glue):=fil;@/
+stretch(fill_glue):=unity; stretch_order(fill_glue):=fill;@/
+stretch(ss_glue):=unity; stretch_order(ss_glue):=fil;@/
+shrink(ss_glue):=unity; shrink_order(ss_glue):=fil;@/
+stretch(fil_neg_glue):=-unity; stretch_order(fil_neg_glue):=fil;@/
+rover:=lo_mem_stat_max+1;
+link(rover):=empty_flag; {now initialize the dynamic memory}
+node_size(rover):=1000; {which is a 1000-word available node}
+llink(rover):=rover; rlink(rover):=rover;@/
+lo_mem_max:=rover+1000; link(lo_mem_max):=null; info(lo_mem_max):=null;@/
+for k:=hi_mem_stat_min to mem_top do
+ mem[k]:=mem[lo_mem_max]; {clear list heads}
+@<Initialize the special list heads and constant nodes@>;
+avail:=null; mem_end:=mem_top;
+hi_mem_min:=hi_mem_stat_min; {initialize the one-word memory}
+var_used:=lo_mem_stat_max+1-mem_bot; dyn_used:=hi_mem_stat_usage;
+ {initialize statistics}
+
+@ If \TeX\ is extended improperly, the |mem| array might get screwed up.
+For example, some pointers might be wrong, or some ``dead'' nodes might not
+have been freed when the last reference to them disappeared. Procedures
+|check_mem| and |search_mem| are available to help diagnose such
+problems. These procedures make use of two arrays called |free| and
+|was_free| that are present only if \TeX's debugging routines have
+been included. (You may want to decrease the size of |mem| while you
+@^debugging@>
+are debugging.)
+
+@<Glob...@>=
+@!debug @!free: packed array [mem_min..mem_max] of boolean; {free cells}
+@t\hskip10pt@>@!was_free: packed array [mem_min..mem_max] of boolean;
+ {previously free cells}
+@t\hskip10pt@>@!was_mem_end,@!was_lo_max,@!was_hi_min: pointer;
+ {previous |mem_end|, |lo_mem_max|, and |hi_mem_min|}
+@t\hskip10pt@>@!panicking:boolean; {do we want to check memory constantly?}
+gubed
+
+@ @<Set initial...@>=
+@!debug was_mem_end:=mem_min; {indicate that everything was previously free}
+was_lo_max:=mem_min; was_hi_min:=mem_max;
+panicking:=false;
+gubed
+
+@ Procedure |check_mem| makes sure that the available space lists of
+|mem| are well formed, and it optionally prints out all locations
+that are reserved now but were free the last time this procedure was called.
+
+@p @!debug procedure check_mem(@!print_locs : boolean);
+label done1,done2; {loop exits}
+var p,@!q:pointer; {current locations of interest in |mem|}
+@!clobbered:boolean; {is something amiss?}
+begin for p:=mem_min to lo_mem_max do free[p]:=false; {you can probably
+ do this faster}
+for p:=hi_mem_min to mem_end do free[p]:=false; {ditto}
+@<Check single-word |avail| list@>;
+@<Check variable-size |avail| list@>;
+@<Check flags of unavailable nodes@>;
+if print_locs then @<Print newly busy locations@>;
+for p:=mem_min to lo_mem_max do was_free[p]:=free[p];
+for p:=hi_mem_min to mem_end do was_free[p]:=free[p];
+ {|was_free:=free| might be faster}
+was_mem_end:=mem_end; was_lo_max:=lo_mem_max; was_hi_min:=hi_mem_min;
+end;
+gubed
+
+@ @<Check single-word...@>=
+p:=avail; q:=null; clobbered:=false;
+while p<>null do
+ begin if (p>mem_end)or(p<hi_mem_min) then clobbered:=true
+ else if free[p] then clobbered:=true;
+ if clobbered then
+ begin print_nl("AVAIL list clobbered at ");
+@.AVAIL list clobbered...@>
+ print_int(q); goto done1;
+ end;
+ free[p]:=true; q:=p; p:=link(q);
+ end;
+done1:
+
+@ @<Check variable-size...@>=
+p:=rover; q:=null; clobbered:=false;
+repeat if (p>=lo_mem_max)or(p<mem_min) then clobbered:=true
+ else if (rlink(p)>=lo_mem_max)or(rlink(p)<mem_min) then clobbered:=true
+ else if not(is_empty(p))or(node_size(p)<2)or@|
+ (p+node_size(p)>lo_mem_max)or@| (llink(rlink(p))<>p) then clobbered:=true;
+ if clobbered then
+ begin print_nl("Double-AVAIL list clobbered at ");
+ print_int(q); goto done2;
+ end;
+for q:=p to p+node_size(p)-1 do {mark all locations free}
+ begin if free[q] then
+ begin print_nl("Doubly free location at ");
+@.Doubly free location...@>
+ print_int(q); goto done2;
+ end;
+ free[q]:=true;
+ end;
+q:=p; p:=rlink(p);
+until p=rover;
+done2:
+
+@ @<Check flags...@>=
+p:=mem_min;
+while p<=lo_mem_max do {node |p| should not be empty}
+ begin if is_empty(p) then
+ begin print_nl("Bad flag at "); print_int(p);
+@.Bad flag...@>
+ end;
+ while (p<=lo_mem_max) and not free[p] do incr(p);
+ while (p<=lo_mem_max) and free[p] do incr(p);
+ end
+
+@ @<Print newly busy...@>=
+begin print_nl("New busy locs:");
+for p:=mem_min to lo_mem_max do
+ if not free[p] and ((p>was_lo_max) or was_free[p]) then
+ begin print_char(" "); print_int(p);
+ end;
+for p:=hi_mem_min to mem_end do
+ if not free[p] and
+ ((p<was_hi_min) or (p>was_mem_end) or was_free[p]) then
+ begin print_char(" "); print_int(p);
+ end;
+end
+
+@ The |search_mem| procedure attempts to answer the question ``Who points
+to node~|p|?'' In doing so, it fetches |link| and |info| fields of |mem|
+that might not be of type |two_halves|. Strictly speaking, this is
+@^dirty \PASCAL@>
+undefined in \PASCAL, and it can lead to ``false drops'' (words that seem to
+point to |p| purely by coincidence). But for debugging purposes, we want
+to rule out the places that do {\sl not\/} point to |p|, so a few false
+drops are tolerable.
+
+@p @!debug procedure search_mem(@!p:pointer); {look for pointers to |p|}
+var q:integer; {current position being searched}
+begin for q:=mem_min to lo_mem_max do
+ begin if link(q)=p then
+ begin print_nl("LINK("); print_int(q); print_char(")");
+ end;
+ if info(q)=p then
+ begin print_nl("INFO("); print_int(q); print_char(")");
+ end;
+ end;
+for q:=hi_mem_min to mem_end do
+ begin if link(q)=p then
+ begin print_nl("LINK("); print_int(q); print_char(")");
+ end;
+ if info(q)=p then
+ begin print_nl("INFO("); print_int(q); print_char(")");
+ end;
+ end;
+@<Search |eqtb| for equivalents equal to |p|@>;
+@<Search |save_stack| for equivalents that point to |p|@>;
+@<Search |hyph_list| for pointers to |p|@>;
+end;
+gubed
+
+@* \[12] Displaying boxes.
+We can reinforce our knowledge of the data structures just introduced
+by considering two procedures that display a list in symbolic form.
+The first of these, called |short_display|, is used in ``overfull box''
+messages to give the top-level description of a list. The other one,
+called |show_node_list|, prints a detailed description of exactly what
+is in the data structure.
+
+The philosophy of |short_display| is to ignore the fine points about exactly
+what is inside boxes, except that ligatures and discretionary breaks are
+expanded. As a result, |short_display| is a recursive procedure, but the
+recursion is never more than one level deep.
+@^recursion@>
+
+A global variable |font_in_short_display| keeps track of the font code that
+is assumed to be present when |short_display| begins; deviations from this
+font will be printed.
+
+@<Glob...@>=
+@!font_in_short_display:integer; {an internal font number}
+
+@ Boxes, rules, inserts, whatsits, marks, and things in general that are
+sort of ``complicated'' are indicated only by printing `\.{[]}'.
+
+@p procedure short_display(@!p:integer); {prints highlights of list |p|}
+var n:integer; {for replacement counts}
+begin while p>mem_min do
+ begin if is_char_node(p) then
+ begin if p<=mem_end then
+ begin if font(p)<>font_in_short_display then
+ begin if (font(p)<font_base)or(font(p)>font_max) then
+ print_char("*")
+@.*\relax@>
+ else @<Print the font identifier for |font(p)|@>;
+ print_char(" "); font_in_short_display:=font(p);
+ end;
+ print_ASCII(qo(character(p)));
+ end;
+ end
+ else @<Print a short indication of the contents of node |p|@>;
+ p:=link(p);
+ end;
+end;
+
+@ @<Print a short indication of the contents of node |p|@>=
+case type(p) of
+hlist_node,vlist_node,ins_node,whatsit_node,mark_node,adjust_node,
+ unset_node: print("[]");
+rule_node: print_char("|");
+glue_node: if glue_ptr(p)<>zero_glue then print_char(" ");
+math_node: print_char("$");
+ligature_node: short_display(lig_ptr(p));
+disc_node: begin short_display(pre_break(p));
+ short_display(post_break(p));@/
+ n:=replace_count(p);
+ while n>0 do
+ begin if link(p)<>null then p:=link(p);
+ decr(n);
+ end;
+ end;
+othercases do_nothing
+endcases
+
+@ The |show_node_list| routine requires some auxiliary subroutines: one to
+print a font-and-character combination, one to print a token list without
+its reference count, and one to print a rule dimension.
+
+@p procedure print_font_and_char(@!p:integer); {prints |char_node| data}
+begin if p>mem_end then print_esc("CLOBBERED.")
+else begin if (font(p)<font_base)or(font(p)>font_max) then print_char("*")
+@.*\relax@>
+ else @<Print the font identifier for |font(p)|@>;
+ print_char(" "); print_ASCII(qo(character(p)));
+ end;
+end;
+@#
+procedure print_mark(@!p:integer); {prints token list data in braces}
+begin print_char("{");
+if (p<hi_mem_min)or(p>mem_end) then print_esc("CLOBBERED.")
+else show_token_list(link(p),null,max_print_line-10);
+print_char("}");
+end;
+@#
+procedure print_rule_dimen(@!d:scaled); {prints dimension in rule node}
+begin if is_running(d) then print_char("*") else print_scaled(d);
+@.*\relax@>
+end;
+
+@ Then there is a subroutine that prints glue stretch and shrink, possibly
+followed by the name of finite units:
+
+@p procedure print_glue(@!d:scaled;@!order:integer;@!s:str_number);
+ {prints a glue component}
+begin print_scaled(d);
+if (order<normal)or(order>filll) then print("foul")
+else if order>normal then
+ begin print("fil");
+ while order>fil do
+ begin print_char("l"); decr(order);
+ end;
+ end
+else if s<>0 then print(s);
+end;
+
+@ The next subroutine prints a whole glue specification.
+
+@p procedure print_spec(@!p:integer;@!s:str_number);
+ {prints a glue specification}
+begin if (p<mem_min)or(p>=lo_mem_max) then print_char("*")
+@.*\relax@>
+else begin print_scaled(width(p));
+ if s<>0 then print(s);
+ if stretch(p)<>0 then
+ begin print(" plus "); print_glue(stretch(p),stretch_order(p),s);
+ end;
+ if shrink(p)<>0 then
+ begin print(" minus "); print_glue(shrink(p),shrink_order(p),s);
+ end;
+ end;
+end;
+
+@ We also need to declare some procedures that appear later in this
+documentation.
+
+@p @<Declare procedures needed for displaying the elements of mlists@>@;
+@<Declare the procedure called |print_skip_param|@>
+
+@ Since boxes can be inside of boxes, |show_node_list| is inherently recursive,
+@^recursion@>
+up to a given maximum number of levels. The history of nesting is indicated
+by the current string, which will be printed at the beginning of each line;
+the length of this string, namely |cur_length|, is the depth of nesting.
+
+Recursive calls on |show_node_list| therefore use the following pattern:
+
+@d node_list_display(#)==
+ begin append_char("."); show_node_list(#); flush_char;
+ end {|str_room| need not be checked; see |show_box| below}
+
+@ A global variable called |depth_threshold| is used to record the maximum
+depth of nesting for which |show_node_list| will show information. If we
+have |depth_threshold=0|, for example, only the top level information will
+be given and no sublists will be traversed. Another global variable, called
+|breadth_max|, tells the maximum number of items to show at each level;
+|breadth_max| had better be positive, or you won't see anything.
+
+@<Glob...@>=
+@!depth_threshold : integer; {maximum nesting depth in box displays}
+@!breadth_max : integer; {maximum number of items shown at the same list level}
+
+@ Now we are ready for |show_node_list| itself. This procedure has been
+written to be ``extra robust'' in the sense that it should not crash or get
+into a loop even if the data structures have been messed up by bugs in
+the rest of the program. You can safely call its parent routine
+|show_box(p)| for arbitrary values of |p| when you are debugging \TeX.
+However, in the presence of bad data, the procedure may
+@^dirty \PASCAL@>@^debugging@>
+fetch a |memory_word| whose variant is different from the way it was stored;
+for example, it might try to read |mem[p].hh| when |mem[p]|
+contains a scaled integer, if |p| is a pointer that has been
+clobbered or chosen at random.
+
+@p procedure show_node_list(@!p:integer); {prints a node list symbolically}
+label exit;
+var n:integer; {the number of items already printed at this level}
+@!g:real; {a glue ratio, as a floating point number}
+begin if cur_length>depth_threshold then
+ begin if p>null then print(" []");
+ {indicate that there's been some truncation}
+ return;
+ end;
+n:=0;
+while p>mem_min do
+ begin print_ln; print_current_string; {display the nesting history}
+ if p>mem_end then {pointer out of range}
+ begin print("Bad link, display aborted."); return;
+@.Bad link...@>
+ end;
+ incr(n); if n>breadth_max then {time to stop}
+ begin print("etc."); return;
+@.etc@>
+ end;
+ @<Display node |p|@>;
+ p:=link(p);
+ end;
+exit:
+end;
+
+@ @<Display node |p|@>=
+if is_char_node(p) then print_font_and_char(p)
+else case type(p) of
+ hlist_node,vlist_node,unset_node: @<Display box |p|@>;
+ rule_node: @<Display rule |p|@>;
+ ins_node: @<Display insertion |p|@>;
+ whatsit_node: @<Display the whatsit node |p|@>;
+ glue_node: @<Display glue |p|@>;
+ kern_node: @<Display kern |p|@>;
+ math_node: @<Display math node |p|@>;
+ ligature_node: @<Display ligature |p|@>;
+ penalty_node: @<Display penalty |p|@>;
+ disc_node: @<Display discretionary |p|@>;
+ mark_node: @<Display mark |p|@>;
+ adjust_node: @<Display adjustment |p|@>;
+ @t\4@>@<Cases of |show_node_list| that arise in mlists only@>@;
+ othercases print("Unknown node type!")
+ endcases
+
+@ @<Display box |p|@>=
+begin if type(p)=hlist_node then print_esc("h")
+else if type(p)=vlist_node then print_esc("v")
+else print_esc("unset");
+print("box("); print_scaled(height(p)); print_char("+");
+print_scaled(depth(p)); print(")x"); print_scaled(width(p));
+if type(p)=unset_node then
+ @<Display special fields of the unset node |p|@>
+else begin @<Display the value of |glue_set(p)|@>;
+ if shift_amount(p)<>0 then
+ begin print(", shifted "); print_scaled(shift_amount(p));
+ end;
+ end;
+node_list_display(list_ptr(p)); {recursive call}
+end
+
+@ @<Display special fields of the unset node |p|@>=
+begin if span_count(p)<>min_quarterword then
+ begin print(" ("); print_int(qo(span_count(p))+1);
+ print(" columns)");
+ end;
+if glue_stretch(p)<>0 then
+ begin print(", stretch "); print_glue(glue_stretch(p),glue_order(p),0);
+ end;
+if glue_shrink(p)<>0 then
+ begin print(", shrink "); print_glue(glue_shrink(p),glue_sign(p),0);
+ end;
+end
+
+@ The code will have to change in this place if |glue_ratio| is
+a structured type instead of an ordinary |real|. Note that this routine
+should avoid arithmetic errors even if the |glue_set| field holds an
+arbitrary random value. The following code assumes that a properly
+formed nonzero |real| number has absolute value $2^{20}$ or more when
+it is regarded as an integer; this precaution was adequate to prevent
+floating point underflow on the author's computer.
+@^system dependencies@>
+@^dirty \PASCAL@>
+
+@<Display the value of |glue_set(p)|@>=
+g:=float(glue_set(p));
+if (g<>float_constant(0))and(glue_sign(p)<>normal) then
+ begin print(", glue set ");
+ if glue_sign(p)=shrinking then print("- ");
+ if abs(mem[p+glue_offset].int)<@'4000000 then print("?.?")
+ else if abs(g)>float_constant(20000) then
+ begin if g>float_constant(0) then print_char(">")
+ else print("< -");
+ print_glue(20000*unity,glue_order(p),0);
+ end
+ else print_glue(round(unity*g),glue_order(p),0);
+@^real multiplication@>
+ end
+
+@ @<Display rule |p|@>=
+begin print_esc("rule("); print_rule_dimen(height(p)); print_char("+");
+print_rule_dimen(depth(p)); print(")x"); print_rule_dimen(width(p));
+end
+
+@ @<Display insertion |p|@>=
+begin print_esc("insert"); print_int(qo(subtype(p)));
+print(", natural size "); print_scaled(height(p));
+print("; split("); print_spec(split_top_ptr(p),0);
+print_char(","); print_scaled(depth(p));
+print("); float cost "); print_int(float_cost(p));
+node_list_display(ins_ptr(p)); {recursive call}
+end
+
+@ @<Display glue |p|@>=
+if subtype(p)>=a_leaders then @<Display leaders |p|@>
+else begin print_esc("glue");
+ if subtype(p)<>normal then
+ begin print_char("(");
+ if subtype(p)<cond_math_glue then
+ print_skip_param(subtype(p)-1)
+ else if subtype(p)=cond_math_glue then print_esc("nonscript")
+ else print_esc("mskip");
+ print_char(")");
+ end;
+ if subtype(p)<>cond_math_glue then
+ begin print_char(" ");
+ if subtype(p)<cond_math_glue then print_spec(glue_ptr(p),0)
+ else print_spec(glue_ptr(p),"mu");
+ end;
+ end
+
+@ @<Display leaders |p|@>=
+begin print_esc("");
+if subtype(p)=c_leaders then print_char("c")
+else if subtype(p)=x_leaders then print_char("x");
+print("leaders "); print_spec(glue_ptr(p),0);
+node_list_display(leader_ptr(p)); {recursive call}
+end
+
+@ An ``explicit'' kern value is indicated implicitly by an explicit space.
+
+@<Display kern |p|@>=
+if subtype(p)<>mu_glue then
+ begin print_esc("kern");
+ if subtype(p)<>normal then print_char(" ");
+ print_scaled(width(p));
+ if subtype(p)=acc_kern then print(" (for accent)");
+@.for accent@>
+ end
+else begin print_esc("mkern"); print_scaled(width(p)); print("mu");
+ end
+
+@ @<Display math node |p|@>=
+begin print_esc("math");
+if subtype(p)=before then print("on")
+else print("off");
+if width(p)<>0 then
+ begin print(", surrounded "); print_scaled(width(p));
+ end;
+end
+
+@ @<Display ligature |p|@>=
+begin print_font_and_char(lig_char(p)); print(" (ligature ");
+if subtype(p)>1 then print_char("|");
+font_in_short_display:=font(lig_char(p)); short_display(lig_ptr(p));
+if odd(subtype(p)) then print_char("|");
+print_char(")");
+end
+
+@ @<Display penalty |p|@>=
+begin print_esc("penalty "); print_int(penalty(p));
+end
+
+@ The |post_break| list of a discretionary node is indicated by a prefixed
+`\.{\char'174}' instead of the `\..' before the |pre_break| list.
+
+@<Display discretionary |p|@>=
+begin print_esc("discretionary");
+if replace_count(p)>0 then
+ begin print(" replacing "); print_int(replace_count(p));
+ end;
+node_list_display(pre_break(p)); {recursive call}
+append_char("|"); show_node_list(post_break(p)); flush_char; {recursive call}
+end
+
+@ @<Display mark |p|@>=
+begin print_esc("mark"); print_mark(mark_ptr(p));
+end
+
+@ @<Display adjustment |p|@>=
+begin print_esc("vadjust"); node_list_display(adjust_ptr(p)); {recursive call}
+end
+
+@ The recursive machinery is started by calling |show_box|.
+@^recursion@>
+
+@p procedure show_box(@!p:pointer);
+begin @<Assign the values |depth_threshold:=show_box_depth| and
+ |breadth_max:=show_box_breadth|@>;
+if breadth_max<=0 then breadth_max:=5;
+if pool_ptr+depth_threshold>=pool_size then
+ depth_threshold:=pool_size-pool_ptr-1;
+ {now there's enough room for prefix string}
+show_node_list(p); {the show starts at |p|}
+print_ln;
+end;
+
+@* \[13] Destroying boxes.
+When we are done with a node list, we are obliged to return it to free
+storage, including all of its sublists. The recursive procedure
+|flush_node_list| does this for us.
+
+@ First, however, we shall consider two non-recursive procedures that do
+simpler tasks. The first of these, |delete_token_ref|, is called when
+a pointer to a token list's reference count is being removed. This means
+that the token list should disappear if the reference count was |null|,
+otherwise the count should be decreased by one.
+@^reference counts@>
+
+@d token_ref_count(#) == info(#) {reference count preceding a token list}
+
+@p procedure delete_token_ref(@!p:pointer); {|p| points to the reference count
+ of a token list that is losing one reference}
+begin if token_ref_count(p)=null then flush_list(p)
+else decr(token_ref_count(p));
+end;
+
+@ Similarly, |delete_glue_ref| is called when a pointer to a glue
+specification is being withdrawn.
+@^reference counts@>
+@d fast_delete_glue_ref(#)==@t@>@;@/
+ begin if glue_ref_count(#)=null then free_node(#,glue_spec_size)
+ else decr(glue_ref_count(#));
+ end
+
+@p procedure delete_glue_ref(@!p:pointer); {|p| points to a glue specification}
+fast_delete_glue_ref(p);
+
+@ Now we are ready to delete any node list, recursively.
+In practice, the nodes deleted are usually charnodes (about 2/3 of the time),
+and they are glue nodes in about half of the remaining cases.
+@^recursion@>
+
+@p procedure flush_node_list(@!p:pointer); {erase list of nodes starting at |p|}
+label done; {go here when node |p| has been freed}
+var q:pointer; {successor to node |p|}
+begin while p<>null do
+@^inner loop@>
+ begin q:=link(p);
+ if is_char_node(p) then free_avail(p)
+ else begin case type(p) of
+ hlist_node,vlist_node,unset_node: begin flush_node_list(list_ptr(p));
+ free_node(p,box_node_size); goto done;
+ end;
+ rule_node: begin free_node(p,rule_node_size); goto done;
+ end;
+ ins_node: begin flush_node_list(ins_ptr(p));
+ delete_glue_ref(split_top_ptr(p));
+ free_node(p,ins_node_size); goto done;
+ end;
+ whatsit_node: @<Wipe out the whatsit node |p| and |goto done|@>;
+ glue_node: begin fast_delete_glue_ref(glue_ptr(p));
+ if leader_ptr(p)<>null then flush_node_list(leader_ptr(p));
+ end;
+ kern_node,math_node,penalty_node: do_nothing;
+ ligature_node: flush_node_list(lig_ptr(p));
+ mark_node: delete_token_ref(mark_ptr(p));
+ disc_node: begin flush_node_list(pre_break(p));
+ flush_node_list(post_break(p));
+ end;
+ adjust_node: flush_node_list(adjust_ptr(p));
+ @t\4@>@<Cases of |flush_node_list| that arise in mlists only@>@;
+ othercases confusion("flushing")
+@:this can't happen flushing}{\quad flushing@>
+ endcases;@/
+ free_node(p,small_node_size);
+ done:end;
+ p:=q;
+ end;
+end;
+
+@* \[14] Copying boxes.
+Another recursive operation that acts on boxes is sometimes needed: The
+procedure |copy_node_list| returns a pointer to another node list that has
+the same structure and meaning as the original. Note that since glue
+specifications and token lists have reference counts, we need not make
+copies of them. Reference counts can never get too large to fit in a
+halfword, since each pointer to a node is in a different memory address,
+and the total number of memory addresses fits in a halfword.
+@^recursion@>
+@^reference counts@>
+
+(Well, there actually are also references from outside |mem|; if the
+|save_stack| is made arbitrarily large, it would theoretically be possible
+to break \TeX\ by overflowing a reference count. But who would want to do that?)
+
+@d add_token_ref(#)==incr(token_ref_count(#)) {new reference to a token list}
+@d add_glue_ref(#)==incr(glue_ref_count(#)) {new reference to a glue spec}
+
+@ The copying procedure copies words en masse without bothering
+to look at their individual fields. If the node format changes---for
+example, if the size is altered, or if some link field is moved to another
+relative position---then this code may need to be changed too.
+@^data structure assumptions@>
+
+@p function copy_node_list(@!p:pointer):pointer; {makes a duplicate of the
+ node list that starts at |p| and returns a pointer to the new list}
+var h:pointer; {temporary head of copied list}
+@!q:pointer; {previous position in new list}
+@!r:pointer; {current node being fabricated for new list}
+@!words:0..5; {number of words remaining to be copied}
+begin h:=get_avail; q:=h;
+while p<>null do
+ begin @<Make a copy of node |p| in node |r|@>;
+ link(q):=r; q:=r; p:=link(p);
+ end;
+link(q):=null; q:=link(h); free_avail(h);
+copy_node_list:=q;
+end;
+
+@ @<Make a copy of node |p|...@>=
+words:=1; {this setting occurs in more branches than any other}
+if is_char_node(p) then r:=get_avail
+else @<Case statement to copy different types and set |words| to the number
+ of initial words not yet copied@>;
+while words>0 do
+ begin decr(words); mem[r+words]:=mem[p+words];
+ end
+
+@ @<Case statement to copy...@>=
+case type(p) of
+hlist_node,vlist_node,unset_node: begin r:=get_node(box_node_size);
+ mem[r+6]:=mem[p+6]; mem[r+5]:=mem[p+5]; {copy the last two words}
+ list_ptr(r):=copy_node_list(list_ptr(p)); {this affects |mem[r+5]|}
+ words:=5;
+ end;
+rule_node: begin r:=get_node(rule_node_size); words:=rule_node_size;
+ end;
+ins_node: begin r:=get_node(ins_node_size); mem[r+4]:=mem[p+4];
+ add_glue_ref(split_top_ptr(p));
+ ins_ptr(r):=copy_node_list(ins_ptr(p)); {this affects |mem[r+4]|}
+ words:=ins_node_size-1;
+ end;
+whatsit_node:@<Make a partial copy of the whatsit node |p| and make |r|
+ point to it; set |words| to the number of initial words not yet copied@>;
+glue_node: begin r:=get_node(small_node_size); add_glue_ref(glue_ptr(p));
+ glue_ptr(r):=glue_ptr(p); leader_ptr(r):=copy_node_list(leader_ptr(p));
+ end;
+kern_node,math_node,penalty_node: begin r:=get_node(small_node_size);
+ words:=small_node_size;
+ end;
+ligature_node: begin r:=get_node(small_node_size);
+ mem[lig_char(r)]:=mem[lig_char(p)]; {copy |font| and |character|}
+ lig_ptr(r):=copy_node_list(lig_ptr(p));
+ end;
+disc_node: begin r:=get_node(small_node_size);
+ pre_break(r):=copy_node_list(pre_break(p));
+ post_break(r):=copy_node_list(post_break(p));
+ end;
+mark_node: begin r:=get_node(small_node_size); add_token_ref(mark_ptr(p));
+ words:=small_node_size;
+ end;
+adjust_node: begin r:=get_node(small_node_size);
+ adjust_ptr(r):=copy_node_list(adjust_ptr(p));
+ end; {|words=1=small_node_size-1|}
+othercases confusion("copying")
+@:this can't happen copying}{\quad copying@>
+endcases
+
+@* \[15] The command codes.
+Before we can go any further, we need to define symbolic names for the internal
+code numbers that represent the various commands obeyed by \TeX. These codes
+are somewhat arbitrary, but not completely so. For example, the command
+codes for character types are fixed by the language, since a user says,
+e.g., `\.{\\catcode \`\\\${} = 3}' to make \.{\char'44} a math delimiter,
+and the command code |math_shift| is equal to~3. Some other codes have
+been made adjacent so that |case| statements in the program need not consider
+cases that are widely spaced, or so that |case| statements can be replaced
+by |if| statements.
+
+At any rate, here is the list, for future reference. First come the
+``catcode'' commands, several of which share their numeric codes with
+ordinary commands when the catcode cannot emerge from \TeX's scanning routine.
+
+@d escape=0 {escape delimiter (called \.\\ in {\sl The \TeX book\/})}
+@:TeXbook}{\sl The \TeX book@>
+@d relax=0 {do nothing ( \.{\\relax} )}
+@d left_brace=1 {beginning of a group ( \.\{ )}
+@d right_brace=2 {ending of a group ( \.\} )}
+@d math_shift=3 {mathematics shift character ( \.\$ )}
+@d tab_mark=4 {alignment delimiter ( \.\&, \.{\\span} )}
+@d car_ret=5 {end of line ( |carriage_return|, \.{\\cr}, \.{\\crcr} )}
+@d out_param=5 {output a macro parameter}
+@d mac_param=6 {macro parameter symbol ( \.\# )}
+@d sup_mark=7 {superscript ( \.{\char'136} )}
+@d sub_mark=8 {subscript ( \.{\char'137} )}
+@d ignore=9 {characters to ignore ( \.{\^\^@@} )}
+@d endv=9 {end of \<v_j> list in alignment template}
+@d spacer=10 {characters equivalent to blank space ( \.{\ } )}
+@d letter=11 {characters regarded as letters ( \.{A..Z}, \.{a..z} )}
+@d other_char=12 {none of the special character types}
+@d active_char=13 {characters that invoke macros ( \.{\char`\~} )}
+@d par_end=13 {end of paragraph ( \.{\\par} )}
+@d match=13 {match a macro parameter}
+@d comment=14 {characters that introduce comments ( \.\% )}
+@d end_match=14 {end of parameters to macro}
+@d stop=14 {end of job ( \.{\\end}, \.{\\dump} )}
+@d invalid_char=15 {characters that shouldn't appear ( \.{\^\^?} )}
+@d delim_num=15 {specify delimiter numerically ( \.{\\delimiter} )}
+@d max_char_code=15 {largest catcode for individual characters}
+
+@ Next are the ordinary run-of-the-mill command codes. Codes that are
+|min_internal| or more represent internal quantities that might be
+expanded by `\.{\\the}'.
+
+@d char_num=16 {character specified numerically ( \.{\\char} )}
+@d math_char_num=17 {explicit math code ( \.{\\mathchar} )}
+@d mark=18 {mark definition ( \.{\\mark} )}
+@d xray=19 {peek inside of \TeX\ ( \.{\\show}, \.{\\showbox}, etc.~)}
+@d make_box=20 {make a box ( \.{\\box}, \.{\\copy}, \.{\\hbox}, etc.~)}
+@d hmove=21 {horizontal motion ( \.{\\moveleft}, \.{\\moveright} )}
+@d vmove=22 {vertical motion ( \.{\\raise}, \.{\\lower} )}
+@d un_hbox=23 {unglue a box ( \.{\\unhbox}, \.{\\unhcopy} )}
+@d un_vbox=24 {unglue a box ( \.{\\unvbox}, \.{\\unvcopy} )}
+@d remove_item=25 {nullify last item ( \.{\\unpenalty},
+ \.{\\unkern}, \.{\\unskip} )}
+@d hskip=26 {horizontal glue ( \.{\\hskip}, \.{\\hfil}, etc.~)}
+@d vskip=27 {vertical glue ( \.{\\vskip}, \.{\\vfil}, etc.~)}
+@d mskip=28 {math glue ( \.{\\mskip} )}
+@d kern=29 {fixed space ( \.{\\kern})}
+@d mkern=30 {math kern ( \.{\\mkern} )}
+@d leader_ship=31 {use a box ( \.{\\shipout}, \.{\\leaders}, etc.~)}
+@d halign=32 {horizontal table alignment ( \.{\\halign} )}
+@d valign=33 {vertical table alignment ( \.{\\valign} )}
+@d no_align=34 {temporary escape from alignment ( \.{\\noalign} )}
+@d vrule=35 {vertical rule ( \.{\\vrule} )}
+@d hrule=36 {horizontal rule ( \.{\\hrule} )}
+@d insert=37 {vlist inserted in box ( \.{\\insert} )}
+@d vadjust=38 {vlist inserted in enclosing paragraph ( \.{\\vadjust} )}
+@d ignore_spaces=39 {gobble |spacer| tokens ( \.{\\ignorespaces} )}
+@d after_assignment=40 {save till assignment is done ( \.{\\afterassignment} )}
+@d after_group=41 {save till group is done ( \.{\\aftergroup} )}
+@d break_penalty=42 {additional badness ( \.{\\penalty} )}
+@d start_par=43 {begin paragraph ( \.{\\indent}, \.{\\noindent} )}
+@d ital_corr=44 {italic correction ( \.{\\/} )}
+@d accent=45 {attach accent in text ( \.{\\accent} )}
+@d math_accent=46 {attach accent in math ( \.{\\mathaccent} )}
+@d discretionary=47 {discretionary texts ( \.{\\-}, \.{\\discretionary} )}
+@d eq_no=48 {equation number ( \.{\\eqno}, \.{\\leqno} )}
+@d left_right=49 {variable delimiter ( \.{\\left}, \.{\\right} )}
+@d math_comp=50 {component of formula ( \.{\\mathbin}, etc.~)}
+@d limit_switch=51 {diddle limit conventions ( \.{\\displaylimits}, etc.~)}
+@d above=52 {generalized fraction ( \.{\\above}, \.{\\atop}, etc.~)}
+@d math_style=53 {style specification ( \.{\\displaystyle}, etc.~)}
+@d math_choice=54 {choice specification ( \.{\\mathchoice} )}
+@d non_script=55 {conditional math glue ( \.{\\nonscript} )}
+@d vcenter=56 {vertically center a vbox ( \.{\\vcenter} )}
+@d case_shift=57 {force specific case ( \.{\\lowercase}, \.{\\uppercase}~)}
+@d message=58 {send to user ( \.{\\message}, \.{\\errmessage} )}
+@d extension=59 {extensions to \TeX\ ( \.{\\write}, \.{\\special}, etc.~)}
+@d in_stream=60 {files for reading ( \.{\\openin}, \.{\\closein} )}
+@d begin_group=61 {begin local grouping ( \.{\\begingroup} )}
+@d end_group=62 {end local grouping ( \.{\\endgroup} )}
+@d omit=63 {omit alignment template ( \.{\\omit} )}
+@d ex_space=64 {explicit space ( \.{\\\ } )}
+@d no_boundary=65 {suppress boundary ligatures ( \.{\\noboundary} )}
+@d radical=66 {square root and similar signs ( \.{\\radical} )}
+@d end_cs_name=67 {end control sequence ( \.{\\endcsname} )}
+@d min_internal=68 {the smallest code that can follow \.{\\the}}
+@d char_given=68 {character code defined by \.{\\chardef}}
+@d math_given=69 {math code defined by \.{\\mathchardef}}
+@d last_item=70 {most recent item ( \.{\\lastpenalty},
+ \.{\\lastkern}, \.{\\lastskip} )}
+@d max_non_prefixed_command=70 {largest command code that can't be \.{\\global}}
+
+@ The next codes are special; they all relate to mode-independent
+assignment of values to \TeX's internal registers or tables.
+Codes that are |max_internal| or less represent internal quantities
+that might be expanded by `\.{\\the}'.
+
+@d toks_register=71 {token list register ( \.{\\toks} )}
+@d assign_toks=72 {special token list ( \.{\\output}, \.{\\everypar}, etc.~)}
+@d assign_int=73 {user-defined integer ( \.{\\tolerance}, \.{\\day}, etc.~)}
+@d assign_dimen=74 {user-defined length ( \.{\\hsize}, etc.~)}
+@d assign_glue=75 {user-defined glue ( \.{\\baselineskip}, etc.~)}
+@d assign_mu_glue=76 {user-defined muglue ( \.{\\thinmuskip}, etc.~)}
+@d assign_font_dimen=77 {user-defined font dimension ( \.{\\fontdimen} )}
+@d assign_font_int=78 {user-defined font integer ( \.{\\hyphenchar},
+ \.{\\skewchar} )}
+@d set_aux=79 {specify state info ( \.{\\spacefactor}, \.{\\prevdepth} )}
+@d set_prev_graf=80 {specify state info ( \.{\\prevgraf} )}
+@d set_page_dimen=81 {specify state info ( \.{\\pagegoal}, etc.~)}
+@d set_page_int=82 {specify state info ( \.{\\deadcycles},
+ \.{\\insertpenalties} )}
+@d set_box_dimen=83 {change dimension of box ( \.{\\wd}, \.{\\ht}, \.{\\dp} )}
+@d set_shape=84 {specify fancy paragraph shape ( \.{\\parshape} )}
+@d def_code=85 {define a character code ( \.{\\catcode}, etc.~)}
+@d def_family=86 {declare math fonts ( \.{\\textfont}, etc.~)}
+@d set_font=87 {set current font ( font identifiers )}
+@d def_font=88 {define a font file ( \.{\\font} )}
+@d register=89 {internal register ( \.{\\count}, \.{\\dimen}, etc.~)}
+@d max_internal=89 {the largest code that can follow \.{\\the}}
+@d advance=90 {advance a register or parameter ( \.{\\advance} )}
+@d multiply=91 {multiply a register or parameter ( \.{\\multiply} )}
+@d divide=92 {divide a register or parameter ( \.{\\divide} )}
+@d prefix=93 {qualify a definition ( \.{\\global}, \.{\\long}, \.{\\outer} )}
+@d let=94 {assign a command code ( \.{\\let}, \.{\\futurelet} )}
+@d shorthand_def=95 {code definition ( \.{\\chardef}, \.{\\countdef}, etc.~)}
+@d read_to_cs=96 {read into a control sequence ( \.{\\read} )}
+@d def=97 {macro definition ( \.{\\def}, \.{\\gdef}, \.{\\xdef}, \.{\\edef} )}
+@d set_box=98 {set a box ( \.{\\setbox} )}
+@d hyph_data=99 {hyphenation data ( \.{\\hyphenation}, \.{\\patterns} )}
+@d set_interaction=100 {define level of interaction ( \.{\\batchmode}, etc.~)}
+@d max_command=100 {the largest command code seen at |big_switch|}
+
+@ The remaining command codes are extra special, since they cannot get through
+\TeX's scanner to the main control routine. They have been given values higher
+than |max_command| so that their special nature is easily discernible.
+The ``expandable'' commands come first.
+
+@d undefined_cs=max_command+1 {initial state of most |eq_type| fields}
+@d expand_after=max_command+2 {special expansion ( \.{\\expandafter} )}
+@d no_expand=max_command+3 {special nonexpansion ( \.{\\noexpand} )}
+@d input=max_command+4 {input a source file ( \.{\\input}, \.{\\endinput} )}
+@d if_test=max_command+5 {conditional text ( \.{\\if}, \.{\\ifcase}, etc.~)}
+@d fi_or_else=max_command+6 {delimiters for conditionals ( \.{\\else}, etc.~)}
+@d cs_name=max_command+7 {make a control sequence from tokens ( \.{\\csname} )}
+@d convert=max_command+8 {convert to text ( \.{\\number}, \.{\\string}, etc.~)}
+@d the=max_command+9 {expand an internal quantity ( \.{\\the} )}
+@d top_bot_mark=max_command+10 {inserted mark ( \.{\\topmark}, etc.~)}
+@d call=max_command+11 {non-long, non-outer control sequence}
+@d long_call=max_command+12 {long, non-outer control sequence}
+@d outer_call=max_command+13 {non-long, outer control sequence}
+@d long_outer_call=max_command+14 {long, outer control sequence}
+@d end_template=max_command+15 {end of an alignment template}
+@d dont_expand=max_command+16 {the following token was marked by \.{\\noexpand}}
+@d glue_ref=max_command+17 {the equivalent points to a glue specification}
+@d shape_ref=max_command+18 {the equivalent points to a parshape specification}
+@d box_ref=max_command+19 {the equivalent points to a box node, or is |null|}
+@d data=max_command+20 {the equivalent is simply a halfword number}
+
+@* \[16] The semantic nest.
+\TeX\ is typically in the midst of building many lists at once. For example,
+when a math formula is being processed, \TeX\ is in math mode and
+working on an mlist; this formula has temporarily interrupted \TeX\ from
+being in horizontal mode and building the hlist of a paragraph; and this
+paragraph has temporarily interrupted \TeX\ from being in vertical mode
+and building the vlist for the next page of a document. Similarly, when a
+\.{\\vbox} occurs inside of an \.{\\hbox}, \TeX\ is temporarily
+interrupted from working in restricted horizontal mode, and it enters
+internal vertical mode. The ``semantic nest'' is a stack that
+keeps track of what lists and modes are currently suspended.
+
+At each level of processing we are in one of six modes:
+
+\yskip\hang|vmode| stands for vertical mode (the page builder);
+
+\hang|hmode| stands for horizontal mode (the paragraph builder);
+
+\hang|mmode| stands for displayed formula mode;
+
+\hang|-vmode| stands for internal vertical mode (e.g., in a \.{\\vbox});
+
+\hang|-hmode| stands for restricted horizontal mode (e.g., in an \.{\\hbox});
+
+\hang|-mmode| stands for math formula mode (not displayed).
+
+\yskip\noindent The mode is temporarily set to zero while processing \.{\\write}
+texts in the |ship_out| routine.
+
+Numeric values are assigned to |vmode|, |hmode|, and |mmode| so that
+\TeX's ``big semantic switch'' can select the appropriate thing to
+do by computing the value |abs(mode)+cur_cmd|, where |mode| is the current
+mode and |cur_cmd| is the current command code.
+
+@d vmode=1 {vertical mode}
+@d hmode=vmode+max_command+1 {horizontal mode}
+@d mmode=hmode+max_command+1 {math mode}
+
+@p procedure print_mode(@!m:integer); {prints the mode represented by |m|}
+begin if m>0 then
+ case m div (max_command+1) of
+ 0:print("vertical");
+ 1:print("horizontal");
+ 2:print("display math");
+ end
+else if m=0 then print("no")
+else case (-m) div (max_command+1) of
+ 0:print("internal vertical");
+ 1:print("restricted horizontal");
+ 2:print("math");
+ end;
+print(" mode");
+end;
+
+@ The state of affairs at any semantic level can be represented by
+five values:
+
+\yskip\hang|mode| is the number representing the semantic mode, as
+just explained.
+
+\yskip\hang|head| is a |pointer| to a list head for the list being built;
+|link(head)| therefore points to the first element of the list, or
+to |null| if the list is empty.
+
+\yskip\hang|tail| is a |pointer| to the final node of the list being
+built; thus, |tail=head| if and only if the list is empty.
+
+\yskip\hang|prev_graf| is the number of lines of the current paragraph that
+have already been put into the present vertical list.
+
+\yskip\hang|aux| is an auxiliary |memory_word| that gives further information
+that is needed to characterize the situation.
+
+\yskip\noindent
+In vertical mode, |aux| is also known as |prev_depth|; it is the scaled
+value representing the depth of the previous box, for use in baseline
+calculations, or it is |<=-1000|pt if the next box on the vertical list is to
+be exempt from baseline calculations. In horizontal mode, |aux| is also
+known as |space_factor| and |clang|; it holds the current space factor used in
+spacing calculations, and the current language used for hyphenation.
+(The value of |clang| is undefined in restricted horizontal mode.)
+In math mode, |aux| is also known as |incompleat_noad|; if
+not |null|, it points to a record that represents the numerator of a
+generalized fraction for which the denominator is currently being formed
+in the current list.
+
+There is also a sixth quantity, |mode_line|, which correlates
+the semantic nest with the user's input; |mode_line| contains the source
+line number at which the current level of nesting was entered. The negative
+of this line number is the |mode_line| at the level of the
+user's output routine.
+
+In horizontal mode, the |prev_graf| field is used for initial language data.
+
+The semantic nest is an array called |nest| that holds the |mode|, |head|,
+|tail|, |prev_graf|, |aux|, and |mode_line| values for all semantic levels
+below the currently active one. Information about the currently active
+level is kept in the global quantities |mode|, |head|, |tail|, |prev_graf|,
+|aux|, and |mode_line|, which live in a \PASCAL\ record that is ready to
+be pushed onto |nest| if necessary.
+
+@d ignore_depth==-65536000 {|prev_depth| value that is ignored}
+
+@<Types...@>=
+@!list_state_record=record@!mode_field:-mmode..mmode;@+
+ @!head_field,@!tail_field: pointer;
+ @!pg_field,@!ml_field: integer;@+
+ @!aux_field: memory_word;
+ end;
+
+@ @d mode==cur_list.mode_field {current mode}
+@d head==cur_list.head_field {header node of current list}
+@d tail==cur_list.tail_field {final node on current list}
+@d prev_graf==cur_list.pg_field {number of paragraph lines accumulated}
+@d aux==cur_list.aux_field {auxiliary data about the current list}
+@d prev_depth==aux.sc {the name of |aux| in vertical mode}
+@d space_factor==aux.hh.lh {part of |aux| in horizontal mode}
+@d clang==aux.hh.rh {the other part of |aux| in horizontal mode}
+@d incompleat_noad==aux.int {the name of |aux| in math mode}
+@d mode_line==cur_list.ml_field {source file line number at beginning of list}
+
+@<Glob...@>=
+@!nest:array[0..nest_size] of list_state_record;
+@!nest_ptr:0..nest_size; {first unused location of |nest|}
+@!max_nest_stack:0..nest_size; {maximum of |nest_ptr| when pushing}
+@!cur_list:list_state_record; {the ``top'' semantic state}
+@!shown_mode:-mmode..mmode; {most recent mode shown by \.{\\tracingcommands}}
+
+@ Here is a common way to make the current list grow:
+
+@d tail_append(#)==begin link(tail):=#; tail:=link(tail);
+ end
+
+@ We will see later that the vertical list at the bottom semantic level is split
+into two parts; the ``current page'' runs from |page_head| to |page_tail|,
+and the ``contribution list'' runs from |contrib_head| to |tail| of
+semantic level zero. The idea is that contributions are first formed in
+vertical mode, then ``contributed'' to the current page (during which time
+the page-breaking decisions are made). For now, we don't need to know
+any more details about the page-building process.
+
+@<Set init...@>=
+nest_ptr:=0; max_nest_stack:=0;
+mode:=vmode; head:=contrib_head; tail:=contrib_head;
+prev_depth:=ignore_depth; mode_line:=0;
+prev_graf:=0; shown_mode:=0;
+@<Start a new current page@>;
+
+@ When \TeX's work on one level is interrupted, the state is saved by
+calling |push_nest|. This routine changes |head| and |tail| so that
+a new (empty) list is begun; it does not change |mode| or |aux|.
+
+@p procedure push_nest; {enter a new semantic level, save the old}
+begin if nest_ptr>max_nest_stack then
+ begin max_nest_stack:=nest_ptr;
+ if nest_ptr=nest_size then overflow("semantic nest size",nest_size);
+@:TeX capacity exceeded semantic nest size}{\quad semantic nest size@>
+ end;
+nest[nest_ptr]:=cur_list; {stack the record}
+incr(nest_ptr); head:=get_avail; tail:=head; prev_graf:=0; mode_line:=line;
+end;
+
+@ Conversely, when \TeX\ is finished on the current level, the former
+state is restored by calling |pop_nest|. This routine will never be
+called at the lowest semantic level, nor will it be called unless |head|
+is a node that should be returned to free memory.
+
+@p procedure pop_nest; {leave a semantic level, re-enter the old}
+begin free_avail(head); decr(nest_ptr); cur_list:=nest[nest_ptr];
+end;
+
+@ Here is a procedure that displays what \TeX\ is working on, at all levels.
+
+@p procedure@?print_totals; forward;@t\2@>
+procedure show_activities;
+var p:0..nest_size; {index into |nest|}
+@!m:-mmode..mmode; {mode}
+@!a:memory_word; {auxiliary}
+@!q,@!r:pointer; {for showing the current page}
+@!t:integer; {ditto}
+begin nest[nest_ptr]:=cur_list; {put the top level into the array}
+print_nl(""); print_ln;
+for p:=nest_ptr downto 0 do
+ begin m:=nest[p].mode_field; a:=nest[p].aux_field;
+ print_nl("### "); print_mode(m);
+ print(" entered at line "); print_int(abs(nest[p].ml_field));
+ if m=hmode then if nest[p].pg_field <> @'40600000 then
+ begin print(" (language"); print_int(nest[p].pg_field mod @'200000);
+ print(":hyphenmin"); print_int(nest[p].pg_field div @'20000000);
+ print_char(","); print_int((nest[p].pg_field div @'200000) mod @'100);
+ print_char(")");
+ end;
+ if nest[p].ml_field<0 then print(" (\output routine)");
+ if p=0 then
+ begin @<Show the status of the current page@>;
+ if link(contrib_head)<>null then
+ print_nl("### recent contributions:");
+ end;
+ show_box(link(nest[p].head_field));
+ @<Show the auxiliary field, |a|@>;
+ end;
+end;
+
+@ @<Show the auxiliary...@>=
+case abs(m) div (max_command+1) of
+0: begin print_nl("prevdepth ");
+ if a.sc<=ignore_depth then print("ignored")
+ else print_scaled(a.sc);
+ if nest[p].pg_field<>0 then
+ begin print(", prevgraf ");
+ print_int(nest[p].pg_field); print(" line");
+ if nest[p].pg_field<>1 then print_char("s");
+ end;
+ end;
+1: begin print_nl("spacefactor "); print_int(a.hh.lh);
+ if m>0 then@+ if a.hh.rh>0 then
+ begin print(", current language "); print_int(a.hh.rh);@+
+ end;
+ end;
+2: if a.int<>null then
+ begin print("this will be denominator of:"); show_box(a.int);@+
+ end;
+end {there are no other cases}
+
+@* \[17] The table of equivalents.
+Now that we have studied the data structures for \TeX's semantic routines,
+we ought to consider the data structures used by its syntactic routines. In
+other words, our next concern will be
+the tables that \TeX\ looks at when it is scanning
+what the user has written.
+
+The biggest and most important such table is called |eqtb|. It holds the
+current ``equivalents'' of things; i.e., it explains what things mean
+or what their current values are, for all quantities that are subject to
+the nesting structure provided by \TeX's grouping mechanism. There are six
+parts to |eqtb|:
+
+\yskip\hangg 1) |eqtb[active_base..(hash_base-1)]| holds the current
+equivalents of single-character control sequences.
+
+\yskip\hangg 2) |eqtb[hash_base..(glue_base-1)]| holds the current
+equivalents of multiletter control sequences.
+
+\yskip\hangg 3) |eqtb[glue_base..(local_base-1)]| holds the current
+equivalents of glue parameters like the current baselineskip.
+
+\yskip\hangg 4) |eqtb[local_base..(int_base-1)]| holds the current
+equivalents of local halfword quantities like the current box registers,
+the current ``catcodes,'' the current font, and a pointer to the current
+paragraph shape.
+
+\yskip\hangg 5) |eqtb[int_base..(dimen_base-1)]| holds the current
+equivalents of fullword integer parameters like the current hyphenation
+penalty.
+
+\yskip\hangg 6) |eqtb[dimen_base..eqtb_size]| holds the current equivalents
+of fullword dimension parameters like the current hsize or amount of
+hanging indentation.
+
+\yskip\noindent Note that, for example, the current amount of
+baselineskip glue is determined by the setting of a particular location
+in region~3 of |eqtb|, while the current meaning of the control sequence
+`\.{\\baselineskip}' (which might have been changed by \.{\\def} or
+\.{\\let}) appears in region~2.
+
+@ Each entry in |eqtb| is a |memory_word|. Most of these words are of type
+|two_halves|, and subdivided into three fields:
+
+\yskip\hangg 1) The |eq_level| (a quarterword) is the level of grouping at
+which this equivalent was defined. If the level is |level_zero|, the
+equivalent has never been defined; |level_one| refers to the outer level
+(outside of all groups), and this level is also used for global
+definitions that never go away. Higher levels are for equivalents that
+will disappear at the end of their group. @^global definitions@>
+
+\yskip\hangg 2) The |eq_type| (another quarterword) specifies what kind of
+entry this is. There are many types, since each \TeX\ primitive like
+\.{\\hbox}, \.{\\def}, etc., has its own special code. The list of
+command codes above includes all possible settings of the |eq_type| field.
+
+\yskip\hangg 3) The |equiv| (a halfword) is the current equivalent value.
+This may be a font number, a pointer into |mem|, or a variety of other
+things.
+
+@d eq_level_field(#)==#.hh.b1
+@d eq_type_field(#)==#.hh.b0
+@d equiv_field(#)==#.hh.rh
+@d eq_level(#)==eq_level_field(eqtb[#]) {level of definition}
+@d eq_type(#)==eq_type_field(eqtb[#]) {command code for equivalent}
+@d equiv(#)==equiv_field(eqtb[#]) {equivalent value}
+@d level_zero=min_quarterword {level for undefined quantities}
+@d level_one=level_zero+1 {outermost level for defined quantities}
+
+@ Many locations in |eqtb| have symbolic names. The purpose of the next
+paragraphs is to define these names, and to set up the initial values of the
+equivalents.
+
+In the first region we have 256 equivalents for ``active characters'' that
+act as control sequences, followed by 256 equivalents for single-character
+control sequences.
+
+Then comes region~2, which corresponds to the hash table that we will
+define later. The maximum address in this region is used for a dummy
+control sequence that is perpetually undefined. There also are several
+locations for control sequences that are perpetually defined
+(since they are used in error recovery).
+
+@d active_base=1 {beginning of region 1, for active character equivalents}
+@d single_base=active_base+256 {equivalents of one-character control sequences}
+@d null_cs=single_base+256 {equivalent of \.{\\csname\\endcsname}}
+@d hash_base=null_cs+1 {beginning of region 2, for the hash table}
+@d frozen_control_sequence=hash_base+hash_size {for error recovery}
+@d frozen_protection=frozen_control_sequence {inaccessible but definable}
+@d frozen_cr=frozen_control_sequence+1 {permanent `\.{\\cr}'}
+@d frozen_end_group=frozen_control_sequence+2 {permanent `\.{\\endgroup}'}
+@d frozen_right=frozen_control_sequence+3 {permanent `\.{\\right}'}
+@d frozen_fi=frozen_control_sequence+4 {permanent `\.{\\fi}'}
+@d frozen_end_template=frozen_control_sequence+5 {permanent `\.{\\endtemplate}'}
+@d frozen_endv=frozen_control_sequence+6 {second permanent `\.{\\endtemplate}'}
+@d frozen_relax=frozen_control_sequence+7 {permanent `\.{\\relax}'}
+@d end_write=frozen_control_sequence+8 {permanent `\.{\\endwrite}'}
+@d frozen_dont_expand=frozen_control_sequence+9
+ {permanent `\.{\\notexpanded:}'}
+@d frozen_null_font=frozen_control_sequence+10
+ {permanent `\.{\\nullfont}'}
+@d font_id_base=frozen_null_font-font_base
+ {begins table of 257 permanent font identifiers}
+@d undefined_control_sequence=frozen_null_font+257 {dummy location}
+@d glue_base=undefined_control_sequence+1 {beginning of region 3}
+
+@<Initialize table entries...@>=
+eq_type(undefined_control_sequence):=undefined_cs;
+equiv(undefined_control_sequence):=null;
+eq_level(undefined_control_sequence):=level_zero;
+for k:=active_base to undefined_control_sequence-1 do
+ eqtb[k]:=eqtb[undefined_control_sequence];
+
+@ Here is a routine that displays the current meaning of an |eqtb| entry
+in region 1 or~2. (Similar routines for the other regions will appear
+below.)
+
+@<Show equivalent |n|, in region 1 or 2@>=
+begin sprint_cs(n); print_char("="); print_cmd_chr(eq_type(n),equiv(n));
+if eq_type(n)>=call then
+ begin print_char(":"); show_token_list(link(equiv(n)),null,32);
+ end;
+end
+
+@ Region 3 of |eqtb| contains the 256 \.{\\skip} registers, as well as the
+glue parameters defined here. It is important that the ``muskip''
+parameters have larger numbers than the others.
+
+@d line_skip_code=0 {interline glue if |baseline_skip| is infeasible}
+@d baseline_skip_code=1 {desired glue between baselines}
+@d par_skip_code=2 {extra glue just above a paragraph}
+@d above_display_skip_code=3 {extra glue just above displayed math}
+@d below_display_skip_code=4 {extra glue just below displayed math}
+@d above_display_short_skip_code=5
+ {glue above displayed math following short lines}
+@d below_display_short_skip_code=6
+ {glue below displayed math following short lines}
+@d left_skip_code=7 {glue at left of justified lines}
+@d right_skip_code=8 {glue at right of justified lines}
+@d top_skip_code=9 {glue at top of main pages}
+@d split_top_skip_code=10 {glue at top of split pages}
+@d tab_skip_code=11 {glue between aligned entries}
+@d space_skip_code=12 {glue between words (if not |zero_glue|)}
+@d xspace_skip_code=13 {glue after sentences (if not |zero_glue|)}
+@d par_fill_skip_code=14 {glue on last line of paragraph}
+@d thin_mu_skip_code=15 {thin space in math formula}
+@d med_mu_skip_code=16 {medium space in math formula}
+@d thick_mu_skip_code=17 {thick space in math formula}
+@d glue_pars=18 {total number of glue parameters}
+@d skip_base=glue_base+glue_pars {table of 256 ``skip'' registers}
+@d mu_skip_base=skip_base+256 {table of 256 ``muskip'' registers}
+@d local_base=mu_skip_base+256 {beginning of region 4}
+@#
+@d skip(#)==equiv(skip_base+#) {|mem| location of glue specification}
+@d mu_skip(#)==equiv(mu_skip_base+#) {|mem| location of math glue spec}
+@d glue_par(#)==equiv(glue_base+#) {|mem| location of glue specification}
+@d line_skip==glue_par(line_skip_code)
+@d baseline_skip==glue_par(baseline_skip_code)
+@d par_skip==glue_par(par_skip_code)
+@d above_display_skip==glue_par(above_display_skip_code)
+@d below_display_skip==glue_par(below_display_skip_code)
+@d above_display_short_skip==glue_par(above_display_short_skip_code)
+@d below_display_short_skip==glue_par(below_display_short_skip_code)
+@d left_skip==glue_par(left_skip_code)
+@d right_skip==glue_par(right_skip_code)
+@d top_skip==glue_par(top_skip_code)
+@d split_top_skip==glue_par(split_top_skip_code)
+@d tab_skip==glue_par(tab_skip_code)
+@d space_skip==glue_par(space_skip_code)
+@d xspace_skip==glue_par(xspace_skip_code)
+@d par_fill_skip==glue_par(par_fill_skip_code)
+@d thin_mu_skip==glue_par(thin_mu_skip_code)
+@d med_mu_skip==glue_par(med_mu_skip_code)
+@d thick_mu_skip==glue_par(thick_mu_skip_code)
+
+@<Current |mem| equivalent of glue parameter number |n|@>=glue_par(n)
+
+@ Sometimes we need to convert \TeX's internal code numbers into symbolic
+form. The |print_skip_param| routine gives the symbolic name of a glue
+parameter.
+
+@<Declare the procedure called |print_skip_param|@>=
+procedure print_skip_param(@!n:integer);
+begin case n of
+line_skip_code: print_esc("lineskip");
+baseline_skip_code: print_esc("baselineskip");
+par_skip_code: print_esc("parskip");
+above_display_skip_code: print_esc("abovedisplayskip");
+below_display_skip_code: print_esc("belowdisplayskip");
+above_display_short_skip_code: print_esc("abovedisplayshortskip");
+below_display_short_skip_code: print_esc("belowdisplayshortskip");
+left_skip_code: print_esc("leftskip");
+right_skip_code: print_esc("rightskip");
+top_skip_code: print_esc("topskip");
+split_top_skip_code: print_esc("splittopskip");
+tab_skip_code: print_esc("tabskip");
+space_skip_code: print_esc("spaceskip");
+xspace_skip_code: print_esc("xspaceskip");
+par_fill_skip_code: print_esc("parfillskip");
+thin_mu_skip_code: print_esc("thinmuskip");
+med_mu_skip_code: print_esc("medmuskip");
+thick_mu_skip_code: print_esc("thickmuskip");
+othercases print("[unknown glue parameter!]")
+endcases;
+end;
+
+@ The symbolic names for glue parameters are put into \TeX's hash table
+by using the routine called |primitive|, defined below. Let us enter them
+now, so that we don't have to list all those parameter names anywhere else.
+
+@<Put each of \TeX's primitives into the hash table@>=
+primitive("lineskip",assign_glue,glue_base+line_skip_code);@/
+@!@:line_skip_}{\.{\\lineskip} primitive@>
+primitive("baselineskip",assign_glue,glue_base+baseline_skip_code);@/
+@!@:baseline_skip_}{\.{\\baselineskip} primitive@>
+primitive("parskip",assign_glue,glue_base+par_skip_code);@/
+@!@:par_skip_}{\.{\\parskip} primitive@>
+primitive("abovedisplayskip",assign_glue,glue_base+above_display_skip_code);@/
+@!@:above_display_skip_}{\.{\\abovedisplayskip} primitive@>
+primitive("belowdisplayskip",assign_glue,glue_base+below_display_skip_code);@/
+@!@:below_display_skip_}{\.{\\belowdisplayskip} primitive@>
+primitive("abovedisplayshortskip",
+ assign_glue,glue_base+above_display_short_skip_code);@/
+@!@:above_display_short_skip_}{\.{\\abovedisplayshortskip} primitive@>
+primitive("belowdisplayshortskip",
+ assign_glue,glue_base+below_display_short_skip_code);@/
+@!@:below_display_short_skip_}{\.{\\belowdisplayshortskip} primitive@>
+primitive("leftskip",assign_glue,glue_base+left_skip_code);@/
+@!@:left_skip_}{\.{\\leftskip} primitive@>
+primitive("rightskip",assign_glue,glue_base+right_skip_code);@/
+@!@:right_skip_}{\.{\\rightskip} primitive@>
+primitive("topskip",assign_glue,glue_base+top_skip_code);@/
+@!@:top_skip_}{\.{\\topskip} primitive@>
+primitive("splittopskip",assign_glue,glue_base+split_top_skip_code);@/
+@!@:split_top_skip_}{\.{\\splittopskip} primitive@>
+primitive("tabskip",assign_glue,glue_base+tab_skip_code);@/
+@!@:tab_skip_}{\.{\\tabskip} primitive@>
+primitive("spaceskip",assign_glue,glue_base+space_skip_code);@/
+@!@:space_skip_}{\.{\\spaceskip} primitive@>
+primitive("xspaceskip",assign_glue,glue_base+xspace_skip_code);@/
+@!@:xspace_skip_}{\.{\\xspaceskip} primitive@>
+primitive("parfillskip",assign_glue,glue_base+par_fill_skip_code);@/
+@!@:par_fill_skip_}{\.{\\parfillskip} primitive@>
+primitive("thinmuskip",assign_mu_glue,glue_base+thin_mu_skip_code);@/
+@!@:thin_mu_skip_}{\.{\\thinmuskip} primitive@>
+primitive("medmuskip",assign_mu_glue,glue_base+med_mu_skip_code);@/
+@!@:med_mu_skip_}{\.{\\medmuskip} primitive@>
+primitive("thickmuskip",assign_mu_glue,glue_base+thick_mu_skip_code);@/
+@!@:thick_mu_skip_}{\.{\\thickmuskip} primitive@>
+
+@ @<Cases of |print_cmd_chr| for symbolic printing of primitives@>=
+assign_glue,assign_mu_glue: if chr_code<skip_base then
+ print_skip_param(chr_code-glue_base)
+ else if chr_code<mu_skip_base then
+ begin print_esc("skip"); print_int(chr_code-skip_base);
+ end
+ else begin print_esc("muskip"); print_int(chr_code-mu_skip_base);
+ end;
+
+@ All glue parameters and registers are initially `\.{0pt plus0pt minus0pt}'.
+
+@<Initialize table entries...@>=
+equiv(glue_base):=zero_glue; eq_level(glue_base):=level_one;
+eq_type(glue_base):=glue_ref;
+for k:=glue_base+1 to local_base-1 do eqtb[k]:=eqtb[glue_base];
+glue_ref_count(zero_glue):=glue_ref_count(zero_glue)+local_base-glue_base;
+
+@ @<Show equivalent |n|, in region 3@>=
+if n<skip_base then
+ begin print_skip_param(n-glue_base); print_char("=");
+ if n<glue_base+thin_mu_skip_code then print_spec(equiv(n),"pt")
+ else print_spec(equiv(n),"mu");
+ end
+else if n<mu_skip_base then
+ begin print_esc("skip"); print_int(n-skip_base); print_char("=");
+ print_spec(equiv(n),"pt");
+ end
+else begin print_esc("muskip"); print_int(n-mu_skip_base); print_char("=");
+ print_spec(equiv(n),"mu");
+ end
+
+@ Region 4 of |eqtb| contains the local quantities defined here. The
+bulk of this region is taken up by five tables that are indexed by eight-bit
+characters; these tables are important to both the syntactic and semantic
+portions of \TeX. There are also a bunch of special things like font and
+token parameters, as well as the tables of \.{\\toks} and \.{\\box}
+registers.
+
+@d par_shape_loc=local_base {specifies paragraph shape}
+@d output_routine_loc=local_base+1 {points to token list for \.{\\output}}
+@d every_par_loc=local_base+2 {points to token list for \.{\\everypar}}
+@d every_math_loc=local_base+3 {points to token list for \.{\\everymath}}
+@d every_display_loc=local_base+4 {points to token list for \.{\\everydisplay}}
+@d every_hbox_loc=local_base+5 {points to token list for \.{\\everyhbox}}
+@d every_vbox_loc=local_base+6 {points to token list for \.{\\everyvbox}}
+@d every_job_loc=local_base+7 {points to token list for \.{\\everyjob}}
+@d every_cr_loc=local_base+8 {points to token list for \.{\\everycr}}
+@d err_help_loc=local_base+9 {points to token list for \.{\\errhelp}}
+@d toks_base=local_base+10 {table of 256 token list registers}
+@d box_base=toks_base+256 {table of 256 box registers}
+@d cur_font_loc=box_base+256 {internal font number outside math mode}
+@d math_font_base=cur_font_loc+1 {table of 48 math font numbers}
+@d cat_code_base=math_font_base+48
+ {table of 256 command codes (the ``catcodes'')}
+@d lc_code_base=cat_code_base+256 {table of 256 lowercase mappings}
+@d uc_code_base=lc_code_base+256 {table of 256 uppercase mappings}
+@d sf_code_base=uc_code_base+256 {table of 256 spacefactor mappings}
+@d math_code_base=sf_code_base+256 {table of 256 math mode mappings}
+@d int_base=math_code_base+256 {beginning of region 5}
+@#
+@d par_shape_ptr==equiv(par_shape_loc)
+@d output_routine==equiv(output_routine_loc)
+@d every_par==equiv(every_par_loc)
+@d every_math==equiv(every_math_loc)
+@d every_display==equiv(every_display_loc)
+@d every_hbox==equiv(every_hbox_loc)
+@d every_vbox==equiv(every_vbox_loc)
+@d every_job==equiv(every_job_loc)
+@d every_cr==equiv(every_cr_loc)
+@d err_help==equiv(err_help_loc)
+@d toks(#)==equiv(toks_base+#)
+@d box(#)==equiv(box_base+#)
+@d cur_font==equiv(cur_font_loc)
+@d fam_fnt(#)==equiv(math_font_base+#)
+@d cat_code(#)==equiv(cat_code_base+#)
+@d lc_code(#)==equiv(lc_code_base+#)
+@d uc_code(#)==equiv(uc_code_base+#)
+@d sf_code(#)==equiv(sf_code_base+#)
+@d math_code(#)==equiv(math_code_base+#)
+ {Note: |math_code(c)| is the true math code plus |min_halfword|}
+
+@<Put each...@>=
+primitive("output",assign_toks,output_routine_loc);
+@!@:output_}{\.{\\output} primitive@>
+primitive("everypar",assign_toks,every_par_loc);
+@!@:every_par_}{\.{\\everypar} primitive@>
+primitive("everymath",assign_toks,every_math_loc);
+@!@:every_math_}{\.{\\everymath} primitive@>
+primitive("everydisplay",assign_toks,every_display_loc);
+@!@:every_display_}{\.{\\everydisplay} primitive@>
+primitive("everyhbox",assign_toks,every_hbox_loc);
+@!@:every_hbox_}{\.{\\everyhbox} primitive@>
+primitive("everyvbox",assign_toks,every_vbox_loc);
+@!@:every_vbox_}{\.{\\everyvbox} primitive@>
+primitive("everyjob",assign_toks,every_job_loc);
+@!@:every_job_}{\.{\\everyjob} primitive@>
+primitive("everycr",assign_toks,every_cr_loc);
+@!@:every_cr_}{\.{\\everycr} primitive@>
+primitive("errhelp",assign_toks,err_help_loc);
+@!@:err_help_}{\.{\\errhelp} primitive@>
+
+@ @<Cases of |print_cmd_chr|...@>=
+assign_toks: if chr_code>=toks_base then
+ begin print_esc("toks"); print_int(chr_code-toks_base);
+ end
+else case chr_code of
+ output_routine_loc: print_esc("output");
+ every_par_loc: print_esc("everypar");
+ every_math_loc: print_esc("everymath");
+ every_display_loc: print_esc("everydisplay");
+ every_hbox_loc: print_esc("everyhbox");
+ every_vbox_loc: print_esc("everyvbox");
+ every_job_loc: print_esc("everyjob");
+ every_cr_loc: print_esc("everycr");
+ othercases print_esc("errhelp")
+ endcases;
+
+@ We initialize most things to null or undefined values. An undefined font
+is represented by the internal code |font_base|.
+
+However, the character code tables are given initial values based on the
+conventional interpretation of ASCII code. These initial values should
+not be changed when \TeX\ is adapted for use with non-English languages;
+all changes to the initialization conventions should be made in format
+packages, not in \TeX\ itself, so that global interchange of formats is
+possible.
+
+@d null_font==font_base
+@d var_code==@'70000 {math code meaning ``use the current family''}
+
+@<Initialize table entries...@>=
+par_shape_ptr:=null; eq_type(par_shape_loc):=shape_ref;
+eq_level(par_shape_loc):=level_one;@/
+for k:=output_routine_loc to toks_base+255 do
+ eqtb[k]:=eqtb[undefined_control_sequence];
+box(0):=null; eq_type(box_base):=box_ref; eq_level(box_base):=level_one;
+for k:=box_base+1 to box_base+255 do eqtb[k]:=eqtb[box_base];
+cur_font:=null_font; eq_type(cur_font_loc):=data;
+eq_level(cur_font_loc):=level_one;@/
+for k:=math_font_base to math_font_base+47 do eqtb[k]:=eqtb[cur_font_loc];
+equiv(cat_code_base):=0; eq_type(cat_code_base):=data;
+eq_level(cat_code_base):=level_one;@/
+for k:=cat_code_base+1 to int_base-1 do eqtb[k]:=eqtb[cat_code_base];
+for k:=0 to 255 do
+ begin cat_code(k):=other_char; math_code(k):=hi(k); sf_code(k):=1000;
+ end;
+cat_code(carriage_return):=car_ret; cat_code(" "):=spacer;
+cat_code("\"):=escape; cat_code("%"):=comment;
+cat_code(invalid_code):=invalid_char; cat_code(null_code):=ignore;
+for k:="0" to "9" do math_code(k):=hi(k+var_code);
+for k:="A" to "Z" do
+ begin cat_code(k):=letter; cat_code(k+"a"-"A"):=letter;@/
+ math_code(k):=hi(k+var_code+@"100);
+ math_code(k+"a"-"A"):=hi(k+"a"-"A"+var_code+@"100);@/
+ lc_code(k):=k+"a"-"A"; lc_code(k+"a"-"A"):=k+"a"-"A";@/
+ uc_code(k):=k; uc_code(k+"a"-"A"):=k;@/
+ sf_code(k):=999;
+ end;
+
+@ @<Show equivalent |n|, in region 4@>=
+if n=par_shape_loc then
+ begin print_esc("parshape"); print_char("=");
+ if par_shape_ptr=null then print_char("0")
+ else print_int(info(par_shape_ptr));
+ end
+else if n<toks_base then
+ begin print_cmd_chr(assign_toks,n); print_char("=");
+ if equiv(n)<>null then show_token_list(link(equiv(n)),null,32);
+ end
+else if n<box_base then
+ begin print_esc("toks"); print_int(n-toks_base); print_char("=");
+ if equiv(n)<>null then show_token_list(link(equiv(n)),null,32);
+ end
+else if n<cur_font_loc then
+ begin print_esc("box"); print_int(n-box_base); print_char("=");
+ if equiv(n)=null then print("void")
+ else begin depth_threshold:=0; breadth_max:=1; show_node_list(equiv(n));
+ end;
+ end
+else if n<cat_code_base then @<Show the font identifier in |eqtb[n]|@>
+else @<Show the halfword code in |eqtb[n]|@>
+
+@ @<Show the font identifier in |eqtb[n]|@>=
+begin if n=cur_font_loc then print("current font")
+else if n<math_font_base+16 then
+ begin print_esc("textfont"); print_int(n-math_font_base);
+ end
+else if n<math_font_base+32 then
+ begin print_esc("scriptfont"); print_int(n-math_font_base-16);
+ end
+else begin print_esc("scriptscriptfont"); print_int(n-math_font_base-32);
+ end;
+print_char("=");@/
+print_esc(hash[font_id_base+equiv(n)].rh);
+ {that's |font_id_text(equiv(n))|}
+end
+
+@ @<Show the halfword code in |eqtb[n]|@>=
+if n<math_code_base then
+ begin if n<lc_code_base then
+ begin print_esc("catcode"); print_int(n-cat_code_base);
+ end
+ else if n<uc_code_base then
+ begin print_esc("lccode"); print_int(n-lc_code_base);
+ end
+ else if n<sf_code_base then
+ begin print_esc("uccode"); print_int(n-uc_code_base);
+ end
+ else begin print_esc("sfcode"); print_int(n-sf_code_base);
+ end;
+ print_char("="); print_int(equiv(n));
+ end
+else begin print_esc("mathcode"); print_int(n-math_code_base);
+ print_char("="); print_int(ho(equiv(n)));
+ end
+
+@ Region 5 of |eqtb| contains the integer parameters and registers defined
+here, as well as the |del_code| table. The latter table differs from the
+|cat_code..math_code| tables that precede it, since delimiter codes are
+fullword integers while the other kinds of codes occupy at most a
+halfword. This is what makes region~5 different from region~4. We will
+store the |eq_level| information in an auxiliary array of quarterwords
+that will be defined later.
+
+@d pretolerance_code=0 {badness tolerance before hyphenation}
+@d tolerance_code=1 {badness tolerance after hyphenation}
+@d line_penalty_code=2 {added to the badness of every line}
+@d hyphen_penalty_code=3 {penalty for break after discretionary hyphen}
+@d ex_hyphen_penalty_code=4 {penalty for break after explicit hyphen}
+@d club_penalty_code=5 {penalty for creating a club line}
+@d widow_penalty_code=6 {penalty for creating a widow line}
+@d display_widow_penalty_code=7 {ditto, just before a display}
+@d broken_penalty_code=8 {penalty for breaking a page at a broken line}
+@d bin_op_penalty_code=9 {penalty for breaking after a binary operation}
+@d rel_penalty_code=10 {penalty for breaking after a relation}
+@d pre_display_penalty_code=11
+ {penalty for breaking just before a displayed formula}
+@d post_display_penalty_code=12
+ {penalty for breaking just after a displayed formula}
+@d inter_line_penalty_code=13 {additional penalty between lines}
+@d double_hyphen_demerits_code=14 {demerits for double hyphen break}
+@d final_hyphen_demerits_code=15 {demerits for final hyphen break}
+@d adj_demerits_code=16 {demerits for adjacent incompatible lines}
+@d mag_code=17 {magnification ratio}
+@d delimiter_factor_code=18 {ratio for variable-size delimiters}
+@d looseness_code=19 {change in number of lines for a paragraph}
+@d time_code=20 {current time of day}
+@d day_code=21 {current day of the month}
+@d month_code=22 {current month of the year}
+@d year_code=23 {current year of our Lord}
+@d show_box_breadth_code=24 {nodes per level in |show_box|}
+@d show_box_depth_code=25 {maximum level in |show_box|}
+@d hbadness_code=26 {hboxes exceeding this badness will be shown by |hpack|}
+@d vbadness_code=27 {vboxes exceeding this badness will be shown by |vpack|}
+@d pausing_code=28 {pause after each line is read from a file}
+@d tracing_online_code=29 {show diagnostic output on terminal}
+@d tracing_macros_code=30 {show macros as they are being expanded}
+@d tracing_stats_code=31 {show memory usage if \TeX\ knows it}
+@d tracing_paragraphs_code=32 {show line-break calculations}
+@d tracing_pages_code=33 {show page-break calculations}
+@d tracing_output_code=34 {show boxes when they are shipped out}
+@d tracing_lost_chars_code=35 {show characters that aren't in the font}
+@d tracing_commands_code=36 {show command codes at |big_switch|}
+@d tracing_restores_code=37 {show equivalents when they are restored}
+@d uc_hyph_code=38 {hyphenate words beginning with a capital letter}
+@d output_penalty_code=39 {penalty found at current page break}
+@d max_dead_cycles_code=40 {bound on consecutive dead cycles of output}
+@d hang_after_code=41 {hanging indentation changes after this many lines}
+@d floating_penalty_code=42 {penalty for insertions heldover after a split}
+@d global_defs_code=43 {override \.{\\global} specifications}
+@d cur_fam_code=44 {current family}
+@d escape_char_code=45 {escape character for token output}
+@d default_hyphen_char_code=46 {value of \.{\\hyphenchar} when a font is loaded}
+@d default_skew_char_code=47 {value of \.{\\skewchar} when a font is loaded}
+@d end_line_char_code=48 {character placed at the right end of the buffer}
+@d new_line_char_code=49 {character that prints as |print_ln|}
+@d language_code=50 {current hyphenation table}
+@d left_hyphen_min_code=51 {minimum left hyphenation fragment size}
+@d right_hyphen_min_code=52 {minimum right hyphenation fragment size}
+@d holding_inserts_code=53 {do not remove insertion nodes from \.{\\box255}}
+@d error_context_lines_code=54 {maximum intermediate line pairs shown}
+@d int_pars=55 {total number of integer parameters}
+@d count_base=int_base+int_pars {256 user \.{\\count} registers}
+@d del_code_base=count_base+256 {256 delimiter code mappings}
+@d dimen_base=del_code_base+256 {beginning of region 6}
+@#
+@d del_code(#)==eqtb[del_code_base+#].int
+@d count(#)==eqtb[count_base+#].int
+@d int_par(#)==eqtb[int_base+#].int {an integer parameter}
+@d pretolerance==int_par(pretolerance_code)
+@d tolerance==int_par(tolerance_code)
+@d line_penalty==int_par(line_penalty_code)
+@d hyphen_penalty==int_par(hyphen_penalty_code)
+@d ex_hyphen_penalty==int_par(ex_hyphen_penalty_code)
+@d club_penalty==int_par(club_penalty_code)
+@d widow_penalty==int_par(widow_penalty_code)
+@d display_widow_penalty==int_par(display_widow_penalty_code)
+@d broken_penalty==int_par(broken_penalty_code)
+@d bin_op_penalty==int_par(bin_op_penalty_code)
+@d rel_penalty==int_par(rel_penalty_code)
+@d pre_display_penalty==int_par(pre_display_penalty_code)
+@d post_display_penalty==int_par(post_display_penalty_code)
+@d inter_line_penalty==int_par(inter_line_penalty_code)
+@d double_hyphen_demerits==int_par(double_hyphen_demerits_code)
+@d final_hyphen_demerits==int_par(final_hyphen_demerits_code)
+@d adj_demerits==int_par(adj_demerits_code)
+@d mag==int_par(mag_code)
+@d delimiter_factor==int_par(delimiter_factor_code)
+@d looseness==int_par(looseness_code)
+@d time==int_par(time_code)
+@d day==int_par(day_code)
+@d month==int_par(month_code)
+@d year==int_par(year_code)
+@d show_box_breadth==int_par(show_box_breadth_code)
+@d show_box_depth==int_par(show_box_depth_code)
+@d hbadness==int_par(hbadness_code)
+@d vbadness==int_par(vbadness_code)
+@d pausing==int_par(pausing_code)
+@d tracing_online==int_par(tracing_online_code)
+@d tracing_macros==int_par(tracing_macros_code)
+@d tracing_stats==int_par(tracing_stats_code)
+@d tracing_paragraphs==int_par(tracing_paragraphs_code)
+@d tracing_pages==int_par(tracing_pages_code)
+@d tracing_output==int_par(tracing_output_code)
+@d tracing_lost_chars==int_par(tracing_lost_chars_code)
+@d tracing_commands==int_par(tracing_commands_code)
+@d tracing_restores==int_par(tracing_restores_code)
+@d uc_hyph==int_par(uc_hyph_code)
+@d output_penalty==int_par(output_penalty_code)
+@d max_dead_cycles==int_par(max_dead_cycles_code)
+@d hang_after==int_par(hang_after_code)
+@d floating_penalty==int_par(floating_penalty_code)
+@d global_defs==int_par(global_defs_code)
+@d cur_fam==int_par(cur_fam_code)
+@d escape_char==int_par(escape_char_code)
+@d default_hyphen_char==int_par(default_hyphen_char_code)
+@d default_skew_char==int_par(default_skew_char_code)
+@d end_line_char==int_par(end_line_char_code)
+@d new_line_char==int_par(new_line_char_code)
+@d language==int_par(language_code)
+@d left_hyphen_min==int_par(left_hyphen_min_code)
+@d right_hyphen_min==int_par(right_hyphen_min_code)
+@d holding_inserts==int_par(holding_inserts_code)
+@d error_context_lines==int_par(error_context_lines_code)
+
+@<Assign the values |depth_threshold:=show_box_depth|...@>=
+depth_threshold:=show_box_depth;
+breadth_max:=show_box_breadth
+
+@ We can print the symbolic name of an integer parameter as follows.
+
+@p procedure print_param(@!n:integer);
+begin case n of
+pretolerance_code:print_esc("pretolerance");
+tolerance_code:print_esc("tolerance");
+line_penalty_code:print_esc("linepenalty");
+hyphen_penalty_code:print_esc("hyphenpenalty");
+ex_hyphen_penalty_code:print_esc("exhyphenpenalty");
+club_penalty_code:print_esc("clubpenalty");
+widow_penalty_code:print_esc("widowpenalty");
+display_widow_penalty_code:print_esc("displaywidowpenalty");
+broken_penalty_code:print_esc("brokenpenalty");
+bin_op_penalty_code:print_esc("binoppenalty");
+rel_penalty_code:print_esc("relpenalty");
+pre_display_penalty_code:print_esc("predisplaypenalty");
+post_display_penalty_code:print_esc("postdisplaypenalty");
+inter_line_penalty_code:print_esc("interlinepenalty");
+double_hyphen_demerits_code:print_esc("doublehyphendemerits");
+final_hyphen_demerits_code:print_esc("finalhyphendemerits");
+adj_demerits_code:print_esc("adjdemerits");
+mag_code:print_esc("mag");
+delimiter_factor_code:print_esc("delimiterfactor");
+looseness_code:print_esc("looseness");
+time_code:print_esc("time");
+day_code:print_esc("day");
+month_code:print_esc("month");
+year_code:print_esc("year");
+show_box_breadth_code:print_esc("showboxbreadth");
+show_box_depth_code:print_esc("showboxdepth");
+hbadness_code:print_esc("hbadness");
+vbadness_code:print_esc("vbadness");
+pausing_code:print_esc("pausing");
+tracing_online_code:print_esc("tracingonline");
+tracing_macros_code:print_esc("tracingmacros");
+tracing_stats_code:print_esc("tracingstats");
+tracing_paragraphs_code:print_esc("tracingparagraphs");
+tracing_pages_code:print_esc("tracingpages");
+tracing_output_code:print_esc("tracingoutput");
+tracing_lost_chars_code:print_esc("tracinglostchars");
+tracing_commands_code:print_esc("tracingcommands");
+tracing_restores_code:print_esc("tracingrestores");
+uc_hyph_code:print_esc("uchyph");
+output_penalty_code:print_esc("outputpenalty");
+max_dead_cycles_code:print_esc("maxdeadcycles");
+hang_after_code:print_esc("hangafter");
+floating_penalty_code:print_esc("floatingpenalty");
+global_defs_code:print_esc("globaldefs");
+cur_fam_code:print_esc("fam");
+escape_char_code:print_esc("escapechar");
+default_hyphen_char_code:print_esc("defaulthyphenchar");
+default_skew_char_code:print_esc("defaultskewchar");
+end_line_char_code:print_esc("endlinechar");
+new_line_char_code:print_esc("newlinechar");
+language_code:print_esc("language");
+left_hyphen_min_code:print_esc("lefthyphenmin");
+right_hyphen_min_code:print_esc("righthyphenmin");
+holding_inserts_code:print_esc("holdinginserts");
+error_context_lines_code:print_esc("errorcontextlines");
+othercases print("[unknown integer parameter!]")
+endcases;
+end;
+
+@ The integer parameter names must be entered into the hash table.
+
+@<Put each...@>=
+primitive("pretolerance",assign_int,int_base+pretolerance_code);@/
+@!@:pretolerance_}{\.{\\pretolerance} primitive@>
+primitive("tolerance",assign_int,int_base+tolerance_code);@/
+@!@:tolerance_}{\.{\\tolerance} primitive@>
+primitive("linepenalty",assign_int,int_base+line_penalty_code);@/
+@!@:line_penalty_}{\.{\\linepenalty} primitive@>
+primitive("hyphenpenalty",assign_int,int_base+hyphen_penalty_code);@/
+@!@:hyphen_penalty_}{\.{\\hyphenpenalty} primitive@>
+primitive("exhyphenpenalty",assign_int,int_base+ex_hyphen_penalty_code);@/
+@!@:ex_hyphen_penalty_}{\.{\\exhyphenpenalty} primitive@>
+primitive("clubpenalty",assign_int,int_base+club_penalty_code);@/
+@!@:club_penalty_}{\.{\\clubpenalty} primitive@>
+primitive("widowpenalty",assign_int,int_base+widow_penalty_code);@/
+@!@:widow_penalty_}{\.{\\widowpenalty} primitive@>
+primitive("displaywidowpenalty",
+ assign_int,int_base+display_widow_penalty_code);@/
+@!@:display_widow_penalty_}{\.{\\displaywidowpenalty} primitive@>
+primitive("brokenpenalty",assign_int,int_base+broken_penalty_code);@/
+@!@:broken_penalty_}{\.{\\brokenpenalty} primitive@>
+primitive("binoppenalty",assign_int,int_base+bin_op_penalty_code);@/
+@!@:bin_op_penalty_}{\.{\\binoppenalty} primitive@>
+primitive("relpenalty",assign_int,int_base+rel_penalty_code);@/
+@!@:rel_penalty_}{\.{\\relpenalty} primitive@>
+primitive("predisplaypenalty",assign_int,int_base+pre_display_penalty_code);@/
+@!@:pre_display_penalty_}{\.{\\predisplaypenalty} primitive@>
+primitive("postdisplaypenalty",assign_int,int_base+post_display_penalty_code);@/
+@!@:post_display_penalty_}{\.{\\postdisplaypenalty} primitive@>
+primitive("interlinepenalty",assign_int,int_base+inter_line_penalty_code);@/
+@!@:inter_line_penalty_}{\.{\\interlinepenalty} primitive@>
+primitive("doublehyphendemerits",
+ assign_int,int_base+double_hyphen_demerits_code);@/
+@!@:double_hyphen_demerits_}{\.{\\doublehyphendemerits} primitive@>
+primitive("finalhyphendemerits",
+ assign_int,int_base+final_hyphen_demerits_code);@/
+@!@:final_hyphen_demerits_}{\.{\\finalhyphendemerits} primitive@>
+primitive("adjdemerits",assign_int,int_base+adj_demerits_code);@/
+@!@:adj_demerits_}{\.{\\adjdemerits} primitive@>
+primitive("mag",assign_int,int_base+mag_code);@/
+@!@:mag_}{\.{\\mag} primitive@>
+primitive("delimiterfactor",assign_int,int_base+delimiter_factor_code);@/
+@!@:delimiter_factor_}{\.{\\delimiterfactor} primitive@>
+primitive("looseness",assign_int,int_base+looseness_code);@/
+@!@:looseness_}{\.{\\looseness} primitive@>
+primitive("time",assign_int,int_base+time_code);@/
+@!@:time_}{\.{\\time} primitive@>
+primitive("day",assign_int,int_base+day_code);@/
+@!@:day_}{\.{\\day} primitive@>
+primitive("month",assign_int,int_base+month_code);@/
+@!@:month_}{\.{\\month} primitive@>
+primitive("year",assign_int,int_base+year_code);@/
+@!@:year_}{\.{\\year} primitive@>
+primitive("showboxbreadth",assign_int,int_base+show_box_breadth_code);@/
+@!@:show_box_breadth_}{\.{\\showboxbreadth} primitive@>
+primitive("showboxdepth",assign_int,int_base+show_box_depth_code);@/
+@!@:show_box_depth_}{\.{\\showboxdepth} primitive@>
+primitive("hbadness",assign_int,int_base+hbadness_code);@/
+@!@:hbadness_}{\.{\\hbadness} primitive@>
+primitive("vbadness",assign_int,int_base+vbadness_code);@/
+@!@:vbadness_}{\.{\\vbadness} primitive@>
+primitive("pausing",assign_int,int_base+pausing_code);@/
+@!@:pausing_}{\.{\\pausing} primitive@>
+primitive("tracingonline",assign_int,int_base+tracing_online_code);@/
+@!@:tracing_online_}{\.{\\tracingonline} primitive@>
+primitive("tracingmacros",assign_int,int_base+tracing_macros_code);@/
+@!@:tracing_macros_}{\.{\\tracingmacros} primitive@>
+primitive("tracingstats",assign_int,int_base+tracing_stats_code);@/
+@!@:tracing_stats_}{\.{\\tracingstats} primitive@>
+primitive("tracingparagraphs",assign_int,int_base+tracing_paragraphs_code);@/
+@!@:tracing_paragraphs_}{\.{\\tracingparagraphs} primitive@>
+primitive("tracingpages",assign_int,int_base+tracing_pages_code);@/
+@!@:tracing_pages_}{\.{\\tracingpages} primitive@>
+primitive("tracingoutput",assign_int,int_base+tracing_output_code);@/
+@!@:tracing_output_}{\.{\\tracingoutput} primitive@>
+primitive("tracinglostchars",assign_int,int_base+tracing_lost_chars_code);@/
+@!@:tracing_lost_chars_}{\.{\\tracinglostchars} primitive@>
+primitive("tracingcommands",assign_int,int_base+tracing_commands_code);@/
+@!@:tracing_commands_}{\.{\\tracingcommands} primitive@>
+primitive("tracingrestores",assign_int,int_base+tracing_restores_code);@/
+@!@:tracing_restores_}{\.{\\tracingrestores} primitive@>
+primitive("uchyph",assign_int,int_base+uc_hyph_code);@/
+@!@:uc_hyph_}{\.{\\uchyph} primitive@>
+primitive("outputpenalty",assign_int,int_base+output_penalty_code);@/
+@!@:output_penalty_}{\.{\\outputpenalty} primitive@>
+primitive("maxdeadcycles",assign_int,int_base+max_dead_cycles_code);@/
+@!@:max_dead_cycles_}{\.{\\maxdeadcycles} primitive@>
+primitive("hangafter",assign_int,int_base+hang_after_code);@/
+@!@:hang_after_}{\.{\\hangafter} primitive@>
+primitive("floatingpenalty",assign_int,int_base+floating_penalty_code);@/
+@!@:floating_penalty_}{\.{\\floatingpenalty} primitive@>
+primitive("globaldefs",assign_int,int_base+global_defs_code);@/
+@!@:global_defs_}{\.{\\globaldefs} primitive@>
+primitive("fam",assign_int,int_base+cur_fam_code);@/
+@!@:fam_}{\.{\\fam} primitive@>
+primitive("escapechar",assign_int,int_base+escape_char_code);@/
+@!@:escape_char_}{\.{\\escapechar} primitive@>
+primitive("defaulthyphenchar",assign_int,int_base+default_hyphen_char_code);@/
+@!@:default_hyphen_char_}{\.{\\defaulthyphenchar} primitive@>
+primitive("defaultskewchar",assign_int,int_base+default_skew_char_code);@/
+@!@:default_skew_char_}{\.{\\defaultskewchar} primitive@>
+primitive("endlinechar",assign_int,int_base+end_line_char_code);@/
+@!@:end_line_char_}{\.{\\endlinechar} primitive@>
+primitive("newlinechar",assign_int,int_base+new_line_char_code);@/
+@!@:new_line_char_}{\.{\\newlinechar} primitive@>
+primitive("language",assign_int,int_base+language_code);@/
+@!@:language_}{\.{\\language} primitive@>
+primitive("lefthyphenmin",assign_int,int_base+left_hyphen_min_code);@/
+@!@:left_hyphen_min_}{\.{\\lefthyphenmin} primitive@>
+primitive("righthyphenmin",assign_int,int_base+right_hyphen_min_code);@/
+@!@:right_hyphen_min_}{\.{\\righthyphenmin} primitive@>
+primitive("holdinginserts",assign_int,int_base+holding_inserts_code);@/
+@!@:holding_inserts_}{\.{\\holdinginserts} primitive@>
+primitive("errorcontextlines",assign_int,int_base+error_context_lines_code);@/
+@!@:error_context_lines_}{\.{\\errorcontextlines} primitive@>
+
+@ @<Cases of |print_cmd_chr|...@>=
+assign_int: if chr_code<count_base then print_param(chr_code-int_base)
+ else begin print_esc("count"); print_int(chr_code-count_base);
+ end;
+
+@ The integer parameters should really be initialized by a macro package;
+the following initialization does the minimum to keep \TeX\ from
+complete failure.
+@^null delimiter@>
+
+@<Initialize table entries...@>=
+for k:=int_base to del_code_base-1 do eqtb[k].int:=0;
+mag:=1000; tolerance:=10000; hang_after:=1; max_dead_cycles:=25;
+escape_char:="\"; end_line_char:=carriage_return;
+for k:=0 to 255 do del_code(k):=-1;
+del_code("."):=0; {this null delimiter is used in error recovery}
+
+@ The following procedure, which is called just before \TeX\ initializes its
+input and output, establishes the initial values of the date and time.
+@^system dependencies@>
+Since standard \PASCAL\ cannot provide such information, something special
+is needed. The program here simply specifies July 4, 1776, at noon; but
+users probably want a better approximation to the truth.
+
+@p procedure fix_date_and_time;
+begin time:=12*60; {minutes since midnight}
+day:=4; {fourth day of the month}
+month:=7; {seventh month of the year}
+year:=1776; {Anno Domini}
+end;
+
+@ @<Show equivalent |n|, in region 5@>=
+begin if n<count_base then print_param(n-int_base)
+else if n<del_code_base then
+ begin print_esc("count"); print_int(n-count_base);
+ end
+else begin print_esc("delcode"); print_int(n-del_code_base);
+ end;
+print_char("="); print_int(eqtb[n].int);
+end
+
+@ @<Set variable |c| to the current escape character@>=c:=escape_char
+
+@ @<Character |s| is the current new-line character@>=s=new_line_char
+
+@ \TeX\ is occasionally supposed to print diagnostic information that
+goes only into the transcript file, unless |tracing_online| is positive.
+Here are two routines that adjust the destination of print commands:
+
+@p procedure begin_diagnostic; {prepare to do some tracing}
+begin old_setting:=selector;
+if (tracing_online<=0)and(selector=term_and_log) then
+ begin decr(selector);
+ if history=spotless then history:=warning_issued;
+ end;
+end;
+@#
+procedure end_diagnostic(@!blank_line:boolean);
+ {restore proper conditions after tracing}
+begin print_nl("");
+if blank_line then print_ln;
+selector:=old_setting;
+end;
+
+@ Of course we had better declare another global variable, if the previous
+routines are going to work.
+
+@<Glob...@>=
+@!old_setting:0..max_selector;
+
+@ The final region of |eqtb| contains the dimension parameters defined
+here, and the 256 \.{\\dimen} registers.
+
+@d par_indent_code=0 {indentation of paragraphs}
+@d math_surround_code=1 {space around math in text}
+@d line_skip_limit_code=2 {threshold for |line_skip| instead of |baseline_skip|}
+@d hsize_code=3 {line width in horizontal mode}
+@d vsize_code=4 {page height in vertical mode}
+@d max_depth_code=5 {maximum depth of boxes on main pages}
+@d split_max_depth_code=6 {maximum depth of boxes on split pages}
+@d box_max_depth_code=7 {maximum depth of explicit vboxes}
+@d hfuzz_code=8 {tolerance for overfull hbox messages}
+@d vfuzz_code=9 {tolerance for overfull vbox messages}
+@d delimiter_shortfall_code=10 {maximum amount uncovered by variable delimiters}
+@d null_delimiter_space_code=11 {blank space in null delimiters}
+@d script_space_code=12 {extra space after subscript or superscript}
+@d pre_display_size_code=13 {length of text preceding a display}
+@d display_width_code=14 {length of line for displayed equation}
+@d display_indent_code=15 {indentation of line for displayed equation}
+@d overfull_rule_code=16 {width of rule that identifies overfull hboxes}
+@d hang_indent_code=17 {amount of hanging indentation}
+@d h_offset_code=18 {amount of horizontal offset when shipping pages out}
+@d v_offset_code=19 {amount of vertical offset when shipping pages out}
+@d emergency_stretch_code=20 {reduces badnesses on final pass of line-breaking}
+@d dimen_pars=21 {total number of dimension parameters}
+@d scaled_base=dimen_base+dimen_pars
+ {table of 256 user-defined \.{\\dimen} registers}
+@d eqtb_size=scaled_base+255 {largest subscript of |eqtb|}
+@#
+@d dimen(#)==eqtb[scaled_base+#].sc
+@d dimen_par(#)==eqtb[dimen_base+#].sc {a scaled quantity}
+@d par_indent==dimen_par(par_indent_code)
+@d math_surround==dimen_par(math_surround_code)
+@d line_skip_limit==dimen_par(line_skip_limit_code)
+@d hsize==dimen_par(hsize_code)
+@d vsize==dimen_par(vsize_code)
+@d max_depth==dimen_par(max_depth_code)
+@d split_max_depth==dimen_par(split_max_depth_code)
+@d box_max_depth==dimen_par(box_max_depth_code)
+@d hfuzz==dimen_par(hfuzz_code)
+@d vfuzz==dimen_par(vfuzz_code)
+@d delimiter_shortfall==dimen_par(delimiter_shortfall_code)
+@d null_delimiter_space==dimen_par(null_delimiter_space_code)
+@d script_space==dimen_par(script_space_code)
+@d pre_display_size==dimen_par(pre_display_size_code)
+@d display_width==dimen_par(display_width_code)
+@d display_indent==dimen_par(display_indent_code)
+@d overfull_rule==dimen_par(overfull_rule_code)
+@d hang_indent==dimen_par(hang_indent_code)
+@d h_offset==dimen_par(h_offset_code)
+@d v_offset==dimen_par(v_offset_code)
+@d emergency_stretch==dimen_par(emergency_stretch_code)
+
+@p procedure print_length_param(@!n:integer);
+begin case n of
+par_indent_code:print_esc("parindent");
+math_surround_code:print_esc("mathsurround");
+line_skip_limit_code:print_esc("lineskiplimit");
+hsize_code:print_esc("hsize");
+vsize_code:print_esc("vsize");
+max_depth_code:print_esc("maxdepth");
+split_max_depth_code:print_esc("splitmaxdepth");
+box_max_depth_code:print_esc("boxmaxdepth");
+hfuzz_code:print_esc("hfuzz");
+vfuzz_code:print_esc("vfuzz");
+delimiter_shortfall_code:print_esc("delimitershortfall");
+null_delimiter_space_code:print_esc("nulldelimiterspace");
+script_space_code:print_esc("scriptspace");
+pre_display_size_code:print_esc("predisplaysize");
+display_width_code:print_esc("displaywidth");
+display_indent_code:print_esc("displayindent");
+overfull_rule_code:print_esc("overfullrule");
+hang_indent_code:print_esc("hangindent");
+h_offset_code:print_esc("hoffset");
+v_offset_code:print_esc("voffset");
+emergency_stretch_code:print_esc("emergencystretch");
+othercases print("[unknown dimen parameter!]")
+endcases;
+end;
+
+@ @<Put each...@>=
+primitive("parindent",assign_dimen,dimen_base+par_indent_code);@/
+@!@:par_indent_}{\.{\\parindent} primitive@>
+primitive("mathsurround",assign_dimen,dimen_base+math_surround_code);@/
+@!@:math_surround_}{\.{\\mathsurround} primitive@>
+primitive("lineskiplimit",assign_dimen,dimen_base+line_skip_limit_code);@/
+@!@:line_skip_limit_}{\.{\\lineskiplimit} primitive@>
+primitive("hsize",assign_dimen,dimen_base+hsize_code);@/
+@!@:hsize_}{\.{\\hsize} primitive@>
+primitive("vsize",assign_dimen,dimen_base+vsize_code);@/
+@!@:vsize_}{\.{\\vsize} primitive@>
+primitive("maxdepth",assign_dimen,dimen_base+max_depth_code);@/
+@!@:max_depth_}{\.{\\maxdepth} primitive@>
+primitive("splitmaxdepth",assign_dimen,dimen_base+split_max_depth_code);@/
+@!@:split_max_depth_}{\.{\\splitmaxdepth} primitive@>
+primitive("boxmaxdepth",assign_dimen,dimen_base+box_max_depth_code);@/
+@!@:box_max_depth_}{\.{\\boxmaxdepth} primitive@>
+primitive("hfuzz",assign_dimen,dimen_base+hfuzz_code);@/
+@!@:hfuzz_}{\.{\\hfuzz} primitive@>
+primitive("vfuzz",assign_dimen,dimen_base+vfuzz_code);@/
+@!@:vfuzz_}{\.{\\vfuzz} primitive@>
+primitive("delimitershortfall",
+ assign_dimen,dimen_base+delimiter_shortfall_code);@/
+@!@:delimiter_shortfall_}{\.{\\delimitershortfall} primitive@>
+primitive("nulldelimiterspace",
+ assign_dimen,dimen_base+null_delimiter_space_code);@/
+@!@:null_delimiter_space_}{\.{\\nulldelimiterspace} primitive@>
+primitive("scriptspace",assign_dimen,dimen_base+script_space_code);@/
+@!@:script_space_}{\.{\\scriptspace} primitive@>
+primitive("predisplaysize",assign_dimen,dimen_base+pre_display_size_code);@/
+@!@:pre_display_size_}{\.{\\predisplaysize} primitive@>
+primitive("displaywidth",assign_dimen,dimen_base+display_width_code);@/
+@!@:display_width_}{\.{\\displaywidth} primitive@>
+primitive("displayindent",assign_dimen,dimen_base+display_indent_code);@/
+@!@:display_indent_}{\.{\\displayindent} primitive@>
+primitive("overfullrule",assign_dimen,dimen_base+overfull_rule_code);@/
+@!@:overfull_rule_}{\.{\\overfullrule} primitive@>
+primitive("hangindent",assign_dimen,dimen_base+hang_indent_code);@/
+@!@:hang_indent_}{\.{\\hangindent} primitive@>
+primitive("hoffset",assign_dimen,dimen_base+h_offset_code);@/
+@!@:h_offset_}{\.{\\hoffset} primitive@>
+primitive("voffset",assign_dimen,dimen_base+v_offset_code);@/
+@!@:v_offset_}{\.{\\voffset} primitive@>
+primitive("emergencystretch",assign_dimen,dimen_base+emergency_stretch_code);@/
+@!@:emergency_stretch_}{\.{\\emergencystretch} primitive@>
+
+@ @<Cases of |print_cmd_chr|...@>=
+assign_dimen: if chr_code<scaled_base then
+ print_length_param(chr_code-dimen_base)
+ else begin print_esc("dimen"); print_int(chr_code-scaled_base);
+ end;
+
+@ @<Initialize table entries...@>=
+for k:=dimen_base to eqtb_size do eqtb[k].sc:=0;
+
+@ @<Show equivalent |n|, in region 6@>=
+begin if n<scaled_base then print_length_param(n-dimen_base)
+else begin print_esc("dimen"); print_int(n-scaled_base);
+ end;
+print_char("="); print_scaled(eqtb[n].sc); print("pt");
+end
+
+@ Here is a procedure that displays the contents of |eqtb[n]|
+symbolically.
+
+@p@t\4@>@<Declare the procedure called |print_cmd_chr|@>@;@/
+@!stat procedure show_eqtb(@!n:pointer);
+begin if n<active_base then print_char("?") {this can't happen}
+else if n<glue_base then @<Show equivalent |n|, in region 1 or 2@>
+else if n<local_base then @<Show equivalent |n|, in region 3@>
+else if n<int_base then @<Show equivalent |n|, in region 4@>
+else if n<dimen_base then @<Show equivalent |n|, in region 5@>
+else if n<=eqtb_size then @<Show equivalent |n|, in region 6@>
+else print_char("?"); {this can't happen either}
+end;
+tats
+
+@ The last two regions of |eqtb| have fullword values instead of the
+three fields |eq_level|, |eq_type|, and |equiv|. An |eq_type| is unnecessary,
+but \TeX\ needs to store the |eq_level| information in another array
+called |xeq_level|.
+
+@<Glob...@>=
+@!eqtb:array[active_base..eqtb_size] of memory_word;
+@!xeq_level:array[int_base..eqtb_size] of quarterword;
+
+@ @<Set init...@>=
+for k:=int_base to eqtb_size do xeq_level[k]:=level_one;
+
+@ When the debugging routine |search_mem| is looking for pointers having a
+given value, it is interested only in regions 1 to~3 of~|eqtb|, and in the
+first part of region~4.
+
+@<Search |eqtb| for equivalents equal to |p|@>=
+for q:=active_base to box_base+255 do
+ begin if equiv(q)=p then
+ begin print_nl("EQUIV("); print_int(q); print_char(")");
+ end;
+ end
+
+@* \[18] The hash table.
+Control sequences are stored and retrieved by means of a fairly standard hash
+table algorithm called the method of ``coalescing lists'' (cf.\ Algorithm 6.4C
+in {\sl The Art of Computer Programming\/}). Once a control sequence enters the
+table, it is never removed, because there are complicated situations
+involving \.{\\gdef} where the removal of a control sequence at the end of
+a group would be a mistake preventable only by the introduction of a
+complicated reference-count mechanism.
+
+The actual sequence of letters forming a control sequence identifier is
+stored in the |str_pool| array together with all the other strings. An
+auxiliary array |hash| consists of items with two halfword fields per
+word. The first of these, called |next(p)|, points to the next identifier
+belonging to the same coalesced list as the identifier corresponding to~|p|;
+and the other, called |text(p)|, points to the |str_start| entry for
+|p|'s identifier. If position~|p| of the hash table is empty, we have
+|text(p)=0|; if position |p| is either empty or the end of a coalesced
+hash list, we have |next(p)=0|. An auxiliary pointer variable called
+|hash_used| is maintained in such a way that all locations |p>=hash_used|
+are nonempty. The global variable |cs_count| tells how many multiletter
+control sequences have been defined, if statistics are being kept.
+
+A global boolean variable called |no_new_control_sequence| is set to
+|true| during the time that new hash table entries are forbidden.
+
+@d next(#) == hash[#].lh {link for coalesced lists}
+@d text(#) == hash[#].rh {string number for control sequence name}
+@d hash_is_full == (hash_used=hash_base) {test if all positions are occupied}
+@d font_id_text(#) == text(font_id_base+#) {a frozen font identifier's name}
+
+@<Glob...@>=
+@!hash: array[hash_base..undefined_control_sequence-1] of two_halves;
+ {the hash table}
+@!hash_used:pointer; {allocation pointer for |hash|}
+@!no_new_control_sequence:boolean; {are new identifiers legal?}
+@!cs_count:integer; {total number of known identifiers}
+
+@ @<Set init...@>=
+no_new_control_sequence:=true; {new identifiers are usually forbidden}
+next(hash_base):=0; text(hash_base):=0;
+for k:=hash_base+1 to undefined_control_sequence-1 do hash[k]:=hash[hash_base];
+
+@ @<Initialize table entries...@>=
+hash_used:=frozen_control_sequence; {nothing is used}
+cs_count:=0;
+eq_type(frozen_dont_expand):=dont_expand;
+text(frozen_dont_expand):="notexpanded:";
+@.notexpanded:@>
+
+@ Here is the subroutine that searches the hash table for an identifier
+that matches a given string of length |l>1| appearing in |buffer[j..
+(j+l-1)]|. If the identifier is found, the corresponding hash table address
+is returned. Otherwise, if the global variable |no_new_control_sequence|
+is |true|, the dummy address |undefined_control_sequence| is returned.
+Otherwise the identifier is inserted into the hash table and its location
+is returned.
+
+@p function id_lookup(@!j,@!l:integer):pointer; {search the hash table}
+label found; {go here if you found it}
+var h:integer; {hash code}
+@!d:integer; {number of characters in incomplete current string}
+@!p:pointer; {index in |hash| array}
+@!k:pointer; {index in |buffer| array}
+begin @<Compute the hash code |h|@>;
+p:=h+hash_base; {we start searching here; note that |0<=h<hash_prime|}
+loop@+begin if text(p)>0 then if length(text(p))=l then
+ if str_eq_buf(text(p),j) then goto found;
+ if next(p)=0 then
+ begin if no_new_control_sequence then
+ p:=undefined_control_sequence
+ else @<Insert a new control sequence after |p|, then make
+ |p| point to it@>;
+ goto found;
+ end;
+ p:=next(p);
+ end;
+found: id_lookup:=p;
+end;
+
+@ @<Insert a new control...@>=
+begin if text(p)>0 then
+ begin repeat if hash_is_full then overflow("hash size",hash_size);
+@:TeX capacity exceeded hash size}{\quad hash size@>
+ decr(hash_used);
+ until text(hash_used)=0; {search for an empty location in |hash|}
+ next(p):=hash_used; p:=hash_used;
+ end;
+str_room(l); d:=cur_length;
+while pool_ptr>str_start[str_ptr] do
+ begin decr(pool_ptr); str_pool[pool_ptr+l]:=str_pool[pool_ptr];
+ end; {move current string up to make room for another}
+for k:=j to j+l-1 do append_char(buffer[k]);
+text(p):=make_string; pool_ptr:=pool_ptr+d;
+@!stat incr(cs_count);@+tats@;@/
+end
+
+@ The value of |hash_prime| should be roughly 85\pct! of |hash_size|, and it
+should be a prime number. The theory of hashing tells us to expect fewer
+than two table probes, on the average, when the search is successful.
+[See J.~S. Vitter, {\sl Journal of the ACM\/ \bf30} (1983), 231--258.]
+@^Vitter, Jeffrey Scott@>
+
+@<Compute the hash code |h|@>=
+h:=buffer[j];
+for k:=j+1 to j+l-1 do
+ begin h:=h+h+buffer[k];
+ while h>=hash_prime do h:=h-hash_prime;
+ end
+
+@ Single-character control sequences do not need to be looked up in a hash
+table, since we can use the character code itself as a direct address.
+The procedure |print_cs| prints the name of a control sequence, given
+a pointer to its address in |eqtb|. A space is printed after the name
+unless it is a single nonletter or an active character. This procedure
+might be invoked with invalid data, so it is ``extra robust.'' The
+individual characters must be printed one at a time using |print|, since
+they may be unprintable.
+
+@<Basic printing...@>=
+procedure print_cs(@!p:integer); {prints a purported control sequence}
+begin if p<hash_base then {single character}
+ if p>=single_base then
+ if p=null_cs then
+ begin print_esc("csname"); print_esc("endcsname");
+ end
+ else begin print_esc(p-single_base);
+ if cat_code(p-single_base)=letter then print_char(" ");
+ end
+ else if p<active_base then print_esc("IMPOSSIBLE.")
+@.IMPOSSIBLE@>
+ else print(p-active_base)
+else if p>=undefined_control_sequence then print_esc("IMPOSSIBLE.")
+else if (text(p)<0)or(text(p)>=str_ptr) then print_esc("NONEXISTENT.")
+@.NONEXISTENT@>
+else begin print_esc(text(p));
+ print_char(" ");
+ end;
+end;
+
+@ Here is a similar procedure; it avoids the error checks, and it never
+prints a space after the control sequence.
+
+@<Basic printing procedures@>=
+procedure sprint_cs(@!p:pointer); {prints a control sequence}
+begin if p<hash_base then
+ if p<single_base then print(p-active_base)
+ else if p<null_cs then print_esc(p-single_base)
+ else begin print_esc("csname"); print_esc("endcsname");
+ end
+else print_esc(text(p));
+end;
+
+@ We need to put \TeX's ``primitive'' control sequences into the hash
+table, together with their command code (which will be the |eq_type|)
+and an operand (which will be the |equiv|). The |primitive| procedure
+does this, in a way that no \TeX\ user can. The global value |cur_val|
+contains the new |eqtb| pointer after |primitive| has acted.
+
+@p @!init procedure primitive(@!s:str_number;@!c:quarterword;@!o:halfword);
+var k:pool_pointer; {index into |str_pool|}
+@!j:small_number; {index into |buffer|}
+@!l:small_number; {length of the string}
+begin if s<256 then cur_val:=s+single_base
+else begin k:=str_start[s]; l:=str_start[s+1]-k;
+ {we will move |s| into the (empty) |buffer|}
+ for j:=0 to l-1 do buffer[j]:=so(str_pool[k+j]);
+ cur_val:=id_lookup(0,l); {|no_new_control_sequence| is |false|}
+ flush_string; text(cur_val):=s; {we don't want to have the string twice}
+ end;
+eq_level(cur_val):=level_one; eq_type(cur_val):=c; equiv(cur_val):=o;
+end;
+tini
+
+@ Many of \TeX's primitives need no |equiv|, since they are identifiable
+by their |eq_type| alone. These primitives are loaded into the hash table
+as follows:
+
+@<Put each of \TeX's primitives into the hash table@>=
+primitive(" ",ex_space,0);@/
+@!@:Single-character primitives /}{\quad\.{\\\ }@>
+primitive("/",ital_corr,0);@/
+@!@:Single-character primitives /}{\quad\.{\\/}@>
+primitive("accent",accent,0);@/
+@!@:accent_}{\.{\\accent} primitive@>
+primitive("advance",advance,0);@/
+@!@:advance_}{\.{\\advance} primitive@>
+primitive("afterassignment",after_assignment,0);@/
+@!@:after_assignment_}{\.{\\afterassignment} primitive@>
+primitive("aftergroup",after_group,0);@/
+@!@:after_group_}{\.{\\aftergroup} primitive@>
+primitive("begingroup",begin_group,0);@/
+@!@:begin_group_}{\.{\\begingroup} primitive@>
+primitive("char",char_num,0);@/
+@!@:char_}{\.{\\char} primitive@>
+primitive("csname",cs_name,0);@/
+@!@:cs_name_}{\.{\\csname} primitive@>
+primitive("delimiter",delim_num,0);@/
+@!@:delimiter_}{\.{\\delimiter} primitive@>
+primitive("divide",divide,0);@/
+@!@:divide_}{\.{\\divide} primitive@>
+primitive("endcsname",end_cs_name,0);@/
+@!@:end_cs_name_}{\.{\\endcsname} primitive@>
+primitive("endgroup",end_group,0);
+@!@:end_group_}{\.{\\endgroup} primitive@>
+text(frozen_end_group):="endgroup"; eqtb[frozen_end_group]:=eqtb[cur_val];@/
+primitive("expandafter",expand_after,0);@/
+@!@:expand_after_}{\.{\\expandafter} primitive@>
+primitive("font",def_font,0);@/
+@!@:font_}{\.{\\font} primitive@>
+primitive("fontdimen",assign_font_dimen,0);@/
+@!@:font_dimen_}{\.{\\fontdimen} primitive@>
+primitive("halign",halign,0);@/
+@!@:halign_}{\.{\\halign} primitive@>
+primitive("hrule",hrule,0);@/
+@!@:hrule_}{\.{\\hrule} primitive@>
+primitive("ignorespaces",ignore_spaces,0);@/
+@!@:ignore_spaces_}{\.{\\ignorespaces} primitive@>
+primitive("insert",insert,0);@/
+@!@:insert_}{\.{\\insert} primitive@>
+primitive("mark",mark,0);@/
+@!@:mark_}{\.{\\mark} primitive@>
+primitive("mathaccent",math_accent,0);@/
+@!@:math_accent_}{\.{\\mathaccent} primitive@>
+primitive("mathchar",math_char_num,0);@/
+@!@:math_char_}{\.{\\mathchar} primitive@>
+primitive("mathchoice",math_choice,0);@/
+@!@:math_choice_}{\.{\\mathchoice} primitive@>
+primitive("multiply",multiply,0);@/
+@!@:multiply_}{\.{\\multiply} primitive@>
+primitive("noalign",no_align,0);@/
+@!@:no_align_}{\.{\\noalign} primitive@>
+primitive("noboundary",no_boundary,0);@/
+@!@:no_boundary_}{\.{\\noboundary} primitive@>
+primitive("noexpand",no_expand,0);@/
+@!@:no_expand_}{\.{\\noexpand} primitive@>
+primitive("nonscript",non_script,0);@/
+@!@:non_script_}{\.{\\nonscript} primitive@>
+primitive("omit",omit,0);@/
+@!@:omit_}{\.{\\omit} primitive@>
+primitive("parshape",set_shape,0);@/
+@!@:par_shape_}{\.{\\parshape} primitive@>
+primitive("penalty",break_penalty,0);@/
+@!@:penalty_}{\.{\\penalty} primitive@>
+primitive("prevgraf",set_prev_graf,0);@/
+@!@:prev_graf_}{\.{\\prevgraf} primitive@>
+primitive("radical",radical,0);@/
+@!@:radical_}{\.{\\radical} primitive@>
+primitive("read",read_to_cs,0);@/
+@!@:read_}{\.{\\read} primitive@>
+primitive("relax",relax,256); {cf.\ |scan_file_name|}
+@!@:relax_}{\.{\\relax} primitive@>
+text(frozen_relax):="relax"; eqtb[frozen_relax]:=eqtb[cur_val];@/
+primitive("setbox",set_box,0);@/
+@!@:set_box_}{\.{\\setbox} primitive@>
+primitive("the",the,0);@/
+@!@:the_}{\.{\\the} primitive@>
+primitive("toks",toks_register,0);@/
+@!@:toks_}{\.{\\toks} primitive@>
+primitive("vadjust",vadjust,0);@/
+@!@:vadjust_}{\.{\\vadjust} primitive@>
+primitive("valign",valign,0);@/
+@!@:valign_}{\.{\\valign} primitive@>
+primitive("vcenter",vcenter,0);@/
+@!@:vcenter_}{\.{\\vcenter} primitive@>
+primitive("vrule",vrule,0);@/
+@!@:vrule_}{\.{\\vrule} primitive@>
+
+@ Each primitive has a corresponding inverse, so that it is possible to
+display the cryptic numeric contents of |eqtb| in symbolic form.
+Every call of |primitive| in this program is therefore accompanied by some
+straightforward code that forms part of the |print_cmd_chr| routine
+below.
+
+@<Cases of |print_cmd_chr|...@>=
+accent: print_esc("accent");
+advance: print_esc("advance");
+after_assignment: print_esc("afterassignment");
+after_group: print_esc("aftergroup");
+assign_font_dimen: print_esc("fontdimen");
+begin_group: print_esc("begingroup");
+break_penalty: print_esc("penalty");
+char_num: print_esc("char");
+cs_name: print_esc("csname");
+def_font: print_esc("font");
+delim_num: print_esc("delimiter");
+divide: print_esc("divide");
+end_cs_name: print_esc("endcsname");
+end_group: print_esc("endgroup");
+ex_space: print_esc(" ");
+expand_after: print_esc("expandafter");
+halign: print_esc("halign");
+hrule: print_esc("hrule");
+ignore_spaces: print_esc("ignorespaces");
+insert: print_esc("insert");
+ital_corr: print_esc("/");
+mark: print_esc("mark");
+math_accent: print_esc("mathaccent");
+math_char_num: print_esc("mathchar");
+math_choice: print_esc("mathchoice");
+multiply: print_esc("multiply");
+no_align: print_esc("noalign");
+no_boundary:print_esc("noboundary");
+no_expand: print_esc("noexpand");
+non_script: print_esc("nonscript");
+omit: print_esc("omit");
+radical: print_esc("radical");
+read_to_cs: print_esc("read");
+relax: print_esc("relax");
+set_box: print_esc("setbox");
+set_prev_graf: print_esc("prevgraf");
+set_shape: print_esc("parshape");
+the: print_esc("the");
+toks_register: print_esc("toks");
+vadjust: print_esc("vadjust");
+valign: print_esc("valign");
+vcenter: print_esc("vcenter");
+vrule: print_esc("vrule");
+
+@ We will deal with the other primitives later, at some point in the program
+where their |eq_type| and |equiv| values are more meaningful. For example,
+the primitives for math mode will be loaded when we consider the routines
+that deal with formulas. It is easy to find where each particular
+primitive was treated by looking in the index at the end; for example, the
+section where |"radical"| entered |eqtb| is listed under `\.{\\radical}
+primitive'. (Primitives consisting of a single nonalphabetic character,
+@!like `\.{\\/}', are listed under `Single-character primitives'.)
+@!@^Single-character primitives@>
+
+Meanwhile, this is a convenient place to catch up on something we were unable
+to do before the hash table was defined:
+
+@<Print the font identifier for |font(p)|@>=
+print_esc(font_id_text(font(p)))
+
+@* \[19] Saving and restoring equivalents.
+The nested structure provided by `$\.{\char'173}\ldots\.{\char'175}$' groups
+in \TeX\ means that |eqtb| entries valid in outer groups should be saved
+and restored later if they are overridden inside the braces. When a new |eqtb|
+value is being assigned, the program therefore checks to see if the previous
+entry belongs to an outer level. In such a case, the old value is placed
+on the |save_stack| just before the new value enters |eqtb|. At the
+end of a grouping level, i.e., when the right brace is sensed, the
+|save_stack| is used to restore the outer values, and the inner ones are
+destroyed.
+
+Entries on the |save_stack| are of type |memory_word|. The top item on
+this stack is |save_stack[p]|, where |p=save_ptr-1|; it contains three
+fields called |save_type|, |save_level|, and |save_index|, and it is
+interpreted in one of four ways:
+
+\yskip\hangg 1) If |save_type(p)=restore_old_value|, then
+|save_index(p)| is a location in |eqtb| whose current value should
+be destroyed at the end of the current group and replaced by |save_stack[p-1]|.
+Furthermore if |save_index(p)>=int_base|, then |save_level(p)|
+should replace the corresponding entry in |xeq_level|.
+
+\yskip\hangg 2) If |save_type(p)=restore_zero|, then |save_index(p)|
+is a location in |eqtb| whose current value should be destroyed at the end
+of the current group, when it should be
+replaced by the current value of |eqtb[undefined_control_sequence]|.
+
+\yskip\hangg 3) If |save_type(p)=insert_token|, then |save_index(p)|
+is a token that should be inserted into \TeX's input when the current
+group ends.
+
+\yskip\hangg 4) If |save_type(p)=level_boundary|, then |save_level(p)|
+is a code explaining what kind of group we were previously in, and
+|save_index(p)| points to the level boundary word at the bottom of
+the entries for that group.
+
+@d save_type(#)==save_stack[#].hh.b0 {classifies a |save_stack| entry}
+@d save_level(#)==save_stack[#].hh.b1
+ {saved level for regions 5 and 6, or group code}
+@d save_index(#)==save_stack[#].hh.rh
+ {|eqtb| location or |save_stack| location}
+@d restore_old_value=0 {|save_type| when a value should be restored later}
+@d restore_zero=1 {|save_type| when an undefined entry should be restored}
+@d insert_token=2 {|save_type| when a token is being saved for later use}
+@d level_boundary=3 {|save_type| corresponding to beginning of group}
+
+@ Here are the group codes that are used to discriminate between different
+kinds of groups. They allow \TeX\ to decide what special actions, if any,
+should be performed when a group ends.
+\def\grp{\.{\char'173...\char'175}}
+
+Some groups are not supposed to be ended by right braces. For example,
+the `\.\$' that begins a math formula causes a |math_shift_group| to
+be started, and this should be terminated by a matching `\.\$'. Similarly,
+a group that starts with \.{\\left} should end with \.{\\right}, and
+one that starts with \.{\\begingroup} should end with \.{\\endgroup}.
+
+@d bottom_level=0 {group code for the outside world}
+@d simple_group=1 {group code for local structure only}
+@d hbox_group=2 {code for `\.{\\hbox}\grp'}
+@d adjusted_hbox_group=3 {code for `\.{\\hbox}\grp' in vertical mode}
+@d vbox_group=4 {code for `\.{\\vbox}\grp'}
+@d vtop_group=5 {code for `\.{\\vtop}\grp'}
+@d align_group=6 {code for `\.{\\halign}\grp', `\.{\\valign}\grp'}
+@d no_align_group=7 {code for `\.{\\noalign}\grp'}
+@d output_group=8 {code for output routine}
+@d math_group=9 {code for, e.g, `\.{\char'136}\grp'}
+@d disc_group=10 {code for `\.{\\discretionary}\grp\grp\grp'}
+@d insert_group=11 {code for `\.{\\insert}\grp', `\.{\\vadjust}\grp'}
+@d vcenter_group=12 {code for `\.{\\vcenter}\grp'}
+@d math_choice_group=13 {code for `\.{\\mathchoice}\grp\grp\grp\grp'}
+@d semi_simple_group=14 {code for `\.{\\begingroup...\\endgroup}'}
+@d math_shift_group=15 {code for `\.{\$...\$}'}
+@d math_left_group=16 {code for `\.{\\left...\\right}'}
+@d max_group_code=16
+
+@<Types...@>=
+@!group_code=0..max_group_code; {|save_level| for a level boundary}
+
+@ The global variable |cur_group| keeps track of what sort of group we are
+currently in. Another global variable, |cur_boundary|, points to the
+topmost |level_boundary| word. And |cur_level| is the current depth of
+nesting. The routines are designed to preserve the condition that no entry
+in the |save_stack| or in |eqtb| ever has a level greater than |cur_level|.
+
+@ @<Glob...@>=
+@!save_stack : array[0..save_size] of memory_word;
+@!save_ptr : 0..save_size; {first unused entry on |save_stack|}
+@!max_save_stack:0..save_size; {maximum usage of save stack}
+@!cur_level: quarterword; {current nesting level for groups}
+@!cur_group: group_code; {current group type}
+@!cur_boundary: 0..save_size; {where the current level begins}
+
+@ At this time it might be a good idea for the reader to review the introduction
+to |eqtb| that was given above just before the long lists of parameter names.
+Recall that the ``outer level'' of the program is |level_one|, since
+undefined control sequences are assumed to be ``defined'' at |level_zero|.
+
+@<Set init...@>=
+save_ptr:=0; cur_level:=level_one; cur_group:=bottom_level; cur_boundary:=0;
+max_save_stack:=0;
+
+@ The following macro is used to test if there is room for up to six more
+entries on |save_stack|. By making a conservative test like this, we can
+get by with testing for overflow in only a few places.
+
+@d check_full_save_stack==if save_ptr>max_save_stack then
+ begin max_save_stack:=save_ptr;
+ if max_save_stack>save_size-6 then overflow("save size",save_size);
+@:TeX capacity exceeded save size}{\quad save size@>
+ end
+
+@ Procedure |new_save_level| is called when a group begins. The
+argument is a group identification code like `|hbox_group|'. After
+calling this routine, it is safe to put five more entries on |save_stack|.
+
+In some cases integer-valued items are placed onto the
+|save_stack| just below a |level_boundary| word, because this is a
+convenient place to keep information that is supposed to ``pop up'' just
+when the group has finished.
+For example, when `\.{\\hbox to 100pt}\grp' is being treated, the 100pt
+dimension is stored on |save_stack| just before |new_save_level| is
+called.
+
+We use the notation |saved(k)| to stand for an integer item that
+appears in location |save_ptr+k| of the save stack.
+
+@d saved(#)==save_stack[save_ptr+#].int
+
+@p procedure new_save_level(@!c:group_code); {begin a new level of grouping}
+begin check_full_save_stack;
+save_type(save_ptr):=level_boundary; save_level(save_ptr):=cur_group;
+save_index(save_ptr):=cur_boundary;
+if cur_level=max_quarterword then overflow("grouping levels",
+@:TeX capacity exceeded grouping levels}{\quad grouping levels@>
+ max_quarterword-min_quarterword);
+ {quit if |(cur_level+1)| is too big to be stored in |eqtb|}
+cur_boundary:=save_ptr; incr(cur_level); incr(save_ptr); cur_group:=c;
+end;
+
+@ Just before an entry of |eqtb| is changed, the following procedure should
+be called to update the other data structures properly. It is important
+to keep in mind that reference counts in |mem| include references from
+within |save_stack|, so these counts must be handled carefully.
+@^reference counts@>
+
+@p procedure eq_destroy(@!w:memory_word); {gets ready to forget |w|}
+var q:pointer; {|equiv| field of |w|}
+begin case eq_type_field(w) of
+call,long_call,outer_call,long_outer_call: delete_token_ref(equiv_field(w));
+glue_ref: delete_glue_ref(equiv_field(w));
+shape_ref: begin q:=equiv_field(w); {we need to free a \.{\\parshape} block}
+ if q<>null then free_node(q,info(q)+info(q)+1);
+ end; {such a block is |2n+1| words long, where |n=info(q)|}
+box_ref: flush_node_list(equiv_field(w));
+othercases do_nothing
+endcases;
+end;
+
+@ To save a value of |eqtb[p]| that was established at level |l|, we
+can use the following subroutine.
+
+@p procedure eq_save(@!p:pointer;@!l:quarterword); {saves |eqtb[p]|}
+begin check_full_save_stack;
+if l=level_zero then save_type(save_ptr):=restore_zero
+else begin save_stack[save_ptr]:=eqtb[p]; incr(save_ptr);
+ save_type(save_ptr):=restore_old_value;
+ end;
+save_level(save_ptr):=l; save_index(save_ptr):=p; incr(save_ptr);
+end;
+
+@ The procedure |eq_define| defines an |eqtb| entry having specified
+|eq_type| and |equiv| fields, and saves the former value if appropriate.
+This procedure is used only for entries in the first four regions of |eqtb|,
+i.e., only for entries that have |eq_type| and |equiv| fields.
+After calling this routine, it is safe to put four more entries on
+|save_stack|, provided that there was room for four more entries before
+the call, since |eq_save| makes the necessary test.
+
+@p procedure eq_define(@!p:pointer;@!t:quarterword;@!e:halfword);
+ {new data for |eqtb|}
+begin if eq_level(p)=cur_level then eq_destroy(eqtb[p])
+else if cur_level>level_one then eq_save(p,eq_level(p));
+eq_level(p):=cur_level; eq_type(p):=t; equiv(p):=e;
+end;
+
+@ The counterpart of |eq_define| for the remaining (fullword) positions in
+|eqtb| is called |eq_word_define|. Since |xeq_level[p]>=level_one| for all
+|p|, a `|restore_zero|' will never be used in this case.
+
+@p procedure eq_word_define(@!p:pointer;@!w:integer);
+begin if xeq_level[p]<>cur_level then
+ begin eq_save(p,xeq_level[p]); xeq_level[p]:=cur_level;
+ end;
+eqtb[p].int:=w;
+end;
+
+@ The |eq_define| and |eq_word_define| routines take care of local definitions.
+@^global definitions@>
+Global definitions are done in almost the same way, but there is no need
+to save old values, and the new value is associated with |level_one|.
+
+@p procedure geq_define(@!p:pointer;@!t:quarterword;@!e:halfword);
+ {global |eq_define|}
+begin eq_destroy(eqtb[p]);
+eq_level(p):=level_one; eq_type(p):=t; equiv(p):=e;
+end;
+@#
+procedure geq_word_define(@!p:pointer;@!w:integer); {global |eq_word_define|}
+begin eqtb[p].int:=w; xeq_level[p]:=level_one;
+end;
+
+@ Subroutine |save_for_after| puts a token on the stack for save-keeping.
+
+@p procedure save_for_after(@!t:halfword);
+begin if cur_level>level_one then
+ begin check_full_save_stack;
+ save_type(save_ptr):=insert_token; save_level(save_ptr):=level_zero;
+ save_index(save_ptr):=t; incr(save_ptr);
+ end;
+end;
+
+@ The |unsave| routine goes the other way, taking items off of |save_stack|.
+This routine takes care of restoration when a level ends; everything
+belonging to the topmost group is cleared off of the save stack.
+
+@p@t\4@>@<Declare the procedure called |restore_trace|@>@;@/
+procedure@?back_input; forward; @t\2@>
+procedure unsave; {pops the top level off the save stack}
+label done;
+var p:pointer; {position to be restored}
+@!l:quarterword; {saved level, if in fullword regions of |eqtb|}
+@!t:halfword; {saved value of |cur_tok|}
+begin if cur_level>level_one then
+ begin decr(cur_level);
+ @<Clear off top level from |save_stack|@>;
+ end
+else confusion("curlevel"); {|unsave| is not used when |cur_group=bottom_level|}
+@:this can't happen curlevel}{\quad curlevel@>
+end;
+
+@ @<Clear off...@>=
+loop@+begin decr(save_ptr);
+ if save_type(save_ptr)=level_boundary then goto done;
+ p:=save_index(save_ptr);
+ if save_type(save_ptr)=insert_token then
+ @<Insert token |p| into \TeX's input@>
+ else begin if save_type(save_ptr)=restore_old_value then
+ begin l:=save_level(save_ptr); decr(save_ptr);
+ end
+ else save_stack[save_ptr]:=eqtb[undefined_control_sequence];
+ @<Store \(s)|save_stack[save_ptr]| in |eqtb[p]|, unless
+ |eqtb[p]| holds a global value@>;
+ end;
+ end;
+done: cur_group:=save_level(save_ptr); cur_boundary:=save_index(save_ptr)
+
+@ A global definition, which sets the level to |level_one|,
+@^global definitions@>
+will not be undone by |unsave|. If at least one global definition of
+|eqtb[p]| has been carried out within the group that just ended, the
+last such definition will therefore survive.
+
+@<Store \(s)|save...@>=
+if p<int_base then
+ if eq_level(p)=level_one then
+ begin eq_destroy(save_stack[save_ptr]); {destroy the saved value}
+ @!stat if tracing_restores>0 then restore_trace(p,"retaining");@+tats@;@/
+ end
+ else begin eq_destroy(eqtb[p]); {destroy the current value}
+ eqtb[p]:=save_stack[save_ptr]; {restore the saved value}
+ @!stat if tracing_restores>0 then restore_trace(p,"restoring");@+tats@;@/
+ end
+else if xeq_level[p]<>level_one then
+ begin eqtb[p]:=save_stack[save_ptr]; xeq_level[p]:=l;
+ @!stat if tracing_restores>0 then restore_trace(p,"restoring");@+tats@;@/
+ end
+else begin
+ @!stat if tracing_restores>0 then restore_trace(p,"retaining");@+tats@;@/
+ end
+
+@ @<Declare the procedure called |restore_trace|@>=
+@!stat procedure restore_trace(@!p:pointer;@!s:str_number);
+ {|eqtb[p]| has just been restored or retained}
+begin begin_diagnostic; print_char("{"); print(s); print_char(" ");
+show_eqtb(p); print_char("}");
+end_diagnostic(false);
+end;
+tats
+
+@ When looking for possible pointers to a memory location, it is helpful
+to look for references from |eqtb| that might be waiting on the
+save stack. Of course, we might find spurious pointers too; but this
+routine is merely an aid when debugging, and at such times we are
+grateful for any scraps of information, even if they prove to be irrelevant.
+@^dirty \PASCAL@>
+
+@<Search |save_stack| for equivalents that point to |p|@>=
+if save_ptr>0 then for q:=0 to save_ptr-1 do
+ begin if equiv_field(save_stack[q])=p then
+ begin print_nl("SAVE("); print_int(q); print_char(")");
+ end;
+ end
+
+@ Most of the parameters kept in |eqtb| can be changed freely, but there's
+an exception: The magnification should not be used with two different
+values during any \TeX\ job, since a single magnification is applied to an
+entire run. The global variable |mag_set| is set to the current magnification
+whenever it becomes necessary to ``freeze'' it at a particular value.
+
+@<Glob...@>=
+@!mag_set:integer; {if nonzero, this magnification should be used henceforth}
+
+@ @<Set init...@>=
+mag_set:=0;
+
+@ The |prepare_mag| subroutine is called whenever \TeX\ wants to use |mag|
+for magnification.
+
+@p procedure prepare_mag;
+begin if (mag_set>0)and(mag<>mag_set) then
+ begin print_err("Incompatible magnification ("); print_int(mag);
+@.Incompatible magnification@>
+ print(");"); print_nl(" the previous value will be retained");
+ help2("I can handle only one magnification ratio per job. So I've")@/
+ ("reverted to the magnification you used earlier on this run.");@/
+ int_error(mag_set);
+ geq_word_define(int_base+mag_code,mag_set); {|mag:=mag_set|}
+ end;
+if (mag<=0)or(mag>32768) then
+ begin print_err("Illegal magnification has been changed to 1000");@/
+@.Illegal magnification...@>
+ help1("The magnification ratio must be between 1 and 32768.");
+ int_error(mag); geq_word_define(int_base+mag_code,1000);
+ end;
+mag_set:=mag;
+end;
+
+@* \[20] Token lists.
+A \TeX\ token is either a character or a control sequence, and it is
+@^token@>
+represented internally in one of two ways: (1)~A character whose ASCII
+code number is |c| and whose command code is |m| is represented as the
+number $2^8m+c$; the command code is in the range |1<=m<=14|. (2)~A control
+sequence whose |eqtb| address is |p| is represented as the number
+|cs_token_flag+p|. Here |cs_token_flag=@t$2^{12}-1$@>| is larger than
+$2^8m+c$, yet it is small enough that |cs_token_flag+p< max_halfword|;
+thus, a token fits comfortably in a halfword.
+
+A token |t| represents a |left_brace| command if and only if
+|t<left_brace_limit|; it represents a |right_brace| command if and only if
+we have |left_brace_limit<=t<right_brace_limit|; and it represents a |match| or
+|end_match| command if and only if |match_token<=t<=end_match_token|.
+The following definitions take care of these token-oriented constants
+and a few others.
+
+@d cs_token_flag==@'7777 {amount added to the |eqtb| location in a
+ token that stands for a control sequence; is a multiple of~256, less~1}
+@d left_brace_token=@'0400 {$2^8\cdot|left_brace|$}
+@d left_brace_limit=@'1000 {$2^8\cdot(|left_brace|+1)$}
+@d right_brace_token=@'1000 {$2^8\cdot|right_brace|$}
+@d right_brace_limit=@'1400 {$2^8\cdot(|right_brace|+1)$}
+@d math_shift_token=@'1400 {$2^8\cdot|math_shift|$}
+@d tab_token=@'2000 {$2^8\cdot|tab_mark|$}
+@d out_param_token=@'2400 {$2^8\cdot|out_param|$}
+@d space_token=@'5040 {$2^8\cdot|spacer|+|" "|$}
+@d letter_token=@'5400 {$2^8\cdot|letter|$}
+@d other_token=@'6000 {$2^8\cdot|other_char|$}
+@d match_token=@'6400 {$2^8\cdot|match|$}
+@d end_match_token=@'7000 {$2^8\cdot|end_match|$}
+
+@ @<Check the ``constant''...@>=
+if cs_token_flag+undefined_control_sequence>max_halfword then bad:=21;
+
+@ A token list is a singly linked list of one-word nodes in |mem|, where
+each word contains a token and a link. Macro definitions, output-routine
+definitions, marks, \.{\\write} texts, and a few other things
+are remembered by \TeX\ in the form
+of token lists, usually preceded by a node with a reference count in its
+|token_ref_count| field. The token stored in location |p| is called
+|info(p)|.
+
+Three special commands appear in the token lists of macro definitions.
+When |m=match|, it means that \TeX\ should scan a parameter
+for the current macro; when |m=end_match|, it means that parameter
+matching should end and \TeX\ should start reading the macro text; and
+when |m=out_param|, it means that \TeX\ should insert parameter
+number |c| into the text at this point.
+
+The enclosing \.{\char'173} and \.{\char'175} characters of a macro
+definition are omitted, but the final right brace of an output routine
+is included at the end of its token list.
+
+Here is an example macro definition that illustrates these conventions.
+After \TeX\ processes the text
+$$\.{\\def\\mac a\#1\#2 \\b \{\#1\\-a \#\#1\#2 \#2\}}$$
+the definition of \.{\\mac} is represented as a token list containing
+$$\def\,{\hskip2pt}
+\vbox{\halign{\hfil#\hfil\cr
+(reference count), |letter|\,\.a, |match|\,\#, |match|\,\#, |spacer|\,\.\ ,
+\.{\\b}, |end_match|,\cr
+|out_param|\,1, \.{\\-}, |letter|\,\.a, |spacer|\,\.\ , |mac_param|\,\#,
+|other_char|\,\.1,\cr
+|out_param|\,2, |spacer|\,\.\ , |out_param|\,2.\cr}}$$
+The procedure |scan_toks| builds such token lists, and |macro_call|
+does the parameter matching.
+@^reference counts@>
+
+Examples such as
+$$\.{\\def\\m\{\\def\\m\{a\}\ b\}}$$
+explain why reference counts would be needed even if \TeX\ had no \.{\\let}
+operation: When the token list for \.{\\m} is being read, the redefinition of
+\.{\\m} changes the |eqtb| entry before the token list has been fully
+consumed, so we dare not simply destroy a token list when its
+control sequence is being redefined.
+
+If the parameter-matching part of a definition ends with `\.{\#\{}',
+the corresponding token list will have `\.\{' just before the `|end_match|'
+and also at the very end. The first `\.\{' is used to delimit the parameter; the
+second one keeps the first from disappearing.
+
+@ The procedure |show_token_list|, which prints a symbolic form of
+the token list that starts at a given node |p|, illustrates these
+conventions. The token list being displayed should not begin with a reference
+count. However, the procedure is intended to be robust, so that if the
+memory links are awry or if |p| is not really a pointer to a token list,
+nothing catastrophic will happen.
+
+An additional parameter |q| is also given; this parameter is either null
+or it points to a node in the token list where a certain magic computation
+takes place that will be explained later. (Basically, |q| is non-null when
+we are printing the two-line context information at the time of an error
+message; |q| marks the place corresponding to where the second line
+should begin.)
+
+For example, if |p| points to the node containing the first \.a in the
+token list above, then |show_token_list| will print the string
+$$\hbox{`\.{a\#1\#2\ \\b\ ->\#1\\-a\ \#\#1\#2\ \#2}';}$$
+and if |q| points to the node containing the second \.a,
+the magic computation will be performed just before the second \.a is printed.
+
+The generation will stop, and `\.{\\ETC.}' will be printed, if the length
+of printing exceeds a given limit~|l|. Anomalous entries are printed in the
+form of control sequences that are not followed by a blank space, e.g.,
+`\.{\\BAD.}'; this cannot be confused with actual control sequences because
+a real control sequence named \.{BAD} would come out `\.{\\BAD\ }'.
+
+@<Declare the procedure called |show_token_list|@>=
+procedure show_token_list(@!p,@!q:integer;@!l:integer);
+label exit;
+var m,@!c:integer; {pieces of a token}
+@!match_chr:ASCII_code; {character used in a `|match|'}
+@!n:ASCII_code; {the highest parameter number, as an ASCII digit}
+begin match_chr:="#"; n:="0"; tally:=0;
+while (p<>null) and (tally<l) do
+ begin if p=q then @<Do magic computation@>;
+ @<Display token |p|, and |return| if there are problems@>;
+ p:=link(p);
+ end;
+if p<>null then print_esc("ETC.");
+@.ETC@>
+exit:
+end;
+
+@ @<Display token |p|...@>=
+if (p<hi_mem_min) or (p>mem_end) then
+ begin print_esc("CLOBBERED."); return;
+@.CLOBBERED@>
+ end;
+if info(p)>=cs_token_flag then print_cs(info(p)-cs_token_flag)
+else begin m:=info(p) div @'400; c:=info(p) mod @'400;
+ if info(p)<0 then print_esc("BAD.")
+@.BAD@>
+ else @<Display the token $(|m|,|c|)$@>;
+ end
+
+@ The procedure usually ``learns'' the character code used for macro
+parameters by seeing one in a |match| command before it runs into any
+|out_param| commands.
+
+@<Display the token ...@>=
+case m of
+left_brace,right_brace,math_shift,tab_mark,sup_mark,sub_mark,spacer,
+ letter,other_char: print(c);
+mac_param: begin print(c); print(c);
+ end;
+out_param: begin print(match_chr);
+ if c<=9 then print_char(c+"0")
+ else begin print_char("!"); return;
+ end;
+ end;
+match: begin match_chr:=c; print(c); incr(n); print_char(n);
+ if n>"9" then return;
+ end;
+end_match: print("->");
+@.->@>
+othercases print_esc("BAD.")
+@.BAD@>
+endcases
+
+@ Here's the way we sometimes want to display a token list, given a pointer
+to its reference count; the pointer may be null.
+
+@p procedure token_show(@!p:pointer);
+begin if p<>null then show_token_list(link(p),null,10000000);
+end;
+
+@ The |print_meaning| subroutine displays |cur_cmd| and |cur_chr| in
+symbolic form, including the expansion of a macro or mark.
+
+@p procedure print_meaning;
+begin print_cmd_chr(cur_cmd,cur_chr);
+if cur_cmd>=call then
+ begin print_char(":"); print_ln; token_show(cur_chr);
+ end
+else if cur_cmd=top_bot_mark then
+ begin print_char(":"); print_ln;
+ token_show(cur_mark[cur_chr]);
+ end;
+end;
+
+@* \[21] Introduction to the syntactic routines.
+Let's pause a moment now and try to look at the Big Picture.
+The \TeX\ program consists of three main parts: syntactic routines,
+semantic routines, and output routines. The chief purpose of the
+syntactic routines is to deliver the user's input to the semantic routines,
+one token at a time. The semantic routines act as an interpreter
+responding to these tokens, which may be regarded as commands. And the
+output routines are periodically called on to convert box-and-glue
+lists into a compact set of instructions that will be sent
+to a typesetter. We have discussed the basic data structures and utility
+routines of \TeX, so we are good and ready to plunge into the real activity by
+considering the syntactic routines.
+
+Our current goal is to come to grips with the |get_next| procedure,
+which is the keystone of \TeX's input mechanism. Each call of |get_next|
+sets the value of three variables |cur_cmd|, |cur_chr|, and |cur_cs|,
+representing the next input token.
+$$\vbox{\halign{#\hfil\cr
+ \hbox{|cur_cmd| denotes a command code from the long list of codes
+ given above;}\cr
+ \hbox{|cur_chr| denotes a character code or other modifier of the command
+ code;}\cr
+ \hbox{|cur_cs| is the |eqtb| location of the current control sequence,}\cr
+ \hbox{\qquad if the current token was a control sequence,
+ otherwise it's zero.}\cr}}$$
+Underlying this external behavior of |get_next| is all the machinery
+necessary to convert from character files to tokens. At a given time we
+may be only partially finished with the reading of several files (for
+which \.{\\input} was specified), and partially finished with the expansion
+of some user-defined macros and/or some macro parameters, and partially
+finished with the generation of some text in a template for \.{\\halign},
+and so on. When reading a character file, special characters must be
+classified as math delimiters, etc.; comments and extra blank spaces must
+be removed, paragraphs must be recognized, and control sequences must be
+found in the hash table. Furthermore there are occasions in which the
+scanning routines have looked ahead for a word like `\.{plus}' but only
+part of that word was found, hence a few characters must be put back
+into the input and scanned again.
+
+To handle these situations, which might all be present simultaneously,
+\TeX\ uses various stacks that hold information about the incomplete
+activities, and there is a finite state control for each level of the
+input mechanism. These stacks record the current state of an implicitly
+recursive process, but the |get_next| procedure is not recursive.
+Therefore it will not be difficult to translate these algorithms into
+low-level languages that do not support recursion.
+
+@<Glob...@>=
+@!cur_cmd: eight_bits; {current command set by |get_next|}
+@!cur_chr: halfword; {operand of current command}
+@!cur_cs: pointer; {control sequence found here, zero if none found}
+@!cur_tok: halfword; {packed representative of |cur_cmd| and |cur_chr|}
+
+@ The |print_cmd_chr| routine prints a symbolic interpretation of a
+command code and its modifier. This is used in certain `\.{You can\'t}'
+error messages, and in the implementation of diagnostic routines like
+\.{\\show}.
+
+The body of |print_cmd_chr| is a rather tedious listing of print
+commands, and most of it is essentially an inverse to the |primitive|
+routine that enters a \TeX\ primitive into |eqtb|. Therefore much of
+this procedure appears elsewhere in the program,
+together with the corresponding |primitive| calls.
+
+@d chr_cmd(#)==begin print(#); print_ASCII(chr_code);
+ end
+
+@<Declare the procedure called |print_cmd_chr|@>=
+procedure print_cmd_chr(@!cmd:quarterword;@!chr_code:halfword);
+begin case cmd of
+left_brace: chr_cmd("begin-group character ");
+right_brace: chr_cmd("end-group character ");
+math_shift: chr_cmd("math shift character ");
+mac_param: chr_cmd("macro parameter character ");
+sup_mark: chr_cmd("superscript character ");
+sub_mark: chr_cmd("subscript character ");
+endv: print("end of alignment template");
+spacer: chr_cmd("blank space ");
+letter: chr_cmd("the letter ");
+other_char: chr_cmd("the character ");
+@t\4@>@<Cases of |print_cmd_chr| for symbolic printing of primitives@>@/
+othercases print("[unknown command code!]")
+endcases;
+end;
+
+@ Here is a procedure that displays the current command.
+
+@p procedure show_cur_cmd_chr;
+begin begin_diagnostic; print_nl("{");
+if mode<>shown_mode then
+ begin print_mode(mode); print(": "); shown_mode:=mode;
+ end;
+print_cmd_chr(cur_cmd,cur_chr); print_char("}");
+end_diagnostic(false);
+end;
+
+@* \[22] Input stacks and states.
+This implementation of
+\TeX\ uses two different conventions for representing sequential stacks.
+@^stack conventions@>@^conventions for representing stacks@>
+
+\yskip\hangg 1) If there is frequent access to the top entry, and if the
+stack is essentially never empty, then the top entry is kept in a global
+variable (even better would be a machine register), and the other entries
+appear in the array $\\{stack}[0\to(\\{ptr}-1)]$. For example, the
+semantic stack described above is handled this way, and so is the input
+stack that we are about to study.
+
+\yskip\hangg 2) If there is infrequent top access, the entire stack contents
+are in the array $\\{stack}[0\to(\\{ptr}-1)]$. For example, the |save_stack|
+is treated this way, as we have seen.
+
+\yskip\noindent
+The state of \TeX's input mechanism appears in the input stack, whose
+entries are records with six fields, called |state|, |index|, |start|, |loc|,
+|limit|, and |name|. This stack is maintained with
+convention~(1), so it is declared in the following way:
+
+@<Types...@>=
+@!in_state_record = record
+ @!state_field, @!index_field: quarterword;
+ @!start_field,@!loc_field, @!limit_field, @!name_field: halfword;
+ end;
+
+@ @<Glob...@>=
+@!input_stack : array[0..stack_size] of in_state_record;
+@!input_ptr : 0..stack_size; {first unused location of |input_stack|}
+@!max_in_stack: 0..stack_size; {largest value of |input_ptr| when pushing}
+@!cur_input : in_state_record;
+ {the ``top'' input state, according to convention (1)}
+
+@ We've already defined the special variable |loc==cur_input.loc_field|
+in our discussion of basic input-output routines. The other components of
+|cur_input| are defined in the same way:
+
+@d state==cur_input.state_field {current scanner state}
+@d index==cur_input.index_field {reference for buffer information}
+@d start==cur_input.start_field {starting position in |buffer|}
+@d limit==cur_input.limit_field {end of current line in |buffer|}
+@d name==cur_input.name_field {name of the current file}
+
+@ Let's look more closely now at the control variables
+(|state|,~|index|,~|start|,~|loc|,~|limit|,~|name|),
+assuming that \TeX\ is reading a line of characters that have been input
+from some file or from the user's terminal. There is an array called
+|buffer| that acts as a stack of all lines of characters that are
+currently being read from files, including all lines on subsidiary
+levels of the input stack that are not yet completed. \TeX\ will return to
+the other lines when it is finished with the present input file.
+
+(Incidentally, on a machine with byte-oriented addressing, it might be
+appropriate to combine |buffer| with the |str_pool| array,
+letting the buffer entries grow downward from the top of the string pool
+and checking that these two tables don't bump into each other.)
+
+The line we are currently working on begins in position |start| of the
+buffer; the next character we are about to read is |buffer[loc]|; and
+|limit| is the location of the last character present. If |loc>limit|,
+the line has been completely read. Usually |buffer[limit]| is the
+|end_line_char|, denoting the end of a line, but this is not
+true if the current line is an insertion that was entered on the user's
+terminal in response to an error message.
+
+The |name| variable is a string number that designates the name of
+the current file, if we are reading a text file. It is zero if we
+are reading from the terminal; it is |n+1| if we are reading from
+input stream |n|, where |0<=n<=16|. (Input stream 16 stands for
+an invalid stream number; in such cases the input is actually from
+the terminal, under control of the procedure |read_toks|.)
+
+The |state| variable has one of three values, when we are scanning such
+files:
+$$\baselineskip 15pt\vbox{\halign{#\hfil\cr
+1) |state=mid_line| is the normal state.\cr
+2) |state=skip_blanks| is like |mid_line|, but blanks are ignored.\cr
+3) |state=new_line| is the state at the beginning of a line.\cr}}$$
+These state values are assigned numeric codes so that if we add the state
+code to the next character's command code, we get distinct values. For
+example, `|mid_line+spacer|' stands for the case that a blank
+space character occurs in the middle of a line when it is not being
+ignored; after this case is processed, the next value of |state| will
+be |skip_blanks|.
+
+@d mid_line=1 {|state| code when scanning a line of characters}
+@d skip_blanks=2+max_char_code {|state| code when ignoring blanks}
+@d new_line=3+max_char_code+max_char_code {|state| code at start of line}
+
+@ Additional information about the current line is available via the
+|index| variable, which counts how many lines of characters are present
+in the buffer below the current level. We have |index=0| when reading
+from the terminal and prompting the user for each line; then if the user types,
+e.g., `\.{\\input paper}', we will have |index=1| while reading
+the file \.{paper.tex}. However, it does not follow that |index| is the
+same as the input stack pointer, since many of the levels on the input
+stack may come from token lists. For example, the instruction `\.{\\input
+paper}' might occur in a token list.
+
+The global variable |in_open| is equal to the |index|
+value of the highest non-token-list level. Thus, the number of partially read
+lines in the buffer is |in_open+1|, and we have |in_open=index|
+when we are not reading a token list.
+
+If we are not currently reading from the terminal, or from an input
+stream, we are reading from the file variable |input_file[index]|. We use
+the notation |terminal_input| as a convenient abbreviation for |name=0|,
+and |cur_file| as an abbreviation for |input_file[index]|.
+
+The global variable |line| contains the line number in the topmost
+open file, for use in error messages. If we are not reading from
+the terminal, |line_stack[index]| holds the line number for the
+enclosing level, so that |line| can be restored when the current
+file has been read. Line numbers should never be negative, since the
+negative of the current line number is used to identify the user's output
+routine in the |mode_line| field of the semantic nest entries.
+
+If more information about the input state is needed, it can be
+included in small arrays like those shown here. For example,
+the current page or segment number in the input file might be
+put into a variable |@!page|, maintained for enclosing levels in
+`\ignorespaces|@!page_stack:array[1..max_in_open] of integer|\unskip'
+by analogy with |line_stack|.
+@^system dependencies@>
+
+@d terminal_input==(name=0) {are we reading from the terminal?}
+@d cur_file==input_file[index] {the current |alpha_file| variable}
+
+@<Glob...@>=
+@!in_open : 0..max_in_open; {the number of lines in the buffer, less one}
+@!open_parens : 0..max_in_open; {the number of open text files}
+@!input_file : array[1..max_in_open] of alpha_file;
+@!line : integer; {current line number in the current source file}
+@!line_stack : array[1..max_in_open] of integer;
+
+@ Users of \TeX\ sometimes forget to balance left and right braces properly,
+and one of the ways \TeX\ tries to spot such errors is by considering an
+input file as broken into subfiles by control sequences that
+are declared to be \.{\\outer}.
+
+A variable called |scanner_status| tells \TeX\ whether or not to complain
+when a subfile ends. This variable has six possible values:
+
+\yskip\hang|normal|, means that a subfile can safely end here without incident.
+
+\yskip\hang|skipping|, means that a subfile can safely end here, but not a file,
+because we're reading past some conditional text that was not selected.
+
+\yskip\hang|defining|, means that a subfile shouldn't end now because a
+macro is being defined.
+
+\yskip\hang|matching|, means that a subfile shouldn't end now because a
+macro is being used and we are searching for the end of its arguments.
+
+\yskip\hang|aligning|, means that a subfile shouldn't end now because we are
+not finished with the preamble of an \.{\\halign} or \.{\\valign}.
+
+\yskip\hang|absorbing|, means that a subfile shouldn't end now because we are
+reading a balanced token list for \.{\\message}, \.{\\write}, etc.
+
+\yskip\noindent
+If the |scanner_status| is not |normal|, the variable |warning_index| points
+to the |eqtb| location for the relevant control sequence name to print
+in an error message.
+
+@d skipping=1 {|scanner_status| when passing conditional text}
+@d defining=2 {|scanner_status| when reading a macro definition}
+@d matching=3 {|scanner_status| when reading macro arguments}
+@d aligning=4 {|scanner_status| when reading an alignment preamble}
+@d absorbing=5 {|scanner_status| when reading a balanced text}
+
+@<Glob...@>=
+@!scanner_status : normal..absorbing; {can a subfile end now?}
+@!warning_index : pointer; {identifier relevant to non-|normal| scanner status}
+@!def_ref : pointer; {reference count of token list being defined}
+
+@ Here is a procedure that uses |scanner_status| to print a warning message
+when a subfile has ended, and at certain other crucial times:
+
+@<Declare the procedure called |runaway|@>=
+procedure runaway;
+var p:pointer; {head of runaway list}
+begin if scanner_status>skipping then
+ begin print_nl("Runaway ");
+@.Runaway...@>
+ case scanner_status of
+ defining: begin print("definition"); p:=def_ref;
+ end;
+ matching: begin print("argument"); p:=temp_head;
+ end;
+ aligning: begin print("preamble"); p:=hold_head;
+ end;
+ absorbing: begin print("text"); p:=def_ref;
+ end;
+ end; {there are no other cases}
+ print_char("?");print_ln; show_token_list(link(p),null,error_line-10);
+ end;
+end;
+
+@ However, all this discussion about input state really applies only to the
+case that we are inputting from a file. There is another important case,
+namely when we are currently getting input from a token list. In this case
+|state=token_list|, and the conventions about the other state variables
+are different:
+
+\yskip\hang|loc| is a pointer to the current node in the token list, i.e.,
+the node that will be read next. If |loc=null|, the token list has been
+fully read.
+
+\yskip\hang|start| points to the first node of the token list; this node
+may or may not contain a reference count, depending on the type of token
+list involved.
+
+\yskip\hang|token_type|, which takes the place of |index| in the
+discussion above, is a code number that explains what kind of token list
+is being scanned.
+
+\yskip\hang|name| points to the |eqtb| address of the control sequence
+being expanded, if the current token list is a macro.
+
+\yskip\hang|param_start|, which takes the place of |limit|, tells where
+the parameters of the current macro begin in the |param_stack|, if the
+current token list is a macro.
+
+\yskip\noindent The |token_type| can take several values, depending on
+where the current token list came from:
+
+\yskip\hang|parameter|, if a parameter is being scanned;
+
+\hang|u_template|, if the \<u_j> part of an alignment
+template is being scanned;
+
+\hang|v_template|, if the \<v_j> part of an alignment
+template is being scanned;
+
+\hang|backed_up|, if the token list being scanned has been inserted as
+`to be read again'.
+
+\hang|inserted|, if the token list being scanned has been inserted as
+the text expansion of a \.{\\count} or similar variable;
+
+\hang|macro|, if a user-defined control sequence is being scanned;
+
+\hang|output_text|, if an \.{\\output} routine is being scanned;
+
+\hang|every_par_text|, if the text of \.{\\everypar} is being scanned;
+
+\hang|every_math_text|, if the text of \.{\\everymath} is being scanned;
+
+\hang|every_display_text|, if the text of \.{\\everydisplay} is being scanned;
+
+\hang|every_hbox_text|, if the text of \.{\\everyhbox} is being scanned;
+
+\hang|every_vbox_text|, if the text of \.{\\everyvbox} is being scanned;
+
+\hang|every_job_text|, if the text of \.{\\everyjob} is being scanned;
+
+\hang|every_cr_text|, if the text of \.{\\everycr} is being scanned;
+
+\hang|mark_text|, if the text of a \.{\\mark} is being scanned;
+
+\hang|write_text|, if the text of a \.{\\write} is being scanned.
+
+\yskip\noindent
+The codes for |output_text|, |every_par_text|, etc., are equal to a constant
+plus the corresponding codes for token list parameters |output_routine_loc|,
+|every_par_loc|, etc. The token list begins with a reference count if and
+only if |token_type>=macro|.
+@^reference counts@>
+
+@d token_list=0 {|state| code when scanning a token list}
+@d token_type==index {type of current token list}
+@d param_start==limit {base of macro parameters in |param_stack|}
+@d parameter=0 {|token_type| code for parameter}
+@d u_template=1 {|token_type| code for \<u_j> template}
+@d v_template=2 {|token_type| code for \<v_j> template}
+@d backed_up=3 {|token_type| code for text to be reread}
+@d inserted=4 {|token_type| code for inserted texts}
+@d macro=5 {|token_type| code for defined control sequences}
+@d output_text=6 {|token_type| code for output routines}
+@d every_par_text=7 {|token_type| code for \.{\\everypar}}
+@d every_math_text=8 {|token_type| code for \.{\\everymath}}
+@d every_display_text=9 {|token_type| code for \.{\\everydisplay}}
+@d every_hbox_text=10 {|token_type| code for \.{\\everyhbox}}
+@d every_vbox_text=11 {|token_type| code for \.{\\everyvbox}}
+@d every_job_text=12 {|token_type| code for \.{\\everyjob}}
+@d every_cr_text=13 {|token_type| code for \.{\\everycr}}
+@d mark_text=14 {|token_type| code for \.{\\topmark}, etc.}
+@d write_text=15 {|token_type| code for \.{\\write}}
+
+@ The |param_stack| is an auxiliary array used to hold pointers to the token
+lists for parameters at the current level and subsidiary levels of input.
+This stack is maintained with convention (2), and it grows at a different
+rate from the others.
+
+@<Glob...@>=
+@!param_stack:array [0..param_size] of pointer;
+ {token list pointers for parameters}
+@!param_ptr:0..param_size; {first unused entry in |param_stack|}
+@!max_param_stack:integer;
+ {largest value of |param_ptr|, will be |<=param_size+9|}
+
+@ The input routines must also interact with the processing of
+\.{\\halign} and \.{\\valign}, since the appearance of tab marks and
+\.{\\cr} in certain places is supposed to trigger the beginning of special
+\<v_j> template text in the scanner. This magic is accomplished by an
+|align_state| variable that is increased by~1 when a `\.{\char'173}' is
+scanned and decreased by~1 when a `\.{\char'175}' is scanned. The |align_state|
+is nonzero during the \<u_j> template, after which it is set to zero; the
+\<v_j> template begins when a tab mark or \.{\\cr} occurs at a time that
+|align_state=0|.
+
+@<Glob...@>=
+@!align_state:integer; {group level with respect to current alignment}
+
+@ Thus, the ``current input state'' can be very complicated indeed; there
+can be many levels and each level can arise in a variety of ways. The
+|show_context| procedure, which is used by \TeX's error-reporting routine to
+print out the current input state on all levels down to the most recent
+line of characters from an input file, illustrates most of these conventions.
+The global variable |base_ptr| contains the lowest level that was
+displayed by this procedure.
+
+@<Glob...@>=
+@!base_ptr:0..stack_size; {shallowest level shown by |show_context|}
+
+@ The status at each level is indicated by printing two lines, where the first
+line indicates what was read so far and the second line shows what remains
+to be read. The context is cropped, if necessary, so that the first line
+contains at most |half_error_line| characters, and the second contains
+at most |error_line|. Non-current input levels whose |token_type| is
+`|backed_up|' are shown only if they have not been fully read.
+
+@p procedure show_context; {prints where the scanner is}
+label done;
+var old_setting:0..max_selector; {saved |selector| setting}
+@!nn:integer; {number of contexts shown so far, less one}
+@!bottom_line:boolean; {have we reached the final context to be shown?}
+@<Local variables for formatting calculations@>@/
+begin base_ptr:=input_ptr; input_stack[base_ptr]:=cur_input;
+ {store current state}
+nn:=-1; bottom_line:=false;
+loop@+begin cur_input:=input_stack[base_ptr]; {enter into the context}
+ if (state<>token_list) then
+ if (name>17) or (base_ptr=0) then bottom_line:=true;
+ if (base_ptr=input_ptr)or bottom_line or(nn<error_context_lines) then
+ @<Display the current context@>
+ else if nn=error_context_lines then
+ begin print_nl("..."); incr(nn); {omitted if |error_context_lines<0|}
+ end;
+ if bottom_line then goto done;
+ decr(base_ptr);
+ end;
+done: cur_input:=input_stack[input_ptr]; {restore original state}
+end;
+
+@ @<Display the current context@>=
+begin if (base_ptr=input_ptr) or (state<>token_list) or
+ (token_type<>backed_up) or (loc<>null) then
+ {we omit backed-up token lists that have already been read}
+ begin tally:=0; {get ready to count characters}
+ old_setting:=selector;
+ if state<>token_list then
+ begin @<Print location of current line@>;
+ @<Pseudoprint the line@>;
+ end
+ else begin @<Print type of token list@>;
+ @<Pseudoprint the token list@>;
+ end;
+ selector:=old_setting; {stop pseudoprinting}
+ @<Print two lines using the tricky pseudoprinted information@>;
+ incr(nn);
+ end;
+end
+
+@ This routine should be changed, if necessary, to give the best possible
+indication of where the current line resides in the input file.
+For example, on some systems it is best to print both a page and line number.
+@^system dependencies@>
+
+@<Print location of current line@>=
+if name<=17 then
+ if terminal_input then
+ if base_ptr=0 then print_nl("<*>") else print_nl("<insert> ")
+ else begin print_nl("<read ");
+ if name=17 then print_char("*")@+else print_int(name-1);
+@.*\relax@>
+ print_char(">");
+ end
+else begin print_nl("l."); print_int(line);
+ end;
+print_char(" ")
+
+@ @<Print type of token list@>=
+case token_type of
+parameter: print_nl("<argument> ");
+u_template,v_template: print_nl("<template> ");
+backed_up: if loc=null then print_nl("<recently read> ")
+ else print_nl("<to be read again> ");
+inserted: print_nl("<inserted text> ");
+macro: begin print_ln; print_cs(name);
+ end;
+output_text: print_nl("<output> ");
+every_par_text: print_nl("<everypar> ");
+every_math_text: print_nl("<everymath> ");
+every_display_text: print_nl("<everydisplay> ");
+every_hbox_text: print_nl("<everyhbox> ");
+every_vbox_text: print_nl("<everyvbox> ");
+every_job_text: print_nl("<everyjob> ");
+every_cr_text: print_nl("<everycr> ");
+mark_text: print_nl("<mark> ");
+write_text: print_nl("<write> ");
+othercases print_nl("?") {this should never happen}
+endcases
+
+@ Here it is necessary to explain a little trick. We don't want to store a long
+string that corresponds to a token list, because that string might take up
+lots of memory; and we are printing during a time when an error message is
+being given, so we dare not do anything that might overflow one of \TeX's
+tables. So `pseudoprinting' is the answer: We enter a mode of printing
+that stores characters into a buffer of length |error_line|, where character
+$k+1$ is placed into \hbox{|trick_buf[k mod error_line]|} if
+|k<trick_count|, otherwise character |k| is dropped. Initially we set
+|tally:=0| and |trick_count:=1000000|; then when we reach the
+point where transition from line 1 to line 2 should occur, we
+set |first_count:=tally| and |trick_count:=@tmax@>(error_line,
+tally+1+error_line-half_error_line)|. At the end of the
+pseudoprinting, the values of |first_count|, |tally|, and
+|trick_count| give us all the information we need to print the two lines,
+and all of the necessary text is in |trick_buf|.
+
+Namely, let |l| be the length of the descriptive information that appears
+on the first line. The length of the context information gathered for that
+line is |k=first_count|, and the length of the context information
+gathered for line~2 is $m=\min(|tally|, |trick_count|)-k$. If |l+k<=h|,
+where |h=half_error_line|, we print |trick_buf[0..k-1]| after the
+descriptive information on line~1, and set |n:=l+k|; here |n| is the
+length of line~1. If $l+k>h$, some cropping is necessary, so we set |n:=h|
+and print `\.{...}' followed by
+$$\hbox{|trick_buf[(l+k-h+3)..k-1]|,}$$
+where subscripts of |trick_buf| are circular modulo |error_line|. The
+second line consists of |n|~spaces followed by |trick_buf[k..(k+m-1)]|,
+unless |n+m>error_line|; in the latter case, further cropping is done.
+This is easier to program than to explain.
+
+@<Local variables for formatting...@>=
+@!i:0..buf_size; {index into |buffer|}
+@!j:0..buf_size; {end of current line in |buffer|}
+@!l:0..half_error_line; {length of descriptive information on line 1}
+@!m:integer; {context information gathered for line 2}
+@!n:0..error_line; {length of line 1}
+@!p: integer; {starting or ending place in |trick_buf|}
+@!q: integer; {temporary index}
+
+@ The following code sets up the print routines so that they will gather
+the desired information.
+
+@d begin_pseudoprint==
+ begin l:=tally; tally:=0; selector:=pseudo;
+ trick_count:=1000000;
+ end
+@d set_trick_count==
+ begin first_count:=tally;
+ trick_count:=tally+1+error_line-half_error_line;
+ if trick_count<error_line then trick_count:=error_line;
+ end
+
+@ And the following code uses the information after it has been gathered.
+
+@<Print two lines using the tricky pseudoprinted information@>=
+if trick_count=1000000 then set_trick_count;
+ {|set_trick_count| must be performed}
+if tally<trick_count then m:=tally-first_count
+else m:=trick_count-first_count; {context on line 2}
+if l+first_count<=half_error_line then
+ begin p:=0; n:=l+first_count;
+ end
+else begin print("..."); p:=l+first_count-half_error_line+3;
+ n:=half_error_line;
+ end;
+for q:=p to first_count-1 do print_char(trick_buf[q mod error_line]);
+print_ln;
+for q:=1 to n do print_char(" "); {print |n| spaces to begin line~2}
+if m+n<=error_line then p:=first_count+m else p:=first_count+(error_line-n-3);
+for q:=first_count to p-1 do print_char(trick_buf[q mod error_line]);
+if m+n>error_line then print("...")
+
+@ But the trick is distracting us from our current goal, which is to
+understand the input state. So let's concentrate on the data structures that
+are being pseudoprinted as we finish up the |show_context| procedure.
+
+@<Pseudoprint the line@>=
+begin_pseudoprint;
+if buffer[limit]=end_line_char then j:=limit
+else j:=limit+1; {determine the effective end of the line}
+if j>0 then for i:=start to j-1 do
+ begin if i=loc then set_trick_count;
+ print(buffer[i]);
+ end
+
+@ @<Pseudoprint the token list@>=
+begin_pseudoprint;
+if token_type<macro then show_token_list(start,loc,100000)
+else show_token_list(link(start),loc,100000) {avoid reference count}
+
+@ Here is the missing piece of |show_token_list| that is activated when the
+token beginning line~2 is about to be shown:
+
+@<Do magic computation@>=set_trick_count
+
+@* \[23] Maintaining the input stacks.
+The following subroutines change the input status in commonly needed ways.
+
+First comes |push_input|, which stores the current state and creates a
+new level (having, initially, the same properties as the old).
+
+@d push_input==@t@> {enter a new input level, save the old}
+ begin if input_ptr>max_in_stack then
+ begin max_in_stack:=input_ptr;
+ if input_ptr=stack_size then overflow("input stack size",stack_size);
+@:TeX capacity exceeded input stack size}{\quad input stack size@>
+ end;
+ input_stack[input_ptr]:=cur_input; {stack the record}
+ incr(input_ptr);
+ end
+
+@ And of course what goes up must come down.
+
+@d pop_input==@t@> {leave an input level, re-enter the old}
+ begin decr(input_ptr); cur_input:=input_stack[input_ptr];
+ end
+
+@ Here is a procedure that starts a new level of token-list input, given
+a token list |p| and its type |t|. If |t=macro|, the calling routine should
+set |name| and |loc|.
+
+@d back_list(#)==begin_token_list(#,backed_up) {backs up a simple token list}
+@d ins_list(#)==begin_token_list(#,inserted) {inserts a simple token list}
+
+@p procedure begin_token_list(@!p:pointer;@!t:quarterword);
+begin push_input; state:=token_list; start:=p; token_type:=t;
+if t>=macro then {the token list starts with a reference count}
+ begin add_token_ref(p);
+ if t=macro then param_start:=param_ptr
+ else begin loc:=link(p);
+ if tracing_macros>1 then
+ begin begin_diagnostic; print_nl("");
+ case t of
+ mark_text:print_esc("mark");
+ write_text:print_esc("write");
+ othercases print_cmd_chr(assign_toks,t-output_text+output_routine_loc)
+ endcases;@/
+ print("->"); token_show(p); end_diagnostic(false);
+ end;
+ end;
+ end
+else loc:=p;
+end;
+
+@ When a token list has been fully scanned, the following computations
+should be done as we leave that level of input. The |token_type| tends
+to be equal to either |backed_up| or |inserted| about 2/3 of the time.
+@^inner loop@>
+
+@p procedure end_token_list; {leave a token-list input level}
+begin if token_type>=backed_up then {token list to be deleted}
+ begin if token_type<=inserted then flush_list(start)
+ else begin delete_token_ref(start); {update reference count}
+ if token_type=macro then {parameters must be flushed}
+ while param_ptr>param_start do
+ begin decr(param_ptr);
+ flush_list(param_stack[param_ptr]);
+ end;
+ end;
+ end
+else if token_type=u_template then
+ if align_state>500000 then align_state:=0
+ else fatal_error("(interwoven alignment preambles are not allowed)");
+@.interwoven alignment preambles...@>
+pop_input;
+check_interrupt;
+end;
+
+@ Sometimes \TeX\ has read too far and wants to ``unscan'' what it has
+seen. The |back_input| procedure takes care of this by putting the token
+just scanned back into the input stream, ready to be read again. This
+procedure can be used only if |cur_tok| represents the token to be
+replaced. Some applications of \TeX\ use this procedure a lot,
+so it has been slightly optimized for speed.
+@^inner loop@>
+
+@p procedure back_input; {undoes one token of input}
+var p:pointer; {a token list of length one}
+begin while (state=token_list)and(loc=null)and(token_type<>v_template) do
+ end_token_list; {conserve stack space}
+p:=get_avail; info(p):=cur_tok;
+if cur_tok<right_brace_limit then
+ if cur_tok<left_brace_limit then decr(align_state)
+ else incr(align_state);
+push_input; state:=token_list; start:=p; token_type:=backed_up;
+loc:=p; {that was |back_list(p)|, without procedure overhead}
+end;
+
+@ @<Insert token |p| into \TeX's input@>=
+begin t:=cur_tok; cur_tok:=p; back_input; cur_tok:=t;
+end
+
+@ The |back_error| routine is used when we want to replace an offending token
+just before issuing an error message. This routine, like |back_input|,
+requires that |cur_tok| has been set. We disable interrupts during the
+call of |back_input| so that the help message won't be lost.
+
+@p procedure back_error; {back up one token and call |error|}
+begin OK_to_interrupt:=false; back_input; OK_to_interrupt:=true; error;
+end;
+@#
+procedure ins_error; {back up one inserted token and call |error|}
+begin OK_to_interrupt:=false; back_input; token_type:=inserted;
+OK_to_interrupt:=true; error;
+end;
+
+@ The |begin_file_reading| procedure starts a new level of input for lines
+of characters to be read from a file, or as an insertion from the
+terminal. It does not take care of opening the file, nor does it set |loc|
+or |limit| or |line|.
+@^system dependencies@>
+
+@p procedure begin_file_reading;
+begin if in_open=max_in_open then overflow("text input levels",max_in_open);
+@:TeX capacity exceeded text input levels}{\quad text input levels@>
+if first=buf_size then overflow("buffer size",buf_size);
+@:TeX capacity exceeded buffer size}{\quad buffer size@>
+incr(in_open); push_input; index:=in_open;
+line_stack[index]:=line; start:=first; state:=mid_line;
+name:=0; {|terminal_input| is now |true|}
+end;
+
+@ Conversely, the variables must be downdated when such a level of input
+is finished:
+
+@p procedure end_file_reading;
+begin first:=start; line:=line_stack[index];
+if name>17 then a_close(cur_file); {forget it}
+pop_input; decr(in_open);
+end;
+
+@ In order to keep the stack from overflowing during a long sequence of
+inserted `\.{\\show}' commands, the following routine removes completed
+error-inserted lines from memory.
+
+@p procedure clear_for_error_prompt;
+begin while (state<>token_list)and terminal_input and@|
+ (input_ptr>0)and(loc>limit) do end_file_reading;
+print_ln; clear_terminal;
+end;
+
+@ To get \TeX's whole input mechanism going, we perform the following
+actions.
+
+@<Initialize the input routines@>=
+begin input_ptr:=0; max_in_stack:=0;
+in_open:=0; open_parens:=0; max_buf_stack:=0;
+param_ptr:=0; max_param_stack:=0;
+first:=buf_size; repeat buffer[first]:=0; decr(first); until first=0;
+scanner_status:=normal; warning_index:=null; first:=1;
+state:=new_line; start:=1; index:=0; line:=0; name:=0;
+force_eof:=false;
+align_state:=1000000;@/
+if not init_terminal then goto final_end;
+limit:=last; first:=last+1; {|init_terminal| has set |loc| and |last|}
+end
+
+@* \[24] Getting the next token.
+The heart of \TeX's input mechanism is the |get_next| procedure, which
+we shall develop in the next few sections of the program. Perhaps we
+shouldn't actually call it the ``heart,'' however, because it really acts
+as \TeX's eyes and mouth, reading the source files and gobbling them up.
+And it also helps \TeX\ to regurgitate stored token lists that are to be
+processed again.
+@^eyes and mouth@>
+
+The main duty of |get_next| is to input one token and to set |cur_cmd|
+and |cur_chr| to that token's command code and modifier. Furthermore, if
+the input token is a control sequence, the |eqtb| location of that control
+sequence is stored in |cur_cs|; otherwise |cur_cs| is set to zero.
+
+Underlying this simple description is a certain amount of complexity
+because of all the cases that need to be handled.
+However, the inner loop of |get_next| is reasonably short and fast.
+
+When |get_next| is asked to get the next token of a \.{\\read} line,
+it sets |cur_cmd=cur_chr=cur_cs=0| in the case that no more tokens
+appear on that line. (There might not be any tokens at all, if the
+|end_line_char| has |ignore| as its catcode.)
+
+@ The value of |par_loc| is the |eqtb| address of `\.{\\par}'. This quantity
+is needed because a blank line of input is supposed to be exactly equivalent
+to the appearance of \.{\\par}; we must set |cur_cs:=par_loc|
+when detecting a blank line.
+
+@<Glob...@>=
+@!par_loc:pointer; {location of `\.{\\par}' in |eqtb|}
+@!par_token:halfword; {token representing `\.{\\par}'}
+
+@ @<Put each...@>=
+primitive("par",par_end,256); {cf. |scan_file_name|}
+@!@:par_}{\.{\\par} primitive@>
+par_loc:=cur_val; par_token:=cs_token_flag+par_loc;
+
+@ @<Cases of |print_cmd_chr|...@>=
+par_end:print_esc("par");
+
+@ Before getting into |get_next|, let's consider the subroutine that
+is called when an `\.{\\outer}' control sequence has been scanned or
+when the end of a file has been reached. These two cases are distinguished
+by |cur_cs|, which is zero at the end of a file.
+
+@p procedure check_outer_validity;
+var p:pointer; {points to inserted token list}
+@!q:pointer; {auxiliary pointer}
+begin if scanner_status<>normal then
+ begin deletions_allowed:=false;
+ @<Back up an outer control sequence so that it can be reread@>;
+ if scanner_status>skipping then
+ @<Tell the user what has run away and try to recover@>
+ else begin print_err("Incomplete "); print_cmd_chr(if_test,cur_if);
+@.Incomplete \\if...@>
+ print("; all text was ignored after line "); print_int(skip_line);
+ help3("A forbidden control sequence occurred in skipped text.")@/
+ ("This kind of error happens when you say `\if...' and forget")@/
+ ("the matching `\fi'. I've inserted a `\fi'; this might work.");
+ if cur_cs<>0 then cur_cs:=0
+ else help_line[2]:=@|
+ "The file ended while I was skipping conditional text.";
+ cur_tok:=cs_token_flag+frozen_fi; ins_error;
+ end;
+ deletions_allowed:=true;
+ end;
+end;
+
+@ An outer control sequence that occurs in a \.{\\read} will not be reread,
+since the error recovery for \.{\\read} is not very powerful.
+
+@<Back up an outer control sequence so that it can be reread@>=
+if cur_cs<>0 then
+ begin if (state=token_list)or(name<1)or(name>17) then
+ begin p:=get_avail; info(p):=cs_token_flag+cur_cs;
+ back_list(p); {prepare to read the control sequence again}
+ end;
+ cur_cmd:=spacer; cur_chr:=" "; {replace it by a space}
+ end
+
+@ @<Tell the user what has run away...@>=
+begin runaway; {print a definition, argument, or preamble}
+if cur_cs=0 then print_err("File ended")
+@.File ended while scanning...@>
+else begin cur_cs:=0; print_err("Forbidden control sequence found");
+@.Forbidden control sequence...@>
+ end;
+print(" while scanning ");
+@<Print either `\.{definition}' or `\.{use}' or `\.{preamble}' or `\.{text}',
+ and insert tokens that should lead to recovery@>;
+print(" of "); sprint_cs(warning_index);
+help4("I suspect you have forgotten a `}', causing me")@/
+("to read past where you wanted me to stop.")@/
+("I'll try to recover; but if the error is serious,")@/
+("you'd better type `E' or `X' now and fix your file.");@/
+error;
+end
+
+@ The recovery procedure can't be fully understood without knowing more
+about the \TeX\ routines that should be aborted, but we can sketch the
+ideas here: For a runaway definition we will insert a right brace; for a
+runaway preamble, we will insert a special \.{\\cr} token and a right
+brace; and for a runaway argument, we will set |long_state| to
+|outer_call| and insert \.{\\par}.
+
+@<Print either `\.{definition}' or ...@>=
+p:=get_avail;
+case scanner_status of
+defining:begin print("definition"); info(p):=right_brace_token+"}";
+ end;
+matching:begin print("use"); info(p):=par_token; long_state:=outer_call;
+ end;
+aligning:begin print("preamble"); info(p):=right_brace_token+"}"; q:=p;
+ p:=get_avail; link(p):=q; info(p):=cs_token_flag+frozen_cr;
+ align_state:=-1000000;
+ end;
+absorbing:begin print("text"); info(p):=right_brace_token+"}";
+ end;
+end; {there are no other cases}
+ins_list(p)
+
+@ We need to mention a procedure here that may be called by |get_next|.
+
+@p procedure@?firm_up_the_line; forward;
+
+@ Now we're ready to take the plunge into |get_next| itself. Parts of
+this routine are executed more often than any other instructions of \TeX.
+@^mastication@>@^inner loop@>
+
+@d switch=25 {a label in |get_next|}
+@d start_cs=26 {another}
+
+@p procedure get_next; {sets |cur_cmd|, |cur_chr|, |cur_cs| to next token}
+label restart, {go here to get the next input token}
+ switch, {go here to eat the next character from a file}
+ reswitch, {go here to digest it again}
+ start_cs, {go here to start looking for a control sequence}
+ found, {go here when a control sequence has been found}
+ exit; {go here when the next input token has been got}
+var k:0..buf_size; {an index into |buffer|}
+@!t:halfword; {a token}
+@!cat:0..15; {|cat_code(cur_chr)|, usually}
+@!c,@!cc:ASCII_code; {constituents of a possible expanded code}
+@!d:2..3; {number of excess characters in an expanded code}
+begin restart: cur_cs:=0;
+if state<>token_list then
+@<Input from external file, |goto restart| if no input found@>
+else @<Input from token list, |goto restart| if end of list or
+ if a parameter needs to be expanded@>;
+@<If an alignment entry has just ended, take appropriate action@>;
+exit:end;
+
+@ An alignment entry ends when a tab or \.{\\cr} occurs, provided that the
+current level of braces is the same as the level that was present at the
+beginning of that alignment entry; i.e., provided that |align_state| has
+returned to the value it had after the \<u_j> template for that entry.
+@^inner loop@>
+
+@<If an alignment entry has just ended, take appropriate action@>=
+if cur_cmd<=car_ret then if cur_cmd>=tab_mark then if align_state=0 then
+ @<Insert the \(v)\<v_j> template and |goto restart|@>
+
+@ @<Input from external file, |goto restart| if no input found@>=
+@^inner loop@>
+begin switch: if loc<=limit then {current line not yet finished}
+ begin cur_chr:=buffer[loc]; incr(loc);
+ reswitch: cur_cmd:=cat_code(cur_chr);
+ @<Change state if necessary, and |goto switch| if the
+ current character should be ignored,
+ or |goto reswitch| if the current character
+ changes to another@>;
+ end
+else begin state:=new_line;@/
+ @<Move to next line of file,
+ or |goto restart| if there is no next line,
+ or |return| if a \.{\\read} line has finished@>;
+ check_interrupt;
+ goto switch;
+ end;
+end
+
+@ The following 48-way switch accomplishes the scanning quickly, assuming
+that a decent \PASCAL\ compiler has translated the code. Note that the numeric
+values for |mid_line|, |skip_blanks|, and |new_line| are spaced
+apart from each other by |max_char_code+1|, so we can add a character's
+command code to the state to get a single number that characterizes both.
+
+@d any_state_plus(#) == mid_line+#,skip_blanks+#,new_line+#
+
+@<Change state if necessary...@>=
+case state+cur_cmd of
+@<Cases where character is ignored@>: goto switch;
+any_state_plus(escape): @<Scan a control sequence
+ and set |state:=skip_blanks| or |mid_line|@>;
+any_state_plus(active_char): @<Process an active-character control sequence
+ and set |state:=mid_line|@>;
+any_state_plus(sup_mark): @<If this |sup_mark| starts an expanded character
+ like~\.{\^\^A} or~\.{\^\^df}, then |goto reswitch|,
+ otherwise set |state:=mid_line|@>;
+any_state_plus(invalid_char): @<Decry the invalid character and
+ |goto restart|@>;
+@t\4@>@<Handle situations involving spaces, braces, changes of state@>@;
+othercases do_nothing
+endcases
+
+@ @<Cases where character is ignored@>=
+any_state_plus(ignore),skip_blanks+spacer,new_line+spacer
+
+@ We go to |restart| instead of to |switch|, because |state| might equal
+|token_list| after the error has been dealt with
+(cf.\ |clear_for_error_prompt|).
+
+@<Decry the invalid...@>=
+begin print_err("Text line contains an invalid character");
+@.Text line contains...@>
+help2("A funny symbol that I can't read has just been input.")@/
+("Continue, and I'll forget that it ever happened.");@/
+deletions_allowed:=false; error; deletions_allowed:=true;
+goto restart;
+end
+
+@ @d add_delims_to(#)==#+math_shift,#+tab_mark,#+mac_param,
+ #+sub_mark,#+letter,#+other_char
+
+@<Handle situations involving spaces, braces, changes of state@>=
+mid_line+spacer:@<Enter |skip_blanks| state, emit a space@>;
+mid_line+car_ret:@<Finish line, emit a space@>;
+skip_blanks+car_ret,any_state_plus(comment):
+ @<Finish line, |goto switch|@>;
+new_line+car_ret:@<Finish line, emit a \.{\\par}@>;
+mid_line+left_brace: incr(align_state);
+skip_blanks+left_brace,new_line+left_brace: begin
+ state:=mid_line; incr(align_state);
+ end;
+mid_line+right_brace: decr(align_state);
+skip_blanks+right_brace,new_line+right_brace: begin
+ state:=mid_line; decr(align_state);
+ end;
+add_delims_to(skip_blanks),add_delims_to(new_line): state:=mid_line;
+
+@ When a character of type |spacer| gets through, its character code is
+changed to $\.{"\ "}=@'40$. This means that the ASCII codes for tab and space,
+and for the space inserted at the end of a line, will
+be treated alike when macro parameters are being matched. We do this
+since such characters are indistinguishable on most computer terminal displays.
+
+@<Finish line, emit a space@>=
+begin loc:=limit+1; cur_cmd:=spacer; cur_chr:=" ";
+end
+
+@ The following code is performed only when |cur_cmd=spacer|.
+
+@<Enter |skip_blanks| state, emit a space@>=
+begin state:=skip_blanks; cur_chr:=" ";
+end
+
+@ @<Finish line, |goto switch|@>=
+begin loc:=limit+1; goto switch;
+end
+
+@ @<Finish line, emit a \.{\\par}@>=
+begin loc:=limit+1; cur_cs:=par_loc; cur_cmd:=eq_type(cur_cs);
+cur_chr:=equiv(cur_cs);
+if cur_cmd>=outer_call then check_outer_validity;
+end
+
+@ Notice that a code like \.{\^\^8} becomes \.x if not followed by a hex digit.
+
+@d is_hex(#)==(((#>="0")and(#<="9"))or((#>="a")and(#<="f")))
+@d hex_to_cur_chr==
+ if c<="9" then cur_chr:=c-"0" @+else cur_chr:=c-"a"+10;
+ if cc<="9" then cur_chr:=16*cur_chr+cc-"0"
+ else cur_chr:=16*cur_chr+cc-"a"+10
+
+@<If this |sup_mark| starts an expanded character...@>=
+begin if cur_chr=buffer[loc] then if loc<limit then
+ begin c:=buffer[loc+1]; @+if c<@'200 then {yes we have an expanded char}
+ begin loc:=loc+2;
+ if is_hex(c) then if loc<=limit then
+ begin cc:=buffer[loc]; @+if is_hex(cc) then
+ begin incr(loc); hex_to_cur_chr; goto reswitch;
+ end;
+ end;
+ if c<@'100 then cur_chr:=c+@'100 @+else cur_chr:=c-@'100;
+ goto reswitch;
+ end;
+ end;
+state:=mid_line;
+end
+
+@ @<Process an active-character...@>=
+begin cur_cs:=cur_chr+active_base;
+cur_cmd:=eq_type(cur_cs); cur_chr:=equiv(cur_cs); state:=mid_line;
+if cur_cmd>=outer_call then check_outer_validity;
+end
+
+@ Control sequence names are scanned only when they appear in some line of
+a file; once they have been scanned the first time, their |eqtb| location
+serves as a unique identification, so \TeX\ doesn't need to refer to the
+original name any more except when it prints the equivalent in symbolic form.
+
+The program that scans a control sequence has been written carefully
+in order to avoid the blowups that might otherwise occur if a malicious
+user tried something like `\.{\\catcode\'15=0}'. The algorithm might
+look at |buffer[limit+1]|, but it never looks at |buffer[limit+2]|.
+
+If expanded characters like `\.{\^\^A}' or `\.{\^\^df}'
+appear in or just following
+a control sequence name, they are converted to single characters in the
+buffer and the process is repeated, slowly but surely.
+
+@<Scan a control...@>=
+begin if loc>limit then cur_cs:=null_cs {|state| is irrelevant in this case}
+else begin start_cs: k:=loc; cur_chr:=buffer[k]; cat:=cat_code(cur_chr);
+ incr(k);
+ if cat=letter then state:=skip_blanks
+ else if cat=spacer then state:=skip_blanks
+ else state:=mid_line;
+ if (cat=letter)and(k<=limit) then
+ @<Scan ahead in the buffer until finding a nonletter;
+ if an expanded code is encountered, reduce it
+ and |goto start_cs|; otherwise if a multiletter control
+ sequence is found, adjust |cur_cs| and |loc|, and
+ |goto found|@>
+ else @<If an expanded code is present, reduce it and |goto start_cs|@>;
+ cur_cs:=single_base+buffer[loc]; incr(loc);
+ end;
+found: cur_cmd:=eq_type(cur_cs); cur_chr:=equiv(cur_cs);
+if cur_cmd>=outer_call then check_outer_validity;
+end
+
+@ Whenever we reach the following piece of code, we will have
+|cur_chr=buffer[k-1]| and |k<=limit+1| and |cat=cat_code(cur_chr)|. If an
+expanded code like \.{\^\^A} or \.{\^\^df} appears in |buffer[(k-1)..(k+1)]|
+or |buffer[(k-1)..(k+2)]|, we
+will store the corresponding code in |buffer[k-1]| and shift the rest of
+the buffer left two or three places.
+
+@<If an expanded...@>=
+begin if buffer[k]=cur_chr then @+if cat=sup_mark then @+if k<limit then
+ begin c:=buffer[k+1]; @+if c<@'200 then {yes, one is indeed present}
+ begin d:=2;
+ if is_hex(c) then @+if k+2<=limit then
+ begin cc:=buffer[k+2]; @+if is_hex(cc) then incr(d);
+ end;
+ if d>2 then
+ begin hex_to_cur_chr; buffer[k-1]:=cur_chr;
+ end
+ else if c<@'100 then buffer[k-1]:=c+@'100
+ else buffer[k-1]:=c-@'100;
+ limit:=limit-d; first:=first-d;
+ while k<=limit do
+ begin buffer[k]:=buffer[k+d]; incr(k);
+ end;
+ goto start_cs;
+ end;
+ end;
+end
+
+@ @<Scan ahead in the buffer...@>=
+begin repeat cur_chr:=buffer[k]; cat:=cat_code(cur_chr); incr(k);
+until (cat<>letter)or(k>limit);
+@<If an expanded...@>;
+if cat<>letter then decr(k);
+ {now |k| points to first nonletter}
+if k>loc+1 then {multiletter control sequence has been scanned}
+ begin cur_cs:=id_lookup(loc,k-loc); loc:=k; goto found;
+ end;
+end
+
+@ Let's consider now what happens when |get_next| is looking at a token list.
+
+@<Input from token list, |goto restart| if end of list or
+ if a parameter needs to be expanded@>=
+if loc<>null then {list not exhausted}
+@^inner loop@>
+ begin t:=info(loc); loc:=link(loc); {move to next}
+ if t>=cs_token_flag then {a control sequence token}
+ begin cur_cs:=t-cs_token_flag;
+ cur_cmd:=eq_type(cur_cs); cur_chr:=equiv(cur_cs);
+ if cur_cmd>=outer_call then
+ if cur_cmd=dont_expand then
+ @<Get the next token, suppressing expansion@>
+ else check_outer_validity;
+ end
+ else begin cur_cmd:=t div @'400; cur_chr:=t mod @'400;
+ case cur_cmd of
+ left_brace: incr(align_state);
+ right_brace: decr(align_state);
+ out_param: @<Insert macro parameter and |goto restart|@>;
+ othercases do_nothing
+ endcases;
+ end;
+ end
+else begin {we are done with this token list}
+ end_token_list; goto restart; {resume previous level}
+ end
+
+@ The present point in the program is reached only when the |expand|
+routine has inserted a special marker into the input. In this special
+case, |info(loc)| is known to be a control sequence token, and |link(loc)=null|.
+
+@d no_expand_flag=257 {this characterizes a special variant of |relax|}
+
+@<Get the next token, suppressing expansion@>=
+begin cur_cs:=info(loc)-cs_token_flag; loc:=null;@/
+cur_cmd:=eq_type(cur_cs); cur_chr:=equiv(cur_cs);
+if cur_cmd>max_command then
+ begin cur_cmd:=relax; cur_chr:=no_expand_flag;
+ end;
+end
+
+@ @<Insert macro parameter...@>=
+begin begin_token_list(param_stack[param_start+cur_chr-1],parameter);
+goto restart;
+end
+
+@ All of the easy branches of |get_next| have now been taken care of.
+There is one more branch.
+
+@d end_line_char_inactive == (end_line_char<0)or(end_line_char>255)
+
+@<Move to next line of file, or |goto restart|...@>=
+if name>17 then @<Read next line of file into |buffer|, or
+ |goto restart| if the file has ended@>
+else begin if not terminal_input then {\.{\\read} line has ended}
+ begin cur_cmd:=0; cur_chr:=0; return;
+ end;
+ if input_ptr>0 then {text was inserted during error recovery}
+ begin end_file_reading; goto restart; {resume previous level}
+ end;
+ if selector<log_only then open_log_file;
+ if interaction>nonstop_mode then
+ begin if end_line_char_inactive then incr(limit);
+ if limit=start then {previous line was empty}
+ print_nl("(Please type a command or say `\end')");
+@.Please type...@>
+ print_ln; first:=start;
+ prompt_input("*"); {input on-line into |buffer|}
+@.*\relax@>
+ limit:=last;
+ if end_line_char_inactive then decr(limit)
+ else buffer[limit]:=end_line_char;
+ first:=limit+1;
+ loc:=start;
+ end
+ else fatal_error("*** (job aborted, no legal \end found)");
+@.job aborted@>
+ {nonstop mode, which is intended for overnight batch processing,
+ never waits for on-line input}
+ end
+
+@ The global variable |force_eof| is normally |false|; it is set |true|
+by an \.{\\endinput} command.
+
+@<Glob...@>=
+@!force_eof:boolean; {should the next \.{\\input} be aborted early?}
+
+@ @<Read next line of file into |buffer|, or
+ |goto restart| if the file has ended@>=
+begin incr(line); first:=start;
+if not force_eof then
+ begin if input_ln(cur_file,true) then {not end of file}
+ firm_up_the_line {this sets |limit|}
+ else force_eof:=true;
+ end;
+if force_eof then
+ begin print_char(")"); decr(open_parens);
+ update_terminal; {show user that file has been read}
+ force_eof:=false;
+ end_file_reading; {resume previous level}
+ check_outer_validity; goto restart;
+ end;
+if end_line_char_inactive then decr(limit)
+else buffer[limit]:=end_line_char;
+first:=limit+1; loc:=start; {ready to read}
+end
+
+@ If the user has set the |pausing| parameter to some positive value,
+and if nonstop mode has not been selected, each line of input is displayed
+on the terminal and the transcript file, followed by `\.{=>}'.
+\TeX\ waits for a response. If the response is simply |carriage_return|, the
+line is accepted as it stands, otherwise the line typed is
+used instead of the line in the file.
+
+@p procedure firm_up_the_line;
+var k:0..buf_size; {an index into |buffer|}
+begin limit:=last;
+if pausing>0 then if interaction>nonstop_mode then
+ begin wake_up_terminal; print_ln;
+ if start<limit then for k:=start to limit-1 do print(buffer[k]);
+ first:=limit; prompt_input("=>"); {wait for user response}
+@.=>@>
+ if last>first then
+ begin for k:=first to last-1 do {move line down in buffer}
+ buffer[k+start-first]:=buffer[k];
+ limit:=start+last-first;
+ end;
+ end;
+end;
+
+@ Since |get_next| is used so frequently in \TeX, it is convenient
+to define three related procedures that do a little more:
+
+\yskip\hang|get_token| not only sets |cur_cmd| and |cur_chr|, it
+also sets |cur_tok|, a packed halfword version of the current token.
+
+\yskip\hang|get_x_token|, meaning ``get an expanded token,'' is like
+|get_token|, but if the current token turns out to be a user-defined
+control sequence (i.e., a macro call), or a conditional,
+or something like \.{\\topmark} or \.{\\expandafter} or \.{\\csname},
+it is eliminated from the input by beginning the expansion of the macro
+or the evaluation of the conditional.
+
+\yskip\hang|x_token| is like |get_x_token| except that it assumes that
+|get_next| has already been called.
+
+\yskip\noindent
+In fact, these three procedures account for {\sl all\/} uses of |get_next|,
+except for two places in the ``inner loop'' when |cur_tok| need not be set,
+and except when the arguments to \.{\\ifx} are being scanned.
+
+@ No new control sequences will be defined except during a call of
+|get_token|, or when \.{\\csname} compresses a token list, because
+|no_new_control_sequence| is always |true| at other times.
+
+@p procedure get_token; {sets |cur_cmd|, |cur_chr|, |cur_tok|}
+begin no_new_control_sequence:=false; get_next; no_new_control_sequence:=true;
+@^inner loop@>
+if cur_cs=0 then cur_tok:=(cur_cmd*@'400)+cur_chr
+else cur_tok:=cs_token_flag+cur_cs;
+end;
+
+@* \[25] Expanding the next token.
+Only a dozen or so command codes |>max_command| can possibly be returned by
+|get_next|; in increasing order, they are |undefined_cs|, |expand_after|,
+|no_expand|, |input|, |if_test|, |fi_or_else|, |cs_name|, |convert|, |the|,
+|top_bot_mark|, |call|, |long_call|, |outer_call|, |long_outer_call|, and
+|end_template|.{\emergencystretch=40pt\par}
+
+The |expand| subroutine is used when |cur_cmd>max_command|. It removes a
+``call'' or a conditional or one of the other special operations just
+listed. It follows that |expand| might invoke itself recursively. In all
+cases, |expand| destroys the current token, but it sets things up so that
+the next |get_next| will deliver the appropriate next token. The value of
+|cur_tok| need not be known when |expand| is called.
+
+Since several of the basic scanning routines communicate via global variables,
+their values are saved as local variables of |expand| so that
+recursive calls don't invalidate them.
+@^recursion@>
+
+@p@t\4@>@<Declare the procedure called |macro_call|@>@;@/
+@t\4@>@<Declare the procedure called |insert_relax|@>@;@/
+procedure@?pass_text; forward;@t\2@>
+procedure@?start_input; forward;@t\2@>
+procedure@?conditional; forward;@t\2@>
+procedure@?get_x_token; forward;@t\2@>
+procedure@?conv_toks; forward;@t\2@>
+procedure@?ins_the_toks; forward;@t\2@>
+procedure expand;
+var t:halfword; {token that is being ``expanded after''}
+@!p,@!q,@!r:pointer; {for list manipulation}
+@!j:0..buf_size; {index into |buffer|}
+@!cv_backup:integer; {to save the global quantity |cur_val|}
+@!cvl_backup,@!radix_backup,@!co_backup:small_number;
+ {to save |cur_val_level|, etc.}
+@!backup_backup:pointer; {to save |link(backup_head)|}
+@!save_scanner_status:small_number; {temporary storage of |scanner_status|}
+begin cv_backup:=cur_val; cvl_backup:=cur_val_level; radix_backup:=radix;
+co_backup:=cur_order; backup_backup:=link(backup_head);
+if cur_cmd<call then @<Expand a nonmacro@>
+else if cur_cmd<end_template then macro_call
+else @<Insert a token containing |frozen_endv|@>;
+cur_val:=cv_backup; cur_val_level:=cvl_backup; radix:=radix_backup;
+cur_order:=co_backup; link(backup_head):=backup_backup;
+end;
+
+@ @<Expand a nonmacro@>=
+begin if tracing_commands>1 then show_cur_cmd_chr;
+case cur_cmd of
+top_bot_mark:@<Insert the \(a)appropriate mark text into the scanner@>;
+expand_after:@<Expand the token after the next token@>;
+no_expand:@<Suppress expansion of the next token@>;
+cs_name:@<Manufacture a control sequence name@>;
+convert:conv_toks; {this procedure is discussed in Part 27 below}
+the:ins_the_toks; {this procedure is discussed in Part 27 below}
+if_test:conditional; {this procedure is discussed in Part 28 below}
+fi_or_else:@<Terminate the current conditional and skip to \.{\\fi}@>;
+input:@<Initiate or terminate input from a file@>;
+othercases @<Complain about an undefined macro@>
+endcases;
+end
+
+@ It takes only a little shuffling to do what \TeX\ calls \.{\\expandafter}.
+
+@<Expand the token after...@>=
+begin get_token; t:=cur_tok; get_token;
+if cur_cmd>max_command then expand@+else back_input;
+cur_tok:=t; back_input;
+end
+
+@ The implementation of \.{\\noexpand} is a bit trickier, because it is
+necessary to insert a special `|dont_expand|' marker into \TeX's reading
+mechanism. This special marker is processed by |get_next|, but it does
+not slow down the inner loop.
+
+Since \.{\\outer} macros might arise here, we must also
+clear the |scanner_status| temporarily.
+
+@<Suppress expansion...@>=
+begin save_scanner_status:=scanner_status; scanner_status:=normal;
+get_token; scanner_status:=save_scanner_status; t:=cur_tok;
+back_input; {now |start| and |loc| point to the backed-up token |t|}
+if t>=cs_token_flag then
+ begin p:=get_avail; info(p):=cs_token_flag+frozen_dont_expand;
+ link(p):=loc; start:=p; loc:=p;
+ end;
+end
+
+@ @<Complain about an undefined macro@>=
+begin print_err("Undefined control sequence");
+@.Undefined control sequence@>
+help5("The control sequence at the end of the top line")@/
+("of your error message was never \def'ed. If you have")@/
+("misspelled it (e.g., `\hobx'), type `I' and the correct")@/
+("spelling (e.g., `I\hbox'). Otherwise just continue,")@/
+("and I'll forget about whatever was undefined.");
+error;
+end
+
+@ The |expand| procedure and some other routines that construct token
+lists find it convenient to use the following macros, which are valid only if
+the variables |p| and |q| are reserved for token-list building.
+
+@d store_new_token(#)==begin q:=get_avail; link(p):=q; info(q):=#;
+ p:=q; {|link(p)| is |null|}
+ end
+@d fast_store_new_token(#)==begin fast_get_avail(q); link(p):=q; info(q):=#;
+ p:=q; {|link(p)| is |null|}
+ end
+
+@ @<Manufacture a control...@>=
+begin r:=get_avail; p:=r; {head of the list of characters}
+repeat get_x_token;
+if cur_cs=0 then store_new_token(cur_tok);
+until cur_cs<>0;
+if cur_cmd<>end_cs_name then @<Complain about missing \.{\\endcsname}@>;
+@<Look up the characters of list |r| in the hash table, and set |cur_cs|@>;
+flush_list(r);
+if eq_type(cur_cs)=undefined_cs then
+ begin eq_define(cur_cs,relax,256); {N.B.: The |save_stack| might change}
+ end; {the control sequence will now match `\.{\\relax}'}
+cur_tok:=cur_cs+cs_token_flag; back_input;
+end
+
+@ @<Complain about missing \.{\\endcsname}@>=
+begin print_err("Missing "); print_esc("endcsname"); print(" inserted");
+@.Missing \\endcsname...@>
+help2("The control sequence marked <to be read again> should")@/
+ ("not appear between \csname and \endcsname.");
+back_error;
+end
+
+@ @<Look up the characters of list |r| in the hash table...@>=
+j:=first; p:=link(r);
+while p<>null do
+ begin if j>=max_buf_stack then
+ begin max_buf_stack:=j+1;
+ if max_buf_stack=buf_size then
+ overflow("buffer size",buf_size);
+@:TeX capacity exceeded buffer size}{\quad buffer size@>
+ end;
+ buffer[j]:=info(p) mod @'400; incr(j); p:=link(p);
+ end;
+if j>first+1 then
+ begin no_new_control_sequence:=false; cur_cs:=id_lookup(first,j-first);
+ no_new_control_sequence:=true;
+ end
+else if j=first then cur_cs:=null_cs {the list is empty}
+else cur_cs:=single_base+buffer[first] {the list has length one}
+
+@ An |end_template| command is effectively changed to an |endv| command
+by the following code. (The reason for this is discussed below; the
+|frozen_end_template| at the end of the template has passed the
+|check_outer_validity| test, so its mission of error detection has been
+accomplished.)
+
+@<Insert a token containing |frozen_endv|@>=
+begin cur_tok:=cs_token_flag+frozen_endv; back_input;
+end
+
+@ The processing of \.{\\input} involves the |start_input| subroutine,
+which will be declared later; the processing of \.{\\endinput} is trivial.
+
+@<Put each...@>=
+primitive("input",input,0);@/
+@!@:input_}{\.{\\input} primitive@>
+primitive("endinput",input,1);@/
+@!@:end_input_}{\.{\\endinput} primitive@>
+
+@ @<Cases of |print_cmd_chr|...@>=
+input: if chr_code=0 then print_esc("input")@+else print_esc("endinput");
+
+@ @<Initiate or terminate input...@>=
+if cur_chr>0 then force_eof:=true
+else if name_in_progress then insert_relax
+else start_input
+
+@ Sometimes the expansion looks too far ahead, so we want to insert
+a harmless \.{\\relax} into the user's input.
+
+@<Declare the procedure called |insert_relax|@>=
+procedure insert_relax;
+begin cur_tok:=cs_token_flag+cur_cs; back_input;
+cur_tok:=cs_token_flag+frozen_relax; back_input; token_type:=inserted;
+end;
+
+@ Here is a recursive procedure that is \TeX's usual way to get the
+next token of input. It has been slightly optimized to take account of
+common cases.
+
+@p procedure get_x_token; {sets |cur_cmd|, |cur_chr|, |cur_tok|,
+ and expands macros}
+label restart,done;
+begin restart: get_next;
+@^inner loop@>
+if cur_cmd<=max_command then goto done;
+if cur_cmd>=call then
+ if cur_cmd<end_template then macro_call
+ else begin cur_cs:=frozen_endv; cur_cmd:=endv;
+ goto done; {|cur_chr=null_list|}
+ end
+else expand;
+goto restart;
+done: if cur_cs=0 then cur_tok:=(cur_cmd*@'400)+cur_chr
+else cur_tok:=cs_token_flag+cur_cs;
+end;
+
+@ The |get_x_token| procedure is equivalent to two consecutive
+procedure calls: |get_next; x_token|.
+
+@p procedure x_token; {|get_x_token| without the initial |get_next|}
+begin while cur_cmd>max_command do
+ begin expand;
+ get_next;
+ end;
+if cur_cs=0 then cur_tok:=(cur_cmd*@'400)+cur_chr
+else cur_tok:=cs_token_flag+cur_cs;
+end;
+
+@ A control sequence that has been \.{\\def}'ed by the user is expanded by
+\TeX's |macro_call| procedure.
+
+Before we get into the details of |macro_call|, however, let's consider the
+treatment of primitives like \.{\\topmark}, since they are essentially
+macros without parameters. The token lists for such marks are kept in a
+global array of five pointers; we refer to the individual entries of this
+array by symbolic names |top_mark|, etc. The value of |top_mark| is either
+|null| or a pointer to the reference count of a token list.
+
+@d top_mark_code=0 {the mark in effect at the previous page break}
+@d first_mark_code=1 {the first mark between |top_mark| and |bot_mark|}
+@d bot_mark_code=2 {the mark in effect at the current page break}
+@d split_first_mark_code=3 {the first mark found by \.{\\vsplit}}
+@d split_bot_mark_code=4 {the last mark found by \.{\\vsplit}}
+@d top_mark==cur_mark[top_mark_code]
+@d first_mark==cur_mark[first_mark_code]
+@d bot_mark==cur_mark[bot_mark_code]
+@d split_first_mark==cur_mark[split_first_mark_code]
+@d split_bot_mark==cur_mark[split_bot_mark_code]
+
+@<Glob...@>=
+@!cur_mark:array[top_mark_code..split_bot_mark_code] of pointer;
+ {token lists for marks}
+
+@ @<Set init...@>=
+top_mark:=null; first_mark:=null; bot_mark:=null;
+split_first_mark:=null; split_bot_mark:=null;
+
+@ @<Put each...@>=
+primitive("topmark",top_bot_mark,top_mark_code);
+@!@:top_mark_}{\.{\\topmark} primitive@>
+primitive("firstmark",top_bot_mark,first_mark_code);
+@!@:first_mark_}{\.{\\firstmark} primitive@>
+primitive("botmark",top_bot_mark,bot_mark_code);
+@!@:bot_mark_}{\.{\\botmark} primitive@>
+primitive("splitfirstmark",top_bot_mark,split_first_mark_code);
+@!@:split_first_mark_}{\.{\\splitfirstmark} primitive@>
+primitive("splitbotmark",top_bot_mark,split_bot_mark_code);
+@!@:split_bot_mark_}{\.{\\splitbotmark} primitive@>
+
+@ @<Cases of |print_cmd_chr|...@>=
+top_bot_mark: case chr_code of
+ first_mark_code: print_esc("firstmark");
+ bot_mark_code: print_esc("botmark");
+ split_first_mark_code: print_esc("splitfirstmark");
+ split_bot_mark_code: print_esc("splitbotmark");
+ othercases print_esc("topmark")
+ endcases;
+
+@ The following code is activated when |cur_cmd=top_bot_mark| and
+when |cur_chr| is a code like |top_mark_code|.
+
+@<Insert the \(a)appropriate mark text into the scanner@>=
+begin if cur_mark[cur_chr]<>null then
+ begin_token_list(cur_mark[cur_chr],mark_text);
+end
+
+@ Now let's consider |macro_call| itself, which is invoked when \TeX\ is
+scanning a control sequence whose |cur_cmd| is either |call|, |long_call|,
+|outer_call|, or |long_outer_call|. The control sequence definition
+appears in the token list whose reference count is in location |cur_chr|
+of |mem|.
+
+The global variable |long_state| will be set to |call| or to |long_call|,
+depending on whether or not the control sequence disallows \.{\\par}
+in its parameters. The |get_next| routine will set |long_state| to
+|outer_call| and emit \.{\\par}, if a file ends or if an \.{\\outer}
+control sequence occurs in the midst of an argument.
+
+@<Glob...@>=
+@!long_state:call..long_outer_call; {governs the acceptance of \.{\\par}}
+
+@ The parameters, if any, must be scanned before the macro is expanded.
+Parameters are token lists without reference counts. They are placed on
+an auxiliary stack called |pstack| while they are being scanned, since
+the |param_stack| may be losing entries during the matching process.
+(Note that |param_stack| can't be gaining entries, since |macro_call| is
+the only routine that puts anything onto |param_stack|, and it
+is not recursive.)
+
+@<Glob...@>=
+@!pstack:array[0..8] of pointer; {arguments supplied to a macro}
+
+@ After parameter scanning is complete, the parameters are moved to the
+|param_stack|. Then the macro body is fed to the scanner; in other words,
+|macro_call| places the defined text of the control sequence at the
+top of\/ \TeX's input stack, so that |get_next| will proceed to read it
+next.
+
+The global variable |cur_cs| contains the |eqtb| address of the control sequence
+being expanded, when |macro_call| begins. If this control sequence has not been
+declared \.{\\long}, i.e., if its command code in the |eq_type| field is
+not |long_call| or |long_outer_call|, its parameters are not allowed to contain
+the control sequence \.{\\par}. If an illegal \.{\\par} appears, the macro
+call is aborted, and the \.{\\par} will be rescanned.
+
+@<Declare the procedure called |macro_call|@>=
+procedure macro_call; {invokes a user-defined control sequence}
+label exit, continue, done, done1, found;
+var r:pointer; {current node in the macro's token list}
+@!p:pointer; {current node in parameter token list being built}
+@!q:pointer; {new node being put into the token list}
+@!s:pointer; {backup pointer for parameter matching}
+@!t:pointer; {cycle pointer for backup recovery}
+@!u,@!v:pointer; {auxiliary pointers for backup recovery}
+@!rbrace_ptr:pointer; {one step before the last |right_brace| token}
+@!n:small_number; {the number of parameters scanned}
+@!unbalance:halfword; {unmatched left braces in current parameter}
+@!m:halfword; {the number of tokens or groups (usually)}
+@!ref_count:pointer; {start of the token list}
+@!save_scanner_status:small_number; {|scanner_status| upon entry}
+@!save_warning_index:pointer; {|warning_index| upon entry}
+@!match_chr:ASCII_code; {character used in parameter}
+begin save_scanner_status:=scanner_status; save_warning_index:=warning_index;
+warning_index:=cur_cs; ref_count:=cur_chr; r:=link(ref_count); n:=0;
+if tracing_macros>0 then @<Show the text of the macro being expanded@>;
+if info(r)<>end_match_token then
+ @<Scan the parameters and make |link(r)| point to the macro body; but
+ |return| if an illegal \.{\\par} is detected@>;
+@<Feed the macro body and its parameters to the scanner@>;
+exit:scanner_status:=save_scanner_status; warning_index:=save_warning_index;
+end;
+
+@ Before we put a new token list on the input stack, it is wise to clean off
+all token lists that have recently been depleted. Then a user macro that ends
+with a call to itself will not require unbounded stack space.
+
+@<Feed the macro body and its parameters to the scanner@>=
+while (state=token_list)and(loc=null)and(token_type<>v_template) do
+ end_token_list; {conserve stack space}
+begin_token_list(ref_count,macro); name:=warning_index; loc:=link(r);
+if n>0 then
+ begin if param_ptr+n>max_param_stack then
+ begin max_param_stack:=param_ptr+n;
+ if max_param_stack>param_size then
+ overflow("parameter stack size",param_size);
+@:TeX capacity exceeded parameter stack size}{\quad parameter stack size@>
+ end;
+ for m:=0 to n-1 do param_stack[param_ptr+m]:=pstack[m];
+ param_ptr:=param_ptr+n;
+ end
+
+@ At this point, the reader will find it advisable to review the explanation
+of token list format that was presented earlier, since many aspects of that
+format are of importance chiefly in the |macro_call| routine.
+
+The token list might begin with a string of compulsory tokens before the
+first |match| or |end_match|. In that case the macro name is supposed to be
+followed by those tokens; the following program will set |s=null| to
+represent this restriction. Otherwise |s| will be set to the first token of
+a string that will delimit the next parameter.
+
+@<Scan the parameters and make |link(r)| point to the macro body...@>=
+begin scanner_status:=matching; unbalance:=0;
+long_state:=eq_type(cur_cs);
+if long_state>=outer_call then long_state:=long_state-2;
+repeat link(temp_head):=null;
+if (info(r)>match_token+255)or(info(r)<match_token) then s:=null
+else begin match_chr:=info(r)-match_token; s:=link(r); r:=s;
+ p:=temp_head; m:=0;
+ end;
+@<Scan a parameter until its delimiter string has been found; or, if |s=null|,
+ simply scan the delimiter string@>;@/
+{now |info(r)| is a token whose command code is either |match| or |end_match|}
+until info(r)=end_match_token;
+end
+
+@ If |info(r)| is a |match| or |end_match| command, it cannot be equal to
+any token found by |get_token|. Therefore an undelimited parameter---i.e.,
+a |match| that is immediately followed by |match| or |end_match|---will
+always fail the test `|cur_tok=info(r)|' in the following algorithm.
+
+@<Scan a parameter until its delimiter string has been found; or, ...@>=
+continue: get_token; {set |cur_tok| to the next token of input}
+if cur_tok=info(r) then
+ @<Advance \(r)|r|; |goto found| if the parameter delimiter has been
+ fully matched, otherwise |goto continue|@>;
+@<Contribute the recently matched tokens to the current parameter, and
+ |goto continue| if a partial match is still in effect;
+ but abort if |s=null|@>;
+if cur_tok=par_token then if long_state<>long_call then
+ @<Report a runaway argument and abort@>;
+if cur_tok<right_brace_limit then
+ if cur_tok<left_brace_limit then
+ @<Contribute an entire group to the current parameter@>
+ else @<Report an extra right brace and |goto continue|@>
+else @<Store the current token, but |goto continue| if it is
+ a blank space that would become an undelimited parameter@>;
+incr(m);
+if info(r)>end_match_token then goto continue;
+if info(r)<match_token then goto continue;
+found: if s<>null then @<Tidy up the parameter just scanned, and tuck it away@>
+
+@ @<Store the current token, but |goto continue| if it is...@>=
+begin if cur_tok=space_token then
+ if info(r)<=end_match_token then
+ if info(r)>=match_token then goto continue;
+store_new_token(cur_tok);
+end
+
+@ A slightly subtle point arises here: When the parameter delimiter ends
+with `\.{\#\{}', the token list will have a left brace both before and
+after the |end_match|\kern-.4pt. Only one of these should affect the
+|align_state|, but both will be scanned, so we must make a correction.
+
+@<Advance \(r)|r|; |goto found| if the parameter delimiter has been fully...@>=
+begin r:=link(r);
+if (info(r)>=match_token)and(info(r)<=end_match_token) then
+ begin if cur_tok<left_brace_limit then decr(align_state);
+ goto found;
+ end
+else goto continue;
+end
+
+@ @<Report an extra right brace and |goto continue|@>=
+begin back_input; print_err("Argument of "); sprint_cs(warning_index);
+@.Argument of \\x has...@>
+print(" has an extra }");
+help6("I've run across a `}' that doesn't seem to match anything.")@/
+ ("For example, `\def\a#1{...}' and `\a}' would produce")@/
+ ("this error. If you simply proceed now, the `\par' that")@/
+ ("I've just inserted will cause me to report a runaway")@/
+ ("argument that might be the root of the problem. But if")@/
+ ("your `}' was spurious, just type `2' and it will go away.");
+incr(align_state); long_state:=call; cur_tok:=par_token; ins_error;
+end {a white lie; the \.{\\par} won't always trigger a runaway}
+
+@ If |long_state=outer_call|, a runaway argument has already been reported.
+
+@<Report a runaway argument and abort@>=
+begin if long_state=call then
+ begin runaway; print_err("Paragraph ended before ");
+@.Paragraph ended before...@>
+ sprint_cs(warning_index); print(" was complete");
+ help3("I suspect you've forgotten a `}', causing me to apply this")@/
+ ("control sequence to too much text. How can we recover?")@/
+ ("My plan is to forget the whole thing and hope for the best.");
+ back_error;
+ end;
+pstack[n]:=link(temp_head); align_state:=align_state-unbalance;
+for m:=0 to n do flush_list(pstack[m]);
+return;
+end
+
+@ When the following code becomes active, we have matched tokens from |s| to
+the predecessor of |r|, and we have found that |cur_tok<>info(r)|. An
+interesting situation now presents itself: If the parameter is to be
+delimited by a string such as `\.{ab}', and if we have scanned `\.{aa}',
+we want to contribute one `\.a' to the current parameter and resume
+looking for a `\.b'. The program must account for such partial matches and
+for others that can be quite complex. But most of the time we have |s=r|
+and nothing needs to be done.
+
+Incidentally, it is possible for \.{\\par} tokens to sneak in to certain
+parameters of non-\.{\\long} macros. For example, consider a case like
+`\.{\\def\\a\#1\\par!\{...\}}' where the first \.{\\par} is not followed
+by an exclamation point. In such situations it does not seem appropriate
+to prohibit the \.{\\par}, so \TeX\ keeps quiet about this bending of
+the rules.
+
+@<Contribute the recently matched tokens to the current parameter...@>=
+if s<>r then
+ if s=null then @<Report an improper use of the macro and abort@>
+ else begin t:=s;
+ repeat store_new_token(info(t)); incr(m); u:=link(t); v:=s;
+ loop@+ begin if u=r then
+ if cur_tok<>info(v) then goto done
+ else begin r:=link(v); goto continue;
+ end;
+ if info(u)<>info(v) then goto done;
+ u:=link(u); v:=link(v);
+ end;
+ done: t:=link(t);
+ until t=r;
+ r:=s; {at this point, no tokens are recently matched}
+ end
+
+@ @<Report an improper use...@>=
+begin print_err("Use of "); sprint_cs(warning_index);
+@.Use of x doesn't match...@>
+print(" doesn't match its definition");
+help4("If you say, e.g., `\def\a1{...}', then you must always")@/
+ ("put `1' after `\a', since control sequence names are")@/
+ ("made up of letters only. The macro here has not been")@/
+ ("followed by the required stuff, so I'm ignoring it.");
+error; return;
+end
+
+@ @<Contribute an entire group to the current parameter@>=
+begin unbalance:=1;
+@^inner loop@>
+loop@+ begin fast_store_new_token(cur_tok); get_token;
+ if cur_tok=par_token then if long_state<>long_call then
+ @<Report a runaway argument and abort@>;
+ if cur_tok<right_brace_limit then
+ if cur_tok<left_brace_limit then incr(unbalance)
+ else begin decr(unbalance);
+ if unbalance=0 then goto done1;
+ end;
+ end;
+done1: rbrace_ptr:=p; store_new_token(cur_tok);
+end
+
+@ If the parameter consists of a single group enclosed in braces, we must
+strip off the enclosing braces. That's why |rbrace_ptr| was introduced.
+
+@<Tidy up the parameter just scanned, and tuck it away@>=
+begin if (m=1)and(info(p)<right_brace_limit)and(p<>temp_head) then
+ begin link(rbrace_ptr):=null; free_avail(p);
+ p:=link(temp_head); pstack[n]:=link(p); free_avail(p);
+ end
+else pstack[n]:=link(temp_head);
+incr(n);
+if tracing_macros>0 then
+ begin begin_diagnostic; print_nl(match_chr); print_int(n);
+ print("<-"); show_token_list(pstack[n-1],null,1000);
+ end_diagnostic(false);
+ end;
+end
+
+@ @<Show the text of the macro being expanded@>=
+begin begin_diagnostic; print_ln; print_cs(warning_index);
+token_show(ref_count); end_diagnostic(false);
+end
+
+@* \[26] Basic scanning subroutines.
+Let's turn now to some procedures that \TeX\ calls upon frequently to digest
+certain kinds of patterns in the input. Most of these are quite simple;
+some are quite elaborate. Almost all of the routines call |get_x_token|,
+which can cause them to be invoked recursively.
+@^stomach@>
+@^recursion@>
+
+@ The |scan_left_brace| routine is called when a left brace is supposed to be
+the next non-blank token. (The term ``left brace'' means, more precisely,
+a character whose catcode is |left_brace|.) \TeX\ allows \.{\\relax} to
+appear before the |left_brace|.
+
+@p procedure scan_left_brace; {reads a mandatory |left_brace|}
+begin @<Get the next non-blank non-relax non-call token@>;
+if cur_cmd<>left_brace then
+ begin print_err("Missing { inserted");
+@.Missing \{ inserted@>
+ help4("A left brace was mandatory here, so I've put one in.")@/
+ ("You might want to delete and/or insert some corrections")@/
+ ("so that I will find a matching right brace soon.")@/
+ ("(If you're confused by all this, try typing `I}' now.)");
+ back_error; cur_tok:=left_brace_token+"{"; cur_cmd:=left_brace;
+ cur_chr:="{"; incr(align_state);
+ end;
+end;
+
+@ @<Get the next non-blank non-relax non-call token@>=
+repeat get_x_token;
+until (cur_cmd<>spacer)and(cur_cmd<>relax)
+
+@ The |scan_optional_equals| routine looks for an optional `\.=' sign preceded
+by optional spaces; `\.{\\relax}' is not ignored here.
+
+@p procedure scan_optional_equals;
+begin @<Get the next non-blank non-call token@>;
+if cur_tok<>other_token+"=" then back_input;
+end;
+
+@ @<Get the next non-blank non-call token@>=
+repeat get_x_token;
+until cur_cmd<>spacer
+
+@ In case you are getting bored, here is a slightly less trivial routine:
+Given a string of lowercase letters, like `\.{pt}' or `\.{plus}' or
+`\.{width}', the |scan_keyword| routine checks to see whether the next
+tokens of input match this string. The match must be exact, except that
+uppercase letters will match their lowercase counterparts; uppercase
+equivalents are determined by subtracting |"a"-"A"|, rather than using the
+|uc_code| table, since \TeX\ uses this routine only for its own limited
+set of keywords.
+
+If a match is found, the characters are effectively removed from the input
+and |true| is returned. Otherwise |false| is returned, and the input
+is left essentially unchanged (except for the fact that some macros
+may have been expanded, etc.).
+@^inner loop@>
+
+@p function scan_keyword(@!s:str_number):boolean; {look for a given string}
+label exit;
+var p:pointer; {tail of the backup list}
+@!q:pointer; {new node being added to the token list via |store_new_token|}
+@!k:pool_pointer; {index into |str_pool|}
+begin p:=backup_head; link(p):=null; k:=str_start[s];
+while k<str_start[s+1] do
+ begin get_x_token; {recursion is possible here}
+@^recursion@>
+ if (cur_cs=0)and@|
+ ((cur_chr=so(str_pool[k]))or(cur_chr=so(str_pool[k])-"a"+"A")) then
+ begin store_new_token(cur_tok); incr(k);
+ end
+ else if (cur_cmd<>spacer)or(p<>backup_head) then
+ begin back_input;
+ if p<>backup_head then back_list(link(backup_head));
+ scan_keyword:=false; return;
+ end;
+ end;
+flush_list(link(backup_head)); scan_keyword:=true;
+exit:end;
+
+@ Here is a procedure that sounds an alarm when mu and non-mu units
+are being switched.
+
+@p procedure mu_error;
+begin print_err("Incompatible glue units");
+@.Incompatible glue units@>
+help1("I'm going to assume that 1mu=1pt when they're mixed.");
+error;
+end;
+
+@ The next routine `|scan_something_internal|' is used to fetch internal
+numeric quantities like `\.{\\hsize}', and also to handle the `\.{\\the}'
+when expanding constructions like `\.{\\the\\toks0}' and
+`\.{\\the\\baselineskip}'. Soon we will be considering the |scan_int|
+procedure, which calls |scan_something_internal|; on the other hand,
+|scan_something_internal| also calls |scan_int|, for constructions like
+`\.{\\catcode\`\\\$}' or `\.{\\fontdimen} \.3 \.{\\ff}'. So we
+have to declare |scan_int| as a |forward| procedure. A few other
+procedures are also declared at this point.
+
+@p procedure@?scan_int; forward; {scans an integer value}
+@t\4\4@>@<Declare procedures that scan restricted classes of integers@>@;
+@t\4\4@>@<Declare procedures that scan font-related stuff@>
+
+@ \TeX\ doesn't know exactly what to expect when |scan_something_internal|
+begins. For example, an integer or dimension or glue value could occur
+immediately after `\.{\\hskip}'; and one can even say \.{\\the} with
+respect to token lists in constructions like
+`\.{\\xdef\\o\{\\the\\output\}}'. On the other hand, only integers are
+allowed after a construction like `\.{\\count}'. To handle the various
+possibilities, |scan_something_internal| has a |level| parameter, which
+tells the ``highest'' kind of quantity that |scan_something_internal| is
+allowed to produce. Six levels are distinguished, namely |int_val|,
+|dimen_val|, |glue_val|, |mu_val|, |ident_val|, and |tok_val|.
+
+The output of |scan_something_internal| (and of the other routines
+|scan_int|, |scan_dimen|, and |scan_glue| below) is put into the global
+variable |cur_val|, and its level is put into |cur_val_level|. The highest
+values of |cur_val_level| are special: |mu_val| is used only when
+|cur_val| points to something in a ``muskip'' register, or to one of the
+three parameters \.{\\thinmuskip}, \.{\\medmuskip}, \.{\\thickmuskip};
+|ident_val| is used only when |cur_val| points to a font identifier;
+|tok_val| is used only when |cur_val| points to |null| or to the reference
+count of a token list. The last two cases are allowed only when
+|scan_something_internal| is called with |level=tok_val|.
+
+If the output is glue, |cur_val| will point to a glue specification, and
+the reference count of that glue will have been updated to reflect this
+reference; if the output is a nonempty token list, |cur_val| will point to
+its reference count, but in this case the count will not have been updated.
+Otherwise |cur_val| will contain the integer or scaled value in question.
+
+@d int_val=0 {integer values}
+@d dimen_val=1 {dimension values}
+@d glue_val=2 {glue specifications}
+@d mu_val=3 {math glue specifications}
+@d ident_val=4 {font identifier}
+@d tok_val=5 {token lists}
+
+@<Glob...@>=
+@!cur_val:integer; {value returned by numeric scanners}
+@!cur_val_level:int_val..tok_val; {the ``level'' of this value}
+
+@ The hash table is initialized with `\.{\\count}', `\.{\\dimen}', `\.{\\skip}',
+and `\.{\\muskip}' all having |register| as their command code; they are
+distinguished by the |chr_code|, which is either |int_val|, |dimen_val|,
+|glue_val|, or |mu_val|.
+
+@<Put each...@>=
+primitive("count",register,int_val);
+@!@:count_}{\.{\\count} primitive@>
+primitive("dimen",register,dimen_val);
+@!@:dimen_}{\.{\\dimen} primitive@>
+primitive("skip",register,glue_val);
+@!@:skip_}{\.{\\skip} primitive@>
+primitive("muskip",register,mu_val);
+@!@:mu_skip_}{\.{\\muskip} primitive@>
+
+@ @<Cases of |print_cmd_chr|...@>=
+register: if chr_code=int_val then print_esc("count")
+ else if chr_code=dimen_val then print_esc("dimen")
+ else if chr_code=glue_val then print_esc("skip")
+ else print_esc("muskip");
+
+@ OK, we're ready for |scan_something_internal| itself. A second parameter,
+|negative|, is set |true| if the value that is found should be negated.
+It is assumed that |cur_cmd| and |cur_chr| represent the first token of
+the internal quantity to be scanned; an error will be signalled if
+|cur_cmd<min_internal| or |cur_cmd>max_internal|.
+
+@d scanned_result_end(#)==cur_val_level:=#;@+end
+@d scanned_result(#)==@+begin cur_val:=#;scanned_result_end
+
+@p procedure scan_something_internal(@!level:small_number;@!negative:boolean);
+ {fetch an internal parameter}
+var m:halfword; {|chr_code| part of the operand token}
+@!p:0..nest_size; {index into |nest|}
+begin m:=cur_chr;
+case cur_cmd of
+def_code: @<Fetch a character code from some table@>;
+toks_register,assign_toks,def_family,set_font,def_font: @<Fetch a token list or
+ font identifier, provided that |level=tok_val|@>;
+assign_int: scanned_result(eqtb[m].int)(int_val);
+assign_dimen: scanned_result(eqtb[m].sc)(dimen_val);
+assign_glue: scanned_result(equiv(m))(glue_val);
+assign_mu_glue: scanned_result(equiv(m))(mu_val);
+set_aux: @<Fetch the |space_factor| or the |prev_depth|@>;
+set_prev_graf: @<Fetch the |prev_graf|@>;
+set_page_int:@<Fetch the |dead_cycles| or the |insert_penalties|@>;
+set_page_dimen: @<Fetch something on the |page_so_far|@>;
+set_shape: @<Fetch the |par_shape| size@>;
+set_box_dimen: @<Fetch a box dimension@>;
+char_given,math_given: scanned_result(cur_chr)(int_val);
+assign_font_dimen: @<Fetch a font dimension@>;
+assign_font_int: @<Fetch a font integer@>;
+register: @<Fetch a register@>;
+last_item: @<Fetch an item in the current node, if appropriate@>;
+othercases @<Complain that \.{\\the} can't do this; give zero result@>
+endcases;@/
+while cur_val_level>level do @<Convert \(c)|cur_val| to a lower level@>;
+@<Fix the reference count, if any, and negate |cur_val| if |negative|@>;
+end;
+
+@ @<Fetch a character code from some table@>=
+begin scan_char_num;
+if m=math_code_base then scanned_result(ho(math_code(cur_val)))(int_val)
+else if m<math_code_base then scanned_result(equiv(m+cur_val))(int_val)
+else scanned_result(eqtb[m+cur_val].int)(int_val);
+end
+
+@ @<Fetch a token list...@>=
+if level<>tok_val then
+ begin print_err("Missing number, treated as zero");
+@.Missing number...@>
+ help3("A number should have been here; I inserted `0'.")@/
+ ("(If you can't figure out why I needed to see a number,")@/
+ ("look up `weird error' in the index to The TeXbook.)");
+@:TeXbook}{\sl The \TeX book@>
+ back_error; scanned_result(0)(dimen_val);
+ end
+else if cur_cmd<=assign_toks then
+ begin if cur_cmd<assign_toks then {|cur_cmd=toks_register|}
+ begin scan_eight_bit_int; m:=toks_base+cur_val;
+ end;
+ scanned_result(equiv(m))(tok_val);
+ end
+else begin back_input; scan_font_ident;
+ scanned_result(font_id_base+cur_val)(ident_val);
+ end
+
+@ Users refer to `\.{\\the\\spacefactor}' only in horizontal
+mode, and to `\.{\\the\\prevdepth}' only in vertical mode; so we put the
+associated mode in the modifier part of the |set_aux| command.
+The |set_page_int| command has modifier 0 or 1, for `\.{\\deadcycles}' and
+`\.{\\insertpenalties}', respectively. The |set_box_dimen| command is
+modified by either |width_offset|, |height_offset|, or |depth_offset|.
+And the |last_item| command is modified by either |int_val|, |dimen_val|,
+|glue_val|, |input_line_no_code|, or |badness_code|.
+
+@d input_line_no_code=glue_val+1 {code for \.{\\inputlineno}}
+@d badness_code=glue_val+2 {code for \.{\\badness}}
+
+@<Put each...@>=
+primitive("spacefactor",set_aux,hmode);
+@!@:space_factor_}{\.{\\spacefactor} primitive@>
+primitive("prevdepth",set_aux,vmode);@/
+@!@:prev_depth_}{\.{\\prevdepth} primitive@>
+primitive("deadcycles",set_page_int,0);
+@!@:dead_cycles_}{\.{\\deadcycles} primitive@>
+primitive("insertpenalties",set_page_int,1);
+@!@:insert_penalties_}{\.{\\insertpenalties} primitive@>
+primitive("wd",set_box_dimen,width_offset);
+@!@:wd_}{\.{\\wd} primitive@>
+primitive("ht",set_box_dimen,height_offset);
+@!@:ht_}{\.{\\ht} primitive@>
+primitive("dp",set_box_dimen,depth_offset);
+@!@:dp_}{\.{\\dp} primitive@>
+primitive("lastpenalty",last_item,int_val);
+@!@:last_penalty_}{\.{\\lastpenalty} primitive@>
+primitive("lastkern",last_item,dimen_val);
+@!@:last_kern_}{\.{\\lastkern} primitive@>
+primitive("lastskip",last_item,glue_val);
+@!@:last_skip_}{\.{\\lastskip} primitive@>
+primitive("inputlineno",last_item,input_line_no_code);
+@!@:input_line_no_}{\.{\\inputlineno} primitive@>
+primitive("badness",last_item,badness_code);
+@!@:badness_}{\.{\\badness} primitive@>
+
+@ @<Cases of |print_cmd_chr|...@>=
+set_aux: if chr_code=vmode then print_esc("prevdepth")
+@+else print_esc("spacefactor");
+set_page_int: if chr_code=0 then print_esc("deadcycles")
+@+else print_esc("insertpenalties");
+set_box_dimen: if chr_code=width_offset then print_esc("wd")
+else if chr_code=height_offset then print_esc("ht")
+else print_esc("dp");
+last_item: case chr_code of
+ int_val: print_esc("lastpenalty");
+ dimen_val: print_esc("lastkern");
+ glue_val: print_esc("lastskip");
+ input_line_no_code: print_esc("inputlineno");
+ othercases print_esc("badness")
+ endcases;
+
+@ @<Fetch the |space_factor| or the |prev_depth|@>=
+if abs(mode)<>m then
+ begin print_err("Improper "); print_cmd_chr(set_aux,m);
+@.Improper \\spacefactor@>
+@.Improper \\prevdepth@>
+ help4("You can refer to \spacefactor only in horizontal mode;")@/
+ ("you can refer to \prevdepth only in vertical mode; and")@/
+ ("neither of these is meaningful inside \write. So")@/
+ ("I'm forgetting what you said and using zero instead.");
+ error;
+ if level<>tok_val then scanned_result(0)(dimen_val)
+ else scanned_result(0)(int_val);
+ end
+else if m=vmode then
+ begin cur_val:=prev_depth; cur_val_level:=dimen_val;
+ end
+else begin cur_val:=space_factor; cur_val_level:=int_val;
+ end
+
+@ @<Fetch the |dead_cycles| or the |insert_penalties|@>=
+begin if m=0 then cur_val:=dead_cycles@+else cur_val:=insert_penalties;
+cur_val_level:=int_val;
+end
+
+@ @<Fetch a box dimension@>=
+begin scan_eight_bit_int;
+if box(cur_val)=null then cur_val:=0 @+else cur_val:=mem[box(cur_val)+m].sc;
+cur_val_level:=dimen_val;
+end
+
+@ Inside an \.{\\output} routine, a user may wish to look at the page totals
+that were present at the moment when output was triggered.
+
+@d max_dimen==@'7777777777 {$2^{30}-1$}
+
+@<Fetch something on the |page_so_far|@>=
+begin if (page_contents=empty) and (not output_active) then
+ if m=0 then cur_val:=max_dimen@+else cur_val:=0
+else cur_val:=page_so_far[m];
+cur_val_level:=dimen_val;
+end
+
+@ @<Fetch the |prev_graf|@>=
+if mode=0 then scanned_result(0)(int_val) {|prev_graf=0| within \.{\\write}}
+else begin nest[nest_ptr]:=cur_list; p:=nest_ptr;
+ while abs(nest[p].mode_field)<>vmode do decr(p);
+ scanned_result(nest[p].pg_field)(int_val);
+ end
+
+@ @<Fetch the |par_shape| size@>=
+begin if par_shape_ptr=null then cur_val:=0
+else cur_val:=info(par_shape_ptr);
+cur_val_level:=int_val;
+end
+
+@ Here is where \.{\\lastpenalty}, \.{\\lastkern}, and \.{\\lastskip} are
+implemented. The reference count for \.{\\lastskip} will be updated later.
+
+We also handle \.{\\inputlineno} and \.{\\badness} here, because they are
+legal in similar contexts.
+
+@<Fetch an item in the current node...@>=
+if cur_chr>glue_val then
+ begin if cur_chr=input_line_no_code then cur_val:=line
+ else cur_val:=last_badness; {|cur_chr=badness_code|}
+ cur_val_level:=int_val;
+ end
+else begin if cur_chr=glue_val then cur_val:=zero_glue@+else cur_val:=0;
+ cur_val_level:=cur_chr;
+ if not is_char_node(tail)and(mode<>0) then
+ case cur_chr of
+ int_val: if type(tail)=penalty_node then cur_val:=penalty(tail);
+ dimen_val: if type(tail)=kern_node then cur_val:=width(tail);
+ glue_val: if type(tail)=glue_node then
+ begin cur_val:=glue_ptr(tail);
+ if subtype(tail)=mu_glue then cur_val_level:=mu_val;
+ end;
+ end {there are no other cases}
+ else if (mode=vmode)and(tail=head) then
+ case cur_chr of
+ int_val: cur_val:=last_penalty;
+ dimen_val: cur_val:=last_kern;
+ glue_val: if last_glue<>max_halfword then cur_val:=last_glue;
+ end; {there are no other cases}
+ end
+
+@ @<Fetch a font dimension@>=
+begin find_font_dimen(false); font_info[fmem_ptr].sc:=0;
+scanned_result(font_info[cur_val].sc)(dimen_val);
+end
+
+@ @<Fetch a font integer@>=
+begin scan_font_ident;
+if m=0 then scanned_result(hyphen_char[cur_val])(int_val)
+else scanned_result(skew_char[cur_val])(int_val);
+end
+
+@ @<Fetch a register@>=
+begin scan_eight_bit_int;
+case m of
+int_val:cur_val:=count(cur_val);
+dimen_val:cur_val:=dimen(cur_val);
+glue_val: cur_val:=skip(cur_val);
+mu_val: cur_val:=mu_skip(cur_val);
+end; {there are no other cases}
+cur_val_level:=m;
+end
+
+@ @<Complain that \.{\\the} can't do this; give zero result@>=
+begin print_err("You can't use `"); print_cmd_chr(cur_cmd,cur_chr);
+@.You can't use x after ...@>
+print("' after "); print_esc("the");
+help1("I'm forgetting what you said and using zero instead.");
+error;
+if level<>tok_val then scanned_result(0)(dimen_val)
+else scanned_result(0)(int_val);
+end
+
+@ When a |glue_val| changes to a |dimen_val|, we use the width component
+of the glue; there is no need to decrease the reference count, since it
+has not yet been increased. When a |dimen_val| changes to an |int_val|,
+we use scaled points so that the value doesn't actually change. And when a
+|mu_val| changes to a |glue_val|, the value doesn't change either.
+
+@<Convert \(c)|cur_val| to a lower level@>=
+begin if cur_val_level=glue_val then cur_val:=width(cur_val)
+else if cur_val_level=mu_val then mu_error;
+decr(cur_val_level);
+end
+
+@ If |cur_val| points to a glue specification at this point, the reference
+count for the glue does not yet include the reference by |cur_val|.
+If |negative| is |true|, |cur_val_level| is known to be |<=mu_val|.
+
+@<Fix the reference count, if any, ...@>=
+if negative then
+ if cur_val_level>=glue_val then
+ begin cur_val:=new_spec(cur_val);
+ @<Negate all three glue components of |cur_val|@>;
+ end
+ else negate(cur_val)
+else if (cur_val_level>=glue_val)and(cur_val_level<=mu_val) then
+ add_glue_ref(cur_val)
+
+@ @<Negate all three...@>=
+begin negate(width(cur_val));
+negate(stretch(cur_val));
+negate(shrink(cur_val));
+end
+
+@ Our next goal is to write the |scan_int| procedure, which scans anything that
+\TeX\ treats as an integer. But first we might as well look at some simple
+applications of |scan_int| that have already been made inside of
+|scan_something_internal|.
+
+@ @<Declare procedures that scan restricted classes of integers@>=
+procedure scan_eight_bit_int;
+begin scan_int;
+if (cur_val<0)or(cur_val>255) then
+ begin print_err("Bad register code");
+@.Bad register code@>
+ help2("A register number must be between 0 and 255.")@/
+ ("I changed this one to zero."); int_error(cur_val); cur_val:=0;
+ end;
+end;
+
+@ @<Declare procedures that scan restricted classes of integers@>=
+procedure scan_char_num;
+begin scan_int;
+if (cur_val<0)or(cur_val>255) then
+ begin print_err("Bad character code");
+@.Bad character code@>
+ help2("A character number must be between 0 and 255.")@/
+ ("I changed this one to zero."); int_error(cur_val); cur_val:=0;
+ end;
+end;
+
+@ While we're at it, we might as well deal with similar routines that
+will be needed later.
+
+@<Declare procedures that scan restricted classes of integers@>=
+procedure scan_four_bit_int;
+begin scan_int;
+if (cur_val<0)or(cur_val>15) then
+ begin print_err("Bad number");
+@.Bad number@>
+ help2("Since I expected to read a number between 0 and 15,")@/
+ ("I changed this one to zero."); int_error(cur_val); cur_val:=0;
+ end;
+end;
+
+@ @<Declare procedures that scan restricted classes of integers@>=
+procedure scan_fifteen_bit_int;
+begin scan_int;
+if (cur_val<0)or(cur_val>@'77777) then
+ begin print_err("Bad mathchar");
+@.Bad mathchar@>
+ help2("A mathchar number must be between 0 and 32767.")@/
+ ("I changed this one to zero."); int_error(cur_val); cur_val:=0;
+ end;
+end;
+
+@ @<Declare procedures that scan restricted classes of integers@>=
+procedure scan_twenty_seven_bit_int;
+begin scan_int;
+if (cur_val<0)or(cur_val>@'777777777) then
+ begin print_err("Bad delimiter code");
+@.Bad delimiter code@>
+ help2("A numeric delimiter code must be between 0 and 2^{27}-1.")@/
+ ("I changed this one to zero."); int_error(cur_val); cur_val:=0;
+ end;
+end;
+
+@ An integer number can be preceded by any number of spaces and `\.+' or
+`\.-' signs. Then comes either a decimal constant (i.e., radix 10), an
+octal constant (i.e., radix 8, preceded by~\.\'), a hexadecimal constant
+(radix 16, preceded by~\."), an alphabetic constant (preceded by~\.\`), or
+an internal variable. After scanning is complete,
+|cur_val| will contain the answer, which must be at most
+$2^{31}-1=2147483647$ in absolute value. The value of |radix| is set to
+10, 8, or 16 in the cases of decimal, octal, or hexadecimal constants,
+otherwise |radix| is set to zero. An optional space follows a constant.
+
+@d octal_token=other_token+"'" {apostrophe, indicates an octal constant}
+@d hex_token=other_token+"""" {double quote, indicates a hex constant}
+@d alpha_token=other_token+"`" {reverse apostrophe, precedes alpha constants}
+@d point_token=other_token+"." {decimal point}
+@d continental_point_token=other_token+"," {decimal point, Eurostyle}
+
+@<Glob...@>=
+@!radix:small_number; {|scan_int| sets this to 8, 10, 16, or zero}
+
+@ We initialize the following global variables just in case |expand|
+comes into action before any of the basic scanning routines has assigned
+them a value.
+
+@<Set init...@>=
+cur_val:=0; cur_val_level:=int_val; radix:=0; cur_order:=0;
+
+@ The |scan_int| routine is used also to scan the integer part of a
+fraction; for example, the `\.3' in `\.{3.14159}' will be found by
+|scan_int|. The |scan_dimen| routine assumes that |cur_tok=point_token|
+after the integer part of such a fraction has been scanned by |scan_int|,
+and that the decimal point has been backed up to be scanned again.
+
+@p procedure scan_int; {sets |cur_val| to an integer}
+label done;
+var negative:boolean; {should the answer be negated?}
+@!m:integer; {|@t$2^{31}$@> div radix|, the threshold of danger}
+@!d:small_number; {the digit just scanned}
+@!vacuous:boolean; {have no digits appeared?}
+@!OK_so_far:boolean; {has an error message been issued?}
+begin radix:=0; OK_so_far:=true;@/
+@<Get the next non-blank non-sign token; set |negative| appropriately@>;
+if cur_tok=alpha_token then @<Scan an alphabetic character code into |cur_val|@>
+else if (cur_cmd>=min_internal)and(cur_cmd<=max_internal) then
+ scan_something_internal(int_val,false)
+else @<Scan a numeric constant@>;
+if negative then negate(cur_val);
+end;
+
+@ @<Get the next non-blank non-sign token...@>=
+negative:=false;
+repeat @<Get the next non-blank non-call token@>;
+if cur_tok=other_token+"-" then
+ begin negative := not negative; cur_tok:=other_token+"+";
+ end;
+until cur_tok<>other_token+"+"
+
+@ A space is ignored after an alphabetic character constant, so that
+such constants behave like numeric ones.
+
+@<Scan an alphabetic character code into |cur_val|@>=
+begin get_token; {suppress macro expansion}
+if cur_tok<cs_token_flag then
+ begin cur_val:=cur_chr;
+ if cur_cmd<=right_brace then
+ if cur_cmd=right_brace then incr(align_state)
+ else decr(align_state);
+ end
+else if cur_tok<cs_token_flag+single_base then
+ cur_val:=cur_tok-cs_token_flag-active_base
+else cur_val:=cur_tok-cs_token_flag-single_base;
+if cur_val>255 then
+ begin print_err("Improper alphabetic constant");
+@.Improper alphabetic constant@>
+ help2("A one-character control sequence belongs after a ` mark.")@/
+ ("So I'm essentially inserting \0 here.");
+ cur_val:="0"; back_error;
+ end
+else @<Scan an optional space@>;
+end
+
+@ @<Scan an optional space@>=
+begin get_x_token; if cur_cmd<>spacer then back_input;
+end
+
+@ @<Scan a numeric constant@>=
+begin radix:=10; m:=214748364;
+if cur_tok=octal_token then
+ begin radix:=8; m:=@'2000000000; get_x_token;
+ end
+else if cur_tok=hex_token then
+ begin radix:=16; m:=@'1000000000; get_x_token;
+ end;
+vacuous:=true; cur_val:=0;@/
+@<Accumulate the constant until |cur_tok| is not a suitable digit@>;
+if vacuous then @<Express astonishment that no number was here@>
+else if cur_cmd<>spacer then back_input;
+end
+
+@ @d infinity==@'17777777777 {the largest positive value that \TeX\ knows}
+@d zero_token=other_token+"0" {zero, the smallest digit}
+@d A_token=letter_token+"A" {the smallest special hex digit}
+@d other_A_token=other_token+"A" {special hex digit of type |other_char|}
+
+@<Accumulate the constant...@>=
+loop@+ begin if (cur_tok<zero_token+radix)and(cur_tok>=zero_token)and
+ (cur_tok<=zero_token+9) then d:=cur_tok-zero_token
+ else if radix=16 then
+ if (cur_tok<=A_token+5)and(cur_tok>=A_token) then d:=cur_tok-A_token+10
+ else if (cur_tok<=other_A_token+5)and(cur_tok>=other_A_token) then
+ d:=cur_tok-other_A_token+10
+ else goto done
+ else goto done;
+ vacuous:=false;
+ if (cur_val>=m)and((cur_val>m)or(d>7)or(radix<>10)) then
+ begin if OK_so_far then
+ begin print_err("Number too big");
+@.Number too big@>
+ help2("I can only go up to 2147483647='17777777777=""7FFFFFFF,")@/
+ ("so I'm using that number instead of yours.");
+ error; cur_val:=infinity; OK_so_far:=false;
+ end;
+ end
+ else cur_val:=cur_val*radix+d;
+ get_x_token;
+ end;
+done:
+
+@ @<Express astonishment...@>=
+begin print_err("Missing number, treated as zero");
+@.Missing number...@>
+help3("A number should have been here; I inserted `0'.")@/
+ ("(If you can't figure out why I needed to see a number,")@/
+ ("look up `weird error' in the index to The TeXbook.)");
+@:TeXbook}{\sl The \TeX book@>
+back_error;
+end
+
+@ The |scan_dimen| routine is similar to |scan_int|, but it sets |cur_val| to
+a |scaled| value, i.e., an integral number of sp. One of its main tasks
+is therefore to interpret the abbreviations for various kinds of units and
+to convert measurements to scaled points.
+
+There are three parameters: |mu| is |true| if the finite units must be
+`\.{mu}', while |mu| is |false| if `\.{mu}' units are disallowed;
+|inf| is |true| if the infinite units `\.{fil}', `\.{fill}', `\.{filll}'
+are permitted; and |shortcut| is |true| if |cur_val| already contains
+an integer and only the units need to be considered.
+
+The order of infinity that was found in the case of infinite glue is returned
+in the global variable |cur_order|.
+
+@<Glob...@>=
+@!cur_order:glue_ord; {order of infinity found by |scan_dimen|}
+
+@ Constructions like `\.{-\'77 pt}' are legal dimensions, so |scan_dimen|
+may begin with |scan_int|. This explains why it is convenient to use
+|scan_int| also for the integer part of a decimal fraction.
+
+Several branches of |scan_dimen| work with |cur_val| as an integer and
+with an auxiliary fraction |f|, so that the actual quantity of interest is
+$|cur_val|+|f|/2^{16}$. At the end of the routine, this ``unpacked''
+representation is put into the single word |cur_val|, which suddenly
+switches significance from |integer| to |scaled|.
+
+@d attach_fraction=88 {go here to pack |cur_val| and |f| into |cur_val|}
+@d attach_sign=89 {go here when |cur_val| is correct except perhaps for sign}
+@d scan_normal_dimen==scan_dimen(false,false,false)
+
+@p procedure scan_dimen(@!mu,@!inf,@!shortcut:boolean);
+ {sets |cur_val| to a dimension}
+label done, done1, done2, found, not_found, attach_fraction, attach_sign;
+var negative:boolean; {should the answer be negated?}
+@!f:integer; {numerator of a fraction whose denominator is $2^{16}$}
+@<Local variables for dimension calculations@>@;
+begin f:=0; arith_error:=false; cur_order:=normal; negative:=false;
+if not shortcut then
+ begin @<Get the next non-blank non-sign...@>;
+ if (cur_cmd>=min_internal)and(cur_cmd<=max_internal) then
+ @<Fetch an internal dimension and |goto attach_sign|,
+ or fetch an internal integer@>
+ else begin back_input;
+ if cur_tok=continental_point_token then cur_tok:=point_token;
+ if cur_tok<>point_token then scan_int
+ else begin radix:=10; cur_val:=0;
+ end;
+ if cur_tok=continental_point_token then cur_tok:=point_token;
+ if (radix=10)and(cur_tok=point_token) then @<Scan decimal fraction@>;
+ end;
+ end;
+if cur_val<0 then {in this case |f=0|}
+ begin negative := not negative; negate(cur_val);
+ end;
+@<Scan units and set |cur_val| to $x\cdot(|cur_val|+f/2^{16})$, where there
+ are |x| sp per unit; |goto attach_sign| if the units are internal@>;
+@<Scan an optional space@>;
+attach_sign: if arith_error or(abs(cur_val)>=@'10000000000) then
+ @<Report that this dimension is out of range@>;
+if negative then negate(cur_val);
+end;
+
+@ @<Fetch an internal dimension and |goto attach_sign|...@>=
+if mu then
+ begin scan_something_internal(mu_val,false);
+ @<Coerce glue to a dimension@>;
+ if cur_val_level=mu_val then goto attach_sign;
+ if cur_val_level<>int_val then mu_error;
+ end
+else begin scan_something_internal(dimen_val,false);
+ if cur_val_level=dimen_val then goto attach_sign;
+ end
+
+@ @<Local variables for dimension calculations@>=
+@!num,@!denom:1..65536; {conversion ratio for the scanned units}
+@!k,@!kk:small_number; {number of digits in a decimal fraction}
+@!p,@!q:pointer; {top of decimal digit stack}
+@!v:scaled; {an internal dimension}
+@!save_cur_val:integer; {temporary storage of |cur_val|}
+
+@ The following code is executed when |scan_something_internal| was
+called asking for |mu_val|, when we really wanted a ``mudimen'' instead
+of ``muglue.''
+
+@<Coerce glue to a dimension@>=
+if cur_val_level>=glue_val then
+ begin v:=width(cur_val); delete_glue_ref(cur_val); cur_val:=v;
+ end
+
+@ When the following code is executed, we have |cur_tok=point_token|, but this
+token has been backed up using |back_input|; we must first discard it.
+
+It turns out that a decimal point all by itself is equivalent to `\.{0.0}'.
+Let's hope people don't use that fact.
+
+@<Scan decimal fraction@>=
+begin k:=0; p:=null; get_token; {|point_token| is being re-scanned}
+loop@+ begin get_x_token;
+ if (cur_tok>zero_token+9)or(cur_tok<zero_token) then goto done1;
+ if k<17 then {digits for |k>=17| cannot affect the result}
+ begin q:=get_avail; link(q):=p; info(q):=cur_tok-zero_token;
+ p:=q; incr(k);
+ end;
+ end;
+done1: for kk:=k downto 1 do
+ begin dig[kk-1]:=info(p); q:=p; p:=link(p); free_avail(q);
+ end;
+f:=round_decimals(k);
+if cur_cmd<>spacer then back_input;
+end
+
+@ Now comes the harder part: At this point in the program, |cur_val| is a
+nonnegative integer and $f/2^{16}$ is a nonnegative fraction less than 1;
+we want to multiply the sum of these two quantities by the appropriate
+factor, based on the specified units, in order to produce a |scaled|
+result, and we want to do the calculation with fixed point arithmetic that
+does not overflow.
+
+@<Scan units and set |cur_val| to $x\cdot(|cur_val|+f/2^{16})$...@>=
+if inf then @<Scan for \(f)\.{fil} units; |goto attach_fraction| if found@>;
+@<Scan for \(u)units that are internal dimensions;
+ |goto attach_sign| with |cur_val| set if found@>;
+if mu then @<Scan for \(m)\.{mu} units and |goto attach_fraction|@>;
+if scan_keyword("true") then @<Adjust \(f)for the magnification ratio@>;
+@.true@>
+if scan_keyword("pt") then goto attach_fraction; {the easy case}
+@.pt@>
+@<Scan for \(a)all other units and adjust |cur_val| and |f| accordingly;
+ |goto done| in the case of scaled points@>;
+attach_fraction: if cur_val>=@'40000 then arith_error:=true
+else cur_val:=cur_val*unity+f;
+done:
+
+@ A specification like `\.{filllll}' or `\.{fill L L L}' will lead to two
+error messages (one for each additional keyword \.{"l"}).
+
+@<Scan for \(f)\.{fil} units...@>=
+if scan_keyword("fil") then
+@.fil@>
+ begin cur_order:=fil;
+ while scan_keyword("l") do
+ begin if cur_order=filll then
+ begin print_err("Illegal unit of measure (");
+@.Illegal unit of measure@>
+ print("replaced by filll)");
+ help1("I dddon't go any higher than filll."); error;
+ end
+ else incr(cur_order);
+ end;
+ goto attach_fraction;
+ end
+
+@ @<Scan for \(u)units that are internal dimensions...@>=
+save_cur_val:=cur_val;
+@<Get the next non-blank non-call...@>;
+if (cur_cmd<min_internal)or(cur_cmd>max_internal) then back_input
+else begin if mu then
+ begin scan_something_internal(mu_val,false); @<Coerce glue...@>;
+ if cur_val_level<>mu_val then mu_error;
+ end
+ else scan_something_internal(dimen_val,false);
+ v:=cur_val; goto found;
+ end;
+if mu then goto not_found;
+if scan_keyword("em") then v:=(@<The em width for |cur_font|@>)
+@.em@>
+else if scan_keyword("ex") then v:=(@<The x-height for |cur_font|@>)
+@.ex@>
+else goto not_found;
+@<Scan an optional space@>;
+found:cur_val:=nx_plus_y(save_cur_val,v,xn_over_d(v,f,@'200000));
+goto attach_sign;
+not_found:
+
+@ @<Scan for \(m)\.{mu} units and |goto attach_fraction|@>=
+if scan_keyword("mu") then goto attach_fraction
+@.mu@>
+else begin print_err("Illegal unit of measure ("); print("mu inserted)");
+@.Illegal unit of measure@>
+ help4("The unit of measurement in math glue must be mu.")@/
+ ("To recover gracefully from this error, it's best to")@/
+ ("delete the erroneous units; e.g., type `2' to delete")@/
+ ("two letters. (See Chapter 27 of The TeXbook.)");
+@:TeXbook}{\sl The \TeX book@>
+ error; goto attach_fraction;
+ end
+
+@ @<Adjust \(f)for the magnification ratio@>=
+begin prepare_mag;
+if mag<>1000 then
+ begin cur_val:=xn_over_d(cur_val,1000,mag);
+ f:=(1000*f+@'200000*remainder) div mag;
+ cur_val:=cur_val+(f div @'200000); f:=f mod @'200000;
+ end;
+end
+
+@ The necessary conversion factors can all be specified exactly as
+fractions whose numerator and denominator are 32768 or less.
+According to the definitions here, $\rm2660\,dd\approx1000.33297\,mm$;
+this agrees well with the value $\rm1000.333\,mm$ cited by Bosshard
+@^Bosshard, Hans Rudolf@>
+in {\sl Technische Grundlagen zur Satzherstellung\/} (Bern, 1980).
+
+@d set_conversion_end(#)== denom:=#; end
+@d set_conversion(#)==@+begin num:=#; set_conversion_end
+
+@<Scan for \(a)all other units and adjust |cur_val| and |f|...@>=
+if scan_keyword("in") then set_conversion(7227)(100)
+@.in@>
+else if scan_keyword("pc") then set_conversion(12)(1)
+@.pc@>
+else if scan_keyword("cm") then set_conversion(7227)(254)
+@.cm@>
+else if scan_keyword("mm") then set_conversion(7227)(2540)
+@.mm@>
+else if scan_keyword("bp") then set_conversion(7227)(7200)
+@.bp@>
+else if scan_keyword("dd") then set_conversion(1238)(1157)
+@.dd@>
+else if scan_keyword("cc") then set_conversion(14856)(1157)
+@.cc@>
+else if scan_keyword("sp") then goto done
+@.sp@>
+else @<Complain about unknown unit and |goto done2|@>;
+cur_val:=xn_over_d(cur_val,num,denom);
+f:=(num*f+@'200000*remainder) div denom;@/
+cur_val:=cur_val+(f div @'200000); f:=f mod @'200000;
+done2:
+
+@ @<Complain about unknown unit...@>=
+begin print_err("Illegal unit of measure ("); print("pt inserted)");
+@.Illegal unit of measure@>
+help6("Dimensions can be in units of em, ex, in, pt, pc,")@/
+ ("cm, mm, dd, cc, bp, or sp; but yours is a new one!")@/
+ ("I'll assume that you meant to say pt, for printer's points.")@/
+ ("To recover gracefully from this error, it's best to")@/
+ ("delete the erroneous units; e.g., type `2' to delete")@/
+ ("two letters. (See Chapter 27 of The TeXbook.)");
+@:TeXbook}{\sl The \TeX book@>
+error; goto done2;
+end
+
+
+@ @<Report that this dimension is out of range@>=
+begin print_err("Dimension too large");
+@.Dimension too large@>
+help2("I can't work with sizes bigger than about 19 feet.")@/
+ ("Continue and I'll use the largest value I can.");@/
+error; cur_val:=max_dimen; arith_error:=false;
+end
+
+@ The final member of \TeX's value-scanning trio is |scan_glue|, which
+makes |cur_val| point to a glue specification. The reference count of that
+glue spec will take account of the fact that |cur_val| is pointing to~it.
+
+The |level| parameter should be either |glue_val| or |mu_val|.
+
+Since |scan_dimen| was so much more complex than |scan_int|, we might expect
+|scan_glue| to be even worse. But fortunately, it is very simple, since
+most of the work has already been done.
+
+@p procedure scan_glue(@!level:small_number);
+ {sets |cur_val| to a glue spec pointer}
+label exit;
+var negative:boolean; {should the answer be negated?}
+@!q:pointer; {new glue specification}
+@!mu:boolean; {does |level=mu_val|?}
+begin mu:=(level=mu_val); @<Get the next non-blank non-sign...@>;
+if (cur_cmd>=min_internal)and(cur_cmd<=max_internal) then
+ begin scan_something_internal(level,negative);
+ if cur_val_level>=glue_val then
+ begin if cur_val_level<>level then mu_error;
+ return;
+ end;
+ if cur_val_level=int_val then scan_dimen(mu,false,true)
+ else if level=mu_val then mu_error;
+ end
+else begin back_input; scan_dimen(mu,false,false);
+ if negative then negate(cur_val);
+ end;
+@<Create a new glue specification whose width is |cur_val|; scan for its
+ stretch and shrink components@>;
+exit:end;
+
+@ @<Create a new glue specification whose width is |cur_val|...@>=
+q:=new_spec(zero_glue); width(q):=cur_val;
+if scan_keyword("plus") then
+@.plus@>
+ begin scan_dimen(mu,true,false);
+ stretch(q):=cur_val; stretch_order(q):=cur_order;
+ end;
+if scan_keyword("minus") then
+@.minus@>
+ begin scan_dimen(mu,true,false);
+ shrink(q):=cur_val; shrink_order(q):=cur_order;
+ end;
+cur_val:=q
+
+@ Here's a similar procedure that returns a pointer to a rule node. This
+routine is called just after \TeX\ has seen \.{\\hrule} or \.{\\vrule};
+therefore |cur_cmd| will be either |hrule| or |vrule|. The idea is to store
+the default rule dimensions in the node, then to override them if
+`\.{height}' or `\.{width}' or `\.{depth}' specifications are
+found (in any order).
+
+@d default_rule=26214 {0.4\thinspace pt}
+
+@p function scan_rule_spec:pointer;
+label reswitch;
+var q:pointer; {the rule node being created}
+begin q:=new_rule; {|width|, |depth|, and |height| all equal |null_flag| now}
+if cur_cmd=vrule then width(q):=default_rule
+else begin height(q):=default_rule; depth(q):=0;
+ end;
+reswitch: if scan_keyword("width") then
+@.width@>
+ begin scan_normal_dimen; width(q):=cur_val; goto reswitch;
+ end;
+if scan_keyword("height") then
+@.height@>
+ begin scan_normal_dimen; height(q):=cur_val; goto reswitch;
+ end;
+if scan_keyword("depth") then
+@.depth@>
+ begin scan_normal_dimen; depth(q):=cur_val; goto reswitch;
+ end;
+scan_rule_spec:=q;
+end;
+
+@* \[27] Building token lists.
+The token lists for macros and for other things like \.{\\mark} and \.{\\output}
+and \.{\\write} are produced by a procedure called |scan_toks|.
+
+Before we get into the details of |scan_toks|, let's consider a much
+simpler task, that of converting the current string into a token list.
+The |str_toks| function does this; it classifies spaces as type |spacer|
+and everything else as type |other_char|.
+
+The token list created by |str_toks| begins at |link(temp_head)| and ends
+at the value |p| that is returned. (If |p=temp_head|, the list is empty.)
+
+@p function str_toks(@!b:pool_pointer):pointer;
+ {changes the string |str_pool[b..pool_ptr]| to a token list}
+var p:pointer; {tail of the token list}
+@!q:pointer; {new node being added to the token list via |store_new_token|}
+@!t:halfword; {token being appended}
+@!k:pool_pointer; {index into |str_pool|}
+begin str_room(1);
+p:=temp_head; link(p):=null; k:=b;
+while k<pool_ptr do
+ begin t:=so(str_pool[k]);
+ if t=" " then t:=space_token
+ else t:=other_token+t;
+ fast_store_new_token(t);
+ incr(k);
+ end;
+pool_ptr:=b; str_toks:=p;
+end;
+
+@ The main reason for wanting |str_toks| is the next function,
+|the_toks|, which has similar input/output characteristics.
+
+This procedure is supposed to scan something like `\.{\\skip\\count12}',
+i.e., whatever can follow `\.{\\the}', and it constructs a token list
+containing something like `\.{-3.0pt minus 0.5fill}'.
+
+@p function the_toks:pointer;
+var old_setting:0..max_selector; {holds |selector| setting}
+@!p,@!q,@!r:pointer; {used for copying a token list}
+@!b:pool_pointer; {base of temporary string}
+begin get_x_token; scan_something_internal(tok_val,false);
+if cur_val_level>=ident_val then @<Copy the token list@>
+else begin old_setting:=selector; selector:=new_string; b:=pool_ptr;
+ case cur_val_level of
+ int_val:print_int(cur_val);
+ dimen_val:begin print_scaled(cur_val); print("pt");
+ end;
+ glue_val: begin print_spec(cur_val,"pt"); delete_glue_ref(cur_val);
+ end;
+ mu_val: begin print_spec(cur_val,"mu"); delete_glue_ref(cur_val);
+ end;
+ end; {there are no other cases}
+ selector:=old_setting; the_toks:=str_toks(b);
+ end;
+end;
+
+@ @<Copy the token list@>=
+begin p:=temp_head; link(p):=null;
+if cur_val_level=ident_val then store_new_token(cs_token_flag+cur_val)
+else if cur_val<>null then
+ begin r:=link(cur_val); {do not copy the reference count}
+ while r<>null do
+ begin fast_store_new_token(info(r)); r:=link(r);
+ end;
+ end;
+the_toks:=p;
+end
+
+@ Here's part of the |expand| subroutine that we are now ready to complete:
+
+@p procedure ins_the_toks;
+begin link(garbage):=the_toks; ins_list(link(temp_head));
+end;
+
+@ The primitives \.{\\number}, \.{\\romannumeral}, \.{\\string}, \.{\\meaning},
+\.{\\fontname}, and \.{\\jobname} are defined as follows.
+
+@d number_code=0 {command code for \.{\\number}}
+@d roman_numeral_code=1 {command code for \.{\\romannumeral}}
+@d string_code=2 {command code for \.{\\string}}
+@d meaning_code=3 {command code for \.{\\meaning}}
+@d font_name_code=4 {command code for \.{\\fontname}}
+@d job_name_code=5 {command code for \.{\\jobname}}
+
+@<Put each...@>=
+primitive("number",convert,number_code);@/
+@!@:number_}{\.{\\number} primitive@>
+primitive("romannumeral",convert,roman_numeral_code);@/
+@!@:roman_numeral_}{\.{\\romannumeral} primitive@>
+primitive("string",convert,string_code);@/
+@!@:string_}{\.{\\string} primitive@>
+primitive("meaning",convert,meaning_code);@/
+@!@:meaning_}{\.{\\meaning} primitive@>
+primitive("fontname",convert,font_name_code);@/
+@!@:font_name_}{\.{\\fontname} primitive@>
+primitive("jobname",convert,job_name_code);@/
+@!@:job_name_}{\.{\\jobname} primitive@>
+
+@ @<Cases of |print_cmd_chr|...@>=
+convert: case chr_code of
+ number_code: print_esc("number");
+ roman_numeral_code: print_esc("romannumeral");
+ string_code: print_esc("string");
+ meaning_code: print_esc("meaning");
+ font_name_code: print_esc("fontname");
+ othercases print_esc("jobname")
+ endcases;
+
+@ The procedure |conv_toks| uses |str_toks| to insert the token list
+for |convert| functions into the scanner; `\.{\\outer}' control sequences
+are allowed to follow `\.{\\string}' and `\.{\\meaning}'.
+
+@p procedure conv_toks;
+var old_setting:0..max_selector; {holds |selector| setting}
+@!c:number_code..job_name_code; {desired type of conversion}
+@!save_scanner_status:small_number; {|scanner_status| upon entry}
+@!b:pool_pointer; {base of temporary string}
+begin c:=cur_chr; @<Scan the argument for command |c|@>;
+old_setting:=selector; selector:=new_string; b:=pool_ptr;
+@<Print the result of command |c|@>;
+selector:=old_setting; link(garbage):=str_toks(b); ins_list(link(temp_head));
+end;
+
+@ @<Scan the argument for command |c|@>=
+case c of
+number_code,roman_numeral_code: scan_int;
+string_code, meaning_code: begin save_scanner_status:=scanner_status;
+ scanner_status:=normal; get_token; scanner_status:=save_scanner_status;
+ end;
+font_name_code: scan_font_ident;
+job_name_code: if job_name=0 then open_log_file;
+end {there are no other cases}
+
+@ @<Print the result of command |c|@>=
+case c of
+number_code: print_int(cur_val);
+roman_numeral_code: print_roman_int(cur_val);
+string_code:if cur_cs<>0 then sprint_cs(cur_cs)
+ else print_char(cur_chr);
+meaning_code: print_meaning;
+font_name_code: begin print(font_name[cur_val]);
+ if font_size[cur_val]<>font_dsize[cur_val] then
+ begin print(" at "); print_scaled(font_size[cur_val]);
+ print("pt");
+ end;
+ end;
+job_name_code: print(job_name);
+end {there are no other cases}
+
+@ Now we can't postpone the difficulties any longer; we must bravely tackle
+|scan_toks|. This function returns a pointer to the tail of a new token
+list, and it also makes |def_ref| point to the reference count at the
+head of that list.
+
+There are two boolean parameters, |macro_def| and |xpand|. If |macro_def|
+is true, the goal is to create the token list for a macro definition;
+otherwise the goal is to create the token list for some other \TeX\
+primitive: \.{\\mark}, \.{\\output}, \.{\\everypar}, \.{\\lowercase},
+\.{\\uppercase}, \.{\\message}, \.{\\errmessage}, \.{\\write}, or
+\.{\\special}. In the latter cases a left brace must be scanned next; this
+left brace will not be part of the token list, nor will the matching right
+brace that comes at the end. If |xpand| is false, the token list will
+simply be copied from the input using |get_token|. Otherwise all expandable
+tokens will be expanded until unexpandable tokens are left, except that
+the results of expanding `\.{\\the}' are not expanded further.
+If both |macro_def| and |xpand| are true, the expansion applies
+only to the macro body (i.e., to the material following the first
+|left_brace| character).
+
+The value of |cur_cs| when |scan_toks| begins should be the |eqtb|
+address of the control sequence to display in ``runaway'' error
+messages.
+
+@p function scan_toks(@!macro_def,@!xpand:boolean):pointer;
+label found,done,done1,done2;
+var t:halfword; {token representing the highest parameter number}
+@!s:halfword; {saved token}
+@!p:pointer; {tail of the token list being built}
+@!q:pointer; {new node being added to the token list via |store_new_token|}
+@!unbalance:halfword; {number of unmatched left braces}
+@!hash_brace:halfword; {possible `\.{\#\{}' token}
+begin if macro_def then scanner_status:=defining
+@+else scanner_status:=absorbing;
+warning_index:=cur_cs; def_ref:=get_avail; token_ref_count(def_ref):=null;
+p:=def_ref; hash_brace:=0; t:=zero_token;
+if macro_def then @<Scan and build the parameter part of the macro definition@>
+else scan_left_brace; {remove the compulsory left brace}
+@<Scan and build the body of the token list; |goto found| when finished@>;
+found: scanner_status:=normal;
+if hash_brace<>0 then store_new_token(hash_brace);
+scan_toks:=p;
+end;
+
+@ @<Scan and build the parameter part...@>=
+begin loop begin get_token; {set |cur_cmd|, |cur_chr|, |cur_tok|}
+ if cur_tok<right_brace_limit then goto done1;
+ if cur_cmd=mac_param then
+ @<If the next character is a parameter number, make |cur_tok|
+ a |match| token; but if it is a left brace, store
+ `|left_brace|, |end_match|', set |hash_brace|, and |goto done|@>;
+ store_new_token(cur_tok);
+ end;
+done1: store_new_token(end_match_token);
+if cur_cmd=right_brace then
+ @<Express shock at the missing left brace; |goto found|@>;
+done: end
+
+@ @<Express shock...@>=
+begin print_err("Missing { inserted"); incr(align_state);
+@.Missing \{ inserted@>
+help2("Where was the left brace? You said something like `\def\a}',")@/
+ ("which I'm going to interpret as `\def\a{}'."); error; goto found;
+end
+
+@ @<If the next character is a parameter number...@>=
+begin s:=match_token+cur_chr; get_token;
+if cur_cmd=left_brace then
+ begin hash_brace:=cur_tok;
+ store_new_token(cur_tok); store_new_token(end_match_token);
+ goto done;
+ end;
+if t=zero_token+9 then
+ begin print_err("You already have nine parameters");
+@.You already have nine...@>
+ help1("I'm going to ignore the # sign you just used."); error;
+ end
+else begin incr(t);
+ if cur_tok<>t then
+ begin print_err("Parameters must be numbered consecutively");
+@.Parameters...consecutively@>
+ help2("I've inserted the digit you should have used after the #.")@/
+ ("Type `1' to delete what you did use."); back_error;
+ end;
+ cur_tok:=s;
+ end;
+end
+
+@ @<Scan and build the body of the token list; |goto found| when finished@>=
+unbalance:=1;
+loop@+ begin if xpand then @<Expand the next part of the input@>
+ else get_token;
+ if cur_tok<right_brace_limit then
+ if cur_cmd<right_brace then incr(unbalance)
+ else begin decr(unbalance);
+ if unbalance=0 then goto found;
+ end
+ else if cur_cmd=mac_param then
+ if macro_def then @<Look for parameter number or \.{\#\#}@>;
+ store_new_token(cur_tok);
+ end
+
+@ Here we insert an entire token list created by |the_toks| without
+expanding it further.
+
+@<Expand the next part of the input@>=
+begin loop begin get_next;
+ if cur_cmd<=max_command then goto done2;
+ if cur_cmd<>the then expand
+ else begin q:=the_toks;
+ if link(temp_head)<>null then
+ begin link(p):=link(temp_head); p:=q;
+ end;
+ end;
+ end;
+done2: x_token
+end
+
+@ @<Look for parameter number...@>=
+begin s:=cur_tok;
+if xpand then get_x_token else get_token;
+if cur_cmd<>mac_param then
+ if (cur_tok<=zero_token)or(cur_tok>t) then
+ begin print_err("Illegal parameter number in definition of ");
+@.Illegal parameter number...@>
+ sprint_cs(warning_index);
+ help3("You meant to type ## instead of #, right?")@/
+ ("Or maybe a } was forgotten somewhere earlier, and things")@/
+ ("are all screwed up? I'm going to assume that you meant ##.");
+ back_error; cur_tok:=s;
+ end
+ else cur_tok:=out_param_token-"0"+cur_chr;
+end
+
+@ Another way to create a token list is via the \.{\\read} command. The
+sixteen files potentially usable for reading appear in the following
+global variables. The value of |read_open[n]| will be |closed| if
+stream number |n| has not been opened or if it has been fully read;
+|just_open| if an \.{\\openin} but not a \.{\\read} has been done;
+and |normal| if it is open and ready to read the next line.
+
+@d closed=2 {not open, or at end of file}
+@d just_open=1 {newly opened, first line not yet read}
+
+@<Glob...@>=
+@!read_file:array[0..15] of alpha_file; {used for \.{\\read}}
+@!read_open:array[0..16] of normal..closed; {state of |read_file[n]|}
+
+@ @<Set init...@>=
+for k:=0 to 16 do read_open[k]:=closed;
+
+@ The |read_toks| procedure constructs a token list like that for any
+macro definition, and makes |cur_val| point to it. Parameter |r| points
+to the control sequence that will receive this token list.
+
+@p procedure read_toks(@!n:integer;@!r:pointer);
+label done;
+var p:pointer; {tail of the token list}
+@!q:pointer; {new node being added to the token list via |store_new_token|}
+@!s:integer; {saved value of |align_state|}
+@!m:small_number; {stream number}
+begin scanner_status:=defining; warning_index:=r;
+def_ref:=get_avail; token_ref_count(def_ref):=null;
+p:=def_ref; {the reference count}
+store_new_token(end_match_token);
+if (n<0)or(n>15) then m:=16@+else m:=n;
+s:=align_state; align_state:=1000000; {disable tab marks, etc.}
+repeat @<Input and store tokens from the next line of the file@>;
+until align_state=1000000;
+cur_val:=def_ref; scanner_status:=normal; align_state:=s;
+end;
+
+@ @<Input and store tokens from the next line of the file@>=
+begin_file_reading; name:=m+1;
+if read_open[m]=closed then @<Input for \.{\\read} from the terminal@>
+else if read_open[m]=just_open then @<Input the first line of |read_file[m]|@>
+else @<Input the next line of |read_file[m]|@>;
+limit:=last;
+if end_line_char_inactive then decr(limit)
+else buffer[limit]:=end_line_char;
+first:=limit+1; loc:=start; state:=new_line;@/
+loop@+ begin get_token;
+ if cur_tok=0 then goto done;
+ {|cur_cmd=cur_chr=0| will occur at the end of the line}
+ if align_state<1000000 then {unmatched `\.\}' aborts the line}
+ begin repeat get_token; until cur_tok=0;
+ align_state:=1000000; goto done;
+ end;
+ store_new_token(cur_tok);
+ end;
+done: end_file_reading
+
+@ Here we input on-line into the |buffer| array, prompting the user explicitly
+if |n>=0|. The value of |n| is set negative so that additional prompts
+will not be given in the case of multi-line input.
+
+@<Input for \.{\\read} from the terminal@>=
+if interaction>nonstop_mode then
+ if n<0 then prompt_input("")
+ else begin wake_up_terminal;
+ print_ln; sprint_cs(r); prompt_input("="); n:=-1;
+ end
+else fatal_error("*** (cannot \read from terminal in nonstop modes)")
+@.cannot \\read@>
+
+@ The first line of a file must be treated specially, since |input_ln|
+must be told not to start with |get|.
+@^system dependencies@>
+
+@<Input the first line of |read_file[m]|@>=
+if input_ln(read_file[m],false) then read_open[m]:=normal
+else begin a_close(read_file[m]); read_open[m]:=closed;
+ end
+
+@ An empty line is appended at the end of a |read_file|.
+@^empty line at end of file@>
+
+@<Input the next line of |read_file[m]|@>=
+begin if not input_ln(read_file[m],true) then
+ begin a_close(read_file[m]); read_open[m]:=closed;
+ if align_state<>1000000 then
+ begin runaway;
+ print_err("File ended within "); print_esc("read");
+@.File ended within \\read@>
+ help1("This \read has unbalanced braces.");
+ align_state:=1000000; error;
+ end;
+ end;
+end
+
+@* \[28] Conditional processing.
+We consider now the way \TeX\ handles various kinds of \.{\\if} commands.
+
+@d if_char_code=0 { `\.{\\if}' }
+@d if_cat_code=1 { `\.{\\ifcat}' }
+@d if_int_code=2 { `\.{\\ifnum}' }
+@d if_dim_code=3 { `\.{\\ifdim}' }
+@d if_odd_code=4 { `\.{\\ifodd}' }
+@d if_vmode_code=5 { `\.{\\ifvmode}' }
+@d if_hmode_code=6 { `\.{\\ifhmode}' }
+@d if_mmode_code=7 { `\.{\\ifmmode}' }
+@d if_inner_code=8 { `\.{\\ifinner}' }
+@d if_void_code=9 { `\.{\\ifvoid}' }
+@d if_hbox_code=10 { `\.{\\ifhbox}' }
+@d if_vbox_code=11 { `\.{\\ifvbox}' }
+@d ifx_code=12 { `\.{\\ifx}' }
+@d if_eof_code=13 { `\.{\\ifeof}' }
+@d if_true_code=14 { `\.{\\iftrue}' }
+@d if_false_code=15 { `\.{\\iffalse}' }
+@d if_case_code=16 { `\.{\\ifcase}' }
+
+@<Put each...@>=
+primitive("if",if_test,if_char_code);
+@!@:if_char_}{\.{\\if} primitive@>
+primitive("ifcat",if_test,if_cat_code);
+@!@:if_cat_code_}{\.{\\ifcat} primitive@>
+primitive("ifnum",if_test,if_int_code);
+@!@:if_int_}{\.{\\ifnum} primitive@>
+primitive("ifdim",if_test,if_dim_code);
+@!@:if_dim_}{\.{\\ifdim} primitive@>
+primitive("ifodd",if_test,if_odd_code);
+@!@:if_odd_}{\.{\\ifodd} primitive@>
+primitive("ifvmode",if_test,if_vmode_code);
+@!@:if_vmode_}{\.{\\ifvmode} primitive@>
+primitive("ifhmode",if_test,if_hmode_code);
+@!@:if_hmode_}{\.{\\ifhmode} primitive@>
+primitive("ifmmode",if_test,if_mmode_code);
+@!@:if_mmode_}{\.{\\ifmmode} primitive@>
+primitive("ifinner",if_test,if_inner_code);
+@!@:if_inner_}{\.{\\ifinner} primitive@>
+primitive("ifvoid",if_test,if_void_code);
+@!@:if_void_}{\.{\\ifvoid} primitive@>
+primitive("ifhbox",if_test,if_hbox_code);
+@!@:if_hbox_}{\.{\\ifhbox} primitive@>
+primitive("ifvbox",if_test,if_vbox_code);
+@!@:if_vbox_}{\.{\\ifvbox} primitive@>
+primitive("ifx",if_test,ifx_code);
+@!@:ifx_}{\.{\\ifx} primitive@>
+primitive("ifeof",if_test,if_eof_code);
+@!@:if_eof_}{\.{\\ifeof} primitive@>
+primitive("iftrue",if_test,if_true_code);
+@!@:if_true_}{\.{\\iftrue} primitive@>
+primitive("iffalse",if_test,if_false_code);
+@!@:if_false_}{\.{\\iffalse} primitive@>
+primitive("ifcase",if_test,if_case_code);
+@!@:if_case_}{\.{\\ifcase} primitive@>
+
+@ @<Cases of |print_cmd_chr|...@>=
+if_test: case chr_code of
+ if_cat_code:print_esc("ifcat");
+ if_int_code:print_esc("ifnum");
+ if_dim_code:print_esc("ifdim");
+ if_odd_code:print_esc("ifodd");
+ if_vmode_code:print_esc("ifvmode");
+ if_hmode_code:print_esc("ifhmode");
+ if_mmode_code:print_esc("ifmmode");
+ if_inner_code:print_esc("ifinner");
+ if_void_code:print_esc("ifvoid");
+ if_hbox_code:print_esc("ifhbox");
+ if_vbox_code:print_esc("ifvbox");
+ ifx_code:print_esc("ifx");
+ if_eof_code:print_esc("ifeof");
+ if_true_code:print_esc("iftrue");
+ if_false_code:print_esc("iffalse");
+ if_case_code:print_esc("ifcase");
+ othercases print_esc("if")
+ endcases;
+
+@ Conditions can be inside conditions, and this nesting has a stack
+that is independent of the |save_stack|.
+
+Four global variables represent the top of the condition stack:
+|cond_ptr| points to pushed-down entries, if any; |if_limit| specifies
+the largest code of a |fi_or_else| command that is syntactically legal;
+|cur_if| is the name of the current type of conditional; and |if_line|
+is the line number at which it began.
+
+If no conditions are currently in progress, the condition stack has the
+special state |cond_ptr=null|, |if_limit=normal|, |cur_if=0|, |if_line=0|.
+Otherwise |cond_ptr| points to a two-word node; the |type|, |subtype|, and
+|link| fields of the first word contain |if_limit|, |cur_if|, and
+|cond_ptr| at the next level, and the second word contains the
+corresponding |if_line|.
+
+@d if_node_size=2 {number of words in stack entry for conditionals}
+@d if_line_field(#)==mem[#+1].int
+@d if_code=1 {code for \.{\\if...} being evaluated}
+@d fi_code=2 {code for \.{\\fi}}
+@d else_code=3 {code for \.{\\else}}
+@d or_code=4 {code for \.{\\or}}
+
+@<Glob...@>=
+@!cond_ptr:pointer; {top of the condition stack}
+@!if_limit:normal..or_code; {upper bound on |fi_or_else| codes}
+@!cur_if:small_number; {type of conditional being worked on}
+@!if_line:integer; {line where that conditional began}
+
+@ @<Set init...@>=
+cond_ptr:=null; if_limit:=normal; cur_if:=0; if_line:=0;
+
+@ @<Put each...@>=
+primitive("fi",fi_or_else,fi_code);
+@!@:fi_}{\.{\\fi} primitive@>
+text(frozen_fi):="fi"; eqtb[frozen_fi]:=eqtb[cur_val];
+primitive("or",fi_or_else,or_code);
+@!@:or_}{\.{\\or} primitive@>
+primitive("else",fi_or_else,else_code);
+@!@:else_}{\.{\\else} primitive@>
+
+@ @<Cases of |print_cmd_chr|...@>=
+fi_or_else: if chr_code=fi_code then print_esc("fi")
+ else if chr_code=or_code then print_esc("or")
+ else print_esc("else");
+
+@ When we skip conditional text, we keep track of the line number
+where skipping began, for use in error messages.
+
+@<Glob...@>=
+@!skip_line:integer; {skipping began here}
+
+@ Here is a procedure that ignores text until coming to an \.{\\or},
+\.{\\else}, or \.{\\fi} at level zero of $\.{\\if}\ldots\.{\\fi}$
+nesting. After it has acted, |cur_chr| will indicate the token that
+was found, but |cur_tok| will not be set (because this makes the
+procedure run faster).
+
+@p procedure pass_text;
+label done;
+var l:integer; {level of $\.{\\if}\ldots\.{\\fi}$ nesting}
+@!save_scanner_status:small_number; {|scanner_status| upon entry}
+begin save_scanner_status:=scanner_status; scanner_status:=skipping; l:=0;
+skip_line:=line;
+loop@+ begin get_next;
+ if cur_cmd=fi_or_else then
+ begin if l=0 then goto done;
+ if cur_chr=fi_code then decr(l);
+ end
+ else if cur_cmd=if_test then incr(l);
+ end;
+done: scanner_status:=save_scanner_status;
+end;
+
+@ When we begin to process a new \.{\\if}, we set |if_limit:=if_code|; then
+if\/ \.{\\or} or \.{\\else} or \.{\\fi} occurs before the current \.{\\if}
+condition has been evaluated, \.{\\relax} will be inserted.
+For example, a sequence of commands like `\.{\\ifvoid1\\else...\\fi}'
+would otherwise require something after the `\.1'.
+
+@<Push the condition stack@>=
+begin p:=get_node(if_node_size); link(p):=cond_ptr; type(p):=if_limit;
+subtype(p):=cur_if; if_line_field(p):=if_line;
+cond_ptr:=p; cur_if:=cur_chr; if_limit:=if_code; if_line:=line;
+end
+
+@ @<Pop the condition stack@>=
+begin p:=cond_ptr; if_line:=if_line_field(p);
+cur_if:=subtype(p); if_limit:=type(p); cond_ptr:=link(p);
+free_node(p,if_node_size);
+end
+
+@ Here's a procedure that changes the |if_limit| code corresponding to
+a given value of |cond_ptr|.
+
+@p procedure change_if_limit(@!l:small_number;@!p:pointer);
+label exit;
+var q:pointer;
+begin if p=cond_ptr then if_limit:=l {that's the easy case}
+else begin q:=cond_ptr;
+ loop@+ begin if q=null then confusion("if");
+@:this can't happen if}{\quad if@>
+ if link(q)=p then
+ begin type(q):=l; return;
+ end;
+ q:=link(q);
+ end;
+ end;
+exit:end;
+
+@ A condition is started when the |expand| procedure encounters
+an |if_test| command; in that case |expand| reduces to |conditional|,
+which is a recursive procedure.
+@^recursion@>
+
+@p procedure conditional;
+label exit,common_ending;
+var b:boolean; {is the condition true?}
+@!r:"<"..">"; {relation to be evaluated}
+@!m,@!n:integer; {to be tested against the second operand}
+@!p,@!q:pointer; {for traversing token lists in \.{\\ifx} tests}
+@!save_scanner_status:small_number; {|scanner_status| upon entry}
+@!save_cond_ptr:pointer; {|cond_ptr| corresponding to this conditional}
+@!this_if:small_number; {type of this conditional}
+begin @<Push the condition stack@>;@+save_cond_ptr:=cond_ptr;this_if:=cur_chr;@/
+@<Either process \.{\\ifcase} or set |b| to the value of a boolean condition@>;
+if tracing_commands>1 then @<Display the value of |b|@>;
+if b then
+ begin change_if_limit(else_code,save_cond_ptr);
+ return; {wait for \.{\\else} or \.{\\fi}}
+ end;
+@<Skip to \.{\\else} or \.{\\fi}, then |goto common_ending|@>;
+common_ending: if cur_chr=fi_code then @<Pop the condition stack@>
+else if_limit:=fi_code; {wait for \.{\\fi}}
+exit:end;
+
+@ In a construction like `\.{\\if\\iftrue abc\\else d\\fi}', the first
+\.{\\else} that we come to after learning that the \.{\\if} is false is
+not the \.{\\else} we're looking for. Hence the following curious
+logic is needed.
+
+@ @<Skip to \.{\\else} or \.{\\fi}...@>=
+loop@+ begin pass_text;
+ if cond_ptr=save_cond_ptr then
+ begin if cur_chr<>or_code then goto common_ending;
+ print_err("Extra "); print_esc("or");
+@.Extra \\or@>
+ help1("I'm ignoring this; it doesn't match any \if.");
+ error;
+ end
+ else if cur_chr=fi_code then @<Pop the condition stack@>;
+ end
+
+@ @<Either process \.{\\ifcase} or set |b|...@>=
+case this_if of
+if_char_code, if_cat_code: @<Test if two characters match@>;
+if_int_code, if_dim_code: @<Test relation between integers or dimensions@>;
+if_odd_code: @<Test if an integer is odd@>;
+if_vmode_code: b:=(abs(mode)=vmode);
+if_hmode_code: b:=(abs(mode)=hmode);
+if_mmode_code: b:=(abs(mode)=mmode);
+if_inner_code: b:=(mode<0);
+if_void_code, if_hbox_code, if_vbox_code: @<Test box register status@>;
+ifx_code: @<Test if two tokens match@>;
+if_eof_code: begin scan_four_bit_int; b:=(read_open[cur_val]=closed);
+ end;
+if_true_code: b:=true;
+if_false_code: b:=false;
+if_case_code: @<Select the appropriate case
+ and |return| or |goto common_ending|@>;
+end {there are no other cases}
+
+@ @<Display the value of |b|@>=
+begin begin_diagnostic;
+if b then print("{true}")@+else print("{false}");
+end_diagnostic(false);
+end
+
+@ Here we use the fact that |"<"|, |"="|, and |">"| are consecutive ASCII
+codes.
+@^ASCII code@>
+
+@<Test relation between integers or dimensions@>=
+begin if this_if=if_int_code then scan_int@+else scan_normal_dimen;
+n:=cur_val; @<Get the next non-blank non-call...@>;
+if (cur_tok>=other_token+"<")and(cur_tok<=other_token+">") then
+ r:=cur_tok-other_token
+else begin print_err("Missing = inserted for ");
+@.Missing = inserted@>
+ print_cmd_chr(if_test,this_if);
+ help1("I was expecting to see `<', `=', or `>'. Didn't.");
+ back_error; r:="=";
+ end;
+if this_if=if_int_code then scan_int@+else scan_normal_dimen;
+case r of
+"<": b:=(n<cur_val);
+"=": b:=(n=cur_val);
+">": b:=(n>cur_val);
+end;
+end
+
+@ @<Test if an integer is odd@>=
+begin scan_int; b:=odd(cur_val);
+end
+
+@ @<Test box register status@>=
+begin scan_eight_bit_int; p:=box(cur_val);
+if this_if=if_void_code then b:=(p=null)
+else if p=null then b:=false
+else if this_if=if_hbox_code then b:=(type(p)=hlist_node)
+else b:=(type(p)=vlist_node);
+end
+
+@ An active character will be treated as category 13 following
+\.{\\if\\noexpand} or following \.{\\ifcat\\noexpand}. We use the fact that
+active characters have the smallest tokens, among all control sequences.
+
+@d get_x_token_or_active_char==@t@>@;
+ begin get_x_token;
+ if cur_cmd=relax then if cur_chr=no_expand_flag then
+ begin cur_cmd:=active_char;
+ cur_chr:=cur_tok-cs_token_flag-active_base;
+ end;
+ end
+
+@<Test if two characters match@>=
+begin get_x_token_or_active_char;
+if (cur_cmd>active_char)or(cur_chr>255) then {not a character}
+ begin m:=relax; n:=256;
+ end
+else begin m:=cur_cmd; n:=cur_chr;
+ end;
+get_x_token_or_active_char;
+if (cur_cmd>active_char)or(cur_chr>255) then
+ begin cur_cmd:=relax; cur_chr:=256;
+ end;
+if this_if=if_char_code then b:=(n=cur_chr)@+else b:=(m=cur_cmd);
+end
+
+@ Note that `\.{\\ifx}' will declare two macros different if one is \\{long}
+or \\{outer} and the other isn't, even though the texts of the macros are
+the same.
+
+We need to reset |scanner_status|, since \.{\\outer} control sequences
+are allowed, but we might be scanning a macro definition or preamble.
+
+@<Test if two tokens match@>=
+begin save_scanner_status:=scanner_status; scanner_status:=normal;
+get_next; n:=cur_cs; p:=cur_cmd; q:=cur_chr;
+get_next; if cur_cmd<>p then b:=false
+else if cur_cmd<call then b:=(cur_chr=q)
+else @<Test if two macro texts match@>;
+scanner_status:=save_scanner_status;
+end
+
+@ Note also that `\.{\\ifx}' decides that macros \.{\\a} and \.{\\b} are
+different in examples like this:
+$$\vbox{\halign{\.{#}\hfil&\qquad\.{#}\hfil\cr
+ {}\\def\\a\{\\c\}&
+ {}\\def\\c\{\}\cr
+ {}\\def\\b\{\\d\}&
+ {}\\def\\d\{\}\cr}}$$
+
+@<Test if two macro texts match@>=
+begin p:=link(cur_chr); q:=link(equiv(n)); {omit reference counts}
+if p=q then b:=true
+else begin while (p<>null)and(q<>null) do
+ if info(p)<>info(q) then p:=null
+ else begin p:=link(p); q:=link(q);
+ end;
+ b:=((p=null)and(q=null));
+ end;
+end
+
+@ @<Select the appropriate case and |return| or |goto common_ending|@>=
+begin scan_int; n:=cur_val; {|n| is the number of cases to pass}
+if tracing_commands>1 then
+ begin begin_diagnostic; print("{case "); print_int(n); print_char("}");
+ end_diagnostic(false);
+ end;
+while n<>0 do
+ begin pass_text;
+ if cond_ptr=save_cond_ptr then
+ if cur_chr=or_code then decr(n)
+ else goto common_ending
+ else if cur_chr=fi_code then @<Pop the condition stack@>;
+ end;
+change_if_limit(or_code,save_cond_ptr);
+return; {wait for \.{\\or}, \.{\\else}, or \.{\\fi}}
+end
+
+@ The processing of conditionals is complete except for the following
+code, which is actually part of |expand|. It comes into play when
+\.{\\or}, \.{\\else}, or \.{\\fi} is scanned.
+
+@<Terminate the current conditional and skip to \.{\\fi}@>=
+if cur_chr>if_limit then
+ if if_limit=if_code then insert_relax {condition not yet evaluated}
+ else begin print_err("Extra "); print_cmd_chr(fi_or_else,cur_chr);
+@.Extra \\or@>
+@.Extra \\else@>
+@.Extra \\fi@>
+ help1("I'm ignoring this; it doesn't match any \if.");
+ error;
+ end
+else begin while cur_chr<>fi_code do pass_text; {skip to \.{\\fi}}
+ @<Pop the condition stack@>;
+ end
+
+@* \[29] File names.
+It's time now to fret about file names. Besides the fact that different
+operating systems treat files in different ways, we must cope with the
+fact that completely different naming conventions are used by different
+groups of people. The following programs show what is required for one
+particular operating system; similar routines for other systems are not
+difficult to devise.
+@^fingers@>
+@^system dependencies@>
+
+\TeX\ assumes that a file name has three parts: the name proper; its
+``extension''; and a ``file area'' where it is found in an external file
+system. The extension of an input file or a write file is assumed to be
+`\.{.tex}' unless otherwise specified; it is `\.{.log}' on the
+transcript file that records each run of \TeX; it is `\.{.tfm}' on the font
+metric files that describe characters in the fonts \TeX\ uses; it is
+`\.{.dvi}' on the output files that specify typesetting information; and it
+is `\.{.fmt}' on the format files written by \.{INITEX} to initialize \TeX.
+The file area can be arbitrary on input files, but files are usually
+output to the user's current area. If an input file cannot be
+found on the specified area, \TeX\ will look for it on a special system
+area; this special area is intended for commonly used input files like
+\.{webmac.tex}.
+
+Simple uses of \TeX\ refer only to file names that have no explicit
+extension or area. For example, a person usually says `\.{\\input} \.{paper}'
+or `\.{\\font\\tenrm} \.= \.{helvetica}' instead of `\.{\\input}
+\.{paper.new}' or `\.{\\font\\tenrm} \.= \.{<csd.knuth>test}'. Simple file
+names are best, because they make the \TeX\ source files portable;
+whenever a file name consists entirely of letters and digits, it should be
+treated in the same way by all implementations of \TeX. However, users
+need the ability to refer to other files in their environment, especially
+when responding to error messages concerning unopenable files; therefore
+we want to let them use the syntax that appears in their favorite
+operating system.
+
+The following procedures don't allow spaces to be part of
+file names; but some users seem to like names that are spaced-out.
+System-dependent changes to allow such things should probably
+be made with reluctance, and only when an entire file name that
+includes spaces is ``quoted'' somehow.
+
+@ In order to isolate the system-dependent aspects of file names, the
+@^system dependencies@>
+system-independent parts of \TeX\ are expressed in terms
+of three system-dependent
+procedures called |begin_name|, |more_name|, and |end_name|. In
+essence, if the user-specified characters of the file name are $c_1\ldots c_n$,
+the system-independent driver program does the operations
+$$|begin_name|;\,|more_name|(c_1);\,\ldots\,;|more_name|(c_n);
+\,|end_name|.$$
+These three procedures communicate with each other via global variables.
+Afterwards the file name will appear in the string pool as three strings
+called |cur_name|\penalty10000\hskip-.05em,
+|cur_area|, and |cur_ext|; the latter two are null (i.e.,
+|""|), unless they were explicitly specified by the user.
+
+Actually the situation is slightly more complicated, because \TeX\ needs
+to know when the file name ends. The |more_name| routine is a function
+(with side effects) that returns |true| on the calls |more_name|$(c_1)$,
+\dots, |more_name|$(c_{n-1})$. The final call |more_name|$(c_n)$
+returns |false|; or, it returns |true| and the token following $c_n$ is
+something like `\.{\\hbox}' (i.e., not a character). In other words,
+|more_name| is supposed to return |true| unless it is sure that the
+file name has been completely scanned; and |end_name| is supposed to be able
+to finish the assembly of |cur_name|, |cur_area|, and |cur_ext| regardless of
+whether $|more_name|(c_n)$ returned |true| or |false|.
+
+@<Glob...@>=
+@!cur_name:str_number; {name of file just scanned}
+@!cur_area:str_number; {file area just scanned, or \.{""}}
+@!cur_ext:str_number; {file extension just scanned, or \.{""}}
+
+@ The file names we shall deal with for illustrative purposes have the
+following structure: If the name contains `\.>' or `\.:', the file area
+consists of all characters up to and including the final such character;
+otherwise the file area is null. If the remaining file name contains
+`\..', the file extension consists of all such characters from the first
+remaining `\..' to the end, otherwise the file extension is null.
+@^system dependencies@>
+
+We can scan such file names easily by using two global variables that keep track
+of the occurrences of area and extension delimiters:
+
+@<Glob...@>=
+@!area_delimiter:pool_pointer; {the most recent `\.>' or `\.:', if any}
+@!ext_delimiter:pool_pointer; {the relevant `\..', if any}
+
+@ Input files that can't be found in the user's area may appear in a standard
+system area called |TEX_area|. Font metric files whose areas are not given
+explicitly are assumed to appear in a standard system area called
+|TEX_font_area|. These system area names will, of course, vary from place
+to place.
+@^system dependencies@>
+
+@d TEX_area=="TeXinputs:"
+@.TeXinputs@>
+@d TEX_font_area=="TeXfonts:"
+@.TeXfonts@>
+
+@ Here now is the first of the system-dependent routines for file name scanning.
+@^system dependencies@>
+
+@p procedure begin_name;
+begin area_delimiter:=0; ext_delimiter:=0;
+end;
+
+@ And here's the second. The string pool might change as the file name is
+being scanned, since a new \.{\\csname} might be entered; therefore we keep
+|area_delimiter| and |ext_delimiter| relative to the beginning of the current
+string, instead of assigning an absolute address like |pool_ptr| to them.
+@^system dependencies@>
+
+@p function more_name(@!c:ASCII_code):boolean;
+begin if c=" " then more_name:=false
+else begin str_room(1); append_char(c); {contribute |c| to the current string}
+ if (c=">")or(c=":") then
+ begin area_delimiter:=cur_length; ext_delimiter:=0;
+ end
+ else if (c=".")and(ext_delimiter=0) then ext_delimiter:=cur_length;
+ more_name:=true;
+ end;
+end;
+
+@ The third.
+@^system dependencies@>
+
+@p procedure end_name;
+begin if str_ptr+3>max_strings then
+ overflow("number of strings",max_strings-init_str_ptr);
+@:TeX capacity exceeded number of strings}{\quad number of strings@>
+if area_delimiter=0 then cur_area:=""
+else begin cur_area:=str_ptr;
+ str_start[str_ptr+1]:=str_start[str_ptr]+area_delimiter; incr(str_ptr);
+ end;
+if ext_delimiter=0 then
+ begin cur_ext:=""; cur_name:=make_string;
+ end
+else begin cur_name:=str_ptr;
+ str_start[str_ptr+1]:=str_start[str_ptr]+ext_delimiter-area_delimiter-1;
+ incr(str_ptr); cur_ext:=make_string;
+ end;
+end;
+
+@ Conversely, here is a routine that takes three strings and prints a file
+name that might have produced them. (The routine is system dependent, because
+some operating systems put the file area last instead of first.)
+@^system dependencies@>
+
+@<Basic printing...@>=
+procedure print_file_name(@!n,@!a,@!e:integer);
+begin slow_print(a); slow_print(n); slow_print(e);
+end;
+
+@ Another system-dependent routine is needed to convert three internal
+\TeX\ strings
+into the |name_of_file| value that is used to open files. The present code
+allows both lowercase and uppercase letters in the file name.
+@^system dependencies@>
+
+@d append_to_name(#)==begin c:=#; incr(k);
+ if k<=file_name_size then name_of_file[k]:=xchr[c];
+ end
+
+@p procedure pack_file_name(@!n,@!a,@!e:str_number);
+var k:integer; {number of positions filled in |name_of_file|}
+@!c: ASCII_code; {character being packed}
+@!j:pool_pointer; {index into |str_pool|}
+begin k:=0;
+for j:=str_start[a] to str_start[a+1]-1 do append_to_name(so(str_pool[j]));
+for j:=str_start[n] to str_start[n+1]-1 do append_to_name(so(str_pool[j]));
+for j:=str_start[e] to str_start[e+1]-1 do append_to_name(so(str_pool[j]));
+if k<=file_name_size then name_length:=k@+else name_length:=file_name_size;
+for k:=name_length+1 to file_name_size do name_of_file[k]:=' ';
+end;
+
+@ A messier routine is also needed, since format file names must be scanned
+before \TeX's string mechanism has been initialized. We shall use the
+global variable |TEX_format_default| to supply the text for default system areas
+and extensions related to format files.
+@^system dependencies@>
+
+@d format_default_length=20 {length of the |TEX_format_default| string}
+@d format_area_length=11 {length of its area part}
+@d format_ext_length=4 {length of its `\.{.fmt}' part}
+@d format_extension=".fmt" {the extension, as a \.{WEB} constant}
+
+@<Glob...@>=
+@!TEX_format_default:packed array[1..format_default_length] of char;
+
+@ @<Set init...@>=
+TEX_format_default:='TeXformats:plain.fmt';
+@.TeXformats@>
+@.plain@>
+@^system dependencies@>
+
+@ @<Check the ``constant'' values for consistency@>=
+if format_default_length>file_name_size then bad:=31;
+
+@ Here is the messy routine that was just mentioned. It sets |name_of_file|
+from the first |n| characters of |TEX_format_default|, followed by
+|buffer[a..b]|, followed by the last |format_ext_length| characters of
+|TEX_format_default|.
+
+We dare not give error messages here, since \TeX\ calls this routine before
+the |error| routine is ready to roll. Instead, we simply drop excess characters,
+since the error will be detected in another way when a strange file name
+isn't found.
+@^system dependencies@>
+
+@p procedure pack_buffered_name(@!n:small_number;@!a,@!b:integer);
+var k:integer; {number of positions filled in |name_of_file|}
+@!c: ASCII_code; {character being packed}
+@!j:integer; {index into |buffer| or |TEX_format_default|}
+begin if n+b-a+1+format_ext_length>file_name_size then
+ b:=a+file_name_size-n-1-format_ext_length;
+k:=0;
+for j:=1 to n do append_to_name(xord[TEX_format_default[j]]);
+for j:=a to b do append_to_name(buffer[j]);
+for j:=format_default_length-format_ext_length+1 to format_default_length do
+ append_to_name(xord[TEX_format_default[j]]);
+if k<=file_name_size then name_length:=k@+else name_length:=file_name_size;
+for k:=name_length+1 to file_name_size do name_of_file[k]:=' ';
+end;
+
+@ Here is the only place we use |pack_buffered_name|. This part of the program
+becomes active when a ``virgin'' \TeX\ is trying to get going, just after
+the preliminary initialization, or when the user is substituting another
+format file by typing `\.\&' after the initial `\.{**}' prompt. The buffer
+contains the first line of input in |buffer[loc..(last-1)]|, where
+|loc<last| and |buffer[loc]<>" "|.
+
+@<Declare the function called |open_fmt_file|@>=
+function open_fmt_file:boolean;
+label found,exit;
+var j:0..buf_size; {the first space after the format file name}
+begin j:=loc;
+if buffer[loc]="&" then
+ begin incr(loc); j:=loc; buffer[last]:=" ";
+ while buffer[j]<>" " do incr(j);
+ pack_buffered_name(0,loc,j-1); {try first without the system file area}
+ if w_open_in(fmt_file) then goto found;
+ pack_buffered_name(format_area_length,loc,j-1);
+ {now try the system format file area}
+ if w_open_in(fmt_file) then goto found;
+ wake_up_terminal;
+ wterm_ln('Sorry, I can''t find that format;',' will try PLAIN.');
+@.Sorry, I can't find...@>
+ update_terminal;
+ end;
+ {now pull out all the stops: try for the system \.{plain} file}
+pack_buffered_name(format_default_length-format_ext_length,1,0);
+if not w_open_in(fmt_file) then
+ begin wake_up_terminal;
+ wterm_ln('I can''t find the PLAIN format file!');
+@.I can't find PLAIN...@>
+@.plain@>
+ open_fmt_file:=false; return;
+ end;
+found:loc:=j; open_fmt_file:=true;
+exit:end;
+
+@ Operating systems often make it possible to determine the exact name (and
+possible version number) of a file that has been opened. The following routine,
+which simply makes a \TeX\ string from the value of |name_of_file|, should
+ideally be changed to deduce the full name of file~|f|, which is the file
+most recently opened, if it is possible to do this in a \PASCAL\ program.
+@^system dependencies@>
+
+This routine might be called after string memory has overflowed, hence
+we dare not use `|str_room|'.
+
+@p function make_name_string:str_number;
+var k:1..file_name_size; {index into |name_of_file|}
+begin if (pool_ptr+name_length>pool_size)or(str_ptr=max_strings)or
+ (cur_length>0) then
+ make_name_string:="?"
+else begin for k:=1 to name_length do append_char(xord[name_of_file[k]]);
+ make_name_string:=make_string;
+ end;
+end;
+function a_make_name_string(var f:alpha_file):str_number;
+begin a_make_name_string:=make_name_string;
+end;
+function b_make_name_string(var f:byte_file):str_number;
+begin b_make_name_string:=make_name_string;
+end;
+function w_make_name_string(var f:word_file):str_number;
+begin w_make_name_string:=make_name_string;
+end;
+
+@ Now let's consider the ``driver''
+routines by which \TeX\ deals with file names
+in a system-independent manner. First comes a procedure that looks for a
+file name in the input by calling |get_x_token| for the information.
+
+@p procedure scan_file_name;
+label done;
+begin name_in_progress:=true; begin_name;
+@<Get the next non-blank non-call...@>;
+loop@+begin if (cur_cmd>other_char)or(cur_chr>255) then {not a character}
+ begin back_input; goto done;
+ end;
+ if not more_name(cur_chr) then goto done;
+ get_x_token;
+ end;
+done: end_name; name_in_progress:=false;
+end;
+
+@ The global variable |name_in_progress| is used to prevent recursive
+use of |scan_file_name|, since the |begin_name| and other procedures
+communicate via global variables. Recursion would arise only by
+devious tricks like `\.{\\input\\input f}'; such attempts at sabotage
+must be thwarted. Furthermore, |name_in_progress| prevents \.{\\input}
+@^recursion@>
+from being initiated when a font size specification is being scanned.
+
+Another global variable, |job_name|, contains the file name that was first
+\.{\\input} by the user. This name is extended by `\.{.log}' and `\.{.dvi}'
+and `\.{.fmt}' in the names of \TeX's output files.
+
+@<Glob...@>=
+@!name_in_progress:boolean; {is a file name being scanned?}
+@!job_name:str_number; {principal file name}
+@!log_opened:boolean; {has the transcript file been opened?}
+
+@ Initially |job_name=0|; it becomes nonzero as soon as the true name is known.
+We have |job_name=0| if and only if the `\.{log}' file has not been opened,
+except of course for a short time just after |job_name| has become nonzero.
+
+@<Initialize the output...@>=
+job_name:=0; name_in_progress:=false; log_opened:=false;
+
+@ Here is a routine that manufactures the output file names, assuming that
+|job_name<>0|. It ignores and changes the current settings of |cur_area|
+and |cur_ext|.
+
+@d pack_cur_name==pack_file_name(cur_name,cur_area,cur_ext)
+
+@p procedure pack_job_name(@!s:str_number); {|s = ".log"|, |".dvi"|, or
+ |format_extension|}
+begin cur_area:=""; cur_ext:=s;
+cur_name:=job_name; pack_cur_name;
+end;
+
+@ If some trouble arises when \TeX\ tries to open a file, the following
+routine calls upon the user to supply another file name. Parameter~|s|
+is used in the error message to identify the type of file; parameter~|e|
+is the default extension if none is given. Upon exit from the routine,
+variables |cur_name|, |cur_area|, |cur_ext|, and |name_of_file| are
+ready for another attempt at file opening.
+
+@p procedure prompt_file_name(@!s,@!e:str_number);
+label done;
+var k:0..buf_size; {index into |buffer|}
+begin if interaction=scroll_mode then wake_up_terminal;
+if s="input file name" then print_err("I can't find file `")
+@.I can't find file x@>
+else print_err("I can't write on file `");
+@.I can't write on file x@>
+print_file_name(cur_name,cur_area,cur_ext); print("'.");
+if e=".tex" then show_context;
+print_nl("Please type another "); print(s);
+@.Please type...@>
+if interaction<scroll_mode then
+ fatal_error("*** (job aborted, file error in nonstop mode)");
+@.job aborted, file error...@>
+clear_terminal; prompt_input(": "); @<Scan file name in the buffer@>;
+if cur_ext="" then cur_ext:=e;
+pack_cur_name;
+end;
+
+@ @<Scan file name in the buffer@>=
+begin begin_name; k:=first;
+while (buffer[k]=" ")and(k<last) do incr(k);
+loop@+ begin if k=last then goto done;
+ if not more_name(buffer[k]) then goto done;
+ incr(k);
+ end;
+done:end_name;
+end
+
+@ Here's an example of how these conventions are used. Whenever it is time to
+ship out a box of stuff, we shall use the macro |ensure_dvi_open|.
+
+@d ensure_dvi_open==if output_file_name=0 then
+ begin if job_name=0 then open_log_file;
+ pack_job_name(".dvi");
+ while not b_open_out(dvi_file) do
+ prompt_file_name("file name for output",".dvi");
+ output_file_name:=b_make_name_string(dvi_file);
+ end
+
+@<Glob...@>=
+@!dvi_file: byte_file; {the device-independent output goes here}
+@!output_file_name: str_number; {full name of the output file}
+@!log_name:str_number; {full name of the log file}
+
+@ @<Initialize the output...@>=output_file_name:=0;
+
+@ The |open_log_file| routine is used to open the transcript file and to help
+it catch up to what has previously been printed on the terminal.
+
+@p procedure open_log_file;
+var old_setting:0..max_selector; {previous |selector| setting}
+@!k:0..buf_size; {index into |months| and |buffer|}
+@!l:0..buf_size; {end of first input line}
+@!months:packed array [1..36] of char; {abbreviations of month names}
+begin old_setting:=selector;
+if job_name=0 then job_name:="texput";
+@.texput@>
+pack_job_name(".log");
+while not a_open_out(log_file) do @<Try to get a different log file name@>;
+log_name:=a_make_name_string(log_file);
+selector:=log_only; log_opened:=true;
+@<Print the banner line, including the date and time@>;
+input_stack[input_ptr]:=cur_input; {make sure bottom level is in memory}
+print_nl("**");
+@.**@>
+l:=input_stack[0].limit_field; {last position of first line}
+if buffer[l]=end_line_char then decr(l);
+for k:=1 to l do print(buffer[k]);
+print_ln; {now the transcript file contains the first line of input}
+selector:=old_setting+2; {|log_only| or |term_and_log|}
+end;
+
+@ Sometimes |open_log_file| is called at awkward moments when \TeX\ is
+unable to print error messages or even to |show_context|.
+The |prompt_file_name| routine can result in a |fatal_error|, but the |error|
+routine will not be invoked because |log_opened| will be false.
+
+The normal idea of |batch_mode| is that nothing at all should be written
+on the terminal. However, in the unusual case that
+no log file could be opened, we make an exception and allow
+an explanatory message to be seen.
+
+Incidentally, the program always refers to the log file as a `\.{transcript
+file}', because some systems cannot use the extension `\.{.log}' for
+this file.
+
+@<Try to get a different log file name@>=
+begin selector:=term_only;
+prompt_file_name("transcript file name",".log");
+end
+
+@ @<Print the banner...@>=
+begin wlog(banner);
+slow_print(format_ident); print(" ");
+print_int(day); print_char(" ");
+months:='JANFEBMARAPRMAYJUNJULAUGSEPOCTNOVDEC';
+for k:=3*month-2 to 3*month do wlog(months[k]);
+print_char(" "); print_int(year); print_char(" ");
+print_two(time div 60); print_char(":"); print_two(time mod 60);
+end
+
+@ Let's turn now to the procedure that is used to initiate file reading
+when an `\.{\\input}' command is being processed.
+
+@p procedure start_input; {\TeX\ will \.{\\input} something}
+label done;
+begin scan_file_name; {set |cur_name| to desired file name}
+if cur_ext="" then cur_ext:=".tex";
+pack_cur_name;
+loop@+ begin begin_file_reading; {set up |cur_file| and new level of input}
+ if a_open_in(cur_file) then goto done;
+ if cur_area="" then
+ begin pack_file_name(cur_name,TEX_area,cur_ext);
+ if a_open_in(cur_file) then goto done;
+ end;
+ end_file_reading; {remove the level that didn't work}
+ prompt_file_name("input file name",".tex");
+ end;
+done: name:=a_make_name_string(cur_file);
+if job_name=0 then
+ begin job_name:=cur_name; open_log_file;
+ end; {|open_log_file| doesn't |show_context|, so |limit|
+ and |loc| needn't be set to meaningful values yet}
+if term_offset+length(name)>max_print_line-2 then print_ln
+else if (term_offset>0)or(file_offset>0) then print_char(" ");
+print_char("("); incr(open_parens); slow_print(name); update_terminal;
+state:=new_line;
+if name=str_ptr-1 then {we can conserve string pool space now}
+ begin flush_string; name:=cur_name;
+ end;
+@<Read the first line of the new file@>;
+end;
+
+@ Here we have to remember to tell the |input_ln| routine not to
+start with a |get|. If the file is empty, it is considered to
+contain a single blank line.
+@^system dependencies@>
+@^empty line at end of file@>
+
+@<Read the first line...@>=
+begin line:=1;
+if input_ln(cur_file,false) then do_nothing;
+firm_up_the_line;
+if end_line_char_inactive then decr(limit)
+else buffer[limit]:=end_line_char;
+first:=limit+1; loc:=start;
+end
+
+@* \[30] Font metric data.
+\TeX\ gets its knowledge about fonts from font metric files, also called
+\.{TFM} files; the `\.T' in `\.{TFM}' stands for \TeX,
+but other programs know about them too.
+@:TFM files}{\.{TFM} files@>
+@^font metric files@>
+
+The information in a \.{TFM} file appears in a sequence of 8-bit bytes.
+Since the number of bytes is always a multiple of 4, we could
+also regard the file as a sequence of 32-bit words, but \TeX\ uses the
+byte interpretation. The format of \.{TFM} files was designed by
+Lyle Ramshaw in 1980. The intent is to convey a lot of different kinds
+@^Ramshaw, Lyle Harold@>
+of information in a compact but useful form.
+
+@<Glob...@>=
+@!tfm_file:byte_file;
+
+@ The first 24 bytes (6 words) of a \.{TFM} file contain twelve 16-bit
+integers that give the lengths of the various subsequent portions
+of the file. These twelve integers are, in order:
+$$\vbox{\halign{\hfil#&$\null=\null$#\hfil\cr
+|lf|&length of the entire file, in words;\cr
+|lh|&length of the header data, in words;\cr
+|bc|&smallest character code in the font;\cr
+|ec|&largest character code in the font;\cr
+|nw|&number of words in the width table;\cr
+|nh|&number of words in the height table;\cr
+|nd|&number of words in the depth table;\cr
+|ni|&number of words in the italic correction table;\cr
+|nl|&number of words in the lig/kern table;\cr
+|nk|&number of words in the kern table;\cr
+|ne|&number of words in the extensible character table;\cr
+|np|&number of font parameter words.\cr}}$$
+They are all nonnegative and less than $2^{15}$. We must have |bc-1<=ec<=255|,
+and
+$$\hbox{|lf=6+lh+(ec-bc+1)+nw+nh+nd+ni+nl+nk+ne+np|.}$$
+Note that a font may contain as many as 256 characters (if |bc=0| and |ec=255|),
+and as few as 0 characters (if |bc=ec+1|).
+
+Incidentally, when two or more 8-bit bytes are combined to form an integer of
+16 or more bits, the most significant bytes appear first in the file.
+This is called BigEndian order.
+@!@^BigEndian order@>
+
+@ The rest of the \.{TFM} file may be regarded as a sequence of ten data
+arrays having the informal specification
+$$\def\arr$[#1]#2${\&{array} $[#1]$ \&{of} #2}
+\vbox{\halign{\hfil\\{#}&$\,:\,$\arr#\hfil\cr
+header&|[0..lh-1]@t\\{stuff}@>|\cr
+char\_info&|[bc..ec]char_info_word|\cr
+width&|[0..nw-1]fix_word|\cr
+height&|[0..nh-1]fix_word|\cr
+depth&|[0..nd-1]fix_word|\cr
+italic&|[0..ni-1]fix_word|\cr
+lig\_kern&|[0..nl-1]lig_kern_command|\cr
+kern&|[0..nk-1]fix_word|\cr
+exten&|[0..ne-1]extensible_recipe|\cr
+param&|[1..np]fix_word|\cr}}$$
+The most important data type used here is a |@!fix_word|, which is
+a 32-bit representation of a binary fraction. A |fix_word| is a signed
+quantity, with the two's complement of the entire word used to represent
+negation. Of the 32 bits in a |fix_word|, exactly 12 are to the left of the
+binary point; thus, the largest |fix_word| value is $2048-2^{-20}$, and
+the smallest is $-2048$. We will see below, however, that all but two of
+the |fix_word| values must lie between $-16$ and $+16$.
+
+@ The first data array is a block of header information, which contains
+general facts about the font. The header must contain at least two words,
+|header[0]| and |header[1]|, whose meaning is explained below.
+Additional header information of use to other software routines might
+also be included, but \TeX82 does not need to know about such details.
+For example, 16 more words of header information are in use at the Xerox
+Palo Alto Research Center; the first ten specify the character coding
+scheme used (e.g., `\.{XEROX text}' or `\.{TeX math symbols}'), the next five
+give the font identifier (e.g., `\.{HELVETICA}' or `\.{CMSY}'), and the
+last gives the ``face byte.'' The program that converts \.{DVI} files
+to Xerox printing format gets this information by looking at the \.{TFM}
+file, which it needs to read anyway because of other information that
+is not explicitly repeated in \.{DVI}~format.
+
+\yskip\hang|header[0]| is a 32-bit check sum that \TeX\ will copy into
+the \.{DVI} output file. Later on when the \.{DVI} file is printed,
+possibly on another computer, the actual font that gets used is supposed
+to have a check sum that agrees with the one in the \.{TFM} file used by
+\TeX. In this way, users will be warned about potential incompatibilities.
+(However, if the check sum is zero in either the font file or the \.{TFM}
+file, no check is made.) The actual relation between this check sum and
+the rest of the \.{TFM} file is not important; the check sum is simply an
+identification number with the property that incompatible fonts almost
+always have distinct check sums.
+@^check sum@>
+
+\yskip\hang|header[1]| is a |fix_word| containing the design size of
+the font, in units of \TeX\ points. This number must be at least 1.0; it is
+fairly arbitrary, but usually the design size is 10.0 for a ``10 point''
+font, i.e., a font that was designed to look best at a 10-point size,
+whatever that really means. When a \TeX\ user asks for a font
+`\.{at} $\delta$ \.{pt}', the effect is to override the design size
+and replace it by $\delta$, and to multiply the $x$ and~$y$ coordinates
+of the points in the font image by a factor of $\delta$ divided by the
+design size. {\sl All other dimensions in the\/ \.{TFM} file are
+|fix_word|\kern-1pt\ numbers in design-size units}, with the exception of
+|param[1]| (which denotes the slant ratio). Thus, for example, the value
+of |param[6]|, which defines the \.{em} unit, is often the |fix_word| value
+$2^{20}=1.0$, since many fonts have a design size equal to one em.
+The other dimensions must be less than 16 design-size units in absolute
+value; thus, |header[1]| and |param[1]| are the only |fix_word|
+entries in the whole \.{TFM} file whose first byte might be something
+besides 0 or 255.
+
+@ Next comes the |char_info| array, which contains one |@!char_info_word|
+per character. Each word in this part of the file contains six fields
+packed into four bytes as follows.
+
+\yskip\hang first byte: |@!width_index| (8 bits)\par
+\hang second byte: |@!height_index| (4 bits) times 16, plus |@!depth_index|
+ (4~bits)\par
+\hang third byte: |@!italic_index| (6 bits) times 4, plus |@!tag|
+ (2~bits)\par
+\hang fourth byte: |@!remainder| (8 bits)\par
+\yskip\noindent
+The actual width of a character is \\{width}|[width_index]|, in design-size
+units; this is a device for compressing information, since many characters
+have the same width. Since it is quite common for many characters
+to have the same height, depth, or italic correction, the \.{TFM} format
+imposes a limit of 16 different heights, 16 different depths, and
+64 different italic corrections.
+
+@!@^italic correction@>
+The italic correction of a character has two different uses.
+(a)~In ordinary text, the italic correction is added to the width only if
+the \TeX\ user specifies `\.{\\/}' after the character.
+(b)~In math formulas, the italic correction is always added to the width,
+except with respect to the positioning of subscripts.
+
+Incidentally, the relation $\\{width}[0]=\\{height}[0]=\\{depth}[0]=
+\\{italic}[0]=0$ should always hold, so that an index of zero implies a
+value of zero. The |width_index| should never be zero unless the
+character does not exist in the font, since a character is valid if and
+only if it lies between |bc| and |ec| and has a nonzero |width_index|.
+
+@ The |tag| field in a |char_info_word| has four values that explain how to
+interpret the |remainder| field.
+
+\yskip\hangg|tag=0| (|no_tag|) means that |remainder| is unused.\par
+\hangg|tag=1| (|lig_tag|) means that this character has a ligature/kerning
+program starting at position |remainder| in the |lig_kern| array.\par
+\hangg|tag=2| (|list_tag|) means that this character is part of a chain of
+characters of ascending sizes, and not the largest in the chain. The
+|remainder| field gives the character code of the next larger character.\par
+\hangg|tag=3| (|ext_tag|) means that this character code represents an
+extensible character, i.e., a character that is built up of smaller pieces
+so that it can be made arbitrarily large. The pieces are specified in
+|@!exten[remainder]|.\par
+\yskip\noindent
+Characters with |tag=2| and |tag=3| are treated as characters with |tag=0|
+unless they are used in special circumstances in math formulas. For example,
+the \.{\\sum} operation looks for a |list_tag|, and the \.{\\left}
+operation looks for both |list_tag| and |ext_tag|.
+
+@d no_tag=0 {vanilla character}
+@d lig_tag=1 {character has a ligature/kerning program}
+@d list_tag=2 {character has a successor in a charlist}
+@d ext_tag=3 {character is extensible}
+
+@ The |lig_kern| array contains instructions in a simple programming language
+that explains what to do for special letter pairs. Each word in this array is a
+|@!lig_kern_command| of four bytes.
+
+\yskip\hang first byte: |skip_byte|, indicates that this is the final program
+ step if the byte is 128 or more, otherwise the next step is obtained by
+ skipping this number of intervening steps.\par
+\hang second byte: |next_char|, ``if |next_char| follows the current character,
+ then perform the operation and stop, otherwise continue.''\par
+\hang third byte: |op_byte|, indicates a ligature step if less than~128,
+ a kern step otherwise.\par
+\hang fourth byte: |remainder|.\par
+\yskip\noindent
+In a kern step, an
+additional space equal to |kern[256*(op_byte-128)+remainder]| is inserted
+between the current character and |next_char|. This amount is
+often negative, so that the characters are brought closer together
+by kerning; but it might be positive.
+
+There are eight kinds of ligature steps, having |op_byte| codes $4a+2b+c$ where
+$0\le a\le b+c$ and $0\le b,c\le1$. The character whose code is
+|remainder| is inserted between the current character and |next_char|;
+then the current character is deleted if $b=0$, and |next_char| is
+deleted if $c=0$; then we pass over $a$~characters to reach the next
+current character (which may have a ligature/kerning program of its own).
+
+If the very first instruction of the |lig_kern| array has |skip_byte=255|,
+the |next_char| byte is the so-called right boundary character of this font;
+the value of |next_char| need not lie between |bc| and~|ec|.
+If the very last instruction of the |lig_kern| array has |skip_byte=255|,
+there is a special ligature/kerning program for a left boundary character,
+beginning at location |256*op_byte+remainder|.
+The interpretation is that \TeX\ puts implicit boundary characters
+before and after each consecutive string of characters from the same font.
+These implicit characters do not appear in the output, but they can affect
+ligatures and kerning.
+
+If the very first instruction of a character's |lig_kern| program has
+|skip_byte>128|, the program actually begins in location
+|256*op_byte+remainder|. This feature allows access to large |lig_kern|
+arrays, because the first instruction must otherwise
+appear in a location |<=255|.
+
+Any instruction with |skip_byte>128| in the |lig_kern| array must satisfy
+the condition
+$$\hbox{|256*op_byte+remainder<nl|.}$$
+If such an instruction is encountered during
+normal program execution, it denotes an unconditional halt; no ligature
+or kerning command is performed.
+
+@d stop_flag==qi(128) {value indicating `\.{STOP}' in a lig/kern program}
+@d kern_flag==qi(128) {op code for a kern step}
+@d skip_byte(#)==#.b0
+@d next_char(#)==#.b1
+@d op_byte(#)==#.b2
+@d rem_byte(#)==#.b3
+
+@ Extensible characters are specified by an |@!extensible_recipe|, which
+consists of four bytes called |@!top|, |@!mid|, |@!bot|, and |@!rep| (in this
+order). These bytes are the character codes of individual pieces used to
+build up a large symbol. If |top|, |mid|, or |bot| are zero, they are not
+present in the built-up result. For example, an extensible vertical line is
+like an extensible bracket, except that the top and bottom pieces are missing.
+
+Let $T$, $M$, $B$, and $R$ denote the respective pieces, or an empty box
+if the piece isn't present. Then the extensible characters have the form
+$TR^kMR^kB$ from top to bottom, for some |k>=0|, unless $M$ is absent;
+in the latter case we can have $TR^kB$ for both even and odd values of~|k|.
+The width of the extensible character is the width of $R$; and the
+height-plus-depth is the sum of the individual height-plus-depths of the
+components used, since the pieces are butted together in a vertical list.
+
+@d ext_top(#)==#.b0 {|top| piece in a recipe}
+@d ext_mid(#)==#.b1 {|mid| piece in a recipe}
+@d ext_bot(#)==#.b2 {|bot| piece in a recipe}
+@d ext_rep(#)==#.b3 {|rep| piece in a recipe}
+
+@ The final portion of a \.{TFM} file is the |param| array, which is another
+sequence of |fix_word| values.
+
+\yskip\hang|param[1]=slant| is the amount of italic slant, which is used
+to help position accents. For example, |slant=.25| means that when you go
+up one unit, you also go .25 units to the right. The |slant| is a pure
+number; it's the only |fix_word| other than the design size itself that is
+not scaled by the design size.
+
+\hang|param[2]=space| is the normal spacing between words in text.
+Note that character |" "| in the font need not have anything to do with
+blank spaces.
+
+\hang|param[3]=space_stretch| is the amount of glue stretching between words.
+
+\hang|param[4]=space_shrink| is the amount of glue shrinking between words.
+
+\hang|param[5]=x_height| is the size of one ex in the font; it is also
+the height of letters for which accents don't have to be raised or lowered.
+
+\hang|param[6]=quad| is the size of one em in the font.
+
+\hang|param[7]=extra_space| is the amount added to |param[2]| at the
+ends of sentences.
+
+\yskip\noindent
+If fewer than seven parameters are present, \TeX\ sets the missing parameters
+to zero. Fonts used for math symbols are required to have
+additional parameter information, which is explained later.
+
+@d slant_code=1
+@d space_code=2
+@d space_stretch_code=3
+@d space_shrink_code=4
+@d x_height_code=5
+@d quad_code=6
+@d extra_space_code=7
+
+@ So that is what \.{TFM} files hold. Since \TeX\ has to absorb such information
+about lots of fonts, it stores most of the data in a large array called
+|font_info|. Each item of |font_info| is a |memory_word|; the |fix_word|
+data gets converted into |scaled| entries, while everything else goes into
+words of type |four_quarters|.
+
+When the user defines \.{\\font\\f}, say, \TeX\ assigns an internal number
+to the user's font~\.{\\f}. Adding this number to |font_id_base| gives the
+|eqtb| location of a ``frozen'' control sequence that will always select
+the font.
+
+@<Types...@>=
+@!internal_font_number=font_base..font_max; {|font| in a |char_node|}
+@!font_index=0..font_mem_size; {index into |font_info|}
+
+@ Here now is the (rather formidable) array of font arrays.
+
+@d non_char==qi(256) {a |halfword| code that can't match a real character}
+@d non_address=0 {a spurious |bchar_label|}
+
+@<Glob...@>=
+@!font_info:array[font_index] of memory_word;
+ {the big collection of font data}
+@!fmem_ptr:font_index; {first unused word of |font_info|}
+@!font_ptr:internal_font_number; {largest internal font number in use}
+@!font_check:array[internal_font_number] of four_quarters; {check sum}
+@!font_size:array[internal_font_number] of scaled; {``at'' size}
+@!font_dsize:array[internal_font_number] of scaled; {``design'' size}
+@!font_params:array[internal_font_number] of font_index; {how many font
+ parameters are present}
+@!font_name:array[internal_font_number] of str_number; {name of the font}
+@!font_area:array[internal_font_number] of str_number; {area of the font}
+@!font_bc:array[internal_font_number] of eight_bits;
+ {beginning (smallest) character code}
+@!font_ec:array[internal_font_number] of eight_bits;
+ {ending (largest) character code}
+@!font_glue:array[internal_font_number] of pointer;
+ {glue specification for interword space, |null| if not allocated}
+@!font_used:array[internal_font_number] of boolean;
+ {has a character from this font actually appeared in the output?}
+@!hyphen_char:array[internal_font_number] of integer;
+ {current \.{\\hyphenchar} values}
+@!skew_char:array[internal_font_number] of integer;
+ {current \.{\\skewchar} values}
+@!bchar_label:array[internal_font_number] of font_index;
+ {start of |lig_kern| program for left boundary character,
+ |non_address| if there is none}
+@!font_bchar:array[internal_font_number] of min_quarterword..non_char;
+ {right boundary character, |non_char| if there is none}
+@!font_false_bchar:array[internal_font_number] of min_quarterword..non_char;
+ {|font_bchar| if it doesn't exist in the font, otherwise |non_char|}
+
+@ Besides the arrays just enumerated, we have directory arrays that make it
+easy to get at the individual entries in |font_info|. For example, the
+|char_info| data for character |c| in font |f| will be in
+|font_info[char_base[f]+c].qqqq|; and if |w| is the |width_index|
+part of this word (the |b0| field), the width of the character is
+|font_info[width_base[f]+w].sc|. (These formulas assume that
+|min_quarterword| has already been added to |c| and to |w|, since \TeX\
+stores its quarterwords that way.)
+
+@<Glob...@>=
+@!char_base:array[internal_font_number] of integer;
+ {base addresses for |char_info|}
+@!width_base:array[internal_font_number] of integer;
+ {base addresses for widths}
+@!height_base:array[internal_font_number] of integer;
+ {base addresses for heights}
+@!depth_base:array[internal_font_number] of integer;
+ {base addresses for depths}
+@!italic_base:array[internal_font_number] of integer;
+ {base addresses for italic corrections}
+@!lig_kern_base:array[internal_font_number] of integer;
+ {base addresses for ligature/kerning programs}
+@!kern_base:array[internal_font_number] of integer;
+ {base addresses for kerns}
+@!exten_base:array[internal_font_number] of integer;
+ {base addresses for extensible recipes}
+@!param_base:array[internal_font_number] of integer;
+ {base addresses for font parameters}
+
+@ @<Set init...@>=
+for k:=font_base to font_max do font_used[k]:=false;
+
+@ \TeX\ always knows at least one font, namely the null font. It has no
+characters, and its seven parameters are all equal to zero.
+
+@<Initialize table...@>=
+font_ptr:=null_font; fmem_ptr:=7;
+font_name[null_font]:="nullfont"; font_area[null_font]:="";
+hyphen_char[null_font]:="-"; skew_char[null_font]:=-1;
+bchar_label[null_font]:=non_address;
+font_bchar[null_font]:=non_char; font_false_bchar[null_font]:=non_char;
+font_bc[null_font]:=1; font_ec[null_font]:=0;
+font_size[null_font]:=0; font_dsize[null_font]:=0;
+char_base[null_font]:=0; width_base[null_font]:=0;
+height_base[null_font]:=0; depth_base[null_font]:=0;
+italic_base[null_font]:=0; lig_kern_base[null_font]:=0;
+kern_base[null_font]:=0; exten_base[null_font]:=0;
+font_glue[null_font]:=null; font_params[null_font]:=7;
+param_base[null_font]:=-1;
+for k:=0 to 6 do font_info[k].sc:=0;
+
+@ @<Put each...@>=
+primitive("nullfont",set_font,null_font);
+@!@:null_font_}{\.{\\nullfont} primitive@>
+text(frozen_null_font):="nullfont"; eqtb[frozen_null_font]:=eqtb[cur_val];
+
+@ Of course we want to define macros that suppress the detail of how font
+information is actually packed, so that we don't have to write things like
+$$\hbox{|font_info[width_base[f]+font_info[char_base[f]+c].qqqq.b0].sc|}$$
+too often. The \.{WEB} definitions here make |char_info(f)(c)| the
+|four_quarters| word of font information corresponding to character
+|c| of font |f|. If |q| is such a word, |char_width(f)(q)| will be
+the character's width; hence the long formula above is at least
+abbreviated to
+$$\hbox{|char_width(f)(char_info(f)(c))|.}$$
+Usually, of course, we will fetch |q| first and look at several of its
+fields at the same time.
+
+The italic correction of a character will be denoted by
+|char_italic(f)(q)|, so it is analogous to |char_width|. But we will get
+at the height and depth in a slightly different way, since we usually want
+to compute both height and depth if we want either one. The value of
+|height_depth(q)| will be the 8-bit quantity
+$$b=|height_index|\times16+|depth_index|,$$ and if |b| is such a byte we
+will write |char_height(f)(b)| and |char_depth(f)(b)| for the height and
+depth of the character |c| for which |q=char_info(f)(c)|. Got that?
+
+The tag field will be called |char_tag(q)|; the remainder byte will be
+called |rem_byte(q)|, using a macro that we have already defined above.
+
+Access to a character's |width|, |height|, |depth|, and |tag| fields is
+part of \TeX's inner loop, so we want these macros to produce code that is
+as fast as possible under the circumstances.
+@^inner loop@>
+
+@d char_info_end(#)==#].qqqq
+@d char_info(#)==font_info[char_base[#]+char_info_end
+@d char_width_end(#)==#.b0].sc
+@d char_width(#)==font_info[width_base[#]+char_width_end
+@d char_exists(#)==(#.b0>min_quarterword)
+@d char_italic_end(#)==(qo(#.b2)) div 4].sc
+@d char_italic(#)==font_info[italic_base[#]+char_italic_end
+@d height_depth(#)==qo(#.b1)
+@d char_height_end(#)==(#) div 16].sc
+@d char_height(#)==font_info[height_base[#]+char_height_end
+@d char_depth_end(#)==(#) mod 16].sc
+@d char_depth(#)==font_info[depth_base[#]+char_depth_end
+@d char_tag(#)==((qo(#.b2)) mod 4)
+
+@ The global variable |null_character| is set up to be a word of
+|char_info| for a character that doesn't exist. Such a word provides a
+convenient way to deal with erroneous situations.
+
+@<Glob...@>=
+@!null_character:four_quarters; {nonexistent character information}
+
+@ @<Set init...@>=
+null_character.b0:=min_quarterword; null_character.b1:=min_quarterword;
+null_character.b2:=min_quarterword; null_character.b3:=min_quarterword;
+
+@ Here are some macros that help process ligatures and kerns.
+We write |char_kern(f)(j)| to find the amount of kerning specified by
+kerning command~|j| in font~|f|. If |j| is the |char_info| for a character
+with a ligature/kern program, the first instruction of that program is either
+|i=font_info[lig_kern_start(f)(j)]| or |font_info[lig_kern_restart(f)(i)]|,
+depending on whether or not |skip_byte(i)<=stop_flag|.
+
+The constant |kern_base_offset| should be simplified, for \PASCAL\ compilers
+that do not do local optimization.
+@^system dependencies@>
+
+@d char_kern_end(#)==256*op_byte(#)+rem_byte(#)].sc
+@d char_kern(#)==font_info[kern_base[#]+char_kern_end
+@d kern_base_offset==256*(128+min_quarterword)
+@d lig_kern_start(#)==lig_kern_base[#]+rem_byte {beginning of lig/kern program}
+@d lig_kern_restart_end(#)==256*op_byte(#)+rem_byte(#)+32768-kern_base_offset
+@d lig_kern_restart(#)==lig_kern_base[#]+lig_kern_restart_end
+
+@ Font parameters are referred to as |slant(f)|, |space(f)|, etc.
+
+@d param_end(#)==param_base[#]].sc
+@d param(#)==font_info[#+param_end
+@d slant==param(slant_code) {slant to the right, per unit distance upward}
+@d space==param(space_code) {normal space between words}
+@d space_stretch==param(space_stretch_code) {stretch between words}
+@d space_shrink==param(space_shrink_code) {shrink between words}
+@d x_height==param(x_height_code) {one ex}
+@d quad==param(quad_code) {one em}
+@d extra_space==param(extra_space_code) {additional space at end of sentence}
+
+@<The em width for |cur_font|@>=quad(cur_font)
+
+@ @<The x-height for |cur_font|@>=x_height(cur_font)
+
+@ \TeX\ checks the information of a \.{TFM} file for validity as the
+file is being read in, so that no further checks will be needed when
+typesetting is going on. The somewhat tedious subroutine that does this
+is called |read_font_info|. It has four parameters: the user font
+identifier~|u|, the file name and area strings |nom| and |aire|, and the
+``at'' size~|s|. If |s|~is negative, it's the negative of a scale factor
+to be applied to the design size; |s=-1000| is the normal case.
+Otherwise |s| will be substituted for the design size; in this
+case, |s| must be positive and less than $2048\rm\,pt$
+(i.e., it must be less than $2^{27}$ when considered as an integer).
+
+The subroutine opens and closes a global file variable called |tfm_file|.
+It returns the value of the internal font number that was just loaded.
+If an error is detected, an error message is issued and no font
+information is stored; |null_font| is returned in this case.
+
+@d bad_tfm=11 {label for |read_font_info|}
+@d abort==goto bad_tfm {do this when the \.{TFM} data is wrong}
+
+@p function read_font_info(@!u:pointer;@!nom,@!aire:str_number;
+ @!s:scaled):internal_font_number; {input a \.{TFM} file}
+label done,bad_tfm,not_found;
+var k:font_index; {index into |font_info|}
+@!file_opened:boolean; {was |tfm_file| successfully opened?}
+@!lf,@!lh,@!bc,@!ec,@!nw,@!nh,@!nd,@!ni,@!nl,@!nk,@!ne,@!np:halfword;
+ {sizes of subfiles}
+@!f:internal_font_number; {the new font's number}
+@!g:internal_font_number; {the number to return}
+@!a,@!b,@!c,@!d:eight_bits; {byte variables}
+@!qw:four_quarters;@!sw:scaled; {accumulators}
+@!bch_label:integer; {left boundary start location, or infinity}
+@!bchar:0..256; {right boundary character, or 256}
+@!z:scaled; {the design size or the ``at'' size}
+@!alpha:integer;@!beta:1..16;
+ {auxiliary quantities used in fixed-point multiplication}
+begin g:=null_font;@/
+@<Read and check the font data; |abort| if the \.{TFM} file is
+ malformed; if there's no room for this font, say so and |goto
+ done|; otherwise |incr(font_ptr)| and |goto done|@>;
+bad_tfm: @<Report that the font won't be loaded@>;
+done: if file_opened then b_close(tfm_file);
+read_font_info:=g;
+end;
+
+@ There are programs called \.{TFtoPL} and \.{PLtoTF} that convert
+between the \.{TFM} format and a symbolic property-list format
+that can be easily edited. These programs contain extensive
+diagnostic information, so \TeX\ does not have to bother giving
+precise details about why it rejects a particular \.{TFM} file.
+@.TFtoPL@> @.PLtoTF@>
+
+@d start_font_error_message==print_err("Font "); sprint_cs(u);
+ print_char("="); print_file_name(nom,aire,"");
+ if s>=0 then
+ begin print(" at "); print_scaled(s); print("pt");
+ end
+ else if s<>-1000 then
+ begin print(" scaled "); print_int(-s);
+ end
+
+@<Report that the font won't be loaded@>=
+start_font_error_message;
+@.Font x=xx not loadable...@>
+if file_opened then print(" not loadable: Bad metric (TFM) file")
+else print(" not loadable: Metric (TFM) file not found");
+help5("I wasn't able to read the size data for this font,")@/
+("so I will ignore the font specification.")@/
+("[Wizards can fix TFM files using TFtoPL/PLtoTF.]")@/
+("You might try inserting a different font spec;")@/
+("e.g., type `I\font<same font id>=<substitute font name>'.");
+error
+
+@ @<Read and check...@>=
+@<Open |tfm_file| for input@>;
+@<Read the {\.{TFM}} size fields@>;
+@<Use size fields to allocate font information@>;
+@<Read the {\.{TFM}} header@>;
+@<Read character data@>;
+@<Read box dimensions@>;
+@<Read ligature/kern program@>;
+@<Read extensible character recipes@>;
+@<Read font parameters@>;
+@<Make final adjustments and |goto done|@>
+
+@ @<Open |tfm_file| for input@>=
+file_opened:=false;
+if aire="" then pack_file_name(nom,TEX_font_area,".tfm")
+else pack_file_name(nom,aire,".tfm");
+if not b_open_in(tfm_file) then abort;
+file_opened:=true
+
+@ Note: A malformed \.{TFM} file might be shorter than it claims to be;
+thus |eof(tfm_file)| might be true when |read_font_info| refers to
+|tfm_file^| or when it says |get(tfm_file)|. If such circumstances
+cause system error messages, you will have to defeat them somehow,
+for example by defining |fget| to be `\ignorespaces|begin get(tfm_file);|
+|if eof(tfm_file) then abort; end|\unskip'.
+@^system dependencies@>
+
+@d fget==get(tfm_file)
+@d fbyte==tfm_file^
+@d read_sixteen(#)==begin #:=fbyte;
+ if #>127 then abort;
+ fget; #:=#*@'400+fbyte;
+ end
+@d store_four_quarters(#)==begin fget; a:=fbyte; qw.b0:=qi(a);
+ fget; b:=fbyte; qw.b1:=qi(b);
+ fget; c:=fbyte; qw.b2:=qi(c);
+ fget; d:=fbyte; qw.b3:=qi(d);
+ #:=qw;
+ end
+
+@ @<Read the {\.{TFM}} size fields@>=
+begin read_sixteen(lf);
+fget; read_sixteen(lh);
+fget; read_sixteen(bc);
+fget; read_sixteen(ec);
+if (bc>ec+1)or(ec>255) then abort;
+if bc>255 then {|bc=256| and |ec=255|}
+ begin bc:=1; ec:=0;
+ end;
+fget; read_sixteen(nw);
+fget; read_sixteen(nh);
+fget; read_sixteen(nd);
+fget; read_sixteen(ni);
+fget; read_sixteen(nl);
+fget; read_sixteen(nk);
+fget; read_sixteen(ne);
+fget; read_sixteen(np);
+if lf<>6+lh+(ec-bc+1)+nw+nh+nd+ni+nl+nk+ne+np then abort;
+end
+
+@ The preliminary settings of the index-offset variables |char_base|,
+|width_base|, |lig_kern_base|, |kern_base|, and |exten_base| will be
+corrected later by subtracting |min_quarterword| from them; and we will
+subtract 1 from |param_base| too. It's best to forget about such anomalies
+until later.
+
+@<Use size fields to allocate font information@>=
+lf:=lf-6-lh; {|lf| words should be loaded into |font_info|}
+if np<7 then lf:=lf+7-np; {at least seven parameters will appear}
+if (font_ptr=font_max)or(fmem_ptr+lf>font_mem_size) then
+ @<Apologize for not loading the font, |goto done|@>;
+f:=font_ptr+1;
+char_base[f]:=fmem_ptr-bc;
+width_base[f]:=char_base[f]+ec+1;
+height_base[f]:=width_base[f]+nw;
+depth_base[f]:=height_base[f]+nh;
+italic_base[f]:=depth_base[f]+nd;
+lig_kern_base[f]:=italic_base[f]+ni;
+kern_base[f]:=lig_kern_base[f]+nl-kern_base_offset;
+exten_base[f]:=kern_base[f]+kern_base_offset+nk;
+param_base[f]:=exten_base[f]+ne
+
+@ @<Apologize for not loading...@>=
+begin start_font_error_message;
+print(" not loaded: Not enough room left");
+@.Font x=xx not loaded...@>
+help4("I'm afraid I won't be able to make use of this font,")@/
+("because my memory for character-size data is too small.")@/
+("If you're really stuck, ask a wizard to enlarge me.")@/
+("Or maybe try `I\font<same font id>=<name of loaded font>'.");
+error; goto done;
+end
+
+@ Only the first two words of the header are needed by \TeX82.
+
+@<Read the {\.{TFM}} header@>=
+begin if lh<2 then abort;
+store_four_quarters(font_check[f]);
+fget; read_sixteen(z); {this rejects a negative design size}
+fget; z:=z*@'400+fbyte; fget; z:=(z*@'20)+(fbyte div@'20);
+if z<unity then abort;
+while lh>2 do
+ begin fget;fget;fget;fget;decr(lh); {ignore the rest of the header}
+ end;
+font_dsize[f]:=z;
+if s<>-1000 then
+ if s>=0 then z:=s
+ else z:=xn_over_d(z,-s,1000);
+font_size[f]:=z;
+end
+
+@ @<Read character data@>=
+for k:=fmem_ptr to width_base[f]-1 do
+ begin store_four_quarters(font_info[k].qqqq);
+ if (a>=nw)or(b div @'20>=nh)or(b mod @'20>=nd)or
+ (c div 4>=ni) then abort;
+ case c mod 4 of
+ lig_tag: if d>=nl then abort;
+ ext_tag: if d>=ne then abort;
+ list_tag: @<Check for charlist cycle@>;
+ othercases do_nothing {|no_tag|}
+ endcases;
+ end
+
+@ We want to make sure that there is no cycle of characters linked together
+by |list_tag| entries, since such a cycle would get \TeX\ into an endless
+loop. If such a cycle exists, the routine here detects it when processing
+the largest character code in the cycle.
+
+@d check_byte_range(#)==begin if (#<bc)or(#>ec) then abort@+end
+@d current_character_being_worked_on==k+bc-fmem_ptr
+
+@<Check for charlist cycle@>=
+begin check_byte_range(d);
+while d<current_character_being_worked_on do
+ begin qw:=char_info(f)(d);
+ {N.B.: not |qi(d)|, since |char_base[f]| hasn't been adjusted yet}
+ if char_tag(qw)<>list_tag then goto not_found;
+ d:=qo(rem_byte(qw)); {next character on the list}
+ end;
+if d=current_character_being_worked_on then abort; {yes, there's a cycle}
+not_found:end
+
+@ A |fix_word| whose four bytes are $(a,b,c,d)$ from left to right represents
+the number
+$$x=\left\{\vcenter{\halign{$#$,\hfil\qquad&if $#$\hfil\cr
+b\cdot2^{-4}+c\cdot2^{-12}+d\cdot2^{-20}&a=0;\cr
+-16+b\cdot2^{-4}+c\cdot2^{-12}+d\cdot2^{-20}&a=255.\cr}}\right.$$
+(No other choices of |a| are allowed, since the magnitude of a number in
+design-size units must be less than 16.) We want to multiply this
+quantity by the integer~|z|, which is known to be less than $2^{27}$.
+If $|z|<2^{23}$, the individual multiplications $b\cdot z$,
+$c\cdot z$, $d\cdot z$ cannot overflow; otherwise we will divide |z| by 2,
+4, 8, or 16, to obtain a multiplier less than $2^{23}$, and we can
+compensate for this later. If |z| has thereby been replaced by
+$|z|^\prime=|z|/2^e$, let $\beta=2^{4-e}$; we shall compute
+$$\lfloor(b+c\cdot2^{-8}+d\cdot2^{-16})\,z^\prime/\beta\rfloor$$
+if $a=0$, or the same quantity minus $\alpha=2^{4+e}z^\prime$ if $a=255$.
+This calculation must be done exactly, in order to guarantee portability
+of \TeX\ between computers.
+
+@d store_scaled(#)==begin fget; a:=fbyte; fget; b:=fbyte;
+ fget; c:=fbyte; fget; d:=fbyte;@/
+ sw:=(((((d*z)div@'400)+(c*z))div@'400)+(b*z))div beta;
+ if a=0 then #:=sw@+else if a=255 then #:=sw-alpha@+else abort;
+ end
+
+@<Read box dimensions@>=
+begin @<Replace |z| by $|z|^\prime$ and compute $\alpha,\beta$@>;
+for k:=width_base[f] to lig_kern_base[f]-1 do
+ store_scaled(font_info[k].sc);
+if font_info[width_base[f]].sc<>0 then abort; {\\{width}[0] must be zero}
+if font_info[height_base[f]].sc<>0 then abort; {\\{height}[0] must be zero}
+if font_info[depth_base[f]].sc<>0 then abort; {\\{depth}[0] must be zero}
+if font_info[italic_base[f]].sc<>0 then abort; {\\{italic}[0] must be zero}
+end
+
+@ @<Replace |z|...@>=
+begin alpha:=16;
+while z>=@'40000000 do
+ begin z:=z div 2; alpha:=alpha+alpha;
+ end;
+beta:=256 div alpha; alpha:=alpha*z;
+end
+
+@ @d check_existence(#)==@t@>@;@/
+ begin check_byte_range(#);
+ qw:=char_info(f)(#); {N.B.: not |qi(#)|}
+ if not char_exists(qw) then abort;
+ end
+
+@<Read ligature/kern program@>=
+bch_label:=@'77777; bchar:=256;
+if nl>0 then
+ begin for k:=lig_kern_base[f] to kern_base[f]+kern_base_offset-1 do
+ begin store_four_quarters(font_info[k].qqqq);
+ if a>128 then
+ begin if 256*c+d>=nl then abort;
+ if a=255 then if k=lig_kern_base[f] then bchar:=b;
+ end
+ else begin if b<>bchar then check_existence(b);
+ if c<128 then check_existence(d) {check ligature}
+ else if 256*(c-128)+d>=nk then abort; {check kern}
+ if a<128 then if k-lig_kern_base[f]+a+1>=nl then abort;
+ end;
+ end;
+ if a=255 then bch_label:=256*c+d;
+ end;
+for k:=kern_base[f]+kern_base_offset to exten_base[f]-1 do
+ store_scaled(font_info[k].sc);
+
+@ @<Read extensible character recipes@>=
+for k:=exten_base[f] to param_base[f]-1 do
+ begin store_four_quarters(font_info[k].qqqq);
+ if a<>0 then check_existence(a);
+ if b<>0 then check_existence(b);
+ if c<>0 then check_existence(c);
+ check_existence(d);
+ end
+
+@ We check to see that the \.{TFM} file doesn't end prematurely; but
+no error message is given for files having more than |lf| words.
+
+@<Read font parameters@>=
+begin for k:=1 to np do
+ if k=1 then {the |slant| parameter is a pure number}
+ begin fget; sw:=fbyte; if sw>127 then sw:=sw-256;
+ fget; sw:=sw*@'400+fbyte; fget; sw:=sw*@'400+fbyte;
+ fget; font_info[param_base[f]].sc:=
+ (sw*@'20)+(fbyte div@'20);
+ end
+ else store_scaled(font_info[param_base[f]+k-1].sc);
+if eof(tfm_file) then abort;
+for k:=np+1 to 7 do font_info[param_base[f]+k-1].sc:=0;
+end
+
+@ Now to wrap it up, we have checked all the necessary things about the \.{TFM}
+file, and all we need to do is put the finishing touches on the data for
+the new font.
+
+@d adjust(#)==#[f]:=qo(#[f])
+ {correct for the excess |min_quarterword| that was added}
+
+@<Make final adjustments...@>=
+if np>=7 then font_params[f]:=np@+else font_params[f]:=7;
+hyphen_char[f]:=default_hyphen_char; skew_char[f]:=default_skew_char;
+if bch_label<nl then bchar_label[f]:=bch_label+lig_kern_base[f]
+else bchar_label[f]:=non_address;
+font_bchar[f]:=qi(bchar);
+font_false_bchar[f]:=qi(bchar);
+if bchar<=ec then if bchar>=bc then
+ begin qw:=char_info(f)(bchar); {N.B.: not |qi(bchar)|}
+ if char_exists(qw) then font_false_bchar[f]:=non_char;
+ end;
+font_name[f]:=nom;
+font_area[f]:=aire;
+font_bc[f]:=bc; font_ec[f]:=ec; font_glue[f]:=null;
+adjust(char_base); adjust(width_base); adjust(lig_kern_base);
+adjust(kern_base); adjust(exten_base);
+decr(param_base[f]);
+fmem_ptr:=fmem_ptr+lf; font_ptr:=f; g:=f; goto done
+
+@ Before we forget about the format of these tables, let's deal with two
+of \TeX's basic scanning routines related to font information.
+
+@<Declare procedures that scan font-related stuff@>=
+procedure scan_font_ident;
+var f:internal_font_number;
+@!m:halfword;
+begin @<Get the next non-blank non-call...@>;
+if cur_cmd=def_font then f:=cur_font
+else if cur_cmd=set_font then f:=cur_chr
+else if cur_cmd=def_family then
+ begin m:=cur_chr; scan_four_bit_int; f:=equiv(m+cur_val);
+ end
+else begin print_err("Missing font identifier");
+@.Missing font identifier@>
+ help2("I was looking for a control sequence whose")@/
+ ("current meaning has been defined by \font.");
+ back_error; f:=null_font;
+ end;
+cur_val:=f;
+end;
+
+@ The following routine is used to implement `\.{\\fontdimen} |n| |f|'.
+The boolean parameter |writing| is set |true| if the calling program
+intends to change the parameter value.
+
+@<Declare procedures that scan font-related stuff@>=
+procedure find_font_dimen(@!writing:boolean);
+ {sets |cur_val| to |font_info| location}
+var f:internal_font_number;
+@!n:integer; {the parameter number}
+begin scan_int; n:=cur_val; scan_font_ident; f:=cur_val;
+if n<=0 then cur_val:=fmem_ptr
+else begin if writing and(n<=space_shrink_code)and@|
+ (n>=space_code)and(font_glue[f]<>null) then
+ begin delete_glue_ref(font_glue[f]);
+ font_glue[f]:=null;
+ end;
+ if n>font_params[f] then
+ if f<font_ptr then cur_val:=fmem_ptr
+ else @<Increase the number of parameters in the last font@>
+ else cur_val:=n+param_base[f];
+ end;
+@<Issue an error message if |cur_val=fmem_ptr|@>;
+end;
+
+@ @<Issue an error message if |cur_val=fmem_ptr|@>=
+if cur_val=fmem_ptr then
+ begin print_err("Font "); print_esc(font_id_text(f));
+ print(" has only "); print_int(font_params[f]);
+ print(" fontdimen parameters");
+@.Font x has only...@>
+ help2("To increase the number of font parameters, you must")@/
+ ("use \fontdimen immediately after the \font is loaded.");
+ error;
+ end
+
+@ @<Increase the number of parameters...@>=
+begin repeat if fmem_ptr=font_mem_size then
+ overflow("font memory",font_mem_size);
+@:TeX capacity exceeded font memory}{\quad font memory@>
+font_info[fmem_ptr].sc:=0; incr(fmem_ptr); incr(font_params[f]);
+until n=font_params[f];
+cur_val:=fmem_ptr-1; {this equals |param_base[f]+font_params[f]|}
+end
+
+@ When \TeX\ wants to typeset a character that doesn't exist, the
+character node is not created; thus the output routine can assume
+that characters exist when it sees them. The following procedure
+prints a warning message unless the user has suppressed it.
+
+@p procedure char_warning(@!f:internal_font_number;@!c:eight_bits);
+begin if tracing_lost_chars>0 then
+ begin begin_diagnostic;
+ print_nl("Missing character: There is no ");
+@.Missing character@>
+ print_ASCII(c); print(" in font ");
+ slow_print(font_name[f]); print_char("!"); end_diagnostic(false);
+ end;
+end;
+
+@ Here is a function that returns a pointer to a character node for a
+given character in a given font. If that character doesn't exist,
+|null| is returned instead.
+
+@p function new_character(@!f:internal_font_number;@!c:eight_bits):pointer;
+label exit;
+var p:pointer; {newly allocated node}
+begin if font_bc[f]<=c then if font_ec[f]>=c then
+ if char_exists(char_info(f)(qi(c))) then
+ begin p:=get_avail; font(p):=f; character(p):=qi(c);
+ new_character:=p; return;
+ end;
+char_warning(f,c);
+new_character:=null;
+exit:end;
+
+@* \[31] Device-independent file format.
+The most important output produced by a run of \TeX\ is the ``device
+independent'' (\.{DVI}) file that specifies where characters and rules
+are to appear on printed pages. The form of these files was designed by
+David R. Fuchs in 1979. Almost any reasonable typesetting device can be
+@^Fuchs, David Raymond@>
+@:DVI_files}{\.{DVI} files@>
+driven by a program that takes \.{DVI} files as input, and dozens of such
+\.{DVI}-to-whatever programs have been written. Thus, it is possible to
+print the output of \TeX\ on many different kinds of equipment, using \TeX\
+as a device-independent ``front end.''
+
+A \.{DVI} file is a stream of 8-bit bytes, which may be regarded as a
+series of commands in a machine-like language. The first byte of each command
+is the operation code, and this code is followed by zero or more bytes
+that provide parameters to the command. The parameters themselves may consist
+of several consecutive bytes; for example, the `|set_rule|' command has two
+parameters, each of which is four bytes long. Parameters are usually
+regarded as nonnegative integers; but four-byte-long parameters,
+and shorter parameters that denote distances, can be
+either positive or negative. Such parameters are given in two's complement
+notation. For example, a two-byte-long distance parameter has a value between
+$-2^{15}$ and $2^{15}-1$. As in \.{TFM} files, numbers that occupy
+more than one byte position appear in BigEndian order.
+
+A \.{DVI} file consists of a ``preamble,'' followed by a sequence of one
+or more ``pages,'' followed by a ``postamble.'' The preamble is simply a
+|pre| command, with its parameters that define the dimensions used in the
+file; this must come first. Each ``page'' consists of a |bop| command,
+followed by any number of other commands that tell where characters are to
+be placed on a physical page, followed by an |eop| command. The pages
+appear in the order that \TeX\ generated them. If we ignore |nop| commands
+and \\{fnt\_def} commands (which are allowed between any two commands in
+the file), each |eop| command is immediately followed by a |bop| command,
+or by a |post| command; in the latter case, there are no more pages in the
+file, and the remaining bytes form the postamble. Further details about
+the postamble will be explained later.
+
+Some parameters in \.{DVI} commands are ``pointers.'' These are four-byte
+quantities that give the location number of some other byte in the file;
+the first byte is number~0, then comes number~1, and so on. For example,
+one of the parameters of a |bop| command points to the previous |bop|;
+this makes it feasible to read the pages in backwards order, in case the
+results are being directed to a device that stacks its output face up.
+Suppose the preamble of a \.{DVI} file occupies bytes 0 to 99. Now if the
+first page occupies bytes 100 to 999, say, and if the second
+page occupies bytes 1000 to 1999, then the |bop| that starts in byte 1000
+points to 100 and the |bop| that starts in byte 2000 points to 1000. (The
+very first |bop|, i.e., the one starting in byte 100, has a pointer of~$-1$.)
+
+@ The \.{DVI} format is intended to be both compact and easily interpreted
+by a machine. Compactness is achieved by making most of the information
+implicit instead of explicit. When a \.{DVI}-reading program reads the
+commands for a page, it keeps track of several quantities: (a)~The current
+font |f| is an integer; this value is changed only
+by \\{fnt} and \\{fnt\_num} commands. (b)~The current position on the page
+is given by two numbers called the horizontal and vertical coordinates,
+|h| and |v|. Both coordinates are zero at the upper left corner of the page;
+moving to the right corresponds to increasing the horizontal coordinate, and
+moving down corresponds to increasing the vertical coordinate. Thus, the
+coordinates are essentially Cartesian, except that vertical directions are
+flipped; the Cartesian version of |(h,v)| would be |(h,-v)|. (c)~The
+current spacing amounts are given by four numbers |w|, |x|, |y|, and |z|,
+where |w| and~|x| are used for horizontal spacing and where |y| and~|z|
+are used for vertical spacing. (d)~There is a stack containing
+|(h,v,w,x,y,z)| values; the \.{DVI} commands |push| and |pop| are used to
+change the current level of operation. Note that the current font~|f| is
+not pushed and popped; the stack contains only information about
+positioning.
+
+The values of |h|, |v|, |w|, |x|, |y|, and |z| are signed integers having up
+to 32 bits, including the sign. Since they represent physical distances,
+there is a small unit of measurement such that increasing |h| by~1 means
+moving a certain tiny distance to the right. The actual unit of
+measurement is variable, as explained below; \TeX\ sets things up so that
+its \.{DVI} output is in sp units, i.e., scaled points, in agreement with
+all the |scaled| dimensions in \TeX's data structures.
+
+@ Here is a list of all the commands that may appear in a \.{DVI} file. Each
+command is specified by its symbolic name (e.g., |bop|), its opcode byte
+(e.g., 139), and its parameters (if any). The parameters are followed
+by a bracketed number telling how many bytes they occupy; for example,
+`|p[4]|' means that parameter |p| is four bytes long.
+
+\yskip\hang|set_char_0| 0. Typeset character number~0 from font~|f|
+such that the reference point of the character is at |(h,v)|. Then
+increase |h| by the width of that character. Note that a character may
+have zero or negative width, so one cannot be sure that |h| will advance
+after this command; but |h| usually does increase.
+
+\yskip\hang\\{set\_char\_1} through \\{set\_char\_127} (opcodes 1 to 127).
+Do the operations of |set_char_0|; but use the character whose number
+matches the opcode, instead of character~0.
+
+\yskip\hang|set1| 128 |c[1]|. Same as |set_char_0|, except that character
+number~|c| is typeset. \TeX82 uses this command for characters in the
+range |128<=c<256|.
+
+\yskip\hang|@!set2| 129 |c[2]|. Same as |set1|, except that |c|~is two
+bytes long, so it is in the range |0<=c<65536|. \TeX82 never uses this
+command, but it should come in handy for extensions of \TeX\ that deal
+with oriental languages.
+@^oriental characters@>@^Chinese characters@>@^Japanese characters@>
+
+\yskip\hang|@!set3| 130 |c[3]|. Same as |set1|, except that |c|~is three
+bytes long, so it can be as large as $2^{24}-1$. Not even the Chinese
+language has this many characters, but this command might prove useful
+in some yet unforeseen extension.
+
+\yskip\hang|@!set4| 131 |c[4]|. Same as |set1|, except that |c|~is four
+bytes long. Imagine that.
+
+\yskip\hang|set_rule| 132 |a[4]| |b[4]|. Typeset a solid black rectangle
+of height~|a| and width~|b|, with its bottom left corner at |(h,v)|. Then
+set |h:=h+b|. If either |a<=0| or |b<=0|, nothing should be typeset. Note
+that if |b<0|, the value of |h| will decrease even though nothing else happens.
+See below for details about how to typeset rules so that consistency with
+\MF\ is guaranteed.
+
+\yskip\hang|@!put1| 133 |c[1]|. Typeset character number~|c| from font~|f|
+such that the reference point of the character is at |(h,v)|. (The `put'
+commands are exactly like the `set' commands, except that they simply put out a
+character or a rule without moving the reference point afterwards.)
+
+\yskip\hang|@!put2| 134 |c[2]|. Same as |set2|, except that |h| is not changed.
+
+\yskip\hang|@!put3| 135 |c[3]|. Same as |set3|, except that |h| is not changed.
+
+\yskip\hang|@!put4| 136 |c[4]|. Same as |set4|, except that |h| is not changed.
+
+\yskip\hang|put_rule| 137 |a[4]| |b[4]|. Same as |set_rule|, except that
+|h| is not changed.
+
+\yskip\hang|nop| 138. No operation, do nothing. Any number of |nop|'s
+may occur between \.{DVI} commands, but a |nop| cannot be inserted between
+a command and its parameters or between two parameters.
+
+\yskip\hang|bop| 139 $c_0[4]$ $c_1[4]$ $\ldots$ $c_9[4]$ $p[4]$. Beginning
+of a page: Set |(h,v,w,x,y,z):=(0,0,0,0,0,0)| and set the stack empty. Set
+the current font |f| to an undefined value. The ten $c_i$ parameters hold
+the values of \.{\\count0} $\ldots$ \.{\\count9} in \TeX\ at the time
+\.{\\shipout} was invoked for this page; they can be used to identify
+pages, if a user wants to print only part of a \.{DVI} file. The parameter
+|p| points to the previous |bop| in the file; the first
+|bop| has $p=-1$.
+
+\yskip\hang|eop| 140. End of page: Print what you have read since the
+previous |bop|. At this point the stack should be empty. (The \.{DVI}-reading
+programs that drive most output devices will have kept a buffer of the
+material that appears on the page that has just ended. This material is
+largely, but not entirely, in order by |v| coordinate and (for fixed |v|) by
+|h|~coordinate; so it usually needs to be sorted into some order that is
+appropriate for the device in question.)
+
+\yskip\hang|push| 141. Push the current values of |(h,v,w,x,y,z)| onto the
+top of the stack; do not change any of these values. Note that |f| is
+not pushed.
+
+\yskip\hang|pop| 142. Pop the top six values off of the stack and assign
+them respectively to |(h,v,w,x,y,z)|. The number of pops should never
+exceed the number of pushes, since it would be highly embarrassing if the
+stack were empty at the time of a |pop| command.
+
+\yskip\hang|right1| 143 |b[1]|. Set |h:=h+b|, i.e., move right |b| units.
+The parameter is a signed number in two's complement notation, |-128<=b<128|;
+if |b<0|, the reference point moves left.
+
+\yskip\hang|right2| 144 |b[2]|. Same as |right1|, except that |b| is a
+two-byte quantity in the range |-32768<=b<32768|.
+
+\yskip\hang|right3| 145 |b[3]|. Same as |right1|, except that |b| is a
+three-byte quantity in the range |@t$-2^{23}$@><=b<@t$2^{23}$@>|.
+
+\yskip\hang|right4| 146 |b[4]|. Same as |right1|, except that |b| is a
+four-byte quantity in the range |@t$-2^{31}$@><=b<@t$2^{31}$@>|.
+
+\yskip\hang|w0| 147. Set |h:=h+w|; i.e., move right |w| units. With luck,
+this parameterless command will usually suffice, because the same kind of motion
+will occur several times in succession; the following commands explain how
+|w| gets particular values.
+
+\yskip\hang|w1| 148 |b[1]|. Set |w:=b| and |h:=h+b|. The value of |b| is a
+signed quantity in two's complement notation, |-128<=b<128|. This command
+changes the current |w|~spacing and moves right by |b|.
+
+\yskip\hang|@!w2| 149 |b[2]|. Same as |w1|, but |b| is two bytes long,
+|-32768<=b<32768|.
+
+\yskip\hang|@!w3| 150 |b[3]|. Same as |w1|, but |b| is three bytes long,
+|@t$-2^{23}$@><=b<@t$2^{23}$@>|.
+
+\yskip\hang|@!w4| 151 |b[4]|. Same as |w1|, but |b| is four bytes long,
+|@t$-2^{31}$@><=b<@t$2^{31}$@>|.
+
+\yskip\hang|x0| 152. Set |h:=h+x|; i.e., move right |x| units. The `|x|'
+commands are like the `|w|' commands except that they involve |x| instead
+of |w|.
+
+\yskip\hang|x1| 153 |b[1]|. Set |x:=b| and |h:=h+b|. The value of |b| is a
+signed quantity in two's complement notation, |-128<=b<128|. This command
+changes the current |x|~spacing and moves right by |b|.
+
+\yskip\hang|@!x2| 154 |b[2]|. Same as |x1|, but |b| is two bytes long,
+|-32768<=b<32768|.
+
+\yskip\hang|@!x3| 155 |b[3]|. Same as |x1|, but |b| is three bytes long,
+|@t$-2^{23}$@><=b<@t$2^{23}$@>|.
+
+\yskip\hang|@!x4| 156 |b[4]|. Same as |x1|, but |b| is four bytes long,
+|@t$-2^{31}$@><=b<@t$2^{31}$@>|.
+
+\yskip\hang|down1| 157 |a[1]|. Set |v:=v+a|, i.e., move down |a| units.
+The parameter is a signed number in two's complement notation, |-128<=a<128|;
+if |a<0|, the reference point moves up.
+
+\yskip\hang|@!down2| 158 |a[2]|. Same as |down1|, except that |a| is a
+two-byte quantity in the range |-32768<=a<32768|.
+
+\yskip\hang|@!down3| 159 |a[3]|. Same as |down1|, except that |a| is a
+three-byte quantity in the range |@t$-2^{23}$@><=a<@t$2^{23}$@>|.
+
+\yskip\hang|@!down4| 160 |a[4]|. Same as |down1|, except that |a| is a
+four-byte quantity in the range |@t$-2^{31}$@><=a<@t$2^{31}$@>|.
+
+\yskip\hang|y0| 161. Set |v:=v+y|; i.e., move down |y| units. With luck,
+this parameterless command will usually suffice, because the same kind of motion
+will occur several times in succession; the following commands explain how
+|y| gets particular values.
+
+\yskip\hang|y1| 162 |a[1]|. Set |y:=a| and |v:=v+a|. The value of |a| is a
+signed quantity in two's complement notation, |-128<=a<128|. This command
+changes the current |y|~spacing and moves down by |a|.
+
+\yskip\hang|@!y2| 163 |a[2]|. Same as |y1|, but |a| is two bytes long,
+|-32768<=a<32768|.
+
+\yskip\hang|@!y3| 164 |a[3]|. Same as |y1|, but |a| is three bytes long,
+|@t$-2^{23}$@><=a<@t$2^{23}$@>|.
+
+\yskip\hang|@!y4| 165 |a[4]|. Same as |y1|, but |a| is four bytes long,
+|@t$-2^{31}$@><=a<@t$2^{31}$@>|.
+
+\yskip\hang|z0| 166. Set |v:=v+z|; i.e., move down |z| units. The `|z|' commands
+are like the `|y|' commands except that they involve |z| instead of |y|.
+
+\yskip\hang|z1| 167 |a[1]|. Set |z:=a| and |v:=v+a|. The value of |a| is a
+signed quantity in two's complement notation, |-128<=a<128|. This command
+changes the current |z|~spacing and moves down by |a|.
+
+\yskip\hang|@!z2| 168 |a[2]|. Same as |z1|, but |a| is two bytes long,
+|-32768<=a<32768|.
+
+\yskip\hang|@!z3| 169 |a[3]|. Same as |z1|, but |a| is three bytes long,
+|@t$-2^{23}$@><=a<@t$2^{23}$@>|.
+
+\yskip\hang|@!z4| 170 |a[4]|. Same as |z1|, but |a| is four bytes long,
+|@t$-2^{31}$@><=a<@t$2^{31}$@>|.
+
+\yskip\hang|fnt_num_0| 171. Set |f:=0|. Font 0 must previously have been
+defined by a \\{fnt\_def} instruction, as explained below.
+
+\yskip\hang\\{fnt\_num\_1} through \\{fnt\_num\_63} (opcodes 172 to 234). Set
+|f:=1|, \dots, \hbox{|f:=63|}, respectively.
+
+\yskip\hang|fnt1| 235 |k[1]|. Set |f:=k|. \TeX82 uses this command for font
+numbers in the range |64<=k<256|.
+
+\yskip\hang|@!fnt2| 236 |k[2]|. Same as |fnt1|, except that |k|~is two
+bytes long, so it is in the range |0<=k<65536|. \TeX82 never generates this
+command, but large font numbers may prove useful for specifications of
+color or texture, or they may be used for special fonts that have fixed
+numbers in some external coding scheme.
+
+\yskip\hang|@!fnt3| 237 |k[3]|. Same as |fnt1|, except that |k|~is three
+bytes long, so it can be as large as $2^{24}-1$.
+
+\yskip\hang|@!fnt4| 238 |k[4]|. Same as |fnt1|, except that |k|~is four
+bytes long; this is for the really big font numbers (and for the negative ones).
+
+\yskip\hang|xxx1| 239 |k[1]| |x[k]|. This command is undefined in
+general; it functions as a $(k+2)$-byte |nop| unless special \.{DVI}-reading
+programs are being used. \TeX82 generates |xxx1| when a short enough
+\.{\\special} appears, setting |k| to the number of bytes being sent. It
+is recommended that |x| be a string having the form of a keyword followed
+by possible parameters relevant to that keyword.
+
+\yskip\hang|@!xxx2| 240 |k[2]| |x[k]|. Like |xxx1|, but |0<=k<65536|.
+
+\yskip\hang|@!xxx3| 241 |k[3]| |x[k]|. Like |xxx1|, but |0<=k<@t$2^{24}$@>|.
+
+\yskip\hang|xxx4| 242 |k[4]| |x[k]|. Like |xxx1|, but |k| can be ridiculously
+large. \TeX82 uses |xxx4| when sending a string of length 256 or more.
+
+\yskip\hang|fnt_def1| 243 |k[1]| |c[4]| |s[4]| |d[4]| |a[1]| |l[1]| |n[a+l]|.
+Define font |k|, where |0<=k<256|; font definitions will be explained shortly.
+
+\yskip\hang|@!fnt_def2| 244 |k[2]| |c[4]| |s[4]| |d[4]| |a[1]| |l[1]| |n[a+l]|.
+Define font |k|, where |0<=k<65536|.
+
+\yskip\hang|@!fnt_def3| 245 |k[3]| |c[4]| |s[4]| |d[4]| |a[1]| |l[1]| |n[a+l]|.
+Define font |k|, where |0<=k<@t$2^{24}$@>|.
+
+\yskip\hang|@!fnt_def4| 246 |k[4]| |c[4]| |s[4]| |d[4]| |a[1]| |l[1]| |n[a+l]|.
+Define font |k|, where |@t$-2^{31}$@><=k<@t$2^{31}$@>|.
+
+\yskip\hang|pre| 247 |i[1]| |num[4]| |den[4]| |mag[4]| |k[1]| |x[k]|.
+Beginning of the preamble; this must come at the very beginning of the
+file. Parameters |i|, |num|, |den|, |mag|, |k|, and |x| are explained below.
+
+\yskip\hang|post| 248. Beginning of the postamble, see below.
+
+\yskip\hang|post_post| 249. Ending of the postamble, see below.
+
+\yskip\noindent Commands 250--255 are undefined at the present time.
+
+@ @d set_char_0=0 {typeset character 0 and move right}
+@d set1=128 {typeset a character and move right}
+@d set_rule=132 {typeset a rule and move right}
+@d put_rule=137 {typeset a rule}
+@d nop=138 {no operation}
+@d bop=139 {beginning of page}
+@d eop=140 {ending of page}
+@d push=141 {save the current positions}
+@d pop=142 {restore previous positions}
+@d right1=143 {move right}
+@d w0=147 {move right by |w|}
+@d w1=148 {move right and set |w|}
+@d x0=152 {move right by |x|}
+@d x1=153 {move right and set |x|}
+@d down1=157 {move down}
+@d y0=161 {move down by |y|}
+@d y1=162 {move down and set |y|}
+@d z0=166 {move down by |z|}
+@d z1=167 {move down and set |z|}
+@d fnt_num_0=171 {set current font to 0}
+@d fnt1=235 {set current font}
+@d xxx1=239 {extension to \.{DVI} primitives}
+@d xxx4=242 {potentially long extension to \.{DVI} primitives}
+@d fnt_def1=243 {define the meaning of a font number}
+@d pre=247 {preamble}
+@d post=248 {postamble beginning}
+@d post_post=249 {postamble ending}
+
+@ The preamble contains basic information about the file as a whole. As
+stated above, there are six parameters:
+$$\hbox{|@!i[1]| |@!num[4]| |@!den[4]| |@!mag[4]| |@!k[1]| |@!x[k]|.}$$
+The |i| byte identifies \.{DVI} format; currently this byte is always set
+to~2. (The value |i=3| is currently used for an extended format that
+allows a mixture of right-to-left and left-to-right typesetting.
+Some day we will set |i=4|, when \.{DVI} format makes another
+incompatible change---perhaps in the year 2048.)
+
+The next two parameters, |num| and |den|, are positive integers that define
+the units of measurement; they are the numerator and denominator of a
+fraction by which all dimensions in the \.{DVI} file could be multiplied
+in order to get lengths in units of $10^{-7}$ meters. Since $\rm 7227{pt} =
+254{cm}$, and since \TeX\ works with scaled points where there are $2^{16}$
+sp in a point, \TeX\ sets
+$|num|/|den|=(254\cdot10^5)/(7227\cdot2^{16})=25400000/473628672$.
+@^sp@>
+
+The |mag| parameter is what \TeX\ calls \.{\\mag}, i.e., 1000 times the
+desired magnification. The actual fraction by which dimensions are
+multiplied is therefore $|mag|\cdot|num|/1000|den|$. Note that if a \TeX\
+source document does not call for any `\.{true}' dimensions, and if you
+change it only by specifying a different \.{\\mag} setting, the \.{DVI}
+file that \TeX\ creates will be completely unchanged except for the value
+of |mag| in the preamble and postamble. (Fancy \.{DVI}-reading programs allow
+users to override the |mag|~setting when a \.{DVI} file is being printed.)
+
+Finally, |k| and |x| allow the \.{DVI} writer to include a comment, which is not
+interpreted further. The length of comment |x| is |k|, where |0<=k<256|.
+
+@d id_byte=2 {identifies the kind of \.{DVI} files described here}
+
+@ Font definitions for a given font number |k| contain further parameters
+$$\hbox{|c[4]| |s[4]| |d[4]| |a[1]| |l[1]| |n[a+l]|.}$$
+The four-byte value |c| is the check sum that \TeX\ found in the \.{TFM}
+file for this font; |c| should match the check sum of the font found by
+programs that read this \.{DVI} file.
+@^check sum@>
+
+Parameter |s| contains a fixed-point scale factor that is applied to
+the character widths in font |k|; font dimensions in \.{TFM} files and
+other font files are relative to this quantity, which is called the
+``at size'' elsewhere in this documentation. The value of |s| is
+always positive and less than $2^{27}$. It is given in the same units
+as the other \.{DVI} dimensions, i.e., in sp when \TeX82 has made the
+file. Parameter |d| is similar to |s|; it is the ``design size,'' and
+(like~|s|) it is given in \.{DVI} units. Thus, font |k| is to be used
+at $|mag|\cdot s/1000d$ times its normal size.
+
+The remaining part of a font definition gives the external name of the font,
+which is an ASCII string of length |a+l|. The number |a| is the length
+of the ``area'' or directory, and |l| is the length of the font name itself;
+the standard local system font area is supposed to be used when |a=0|.
+The |n| field contains the area in its first |a| bytes.
+
+Font definitions must appear before the first use of a particular font number.
+Once font |k| is defined, it must not be defined again; however, we
+shall see below that font definitions appear in the postamble as well as
+in the pages, so in this sense each font number is defined exactly twice,
+if at all. Like |nop| commands, font definitions can
+appear before the first |bop|, or between an |eop| and a |bop|.
+
+@ Sometimes it is desirable to make horizontal or vertical rules line up
+precisely with certain features in characters of a font. It is possible to
+guarantee the correct matching between \.{DVI} output and the characters
+generated by \MF\ by adhering to the following principles: (1)~The \MF\
+characters should be positioned so that a bottom edge or left edge that is
+supposed to line up with the bottom or left edge of a rule appears at the
+reference point, i.e., in row~0 and column~0 of the \MF\ raster. This
+ensures that the position of the rule will not be rounded differently when
+the pixel size is not a perfect multiple of the units of measurement in
+the \.{DVI} file. (2)~A typeset rule of height $a>0$ and width $b>0$
+should be equivalent to a \MF-generated character having black pixels in
+precisely those raster positions whose \MF\ coordinates satisfy
+|0<=x<@t$\alpha$@>b| and |0<=y<@t$\alpha$@>a|, where $\alpha$ is the number
+of pixels per \.{DVI} unit.
+@:METAFONT}{\MF@>
+@^alignment of rules with characters@>
+@^rules aligning with characters@>
+
+@ The last page in a \.{DVI} file is followed by `|post|'; this command
+introduces the postamble, which summarizes important facts that \TeX\ has
+accumulated about the file, making it possible to print subsets of the data
+with reasonable efficiency. The postamble has the form
+$$\vbox{\halign{\hbox{#\hfil}\cr
+ |post| |p[4]| |num[4]| |den[4]| |mag[4]| |l[4]| |u[4]| |s[2]| |t[2]|\cr
+ $\langle\,$font definitions$\,\rangle$\cr
+ |post_post| |q[4]| |i[1]| 223's$[{\G}4]$\cr}}$$
+Here |p| is a pointer to the final |bop| in the file. The next three
+parameters, |num|, |den|, and |mag|, are duplicates of the quantities that
+appeared in the preamble.
+
+Parameters |l| and |u| give respectively the height-plus-depth of the tallest
+page and the width of the widest page, in the same units as other dimensions
+of the file. These numbers might be used by a \.{DVI}-reading program to
+position individual ``pages'' on large sheets of film or paper; however,
+the standard convention for output on normal size paper is to position each
+page so that the upper left-hand corner is exactly one inch from the left
+and the top. Experience has shown that it is unwise to design \.{DVI}-to-printer
+software that attempts cleverly to center the output; a fixed position of
+the upper left corner is easiest for users to understand and to work with.
+Therefore |l| and~|u| are often ignored.
+
+Parameter |s| is the maximum stack depth (i.e., the largest excess of
+|push| commands over |pop| commands) needed to process this file. Then
+comes |t|, the total number of pages (|bop| commands) present.
+
+The postamble continues with font definitions, which are any number of
+\\{fnt\_def} commands as described above, possibly interspersed with |nop|
+commands. Each font number that is used in the \.{DVI} file must be defined
+exactly twice: Once before it is first selected by a \\{fnt} command, and once
+in the postamble.
+
+@ The last part of the postamble, following the |post_post| byte that
+signifies the end of the font definitions, contains |q|, a pointer to the
+|post| command that started the postamble. An identification byte, |i|,
+comes next; this currently equals~2, as in the preamble.
+
+The |i| byte is followed by four or more bytes that are all equal to
+the decimal number 223 (i.e., @'337 in octal). \TeX\ puts out four to seven of
+these trailing bytes, until the total length of the file is a multiple of
+four bytes, since this works out best on machines that pack four bytes per
+word; but any number of 223's is allowed, as long as there are at least four
+of them. In effect, 223 is a sort of signature that is added at the very end.
+@^Fuchs, David Raymond@>
+
+This curious way to finish off a \.{DVI} file makes it feasible for
+\.{DVI}-reading programs to find the postamble first, on most computers,
+even though \TeX\ wants to write the postamble last. Most operating
+systems permit random access to individual words or bytes of a file, so
+the \.{DVI} reader can start at the end and skip backwards over the 223's
+until finding the identification byte. Then it can back up four bytes, read
+|q|, and move to byte |q| of the file. This byte should, of course,
+contain the value 248 (|post|); now the postamble can be read, so the
+\.{DVI} reader can discover all the information needed for typesetting the
+pages. Note that it is also possible to skip through the \.{DVI} file at
+reasonably high speed to locate a particular page, if that proves
+desirable. This saves a lot of time, since \.{DVI} files used in production
+jobs tend to be large.
+
+Unfortunately, however, standard \PASCAL\ does not include the ability to
+@^system dependencies@>
+access a random position in a file, or even to determine the length of a file.
+Almost all systems nowadays provide the necessary capabilities, so \.{DVI}
+format has been designed to work most efficiently with modern operating systems.
+But if \.{DVI} files have to be processed under the restrictions of standard
+\PASCAL, one can simply read them from front to back, since the necessary
+header information is present in the preamble and in the font definitions.
+(The |l| and |u| and |s| and |t| parameters, which appear only in the
+postamble, are ``frills'' that are handy but not absolutely necessary.)
+
+@* \[32] Shipping pages out.
+After considering \TeX's eyes and stomach, we come now to the bowels.
+@^bowels@>
+
+The |ship_out| procedure is given a pointer to a box; its mission is
+to describe that box in \.{DVI} form, outputting a ``page'' to |dvi_file|.
+The \.{DVI} coordinates $(h,v)=(0,0)$ should correspond to the upper left
+corner of the box being shipped.
+
+Since boxes can be inside of boxes inside of boxes, the main work of
+|ship_out| is done by two mutually recursive routines, |hlist_out|
+and |vlist_out|, which traverse the hlists and vlists inside of horizontal
+and vertical boxes.
+
+As individual pages are being processed, we need to accumulate
+information about the entire set of pages, since such statistics must be
+reported in the postamble. The global variables |total_pages|, |max_v|,
+|max_h|, |max_push|, and |last_bop| are used to record this information.
+
+The variable |doing_leaders| is |true| while leaders are being output.
+The variable |dead_cycles| contains the number of times an output routine
+has been initiated since the last |ship_out|.
+
+A few additional global variables are also defined here for use in
+|vlist_out| and |hlist_out|. They could have been local variables, but
+that would waste stack space when boxes are deeply nested, since the
+values of these variables are not needed during recursive calls.
+@^recursion@>
+
+@<Glob...@>=
+@!total_pages:integer; {the number of pages that have been shipped out}
+@!max_v:scaled; {maximum height-plus-depth of pages shipped so far}
+@!max_h:scaled; {maximum width of pages shipped so far}
+@!max_push:integer; {deepest nesting of |push| commands encountered so far}
+@!last_bop:integer; {location of previous |bop| in the \.{DVI} output}
+@!dead_cycles:integer; {recent outputs that didn't ship anything out}
+@!doing_leaders:boolean; {are we inside a leader box?}
+@#
+@!c,@!f:quarterword; {character and font in current |char_node|}
+@!rule_ht,@!rule_dp,@!rule_wd:scaled; {size of current rule being output}
+@!g:pointer; {current glue specification}
+@!lq,@!lr:integer; {quantities used in calculations for leaders}
+
+@ @<Set init...@>=
+total_pages:=0; max_v:=0; max_h:=0; max_push:=0; last_bop:=-1;
+doing_leaders:=false; dead_cycles:=0; cur_s:=-1;
+
+@ The \.{DVI} bytes are output to a buffer instead of being written directly
+to the output file. This makes it possible to reduce the overhead of
+subroutine calls, thereby measurably speeding up the computation, since
+output of \.{DVI} bytes is part of \TeX's inner loop. And it has another
+advantage as well, since we can change instructions in the buffer in order to
+make the output more compact. For example, a `|down2|' command can be
+changed to a `|y2|', thereby making a subsequent `|y0|' command possible,
+saving two bytes.
+
+The output buffer is divided into two parts of equal size; the bytes found
+in |dvi_buf[0..half_buf-1]| constitute the first half, and those in
+|dvi_buf[half_buf..dvi_buf_size-1]| constitute the second. The global
+variable |dvi_ptr| points to the position that will receive the next
+output byte. When |dvi_ptr| reaches |dvi_limit|, which is always equal
+to one of the two values |half_buf| or |dvi_buf_size|, the half buffer that
+is about to be invaded next is sent to the output and |dvi_limit| is
+changed to its other value. Thus, there is always at least a half buffer's
+worth of information present, except at the very beginning of the job.
+
+Bytes of the \.{DVI} file are numbered sequentially starting with 0;
+the next byte to be generated will be number |dvi_offset+dvi_ptr|.
+A byte is present in the buffer only if its number is |>=dvi_gone|.
+
+@<Types...@>=
+@!dvi_index=0..dvi_buf_size; {an index into the output buffer}
+
+@ Some systems may find it more efficient to make |dvi_buf| a |packed|
+array, since output of four bytes at once may be facilitated.
+@^system dependencies@>
+
+@<Glob...@>=
+@!dvi_buf:array[dvi_index] of eight_bits; {buffer for \.{DVI} output}
+@!half_buf:dvi_index; {half of |dvi_buf_size|}
+@!dvi_limit:dvi_index; {end of the current half buffer}
+@!dvi_ptr:dvi_index; {the next available buffer address}
+@!dvi_offset:integer; {|dvi_buf_size| times the number of times the
+ output buffer has been fully emptied}
+@!dvi_gone:integer; {the number of bytes already output to |dvi_file|}
+
+@ Initially the buffer is all in one piece; we will output half of it only
+after it first fills up.
+
+@<Set init...@>=
+half_buf:=dvi_buf_size div 2; dvi_limit:=dvi_buf_size; dvi_ptr:=0;
+dvi_offset:=0; dvi_gone:=0;
+
+@ The actual output of |dvi_buf[a..b]| to |dvi_file| is performed by calling
+|write_dvi(a,b)|. For best results, this procedure should be optimized to
+run as fast as possible on each particular system, since it is part of
+\TeX's inner loop. It is safe to assume that |a| and |b+1| will both be
+multiples of 4 when |write_dvi(a,b)| is called; therefore it is possible on
+many machines to use efficient methods to pack four bytes per word and to
+output an array of words with one system call.
+@^system dependencies@>
+@^inner loop@>
+@^defecation@>
+
+@p procedure write_dvi(@!a,@!b:dvi_index);
+var k:dvi_index;
+begin for k:=a to b do write(dvi_file,dvi_buf[k]);
+end;
+
+@ To put a byte in the buffer without paying the cost of invoking a procedure
+each time, we use the macro |dvi_out|.
+
+@d dvi_out(#)==@+begin dvi_buf[dvi_ptr]:=#; incr(dvi_ptr);
+ if dvi_ptr=dvi_limit then dvi_swap;
+ end
+
+@p procedure dvi_swap; {outputs half of the buffer}
+begin if dvi_limit=dvi_buf_size then
+ begin write_dvi(0,half_buf-1); dvi_limit:=half_buf;
+ dvi_offset:=dvi_offset+dvi_buf_size; dvi_ptr:=0;
+ end
+else begin write_dvi(half_buf,dvi_buf_size-1); dvi_limit:=dvi_buf_size;
+ end;
+dvi_gone:=dvi_gone+half_buf;
+end;
+
+@ Here is how we clean out the buffer when \TeX\ is all through; |dvi_ptr|
+will be a multiple of~4.
+
+@<Empty the last bytes out of |dvi_buf|@>=
+if dvi_limit=half_buf then write_dvi(half_buf,dvi_buf_size-1);
+if dvi_ptr>0 then write_dvi(0,dvi_ptr-1)
+
+@ The |dvi_four| procedure outputs four bytes in two's complement notation,
+without risking arithmetic overflow.
+
+@p procedure dvi_four(@!x:integer);
+begin if x>=0 then dvi_out(x div @'100000000)
+else begin x:=x+@'10000000000;
+ x:=x+@'10000000000;
+ dvi_out((x div @'100000000) + 128);
+ end;
+x:=x mod @'100000000; dvi_out(x div @'200000);
+x:=x mod @'200000; dvi_out(x div @'400);
+dvi_out(x mod @'400);
+end;
+
+@ A mild optimization of the output is performed by the |dvi_pop|
+routine, which issues a |pop| unless it is possible to cancel a
+`|push| |pop|' pair. The parameter to |dvi_pop| is the byte address
+following the old |push| that matches the new |pop|.
+
+@p procedure dvi_pop(@!l:integer);
+begin if (l=dvi_offset+dvi_ptr)and(dvi_ptr>0) then decr(dvi_ptr)
+else dvi_out(pop);
+end;
+
+@ Here's a procedure that outputs a font definition. Since \TeX82 uses at
+most 256 different fonts per job, |fnt_def1| is always used as the command code.
+
+@p procedure dvi_font_def(@!f:internal_font_number);
+var k:pool_pointer; {index into |str_pool|}
+begin dvi_out(fnt_def1);
+dvi_out(f-font_base-1);@/
+dvi_out(qo(font_check[f].b0));
+dvi_out(qo(font_check[f].b1));
+dvi_out(qo(font_check[f].b2));
+dvi_out(qo(font_check[f].b3));@/
+dvi_four(font_size[f]);
+dvi_four(font_dsize[f]);@/
+dvi_out(length(font_area[f]));
+dvi_out(length(font_name[f]));
+@<Output the font name whose internal number is |f|@>;
+end;
+
+@ @<Output the font name whose internal number is |f|@>=
+for k:=str_start[font_area[f]] to str_start[font_area[f]+1]-1 do
+ dvi_out(so(str_pool[k]));
+for k:=str_start[font_name[f]] to str_start[font_name[f]+1]-1 do
+ dvi_out(so(str_pool[k]))
+
+@ Versions of \TeX\ intended for small computers might well choose to omit
+the ideas in the next few parts of this program, since it is not really
+necessary to optimize the \.{DVI} code by making use of the |w0|, |x0|,
+|y0|, and |z0| commands. Furthermore, the algorithm that we are about to
+describe does not pretend to give an optimum reduction in the length
+of the \.{DVI} code; after all, speed is more important than compactness.
+But the method is surprisingly effective, and it takes comparatively little
+time.
+
+We can best understand the basic idea by first considering a simpler problem
+that has the same essential characteristics. Given a sequence of digits,
+say $3\,1\,4\,1\,5\,9\,2\,6\,5\,3\,5\,8\,9$, we want to assign subscripts
+$d$, $y$, or $z$ to each digit so as to maximize the number of ``$y$-hits''
+and ``$z$-hits''; a $y$-hit is an instance of two appearances of the same
+digit with the subscript $y$, where no $y$'s intervene between the two
+appearances, and a $z$-hit is defined similarly. For example, the sequence
+above could be decorated with subscripts as follows:
+$$3_z\,1_y\,4_d\,1_y\,5_y\,9_d\,2_d\,6_d\,5_y\,3_z\,5_y\,8_d\,9_d.$$
+There are three $y$-hits ($1_y\ldots1_y$ and $5_y\ldots5_y\ldots5_y$) and
+one $z$-hit ($3_z\ldots3_z$); there are no $d$-hits, since the two appearances
+of $9_d$ have $d$'s between them, but we don't count $d$-hits so it doesn't
+matter how many there are. These subscripts are analogous to the \.{DVI}
+commands called \\{down}, $y$, and $z$, and the digits are analogous to
+different amounts of vertical motion; a $y$-hit or $z$-hit corresponds to
+the opportunity to use the one-byte commands |y0| or |z0| in a \.{DVI} file.
+
+\TeX's method of assigning subscripts works like this: Append a new digit,
+say $\delta$, to the right of the sequence. Now look back through the
+sequence until one of the following things happens: (a)~You see
+$\delta_y$ or $\delta_z$, and this was the first time you encountered a
+$y$ or $z$ subscript, respectively. Then assign $y$ or $z$ to the new
+$\delta$; you have scored a hit. (b)~You see $\delta_d$, and no $y$
+subscripts have been encountered so far during this search. Then change
+the previous $\delta_d$ to $\delta_y$ (this corresponds to changing a
+command in the output buffer), and assign $y$ to the new $\delta$; it's
+another hit. (c)~You see $\delta_d$, and a $y$ subscript has been seen
+but not a $z$. Change the previous $\delta_d$ to $\delta_z$ and assign
+$z$ to the new $\delta$. (d)~You encounter both $y$ and $z$ subscripts
+before encountering a suitable $\delta$, or you scan all the way to the
+front of the sequence. Assign $d$ to the new $\delta$; this assignment may
+be changed later.
+
+The subscripts $3_z\,1_y\,4_d\ldots\,$ in the example above were, in fact,
+produced by this procedure, as the reader can verify. (Go ahead and try it.)
+
+@ In order to implement such an idea, \TeX\ maintains a stack of pointers
+to the \\{down}, $y$, and $z$ commands that have been generated for the
+current page. And there is a similar stack for \\{right}, |w|, and |x|
+commands. These stacks are called the down stack and right stack, and their
+top elements are maintained in the variables |down_ptr| and |right_ptr|.
+
+Each entry in these stacks contains four fields: The |width| field is
+the amount of motion down or to the right; the |location| field is the
+byte number of the \.{DVI} command in question (including the appropriate
+|dvi_offset|); the |link| field points to the next item below this one
+on the stack; and the |info| field encodes the options for possible change
+in the \.{DVI} command.
+
+@d movement_node_size=3 {number of words per entry in the down and right stacks}
+@d location(#)==mem[#+2].int {\.{DVI} byte number for a movement command}
+
+@<Glob...@>=
+@!down_ptr,@!right_ptr:pointer; {heads of the down and right stacks}
+
+@ @<Set init...@>=
+down_ptr:=null; right_ptr:=null;
+
+@ Here is a subroutine that produces a \.{DVI} command for some specified
+downward or rightward motion. It has two parameters: |w| is the amount
+of motion, and |o| is either |down1| or |right1|. We use the fact that
+the command codes have convenient arithmetic properties: |y1-down1=w1-right1|
+and |z1-down1=x1-right1|.
+
+@p procedure movement(@!w:scaled;@!o:eight_bits);
+label exit,found,not_found,2,1;
+var mstate:small_number; {have we seen a |y| or |z|?}
+@!p,@!q:pointer; {current and top nodes on the stack}
+@!k:integer; {index into |dvi_buf|, modulo |dvi_buf_size|}
+begin q:=get_node(movement_node_size); {new node for the top of the stack}
+width(q):=w; location(q):=dvi_offset+dvi_ptr;
+if o=down1 then
+ begin link(q):=down_ptr; down_ptr:=q;
+ end
+else begin link(q):=right_ptr; right_ptr:=q;
+ end;
+@<Look at the other stack entries until deciding what sort of \.{DVI} command
+ to generate; |goto found| if node |p| is a ``hit''@>;
+@<Generate a |down| or |right| command for |w| and |return|@>;
+found: @<Generate a |y0| or |z0| command in order to reuse a previous
+ appearance of~|w|@>;
+exit:end;
+
+@ The |info| fields in the entries of the down stack or the right stack
+have six possible settings: |y_here| or |z_here| mean that the \.{DVI}
+command refers to |y| or |z|, respectively (or to |w| or |x|, in the
+case of horizontal motion); |yz_OK| means that the \.{DVI} command is
+\\{down} (or \\{right}) but can be changed to either |y| or |z| (or
+to either |w| or |x|); |y_OK| means that it is \\{down} and can be changed
+to |y| but not |z|; |z_OK| is similar; and |d_fixed| means it must stay
+\\{down}.
+
+The four settings |yz_OK|, |y_OK|, |z_OK|, |d_fixed| would not need to
+be distinguished from each other if we were simply solving the
+digit-subscripting problem mentioned above. But in \TeX's case there is
+a complication because of the nested structure of |push| and |pop|
+commands. Suppose we add parentheses to the digit-subscripting problem,
+redefining hits so that $\delta_y\ldots \delta_y$ is a hit if all $y$'s between
+the $\delta$'s are enclosed in properly nested parentheses, and if the
+parenthesis level of the right-hand $\delta_y$ is deeper than or equal to
+that of the left-hand one. Thus, `(' and `)' correspond to `|push|'
+and `|pop|'. Now if we want to assign a subscript to the final 1 in the
+sequence
+$$2_y\,7_d\,1_d\,(\,8_z\,2_y\,8_z\,)\,1$$
+we cannot change the previous $1_d$ to $1_y$, since that would invalidate
+the $2_y\ldots2_y$ hit. But we can change it to $1_z$, scoring a hit
+since the intervening $8_z$'s are enclosed in parentheses.
+
+The program below removes movement nodes that are introduced after a |push|,
+before it outputs the corresponding |pop|.
+
+@d y_here=1 {|info| when the movement entry points to a |y| command}
+@d z_here=2 {|info| when the movement entry points to a |z| command}
+@d yz_OK=3 {|info| corresponding to an unconstrained \\{down} command}
+@d y_OK=4 {|info| corresponding to a \\{down} that can't become a |z|}
+@d z_OK=5 {|info| corresponding to a \\{down} that can't become a |y|}
+@d d_fixed=6 {|info| corresponding to a \\{down} that can't change}
+
+@ When the |movement| procedure gets to the label |found|, the value of
+|info(p)| will be either |y_here| or |z_here|. If it is, say, |y_here|,
+the procedure generates a |y0| command (or a |w0| command), and marks
+all |info| fields between |q| and |p| so that |y| is not OK in that range.
+
+@<Generate a |y0| or |z0| command...@>=
+info(q):=info(p);
+if info(q)=y_here then
+ begin dvi_out(o+y0-down1); {|y0| or |w0|}
+ while link(q)<>p do
+ begin q:=link(q);
+ case info(q) of
+ yz_OK: info(q):=z_OK;
+ y_OK: info(q):=d_fixed;
+ othercases do_nothing
+ endcases;
+ end;
+ end
+else begin dvi_out(o+z0-down1); {|z0| or |x0|}
+ while link(q)<>p do
+ begin q:=link(q);
+ case info(q) of
+ yz_OK: info(q):=y_OK;
+ z_OK: info(q):=d_fixed;
+ othercases do_nothing
+ endcases;
+ end;
+ end
+
+@ @<Generate a |down| or |right|...@>=
+info(q):=yz_OK;
+if abs(w)>=@'40000000 then
+ begin dvi_out(o+3); {|down4| or |right4|}
+ dvi_four(w); return;
+ end;
+if abs(w)>=@'100000 then
+ begin dvi_out(o+2); {|down3| or |right3|}
+ if w<0 then w:=w+@'100000000;
+ dvi_out(w div @'200000); w:=w mod @'200000; goto 2;
+ end;
+if abs(w)>=@'200 then
+ begin dvi_out(o+1); {|down2| or |right2|}
+ if w<0 then w:=w+@'200000;
+ goto 2;
+ end;
+dvi_out(o); {|down1| or |right1|}
+if w<0 then w:=w+@'400;
+goto 1;
+2: dvi_out(w div @'400);
+1: dvi_out(w mod @'400); return
+
+@ As we search through the stack, we are in one of three states,
+|y_seen|, |z_seen|, or |none_seen|, depending on whether we have
+encountered |y_here| or |z_here| nodes. These states are encoded as
+multiples of 6, so that they can be added to the |info| fields for quick
+decision-making.
+@^inner loop@>
+
+@d none_seen=0 {no |y_here| or |z_here| nodes have been encountered yet}
+@d y_seen=6 {we have seen |y_here| but not |z_here|}
+@d z_seen=12 {we have seen |z_here| but not |y_here|}
+
+@<Look at the other stack entries until deciding...@>=
+p:=link(q); mstate:=none_seen;
+while p<>null do
+ begin if width(p)=w then @<Consider a node with matching width;
+ |goto found| if it's a hit@>
+ else case mstate+info(p) of
+ none_seen+y_here: mstate:=y_seen;
+ none_seen+z_here: mstate:=z_seen;
+ y_seen+z_here,z_seen+y_here: goto not_found;
+ othercases do_nothing
+ endcases;
+ p:=link(p);
+ end;
+not_found:
+
+@ We might find a valid hit in a |y| or |z| byte that is already gone
+from the buffer. But we can't change bytes that are gone forever; ``the
+moving finger writes, $\ldots\,\,$.''
+
+@<Consider a node with matching width...@>=
+case mstate+info(p) of
+none_seen+yz_OK,none_seen+y_OK,z_seen+yz_OK,z_seen+y_OK:@t@>@;@/
+ if location(p)<dvi_gone then goto not_found
+ else @<Change buffered instruction to |y| or |w| and |goto found|@>;
+none_seen+z_OK,y_seen+yz_OK,y_seen+z_OK:@t@>@;@/
+ if location(p)<dvi_gone then goto not_found
+ else @<Change buffered instruction to |z| or |x| and |goto found|@>;
+none_seen+y_here,none_seen+z_here,y_seen+z_here,z_seen+y_here: goto found;
+othercases do_nothing
+endcases
+
+@ @<Change buffered instruction to |y| or |w| and |goto found|@>=
+begin k:=location(p)-dvi_offset;
+if k<0 then k:=k+dvi_buf_size;
+dvi_buf[k]:=dvi_buf[k]+y1-down1;
+info(p):=y_here; goto found;
+end
+
+@ @<Change buffered instruction to |z| or |x| and |goto found|@>=
+begin k:=location(p)-dvi_offset;
+if k<0 then k:=k+dvi_buf_size;
+dvi_buf[k]:=dvi_buf[k]+z1-down1;
+info(p):=z_here; goto found;
+end
+
+@ In case you are wondering when all the movement nodes are removed from
+\TeX's memory, the answer is that they are recycled just before
+|hlist_out| and |vlist_out| finish outputting a box. This restores the
+down and right stacks to the state they were in before the box was output,
+except that some |info|'s may have become more restrictive.
+
+@p procedure prune_movements(@!l:integer);
+ {delete movement nodes with |location>=l|}
+label done,exit;
+var p:pointer; {node being deleted}
+begin while down_ptr<>null do
+ begin if location(down_ptr)<l then goto done;
+ p:=down_ptr; down_ptr:=link(p); free_node(p,movement_node_size);
+ end;
+done: while right_ptr<>null do
+ begin if location(right_ptr)<l then return;
+ p:=right_ptr; right_ptr:=link(p); free_node(p,movement_node_size);
+ end;
+exit:end;
+
+@ The actual distances by which we want to move might be computed as the
+sum of several separate movements. For example, there might be several
+glue nodes in succession, or we might want to move right by the width of
+some box plus some amount of glue. More importantly, the baselineskip
+distances are computed in terms of glue together with the depth and
+height of adjacent boxes, and we want the \.{DVI} file to lump these
+three quantities together into a single motion.
+
+Therefore, \TeX\ maintains two pairs of global variables: |dvi_h| and |dvi_v|
+are the |h| and |v| coordinates corresponding to the commands actually
+output to the \.{DVI} file, while |cur_h| and |cur_v| are the coordinates
+corresponding to the current state of the output routines. Coordinate
+changes will accumulate in |cur_h| and |cur_v| without being reflected
+in the output, until such a change becomes necessary or desirable; we
+can call the |movement| procedure whenever we want to make |dvi_h=cur_h|
+or |dvi_v=cur_v|.
+
+The current font reflected in the \.{DVI} output is called |dvi_f|;
+there is no need for a `\\{cur\_f}' variable.
+
+The depth of nesting of |hlist_out| and |vlist_out| is called |cur_s|;
+this is essentially the depth of |push| commands in the \.{DVI} output.
+
+@d synch_h==if cur_h<>dvi_h then
+ begin movement(cur_h-dvi_h,right1); dvi_h:=cur_h;
+ end
+@d synch_v==if cur_v<>dvi_v then
+ begin movement(cur_v-dvi_v,down1); dvi_v:=cur_v;
+ end
+
+@<Glob...@>=
+@!dvi_h,@!dvi_v:scaled; {a \.{DVI} reader program thinks we are here}
+@!cur_h,@!cur_v:scaled; {\TeX\ thinks we are here}
+@!dvi_f:internal_font_number; {the current font}
+@!cur_s:integer; {current depth of output box nesting, initially $-1$}
+
+@ @<Initialize variables as |ship_out| begins@>=
+dvi_h:=0; dvi_v:=0; cur_h:=h_offset; dvi_f:=null_font;
+ensure_dvi_open;
+if total_pages=0 then
+ begin dvi_out(pre); dvi_out(id_byte); {output the preamble}
+@^preamble of \.{DVI} file@>
+ dvi_four(25400000); dvi_four(473628672); {conversion ratio for sp}
+ prepare_mag; dvi_four(mag); {magnification factor is frozen}
+ old_setting:=selector; selector:=new_string;
+ print(" TeX output "); print_int(year); print_char(".");
+ print_two(month); print_char("."); print_two(day);
+ print_char(":"); print_two(time div 60);
+ print_two(time mod 60);
+ selector:=old_setting; dvi_out(cur_length);
+ for s:=str_start[str_ptr] to pool_ptr-1 do dvi_out(so(str_pool[s]));
+ pool_ptr:=str_start[str_ptr]; {flush the current string}
+ end
+
+@ When |hlist_out| is called, its duty is to output the box represented
+by the |hlist_node| pointed to by |temp_ptr|. The reference point of that
+box has coordinates |(cur_h,cur_v)|.
+
+Similarly, when |vlist_out| is called, its duty is to output the box represented
+by the |vlist_node| pointed to by |temp_ptr|. The reference point of that
+box has coordinates |(cur_h,cur_v)|.
+@^recursion@>
+
+@p procedure@?vlist_out; forward; {|hlist_out| and |vlist_out| are mutually
+ recursive}
+
+@ The recursive procedures |hlist_out| and |vlist_out| each have local variables
+|save_h| and |save_v| to hold the values of |dvi_h| and |dvi_v| just before
+entering a new level of recursion. In effect, the values of |save_h| and
+|save_v| on \TeX's run-time stack correspond to the values of |h| and |v|
+that a \.{DVI}-reading program will push onto its coordinate stack.
+
+@d move_past=13 {go to this label when advancing past glue or a rule}
+@d fin_rule=14 {go to this label to finish processing a rule}
+@d next_p=15 {go to this label when finished with node |p|}
+
+@p @t\4@>@<Declare procedures needed in |hlist_out|, |vlist_out|@>@t@>@/
+procedure hlist_out; {output an |hlist_node| box}
+label reswitch, move_past, fin_rule, next_p;
+var base_line: scaled; {the baseline coordinate for this box}
+@!left_edge: scaled; {the left coordinate for this box}
+@!save_h,@!save_v: scaled; {what |dvi_h| and |dvi_v| should pop to}
+@!this_box: pointer; {pointer to containing box}
+@!g_order: glue_ord; {applicable order of infinity for glue}
+@!g_sign: normal..shrinking; {selects type of glue}
+@!p:pointer; {current position in the hlist}
+@!save_loc:integer; {\.{DVI} byte location upon entry}
+@!leader_box:pointer; {the leader box being replicated}
+@!leader_wd:scaled; {width of leader box being replicated}
+@!lx:scaled; {extra space between leader boxes}
+@!outer_doing_leaders:boolean; {were we doing leaders?}
+@!edge:scaled; {left edge of sub-box, or right edge of leader space}
+@!glue_temp:real; {glue value before rounding}
+@!cur_glue:real; {glue seen so far}
+@!cur_g:scaled; {rounded equivalent of |cur_glue| times the glue ratio}
+begin cur_g:=0; cur_glue:=float_constant(0);
+this_box:=temp_ptr; g_order:=glue_order(this_box);
+g_sign:=glue_sign(this_box); p:=list_ptr(this_box);
+incr(cur_s);
+if cur_s>0 then dvi_out(push);
+if cur_s>max_push then max_push:=cur_s;
+save_loc:=dvi_offset+dvi_ptr; base_line:=cur_v; left_edge:=cur_h;
+while p<>null do @<Output node |p| for |hlist_out| and move to the next node,
+ maintaining the condition |cur_v=base_line|@>;
+prune_movements(save_loc);
+if cur_s>0 then dvi_pop(save_loc);
+decr(cur_s);
+end;
+
+@ We ought to give special care to the efficiency of one part of |hlist_out|,
+since it belongs to \TeX's inner loop. When a |char_node| is encountered,
+we save a little time by processing several nodes in succession until
+reaching a non-|char_node|. The program uses the fact that |set_char_0=0|.
+@^inner loop@>
+
+@<Output node |p| for |hlist_out|...@>=
+reswitch: if is_char_node(p) then
+ begin synch_h; synch_v;
+ repeat f:=font(p); c:=character(p);
+ if f<>dvi_f then @<Change font |dvi_f| to |f|@>;
+ if c>=qi(128) then dvi_out(set1);
+ dvi_out(qo(c));@/
+ cur_h:=cur_h+char_width(f)(char_info(f)(c));
+ p:=link(p);
+ until not is_char_node(p);
+ dvi_h:=cur_h;
+ end
+else @<Output the non-|char_node| |p| for |hlist_out|
+ and move to the next node@>
+
+@ @<Change font |dvi_f| to |f|@>=
+begin if not font_used[f] then
+ begin dvi_font_def(f); font_used[f]:=true;
+ end;
+if f<=64+font_base then dvi_out(f-font_base-1+fnt_num_0)
+else begin dvi_out(fnt1); dvi_out(f-font_base-1);
+ end;
+dvi_f:=f;
+end
+
+@ @<Output the non-|char_node| |p| for |hlist_out|...@>=
+begin case type(p) of
+hlist_node,vlist_node:@<Output a box in an hlist@>;
+rule_node: begin rule_ht:=height(p); rule_dp:=depth(p); rule_wd:=width(p);
+ goto fin_rule;
+ end;
+whatsit_node: @<Output the whatsit node |p| in an hlist@>;
+glue_node: @<Move right or output leaders@>;
+kern_node,math_node:cur_h:=cur_h+width(p);
+ligature_node: @<Make node |p| look like a |char_node| and |goto reswitch|@>;
+othercases do_nothing
+endcases;@/
+goto next_p;
+fin_rule: @<Output a rule in an hlist@>;
+move_past: cur_h:=cur_h+rule_wd;
+next_p:p:=link(p);
+end
+
+@ @<Output a box in an hlist@>=
+if list_ptr(p)=null then cur_h:=cur_h+width(p)
+else begin save_h:=dvi_h; save_v:=dvi_v;
+ cur_v:=base_line+shift_amount(p); {shift the box down}
+ temp_ptr:=p; edge:=cur_h;
+ if type(p)=vlist_node then vlist_out@+else hlist_out;
+ dvi_h:=save_h; dvi_v:=save_v;
+ cur_h:=edge+width(p); cur_v:=base_line;
+ end
+
+@ @<Output a rule in an hlist@>=
+if is_running(rule_ht) then rule_ht:=height(this_box);
+if is_running(rule_dp) then rule_dp:=depth(this_box);
+rule_ht:=rule_ht+rule_dp; {this is the rule thickness}
+if (rule_ht>0)and(rule_wd>0) then {we don't output empty rules}
+ begin synch_h; cur_v:=base_line+rule_dp; synch_v;
+ dvi_out(set_rule); dvi_four(rule_ht); dvi_four(rule_wd);
+ cur_v:=base_line; dvi_h:=dvi_h+rule_wd;
+ end
+
+@ @d billion==float_constant(1000000000)
+@d vet_glue(#)== glue_temp:=#;
+ if glue_temp>billion then
+ glue_temp:=billion
+ else if glue_temp<-billion then
+ glue_temp:=-billion
+
+@<Move right or output leaders@>=
+begin g:=glue_ptr(p); rule_wd:=width(g)-cur_g;
+if g_sign<>normal then
+ begin if g_sign=stretching then
+ begin if stretch_order(g)=g_order then
+ begin cur_glue:=cur_glue+stretch(g);
+ vet_glue(float(glue_set(this_box))*cur_glue);
+@^real multiplication@>
+ cur_g:=round(glue_temp);
+ end;
+ end
+ else if shrink_order(g)=g_order then
+ begin cur_glue:=cur_glue-shrink(g);
+ vet_glue(float(glue_set(this_box))*cur_glue);
+ cur_g:=round(glue_temp);
+ end;
+ end;
+rule_wd:=rule_wd+cur_g;
+if subtype(p)>=a_leaders then
+ @<Output leaders in an hlist, |goto fin_rule| if a rule
+ or to |next_p| if done@>;
+goto move_past;
+end
+
+@ @<Output leaders in an hlist...@>=
+begin leader_box:=leader_ptr(p);
+if type(leader_box)=rule_node then
+ begin rule_ht:=height(leader_box); rule_dp:=depth(leader_box);
+ goto fin_rule;
+ end;
+leader_wd:=width(leader_box);
+if (leader_wd>0)and(rule_wd>0) then
+ begin rule_wd:=rule_wd+10; {compensate for floating-point rounding}
+ edge:=cur_h+rule_wd; lx:=0;
+ @<Let |cur_h| be the position of the first box, and set |leader_wd+lx|
+ to the spacing between corresponding parts of boxes@>;
+ while cur_h+leader_wd<=edge do
+ @<Output a leader box at |cur_h|,
+ then advance |cur_h| by |leader_wd+lx|@>;
+ cur_h:=edge-10; goto next_p;
+ end;
+end
+
+@ The calculations related to leaders require a bit of care. First, in the
+case of |a_leaders| (aligned leaders), we want to move |cur_h| to
+|left_edge| plus the smallest multiple of |leader_wd| for which the result
+is not less than the current value of |cur_h|; i.e., |cur_h| should become
+$|left_edge|+|leader_wd|\times\lceil
+(|cur_h|-|left_edge|)/|leader_wd|\rceil$. The program here should work in
+all cases even though some implementations of \PASCAL\ give nonstandard
+results for the |div| operation when |cur_h| is less than |left_edge|.
+
+In the case of |c_leaders| (centered leaders), we want to increase |cur_h|
+by half of the excess space not occupied by the leaders; and in the
+case of |x_leaders| (expanded leaders) we increase |cur_h|
+by $1/(q+1)$ of this excess space, where $q$ is the number of times the
+leader box will be replicated. Slight inaccuracies in the division might
+accumulate; half of this rounding error is placed at each end of the leaders.
+
+@<Let |cur_h| be the position of the first box, ...@>=
+if subtype(p)=a_leaders then
+ begin save_h:=cur_h;
+ cur_h:=left_edge+leader_wd*((cur_h-left_edge)@!div leader_wd);
+ if cur_h<save_h then cur_h:=cur_h+leader_wd;
+ end
+else begin lq:=rule_wd div leader_wd; {the number of box copies}
+ lr:=rule_wd mod leader_wd; {the remaining space}
+ if subtype(p)=c_leaders then cur_h:=cur_h+(lr div 2)
+ else begin lx:=lr div (lq+1);
+ cur_h:=cur_h+((lr-(lq-1)*lx) div 2);
+ end;
+ end
+
+@ The `\\{synch}' operations here are intended to decrease the number of
+bytes needed to specify horizontal and vertical motion in the \.{DVI} output.
+
+@<Output a leader box at |cur_h|, ...@>=
+begin cur_v:=base_line+shift_amount(leader_box); synch_v; save_v:=dvi_v;@/
+synch_h; save_h:=dvi_h; temp_ptr:=leader_box;
+outer_doing_leaders:=doing_leaders; doing_leaders:=true;
+if type(leader_box)=vlist_node then vlist_out@+else hlist_out;
+doing_leaders:=outer_doing_leaders;
+dvi_v:=save_v; dvi_h:=save_h; cur_v:=base_line;
+cur_h:=save_h+leader_wd+lx;
+end
+
+@ The |vlist_out| routine is similar to |hlist_out|, but a bit simpler.
+
+@p procedure vlist_out; {output a |vlist_node| box}
+label move_past, fin_rule, next_p;
+var left_edge: scaled; {the left coordinate for this box}
+@!top_edge: scaled; {the top coordinate for this box}
+@!save_h,@!save_v: scaled; {what |dvi_h| and |dvi_v| should pop to}
+@!this_box: pointer; {pointer to containing box}
+@!g_order: glue_ord; {applicable order of infinity for glue}
+@!g_sign: normal..shrinking; {selects type of glue}
+@!p:pointer; {current position in the vlist}
+@!save_loc:integer; {\.{DVI} byte location upon entry}
+@!leader_box:pointer; {the leader box being replicated}
+@!leader_ht:scaled; {height of leader box being replicated}
+@!lx:scaled; {extra space between leader boxes}
+@!outer_doing_leaders:boolean; {were we doing leaders?}
+@!edge:scaled; {bottom boundary of leader space}
+@!glue_temp:real; {glue value before rounding}
+@!cur_glue:real; {glue seen so far}
+@!cur_g:scaled; {rounded equivalent of |cur_glue| times the glue ratio}
+begin cur_g:=0; cur_glue:=float_constant(0);
+this_box:=temp_ptr; g_order:=glue_order(this_box);
+g_sign:=glue_sign(this_box); p:=list_ptr(this_box);
+incr(cur_s);
+if cur_s>0 then dvi_out(push);
+if cur_s>max_push then max_push:=cur_s;
+save_loc:=dvi_offset+dvi_ptr; left_edge:=cur_h; cur_v:=cur_v-height(this_box);
+top_edge:=cur_v;
+while p<>null do @<Output node |p| for |vlist_out| and move to the next node,
+ maintaining the condition |cur_h=left_edge|@>;
+prune_movements(save_loc);
+if cur_s>0 then dvi_pop(save_loc);
+decr(cur_s);
+end;
+
+@ @<Output node |p| for |vlist_out|...@>=
+begin if is_char_node(p) then confusion("vlistout")
+@:this can't happen vlistout}{\quad vlistout@>
+else @<Output the non-|char_node| |p| for |vlist_out|@>;
+next_p:p:=link(p);
+end
+
+@ @<Output the non-|char_node| |p| for |vlist_out|@>=
+begin case type(p) of
+hlist_node,vlist_node:@<Output a box in a vlist@>;
+rule_node: begin rule_ht:=height(p); rule_dp:=depth(p); rule_wd:=width(p);
+ goto fin_rule;
+ end;
+whatsit_node: @<Output the whatsit node |p| in a vlist@>;
+glue_node: @<Move down or output leaders@>;
+kern_node:cur_v:=cur_v+width(p);
+othercases do_nothing
+endcases;@/
+goto next_p;
+fin_rule: @<Output a rule in a vlist, |goto next_p|@>;
+move_past: cur_v:=cur_v+rule_ht;
+end
+
+@ The |synch_v| here allows the \.{DVI} output to use one-byte commands
+for adjusting |v| in most cases, since the baselineskip distance will
+usually be constant.
+
+@<Output a box in a vlist@>=
+if list_ptr(p)=null then cur_v:=cur_v+height(p)+depth(p)
+else begin cur_v:=cur_v+height(p); synch_v;
+ save_h:=dvi_h; save_v:=dvi_v;
+ cur_h:=left_edge+shift_amount(p); {shift the box right}
+ temp_ptr:=p;
+ if type(p)=vlist_node then vlist_out@+else hlist_out;
+ dvi_h:=save_h; dvi_v:=save_v;
+ cur_v:=save_v+depth(p); cur_h:=left_edge;
+ end
+
+@ @<Output a rule in a vlist...@>=
+if is_running(rule_wd) then rule_wd:=width(this_box);
+rule_ht:=rule_ht+rule_dp; {this is the rule thickness}
+cur_v:=cur_v+rule_ht;
+if (rule_ht>0)and(rule_wd>0) then {we don't output empty rules}
+ begin synch_h; synch_v;
+ dvi_out(put_rule); dvi_four(rule_ht); dvi_four(rule_wd);
+ end;
+goto next_p
+
+@ @<Move down or output leaders@>=
+begin g:=glue_ptr(p); rule_ht:=width(g)-cur_g;
+if g_sign<>normal then
+ begin if g_sign=stretching then
+ begin if stretch_order(g)=g_order then
+ begin cur_glue:=cur_glue+stretch(g);
+ vet_glue(float(glue_set(this_box))*cur_glue);
+@^real multiplication@>
+ cur_g:=round(glue_temp);
+ end;
+ end
+ else if shrink_order(g)=g_order then
+ begin cur_glue:=cur_glue-shrink(g);
+ vet_glue(float(glue_set(this_box))*cur_glue);
+ cur_g:=round(glue_temp);
+ end;
+ end;
+rule_ht:=rule_ht+cur_g;
+if subtype(p)>=a_leaders then
+ @<Output leaders in a vlist, |goto fin_rule| if a rule
+ or to |next_p| if done@>;
+goto move_past;
+end
+
+@ @<Output leaders in a vlist...@>=
+begin leader_box:=leader_ptr(p);
+if type(leader_box)=rule_node then
+ begin rule_wd:=width(leader_box); rule_dp:=0;
+ goto fin_rule;
+ end;
+leader_ht:=height(leader_box)+depth(leader_box);
+if (leader_ht>0)and(rule_ht>0) then
+ begin rule_ht:=rule_ht+10; {compensate for floating-point rounding}
+ edge:=cur_v+rule_ht; lx:=0;
+ @<Let |cur_v| be the position of the first box, and set |leader_ht+lx|
+ to the spacing between corresponding parts of boxes@>;
+ while cur_v+leader_ht<=edge do
+ @<Output a leader box at |cur_v|,
+ then advance |cur_v| by |leader_ht+lx|@>;
+ cur_v:=edge-10; goto next_p;
+ end;
+end
+
+@ @<Let |cur_v| be the position of the first box, ...@>=
+if subtype(p)=a_leaders then
+ begin save_v:=cur_v;
+ cur_v:=top_edge+leader_ht*((cur_v-top_edge)@!div leader_ht);
+ if cur_v<save_v then cur_v:=cur_v+leader_ht;
+ end
+else begin lq:=rule_ht div leader_ht; {the number of box copies}
+ lr:=rule_ht mod leader_ht; {the remaining space}
+ if subtype(p)=c_leaders then cur_v:=cur_v+(lr div 2)
+ else begin lx:=lr div (lq+1);
+ cur_v:=cur_v+((lr-(lq-1)*lx) div 2);
+ end;
+ end
+
+@ When we reach this part of the program, |cur_v| indicates the top of a
+leader box, not its baseline.
+
+@<Output a leader box at |cur_v|, ...@>=
+begin cur_h:=left_edge+shift_amount(leader_box); synch_h; save_h:=dvi_h;@/
+cur_v:=cur_v+height(leader_box); synch_v; save_v:=dvi_v;
+temp_ptr:=leader_box;
+outer_doing_leaders:=doing_leaders; doing_leaders:=true;
+if type(leader_box)=vlist_node then vlist_out@+else hlist_out;
+doing_leaders:=outer_doing_leaders;
+dvi_v:=save_v; dvi_h:=save_h; cur_h:=left_edge;
+cur_v:=save_v-height(leader_box)+leader_ht+lx;
+end
+
+@ The |hlist_out| and |vlist_out| procedures are now complete, so we are
+ready for the |ship_out| routine that gets them started in the first place.
+
+@p procedure ship_out(@!p:pointer); {output the box |p|}
+label done;
+var page_loc:integer; {location of the current |bop|}
+@!j,@!k:0..9; {indices to first ten count registers}
+@!s:pool_pointer; {index into |str_pool|}
+@!old_setting:0..max_selector; {saved |selector| setting}
+begin if tracing_output>0 then
+ begin print_nl(""); print_ln;
+ print("Completed box being shipped out");
+@.Completed box...@>
+ end;
+if term_offset>max_print_line-9 then print_ln
+else if (term_offset>0)or(file_offset>0) then print_char(" ");
+print_char("["); j:=9;
+while (count(j)=0)and(j>0) do decr(j);
+for k:=0 to j do
+ begin print_int(count(k));
+ if k<j then print_char(".");
+ end;
+update_terminal;
+if tracing_output>0 then
+ begin print_char("]");
+ begin_diagnostic; show_box(p); end_diagnostic(true);
+ end;
+@<Ship box |p| out@>;
+if tracing_output<=0 then print_char("]");
+dead_cycles:=0;
+update_terminal; {progress report}
+@<Flush the box from memory, showing statistics if requested@>;
+end;
+
+@ @<Flush the box from memory, showing statistics if requested@>=
+@!stat if tracing_stats>1 then
+ begin print_nl("Memory usage before: ");
+@.Memory usage...@>
+ print_int(var_used); print_char("&");
+ print_int(dyn_used); print_char(";");
+ end;
+tats@/
+flush_node_list(p);
+@!stat if tracing_stats>1 then
+ begin print(" after: ");
+ print_int(var_used); print_char("&");
+ print_int(dyn_used); print("; still untouched: ");
+ print_int(hi_mem_min-lo_mem_max-1); print_ln;
+ end;
+tats
+
+@ @<Ship box |p| out@>=
+@<Update the values of |max_h| and |max_v|; but if the page is too large,
+ |goto done|@>;
+@<Initialize variables as |ship_out| begins@>;
+page_loc:=dvi_offset+dvi_ptr;
+dvi_out(bop);
+for k:=0 to 9 do dvi_four(count(k));
+dvi_four(last_bop); last_bop:=page_loc;
+cur_v:=height(p)+v_offset; temp_ptr:=p;
+if type(p)=vlist_node then vlist_out@+else hlist_out;
+dvi_out(eop); incr(total_pages); cur_s:=-1;
+done:
+
+@ Sometimes the user will generate a huge page because other error messages
+are being ignored. Such pages are not output to the \.{dvi} file, since they
+may confuse the printing software.
+
+@<Update the values of |max_h| and |max_v|; but if the page is too large...@>=
+if (height(p)>max_dimen)or@|(depth(p)>max_dimen)or@|
+ (height(p)+depth(p)+v_offset>max_dimen)or@|
+ (width(p)+h_offset>max_dimen) then
+ begin print_err("Huge page cannot be shipped out");
+@.Huge page...@>
+ help2("The page just created is more than 18 feet tall or")@/
+ ("more than 18 feet wide, so I suspect something went wrong.");
+ error;
+ if tracing_output<=0 then
+ begin begin_diagnostic;
+ print_nl("The following box has been deleted:");
+@.The following...deleted@>
+ show_box(p);
+ end_diagnostic(true);
+ end;
+ goto done;
+ end;
+if height(p)+depth(p)+v_offset>max_v then max_v:=height(p)+depth(p)+v_offset;
+if width(p)+h_offset>max_h then max_h:=width(p)+h_offset
+
+@ At the end of the program, we must finish things off by writing the
+post\-amble. If |total_pages=0|, the \.{DVI} file was never opened.
+If |total_pages>=65536|, the \.{DVI} file will lie.
+
+An integer variable |k| will be declared for use by this routine.
+
+@<Finish the \.{DVI} file@>=
+while cur_s>-1 do
+ begin if cur_s>0 then dvi_out(pop)
+ else begin dvi_out(eop); incr(total_pages);
+ end;
+ decr(cur_s);
+ end;
+if total_pages=0 then print_nl("No pages of output.")
+@.No pages of output@>
+else begin dvi_out(post); {beginning of the postamble}
+ dvi_four(last_bop); last_bop:=dvi_offset+dvi_ptr-5; {|post| location}
+ dvi_four(25400000); dvi_four(473628672); {conversion ratio for sp}
+ prepare_mag; dvi_four(mag); {magnification factor}
+ dvi_four(max_v); dvi_four(max_h);@/
+ dvi_out(max_push div 256); dvi_out(max_push mod 256);@/
+ dvi_out((total_pages div 256) mod 256); dvi_out(total_pages mod 256);@/
+ @<Output the font definitions for all fonts that were used@>;
+ dvi_out(post_post); dvi_four(last_bop); dvi_out(id_byte);@/
+ k:=4+((dvi_buf_size-dvi_ptr) mod 4); {the number of 223's}
+ while k>0 do
+ begin dvi_out(223); decr(k);
+ end;
+ @<Empty the last bytes out of |dvi_buf|@>;
+ print_nl("Output written on "); slow_print(output_file_name);
+@.Output written on x@>
+ print(" ("); print_int(total_pages); print(" page");
+ if total_pages<>1 then print_char("s");
+ print(", "); print_int(dvi_offset+dvi_ptr); print(" bytes).");
+ b_close(dvi_file);
+ end
+
+@ @<Output the font definitions...@>=
+while font_ptr>font_base do
+ begin if font_used[font_ptr] then dvi_font_def(font_ptr);
+ decr(font_ptr);
+ end
+
+@* \[33] Packaging.
+We're essentially done with the parts of \TeX\ that are concerned with
+the input (|get_next|) and the output (|ship_out|). So it's time to
+get heavily into the remaining part, which does the real work of typesetting.
+
+After lists are constructed, \TeX\ wraps them up and puts them into boxes.
+Two major subroutines are given the responsibility for this task: |hpack|
+applies to horizontal lists (hlists) and |vpack| applies to vertical lists
+(vlists). The main duty of |hpack| and |vpack| is to compute the dimensions
+of the resulting boxes, and to adjust the glue if one of those dimensions
+is pre-specified. The computed sizes normally enclose all of the material
+inside the new box; but some items may stick out if negative glue is used,
+if the box is overfull, or if a \.{\\vbox} includes other boxes that have
+been shifted left.
+
+The subroutine call |hpack(p,w,m)| returns a pointer to an |hlist_node|
+for a box containing the hlist that starts at |p|. Parameter |w| specifies
+a width; and parameter |m| is either `|exactly|' or `|additional|'. Thus,
+|hpack(p,w,exactly)| produces a box whose width is exactly |w|, while
+|hpack(p,w,additional)| yields a box whose width is the natural width plus
+|w|. It is convenient to define a macro called `|natural|' to cover the
+most common case, so that we can say |hpack(p,natural)| to get a box that
+has the natural width of list |p|.
+
+Similarly, |vpack(p,w,m)| returns a pointer to a |vlist_node| for a
+box containing the vlist that starts at |p|. In this case |w| represents
+a height instead of a width; the parameter |m| is interpreted as in |hpack|.
+
+@d exactly=0 {a box dimension is pre-specified}
+@d additional=1 {a box dimension is increased from the natural one}
+@d natural==0,additional {shorthand for parameters to |hpack| and |vpack|}
+
+@ The parameters to |hpack| and |vpack| correspond to \TeX's primitives
+like `\.{\\hbox} \.{to} \.{300pt}', `\.{\\hbox} \.{spread} \.{10pt}'; note
+that `\.{\\hbox}' with no dimension following it is equivalent to
+`\.{\\hbox} \.{spread} \.{0pt}'. The |scan_spec| subroutine scans such
+constructions in the user's input, including the mandatory left brace that
+follows them, and it puts the specification onto |save_stack| so that the
+desired box can later be obtained by executing the following code:
+$$\vbox{\halign{#\hfil\cr
+|save_ptr:=save_ptr-2;|\cr
+|hpack(p,saved(1),saved(0)).|\cr}}$$
+Special care is necessary to ensure that the special |save_stack| codes
+are placed just below the new group code, because scanning can change
+|save_stack| when \.{\\csname} appears.
+
+@p procedure scan_spec(@!c:group_code;@!three_codes:boolean);
+ {scans a box specification and left brace}
+label found;
+var @!s:integer; {temporarily saved value}
+@!spec_code:exactly..additional;
+begin if three_codes then s:=saved(0);
+if scan_keyword("to") then spec_code:=exactly
+@.to@>
+else if scan_keyword("spread") then spec_code:=additional
+@.spread@>
+else begin spec_code:=additional; cur_val:=0;
+ goto found;
+ end;
+scan_normal_dimen;
+found: if three_codes then
+ begin saved(0):=s; incr(save_ptr);
+ end;
+saved(0):=spec_code; saved(1):=cur_val; save_ptr:=save_ptr+2;
+new_save_level(c); scan_left_brace;
+end;
+
+@ To figure out the glue setting, |hpack| and |vpack| determine how much
+stretchability and shrinkability are present, considering all four orders
+of infinity. The highest order of infinity that has a nonzero coefficient
+is then used as if no other orders were present.
+
+For example, suppose that the given list contains six glue nodes with
+the respective stretchabilities 3pt, 8fill, 5fil, 6pt, $-3$fil, $-8$fill.
+Then the total is essentially 2fil; and if a total additional space of 6pt
+is to be achieved by stretching, the actual amounts of stretch will be
+0pt, 0pt, 15pt, 0pt, $-9$pt, and 0pt, since only `fil' glue will be
+considered. (The `fill' glue is therefore not really stretching infinitely
+with respect to `fil'; nobody would actually want that to happen.)
+
+The arrays |total_stretch| and |total_shrink| are used to determine how much
+glue of each kind is present. A global variable |last_badness| is used
+to implement \.{\\badness}.
+
+@<Glob...@>=
+@!total_stretch, @!total_shrink: array[glue_ord] of scaled;
+ {glue found by |hpack| or |vpack|}
+@!last_badness:integer; {badness of the most recently packaged box}
+
+@ If the global variable |adjust_tail| is non-null, the |hpack| routine
+also removes all occurrences of |ins_node|, |mark_node|, and |adjust_node|
+items and appends the resulting material onto the list that ends at
+location |adjust_tail|.
+
+@< Glob...@>=
+@!adjust_tail:pointer; {tail of adjustment list}
+
+@ @<Set init...@>=adjust_tail:=null; last_badness:=0;
+
+@ Here now is |hpack|, which contains few if any surprises.
+
+@p function hpack(@!p:pointer;@!w:scaled;@!m:small_number):pointer;
+label reswitch, common_ending, exit;
+var r:pointer; {the box node that will be returned}
+@!q:pointer; {trails behind |p|}
+@!h,@!d,@!x:scaled; {height, depth, and natural width}
+@!s:scaled; {shift amount}
+@!g:pointer; {points to a glue specification}
+@!o:glue_ord; {order of infinity}
+@!f:internal_font_number; {the font in a |char_node|}
+@!i:four_quarters; {font information about a |char_node|}
+@!hd:eight_bits; {height and depth indices for a character}
+begin last_badness:=0; r:=get_node(box_node_size); type(r):=hlist_node;
+subtype(r):=min_quarterword; shift_amount(r):=0;
+q:=r+list_offset; link(q):=p;@/
+h:=0; @<Clear dimensions to zero@>;
+while p<>null do @<Examine node |p| in the hlist, taking account of its effect
+ on the dimensions of the new box, or moving it to the adjustment list;
+ then advance |p| to the next node@>;
+if adjust_tail<>null then link(adjust_tail):=null;
+height(r):=h; depth(r):=d;@/
+@<Determine the value of |width(r)| and the appropriate glue setting;
+ then |return| or |goto common_ending|@>;
+common_ending: @<Finish issuing a diagnostic message
+ for an overfull or underfull hbox@>;
+exit: hpack:=r;
+end;
+
+@ @<Clear dimensions to zero@>=
+d:=0; x:=0;
+total_stretch[normal]:=0; total_shrink[normal]:=0;
+total_stretch[fil]:=0; total_shrink[fil]:=0;
+total_stretch[fill]:=0; total_shrink[fill]:=0;
+total_stretch[filll]:=0; total_shrink[filll]:=0
+
+@ @<Examine node |p| in the hlist, taking account of its effect...@>=
+@^inner loop@>
+begin reswitch: while is_char_node(p) do
+ @<Incorporate character dimensions into the dimensions of
+ the hbox that will contain~it, then move to the next node@>;
+if p<>null then
+ begin case type(p) of
+ hlist_node,vlist_node,rule_node,unset_node:
+ @<Incorporate box dimensions into the dimensions of
+ the hbox that will contain~it@>;
+ ins_node,mark_node,adjust_node: if adjust_tail<>null then
+ @<Transfer node |p| to the adjustment list@>;
+ whatsit_node:@<Incorporate a whatsit node into an hbox@>;
+ glue_node:@<Incorporate glue into the horizontal totals@>;
+ kern_node,math_node: x:=x+width(p);
+ ligature_node: @<Make node |p| look like a |char_node|
+ and |goto reswitch|@>;
+ othercases do_nothing
+ endcases;@/
+ p:=link(p);
+ end;
+end
+
+
+@ @<Make node |p| look like a |char_node| and |goto reswitch|@>=
+begin mem[lig_trick]:=mem[lig_char(p)]; link(lig_trick):=link(p);
+p:=lig_trick; goto reswitch;
+end
+
+@ The code here implicitly uses the fact that running dimensions are
+indicated by |null_flag|, which will be ignored in the calculations
+because it is a highly negative number.
+
+@<Incorporate box dimensions into the dimensions of the hbox...@>=
+begin x:=x+width(p);
+if type(p)>=rule_node then s:=0 @+else s:=shift_amount(p);
+if height(p)-s>h then h:=height(p)-s;
+if depth(p)+s>d then d:=depth(p)+s;
+end
+
+@ The following code is part of \TeX's inner loop; i.e., adding another
+character of text to the user's input will cause each of these instructions
+to be exercised one more time.
+@^inner loop@>
+
+@<Incorporate character dimensions into the dimensions of the hbox...@>=
+begin f:=font(p); i:=char_info(f)(character(p)); hd:=height_depth(i);
+x:=x+char_width(f)(i);@/
+s:=char_height(f)(hd);@+if s>h then h:=s;
+s:=char_depth(f)(hd);@+if s>d then d:=s;
+p:=link(p);
+end
+
+@ Although node |q| is not necessarily the immediate predecessor of node |p|,
+it always points to some node in the list preceding |p|. Thus, we can delete
+nodes by moving |q| when necessary. The algorithm takes linear time, and the
+extra computation does not intrude on the inner loop unless it is necessary
+to make a deletion.
+@^inner loop@>
+
+@<Transfer node |p| to the adjustment list@>=
+begin while link(q)<>p do q:=link(q);
+if type(p)=adjust_node then
+ begin link(adjust_tail):=adjust_ptr(p);
+ while link(adjust_tail)<>null do adjust_tail:=link(adjust_tail);
+ p:=link(p); free_node(link(q),small_node_size);
+ end
+else begin link(adjust_tail):=p; adjust_tail:=p; p:=link(p);
+ end;
+link(q):=p; p:=q;
+end
+
+@ @<Incorporate glue into the horizontal totals@>=
+begin g:=glue_ptr(p); x:=x+width(g);@/
+o:=stretch_order(g); total_stretch[o]:=total_stretch[o]+stretch(g);
+o:=shrink_order(g); total_shrink[o]:=total_shrink[o]+shrink(g);
+if subtype(p)>=a_leaders then
+ begin g:=leader_ptr(p);
+ if height(g)>h then h:=height(g);
+ if depth(g)>d then d:=depth(g);
+ end;
+end
+
+@ When we get to the present part of the program, |x| is the natural width
+of the box being packaged.
+
+@<Determine the value of |width(r)| and the appropriate glue setting...@>=
+if m=additional then w:=x+w;
+width(r):=w; x:=w-x; {now |x| is the excess to be made up}
+if x=0 then
+ begin glue_sign(r):=normal; glue_order(r):=normal;
+ set_glue_ratio_zero(glue_set(r));
+ return;
+ end
+else if x>0 then @<Determine horizontal glue stretch setting, then |return|
+ or \hbox{|goto common_ending|}@>
+else @<Determine horizontal glue shrink setting, then |return|
+ or \hbox{|goto common_ending|}@>
+
+@ @<Determine horizontal glue stretch setting...@>=
+begin @<Determine the stretch order@>;
+glue_order(r):=o; glue_sign(r):=stretching;
+if total_stretch[o]<>0 then glue_set(r):=unfloat(x/total_stretch[o])
+@^real division@>
+else begin glue_sign(r):=normal;
+ set_glue_ratio_zero(glue_set(r)); {there's nothing to stretch}
+ end;
+if o=normal then if list_ptr(r)<>null then
+ @<Report an underfull hbox and |goto common_ending|, if this box
+ is sufficiently bad@>;
+return;
+end
+
+@ @<Determine the stretch order@>=
+if total_stretch[filll]<>0 then o:=filll
+else if total_stretch[fill]<>0 then o:=fill
+else if total_stretch[fil]<>0 then o:=fil
+else o:=normal
+
+@ @<Report an underfull hbox and |goto common_ending|, if...@>=
+begin last_badness:=badness(x,total_stretch[normal]);
+if last_badness>hbadness then
+ begin print_ln;
+ if last_badness>100 then print_nl("Underfull")@+else print_nl("Loose");
+ print(" \hbox (badness "); print_int(last_badness);
+@.Underfull \\hbox...@>
+@.Loose \\hbox...@>
+ goto common_ending;
+ end;
+end
+
+@ In order to provide a decent indication of where an overfull or underfull
+box originated, we use a global variable |pack_begin_line| that is
+set nonzero only when |hpack| is being called by the paragraph builder
+or the alignment finishing routine.
+
+@<Glob...@>=
+@!pack_begin_line:integer; {source file line where the current paragraph
+ or alignment began; a negative value denotes alignment}
+
+@ @<Set init...@>=
+pack_begin_line:=0;
+
+@ @<Finish issuing a diagnostic message for an overfull or underfull hbox@>=
+if output_active then print(") has occurred while \output is active")
+else begin if pack_begin_line<>0 then
+ begin if pack_begin_line>0 then print(") in paragraph at lines ")
+ else print(") in alignment at lines ");
+ print_int(abs(pack_begin_line));
+ print("--");
+ end
+ else print(") detected at line ");
+ print_int(line);
+ end;
+print_ln;@/
+font_in_short_display:=null_font; short_display(list_ptr(r)); print_ln;@/
+begin_diagnostic; show_box(r); end_diagnostic(true)
+
+@ @<Determine horizontal glue shrink setting...@>=
+begin @<Determine the shrink order@>;
+glue_order(r):=o; glue_sign(r):=shrinking;
+if total_shrink[o]<>0 then glue_set(r):=unfloat((-x)/total_shrink[o])
+@^real division@>
+else begin glue_sign(r):=normal;
+ set_glue_ratio_zero(glue_set(r)); {there's nothing to shrink}
+ end;
+if (total_shrink[o]<-x)and(o=normal)and(list_ptr(r)<>null) then
+ begin last_badness:=1000000;
+ set_glue_ratio_one(glue_set(r)); {use the maximum shrinkage}
+ @<Report an overfull hbox and |goto common_ending|, if this box
+ is sufficiently bad@>;
+ end
+else if o=normal then if list_ptr(r)<>null then
+ @<Report a tight hbox and |goto common_ending|, if this box
+ is sufficiently bad@>;
+return;
+end
+
+@ @<Determine the shrink order@>=
+if total_shrink[filll]<>0 then o:=filll
+else if total_shrink[fill]<>0 then o:=fill
+else if total_shrink[fil]<>0 then o:=fil
+else o:=normal
+
+@ @<Report an overfull hbox and |goto common_ending|, if...@>=
+if (-x-total_shrink[normal]>hfuzz)or(hbadness<100) then
+ begin if (overfull_rule>0)and(-x-total_shrink[normal]>hfuzz) then
+ begin while link(q)<>null do q:=link(q);
+ link(q):=new_rule;
+ width(link(q)):=overfull_rule;
+ end;
+ print_ln; print_nl("Overfull \hbox (");
+@.Overfull \\hbox...@>
+ print_scaled(-x-total_shrink[normal]); print("pt too wide");
+ goto common_ending;
+ end
+
+@ @<Report a tight hbox and |goto common_ending|, if...@>=
+begin last_badness:=badness(-x,total_shrink[normal]);
+if last_badness>hbadness then
+ begin print_ln; print_nl("Tight \hbox (badness "); print_int(last_badness);
+@.Tight \\hbox...@>
+ goto common_ending;
+ end;
+end
+
+@ The |vpack| subroutine is actually a special case of a slightly more
+general routine called |vpackage|, which has four parameters. The fourth
+parameter, which is |max_dimen| in the case of |vpack|, specifies the
+maximum depth of the page box that is constructed. The depth is first
+computed by the normal rules; if it exceeds this limit, the reference
+point is simply moved down until the limiting depth is attained.
+
+@d vpack(#)==vpackage(#,max_dimen) {special case of unconstrained depth}
+
+@p function vpackage(@!p:pointer;@!h:scaled;@!m:small_number;@!l:scaled):
+ pointer;
+label common_ending, exit;
+var r:pointer; {the box node that will be returned}
+@!w,@!d,@!x:scaled; {width, depth, and natural height}
+@!s:scaled; {shift amount}
+@!g:pointer; {points to a glue specification}
+@!o:glue_ord; {order of infinity}
+begin last_badness:=0; r:=get_node(box_node_size); type(r):=vlist_node;
+subtype(r):=min_quarterword; shift_amount(r):=0;
+list_ptr(r):=p;@/
+w:=0; @<Clear dimensions to zero@>;
+while p<>null do @<Examine node |p| in the vlist, taking account of its effect
+ on the dimensions of the new box; then advance |p| to the next node@>;
+width(r):=w;
+if d>l then
+ begin x:=x+d-l; depth(r):=l;
+ end
+else depth(r):=d;
+@<Determine the value of |height(r)| and the appropriate glue setting;
+ then |return| or |goto common_ending|@>;
+common_ending: @<Finish issuing a diagnostic message
+ for an overfull or underfull vbox@>;
+exit: vpackage:=r;
+end;
+
+@ @<Examine node |p| in the vlist, taking account of its effect...@>=
+begin if is_char_node(p) then confusion("vpack")
+@:this can't happen vpack}{\quad vpack@>
+else case type(p) of
+ hlist_node,vlist_node,rule_node,unset_node:
+ @<Incorporate box dimensions into the dimensions of
+ the vbox that will contain~it@>;
+ whatsit_node:@<Incorporate a whatsit node into a vbox@>;
+ glue_node: @<Incorporate glue into the vertical totals@>;
+ kern_node: begin x:=x+d+width(p); d:=0;
+ end;
+ othercases do_nothing
+ endcases;
+p:=link(p);
+end
+
+@ @<Incorporate box dimensions into the dimensions of the vbox...@>=
+begin x:=x+d+height(p); d:=depth(p);
+if type(p)>=rule_node then s:=0 @+else s:=shift_amount(p);
+if width(p)+s>w then w:=width(p)+s;
+end
+
+@ @<Incorporate glue into the vertical totals@>=
+begin x:=x+d; d:=0;@/
+g:=glue_ptr(p); x:=x+width(g);@/
+o:=stretch_order(g); total_stretch[o]:=total_stretch[o]+stretch(g);
+o:=shrink_order(g); total_shrink[o]:=total_shrink[o]+shrink(g);
+if subtype(p)>=a_leaders then
+ begin g:=leader_ptr(p);
+ if width(g)>w then w:=width(g);
+ end;
+end
+
+@ When we get to the present part of the program, |x| is the natural height
+of the box being packaged.
+
+@<Determine the value of |height(r)| and the appropriate glue setting...@>=
+if m=additional then h:=x+h;
+height(r):=h; x:=h-x; {now |x| is the excess to be made up}
+if x=0 then
+ begin glue_sign(r):=normal; glue_order(r):=normal;
+ set_glue_ratio_zero(glue_set(r));
+ return;
+ end
+else if x>0 then @<Determine vertical glue stretch setting, then |return|
+ or \hbox{|goto common_ending|}@>
+else @<Determine vertical glue shrink setting, then |return|
+ or \hbox{|goto common_ending|}@>
+
+@ @<Determine vertical glue stretch setting...@>=
+begin @<Determine the stretch order@>;
+glue_order(r):=o; glue_sign(r):=stretching;
+if total_stretch[o]<>0 then glue_set(r):=unfloat(x/total_stretch[o])
+@^real division@>
+else begin glue_sign(r):=normal;
+ set_glue_ratio_zero(glue_set(r)); {there's nothing to stretch}
+ end;
+if o=normal then if list_ptr(r)<>null then
+ @<Report an underfull vbox and |goto common_ending|, if this box
+ is sufficiently bad@>;
+return;
+end
+
+@ @<Report an underfull vbox and |goto common_ending|, if...@>=
+begin last_badness:=badness(x,total_stretch[normal]);
+if last_badness>vbadness then
+ begin print_ln;
+ if last_badness>100 then print_nl("Underfull")@+else print_nl("Loose");
+ print(" \vbox (badness "); print_int(last_badness);
+@.Underfull \\vbox...@>
+@.Loose \\vbox...@>
+ goto common_ending;
+ end;
+end
+
+@ @<Finish issuing a diagnostic message for an overfull or underfull vbox@>=
+if output_active then print(") has occurred while \output is active")
+else begin if pack_begin_line<>0 then {it's actually negative}
+ begin print(") in alignment at lines ");
+ print_int(abs(pack_begin_line));
+ print("--");
+ end
+ else print(") detected at line ");
+ print_int(line);
+ print_ln;@/
+ end;
+begin_diagnostic; show_box(r); end_diagnostic(true)
+
+@ @<Determine vertical glue shrink setting...@>=
+begin @<Determine the shrink order@>;
+glue_order(r):=o; glue_sign(r):=shrinking;
+if total_shrink[o]<>0 then glue_set(r):=unfloat((-x)/total_shrink[o])
+@^real division@>
+else begin glue_sign(r):=normal;
+ set_glue_ratio_zero(glue_set(r)); {there's nothing to shrink}
+ end;
+if (total_shrink[o]<-x)and(o=normal)and(list_ptr(r)<>null) then
+ begin last_badness:=1000000;
+ set_glue_ratio_one(glue_set(r)); {use the maximum shrinkage}
+ @<Report an overfull vbox and |goto common_ending|, if this box
+ is sufficiently bad@>;
+ end
+else if o=normal then if list_ptr(r)<>null then
+ @<Report a tight vbox and |goto common_ending|, if this box
+ is sufficiently bad@>;
+return;
+end
+
+@ @<Report an overfull vbox and |goto common_ending|, if...@>=
+if (-x-total_shrink[normal]>vfuzz)or(vbadness<100) then
+ begin print_ln; print_nl("Overfull \vbox (");
+@.Overfull \\vbox...@>
+ print_scaled(-x-total_shrink[normal]); print("pt too high");
+ goto common_ending;
+ end
+
+@ @<Report a tight vbox and |goto common_ending|, if...@>=
+begin last_badness:=badness(-x,total_shrink[normal]);
+if last_badness>vbadness then
+ begin print_ln; print_nl("Tight \vbox (badness "); print_int(last_badness);
+@.Tight \\vbox...@>
+ goto common_ending;
+ end;
+end
+
+@ When a box is being appended to the current vertical list, the
+baselineskip calculation is handled by the |append_to_vlist| routine.
+
+@p procedure append_to_vlist(@!b:pointer);
+var d:scaled; {deficiency of space between baselines}
+@!p:pointer; {a new glue specification}
+begin if prev_depth>ignore_depth then
+ begin d:=width(baseline_skip)-prev_depth-height(b);
+ if d<line_skip_limit then p:=new_param_glue(line_skip_code)
+ else begin p:=new_skip_param(baseline_skip_code);
+ width(temp_ptr):=d; {|temp_ptr=glue_ptr(p)|}
+ end;
+ link(tail):=p; tail:=p;
+ end;
+link(tail):=b; tail:=b; prev_depth:=depth(b);
+end;
+
+@* \[34] Data structures for math mode.
+When \TeX\ reads a formula that is enclosed between \.\$'s, it constructs an
+{\sl mlist}, which is essentially a tree structure representing that
+formula. An mlist is a linear sequence of items, but we can regard it as
+a tree structure because mlists can appear within mlists. For example, many
+of the entries can be subscripted or superscripted, and such ``scripts''
+are mlists in their own right.
+
+An entire formula is parsed into such a tree before any of the actual
+typesetting is done, because the current style of type is usually not
+known until the formula has been fully scanned. For example, when the
+formula `\.{\$a+b \\over c+d\$}' is being read, there is no way to tell
+that `\.{a+b}' will be in script size until `\.{\\over}' has appeared.
+
+During the scanning process, each element of the mlist being built is
+classified as a relation, a binary operator, an open parenthesis, etc.,
+or as a construct like `\.{\\sqrt}' that must be built up. This classification
+appears in the mlist data structure.
+
+After a formula has been fully scanned, the mlist is converted to an hlist
+so that it can be incorporated into the surrounding text. This conversion is
+controlled by a recursive procedure that decides all of the appropriate
+styles by a ``top-down'' process starting at the outermost level and working
+in towards the subformulas. The formula is ultimately pasted together using
+combinations of horizontal and vertical boxes, with glue and penalty nodes
+inserted as necessary.
+
+An mlist is represented internally as a linked list consisting chiefly
+of ``noads'' (pronounced ``no-adds''), to distinguish them from the somewhat
+similar ``nodes'' in hlists and vlists. Certain kinds of ordinary nodes are
+allowed to appear in mlists together with the noads; \TeX\ tells the difference
+by means of the |type| field, since a noad's |type| is always greater than
+that of a node. An mlist does not contain character nodes, hlist nodes, vlist
+nodes, math nodes, ligature nodes,
+or unset nodes; in particular, each mlist item appears in the
+variable-size part of |mem|, so the |type| field is always present.
+
+@ Each noad is four or more words long. The first word contains the |type|
+and |subtype| and |link| fields that are already so familiar to us; the
+second, third, and fourth words are called the noad's |nucleus|, |subscr|,
+and |supscr| fields.
+
+Consider, for example, the simple formula `\.{\$x\^2\$}', which would be
+parsed into an mlist containing a single element called an |ord_noad|.
+The |nucleus| of this noad is a representation of `\.x', the |subscr| is
+empty, and the |supscr| is a representation of `\.2'.
+
+The |nucleus|, |subscr|, and |supscr| fields are further broken into
+subfields. If |p| points to a noad, and if |q| is one of its principal
+fields (e.g., |q=subscr(p)|), there are several possibilities for the
+subfields, depending on the |math_type| of |q|.
+
+\yskip\hang|math_type(q)=math_char| means that |fam(q)| refers to one of
+the sixteen font families, and |character(q)| is the number of a character
+within a font of that family, as in a character node.
+
+\yskip\hang|math_type(q)=math_text_char| is similar, but the character is
+unsubscripted and unsuperscripted and it is followed immediately by another
+character from the same font. (This |math_type| setting appears only
+briefly during the processing; it is used to suppress unwanted italic
+corrections.)
+
+\yskip\hang|math_type(q)=empty| indicates a field with no value (the
+corresponding attribute of noad |p| is not present).
+
+\yskip\hang|math_type(q)=sub_box| means that |info(q)| points to a box
+node (either an |hlist_node| or a |vlist_node|) that should be used as the
+value of the field. The |shift_amount| in the subsidiary box node is the
+amount by which that box will be shifted downward.
+
+\yskip\hang|math_type(q)=sub_mlist| means that |info(q)| points to
+an mlist; the mlist must be converted to an hlist in order to obtain
+the value of this field.
+
+\yskip\noindent In the latter case, we might have |info(q)=null|. This
+is not the same as |math_type(q)=empty|; for example, `\.{\$P\_\{\}\$}'
+and `\.{\$P\$}' produce different results (the former will not have the
+``italic correction'' added to the width of |P|, but the ``script skip''
+will be added).
+
+The definitions of subfields given here are evidently wasteful of space,
+since a halfword is being used for the |math_type| although only three
+bits would be needed. However, there are hardly ever many noads present at
+once, since they are soon converted to nodes that take up even more space,
+so we can afford to represent them in whatever way simplifies the
+programming.
+
+@d noad_size=4 {number of words in a normal noad}
+@d nucleus(#)==#+1 {the |nucleus| field of a noad}
+@d supscr(#)==#+2 {the |supscr| field of a noad}
+@d subscr(#)==#+3 {the |subscr| field of a noad}
+@d math_type==link {a |halfword| in |mem|}
+@d fam==font {a |quarterword| in |mem|}
+@d math_char=1 {|math_type| when the attribute is simple}
+@d sub_box=2 {|math_type| when the attribute is a box}
+@d sub_mlist=3 {|math_type| when the attribute is a formula}
+@d math_text_char=4 {|math_type| when italic correction is dubious}
+
+@ Each portion of a formula is classified as Ord, Op, Bin, Rel, Ope,
+Clo, Pun, or Inn, for purposes of spacing and line breaking. An
+|ord_noad|, |op_noad|, |bin_noad|, |rel_noad|, |open_noad|, |close_noad|,
+|punct_noad|, or |inner_noad| is used to represent portions of the various
+types. For example, an `\.=' sign in a formula leads to the creation of a
+|rel_noad| whose |nucleus| field is a representation of an equals sign
+(usually |fam=0|, |character=@'75|). A formula preceded by \.{\\mathrel}
+also results in a |rel_noad|. When a |rel_noad| is followed by an
+|op_noad|, say, and possibly separated by one or more ordinary nodes (not
+noads), \TeX\ will insert a penalty node (with the current |rel_penalty|)
+just after the formula that corresponds to the |rel_noad|, unless there
+already was a penalty immediately following; and a ``thick space'' will be
+inserted just before the formula that corresponds to the |op_noad|.
+
+A noad of type |ord_noad|, |op_noad|, \dots, |inner_noad| usually
+has a |subtype=normal|. The only exception is that an |op_noad| might
+have |subtype=limits| or |no_limits|, if the normal positioning of
+limits has been overridden for this operator.
+
+@d ord_noad=unset_node+3 {|type| of a noad classified Ord}
+@d op_noad=ord_noad+1 {|type| of a noad classified Op}
+@d bin_noad=ord_noad+2 {|type| of a noad classified Bin}
+@d rel_noad=ord_noad+3 {|type| of a noad classified Rel}
+@d open_noad=ord_noad+4 {|type| of a noad classified Ope}
+@d close_noad=ord_noad+5 {|type| of a noad classified Clo}
+@d punct_noad=ord_noad+6 {|type| of a noad classified Pun}
+@d inner_noad=ord_noad+7 {|type| of a noad classified Inn}
+@d limits=1 {|subtype| of |op_noad| whose scripts are to be above, below}
+@d no_limits=2 {|subtype| of |op_noad| whose scripts are to be normal}
+
+@ A |radical_noad| is five words long; the fifth word is the |left_delimiter|
+field, which usually represents a square root sign.
+
+A |fraction_noad| is six words long; it has a |right_delimiter| field
+as well as a |left_delimiter|.
+
+Delimiter fields are of type |four_quarters|, and they have four subfields
+called |small_fam|, |small_char|, |large_fam|, |large_char|. These subfields
+represent variable-size delimiters by giving the ``small'' and ``large''
+starting characters, as explained in Chapter~17 of {\sl The \TeX book}.
+@:TeXbook}{\sl The \TeX book@>
+
+A |fraction_noad| is actually quite different from all other noads. Not
+only does it have six words, it has |thickness|, |denominator|, and
+|numerator| fields instead of |nucleus|, |subscr|, and |supscr|. The
+|thickness| is a scaled value that tells how thick to make a fraction
+rule; however, the special value |default_code| is used to stand for the
+|default_rule_thickness| of the current size. The |numerator| and
+|denominator| point to mlists that define a fraction; we always have
+$$\hbox{|math_type(numerator)=math_type(denominator)=sub_mlist|}.$$ The
+|left_delimiter| and |right_delimiter| fields specify delimiters that will
+be placed at the left and right of the fraction. In this way, a
+|fraction_noad| is able to represent all of \TeX's operators \.{\\over},
+\.{\\atop}, \.{\\above}, \.{\\overwithdelims}, \.{\\atopwithdelims}, and
+ \.{\\abovewithdelims}.
+
+@d left_delimiter(#)==#+4 {first delimiter field of a noad}
+@d right_delimiter(#)==#+5 {second delimiter field of a fraction noad}
+@d radical_noad=inner_noad+1 {|type| of a noad for square roots}
+@d radical_noad_size=5 {number of |mem| words in a radical noad}
+@d fraction_noad=radical_noad+1 {|type| of a noad for generalized fractions}
+@d fraction_noad_size=6 {number of |mem| words in a fraction noad}
+@d small_fam(#)==mem[#].qqqq.b0 {|fam| for ``small'' delimiter}
+@d small_char(#)==mem[#].qqqq.b1 {|character| for ``small'' delimiter}
+@d large_fam(#)==mem[#].qqqq.b2 {|fam| for ``large'' delimiter}
+@d large_char(#)==mem[#].qqqq.b3 {|character| for ``large'' delimiter}
+@d thickness==width {|thickness| field in a fraction noad}
+@d default_code==@'10000000000 {denotes |default_rule_thickness|}
+@d numerator==supscr {|numerator| field in a fraction noad}
+@d denominator==subscr {|denominator| field in a fraction noad}
+
+@ The global variable |empty_field| is set up for initialization of empty
+fields in new noads. Similarly, |null_delimiter| is for the initialization
+of delimiter fields.
+
+@<Glob...@>=
+@!empty_field:two_halves;
+@!null_delimiter:four_quarters;
+
+@ @<Set init...@>=
+empty_field.rh:=empty; empty_field.lh:=null;@/
+null_delimiter.b0:=0; null_delimiter.b1:=min_quarterword;@/
+null_delimiter.b2:=0; null_delimiter.b3:=min_quarterword;
+
+@ The |new_noad| function creates an |ord_noad| that is completely null.
+
+@p function new_noad:pointer;
+var p:pointer;
+begin p:=get_node(noad_size);
+type(p):=ord_noad; subtype(p):=normal;
+mem[nucleus(p)].hh:=empty_field;
+mem[subscr(p)].hh:=empty_field;
+mem[supscr(p)].hh:=empty_field;
+new_noad:=p;
+end;
+
+@ A few more kinds of noads will complete the set: An |under_noad| has its
+nucleus underlined; an |over_noad| has it overlined. An |accent_noad| places
+an accent over its nucleus; the accent character appears as
+|fam(accent_chr(p))| and |character(accent_chr(p))|. A |vcenter_noad|
+centers its nucleus vertically with respect to the axis of the formula;
+in such noads we always have |math_type(nucleus(p))=sub_box|.
+
+And finally, we have |left_noad| and |right_noad| types, to implement
+\TeX's \.{\\left} and \.{\\right}. The |nucleus| of such noads is
+replaced by a |delimiter| field; thus, for example, `\.{\\left(}' produces
+a |left_noad| such that |delimiter(p)| holds the family and character
+codes for all left parentheses. A |left_noad| never appears in an mlist
+except as the first element, and a |right_noad| never appears in an mlist
+except as the last element; furthermore, we either have both a |left_noad|
+and a |right_noad|, or neither one is present. The |subscr| and |supscr|
+fields are always |empty| in a |left_noad| and a |right_noad|.
+
+@d under_noad=fraction_noad+1 {|type| of a noad for underlining}
+@d over_noad=under_noad+1 {|type| of a noad for overlining}
+@d accent_noad=over_noad+1 {|type| of a noad for accented subformulas}
+@d accent_noad_size=5 {number of |mem| words in an accent noad}
+@d accent_chr(#)==#+4 {the |accent_chr| field of an accent noad}
+@d vcenter_noad=accent_noad+1 {|type| of a noad for \.{\\vcenter}}
+@d left_noad=vcenter_noad+1 {|type| of a noad for \.{\\left}}
+@d right_noad=left_noad+1 {|type| of a noad for \.{\\right}}
+@d delimiter==nucleus {|delimiter| field in left and right noads}
+@d scripts_allowed(#)==(type(#)>=ord_noad)and(type(#)<left_noad)
+
+@ Math formulas can also contain instructions like \.{\\textstyle} that
+override \TeX's normal style rules. A |style_node| is inserted into the
+data structure to record such instructions; it is three words long, so it
+is considered a node instead of a noad. The |subtype| is either |display_style|
+or |text_style| or |script_style| or |script_script_style|. The
+second and third words of a |style_node| are not used, but they are
+present because a |choice_node| is converted to a |style_node|.
+
+\TeX\ uses even numbers 0, 2, 4, 6 to encode the basic styles
+|display_style|, \dots, |script_script_style|, and adds~1 to get the
+``cramped'' versions of these styles. This gives a numerical order that
+is backwards from the convention of Appendix~G in {\sl The \TeX book\/};
+i.e., a smaller style has a larger numerical value.
+@:TeXbook}{\sl The \TeX book@>
+
+@d style_node=unset_node+1 {|type| of a style node}
+@d style_node_size=3 {number of words in a style node}
+@d display_style=0 {|subtype| for \.{\\displaystyle}}
+@d text_style=2 {|subtype| for \.{\\textstyle}}
+@d script_style=4 {|subtype| for \.{\\scriptstyle}}
+@d script_script_style=6 {|subtype| for \.{\\scriptscriptstyle}}
+@d cramped=1 {add this to an uncramped style if you want to cramp it}
+
+@p function new_style(@!s:small_number):pointer; {create a style node}
+var p:pointer; {the new node}
+begin p:=get_node(style_node_size); type(p):=style_node;
+subtype(p):=s; width(p):=0; depth(p):=0; {the |width| and |depth| are not used}
+new_style:=p;
+end;
+
+@ Finally, the \.{\\mathchoice} primitive creates a |choice_node|, which
+has special subfields |display_mlist|, |text_mlist|, |script_mlist|,
+and |script_script_mlist| pointing to the mlists for each style.
+
+@d choice_node=unset_node+2 {|type| of a choice node}
+@d display_mlist(#)==info(#+1) {mlist to be used in display style}
+@d text_mlist(#)==link(#+1) {mlist to be used in text style}
+@d script_mlist(#)==info(#+2) {mlist to be used in script style}
+@d script_script_mlist(#)==link(#+2) {mlist to be used in scriptscript style}
+
+@p function new_choice:pointer; {create a choice node}
+var p:pointer; {the new node}
+begin p:=get_node(style_node_size); type(p):=choice_node;
+subtype(p):=0; {the |subtype| is not used}
+display_mlist(p):=null; text_mlist(p):=null; script_mlist(p):=null;
+script_script_mlist(p):=null;
+new_choice:=p;
+end;
+
+@ Let's consider now the previously unwritten part of |show_node_list|
+that displays the things that can only be present in mlists; this
+program illustrates how to access the data structures just defined.
+
+In the context of the following program, |p| points to a node or noad that
+should be displayed, and the current string contains the ``recursion history''
+that leads to this point. The recursion history consists of a dot for each
+outer level in which |p| is subsidiary to some node, or in which |p| is
+subsidiary to the |nucleus| field of some noad; the dot is replaced by
+`\.\_' or `\.\^' or `\./' or `\.\\' if |p| is descended from the |subscr|
+or |supscr| or |denominator| or |numerator| fields of noads. For example,
+the current string would be `\.{.\^.\_/}' if |p| points to the |ord_noad| for
+|x| in the (ridiculous) formula
+`\.{\$\\sqrt\{a\^\{\\mathinner\{b\_\{c\\over x+y\}\}\}\}\$}'.
+
+@<Cases of |show_node_list| that arise...@>=
+style_node:print_style(subtype(p));
+choice_node:@<Display choice node |p|@>;
+ord_noad,op_noad,bin_noad,rel_noad,open_noad,close_noad,punct_noad,inner_noad,
+ radical_noad,over_noad,under_noad,vcenter_noad,accent_noad,
+ left_noad,right_noad:@<Display normal noad |p|@>;
+fraction_noad:@<Display fraction noad |p|@>;
+
+@ Here are some simple routines used in the display of noads.
+
+@<Declare procedures needed for displaying the elements of mlists@>=
+procedure print_fam_and_char(@!p:pointer); {prints family and character}
+begin print_esc("fam"); print_int(fam(p)); print_char(" ");
+print_ASCII(qo(character(p)));
+end;
+@#
+procedure print_delimiter(@!p:pointer); {prints a delimiter as 24-bit hex value}
+var a:integer; {accumulator}
+begin a:=small_fam(p)*256+qo(small_char(p));
+a:=a*@"1000+large_fam(p)*256+qo(large_char(p));
+if a<0 then print_int(a) {this should never happen}
+else print_hex(a);
+end;
+
+@ The next subroutine will descend to another level of recursion when a
+subsidiary mlist needs to be displayed. The parameter |c| indicates what
+character is to become part of the recursion history. An empty mlist is
+distinguished from a field with |math_type(p)=empty|, because these are
+not equivalent (as explained above).
+@^recursion@>
+
+@<Declare procedures needed for displaying...@>=
+procedure@?show_info; forward;@t\2@>@?{|show_node_list(info(temp_ptr))|}
+procedure print_subsidiary_data(@!p:pointer;@!c:ASCII_code);
+ {display a noad field}
+begin if cur_length>=depth_threshold then
+ begin if math_type(p)<>empty then print(" []");
+ end
+else begin append_char(c); {include |c| in the recursion history}
+ temp_ptr:=p; {prepare for |show_info| if recursion is needed}
+ case math_type(p) of
+ math_char: begin print_ln; print_current_string; print_fam_and_char(p);
+ end;
+ sub_box: show_info; {recursive call}
+ sub_mlist: if info(p)=null then
+ begin print_ln; print_current_string; print("{}");
+ end
+ else show_info; {recursive call}
+ othercases do_nothing {|empty|}
+ endcases;@/
+ flush_char; {remove |c| from the recursion history}
+ end;
+end;
+
+@ The inelegant introduction of |show_info| in the code above seems better
+than the alternative of using \PASCAL's strange |forward| declaration for a
+procedure with parameters. The \PASCAL\ convention about dropping parameters
+from a post-|forward| procedure is, frankly, so intolerable to the author
+of \TeX\ that he would rather stoop to communication via a global temporary
+variable. (A similar stoopidity occurred with respect to |hlist_out| and
+|vlist_out| above, and it will occur with respect to |mlist_to_hlist| below.)
+@^Knuth, Donald Ervin@>
+@:PASCAL}{\PASCAL@>
+
+@p procedure show_info; {the reader will kindly forgive this}
+begin show_node_list(info(temp_ptr));
+end;
+
+@ @<Declare procedures needed for displaying...@>=
+procedure print_style(@!c:integer);
+begin case c div 2 of
+0: print_esc("displaystyle"); {|display_style=0|}
+1: print_esc("textstyle"); {|text_style=2|}
+2: print_esc("scriptstyle"); {|script_style=4|}
+3: print_esc("scriptscriptstyle"); {|script_script_style=6|}
+othercases print("Unknown style!")
+endcases;
+end;
+
+@ @<Display choice node |p|@>=
+begin print_esc("mathchoice");
+append_char("D"); show_node_list(display_mlist(p)); flush_char;
+append_char("T"); show_node_list(text_mlist(p)); flush_char;
+append_char("S"); show_node_list(script_mlist(p)); flush_char;
+append_char("s"); show_node_list(script_script_mlist(p)); flush_char;
+end
+
+@ @<Display normal noad |p|@>=
+begin case type(p) of
+ord_noad: print_esc("mathord");
+op_noad: print_esc("mathop");
+bin_noad: print_esc("mathbin");
+rel_noad: print_esc("mathrel");
+open_noad: print_esc("mathopen");
+close_noad: print_esc("mathclose");
+punct_noad: print_esc("mathpunct");
+inner_noad: print_esc("mathinner");
+over_noad: print_esc("overline");
+under_noad: print_esc("underline");
+vcenter_noad: print_esc("vcenter");
+radical_noad: begin print_esc("radical"); print_delimiter(left_delimiter(p));
+ end;
+accent_noad: begin print_esc("accent"); print_fam_and_char(accent_chr(p));
+ end;
+left_noad: begin print_esc("left"); print_delimiter(nucleus(p));
+ end;
+right_noad: begin print_esc("right"); print_delimiter(nucleus(p));
+ end;
+end;
+if subtype(p)<>normal then
+ if subtype(p)=limits then print_esc("limits")
+ else print_esc("nolimits");
+if type(p)<left_noad then print_subsidiary_data(nucleus(p),".");
+print_subsidiary_data(supscr(p),"^");
+print_subsidiary_data(subscr(p),"_");
+end
+
+@ @<Display fraction noad |p|@>=
+begin print_esc("fraction, thickness ");
+if thickness(p)=default_code then print("= default")
+else print_scaled(thickness(p));
+if (small_fam(left_delimiter(p))<>0)or@+
+ (small_char(left_delimiter(p))<>min_quarterword)or@|
+ (large_fam(left_delimiter(p))<>0)or@|
+ (large_char(left_delimiter(p))<>min_quarterword) then
+ begin print(", left-delimiter "); print_delimiter(left_delimiter(p));
+ end;
+if (small_fam(right_delimiter(p))<>0)or@|
+ (small_char(right_delimiter(p))<>min_quarterword)or@|
+ (large_fam(right_delimiter(p))<>0)or@|
+ (large_char(right_delimiter(p))<>min_quarterword) then
+ begin print(", right-delimiter "); print_delimiter(right_delimiter(p));
+ end;
+print_subsidiary_data(numerator(p),"\");
+print_subsidiary_data(denominator(p),"/");
+end
+
+@ That which can be displayed can also be destroyed.
+
+@<Cases of |flush_node_list| that arise...@>=
+style_node: begin free_node(p,style_node_size); goto done;
+ end;
+choice_node:begin flush_node_list(display_mlist(p));
+ flush_node_list(text_mlist(p));
+ flush_node_list(script_mlist(p));
+ flush_node_list(script_script_mlist(p));
+ free_node(p,style_node_size); goto done;
+ end;
+ord_noad,op_noad,bin_noad,rel_noad,open_noad,close_noad,punct_noad,inner_noad,
+ radical_noad,over_noad,under_noad,vcenter_noad,accent_noad:@t@>@;@/
+ begin if math_type(nucleus(p))>=sub_box then
+ flush_node_list(info(nucleus(p)));
+ if math_type(supscr(p))>=sub_box then
+ flush_node_list(info(supscr(p)));
+ if math_type(subscr(p))>=sub_box then
+ flush_node_list(info(subscr(p)));
+ if type(p)=radical_noad then free_node(p,radical_noad_size)
+ else if type(p)=accent_noad then free_node(p,accent_noad_size)
+ else free_node(p,noad_size);
+ goto done;
+ end;
+left_noad,right_noad: begin free_node(p,noad_size); goto done;
+ end;
+fraction_noad: begin flush_node_list(info(numerator(p)));
+ flush_node_list(info(denominator(p)));
+ free_node(p,fraction_noad_size); goto done;
+ end;
+
+@* \[35] Subroutines for math mode.
+In order to convert mlists to hlists, i.e., noads to nodes, we need several
+subroutines that are conveniently dealt with now.
+
+Let us first introduce the macros that make it easy to get at the parameters and
+other font information. A size code, which is a multiple of 16, is added to a
+family number to get an index into the table of internal font numbers
+for each combination of family and size. (Be alert: Size codes get
+larger as the type gets smaller.)
+
+@d text_size=0 {size code for the largest size in a family}
+@d script_size=16 {size code for the medium size in a family}
+@d script_script_size=32 {size code for the smallest size in a family}
+
+@<Basic printing procedures@>=
+procedure print_size(@!s:integer);
+begin if s=0 then print_esc("textfont")
+else if s=script_size then print_esc("scriptfont")
+else print_esc("scriptscriptfont");
+end;
+
+@ Before an mlist is converted to an hlist, \TeX\ makes sure that
+the fonts in family~2 have enough parameters to be math-symbol
+fonts, and that the fonts in family~3 have enough parameters to be
+math-extension fonts. The math-symbol parameters are referred to by using the
+following macros, which take a size code as their parameter; for example,
+|num1(cur_size)| gives the value of the |num1| parameter for the current size.
+@^parameters for symbols@>
+@^font parameters@>
+
+@d mathsy_end(#)==fam_fnt(2+#)]].sc
+@d mathsy(#)==font_info[#+param_base[mathsy_end
+@d math_x_height==mathsy(5) {height of `\.x'}
+@d math_quad==mathsy(6) {\.{18mu}}
+@d num1==mathsy(8) {numerator shift-up in display styles}
+@d num2==mathsy(9) {numerator shift-up in non-display, non-\.{\\atop}}
+@d num3==mathsy(10) {numerator shift-up in non-display \.{\\atop}}
+@d denom1==mathsy(11) {denominator shift-down in display styles}
+@d denom2==mathsy(12) {denominator shift-down in non-display styles}
+@d sup1==mathsy(13) {superscript shift-up in uncramped display style}
+@d sup2==mathsy(14) {superscript shift-up in uncramped non-display}
+@d sup3==mathsy(15) {superscript shift-up in cramped styles}
+@d sub1==mathsy(16) {subscript shift-down if superscript is absent}
+@d sub2==mathsy(17) {subscript shift-down if superscript is present}
+@d sup_drop==mathsy(18) {superscript baseline below top of large box}
+@d sub_drop==mathsy(19) {subscript baseline below bottom of large box}
+@d delim1==mathsy(20) {size of \.{\\atopwithdelims} delimiters
+ in display styles}
+@d delim2==mathsy(21) {size of \.{\\atopwithdelims} delimiters in non-displays}
+@d axis_height==mathsy(22) {height of fraction lines above the baseline}
+@d total_mathsy_params=22
+
+@ The math-extension parameters have similar macros, but the size code is
+omitted (since it is always |cur_size| when we refer to such parameters).
+@^parameters for symbols@>
+@^font parameters@>
+
+@d mathex(#)==font_info[#+param_base[fam_fnt(3+cur_size)]].sc
+@d default_rule_thickness==mathex(8) {thickness of \.{\\over} bars}
+@d big_op_spacing1==mathex(9) {minimum clearance above a displayed op}
+@d big_op_spacing2==mathex(10) {minimum clearance below a displayed op}
+@d big_op_spacing3==mathex(11) {minimum baselineskip above displayed op}
+@d big_op_spacing4==mathex(12) {minimum baselineskip below displayed op}
+@d big_op_spacing5==mathex(13) {padding above and below displayed limits}
+@d total_mathex_params=13
+
+@ We also need to compute the change in style between mlists and their
+subsidiaries. The following macros define the subsidiary style for
+an overlined nucleus (|cramped_style|), for a subscript or a superscript
+(|sub_style| or |sup_style|), or for a numerator or denominator (|num_style|
+or |denom_style|).
+
+@d cramped_style(#)==2*(# div 2)+cramped {cramp the style}
+@d sub_style(#)==2*(# div 4)+script_style+cramped {smaller and cramped}
+@d sup_style(#)==2*(# div 4)+script_style+(# mod 2) {smaller}
+@d num_style(#)==#+2-2*(# div 6) {smaller unless already script-script}
+@d denom_style(#)==2*(# div 2)+cramped+2-2*(# div 6) {smaller, cramped}
+
+@ When the style changes, the following piece of program computes associated
+information:
+
+@<Set up the values of |cur_size| and |cur_mu|, based on |cur_style|@>=
+begin if cur_style<script_style then cur_size:=text_size
+else cur_size:=16*((cur_style-text_style) div 2);
+cur_mu:=x_over_n(math_quad(cur_size),18);
+end
+
+@ Here is a function that returns a pointer to a rule node having a given
+thickness |t|. The rule will extend horizontally to the boundary of the vlist
+that eventually contains it.
+
+@p function fraction_rule(@!t:scaled):pointer;
+ {construct the bar for a fraction}
+var p:pointer; {the new node}
+begin p:=new_rule; height(p):=t; depth(p):=0; fraction_rule:=p;
+end;
+
+@ The |overbar| function returns a pointer to a vlist box that consists of
+a given box |b|, above which has been placed a kern of height |k| under a
+fraction rule of thickness |t| under additional space of height |t|.
+
+@p function overbar(@!b:pointer;@!k,@!t:scaled):pointer;
+var p,@!q:pointer; {nodes being constructed}
+begin p:=new_kern(k); link(p):=b; q:=fraction_rule(t); link(q):=p;
+p:=new_kern(t); link(p):=q; overbar:=vpack(p,natural);
+end;
+
+@ The |var_delimiter| function, which finds or constructs a sufficiently
+large delimiter, is the most interesting of the auxiliary functions that
+currently concern us. Given a pointer |d| to a delimiter field in some noad,
+together with a size code |s| and a vertical distance |v|, this function
+returns a pointer to a box that contains the smallest variant of |d| whose
+height plus depth is |v| or more. (And if no variant is large enough, it
+returns the largest available variant.) In particular, this routine will
+construct arbitrarily large delimiters from extensible components, if
+|d| leads to such characters.
+
+The value returned is a box whose |shift_amount| has been set so that
+the box is vertically centered with respect to the axis in the given size.
+If a built-up symbol is returned, the height of the box before shifting
+will be the height of its topmost component.
+
+@p@t\4@>@<Declare subprocedures for |var_delimiter|@>
+function var_delimiter(@!d:pointer;@!s:small_number;@!v:scaled):pointer;
+label found,continue;
+var b:pointer; {the box that will be constructed}
+@!f,@!g: internal_font_number; {best-so-far and tentative font codes}
+@!c,@!x,@!y: quarterword; {best-so-far and tentative character codes}
+@!m,@!n: integer; {the number of extensible pieces}
+@!u: scaled; {height-plus-depth of a tentative character}
+@!w: scaled; {largest height-plus-depth so far}
+@!q: four_quarters; {character info}
+@!hd: eight_bits; {height-depth byte}
+@!r: four_quarters; {extensible pieces}
+@!z: small_number; {runs through font family members}
+@!large_attempt: boolean; {are we trying the ``large'' variant?}
+begin f:=null_font; w:=0; large_attempt:=false;
+z:=small_fam(d); x:=small_char(d);
+loop@+ begin @<Look at the variants of |(z,x)|; set |f| and |c| whenever
+ a better character is found; |goto found| as soon as a
+ large enough variant is encountered@>;
+ if large_attempt then goto found; {there were none large enough}
+ large_attempt:=true; z:=large_fam(d); x:=large_char(d);
+ end;
+found: if f<>null_font then
+ @<Make variable |b| point to a box for |(f,c)|@>
+else begin b:=new_null_box;
+ width(b):=null_delimiter_space; {use this width if no delimiter was found}
+ end;
+shift_amount(b):=half(height(b)-depth(b)) - axis_height(s);
+var_delimiter:=b;
+end;
+
+@ The search process is complicated slightly by the facts that some of the
+characters might not be present in some of the fonts, and they might not
+be probed in increasing order of height.
+
+@<Look at the variants of |(z,x)|; set |f| and |c|...@>=
+if (z<>0)or(x<>min_quarterword) then
+ begin z:=z+s+16;
+ repeat z:=z-16; g:=fam_fnt(z);
+ if g<>null_font then
+ @<Look at the list of characters starting with |x| in
+ font |g|; set |f| and |c| whenever
+ a better character is found; |goto found| as soon as a
+ large enough variant is encountered@>;
+ until z<16;
+ end
+
+@ @<Look at the list of characters starting with |x|...@>=
+begin y:=x;
+if (qo(y)>=font_bc[g])and(qo(y)<=font_ec[g]) then
+ begin continue: q:=char_info(g)(y);
+ if char_exists(q) then
+ begin if char_tag(q)=ext_tag then
+ begin f:=g; c:=y; goto found;
+ end;
+ hd:=height_depth(q);
+ u:=char_height(g)(hd)+char_depth(g)(hd);
+ if u>w then
+ begin f:=g; c:=y; w:=u;
+ if u>=v then goto found;
+ end;
+ if char_tag(q)=list_tag then
+ begin y:=rem_byte(q); goto continue;
+ end;
+ end;
+ end;
+end
+
+@ Here is a subroutine that creates a new box, whose list contains a
+single character, and whose width includes the italic correction for
+that character. The height or depth of the box will be negative, if
+the height or depth of the character is negative; thus, this routine
+may deliver a slightly different result than |hpack| would produce.
+
+@<Declare subprocedures for |var_delimiter|@>=
+function char_box(@!f:internal_font_number;@!c:quarterword):pointer;
+var q:four_quarters;
+@!hd:eight_bits; {|height_depth| byte}
+@!b,@!p:pointer; {the new box and its character node}
+begin q:=char_info(f)(c); hd:=height_depth(q);
+b:=new_null_box; width(b):=char_width(f)(q)+char_italic(f)(q);
+height(b):=char_height(f)(hd); depth(b):=char_depth(f)(hd);
+p:=get_avail; character(p):=c; font(p):=f; list_ptr(b):=p; char_box:=b;
+end;
+
+@ When the following code is executed, |char_tag(q)| will be equal to
+|ext_tag| if and only if a built-up symbol is supposed to be returned.
+
+@<Make variable |b| point to a box for |(f,c)|@>=
+if char_tag(q)=ext_tag then
+ @<Construct an extensible character in a new box |b|,
+ using recipe |rem_byte(q)| and font |f|@>
+else b:=char_box(f,c)
+
+@ When we build an extensible character, it's handy to have the
+following subroutine, which puts a given character on top
+of the characters already in box |b|:
+
+@<Declare subprocedures for |var_delimiter|@>=
+procedure stack_into_box(@!b:pointer;@!f:internal_font_number;
+ @!c:quarterword);
+var p:pointer; {new node placed into |b|}
+begin p:=char_box(f,c); link(p):=list_ptr(b); list_ptr(b):=p;
+height(b):=height(p);
+end;
+
+@ Another handy subroutine computes the height plus depth of
+a given character:
+
+@<Declare subprocedures for |var_delimiter|@>=
+function height_plus_depth(@!f:internal_font_number;@!c:quarterword):scaled;
+var q:four_quarters;
+@!hd:eight_bits; {|height_depth| byte}
+begin q:=char_info(f)(c); hd:=height_depth(q);
+height_plus_depth:=char_height(f)(hd)+char_depth(f)(hd);
+end;
+
+@ @<Construct an extensible...@>=
+begin b:=new_null_box;
+type(b):=vlist_node;
+r:=font_info[exten_base[f]+rem_byte(q)].qqqq;@/
+@<Compute the minimum suitable height, |w|, and the corresponding
+ number of extension steps, |n|; also set |width(b)|@>;
+c:=ext_bot(r);
+if c<>min_quarterword then stack_into_box(b,f,c);
+c:=ext_rep(r);
+for m:=1 to n do stack_into_box(b,f,c);
+c:=ext_mid(r);
+if c<>min_quarterword then
+ begin stack_into_box(b,f,c); c:=ext_rep(r);
+ for m:=1 to n do stack_into_box(b,f,c);
+ end;
+c:=ext_top(r);
+if c<>min_quarterword then stack_into_box(b,f,c);
+depth(b):=w-height(b);
+end
+
+@ The width of an extensible character is the width of the repeatable
+module. If this module does not have positive height plus depth,
+we don't use any copies of it, otherwise we use as few as possible
+(in groups of two if there is a middle part).
+
+@<Compute the minimum suitable height, |w|, and...@>=
+c:=ext_rep(r); u:=height_plus_depth(f,c);
+w:=0; q:=char_info(f)(c); width(b):=char_width(f)(q)+char_italic(f)(q);@/
+c:=ext_bot(r);@+if c<>min_quarterword then w:=w+height_plus_depth(f,c);
+c:=ext_mid(r);@+if c<>min_quarterword then w:=w+height_plus_depth(f,c);
+c:=ext_top(r);@+if c<>min_quarterword then w:=w+height_plus_depth(f,c);
+n:=0;
+if u>0 then while w<v do
+ begin w:=w+u; incr(n);
+ if ext_mid(r)<>min_quarterword then w:=w+u;
+ end
+
+@ The next subroutine is much simpler; it is used for numerators and
+denominators of fractions as well as for displayed operators and
+their limits above and below. It takes a given box~|b| and
+changes it so that the new box is centered in a box of width~|w|.
+The centering is done by putting \.{\\hss} glue at the left and right
+of the list inside |b|, then packaging the new box; thus, the
+actual box might not really be centered, if it already contains
+infinite glue.
+
+The given box might contain a single character whose italic correction
+has been added to the width of the box; in this case a compensating
+kern is inserted.
+
+@p function rebox(@!b:pointer;@!w:scaled):pointer;
+var p:pointer; {temporary register for list manipulation}
+@!f:internal_font_number; {font in a one-character box}
+@!v:scaled; {width of a character without italic correction}
+begin if (width(b)<>w)and(list_ptr(b)<>null) then
+ begin if type(b)=vlist_node then b:=hpack(b,natural);
+ p:=list_ptr(b);
+ if (is_char_node(p))and(link(p)=null) then
+ begin f:=font(p); v:=char_width(f)(char_info(f)(character(p)));
+ if v<>width(b) then link(p):=new_kern(width(b)-v);
+ end;
+ free_node(b,box_node_size);
+ b:=new_glue(ss_glue); link(b):=p;
+ while link(p)<>null do p:=link(p);
+ link(p):=new_glue(ss_glue);
+ rebox:=hpack(b,w,exactly);
+ end
+else begin width(b):=w; rebox:=b;
+ end;
+end;
+
+@ Here is a subroutine that creates a new glue specification from another
+one that is expressed in `\.{mu}', given the value of the math unit.
+
+@d mu_mult(#)==nx_plus_y(n,#,xn_over_d(#,f,@'200000))
+
+@p function math_glue(@!g:pointer;@!m:scaled):pointer;
+var p:pointer; {the new glue specification}
+@!n:integer; {integer part of |m|}
+@!f:scaled; {fraction part of |m|}
+begin n:=x_over_n(m,@'200000); f:=remainder;@/
+if f<0 then
+ begin decr(n); f:=f+@'200000;
+ end;
+p:=get_node(glue_spec_size);
+width(p):=mu_mult(width(g)); {convert \.{mu} to \.{pt}}
+stretch_order(p):=stretch_order(g);
+if stretch_order(p)=normal then stretch(p):=mu_mult(stretch(g))
+else stretch(p):=stretch(g);
+shrink_order(p):=shrink_order(g);
+if shrink_order(p)=normal then shrink(p):=mu_mult(shrink(g))
+else shrink(p):=shrink(g);
+math_glue:=p;
+end;
+
+@ The |math_kern| subroutine removes |mu_glue| from a kern node, given
+the value of the math unit.
+
+@p procedure math_kern(@!p:pointer;@!m:scaled);
+var @!n:integer; {integer part of |m|}
+@!f:scaled; {fraction part of |m|}
+begin if subtype(p)=mu_glue then
+ begin n:=x_over_n(m,@'200000); f:=remainder;@/
+ if f<0 then
+ begin decr(n); f:=f+@'200000;
+ end;
+ width(p):=mu_mult(width(p)); subtype(p):=explicit;
+ end;
+end;
+
+@ Sometimes it is necessary to destroy an mlist. The following
+subroutine empties the current list, assuming that |abs(mode)=mmode|.
+
+@p procedure flush_math;
+begin flush_node_list(link(head)); flush_node_list(incompleat_noad);
+link(head):=null; tail:=head; incompleat_noad:=null;
+end;
+
+@* \[36] Typesetting math formulas.
+\TeX's most important routine for dealing with formulas is called
+|mlist_to_hlist|. After a formula has been scanned and represented as an
+mlist, this routine converts it to an hlist that can be placed into a box
+or incorporated into the text of a paragraph. There are three implicit
+parameters, passed in global variables: |cur_mlist| points to the first
+node or noad in the given mlist (and it might be |null|); |cur_style| is a
+style code; and |mlist_penalties| is |true| if penalty nodes for potential
+line breaks are to be inserted into the resulting hlist. After
+|mlist_to_hlist| has acted, |link(temp_head)| points to the translated hlist.
+
+Since mlists can be inside mlists, the procedure is recursive. And since this
+is not part of \TeX's inner loop, the program has been written in a manner
+that stresses compactness over efficiency.
+@^recursion@>
+
+@<Glob...@>=
+@!cur_mlist:pointer; {beginning of mlist to be translated}
+@!cur_style:small_number; {style code at current place in the list}
+@!cur_size:small_number; {size code corresponding to |cur_style|}
+@!cur_mu:scaled; {the math unit width corresponding to |cur_size|}
+@!mlist_penalties:boolean; {should |mlist_to_hlist| insert penalties?}
+
+@ The recursion in |mlist_to_hlist| is due primarily to a subroutine
+called |clean_box| that puts a given noad field into a box using a given
+math style; |mlist_to_hlist| can call |clean_box|, which can call
+|mlist_to_hlist|.
+@^recursion@>
+
+The box returned by |clean_box| is ``clean'' in the
+sense that its |shift_amount| is zero.
+
+@p procedure@?mlist_to_hlist; forward;@t\2@>@/
+function clean_box(@!p:pointer;@!s:small_number):pointer;
+label found;
+var q:pointer; {beginning of a list to be boxed}
+@!save_style:small_number; {|cur_style| to be restored}
+@!x:pointer; {box to be returned}
+@!r:pointer; {temporary pointer}
+begin case math_type(p) of
+math_char: begin cur_mlist:=new_noad; mem[nucleus(cur_mlist)]:=mem[p];
+ end;
+sub_box: begin q:=info(p); goto found;
+ end;
+sub_mlist: cur_mlist:=info(p);
+othercases begin q:=new_null_box; goto found;
+ end
+endcases;@/
+save_style:=cur_style; cur_style:=s; mlist_penalties:=false;@/
+mlist_to_hlist; q:=link(temp_head); {recursive call}
+cur_style:=save_style; {restore the style}
+@<Set up the values of |cur_size| and |cur_mu|, based on |cur_style|@>;
+found: if is_char_node(q)or(q=null) then x:=hpack(q,natural)
+ else if (link(q)=null)and(type(q)<=vlist_node)and(shift_amount(q)=0) then
+ x:=q {it's already clean}
+ else x:=hpack(q,natural);
+@<Simplify a trivial box@>;
+clean_box:=x;
+end;
+
+@ Here we save memory space in a common case.
+
+@<Simplify a trivial box@>=
+q:=list_ptr(x);
+if is_char_node(q) then
+ begin r:=link(q);
+ if r<>null then if link(r)=null then if not is_char_node(r) then
+ if type(r)=kern_node then {unneeded italic correction}
+ begin free_node(r,small_node_size); link(q):=null;
+ end;
+ end
+
+@ It is convenient to have a procedure that converts a |math_char|
+field to an ``unpacked'' form. The |fetch| routine sets |cur_f|, |cur_c|,
+and |cur_i| to the font code, character code, and character information bytes of
+a given noad field. It also takes care of issuing error messages for
+nonexistent characters; in such cases, |char_exists(cur_i)| will be |false|
+after |fetch| has acted, and the field will also have been reset to |empty|.
+
+@p procedure fetch(@!a:pointer); {unpack the |math_char| field |a|}
+begin cur_c:=character(a); cur_f:=fam_fnt(fam(a)+cur_size);
+if cur_f=null_font then
+ @<Complain about an undefined family and set |cur_i| null@>
+else begin if (qo(cur_c)>=font_bc[cur_f])and(qo(cur_c)<=font_ec[cur_f]) then
+ cur_i:=char_info(cur_f)(cur_c)
+ else cur_i:=null_character;
+ if not(char_exists(cur_i)) then
+ begin char_warning(cur_f,qo(cur_c));
+ math_type(a):=empty;
+ end;
+ end;
+end;
+
+@ @<Complain about an undefined family...@>=
+begin print_err(""); print_size(cur_size); print_char(" ");
+print_int(fam(a)); print(" is undefined (character ");
+print_ASCII(qo(cur_c)); print_char(")");
+help4("Somewhere in the math formula just ended, you used the")@/
+("stated character from an undefined font family. For example,")@/
+("plain TeX doesn't allow \it or \sl in subscripts. Proceed,")@/
+("and I'll try to forget that I needed that character.");
+error; cur_i:=null_character; math_type(a):=empty;
+end
+
+@ The outputs of |fetch| are placed in global variables.
+
+@<Glob...@>=
+@!cur_f:internal_font_number; {the |font| field of a |math_char|}
+@!cur_c:quarterword; {the |character| field of a |math_char|}
+@!cur_i:four_quarters; {the |char_info| of a |math_char|,
+ or a lig/kern instruction}
+
+@ We need to do a lot of different things, so |mlist_to_hlist| makes two
+passes over the given mlist.
+
+The first pass does most of the processing: It removes ``mu'' spacing from
+glue, it recursively evaluates all subsidiary mlists so that only the
+top-level mlist remains to be handled, it puts fractions and square roots
+and such things into boxes, it attaches subscripts and superscripts, and
+it computes the overall height and depth of the top-level mlist so that
+the size of delimiters for a |left_noad| and a |right_noad| will be known.
+The hlist resulting from each noad is recorded in that noad's |new_hlist|
+field, an integer field that replaces the |nucleus| or |thickness|.
+@^recursion@>
+
+The second pass eliminates all noads and inserts the correct glue and
+penalties between nodes.
+
+@d new_hlist(#)==mem[nucleus(#)].int {the translation of an mlist}
+
+@ Here is the overall plan of |mlist_to_hlist|, and the list of its
+local variables.
+
+@d done_with_noad=80 {go here when a noad has been fully translated}
+@d done_with_node=81 {go here when a node has been fully converted}
+@d check_dimensions=82 {go here to update |max_h| and |max_d|}
+@d delete_q=83 {go here to delete |q| and move to the next node}
+
+@p@t\4@>@<Declare math construction procedures@>
+procedure mlist_to_hlist;
+label reswitch, check_dimensions, done_with_noad, done_with_node, delete_q,
+ done;
+var mlist:pointer; {beginning of the given list}
+@!penalties:boolean; {should penalty nodes be inserted?}
+@!style:small_number; {the given style}
+@!save_style:small_number; {holds |cur_style| during recursion}
+@!q:pointer; {runs through the mlist}
+@!r:pointer; {the most recent noad preceding |q|}
+@!r_type:small_number; {the |type| of noad |r|, or |op_noad| if |r=null|}
+@!t:small_number; {the effective |type| of noad |q| during the second pass}
+@!p,@!x,@!y,@!z: pointer; {temporary registers for list construction}
+@!pen:integer; {a penalty to be inserted}
+@!s:small_number; {the size of a noad to be deleted}
+@!max_h,@!max_d:scaled; {maximum height and depth of the list translated so far}
+@!delta:scaled; {offset between subscript and superscript}
+begin mlist:=cur_mlist; penalties:=mlist_penalties;
+style:=cur_style; {tuck global parameters away as local variables}
+q:=mlist; r:=null; r_type:=op_noad; max_h:=0; max_d:=0;
+@<Set up the values of |cur_size| and |cur_mu|, based on |cur_style|@>;
+while q<>null do @<Process node-or-noad |q| as much as possible in preparation
+ for the second pass of |mlist_to_hlist|, then move to the next
+ item in the mlist@>;
+@<Convert \(a)a final |bin_noad| to an |ord_noad|@>;
+@<Make a second pass over the mlist, removing all noads and inserting the
+ proper spacing and penalties@>;
+end;
+
+@ We use the fact that no character nodes appear in an mlist, hence
+the field |type(q)| is always present.
+
+@<Process node-or-noad...@>=
+begin @<Do first-pass processing based on |type(q)|; |goto done_with_noad|
+ if a noad has been fully processed, |goto check_dimensions| if it
+ has been translated into |new_hlist(q)|, or |goto done_with_node|
+ if a node has been fully processed@>;
+check_dimensions: z:=hpack(new_hlist(q),natural);
+if height(z)>max_h then max_h:=height(z);
+if depth(z)>max_d then max_d:=depth(z);
+free_node(z,box_node_size);
+done_with_noad: r:=q; r_type:=type(r);
+done_with_node: q:=link(q);
+end
+
+@ One of the things we must do on the first pass is change a |bin_noad| to
+an |ord_noad| if the |bin_noad| is not in the context of a binary operator.
+The values of |r| and |r_type| make this fairly easy.
+
+@<Do first-pass processing...@>=
+reswitch: delta:=0;
+case type(q) of
+bin_noad: case r_type of
+ bin_noad,op_noad,rel_noad,open_noad,punct_noad,left_noad:
+ begin type(q):=ord_noad; goto reswitch;
+ end;
+ othercases do_nothing
+ endcases;
+rel_noad,close_noad,punct_noad,right_noad: begin@t@>@;@/
+ @<Convert \(a)a final |bin_noad| to an |ord_noad|@>;
+ if type(q)=right_noad then goto done_with_noad;
+ end;
+@t\4@>@<Cases for noads that can follow a |bin_noad|@>@;
+@t\4@>@<Cases for nodes that can appear in an mlist, after which we
+ |goto done_with_node|@>@;
+othercases confusion("mlist1")
+@:this can't happen mlist1}{\quad mlist1@>
+endcases;@/
+@<Convert \(n)|nucleus(q)| to an hlist and attach the sub/superscripts@>
+
+@ @<Convert \(a)a final |bin_noad| to an |ord_noad|@>=
+if r_type=bin_noad then type(r):=ord_noad
+
+@ @<Cases for nodes that can appear in an mlist...@>=
+style_node: begin cur_style:=subtype(q);
+ @<Set up the values of |cur_size| and |cur_mu|, based on |cur_style|@>;
+ goto done_with_node;
+ end;
+choice_node: @<Change this node to a style node followed by the correct choice,
+ then |goto done_with_node|@>;
+ins_node,mark_node,adjust_node,
+ whatsit_node,penalty_node,disc_node: goto done_with_node;
+rule_node: begin if height(q)>max_h then max_h:=height(q);
+ if depth(q)>max_d then max_d:=depth(q); goto done_with_node;
+ end;
+glue_node: begin @<Convert \(m)math glue to ordinary glue@>;
+ goto done_with_node;
+ end;
+kern_node: begin math_kern(q,cur_mu); goto done_with_node;
+ end;
+
+@ @d choose_mlist(#)==begin p:=#(q); #(q):=null;@+end
+
+@<Change this node to a style node...@>=
+begin case cur_style div 2 of
+0: choose_mlist(display_mlist); {|display_style=0|}
+1: choose_mlist(text_mlist); {|text_style=2|}
+2: choose_mlist(script_mlist); {|script_style=4|}
+3: choose_mlist(script_script_mlist); {|script_script_style=6|}
+end; {there are no other cases}
+flush_node_list(display_mlist(q));
+flush_node_list(text_mlist(q));
+flush_node_list(script_mlist(q));
+flush_node_list(script_script_mlist(q));@/
+type(q):=style_node; subtype(q):=cur_style; width(q):=0; depth(q):=0;
+if p<>null then
+ begin z:=link(q); link(q):=p;
+ while link(p)<>null do p:=link(p);
+ link(p):=z;
+ end;
+goto done_with_node;
+end
+
+@ Conditional math glue (`\.{\\nonscript}') results in a |glue_node|
+pointing to |zero_glue|, with |subtype(q)=cond_math_glue|; in such a case
+the node following will be eliminated if it is a glue or kern node and if the
+current size is different from |text_size|. Unconditional math glue
+(`\.{\\muskip}') is converted to normal glue by multiplying the dimensions
+by |cur_mu|.
+@!@:non_script_}{\.{\\nonscript} primitive@>
+
+@<Convert \(m)math glue to ordinary glue@>=
+if subtype(q)=mu_glue then
+ begin x:=glue_ptr(q);
+ y:=math_glue(x,cur_mu); delete_glue_ref(x); glue_ptr(q):=y;
+ subtype(q):=normal;
+ end
+else if (cur_size<>text_size)and(subtype(q)=cond_math_glue) then
+ begin p:=link(q);
+ if p<>null then if (type(p)=glue_node)or(type(p)=kern_node) then
+ begin link(q):=link(p); link(p):=null; flush_node_list(p);
+ end;
+ end
+
+@ @<Cases for noads that can follow a |bin_noad|@>=
+left_noad: goto done_with_noad;
+fraction_noad: begin make_fraction(q); goto check_dimensions;
+ end;
+op_noad: begin delta:=make_op(q);
+ if subtype(q)=limits then goto check_dimensions;
+ end;
+ord_noad: make_ord(q);
+open_noad,inner_noad: do_nothing;
+radical_noad: make_radical(q);
+over_noad: make_over(q);
+under_noad: make_under(q);
+accent_noad: make_math_accent(q);
+vcenter_noad: make_vcenter(q);
+
+@ Most of the actual construction work of |mlist_to_hlist| is done
+by procedures with names
+like |make_fraction|, |make_radical|, etc. To illustrate
+the general setup of such procedures, let's begin with a couple of
+simple ones.
+
+@<Declare math...@>=
+procedure make_over(@!q:pointer);
+begin info(nucleus(q)):=@|
+ overbar(clean_box(nucleus(q),cramped_style(cur_style)),@|
+ 3*default_rule_thickness,default_rule_thickness);
+math_type(nucleus(q)):=sub_box;
+end;
+
+@ @<Declare math...@>=
+procedure make_under(@!q:pointer);
+var p,@!x,@!y: pointer; {temporary registers for box construction}
+@!delta:scaled; {overall height plus depth}
+begin x:=clean_box(nucleus(q),cur_style);
+p:=new_kern(3*default_rule_thickness); link(x):=p;
+link(p):=fraction_rule(default_rule_thickness);
+y:=vpack(x,natural);
+delta:=height(y)+depth(y)+default_rule_thickness;
+height(y):=height(x); depth(y):=delta-height(y);
+info(nucleus(q)):=y; math_type(nucleus(q)):=sub_box;
+end;
+
+@ @<Declare math...@>=
+procedure make_vcenter(@!q:pointer);
+var v:pointer; {the box that should be centered vertically}
+@!delta:scaled; {its height plus depth}
+begin v:=info(nucleus(q));
+if type(v)<>vlist_node then confusion("vcenter");
+@:this can't happen vcenter}{\quad vcenter@>
+delta:=height(v)+depth(v);
+height(v):=axis_height(cur_size)+half(delta);
+depth(v):=delta-height(v);
+end;
+
+@ According to the rules in the \.{DVI} file specifications, we ensure alignment
+@^square roots@>
+between a square root sign and the rule above its nucleus by assuming that the
+baseline of the square-root symbol is the same as the bottom of the rule. The
+height of the square-root symbol will be the thickness of the rule, and the
+depth of the square-root symbol should exceed or equal the height-plus-depth
+of the nucleus plus a certain minimum clearance~|clr|. The symbol will be
+placed so that the actual clearance is |clr| plus half the excess.
+
+@<Declare math...@>=
+procedure make_radical(@!q:pointer);
+var x,@!y:pointer; {temporary registers for box construction}
+@!delta,@!clr:scaled; {dimensions involved in the calculation}
+begin x:=clean_box(nucleus(q),cramped_style(cur_style));
+if cur_style<text_style then {display style}
+ clr:=default_rule_thickness+(abs(math_x_height(cur_size)) div 4)
+else begin clr:=default_rule_thickness; clr:=clr + (abs(clr) div 4);
+ end;
+y:=var_delimiter(left_delimiter(q),cur_size,height(x)+depth(x)+clr+
+ default_rule_thickness);
+delta:=depth(y)-(height(x)+depth(x)+clr);
+if delta>0 then clr:=clr+half(delta); {increase the actual clearance}
+shift_amount(y):=-(height(x)+clr);
+link(y):=overbar(x,clr,height(y));
+info(nucleus(q)):=hpack(y,natural); math_type(nucleus(q)):=sub_box;
+end;
+
+@ Slants are not considered when placing accents in math mode. The accenter is
+centered over the accentee, and the accent width is treated as zero with
+respect to the size of the final box.
+
+@<Declare math...@>=
+procedure make_math_accent(@!q:pointer);
+label done,done1;
+var p,@!x,@!y:pointer; {temporary registers for box construction}
+@!a:integer; {address of lig/kern instruction}
+@!c:quarterword; {accent character}
+@!f:internal_font_number; {its font}
+@!i:four_quarters; {its |char_info|}
+@!s:scaled; {amount to skew the accent to the right}
+@!h:scaled; {height of character being accented}
+@!delta:scaled; {space to remove between accent and accentee}
+@!w:scaled; {width of the accentee, not including sub/superscripts}
+begin fetch(accent_chr(q));
+if char_exists(cur_i) then
+ begin i:=cur_i; c:=cur_c; f:=cur_f;@/
+ @<Compute the amount of skew@>;
+ x:=clean_box(nucleus(q),cramped_style(cur_style)); w:=width(x); h:=height(x);
+ @<Switch to a larger accent if available and appropriate@>;
+ if h<x_height(f) then delta:=h@+else delta:=x_height(f);
+ if (math_type(supscr(q))<>empty)or(math_type(subscr(q))<>empty) then
+ if math_type(nucleus(q))=math_char then
+ @<Swap the subscript and superscript into box |x|@>;
+ y:=char_box(f,c);
+ shift_amount(y):=s+half(w-width(y));
+ width(y):=0; p:=new_kern(-delta); link(p):=x; link(y):=p;
+ y:=vpack(y,natural); width(y):=width(x);
+ if height(y)<h then @<Make the height of box |y| equal to |h|@>;
+ info(nucleus(q)):=y;
+ math_type(nucleus(q)):=sub_box;
+ end;
+end;
+
+@ @<Make the height of box |y|...@>=
+begin p:=new_kern(h-height(y)); link(p):=list_ptr(y); list_ptr(y):=p;
+height(y):=h;
+end
+
+@ @<Switch to a larger accent if available and appropriate@>=
+loop@+ begin if char_tag(i)<>list_tag then goto done;
+ y:=rem_byte(i);
+ i:=char_info(f)(y);
+ if not char_exists(i) then goto done;
+ if char_width(f)(i)>w then goto done;
+ c:=y;
+ end;
+done:
+
+@ @<Compute the amount of skew@>=
+s:=0;
+if math_type(nucleus(q))=math_char then
+ begin fetch(nucleus(q));
+ if char_tag(cur_i)=lig_tag then
+ begin a:=lig_kern_start(cur_f)(cur_i);
+ cur_i:=font_info[a].qqqq;
+ if skip_byte(cur_i)>stop_flag then
+ begin a:=lig_kern_restart(cur_f)(cur_i);
+ cur_i:=font_info[a].qqqq;
+ end;
+ loop@+ begin if qo(next_char(cur_i))=skew_char[cur_f] then
+ begin if op_byte(cur_i)>=kern_flag then
+ if skip_byte(cur_i)<=stop_flag then s:=char_kern(cur_f)(cur_i);
+ goto done1;
+ end;
+ if skip_byte(cur_i)>=stop_flag then goto done1;
+ a:=a+qo(skip_byte(cur_i))+1;
+ cur_i:=font_info[a].qqqq;
+ end;
+ end;
+ end;
+done1:
+
+@ @<Swap the subscript and superscript into box |x|@>=
+begin flush_node_list(x); x:=new_noad;
+mem[nucleus(x)]:=mem[nucleus(q)];
+mem[supscr(x)]:=mem[supscr(q)];
+mem[subscr(x)]:=mem[subscr(q)];@/
+mem[supscr(q)].hh:=empty_field;
+mem[subscr(q)].hh:=empty_field;@/
+math_type(nucleus(q)):=sub_mlist; info(nucleus(q)):=x;
+x:=clean_box(nucleus(q),cur_style); delta:=delta+height(x)-h; h:=height(x);
+end
+
+@ The |make_fraction| procedure is a bit different because it sets
+|new_hlist(q)| directly rather than making a sub-box.
+
+@<Declare math...@>=
+procedure make_fraction(@!q:pointer);
+var p,@!v,@!x,@!y,@!z:pointer; {temporary registers for box construction}
+@!delta,@!delta1,@!delta2,@!shift_up,@!shift_down,@!clr:scaled;
+ {dimensions for box calculations}
+begin if thickness(q)=default_code then thickness(q):=default_rule_thickness;
+@<Create equal-width boxes |x| and |z| for the numerator and denominator,
+ and compute the default amounts |shift_up| and |shift_down| by which they
+ are displaced from the baseline@>;
+if thickness(q)=0 then @<Adjust \(s)|shift_up| and |shift_down| for the case
+ of no fraction line@>
+else @<Adjust \(s)|shift_up| and |shift_down| for the case of a fraction line@>;
+@<Construct a vlist box for the fraction, according to |shift_up| and
+ |shift_down|@>;
+@<Put the \(f)fraction into a box with its delimiters, and make |new_hlist(q)|
+ point to it@>;
+end;
+
+@ @<Create equal-width boxes |x| and |z| for the numerator and denom...@>=
+x:=clean_box(numerator(q),num_style(cur_style));
+z:=clean_box(denominator(q),denom_style(cur_style));
+if width(x)<width(z) then x:=rebox(x,width(z))
+else z:=rebox(z,width(x));
+if cur_style<text_style then {display style}
+ begin shift_up:=num1(cur_size); shift_down:=denom1(cur_size);
+ end
+else begin shift_down:=denom2(cur_size);
+ if thickness(q)<>0 then shift_up:=num2(cur_size)
+ else shift_up:=num3(cur_size);
+ end
+
+@ The numerator and denominator must be separated by a certain minimum
+clearance, called |clr| in the following program. The difference between
+|clr| and the actual clearance is |2delta|.
+
+@<Adjust \(s)|shift_up| and |shift_down| for the case of no fraction line@>=
+begin if cur_style<text_style then clr:=7*default_rule_thickness
+else clr:=3*default_rule_thickness;
+delta:=half(clr-((shift_up-depth(x))-(height(z)-shift_down)));
+if delta>0 then
+ begin shift_up:=shift_up+delta;
+ shift_down:=shift_down+delta;
+ end;
+end
+
+@ In the case of a fraction line, the minimum clearance depends on the actual
+thickness of the line.
+
+@<Adjust \(s)|shift_up| and |shift_down| for the case of a fraction line@>=
+begin if cur_style<text_style then clr:=3*thickness(q)
+else clr:=thickness(q);
+delta:=half(thickness(q));
+delta1:=clr-((shift_up-depth(x))-(axis_height(cur_size)+delta));
+delta2:=clr-((axis_height(cur_size)-delta)-(height(z)-shift_down));
+if delta1>0 then shift_up:=shift_up+delta1;
+if delta2>0 then shift_down:=shift_down+delta2;
+end
+
+@ @<Construct a vlist box for the fraction...@>=
+v:=new_null_box; type(v):=vlist_node;
+height(v):=shift_up+height(x); depth(v):=depth(z)+shift_down;
+width(v):=width(x); {this also equals |width(z)|}
+if thickness(q)=0 then
+ begin p:=new_kern((shift_up-depth(x))-(height(z)-shift_down));
+ link(p):=z;
+ end
+else begin y:=fraction_rule(thickness(q));@/
+ p:=new_kern((axis_height(cur_size)-delta)-@|(height(z)-shift_down));@/
+ link(y):=p; link(p):=z;@/
+ p:=new_kern((shift_up-depth(x))-(axis_height(cur_size)+delta));
+ link(p):=y;
+ end;
+link(x):=p; list_ptr(v):=x
+
+@ @<Put the \(f)fraction into a box with its delimiters...@>=
+if cur_style<text_style then delta:=delim1(cur_size)
+else delta:=delim2(cur_size);
+x:=var_delimiter(left_delimiter(q), cur_size, delta); link(x):=v;@/
+z:=var_delimiter(right_delimiter(q), cur_size, delta); link(v):=z;@/
+new_hlist(q):=hpack(x,natural)
+
+@ If the nucleus of an |op_noad| is a single character, it is to be
+centered vertically with respect to the axis, after first being enlarged
+(via a character list in the font) if we are in display style. The normal
+convention for placing displayed limits is to put them above and below the
+operator in display style.
+
+The italic correction is removed from the character if there is a subscript
+and the limits are not being displayed. The |make_op|
+routine returns the value that should be used as an offset between
+subscript and superscript.
+
+After |make_op| has acted, |subtype(q)| will be |limits| if and only if
+the limits have been set above and below the operator. In that case,
+|new_hlist(q)| will already contain the desired final box.
+
+@<Declare math...@>=
+function make_op(@!q:pointer):scaled;
+var delta:scaled; {offset between subscript and superscript}
+@!p,@!v,@!x,@!y,@!z:pointer; {temporary registers for box construction}
+@!c:quarterword;@+@!i:four_quarters; {registers for character examination}
+@!shift_up,@!shift_down:scaled; {dimensions for box calculation}
+begin if (subtype(q)=normal)and(cur_style<text_style) then
+ subtype(q):=limits;
+if math_type(nucleus(q))=math_char then
+ begin fetch(nucleus(q));
+ if (cur_style<text_style)and(char_tag(cur_i)=list_tag) then {make it larger}
+ begin c:=rem_byte(cur_i); i:=char_info(cur_f)(c);
+ if char_exists(i) then
+ begin cur_c:=c; cur_i:=i; character(nucleus(q)):=c;
+ end;
+ end;
+ delta:=char_italic(cur_f)(cur_i); x:=clean_box(nucleus(q),cur_style);
+ if (math_type(subscr(q))<>empty)and(subtype(q)<>limits) then
+ width(x):=width(x)-delta; {remove italic correction}
+ shift_amount(x):=half(height(x)-depth(x)) - axis_height(cur_size);
+ {center vertically}
+ math_type(nucleus(q)):=sub_box; info(nucleus(q)):=x;
+ end
+else delta:=0;
+if subtype(q)=limits then
+ @<Construct a box with limits above and below it, skewed by |delta|@>;
+make_op:=delta;
+end;
+
+@ The following program builds a vlist box |v| for displayed limits. The
+width of the box is not affected by the fact that the limits may be skewed.
+
+@<Construct a box with limits above and below it...@>=
+begin x:=clean_box(supscr(q),sup_style(cur_style));
+y:=clean_box(nucleus(q),cur_style);
+z:=clean_box(subscr(q),sub_style(cur_style));
+v:=new_null_box; type(v):=vlist_node; width(v):=width(y);
+if width(x)>width(v) then width(v):=width(x);
+if width(z)>width(v) then width(v):=width(z);
+x:=rebox(x,width(v)); y:=rebox(y,width(v)); z:=rebox(z,width(v));@/
+shift_amount(x):=half(delta); shift_amount(z):=-shift_amount(x);
+height(v):=height(y); depth(v):=depth(y);
+@<Attach the limits to |y| and adjust |height(v)|, |depth(v)| to
+ account for their presence@>;
+new_hlist(q):=v;
+end
+
+@ We use |shift_up| and |shift_down| in the following program for the
+amount of glue between the displayed operator |y| and its limits |x| and
+|z|. The vlist inside box |v| will consist of |x| followed by |y| followed
+by |z|, with kern nodes for the spaces between and around them.
+
+@<Attach the limits to |y| and adjust |height(v)|, |depth(v)|...@>=
+if math_type(supscr(q))=empty then
+ begin free_node(x,box_node_size); list_ptr(v):=y;
+ end
+else begin shift_up:=big_op_spacing3-depth(x);
+ if shift_up<big_op_spacing1 then shift_up:=big_op_spacing1;
+ p:=new_kern(shift_up); link(p):=y; link(x):=p;@/
+ p:=new_kern(big_op_spacing5); link(p):=x; list_ptr(v):=p;
+ height(v):=height(v)+big_op_spacing5+height(x)+depth(x)+shift_up;
+ end;
+if math_type(subscr(q))=empty then free_node(z,box_node_size)
+else begin shift_down:=big_op_spacing4-height(z);
+ if shift_down<big_op_spacing2 then shift_down:=big_op_spacing2;
+ p:=new_kern(shift_down); link(y):=p; link(p):=z;@/
+ p:=new_kern(big_op_spacing5); link(z):=p;
+ depth(v):=depth(v)+big_op_spacing5+height(z)+depth(z)+shift_down;
+ end
+
+@ A ligature found in a math formula does not create a |ligature_node|, because
+there is no question of hyphenation afterwards; the ligature will simply be
+stored in an ordinary |char_node|, after residing in an |ord_noad|.
+
+The |math_type| is converted to |math_text_char| here if we would not want to
+apply an italic correction to the current character unless it belongs
+to a math font (i.e., a font with |space=0|).
+
+No boundary characters enter into these ligatures.
+
+@<Declare math...@>=
+procedure make_ord(@!q:pointer);
+label restart,exit;
+var a:integer; {address of lig/kern instruction}
+@!p,@!r:pointer; {temporary registers for list manipulation}
+begin restart:@t@>@;@/
+if math_type(subscr(q))=empty then if math_type(supscr(q))=empty then
+ if math_type(nucleus(q))=math_char then
+ begin p:=link(q);
+ if p<>null then if (type(p)>=ord_noad)and(type(p)<=punct_noad) then
+ if math_type(nucleus(p))=math_char then
+ if fam(nucleus(p))=fam(nucleus(q)) then
+ begin math_type(nucleus(q)):=math_text_char;
+ fetch(nucleus(q));
+ if char_tag(cur_i)=lig_tag then
+ begin a:=lig_kern_start(cur_f)(cur_i);
+ cur_c:=character(nucleus(p));
+ cur_i:=font_info[a].qqqq;
+ if skip_byte(cur_i)>stop_flag then
+ begin a:=lig_kern_restart(cur_f)(cur_i);
+ cur_i:=font_info[a].qqqq;
+ end;
+ loop@+ begin @<If instruction |cur_i| is a kern with |cur_c|, attach
+ the kern after~|q|; or if it is a ligature with |cur_c|, combine
+ noads |q| and~|p| appropriately; then |return| if the cursor has
+ moved past a noad, or |goto restart|@>;
+ if skip_byte(cur_i)>=stop_flag then return;
+ a:=a+qo(skip_byte(cur_i))+1;
+ cur_i:=font_info[a].qqqq;
+ end;
+ end;
+ end;
+ end;
+exit:end;
+
+@ Note that a ligature between an |ord_noad| and another kind of noad
+is replaced by an |ord_noad|, when the two noads collapse into one.
+But we could make a parenthesis (say) change shape when it follows
+certain letters. Presumably a font designer will define such
+ligatures only when this convention makes sense.
+
+\chardef\?='174 % vertical line to indicate character retention
+
+@<If instruction |cur_i| is a kern with |cur_c|, ...@>=
+if next_char(cur_i)=cur_c then if skip_byte(cur_i)<=stop_flag then
+ if op_byte(cur_i)>=kern_flag then
+ begin p:=new_kern(char_kern(cur_f)(cur_i));
+ link(p):=link(q); link(q):=p; return;
+ end
+ else begin check_interrupt; {allow a way out of infinite ligature loop}
+ case op_byte(cur_i) of
+ qi(1),qi(5): character(nucleus(q)):=rem_byte(cur_i); {\.{=:\?}, \.{=:\?>}}
+ qi(2),qi(6): character(nucleus(p)):=rem_byte(cur_i); {\.{\?=:}, \.{\?=:>}}
+ qi(3),qi(7),qi(11):begin r:=new_noad; {\.{\?=:\?}, \.{\?=:\?>}, \.{\?=:\?>>}}
+ character(nucleus(r)):=rem_byte(cur_i);
+ fam(nucleus(r)):=fam(nucleus(q));@/
+ link(q):=r; link(r):=p;
+ if op_byte(cur_i)<qi(11) then math_type(nucleus(r)):=math_char
+ else math_type(nucleus(r)):=math_text_char; {prevent combination}
+ end;
+ othercases begin link(q):=link(p);
+ character(nucleus(q)):=rem_byte(cur_i); {\.{=:}}
+ mem[subscr(q)]:=mem[subscr(p)]; mem[supscr(q)]:=mem[supscr(p)];@/
+ free_node(p,noad_size);
+ end
+ endcases;
+ if op_byte(cur_i)>qi(3) then return;
+ math_type(nucleus(q)):=math_char; goto restart;
+ end
+
+@ When we get to the following part of the program, we have ``fallen through''
+from cases that did not lead to |check_dimensions| or |done_with_noad| or
+|done_with_node|. Thus, |q|~points to a noad whose nucleus may need to be
+converted to an hlist, and whose subscripts and superscripts need to be
+appended if they are present.
+
+If |nucleus(q)| is not a |math_char|, the variable |delta| is the amount
+by which a superscript should be moved right with respect to a subscript
+when both are present.
+@^subscripts@>
+@^superscripts@>
+
+@<Convert \(n)|nucleus(q)| to an hlist and attach the sub/superscripts@>=
+case math_type(nucleus(q)) of
+math_char, math_text_char:
+ @<Create a character node |p| for |nucleus(q)|, possibly followed
+ by a kern node for the italic correction, and set |delta| to the
+ italic correction if a subscript is present@>;
+empty: p:=null;
+sub_box: p:=info(nucleus(q));
+sub_mlist: begin cur_mlist:=info(nucleus(q)); save_style:=cur_style;
+ mlist_penalties:=false; mlist_to_hlist; {recursive call}
+@^recursion@>
+ cur_style:=save_style; @<Set up the values...@>;
+ p:=hpack(link(temp_head),natural);
+ end;
+othercases confusion("mlist2")
+@:this can't happen mlist2}{\quad mlist2@>
+endcases;@/
+new_hlist(q):=p;
+if (math_type(subscr(q))=empty)and(math_type(supscr(q))=empty) then
+ goto check_dimensions;
+make_scripts(q,delta)
+
+@ @<Create a character node |p| for |nucleus(q)|...@>=
+begin fetch(nucleus(q));
+if char_exists(cur_i) then
+ begin delta:=char_italic(cur_f)(cur_i); p:=new_character(cur_f,qo(cur_c));
+ if (math_type(nucleus(q))=math_text_char)and(space(cur_f)<>0) then
+ delta:=0; {no italic correction in mid-word of text font}
+ if (math_type(subscr(q))=empty)and(delta<>0) then
+ begin link(p):=new_kern(delta); delta:=0;
+ end;
+ end
+else p:=null;
+end
+
+@ The purpose of |make_scripts(q,delta)| is to attach the subscript and/or
+superscript of noad |q| to the list that starts at |new_hlist(q)|,
+given that subscript and superscript aren't both empty. The superscript
+will appear to the right of the subscript by a given distance |delta|.
+
+We set |shift_down| and |shift_up| to the minimum amounts to shift the
+baseline of subscripts and superscripts based on the given nucleus.
+
+@<Declare math...@>=
+procedure make_scripts(@!q:pointer;@!delta:scaled);
+var p,@!x,@!y,@!z:pointer; {temporary registers for box construction}
+@!shift_up,@!shift_down,@!clr:scaled; {dimensions in the calculation}
+@!t:small_number; {subsidiary size code}
+begin p:=new_hlist(q);
+if is_char_node(p) then
+ begin shift_up:=0; shift_down:=0;
+ end
+else begin z:=hpack(p,natural);
+ if cur_style<script_style then t:=script_size@+else t:=script_script_size;
+ shift_up:=height(z)-sup_drop(t);
+ shift_down:=depth(z)+sub_drop(t);
+ free_node(z,box_node_size);
+ end;
+if math_type(supscr(q))=empty then
+ @<Construct a subscript box |x| when there is no superscript@>
+else begin @<Construct a superscript box |x|@>;
+ if math_type(subscr(q))=empty then shift_amount(x):=-shift_up
+ else @<Construct a sub/superscript combination box |x|, with the
+ superscript offset by |delta|@>;
+ end;
+if new_hlist(q)=null then new_hlist(q):=x
+else begin p:=new_hlist(q);
+ while link(p)<>null do p:=link(p);
+ link(p):=x;
+ end;
+end;
+
+@ When there is a subscript without a superscript, the top of the subscript
+should not exceed the baseline plus four-fifths of the x-height.
+
+@<Construct a subscript box |x| when there is no superscript@>=
+begin x:=clean_box(subscr(q),sub_style(cur_style));
+width(x):=width(x)+script_space;
+if shift_down<sub1(cur_size) then shift_down:=sub1(cur_size);
+clr:=height(x)-(abs(math_x_height(cur_size)*4) div 5);
+if shift_down<clr then shift_down:=clr;
+shift_amount(x):=shift_down;
+end
+
+@ The bottom of a superscript should never descend below the baseline plus
+one-fourth of the x-height.
+
+@<Construct a superscript box |x|@>=
+begin x:=clean_box(supscr(q),sup_style(cur_style));
+width(x):=width(x)+script_space;
+if odd(cur_style) then clr:=sup3(cur_size)
+else if cur_style<text_style then clr:=sup1(cur_size)
+else clr:=sup2(cur_size);
+if shift_up<clr then shift_up:=clr;
+clr:=depth(x)+(abs(math_x_height(cur_size)) div 4);
+if shift_up<clr then shift_up:=clr;
+end
+
+@ When both subscript and superscript are present, the subscript must be
+separated from the superscript by at least four times |default_rule_thickness|.
+If this condition would be violated, the subscript moves down, after which
+both subscript and superscript move up so that the bottom of the superscript
+is at least as high as the baseline plus four-fifths of the x-height.
+
+@<Construct a sub/superscript combination box |x|...@>=
+begin y:=clean_box(subscr(q),sub_style(cur_style));
+width(y):=width(y)+script_space;
+if shift_down<sub2(cur_size) then shift_down:=sub2(cur_size);
+clr:=4*default_rule_thickness-
+ ((shift_up-depth(x))-(height(y)-shift_down));
+if clr>0 then
+ begin shift_down:=shift_down+clr;
+ clr:=(abs(math_x_height(cur_size)*4) div 5)-(shift_up-depth(x));
+ if clr>0 then
+ begin shift_up:=shift_up+clr;
+ shift_down:=shift_down-clr;
+ end;
+ end;
+shift_amount(x):=delta; {superscript is |delta| to the right of the subscript}
+p:=new_kern((shift_up-depth(x))-(height(y)-shift_down)); link(x):=p; link(p):=y;
+x:=vpack(x,natural); shift_amount(x):=shift_down;
+end
+
+@ We have now tied up all the loose ends of the first pass of |mlist_to_hlist|.
+The second pass simply goes through and hooks everything together with the
+proper glue and penalties. It also handles the |left_noad| and |right_noad| that
+might be present, since |max_h| and |max_d| are now known. Variable |p| points
+to a node at the current end of the final hlist.
+
+@<Make a second pass over the mlist, ...@>=
+p:=temp_head; link(p):=null; q:=mlist; r_type:=0; cur_style:=style;
+@<Set up the values of |cur_size| and |cur_mu|, based on |cur_style|@>;
+while q<>null do
+ begin @<If node |q| is a style node, change the style and |goto delete_q|;
+ otherwise if it is not a noad, put it into the hlist,
+ advance |q|, and |goto done|; otherwise set |s| to the size
+ of noad |q|, set |t| to the associated type (|ord_noad..
+ inner_noad|), and set |pen| to the associated penalty@>;
+ @<Append inter-element spacing based on |r_type| and |t|@>;
+ @<Append any |new_hlist| entries for |q|, and any appropriate penalties@>;
+ r_type:=t;
+ delete_q: r:=q; q:=link(q); free_node(r,s);
+ done: end
+
+@ Just before doing the big |case| switch in the second pass, the program
+sets up default values so that most of the branches are short.
+
+@<If node |q| is a style node, change the style...@>=
+t:=ord_noad; s:=noad_size; pen:=inf_penalty;
+case type(q) of
+op_noad,open_noad,close_noad,punct_noad,inner_noad: t:=type(q);
+bin_noad: begin t:=bin_noad; pen:=bin_op_penalty;
+ end;
+rel_noad: begin t:=rel_noad; pen:=rel_penalty;
+ end;
+ord_noad,vcenter_noad,over_noad,under_noad: do_nothing;
+radical_noad: s:=radical_noad_size;
+accent_noad: s:=accent_noad_size;
+fraction_noad: begin t:=inner_noad; s:=fraction_noad_size;
+ end;
+left_noad,right_noad: t:=make_left_right(q,style,max_d,max_h);
+style_node: @<Change the current style and |goto delete_q|@>;
+whatsit_node,penalty_node,rule_node,disc_node,adjust_node,ins_node,mark_node,
+ glue_node,kern_node:@t@>@;@/
+ begin link(p):=q; p:=q; q:=link(q); link(p):=null; goto done;
+ end;
+othercases confusion("mlist3")
+@:this can't happen mlist3}{\quad mlist3@>
+endcases
+
+@ The |make_left_right| function constructs a left or right delimiter of
+the required size and returns the value |open_noad| or |close_noad|. The
+|right_noad| and |left_noad| will both be based on the original |style|,
+so they will have consistent sizes.
+
+We use the fact that |right_noad-left_noad=close_noad-open_noad|.
+
+@<Declare math...@>=
+function make_left_right(@!q:pointer;@!style:small_number;
+ @!max_d,@!max_h:scaled):small_number;
+var delta,@!delta1,@!delta2:scaled; {dimensions used in the calculation}
+begin if style<script_style then cur_size:=text_size
+else cur_size:=16*((style-text_style) div 2);
+delta2:=max_d+axis_height(cur_size);
+delta1:=max_h+max_d-delta2;
+if delta2>delta1 then delta1:=delta2; {|delta1| is max distance from axis}
+delta:=(delta1 div 500)*delimiter_factor;
+delta2:=delta1+delta1-delimiter_shortfall;
+if delta<delta2 then delta:=delta2;
+new_hlist(q):=var_delimiter(delimiter(q),cur_size,delta);
+make_left_right:=type(q)-(left_noad-open_noad); {|open_noad| or |close_noad|}
+end;
+
+@ @<Change the current style and |goto delete_q|@>=
+begin cur_style:=subtype(q); s:=style_node_size;
+@<Set up the values of |cur_size| and |cur_mu|, based on |cur_style|@>;
+goto delete_q;
+end
+
+@ The inter-element spacing in math formulas depends on a $8\times8$ table that
+\TeX\ preloads as a 64-digit string. The elements of this string have the
+following significance:
+$$\vbox{\halign{#\hfil\cr
+\.0 means no space;\cr
+\.1 means a conditional thin space (\.{\\nonscript\\mskip\\thinmuskip});\cr
+\.2 means a thin space (\.{\\mskip\\thinmuskip});\cr
+\.3 means a conditional medium space
+ (\.{\\nonscript\\mskip\\medmuskip});\cr
+\.4 means a conditional thick space
+ (\.{\\nonscript\\mskip\\thickmuskip});\cr
+\.* means an impossible case.\cr}}$$
+This is all pretty cryptic, but {\sl The \TeX book\/} explains what is
+supposed to happen, and the string makes it happen.
+@:TeXbook}{\sl The \TeX book@>
+
+A global variable |magic_offset| is computed so that if |a| and |b| are
+in the range |ord_noad..inner_noad|, then |str_pool[a*8+b+magic_offset]|
+is the digit for spacing between noad types |a| and |b|.
+
+If \PASCAL\ had provided a good way to preload constant arrays, this part of
+the program would not have been so strange.
+@:PASCAL}{\PASCAL@>
+
+@d math_spacing=@;@/
+@t\hskip-35pt@>
+"0234000122*4000133**3**344*0400400*000000234000111*1111112341011"
+@t$ \hskip-35pt$@>
+
+@<Glob...@>=
+@!magic_offset:integer; {used to find inter-element spacing}
+
+@ @<Compute the magic offset@>=
+magic_offset:=str_start[math_spacing]-9*ord_noad
+
+@ @<Append inter-element spacing based on |r_type| and |t|@>=
+if r_type>0 then {not the first noad}
+ begin case so(str_pool[r_type*8+t+magic_offset]) of
+ "0": x:=0;
+ "1": if cur_style<script_style then x:=thin_mu_skip_code@+else x:=0;
+ "2": x:=thin_mu_skip_code;
+ "3": if cur_style<script_style then x:=med_mu_skip_code@+else x:=0;
+ "4": if cur_style<script_style then x:=thick_mu_skip_code@+else x:=0;
+ othercases confusion("mlist4")
+@:this can't happen mlist4}{\quad mlist4@>
+ endcases;
+ if x<>0 then
+ begin y:=math_glue(glue_par(x),cur_mu);
+ z:=new_glue(y); glue_ref_count(y):=null; link(p):=z; p:=z;@/
+ subtype(z):=x+1; {store a symbolic subtype}
+ end;
+ end
+
+@ We insert a penalty node after the hlist entries of noad |q| if |pen|
+is not an ``infinite'' penalty, and if the node immediately following |q|
+is not a penalty node or a |rel_noad| or absent entirely.
+
+@<Append any |new_hlist| entries for |q|, and any appropriate penalties@>=
+if new_hlist(q)<>null then
+ begin link(p):=new_hlist(q);
+ repeat p:=link(p);
+ until link(p)=null;
+ end;
+if penalties then if link(q)<>null then if pen<inf_penalty then
+ begin r_type:=type(link(q));
+ if r_type<>penalty_node then if r_type<>rel_noad then
+ begin z:=new_penalty(pen); link(p):=z; p:=z;
+ end;
+ end
+
+@* \[37] Alignment.
+It's sort of a miracle whenever \.{\\halign} and \.{\\valign} work, because
+they cut across so many of the control structures of \TeX.
+
+Therefore the
+present page is probably not the best place for a beginner to start reading
+this program; it is better to master everything else first.
+
+Let us focus our thoughts on an example of what the input might be, in order
+to get some idea about how the alignment miracle happens. The example doesn't
+do anything useful, but it is sufficiently general to indicate all of the
+special cases that must be dealt with; please do not be disturbed by its
+apparent complexity and meaninglessness.
+$$\vbox{\halign{\.{#}\hfil\cr
+{}\\tabskip 2pt plus 3pt\cr
+{}\\halign to 300pt\{u1\#v1\&\cr
+\hskip 50pt\\tabskip 1pt plus 1fil u2\#v2\&\cr
+\hskip 50pt u3\#v3\\cr\cr
+\hskip 25pt a1\&\\omit a2\&\\vrule\\cr\cr
+\hskip 25pt \\noalign\{\\vskip 3pt\}\cr
+\hskip 25pt b1\\span b2\\cr\cr
+\hskip 25pt \\omit\&c2\\span\\omit\\cr\}\cr}}$$
+Here's what happens:
+
+\yskip
+(0) When `\.{\\halign to 300pt\{}' is scanned, the |scan_spec| routine
+places the 300pt dimension onto the |save_stack|, and an |align_group|
+code is placed above it. This will make it possible to complete the alignment
+when the matching `\.\}' is found.
+
+(1) The preamble is scanned next. Macros in the preamble are not expanded,
+@^preamble@>
+except as part of a tabskip specification. For example, if \.{u2} had been
+a macro in the preamble above, it would have been expanded, since \TeX\
+must look for `\.{minus...}' as part of the tabskip glue. A ``preamble list''
+is constructed based on the user's preamble; in our case it contains the
+following seven items:
+$$\vbox{\halign{\.{#}\hfil\qquad&(#)\hfil\cr
+{}\\glue 2pt plus 3pt&the tabskip preceding column 1\cr
+{}\\alignrecord, width $-\infty$&preamble info for column 1\cr
+{}\\glue 2pt plus 3pt&the tabskip between columns 1 and 2\cr
+{}\\alignrecord, width $-\infty$&preamble info for column 2\cr
+{}\\glue 1pt plus 1fil&the tabskip between columns 2 and 3\cr
+{}\\alignrecord, width $-\infty$&preamble info for column 3\cr
+{}\\glue 1pt plus 1fil&the tabskip following column 3\cr}}$$
+These ``alignrecord'' entries have the same size as an |unset_node|,
+since they will later be converted into such nodes. However, at the
+moment they have no |type| or |subtype| fields; they have |info| fields
+instead, and these |info| fields are initially set to the value |end_span|,
+for reasons explained below. Furthermore, the alignrecord nodes have no
+|height| or |depth| fields; these are renamed |u_part| and |v_part|,
+and they point to token lists for the templates of the alignment.
+For example, the |u_part| field in the first alignrecord points to the
+token list `\.{u1}', i.e., the template preceding the `\.\#' for column~1.
+
+(2) \TeX\ now looks at what follows the \.{\\cr} that ended the preamble.
+It is not `\.{\\noalign}' or `\.{\\omit}', so this input is put back to
+be read again, and the template `\.{u1}' is fed to the scanner. Just
+before reading `\.{u1}', \TeX\ goes into restricted horizontal mode.
+Just after reading `\.{u1}', \TeX\ will see `\.{a1}', and then (when the
+{\.\&} is sensed) \TeX\ will see `\.{v1}'. Then \TeX\ scans an |endv|
+token, indicating the end of a column. At this point an |unset_node| is
+created, containing the contents of the current hlist (i.e., `\.{u1a1v1}').
+The natural width of this unset node replaces the |width| field of the
+alignrecord for column~1; in general, the alignrecords will record the
+maximum natural width that has occurred so far in a given column.
+
+(3) Since `\.{\\omit}' follows the `\.\&', the templates for column~2
+are now bypassed. Again \TeX\ goes into restricted horizontal mode and
+makes an |unset_node| from the resulting hlist; but this time the
+hlist contains simply `\.{a2}'. The natural width of the new unset box
+is remembered in the |width| field of the alignrecord for column~2.
+
+(4) A third |unset_node| is created for column 3, using essentially the
+mechanism that worked for column~1; this unset box contains `\.{u3\\vrule
+v3}'. The vertical rule in this case has running dimensions that will later
+extend to the height and depth of the whole first row, since each |unset_node|
+in a row will eventually inherit the height and depth of its enclosing box.
+
+(5) The first row has now ended; it is made into a single unset box
+comprising the following seven items:
+$$\vbox{\halign{\hbox to 325pt{\qquad\.{#}\hfil}\cr
+{}\\glue 2pt plus 3pt\cr
+{}\\unsetbox for 1 column: u1a1v1\cr
+{}\\glue 2pt plus 3pt\cr
+{}\\unsetbox for 1 column: a2\cr
+{}\\glue 1pt plus 1fil\cr
+{}\\unsetbox for 1 column: u3\\vrule v3\cr
+{}\\glue 1pt plus 1fil\cr}}$$
+The width of this unset row is unimportant, but it has the correct height
+and depth, so the correct baselineskip glue will be computed as the row
+is inserted into a vertical list.
+
+(6) Since `\.{\\noalign}' follows the current \.{\\cr}, \TeX\ appends
+additional material (in this case \.{\\vskip 3pt}) to the vertical list.
+While processing this material, \TeX\ will be in internal vertical
+mode, and |no_align_group| will be on |save_stack|.
+
+(7) The next row produces an unset box that looks like this:
+$$\vbox{\halign{\hbox to 325pt{\qquad\.{#}\hfil}\cr
+{}\\glue 2pt plus 3pt\cr
+{}\\unsetbox for 2 columns: u1b1v1u2b2v2\cr
+{}\\glue 1pt plus 1fil\cr
+{}\\unsetbox for 1 column: {\rm(empty)}\cr
+{}\\glue 1pt plus 1fil\cr}}$$
+The natural width of the unset box that spans columns 1~and~2 is stored
+in a ``span node,'' which we will explain later; the |info| field of the
+alignrecord for column~1 now points to the new span node, and the |info|
+of the span node points to |end_span|.
+
+(8) The final row produces the unset box
+$$\vbox{\halign{\hbox to 325pt{\qquad\.{#}\hfil}\cr
+{}\\glue 2pt plus 3pt\cr
+{}\\unsetbox for 1 column: {\rm(empty)}\cr
+{}\\glue 2pt plus 3pt\cr
+{}\\unsetbox for 2 columns: u2c2v2\cr
+{}\\glue 1pt plus 1fil\cr}}$$
+A new span node is attached to the alignrecord for column 2.
+
+(9) The last step is to compute the true column widths and to change all the
+unset boxes to hboxes, appending the whole works to the vertical list that
+encloses the \.{\\halign}. The rules for deciding on the final widths of
+each unset column box will be explained below.
+
+\yskip\noindent
+Note that as \.{\\halign} is being processed, we fearlessly give up control
+to the rest of \TeX. At critical junctures, an alignment routine is
+called upon to step in and do some little action, but most of the time
+these routines just lurk in the background. It's something like
+post-hypnotic suggestion.
+
+@ We have mentioned that alignrecords contain no |height| or |depth| fields.
+Their |glue_sign| and |glue_order| are pre-empted as well, since it
+is necessary to store information about what to do when a template ends.
+This information is called the |extra_info| field.
+
+@d u_part(#)==mem[#+height_offset].int {pointer to \<u_j> token list}
+@d v_part(#)==mem[#+depth_offset].int {pointer to \<v_j> token list}
+@d extra_info(#)==info(#+list_offset) {info to remember during template}
+
+@ Alignments can occur within alignments, so a small stack is used to access
+the alignrecord information. At each level we have a |preamble| pointer,
+indicating the beginning of the preamble list; a |cur_align| pointer,
+indicating the current position in the preamble list; a |cur_span| pointer,
+indicating the value of |cur_align| at the beginning of a sequence of
+spanned columns; a |cur_loop| pointer, indicating the tabskip glue before
+an alignrecord that should be copied next if the current list is extended;
+and the |align_state| variable, which indicates the nesting of braces so
+that \.{\\cr} and \.{\\span} and tab marks are properly intercepted.
+There also are pointers |cur_head| and |cur_tail| to the head and tail
+of a list of adjustments being moved out from horizontal mode to
+vertical~mode.
+
+The current values of these seven quantities appear in global variables;
+when they have to be pushed down, they are stored in 5-word nodes, and
+|align_ptr| points to the topmost such node.
+
+@d preamble==link(align_head) {the current preamble list}
+@d align_stack_node_size=5 {number of |mem| words to save alignment states}
+
+@<Glob...@>=
+@!cur_align:pointer; {current position in preamble list}
+@!cur_span:pointer; {start of currently spanned columns in preamble list}
+@!cur_loop:pointer; {place to copy when extending a periodic preamble}
+@!align_ptr:pointer; {most recently pushed-down alignment stack node}
+@!cur_head,@!cur_tail:pointer; {adjustment list pointers}
+
+@ The |align_state| and |preamble| variables are initialized elsewhere.
+
+@<Set init...@>=
+align_ptr:=null; cur_align:=null; cur_span:=null; cur_loop:=null;
+cur_head:=null; cur_tail:=null;
+
+@ Alignment stack maintenance is handled by a pair of trivial routines
+called |push_alignment| and |pop_alignment|.
+
+@p procedure push_alignment;
+var p:pointer; {the new alignment stack node}
+begin p:=get_node(align_stack_node_size);
+link(p):=align_ptr; info(p):=cur_align;
+llink(p):=preamble; rlink(p):=cur_span;
+mem[p+2].int:=cur_loop; mem[p+3].int:=align_state;
+info(p+4):=cur_head; link(p+4):=cur_tail;
+align_ptr:=p;
+cur_head:=get_avail;
+end;
+@#
+procedure pop_alignment;
+var p:pointer; {the top alignment stack node}
+begin free_avail(cur_head);
+p:=align_ptr;
+cur_tail:=link(p+4); cur_head:=info(p+4);
+align_state:=mem[p+3].int; cur_loop:=mem[p+2].int;
+cur_span:=rlink(p); preamble:=llink(p);
+cur_align:=info(p); align_ptr:=link(p);
+free_node(p,align_stack_node_size);
+end;
+
+@ \TeX\ has eight procedures that govern alignments: |init_align| and
+|fin_align| are used at the very beginning and the very end; |init_row| and
+|fin_row| are used at the beginning and end of individual rows; |init_span|
+is used at the beginning of a sequence of spanned columns (possibly involving
+only one column); |init_col| and |fin_col| are used at the beginning and
+end of individual columns; and |align_peek| is used after \.{\\cr} to see
+whether the next item is \.{\\noalign}.
+
+We shall consider these routines in the order they are first used during
+the course of a complete \.{\\halign}, namely |init_align|, |align_peek|,
+|init_row|, |init_span|, |init_col|, |fin_col|, |fin_row|, |fin_align|.
+
+@ When \.{\\halign} or \.{\\valign} has been scanned in an appropriate
+mode, \TeX\ calls |init_align|, whose task is to get everything off to a
+good start. This mostly involves scanning the preamble and putting its
+information into the preamble list.
+@^preamble@>
+
+@p @t\4@>@<Declare the procedure called |get_preamble_token|@>@t@>@/
+procedure@?align_peek; forward;@t\2@>@/
+procedure@?normal_paragraph; forward;@t\2@>@/
+procedure init_align;
+label done, done1, done2, continue;
+var save_cs_ptr:pointer; {|warning_index| value for error messages}
+@!p:pointer; {for short-term temporary use}
+begin save_cs_ptr:=cur_cs; {\.{\\halign} or \.{\\valign}, usually}
+push_alignment; align_state:=-1000000; {enter a new alignment level}
+@<Check for improper alignment in displayed math@>;
+push_nest; {enter a new semantic level}
+@<Change current mode to |-vmode| for \.{\\halign}, |-hmode| for \.{\\valign}@>;
+scan_spec(align_group,false);@/
+@<Scan the preamble and record it in the |preamble| list@>;
+new_save_level(align_group);
+if every_cr<>null then begin_token_list(every_cr,every_cr_text);
+align_peek; {look for \.{\\noalign} or \.{\\omit}}
+end;
+
+@ In vertical modes, |prev_depth| already has the correct value. But
+if we are in |mmode| (displayed formula mode), we reach out to the
+enclosing vertical mode for the |prev_depth| value that produces the
+correct baseline calculations.
+
+@<Change current mode...@>=
+if mode=mmode then
+ begin mode:=-vmode; prev_depth:=nest[nest_ptr-2].aux_field.sc;
+ end
+else if mode>0 then negate(mode)
+
+@ When \.{\\halign} is used as a displayed formula, there should be
+no other pieces of mlists present.
+
+@<Check for improper alignment in displayed math@>=
+if (mode=mmode)and((tail<>head)or(incompleat_noad<>null)) then
+ begin print_err("Improper "); print_esc("halign"); print(" inside $$'s");
+@.Improper \\halign...@>
+ help3("Displays can use special alignments (like \eqalignno)")@/
+ ("only if nothing but the alignment itself is between $$'s.")@/
+ ("So I've deleted the formulas that preceded this alignment.");
+ error; flush_math;
+ end
+
+@ @<Scan the preamble and record it in the |preamble| list@>=
+preamble:=null; cur_align:=align_head; cur_loop:=null; scanner_status:=aligning;
+warning_index:=save_cs_ptr; align_state:=-1000000;
+ {at this point, |cur_cmd=left_brace|}
+loop@+ begin @<Append the current tabskip glue to the preamble list@>;
+ if cur_cmd=car_ret then goto done; {\.{\\cr} ends the preamble}
+ @<Scan preamble text until |cur_cmd| is |tab_mark| or |car_ret|,
+ looking for changes in the tabskip glue; append an
+ alignrecord to the preamble list@>;
+ end;
+done: scanner_status:=normal
+
+@ @<Append the current tabskip glue to the preamble list@>=
+link(cur_align):=new_param_glue(tab_skip_code);
+cur_align:=link(cur_align)
+
+@ @<Scan preamble text until |cur_cmd| is |tab_mark| or |car_ret|...@>=
+@<Scan the template \<u_j>, putting the resulting token list in |hold_head|@>;
+link(cur_align):=new_null_box; cur_align:=link(cur_align); {a new alignrecord}
+info(cur_align):=end_span; width(cur_align):=null_flag;
+u_part(cur_align):=link(hold_head);
+@<Scan the template \<v_j>, putting the resulting token list in |hold_head|@>;
+v_part(cur_align):=link(hold_head)
+
+@ We enter `\.{\\span}' into |eqtb| with |tab_mark| as its command code,
+and with |span_code| as the command modifier. This makes \TeX\ interpret it
+essentially the same as an alignment delimiter like `\.\&', yet it is
+recognizably different when we need to distinguish it from a normal delimiter.
+It also turns out to be useful to give a special |cr_code| to `\.{\\cr}',
+and an even larger |cr_cr_code| to `\.{\\crcr}'.
+
+The end of a template is represented by two ``frozen'' control sequences
+called \.{\\endtemplate}. The first has the command code |end_template|, which
+is |>outer_call|, so it will not easily disappear in the presence of errors.
+The |get_x_token| routine converts the first into the second, which has |endv|
+as its command code.
+
+@d span_code=256 {distinct from any character}
+@d cr_code=257 {distinct from |span_code| and from any character}
+@d cr_cr_code=cr_code+1 {this distinguishes \.{\\crcr} from \.{\\cr}}
+@d end_template_token==cs_token_flag+frozen_end_template
+
+@<Put each of \TeX's primitives into the hash table@>=
+primitive("span",tab_mark,span_code);@/
+@!@:span_}{\.{\\span} primitive@>
+primitive("cr",car_ret,cr_code);
+@!@:cr_}{\.{\\cr} primitive@>
+text(frozen_cr):="cr"; eqtb[frozen_cr]:=eqtb[cur_val];@/
+primitive("crcr",car_ret,cr_cr_code);
+@!@:cr_cr_}{\.{\\crcr} primitive@>
+text(frozen_end_template):="endtemplate"; text(frozen_endv):="endtemplate";
+eq_type(frozen_endv):=endv; equiv(frozen_endv):=null_list;
+eq_level(frozen_endv):=level_one;@/
+eqtb[frozen_end_template]:=eqtb[frozen_endv];
+eq_type(frozen_end_template):=end_template;
+
+@ @<Cases of |print_cmd_chr|...@>=
+tab_mark: if chr_code=span_code then print_esc("span")
+ else chr_cmd("alignment tab character ");
+car_ret: if chr_code=cr_code then print_esc("cr")
+ else print_esc("crcr");
+
+@ The preamble is copied directly, except that \.{\\tabskip} causes a change
+to the tabskip glue, thereby possibly expanding macros that immediately
+follow it. An appearance of \.{\\span} also causes such an expansion.
+
+Note that if the preamble contains `\.{\\global\\tabskip}', the `\.{\\global}'
+token survives in the preamble and the `\.{\\tabskip}' defines new
+tabskip glue (locally).
+
+@<Declare the procedure called |get_preamble_token|@>=
+procedure get_preamble_token;
+label restart;
+begin restart: get_token;
+while (cur_chr=span_code)and(cur_cmd=tab_mark) do
+ begin get_token; {this token will be expanded once}
+ if cur_cmd>max_command then
+ begin expand; get_token;
+ end;
+ end;
+if cur_cmd=endv then
+ fatal_error("(interwoven alignment preambles are not allowed)");
+@.interwoven alignment preambles...@>
+if (cur_cmd=assign_glue)and(cur_chr=glue_base+tab_skip_code) then
+ begin scan_optional_equals; scan_glue(glue_val);
+ if global_defs>0 then geq_define(glue_base+tab_skip_code,glue_ref,cur_val)
+ else eq_define(glue_base+tab_skip_code,glue_ref,cur_val);
+ goto restart;
+ end;
+end;
+
+@ Spaces are eliminated from the beginning of a template.
+
+@<Scan the template \<u_j>...@>=
+p:=hold_head; link(p):=null;
+loop@+ begin get_preamble_token;
+ if cur_cmd=mac_param then goto done1;
+ if (cur_cmd<=car_ret)and(cur_cmd>=tab_mark)and(align_state=-1000000) then
+ if (p=hold_head)and(cur_loop=null)and(cur_cmd=tab_mark)
+ then cur_loop:=cur_align
+ else begin print_err("Missing # inserted in alignment preamble");
+@.Missing \# inserted...@>
+ help3("There should be exactly one # between &'s, when an")@/
+ ("\halign or \valign is being set up. In this case you had")@/
+ ("none, so I've put one in; maybe that will work.");
+ back_error; goto done1;
+ end
+ else if (cur_cmd<>spacer)or(p<>hold_head) then
+ begin link(p):=get_avail; p:=link(p); info(p):=cur_tok;
+ end;
+ end;
+done1:
+
+@ @<Scan the template \<v_j>...@>=
+p:=hold_head; link(p):=null;
+loop@+ begin continue: get_preamble_token;
+ if (cur_cmd<=car_ret)and(cur_cmd>=tab_mark)and(align_state=-1000000) then
+ goto done2;
+ if cur_cmd=mac_param then
+ begin print_err("Only one # is allowed per tab");
+@.Only one \# is allowed...@>
+ help3("There should be exactly one # between &'s, when an")@/
+ ("\halign or \valign is being set up. In this case you had")@/
+ ("more than one, so I'm ignoring all but the first.");
+ error; goto continue;
+ end;
+ link(p):=get_avail; p:=link(p); info(p):=cur_tok;
+ end;
+done2: link(p):=get_avail; p:=link(p);
+info(p):=end_template_token {put \.{\\endtemplate} at the end}
+
+@ The tricky part about alignments is getting the templates into the
+scanner at the right time, and recovering control when a row or column
+is finished.
+
+We usually begin a row after each \.{\\cr} has been sensed, unless that
+\.{\\cr} is followed by \.{\\noalign} or by the right brace that terminates
+the alignment. The |align_peek| routine is used to look ahead and do
+the right thing; it either gets a new row started, or gets a \.{\\noalign}
+started, or finishes off the alignment.
+
+@<Declare the procedure called |align_peek|@>=
+procedure align_peek;
+label restart;
+begin restart: align_state:=1000000; @<Get the next non-blank non-call token@>;
+if cur_cmd=no_align then
+ begin scan_left_brace; new_save_level(no_align_group);
+ if mode=-vmode then normal_paragraph;
+ end
+else if cur_cmd=right_brace then fin_align
+else if (cur_cmd=car_ret)and(cur_chr=cr_cr_code) then
+ goto restart {ignore \.{\\crcr}}
+else begin init_row; {start a new row}
+ init_col; {start a new column and replace what we peeked at}
+ end;
+end;
+
+@ To start a row (i.e., a `row' that rhymes with `dough' but not with `bough'),
+we enter a new semantic level, copy the first tabskip glue, and change
+from internal vertical mode to restricted horizontal mode or vice versa.
+The |space_factor| and |prev_depth| are not used on this semantic level,
+but we clear them to zero just to be tidy.
+
+@p @t\4@>@<Declare the procedure called |init_span|@>@t@>@/
+procedure init_row;
+begin push_nest; mode:=(-hmode-vmode)-mode;
+if mode=-hmode then space_factor:=0 @+else prev_depth:=0;
+tail_append(new_glue(glue_ptr(preamble)));
+subtype(tail):=tab_skip_code+1;@/
+cur_align:=link(preamble); cur_tail:=cur_head; init_span(cur_align);
+end;
+
+@ The parameter to |init_span| is a pointer to the alignrecord where the
+next column or group of columns will begin. A new semantic level is
+entered, so that the columns will generate a list for subsequent packaging.
+
+@<Declare the procedure called |init_span|@>=
+procedure init_span(@!p:pointer);
+begin push_nest;
+if mode=-hmode then space_factor:=1000
+else begin prev_depth:=ignore_depth; normal_paragraph;
+ end;
+cur_span:=p;
+end;
+
+@ When a column begins, we assume that |cur_cmd| is either |omit| or else
+the current token should be put back into the input until the \<u_j>
+template has been scanned. (Note that |cur_cmd| might be |tab_mark| or
+|car_ret|.) We also assume that |align_state| is approximately 1000000 at
+this time. We remain in the same mode, and start the template if it is
+called for.
+
+@p procedure init_col;
+begin extra_info(cur_align):=cur_cmd;
+if cur_cmd=omit then align_state:=0
+else begin back_input; begin_token_list(u_part(cur_align),u_template);
+ end; {now |align_state=1000000|}
+end;
+
+@ The scanner sets |align_state| to zero when the \<u_j> template ends. When
+a subsequent \.{\\cr} or \.{\\span} or tab mark occurs with |align_state=0|,
+the scanner activates the following code, which fires up the \<v_j> template.
+We need to remember the |cur_chr|, which is either |cr_cr_code|, |cr_code|,
+|span_code|, or a character code, depending on how the column text has ended.
+
+This part of the program had better not be activated when the preamble
+to another alignment is being scanned, or when no alignment preamble is active.
+
+@<Insert the \(v)\<v_j>...@>=
+begin if (scanner_status=aligning) or (cur_align=null) then
+ fatal_error("(interwoven alignment preambles are not allowed)");
+@.interwoven alignment preambles...@>
+cur_cmd:=extra_info(cur_align); extra_info(cur_align):=cur_chr;
+if cur_cmd=omit then begin_token_list(omit_template,v_template)
+else begin_token_list(v_part(cur_align),v_template);
+align_state:=1000000; goto restart;
+end
+
+@ The token list |omit_template| just referred to is a constant token
+list that contains the special control sequence \.{\\endtemplate} only.
+
+@<Initialize the special...@>=
+info(omit_template):=end_template_token; {|link(omit_template)=null|}
+
+@ When the |endv| command at the end of a \<v_j> template comes through the
+scanner, things really start to happen; and it is the |fin_col| routine
+that makes them happen. This routine returns |true| if a row as well as a
+column has been finished.
+
+@p function fin_col:boolean;
+label exit;
+var p:pointer; {the alignrecord after the current one}
+@!q,@!r:pointer; {temporary pointers for list manipulation}
+@!s:pointer; {a new span node}
+@!u:pointer; {a new unset box}
+@!w:scaled; {natural width}
+@!o:glue_ord; {order of infinity}
+@!n:halfword; {span counter}
+begin if cur_align=null then confusion("endv");
+q:=link(cur_align);@+if q=null then confusion("endv");
+@:this can't happen endv}{\quad endv@>
+if align_state<500000 then
+ fatal_error("(interwoven alignment preambles are not allowed)");
+@.interwoven alignment preambles...@>
+p:=link(q);
+@<If the preamble list has been traversed, check that the row has ended@>;
+if extra_info(cur_align)<>span_code then
+ begin unsave; new_save_level(align_group);@/
+ @<Package an unset box for the current column and record its width@>;
+ @<Copy the tabskip glue between columns@>;
+ if extra_info(cur_align)>=cr_code then
+ begin fin_col:=true; return;
+ end;
+ init_span(p);
+ end;
+align_state:=1000000; @<Get the next non-blank non-call token@>;
+cur_align:=p;
+init_col; fin_col:=false;
+exit: end;
+
+@ @<If the preamble list has been traversed, check that the row has ended@>=
+if (p=null)and(extra_info(cur_align)<cr_code) then
+ if cur_loop<>null then @<Lengthen the preamble periodically@>
+ else begin print_err("Extra alignment tab has been changed to ");
+@.Extra alignment tab...@>
+ print_esc("cr");
+ help3("You have given more \span or & marks than there were")@/
+ ("in the preamble to the \halign or \valign now in progress.")@/
+ ("So I'll assume that you meant to type \cr instead.");
+ extra_info(cur_align):=cr_code; error;
+ end
+
+@ @<Lengthen the preamble...@>=
+begin link(q):=new_null_box; p:=link(q); {a new alignrecord}
+info(p):=end_span; width(p):=null_flag; cur_loop:=link(cur_loop);
+@<Copy the templates from node |cur_loop| into node |p|@>;
+cur_loop:=link(cur_loop);
+link(p):=new_glue(glue_ptr(cur_loop));
+end
+
+@ @<Copy the templates from node |cur_loop| into node |p|@>=
+q:=hold_head; r:=u_part(cur_loop);
+while r<>null do
+ begin link(q):=get_avail; q:=link(q); info(q):=info(r); r:=link(r);
+ end;
+link(q):=null; u_part(p):=link(hold_head);
+q:=hold_head; r:=v_part(cur_loop);
+while r<>null do
+ begin link(q):=get_avail; q:=link(q); info(q):=info(r); r:=link(r);
+ end;
+link(q):=null; v_part(p):=link(hold_head)
+
+@ @<Copy the tabskip glue...@>=
+tail_append(new_glue(glue_ptr(link(cur_align))));
+subtype(tail):=tab_skip_code+1
+
+@ @<Package an unset...@>=
+begin if mode=-hmode then
+ begin adjust_tail:=cur_tail; u:=hpack(link(head),natural); w:=width(u);
+ cur_tail:=adjust_tail; adjust_tail:=null;
+ end
+else begin u:=vpackage(link(head),natural,0); w:=height(u);
+ end;
+n:=min_quarterword; {this represents a span count of 1}
+if cur_span<>cur_align then @<Update width entry for spanned columns@>
+else if w>width(cur_align) then width(cur_align):=w;
+type(u):=unset_node; span_count(u):=n;@/
+@<Determine the stretch order@>;
+glue_order(u):=o; glue_stretch(u):=total_stretch[o];@/
+@<Determine the shrink order@>;
+glue_sign(u):=o; glue_shrink(u):=total_shrink[o];@/
+pop_nest; link(tail):=u; tail:=u;
+end
+
+@ A span node is a 2-word record containing |width|, |info|, and |link|
+fields. The |link| field is not really a link, it indicates the number of
+spanned columns; the |info| field points to a span node for the same
+starting column, having a greater extent of spanning, or to |end_span|,
+which has the largest possible |link| field; the |width| field holds the
+largest natural width corresponding to a particular set of spanned columns.
+
+A list of the maximum widths so far, for spanned columns starting at a
+given column, begins with the |info| field of the alignrecord for that
+column.
+
+@d span_node_size=2 {number of |mem| words for a span node}
+
+@<Initialize the special list heads...@>=
+link(end_span):=max_quarterword+1; info(end_span):=null;
+
+@ @<Update width entry for spanned columns@>=
+begin q:=cur_span;
+repeat incr(n); q:=link(link(q));
+until q=cur_align;
+if n>max_quarterword then confusion("256 spans"); {this can happen, but won't}
+@^system dependencies@>
+@:this can't happen 256 spans}{\quad 256 spans@>
+q:=cur_span; while link(info(q))<n do q:=info(q);
+if link(info(q))>n then
+ begin s:=get_node(span_node_size); info(s):=info(q); link(s):=n;
+ info(q):=s; width(s):=w;
+ end
+else if width(info(q))<w then width(info(q)):=w;
+end
+
+@ At the end of a row, we append an unset box to the current vlist (for
+\.{\\halign}) or the current hlist (for \.{\\valign}). This unset box
+contains the unset boxes for the columns, separated by the tabskip glue.
+Everything will be set later.
+
+@p procedure fin_row;
+var p:pointer; {the new unset box}
+begin if mode=-hmode then
+ begin p:=hpack(link(head),natural);
+ pop_nest; append_to_vlist(p);
+ if cur_head<>cur_tail then
+ begin link(tail):=link(cur_head); tail:=cur_tail;
+ end;
+ end
+else begin p:=vpack(link(head),natural); pop_nest;
+ link(tail):=p; tail:=p; space_factor:=1000;
+ end;
+type(p):=unset_node; glue_stretch(p):=0;
+if every_cr<>null then begin_token_list(every_cr,every_cr_text);
+align_peek;
+end; {note that |glue_shrink(p)=0| since |glue_shrink==shift_amount|}
+
+@ Finally, we will reach the end of the alignment, and we can breathe a
+sigh of relief that memory hasn't overflowed. All the unset boxes will now be
+set so that the columns line up, taking due account of spanned columns.
+
+@p procedure@?do_assignments; forward;@t\2@>@/
+procedure@?resume_after_display; forward;@t\2@>@/
+procedure@?build_page; forward;@t\2@>@/
+procedure fin_align;
+var @!p,@!q,@!r,@!s,@!u,@!v: pointer; {registers for the list operations}
+@!t,@!w:scaled; {width of column}
+@!o:scaled; {shift offset for unset boxes}
+@!n:halfword; {matching span amount}
+@!rule_save:scaled; {temporary storage for |overfull_rule|}
+@!aux_save:memory_word; {temporary storage for |aux|}
+begin if cur_group<>align_group then confusion("align1");
+@:this can't happen align}{\quad align@>
+unsave; {that |align_group| was for individual entries}
+if cur_group<>align_group then confusion("align0");
+unsave; {that |align_group| was for the whole alignment}
+if nest[nest_ptr-1].mode_field=mmode then o:=display_indent
+ else o:=0;
+@<Go through the preamble list, determining the column widths and
+ changing the alignrecords to dummy unset boxes@>;
+@<Package the preamble list, to determine the actual tabskip glue amounts,
+ and let |p| point to this prototype box@>;
+@<Set the glue in all the unset boxes of the current list@>;
+flush_node_list(p); pop_alignment;
+@<Insert the \(c)current list into its environment@>;
+end;@/
+@t\4@>@<Declare the procedure called |align_peek|@>
+
+@ It's time now to dismantle the preamble list and to compute the column
+widths. Let $w_{ij}$ be the maximum of the natural widths of all entries
+that span columns $i$ through $j$, inclusive. The alignrecord for column~$i$
+contains $w_{ii}$ in its |width| field, and there is also a linked list of
+the nonzero $w_{ij}$ for increasing $j$, accessible via the |info| field;
+these span nodes contain the value $j-i-1+|min_quarterword|$ in their
+|link| fields. The values of $w_{ii}$ were initialized to |null_flag|, which
+we regard as $-\infty$.
+
+The final column widths are defined by the formula
+$$w_j=\max_{1\L i\L j}\biggl( w_{ij}-\sum_{i\L k<j}(t_k+w_k)\biggr),$$
+where $t_k$ is the natural width of the tabskip glue between columns
+$k$ and~$k+1$. However, if $w_{ij}=-\infty$ for all |i| in the range
+|1<=i<=j| (i.e., if every entry that involved column~|j| also involved
+column~|j+1|), we let $w_j=0$, and we zero out the tabskip glue after
+column~|j|.
+
+\TeX\ computes these values by using the following scheme: First $w_1=w_{11}$.
+Then replace $w_{2j}$ by $\max(w_{2j},w_{1j}-t_1-w_1)$, for all $j>1$.
+Then $w_2=w_{22}$. Then replace $w_{3j}$ by $\max(w_{3j},w_{2j}-t_2-w_2)$
+for all $j>2$; and so on. If any $w_j$ turns out to be $-\infty$, its
+value is changed to zero and so is the next tabskip.
+
+@<Go through the preamble list,...@>=
+q:=link(preamble);
+repeat flush_list(u_part(q)); flush_list(v_part(q));
+p:=link(link(q));
+if width(q)=null_flag then
+ @<Nullify |width(q)| and the tabskip glue following this column@>;
+if info(q)<>end_span then
+ @<Merge the widths in the span nodes of |q| with those of |p|,
+ destroying the span nodes of |q|@>;
+type(q):=unset_node; span_count(q):=min_quarterword; height(q):=0;
+depth(q):=0; glue_order(q):=normal; glue_sign(q):=normal;
+glue_stretch(q):=0; glue_shrink(q):=0; q:=p;
+until q=null
+
+@ @<Nullify |width(q)| and the tabskip glue following this column@>=
+begin width(q):=0; r:=link(q); s:=glue_ptr(r);
+if s<>zero_glue then
+ begin add_glue_ref(zero_glue); delete_glue_ref(s);
+ glue_ptr(r):=zero_glue;
+ end;
+end
+
+@ Merging of two span-node lists is a typical exercise in the manipulation of
+linearly linked data structures. The essential invariant in the following
+|repeat| loop is that we want to dispense with node |r|, in |q|'s list,
+and |u| is its successor; all nodes of |p|'s list up to and including |s|
+have been processed, and the successor of |s| matches |r| or precedes |r|
+or follows |r|, according as |link(r)=n| or |link(r)>n| or |link(r)<n|.
+
+@<Merge the widths...@>=
+begin t:=width(q)+width(glue_ptr(link(q)));
+r:=info(q); s:=end_span; info(s):=p; n:=min_quarterword+1;
+repeat width(r):=width(r)-t; u:=info(r);
+while link(r)>n do
+ begin s:=info(s); n:=link(info(s))+1;
+ end;
+if link(r)<n then
+ begin info(r):=info(s); info(s):=r; decr(link(r)); s:=r;
+ end
+else begin if width(r)>width(info(s)) then width(info(s)):=width(r);
+ free_node(r,span_node_size);
+ end;
+r:=u;
+until r=end_span;
+end
+
+@ Now the preamble list has been converted to a list of alternating unset
+boxes and tabskip glue, where the box widths are equal to the final
+column sizes. In case of \.{\\valign}, we change the widths to heights,
+so that a correct error message will be produced if the alignment is
+overfull or underfull.
+
+@<Package the preamble list...@>=
+save_ptr:=save_ptr-2; pack_begin_line:=-mode_line;
+if mode=-vmode then
+ begin rule_save:=overfull_rule;
+ overfull_rule:=0; {prevent rule from being packaged}
+ p:=hpack(preamble,saved(1),saved(0)); overfull_rule:=rule_save;
+ end
+else begin q:=link(preamble);
+ repeat height(q):=width(q); width(q):=0; q:=link(link(q));
+ until q=null;
+ p:=vpack(preamble,saved(1),saved(0));
+ q:=link(preamble);
+ repeat width(q):=height(q); height(q):=0; q:=link(link(q));
+ until q=null;
+ end;
+pack_begin_line:=0
+
+@ @<Set the glue in all the unset...@>=
+q:=link(head); s:=head;
+while q<>null do
+ begin if not is_char_node(q) then
+ if type(q)=unset_node then
+ @<Set the unset box |q| and the unset boxes in it@>
+ else if type(q)=rule_node then
+ @<Make the running dimensions in rule |q| extend to the
+ boundaries of the alignment@>;
+ s:=q; q:=link(q);
+ end
+
+@ @<Make the running dimensions in rule |q| extend...@>=
+begin if is_running(width(q)) then width(q):=width(p);
+if is_running(height(q)) then height(q):=height(p);
+if is_running(depth(q)) then depth(q):=depth(p);
+if o<>0 then
+ begin r:=link(q); link(q):=null; q:=hpack(q,natural);
+ shift_amount(q):=o; link(q):=r; link(s):=q;
+ end;
+end
+
+@ The unset box |q| represents a row that contains one or more unset boxes,
+depending on how soon \.{\\cr} occurred in that row.
+
+@<Set the unset box |q| and the unset boxes in it@>=
+begin if mode=-vmode then
+ begin type(q):=hlist_node; width(q):=width(p);
+ end
+else begin type(q):=vlist_node; height(q):=height(p);
+ end;
+glue_order(q):=glue_order(p); glue_sign(q):=glue_sign(p);
+glue_set(q):=glue_set(p); shift_amount(q):=o;
+r:=link(list_ptr(q)); s:=link(list_ptr(p));
+repeat @<Set the glue in node |r| and change it from an unset node@>;
+r:=link(link(r)); s:=link(link(s));
+until r=null;
+end
+
+@ A box made from spanned columns will be followed by tabskip glue nodes and
+by empty boxes as if there were no spanning. This permits perfect alignment
+of subsequent entries, and it prevents values that depend on floating point
+arithmetic from entering into the dimensions of any boxes.
+
+@<Set the glue in node |r|...@>=
+n:=span_count(r); t:=width(s); w:=t; u:=hold_head;
+while n>min_quarterword do
+ begin decr(n);
+ @<Append tabskip glue and an empty box to list |u|,
+ and update |s| and |t| as the prototype nodes are passed@>;
+ end;
+if mode=-vmode then
+ @<Make the unset node |r| into an |hlist_node| of width |w|,
+ setting the glue as if the width were |t|@>
+else @<Make the unset node |r| into a |vlist_node| of height |w|,
+ setting the glue as if the height were |t|@>;
+shift_amount(r):=0;
+if u<>hold_head then {append blank boxes to account for spanned nodes}
+ begin link(u):=link(r); link(r):=link(hold_head); r:=u;
+ end
+
+@ @<Append tabskip glue and an empty box to list |u|...@>=
+s:=link(s); v:=glue_ptr(s); link(u):=new_glue(v); u:=link(u);
+subtype(u):=tab_skip_code+1; t:=t+width(v);
+if glue_sign(p)=stretching then
+ begin if stretch_order(v)=glue_order(p) then
+ t:=t+round(float(glue_set(p))*stretch(v));
+@^real multiplication@>
+ end
+else if glue_sign(p)=shrinking then
+ begin if shrink_order(v)=glue_order(p) then
+ t:=t-round(float(glue_set(p))*shrink(v));
+ end;
+s:=link(s); link(u):=new_null_box; u:=link(u); t:=t+width(s);
+if mode=-vmode then width(u):=width(s)@+else
+ begin type(u):=vlist_node; height(u):=width(s);
+ end
+
+@ @<Make the unset node |r| into an |hlist_node| of width |w|...@>=
+begin height(r):=height(q); depth(r):=depth(q);
+if t=width(r) then
+ begin glue_sign(r):=normal; glue_order(r):=normal;
+ set_glue_ratio_zero(glue_set(r));
+ end
+else if t>width(r) then
+ begin glue_sign(r):=stretching;
+ if glue_stretch(r)=0 then set_glue_ratio_zero(glue_set(r))
+ else glue_set(r):=unfloat((t-width(r))/glue_stretch(r));
+@^real division@>
+ end
+else begin glue_order(r):=glue_sign(r); glue_sign(r):=shrinking;
+ if glue_shrink(r)=0 then set_glue_ratio_zero(glue_set(r))
+ else if (glue_order(r)=normal)and(width(r)-t>glue_shrink(r)) then
+ set_glue_ratio_one(glue_set(r))
+ else glue_set(r):=unfloat((width(r)-t)/glue_shrink(r));
+ end;
+width(r):=w; type(r):=hlist_node;
+end
+
+@ @<Make the unset node |r| into a |vlist_node| of height |w|...@>=
+begin width(r):=width(q);
+if t=height(r) then
+ begin glue_sign(r):=normal; glue_order(r):=normal;
+ set_glue_ratio_zero(glue_set(r));
+ end
+else if t>height(r) then
+ begin glue_sign(r):=stretching;
+ if glue_stretch(r)=0 then set_glue_ratio_zero(glue_set(r))
+ else glue_set(r):=unfloat((t-height(r))/glue_stretch(r));
+@^real division@>
+ end
+else begin glue_order(r):=glue_sign(r); glue_sign(r):=shrinking;
+ if glue_shrink(r)=0 then set_glue_ratio_zero(glue_set(r))
+ else if (glue_order(r)=normal)and(height(r)-t>glue_shrink(r)) then
+ set_glue_ratio_one(glue_set(r))
+ else glue_set(r):=unfloat((height(r)-t)/glue_shrink(r));
+ end;
+height(r):=w; type(r):=vlist_node;
+end
+
+@ We now have a completed alignment, in the list that starts at |head|
+and ends at |tail|. This list will be merged with the one that encloses
+it. (In case the enclosing mode is |mmode|, for displayed formulas,
+we will need to insert glue before and after the display; that part of the
+program will be deferred until we're more familiar with such operations.)
+
+In horizontal mode, the |clang| part of |aux| is undefined; an over-cautious
+\PASCAL\ runtime system may complain about this.
+@^dirty \PASCAL@>
+
+@<Insert the \(c)current list into its environment@>=
+aux_save:=aux; p:=link(head); q:=tail; pop_nest;
+if mode=mmode then @<Finish an alignment in a display@>
+else begin aux:=aux_save; link(tail):=p;
+ if p<>null then tail:=q;
+ if mode=vmode then build_page;
+ end
+
+@* \[38] Breaking paragraphs into lines.
+We come now to what is probably the most interesting algorithm of \TeX:
+the mechanism for choosing the ``best possible'' breakpoints that yield
+the individual lines of a paragraph. \TeX's line-breaking algorithm takes
+a given horizontal list and converts it to a sequence of boxes that are
+appended to the current vertical list. In the course of doing this, it
+creates a special data structure containing three kinds of records that are
+not used elsewhere in \TeX. Such nodes are created while a paragraph is
+being processed, and they are destroyed afterwards; thus, the other parts
+of \TeX\ do not need to know anything about how line-breaking is done.
+
+The method used here is based on an approach devised by Michael F. Plass and
+@^Plass, Michael Frederick@>
+@^Knuth, Donald Ervin@>
+the author in 1977, subsequently generalized and improved by the same two
+people in 1980. A detailed discussion appears in {\sl SOFTWARE---Practice
+\AM\ Experience \bf11} (1981), 1119--1184, where it is shown that the
+line-breaking problem can be regarded as a special case of the problem of
+computing the shortest path in an acyclic network. The cited paper includes
+numerous examples and describes the history of line breaking as it has been
+practiced by printers through the ages. The present implementation adds two
+new ideas to the algorithm of 1980: memory space requirements are considerably
+reduced by using smaller records for inactive nodes than for active ones,
+and arithmetic overflow is avoided by using ``delta distances'' instead of
+keeping track of the total distance from the beginning of the paragraph to the
+current point.
+
+@ The |line_break| procedure should be invoked only in horizontal mode; it
+leaves that mode and places its output into the current vlist of the
+enclosing vertical mode (or internal vertical mode).
+There is one explicit parameter: |final_widow_penalty| is the amount of
+additional penalty to be inserted before the final line of the paragraph.
+
+There are also a number of implicit parameters: The hlist to be broken
+starts at |link(head)|, and it is nonempty. The value of |prev_graf| in the
+enclosing semantic level tells where the paragraph should begin in the
+sequence of line numbers, in case hanging indentation or \.{\\parshape}
+are in use; |prev_graf| is zero unless this paragraph is being continued
+after a displayed formula. Other implicit parameters, such as the
+|par_shape_ptr| and various penalties to use for hyphenation, etc., appear
+in |eqtb|.
+
+After |line_break| has acted, it will have updated the current vlist and the
+value of |prev_graf|. Furthermore, the global variable |just_box| will
+point to the final box created by |line_break|, so that the width of this
+line can be ascertained when it is necessary to decide whether to use
+|above_display_skip| or |above_display_short_skip| before a displayed formula.
+
+@<Glob...@>=
+@!just_box:pointer; {the |hlist_node| for the last line of the new paragraph}
+
+@ Since |line_break| is a rather lengthy procedure---sort of a small world unto
+itself---we must build it up little by little, somewhat more cautiously
+than we have done with the simpler procedures of \TeX. Here is the
+general outline.
+
+@p@t\4@>@<Declare subprocedures for |line_break|@>
+procedure line_break(@!final_widow_penalty:integer);
+label done,done1,done2,done3,done4,done5,continue;
+var @<Local variables for line breaking@>@;
+begin pack_begin_line:=mode_line; {this is for over/underfull box messages}
+@<Get ready to start line breaking@>;
+@<Find optimal breakpoints@>;
+@<Break the paragraph at the chosen breakpoints, justify the resulting lines
+to the correct widths, and append them to the current vertical list@>;
+@<Clean up the memory by removing the break nodes@>;
+pack_begin_line:=0;
+end;
+
+@ The first task is to move the list from |head| to |temp_head| and go
+into the enclosing semantic level. We also append the \.{\\parfillskip}
+glue to the end of the paragraph, removing a space (or other glue node) if
+it was there, since spaces usually precede blank lines and instances of
+`\.{\$\$}'. The |par_fill_skip| is preceded by an infinite penalty, so
+it will never be considered as a potential breakpoint.
+
+This code assumes that a |glue_node| and a |penalty_node| occupy the
+same number of |mem|~words.
+@^data structure assumptions@>
+
+@<Get ready to start...@>=
+link(temp_head):=link(head);
+if is_char_node(tail) then tail_append(new_penalty(inf_penalty))
+else if type(tail)<>glue_node then tail_append(new_penalty(inf_penalty))
+else begin type(tail):=penalty_node; delete_glue_ref(glue_ptr(tail));
+ flush_node_list(leader_ptr(tail)); penalty(tail):=inf_penalty;
+ end;
+link(tail):=new_param_glue(par_fill_skip_code);
+init_cur_lang:=prev_graf mod @'200000;
+init_l_hyf:=prev_graf div @'20000000;
+init_r_hyf:=(prev_graf div @'200000) mod @'100;
+pop_nest;
+
+@ When looking for optimal line breaks, \TeX\ creates a ``break node'' for
+each break that is {\sl feasible}, in the sense that there is a way to end
+a line at the given place without requiring any line to stretch more than
+a given tolerance. A break node is characterized by three things: the position
+of the break (which is a pointer to a |glue_node|, |math_node|, |penalty_node|,
+or |disc_node|); the ordinal number of the line that will follow this
+breakpoint; and the fitness classification of the line that has just
+ended, i.e., |tight_fit|, |decent_fit|, |loose_fit|, or |very_loose_fit|.
+
+@d tight_fit=3 {fitness classification for lines shrinking 0.5 to 1.0 of their
+ shrinkability}
+@d loose_fit=1 {fitness classification for lines stretching 0.5 to 1.0 of their
+ stretchability}
+@d very_loose_fit=0 {fitness classification for lines stretching more than
+ their stretchability}
+@d decent_fit=2 {fitness classification for all other lines}
+
+@ The algorithm essentially determines the best possible way to achieve
+each feasible combination of position, line, and fitness. Thus, it answers
+questions like, ``What is the best way to break the opening part of the
+paragraph so that the fourth line is a tight line ending at such-and-such
+a place?'' However, the fact that all lines are to be the same length
+after a certain point makes it possible to regard all sufficiently large
+line numbers as equivalent, when the looseness parameter is zero, and this
+makes it possible for the algorithm to save space and time.
+
+An ``active node'' and a ``passive node'' are created in |mem| for each
+feasible breakpoint that needs to be considered. Active nodes are three
+words long and passive nodes are two words long. We need active nodes only
+for breakpoints near the place in the paragraph that is currently being
+examined, so they are recycled within a comparatively short time after
+they are created.
+
+@ An active node for a given breakpoint contains six fields:
+
+\yskip\hang|link| points to the next node in the list of active nodes; the
+last active node has |link=last_active|.
+
+\yskip\hang|break_node| points to the passive node associated with this
+breakpoint.
+
+\yskip\hang|line_number| is the number of the line that follows this
+breakpoint.
+
+\yskip\hang|fitness| is the fitness classification of the line ending at this
+breakpoint.
+
+\yskip\hang|type| is either |hyphenated| or |unhyphenated|, depending on
+whether this breakpoint is a |disc_node|.
+
+\yskip\hang|total_demerits| is the minimum possible sum of demerits over all
+lines leading from the beginning of the paragraph to this breakpoint.
+
+\yskip\noindent
+The value of |link(active)| points to the first active node on a linked list
+of all currently active nodes. This list is in order by |line_number|,
+except that nodes with |line_number>easy_line| may be in any order relative
+to each other.
+
+@d active_node_size=3 {number of words in active nodes}
+@d fitness==subtype {|very_loose_fit..tight_fit| on final line for this break}
+@d break_node==rlink {pointer to the corresponding passive node}
+@d line_number==llink {line that begins at this breakpoint}
+@d total_demerits(#)==mem[#+2].int {the quantity that \TeX\ minimizes}
+@d unhyphenated=0 {the |type| of a normal active break node}
+@d hyphenated=1 {the |type| of an active node that breaks at a |disc_node|}
+@d last_active==active {the active list ends where it begins}
+
+@ @<Initialize the special list heads...@>=
+type(last_active):=hyphenated; line_number(last_active):=max_halfword;
+subtype(last_active):=0; {the |subtype| is never examined by the algorithm}
+
+@ The passive node for a given breakpoint contains only four fields:
+
+\yskip\hang|link| points to the passive node created just before this one,
+if any, otherwise it is |null|.
+
+\yskip\hang|cur_break| points to the position of this breakpoint in the
+horizontal list for the paragraph being broken.
+
+\yskip\hang|prev_break| points to the passive node that should precede this
+one in an optimal path to this breakpoint.
+
+\yskip\hang|serial| is equal to |n| if this passive node is the |n|th
+one created during the current pass. (This field is used only when
+printing out detailed statistics about the line-breaking calculations.)
+
+\yskip\noindent
+There is a global variable called |passive| that points to the most
+recently created passive node. Another global variable, |printed_node|,
+is used to help print out the paragraph when detailed information about
+the line-breaking computation is being displayed.
+
+@d passive_node_size=2 {number of words in passive nodes}
+@d cur_break==rlink {in passive node, points to position of this breakpoint}
+@d prev_break==llink {points to passive node that should precede this one}
+@d serial==info {serial number for symbolic identification}
+
+@<Glob...@>=
+@!passive:pointer; {most recent node on passive list}
+@!printed_node:pointer; {most recent node that has been printed}
+@!pass_number:halfword; {the number of passive nodes allocated on this pass}
+
+@ The active list also contains ``delta'' nodes that help the algorithm
+compute the badness of individual lines. Such nodes appear only between two
+active nodes, and they have |type=delta_node|. If |p| and |r| are active nodes
+and if |q| is a delta node between them, so that |link(p)=q| and |link(q)=r|,
+then |q| tells the space difference between lines in the horizontal list that
+start after breakpoint |p| and lines that start after breakpoint |r|. In
+other words, if we know the length of the line that starts after |p| and
+ends at our current position, then the corresponding length of the line that
+starts after |r| is obtained by adding the amounts in node~|q|. A delta node
+contains six scaled numbers, since it must record the net change in glue
+stretchability with respect to all orders of infinity. The natural width
+difference appears in |mem[q+1].sc|; the stretch differences in units of
+pt, fil, fill, and filll appear in |mem[q+2..q+5].sc|; and the shrink difference
+appears in |mem[q+6].sc|. The |subtype| field of a delta node is not used.
+
+@d delta_node_size=7 {number of words in a delta node}
+@d delta_node=2 {|type| field in a delta node}
+
+@ As the algorithm runs, it maintains a set of six delta-like registers
+for the length of the line following the first active breakpoint to the
+current position in the given hlist. When it makes a pass through the
+active list, it also maintains a similar set of six registers for the
+length following the active breakpoint of current interest. A third set
+holds the length of an empty line (namely, the sum of \.{\\leftskip} and
+\.{\\rightskip}); and a fourth set is used to create new delta nodes.
+
+When we pass a delta node we want to do operations like
+$$\hbox{\ignorespaces|for
+k:=1 to 6 do cur_active_width[k]:=cur_active_width[k]+mem[q+k].sc|};$$ and we
+want to do this without the overhead of |for| loops. The |do_all_six|
+macro makes such six-tuples convenient.
+
+@d do_all_six(#)==#(1);#(2);#(3);#(4);#(5);#(6)
+
+@<Glo...@>=
+@!active_width:array[1..6] of scaled;
+ {distance from first active node to~|cur_p|}
+@!cur_active_width:array[1..6] of scaled; {distance from current active node}
+@!background:array[1..6] of scaled; {length of an ``empty'' line}
+@!break_width:array[1..6] of scaled; {length being computed after current break}
+
+@ Let's state the principles of the delta nodes more precisely and concisely,
+so that the following programs will be less obscure. For each legal
+breakpoint~|p| in the paragraph, we define two quantities $\alpha(p)$ and
+$\beta(p)$ such that the length of material in a line from breakpoint~|p|
+to breakpoint~|q| is $\gamma+\beta(q)-\alpha(p)$, for some fixed $\gamma$.
+Intuitively, $\alpha(p)$ and $\beta(q)$ are the total length of material from
+the beginning of the paragraph to a point ``after'' a break at |p| and to a
+point ``before'' a break at |q|; and $\gamma$ is the width of an empty line,
+namely the length contributed by \.{\\leftskip} and \.{\\rightskip}.
+
+Suppose, for example, that the paragraph consists entirely of alternating
+boxes and glue skips; let the boxes have widths $x_1\ldots x_n$ and
+let the skips have widths $y_1\ldots y_n$, so that the paragraph can be
+represented by $x_1y_1\ldots x_ny_n$. Let $p_i$ be the legal breakpoint
+at $y_i$; then $\alpha(p_i)=x_1+y_1+\cdots+x_i+y_i$, and $\beta(p_i)=
+x_1+y_1+\cdots+x_i$. To check this, note that the length of material from
+$p_2$ to $p_5$, say, is $\gamma+x_3+y_3+x_4+y_4+x_5=\gamma+\beta(p_5)
+-\alpha(p_2)$.
+
+The quantities $\alpha$, $\beta$, $\gamma$ involve glue stretchability and
+shrinkability as well as a natural width. If we were to compute $\alpha(p)$
+and $\beta(p)$ for each |p|, we would need multiple precision arithmetic, and
+the multiprecise numbers would have to be kept in the active nodes.
+\TeX\ avoids this problem by working entirely with relative differences
+or ``deltas.'' Suppose, for example, that the active list contains
+$a_1\,\delta_1\,a_2\,\delta_2\,a_3$, where the |a|'s are active breakpoints
+and the $\delta$'s are delta nodes. Then $\delta_1=\alpha(a_1)-\alpha(a_2)$
+and $\delta_2=\alpha(a_2)-\alpha(a_3)$. If the line breaking algorithm is
+currently positioned at some other breakpoint |p|, the |active_width| array
+contains the value $\gamma+\beta(p)-\alpha(a_1)$. If we are scanning through
+the list of active nodes and considering a tentative line that runs from
+$a_2$ to~|p|, say, the |cur_active_width| array will contain the value
+$\gamma+\beta(p)-\alpha(a_2)$. Thus, when we move from $a_2$ to $a_3$,
+we want to add $\alpha(a_2)-\alpha(a_3)$ to |cur_active_width|; and this
+is just $\delta_2$, which appears in the active list between $a_2$ and
+$a_3$. The |background| array contains $\gamma$. The |break_width| array
+will be used to calculate values of new delta nodes when the active
+list is being updated.
+
+@ Glue nodes in a horizontal list that is being paragraphed are not supposed to
+include ``infinite'' shrinkability; that is why the algorithm maintains
+four registers for stretching but only one for shrinking. If the user tries to
+introduce infinite shrinkability, the shrinkability will be reset to finite
+and an error message will be issued. A boolean variable |no_shrink_error_yet|
+prevents this error message from appearing more than once per paragraph.
+
+@d check_shrinkage(#)==if (shrink_order(#)<>normal)and(shrink(#)<>0) then
+ begin #:=finite_shrink(#);
+ end
+
+@<Glob...@>=
+@!no_shrink_error_yet:boolean; {have we complained about infinite shrinkage?}
+
+@ @<Declare subprocedures for |line_break|@>=
+function finite_shrink(@!p:pointer):pointer; {recovers from infinite shrinkage}
+var q:pointer; {new glue specification}
+begin if no_shrink_error_yet then
+ begin no_shrink_error_yet:=false;
+ print_err("Infinite glue shrinkage found in a paragraph");
+@.Infinite glue shrinkage...@>
+ help5("The paragraph just ended includes some glue that has")@/
+ ("infinite shrinkability, e.g., `\hskip 0pt minus 1fil'.")@/
+ ("Such glue doesn't belong there---it allows a paragraph")@/
+ ("of any length to fit on one line. But it's safe to proceed,")@/
+ ("since the offensive shrinkability has been made finite.");
+ error;
+ end;
+q:=new_spec(p); shrink_order(q):=normal;
+delete_glue_ref(p); finite_shrink:=q;
+end;
+
+@ @<Get ready to start...@>=
+no_shrink_error_yet:=true;@/
+check_shrinkage(left_skip); check_shrinkage(right_skip);@/
+q:=left_skip; r:=right_skip; background[1]:=width(q)+width(r);@/
+background[2]:=0; background[3]:=0; background[4]:=0; background[5]:=0;@/
+background[2+stretch_order(q)]:=stretch(q);@/
+background[2+stretch_order(r)]:=@|background[2+stretch_order(r)]+stretch(r);@/
+background[6]:=shrink(q)+shrink(r);
+
+@ A pointer variable |cur_p| runs through the given horizontal list as we look
+for breakpoints. This variable is global, since it is used both by |line_break|
+and by its subprocedure |try_break|.
+
+Another global variable called |threshold| is used to determine the feasibility
+of individual lines: breakpoints are feasible if there is a way to reach
+them without creating lines whose badness exceeds |threshold|. (The
+badness is compared to |threshold| before penalties are added, so that
+penalty values do not affect the feasibility of breakpoints, except that
+no break is allowed when the penalty is 10000 or more.) If |threshold|
+is 10000 or more, all legal breaks are considered feasible, since the
+|badness| function specified above never returns a value greater than~10000.
+
+Up to three passes might be made through the paragraph in an attempt to find at
+least one set of feasible breakpoints. On the first pass, we have
+|threshold=pretolerance| and |second_pass=final_pass=false|.
+If this pass fails to find a
+feasible solution, |threshold| is set to |tolerance|, |second_pass| is set
+|true|, and an attempt is made to hyphenate as many words as possible.
+If that fails too, we add |emergency_stretch| to the background
+stretchability and set |final_pass=true|.
+
+@<Glob...@>=
+@!cur_p:pointer; {the current breakpoint under consideration}
+@!second_pass:boolean; {is this our second attempt to break this paragraph?}
+@!final_pass:boolean; {is this our final attempt to break this paragraph?}
+@!threshold:integer; {maximum badness on feasible lines}
+
+@ The heart of the line-breaking procedure is `|try_break|', a subroutine
+that tests if the current breakpoint |cur_p| is feasible, by running
+through the active list to see what lines of text can be made from active
+nodes to~|cur_p|. If feasible breaks are possible, new break nodes are
+created. If |cur_p| is too far from an active node, that node is
+deactivated.
+
+The parameter |pi| to |try_break| is the penalty associated
+with a break at |cur_p|; we have |pi=eject_penalty| if the break is forced,
+and |pi=inf_penalty| if the break is illegal.
+
+The other parameter, |break_type|, is set to |hyphenated| or |unhyphenated|,
+depending on whether or not the current break is at a |disc_node|. The
+end of a paragraph is also regarded as `|hyphenated|'; this case is
+distinguishable by the condition |cur_p=null|.
+
+@d copy_to_cur_active(#)==cur_active_width[#]:=active_width[#]
+@d deactivate=60 {go here when node |r| should be deactivated}
+
+@<Declare subprocedures for |line_break|@>=
+procedure try_break(@!pi:integer;@!break_type:small_number);
+label exit,done,done1,continue,deactivate;
+var r:pointer; {runs through the active list}
+@!prev_r:pointer; {stays a step behind |r|}
+@!old_l:halfword; {maximum line number in current equivalence class of lines}
+@!no_break_yet:boolean; {have we found a feasible break at |cur_p|?}
+@<Other local variables for |try_break|@>@;
+begin @<Make sure that |pi| is in the proper range@>;
+no_break_yet:=true; prev_r:=active; old_l:=0;
+do_all_six(copy_to_cur_active);
+loop@+ begin continue: r:=link(prev_r);
+ @<If node |r| is of type |delta_node|, update |cur_active_width|,
+ set |prev_r| and |prev_prev_r|, then |goto continue|@>;
+ @<If a line number class has ended, create new active nodes for
+ the best feasible breaks in that class; then |return|
+ if |r=last_active|, otherwise compute the new |line_width|@>;
+ @<Consider the demerits for a line from |r| to |cur_p|;
+ deactivate node |r| if it should no longer be active;
+ then |goto continue| if a line from |r| to |cur_p| is infeasible,
+ otherwise record a new feasible break@>;
+ end;
+exit: @!stat @<Update the value of |printed_node| for
+ symbolic displays@>@+tats@;
+end;
+
+@ @<Other local variables for |try_break|@>=
+@!prev_prev_r:pointer; {a step behind |prev_r|, if |type(prev_r)=delta_node|}
+@!s:pointer; {runs through nodes ahead of |cur_p|}
+@!q:pointer; {points to a new node being created}
+@!v:pointer; {points to a glue specification or a node ahead of |cur_p|}
+@!t:integer; {node count, if |cur_p| is a discretionary node}
+@!f:internal_font_number; {used in character width calculation}
+@!l:halfword; {line number of current active node}
+@!node_r_stays_active:boolean; {should node |r| remain in the active list?}
+@!line_width:scaled; {the current line will be justified to this width}
+@!fit_class:very_loose_fit..tight_fit; {possible fitness class of test line}
+@!b:halfword; {badness of test line}
+@!d:integer; {demerits of test line}
+@!artificial_demerits:boolean; {has |d| been forced to zero?}
+@!save_link:pointer; {temporarily holds value of |link(cur_p)|}
+@!shortfall:scaled; {used in badness calculations}
+
+@ @<Make sure that |pi| is in the proper range@>=
+if abs(pi)>=inf_penalty then
+ if pi>0 then return {this breakpoint is inhibited by infinite penalty}
+ else pi:=eject_penalty {this breakpoint will be forced}
+
+@ The following code uses the fact that |type(last_active)<>delta_node|.
+
+@d update_width(#)==@|
+ cur_active_width[#]:=cur_active_width[#]+mem[r+#].sc
+
+@<If node |r|...@>=
+@^inner loop@>
+if type(r)=delta_node then
+ begin do_all_six(update_width);
+ prev_prev_r:=prev_r; prev_r:=r; goto continue;
+ end
+
+@ As we consider various ways to end a line at |cur_p|, in a given line number
+class, we keep track of the best total demerits known, in an array with
+one entry for each of the fitness classifications. For example,
+|minimal_demerits[tight_fit]| contains the fewest total demerits of feasible
+line breaks ending at |cur_p| with a |tight_fit| line; |best_place[tight_fit]|
+points to the passive node for the break before~|cur_p| that achieves such
+an optimum; and |best_pl_line[tight_fit]| is the |line_number| field in the
+active node corresponding to |best_place[tight_fit]|. When no feasible break
+sequence is known, the |minimal_demerits| entries will be equal to
+|awful_bad|, which is $2^{30}-1$. Another variable, |minimum_demerits|,
+keeps track of the smallest value in the |minimal_demerits| array.
+
+@d awful_bad==@'7777777777 {more than a billion demerits}
+
+@<Global...@>=
+@!minimal_demerits:array[very_loose_fit..tight_fit] of integer; {best total
+ demerits known for current line class and position, given the fitness}
+@!minimum_demerits:integer; {best total demerits known for current line class
+ and position}
+@!best_place:array[very_loose_fit..tight_fit] of pointer; {how to achieve
+ |minimal_demerits|}
+@!best_pl_line:array[very_loose_fit..tight_fit] of halfword; {corresponding
+ line number}
+
+@ @<Get ready to start...@>=
+minimum_demerits:=awful_bad;
+minimal_demerits[tight_fit]:=awful_bad;
+minimal_demerits[decent_fit]:=awful_bad;
+minimal_demerits[loose_fit]:=awful_bad;
+minimal_demerits[very_loose_fit]:=awful_bad;
+
+@ The first part of the following code is part of \TeX's inner loop, so
+we don't want to waste any time. The current active node, namely node |r|,
+contains the line number that will be considered next. At the end of the
+list we have arranged the data structure so that |r=last_active| and
+|line_number(last_active)>old_l|.
+@^inner loop@>
+
+@<If a line number class...@>=
+begin l:=line_number(r);
+if l>old_l then
+ begin {now we are no longer in the inner loop}
+ if (minimum_demerits<awful_bad)and@|
+ ((old_l<>easy_line)or(r=last_active)) then
+ @<Create new active nodes for the best feasible breaks
+ just found@>;
+ if r=last_active then return;
+ @<Compute the new line width@>;
+ end;
+end
+
+@ It is not necessary to create new active nodes having |minimal_demerits|
+greater than
+|minimum_demerits+abs(adj_demerits)|, since such active nodes will never
+be chosen in the final paragraph breaks. This observation allows us to
+omit a substantial number of feasible breakpoints from further consideration.
+
+@<Create new active nodes...@>=
+begin if no_break_yet then @<Compute the values of |break_width|@>;
+@<Insert a delta node to prepare for breaks at |cur_p|@>;
+if abs(adj_demerits)>=awful_bad-minimum_demerits then
+ minimum_demerits:=awful_bad-1
+else minimum_demerits:=minimum_demerits+abs(adj_demerits);
+for fit_class:=very_loose_fit to tight_fit do
+ begin if minimal_demerits[fit_class]<=minimum_demerits then
+ @<Insert a new active node
+ from |best_place[fit_class]| to |cur_p|@>;
+ minimal_demerits[fit_class]:=awful_bad;
+ end;
+minimum_demerits:=awful_bad;
+@<Insert a delta node to prepare for the next active node@>;
+end
+
+@ When we insert a new active node for a break at |cur_p|, suppose this
+new node is to be placed just before active node |a|; then we essentially
+want to insert `$\delta\,|cur_p|\,\delta^\prime$' before |a|, where
+$\delta=\alpha(a)-\alpha(|cur_p|)$ and $\delta^\prime=\alpha(|cur_p|)-\alpha(a)$
+in the notation explained above. The |cur_active_width| array now holds
+$\gamma+\beta(|cur_p|)-\alpha(a)$; so $\delta$ can be obtained by
+subtracting |cur_active_width| from the quantity $\gamma+\beta(|cur_p|)-
+\alpha(|cur_p|)$. The latter quantity can be regarded as the length of a
+line ``from |cur_p| to |cur_p|''; we call it the |break_width| at |cur_p|.
+
+The |break_width| is usually negative, since it consists of the background
+(which is normally zero) minus the width of nodes following~|cur_p| that are
+eliminated after a break. If, for example, node |cur_p| is a glue node, the
+width of this glue is subtracted from the background; and we also look
+ahead to eliminate all subsequent glue and penalty and kern and math
+nodes, subtracting their widths as well.
+
+Kern nodes do not disappear at a line break unless they are |explicit|.
+
+@d set_break_width_to_background(#)==break_width[#]:=background[#]
+
+@<Compute the values of |break...@>=
+begin no_break_yet:=false; do_all_six(set_break_width_to_background);
+s:=cur_p;
+if break_type>unhyphenated then if cur_p<>null then
+ @<Compute the discretionary |break_width| values@>;
+while s<>null do
+ begin if is_char_node(s) then goto done;
+ case type(s) of
+ glue_node:@<Subtract glue from |break_width|@>;
+ penalty_node: do_nothing;
+ math_node: break_width[1]:=break_width[1]-width(s);
+ kern_node: if subtype(s)<>explicit then goto done
+ else break_width[1]:=break_width[1]-width(s);
+ othercases goto done
+ endcases;@/
+ s:=link(s);
+ end;
+done: end
+
+@ @<Subtract glue from |break...@>=
+begin v:=glue_ptr(s); break_width[1]:=break_width[1]-width(v);
+break_width[2+stretch_order(v)]:=break_width[2+stretch_order(v)]-stretch(v);
+break_width[6]:=break_width[6]-shrink(v);
+end
+
+@ When |cur_p| is a discretionary break, the length of a line ``from |cur_p| to
+|cur_p|'' has to be defined properly so that the other calculations work out.
+Suppose that the pre-break text at |cur_p| has length $l_0$, the post-break
+text has length $l_1$, and the replacement text has length |l|. Suppose
+also that |q| is the node following the replacement text. Then length of a
+line from |cur_p| to |q| will be computed as $\gamma+\beta(q)-\alpha(|cur_p|)$,
+where $\beta(q)=\beta(|cur_p|)-l_0+l$. The actual length will be the background
+plus $l_1$, so the length from |cur_p| to |cur_p| should be $\gamma+l_0+l_1-l$.
+If the post-break text of the discretionary is empty, a break may also
+discard~|q|; in that unusual case we subtract the length of~|q| and any
+other nodes that will be discarded after the discretionary break.
+
+The value of $l_0$ need not be computed, since |line_break| will put
+it into the global variable |disc_width| before calling |try_break|.
+
+@<Glob...@>=
+@!disc_width:scaled; {the length of discretionary material preceding a break}
+
+@ @<Compute the discretionary |break...@>=
+begin t:=replace_count(cur_p); v:=cur_p; s:=post_break(cur_p);
+while t>0 do
+ begin decr(t); v:=link(v);
+ @<Subtract the width of node |v| from |break_width|@>;
+ end;
+while s<>null do
+ begin @<Add the width of node |s| to |break_width|@>;
+ s:=link(s);
+ end;
+break_width[1]:=break_width[1]+disc_width;
+if post_break(cur_p)=null then s:=link(v);
+ {nodes may be discardable after the break}
+end
+
+@ Replacement texts and discretionary texts are supposed to contain
+only character nodes, kern nodes, ligature nodes, and box or rule nodes.
+
+@<Subtract the width of node |v|...@>=
+if is_char_node(v) then
+ begin f:=font(v);
+ break_width[1]:=break_width[1]-char_width(f)(char_info(f)(character(v)));
+ end
+else case type(v) of
+ ligature_node: begin f:=font(lig_char(v));@/
+ break_width[1]:=@|break_width[1]-
+ char_width(f)(char_info(f)(character(lig_char(v))));
+ end;
+ hlist_node,vlist_node,rule_node,kern_node:
+ break_width[1]:=break_width[1]-width(v);
+ othercases confusion("disc1")
+@:this can't happen disc1}{\quad disc1@>
+ endcases
+
+@ @<Add the width of node |s| to |b...@>=
+if is_char_node(s) then
+ begin f:=font(s);
+ break_width[1]:=@|break_width[1]+char_width(f)(char_info(f)(character(s)));
+ end
+else case type(s) of
+ ligature_node: begin f:=font(lig_char(s));
+ break_width[1]:=break_width[1]+
+ char_width(f)(char_info(f)(character(lig_char(s))));
+ end;
+ hlist_node,vlist_node,rule_node,kern_node:
+ break_width[1]:=break_width[1]+width(s);
+ othercases confusion("disc2")
+@:this can't happen disc2}{\quad disc2@>
+ endcases
+
+@ We use the fact that |type(active)<>delta_node|.
+
+@d convert_to_break_width(#)==@|
+ mem[prev_r+#].sc:=@|@t\hskip10pt@>mem[prev_r+#].sc
+ -cur_active_width[#]+break_width[#]
+@d store_break_width(#)==active_width[#]:=break_width[#]
+@d new_delta_to_break_width(#)==@|
+ mem[q+#].sc:=break_width[#]-cur_active_width[#]
+
+@<Insert a delta node to prepare for breaks at |cur_p|@>=
+if type(prev_r)=delta_node then {modify an existing delta node}
+ begin do_all_six(convert_to_break_width);
+ end
+else if prev_r=active then {no delta node needed at the beginning}
+ begin do_all_six(store_break_width);
+ end
+else begin q:=get_node(delta_node_size); link(q):=r; type(q):=delta_node;@/
+ subtype(q):=0; {the |subtype| is not used}
+ do_all_six(new_delta_to_break_width);
+ link(prev_r):=q; prev_prev_r:=prev_r; prev_r:=q;
+ end
+
+@ When the following code is performed, we will have just inserted at
+least one active node before |r|, so |type(prev_r)<>delta_node|.
+
+@d new_delta_from_break_width(#)==@|mem[q+#].sc:=
+ cur_active_width[#]-break_width[#]
+
+@<Insert a delta node to prepare for the next active node@>=
+if r<>last_active then
+ begin q:=get_node(delta_node_size); link(q):=r; type(q):=delta_node;@/
+ subtype(q):=0; {the |subtype| is not used}
+ do_all_six(new_delta_from_break_width);
+ link(prev_r):=q; prev_prev_r:=prev_r; prev_r:=q;
+ end
+
+@ When we create an active node, we also create the corresponding
+passive node.
+
+@<Insert a new active node from |best_place[fit_class]| to |cur_p|@>=
+begin q:=get_node(passive_node_size);
+link(q):=passive; passive:=q; cur_break(q):=cur_p;
+@!stat incr(pass_number); serial(q):=pass_number;@+tats@;@/
+prev_break(q):=best_place[fit_class];@/
+q:=get_node(active_node_size); break_node(q):=passive;
+line_number(q):=best_pl_line[fit_class]+1;
+fitness(q):=fit_class; type(q):=break_type;
+total_demerits(q):=minimal_demerits[fit_class];
+link(q):=r; link(prev_r):=q; prev_r:=q;
+@!stat if tracing_paragraphs>0 then
+ @<Print a symbolic description of the new break node@>;
+tats@;@/
+end
+
+@ @<Print a symbolic description of the new break node@>=
+begin print_nl("@@@@"); print_int(serial(passive));
+@.\AT!\AT!@>
+print(": line "); print_int(line_number(q)-1);
+print_char("."); print_int(fit_class);
+if break_type=hyphenated then print_char("-");
+print(" t="); print_int(total_demerits(q));
+print(" -> @@@@");
+if prev_break(passive)=null then print_char("0")
+else print_int(serial(prev_break(passive)));
+end
+
+@ The length of lines depends on whether the user has specified
+\.{\\parshape} or \.{\\hangindent}. If |par_shape_ptr| is not null, it
+points to a $(2n+1)$-word record in |mem|, where the |info| in the first
+word contains the value of |n|, and the other $2n$ words contain the left
+margins and line lengths for the first |n| lines of the paragraph; the
+specifications for line |n| apply to all subsequent lines. If
+|par_shape_ptr=null|, the shape of the paragraph depends on the value of
+|n=hang_after|; if |n>=0|, hanging indentation takes place on lines |n+1|,
+|n+2|, \dots, otherwise it takes place on lines 1, \dots, $\vert
+n\vert$. When hanging indentation is active, the left margin is
+|hang_indent|, if |hang_indent>=0|, else it is 0; the line length is
+$|hsize|-\vert|hang_indent|\vert$. The normal setting is
+|par_shape_ptr=null|, |hang_after=1|, and |hang_indent=0|.
+Note that if |hang_indent=0|, the value of |hang_after| is irrelevant.
+@^length of lines@> @^hanging indentation@>
+
+@<Glob...@>=
+@!easy_line:halfword; {line numbers |>easy_line| are equivalent in break nodes}
+@!last_special_line:halfword; {line numbers |>last_special_line| all have
+ the same width}
+@!first_width:scaled; {the width of all lines |<=last_special_line|, if
+ no \.{\\parshape} has been specified}
+@!second_width:scaled; {the width of all lines |>last_special_line|}
+@!first_indent:scaled; {left margin to go with |first_width|}
+@!second_indent:scaled; {left margin to go with |second_width|}
+
+@ We compute the values of |easy_line| and the other local variables relating
+to line length when the |line_break| procedure is initializing itself.
+
+@<Get ready to start...@>=
+if par_shape_ptr=null then
+ if hang_indent=0 then
+ begin last_special_line:=0; second_width:=hsize;
+ second_indent:=0;
+ end
+ else @<Set line length parameters in preparation for hanging indentation@>
+else begin last_special_line:=info(par_shape_ptr)-1;
+ second_width:=mem[par_shape_ptr+2*(last_special_line+1)].sc;
+ second_indent:=mem[par_shape_ptr+2*last_special_line+1].sc;
+ end;
+if looseness=0 then easy_line:=last_special_line
+else easy_line:=max_halfword
+
+@ @<Set line length parameters in preparation for hanging indentation@>=
+begin last_special_line:=abs(hang_after);
+if hang_after<0 then
+ begin first_width:=hsize-abs(hang_indent);
+ if hang_indent>=0 then first_indent:=hang_indent
+ else first_indent:=0;
+ second_width:=hsize; second_indent:=0;
+ end
+else begin first_width:=hsize; first_indent:=0;
+ second_width:=hsize-abs(hang_indent);
+ if hang_indent>=0 then second_indent:=hang_indent
+ else second_indent:=0;
+ end;
+end
+
+@ When we come to the following code, we have just encountered the first
+active node~|r| whose |line_number| field contains |l|. Thus we want to
+compute the length of the $l\mskip1mu$th line of the current paragraph. Furthermore,
+we want to set |old_l| to the last number in the class of line numbers
+equivalent to~|l|.
+
+@<Compute the new line width@>=
+if l>easy_line then
+ begin line_width:=second_width; old_l:=max_halfword-1;
+ end
+else begin old_l:=l;
+ if l>last_special_line then line_width:=second_width
+ else if par_shape_ptr=null then line_width:=first_width
+ else line_width:=mem[par_shape_ptr+2*l@,].sc;
+ end
+
+@ The remaining part of |try_break| deals with the calculation of
+demerits for a break from |r| to |cur_p|.
+
+The first thing to do is calculate the badness, |b|. This value will always
+be between zero and |inf_bad+1|; the latter value occurs only in the
+case of lines from |r| to |cur_p| that cannot shrink enough to fit the necessary
+width. In such cases, node |r| will be deactivated.
+We also deactivate node~|r| when a break at~|cur_p| is forced, since future
+breaks must go through a forced break.
+
+@<Consider the demerits for a line from |r| to |cur_p|...@>=
+begin artificial_demerits:=false;@/
+@^inner loop@>
+shortfall:=line_width-cur_active_width[1]; {we're this much too short}
+if shortfall>0 then
+ @<Set the value of |b| to the badness for stretching the line,
+ and compute the corresponding |fit_class|@>
+else @<Set the value of |b| to the badness for shrinking the line,
+ and compute the corresponding |fit_class|@>;
+if (b>inf_bad)or(pi=eject_penalty) then
+ @<Prepare to deactivate node~|r|, and |goto deactivate| unless
+ there is a reason to consider lines of text from |r| to |cur_p|@>
+else begin prev_r:=r;
+ if b>threshold then goto continue;
+ node_r_stays_active:=true;
+ end;
+@<Record a new feasible break@>;
+if node_r_stays_active then goto continue; {|prev_r| has been set to |r|}
+deactivate: @<Deactivate node |r|@>;
+end
+
+@ When a line must stretch, the available stretchability can be found in the
+subarray |cur_active_width[2..5]|, in units of points, fil, fill, and filll.
+
+The present section is part of \TeX's inner loop, and it is most often performed
+when the badness is infinite; therefore it is worth while to make a quick
+test for large width excess and small stretchability, before calling the
+|badness| subroutine.
+@^inner loop@>
+
+@<Set the value of |b| to the badness for stretching...@>=
+if (cur_active_width[3]<>0)or(cur_active_width[4]<>0)or@|
+ (cur_active_width[5]<>0) then
+ begin b:=0; fit_class:=decent_fit; {infinite stretch}
+ end
+else begin if shortfall>7230584 then if cur_active_width[2]<1663497 then
+ begin b:=inf_bad; fit_class:=very_loose_fit; goto done1;
+ end;
+ b:=badness(shortfall,cur_active_width[2]);
+ if b>12 then
+ if b>99 then fit_class:=very_loose_fit
+ else fit_class:=loose_fit
+ else fit_class:=decent_fit;
+ done1:
+ end
+
+@ Shrinkability is never infinite in a paragraph;
+we can shrink the line from |r| to |cur_p| by at most |cur_active_width[6]|.
+
+@<Set the value of |b| to the badness for shrinking...@>=
+begin if -shortfall>cur_active_width[6] then b:=inf_bad+1
+else b:=badness(-shortfall,cur_active_width[6]);
+if b>12 then fit_class:=tight_fit@+else fit_class:=decent_fit;
+end
+
+@ During the final pass, we dare not lose all active nodes, lest we lose
+touch with the line breaks already found. The code shown here makes sure
+that such a catastrophe does not happen, by permitting overfull boxes as
+a last resort. This particular part of \TeX\ was a source of several subtle
+bugs before the correct program logic was finally discovered; readers
+who seek to ``improve'' \TeX\ should therefore think thrice before daring
+to make any changes here.
+@^overfull boxes@>
+
+@<Prepare to deactivate node~|r|, and |goto deactivate| unless...@>=
+begin if final_pass and (minimum_demerits=awful_bad) and@|
+ (link(r)=last_active) and
+ (prev_r=active) then
+ artificial_demerits:=true {set demerits zero, this break is forced}
+else if b>threshold then goto deactivate;
+node_r_stays_active:=false;
+end
+
+@ When we get to this part of the code, the line from |r| to |cur_p| is
+feasible, its badness is~|b|, and its fitness classification is |fit_class|.
+We don't want to make an active node for this break yet, but we will
+compute the total demerits and record them in the |minimal_demerits| array,
+if such a break is the current champion among all ways to get to |cur_p|
+in a given line-number class and fitness class.
+
+@<Record a new feasible break@>=
+if artificial_demerits then d:=0
+else @<Compute the demerits, |d|, from |r| to |cur_p|@>;
+@!stat if tracing_paragraphs>0 then
+ @<Print a symbolic description of this feasible break@>;
+tats@;@/
+d:=d+total_demerits(r); {this is the minimum total demerits
+ from the beginning to |cur_p| via |r|}
+if d<=minimal_demerits[fit_class] then
+ begin minimal_demerits[fit_class]:=d;
+ best_place[fit_class]:=break_node(r); best_pl_line[fit_class]:=l;
+ if d<minimum_demerits then minimum_demerits:=d;
+ end
+
+@ @<Print a symbolic description of this feasible break@>=
+begin if printed_node<>cur_p then
+ @<Print the list between |printed_node| and |cur_p|,
+ then set |printed_node:=cur_p|@>;
+print_nl("@@");
+@.\AT!@>
+if cur_p=null then print_esc("par")
+else if type(cur_p)<>glue_node then
+ begin if type(cur_p)=penalty_node then print_esc("penalty")
+ else if type(cur_p)=disc_node then print_esc("discretionary")
+ else if type(cur_p)=kern_node then print_esc("kern")
+ else print_esc("math");
+ end;
+print(" via @@@@");
+if break_node(r)=null then print_char("0")
+else print_int(serial(break_node(r)));
+print(" b=");
+if b>inf_bad then print_char("*")@+else print_int(b);
+@.*\relax@>
+print(" p="); print_int(pi); print(" d=");
+if artificial_demerits then print_char("*")@+else print_int(d);
+end
+
+@ @<Print the list between |printed_node| and |cur_p|...@>=
+begin print_nl("");
+if cur_p=null then short_display(link(printed_node))
+else begin save_link:=link(cur_p);
+ link(cur_p):=null; print_nl(""); short_display(link(printed_node));
+ link(cur_p):=save_link;
+ end;
+printed_node:=cur_p;
+end
+
+@ When the data for a discretionary break is being displayed, we will have
+printed the |pre_break| and |post_break| lists; we want to skip over the
+third list, so that the discretionary data will not appear twice. The
+following code is performed at the very end of |try_break|.
+
+@<Update the value of |printed_node|...@>=
+if cur_p=printed_node then if cur_p<>null then if type(cur_p)=disc_node then
+ begin t:=replace_count(cur_p);
+ while t>0 do
+ begin decr(t); printed_node:=link(printed_node);
+ end;
+ end
+
+@ @<Compute the demerits, |d|, from |r| to |cur_p|@>=
+begin d:=line_penalty+b;
+if abs(d)>=10000 then d:=100000000@+else d:=d*d;
+if pi<>0 then
+ if pi>0 then d:=d+pi*pi
+ else if pi>eject_penalty then d:=d-pi*pi;
+if (break_type=hyphenated)and(type(r)=hyphenated) then
+ if cur_p<>null then d:=d+double_hyphen_demerits
+ else d:=d+final_hyphen_demerits;
+if abs(fit_class-fitness(r))>1 then d:=d+adj_demerits;
+end
+
+@ When an active node disappears, we must delete an adjacent delta node if the
+active node was at the beginning or the end of the active list, or if it
+was surrounded by delta nodes. We also must preserve the property that
+|cur_active_width| represents the length of material from |link(prev_r)|
+to~|cur_p|.
+
+@d combine_two_deltas(#)==@|mem[prev_r+#].sc:=mem[prev_r+#].sc+mem[r+#].sc
+@d downdate_width(#)==@|cur_active_width[#]:=cur_active_width[#]-
+ mem[prev_r+#].sc
+
+@<Deactivate node |r|@>=
+link(prev_r):=link(r); free_node(r,active_node_size);
+if prev_r=active then @<Update the active widths, since the first active
+ node has been deleted@>
+else if type(prev_r)=delta_node then
+ begin r:=link(prev_r);
+ if r=last_active then
+ begin do_all_six(downdate_width);
+ link(prev_prev_r):=last_active;
+ free_node(prev_r,delta_node_size); prev_r:=prev_prev_r;
+ end
+ else if type(r)=delta_node then
+ begin do_all_six(update_width);
+ do_all_six(combine_two_deltas);
+ link(prev_r):=link(r); free_node(r,delta_node_size);
+ end;
+ end
+
+@ The following code uses the fact that |type(last_active)<>delta_node|. If the
+active list has just become empty, we do not need to update the
+|active_width| array, since it will be initialized when an active
+node is next inserted.
+
+@d update_active(#)==active_width[#]:=active_width[#]+mem[r+#].sc
+
+@<Update the active widths,...@>=
+begin r:=link(active);
+if type(r)=delta_node then
+ begin do_all_six(update_active);
+ do_all_six(copy_to_cur_active);
+ link(active):=link(r); free_node(r,delta_node_size);
+ end;
+end
+
+@* \[39] Breaking paragraphs into lines, continued.
+So far we have gotten a little way into the |line_break| routine, having
+covered its important |try_break| subroutine. Now let's consider the
+rest of the process.
+
+The main loop of |line_break| traverses the given hlist,
+starting at |link(temp_head)|, and calls |try_break| at each legal
+breakpoint. A variable called |auto_breaking| is set to true except
+within math formulas, since glue nodes are not legal breakpoints when
+they appear in formulas.
+
+The current node of interest in the hlist is pointed to by |cur_p|. Another
+variable, |prev_p|, is usually one step behind |cur_p|, but the real
+meaning of |prev_p| is this: If |type(cur_p)=glue_node| then |cur_p| is a legal
+breakpoint if and only if |auto_breaking| is true and |prev_p| does not
+point to a glue node, penalty node, explicit kern node, or math node.
+
+The following declarations provide for a few other local variables that are
+used in special calculations.
+
+@<Local variables for line breaking@>=
+@!auto_breaking:boolean; {is node |cur_p| outside a formula?}
+@!prev_p:pointer; {helps to determine when glue nodes are breakpoints}
+@!q,@!r,@!s,@!prev_s:pointer; {miscellaneous nodes of temporary interest}
+@!f:internal_font_number; {used when calculating character widths}
+
+@ The `\ignorespaces|loop|\unskip' in the following code is performed at most
+thrice per call of |line_break|, since it is actually a pass over the
+entire paragraph.
+
+@<Find optimal breakpoints@>=
+threshold:=pretolerance;
+if threshold>=0 then
+ begin @!stat if tracing_paragraphs>0 then
+ begin begin_diagnostic; print_nl("@@firstpass");@+end;@;@+tats@;@/
+ second_pass:=false; final_pass:=false;
+ end
+else begin threshold:=tolerance; second_pass:=true;
+ final_pass:=(emergency_stretch<=0);
+ @!stat if tracing_paragraphs>0 then begin_diagnostic;@+tats@;
+ end;
+loop@+ begin if threshold>inf_bad then threshold:=inf_bad;
+ if second_pass then @<Initialize for hyphenating a paragraph@>;
+ @<Create an active breakpoint representing the beginning of the paragraph@>;
+ cur_p:=link(temp_head); auto_breaking:=true;@/
+ prev_p:=cur_p; {glue at beginning is not a legal breakpoint}
+ while (cur_p<>null)and(link(active)<>last_active) do
+ @<Call |try_break| if |cur_p| is a legal breakpoint;
+ on the second pass, also try to hyphenate the next
+ word, if |cur_p| is a glue node;
+ then advance |cur_p| to the next node of the paragraph
+ that could possibly be a legal breakpoint@>;
+ if cur_p=null then
+ @<Try the final line break at the end of the paragraph,
+ and |goto done| if the desired breakpoints have been found@>;
+ @<Clean up the memory by removing the break nodes@>;
+ if not second_pass then
+ begin@!stat if tracing_paragraphs>0 then print_nl("@@secondpass");@;@+tats@/
+ threshold:=tolerance; second_pass:=true; final_pass:=(emergency_stretch<=0);
+ end {if at first you don't succeed, \dots}
+ else begin @!stat if tracing_paragraphs>0 then
+ print_nl("@@emergencypass");@;@+tats@/
+ background[2]:=background[2]+emergency_stretch; final_pass:=true;
+ end;
+ end;
+done: @!stat if tracing_paragraphs>0 then
+ begin end_diagnostic(true); normalize_selector;
+ end;@+tats@/
+
+@ The active node that represents the starting point does not need a
+corresponding passive node.
+
+@d store_background(#)==active_width[#]:=background[#]
+
+@<Create an active breakpoint representing the beginning of the paragraph@>=
+q:=get_node(active_node_size);
+type(q):=unhyphenated; fitness(q):=decent_fit;
+link(q):=last_active; break_node(q):=null;
+line_number(q):=prev_graf+1; total_demerits(q):=0; link(active):=q;
+do_all_six(store_background);@/
+passive:=null; printed_node:=temp_head; pass_number:=0;
+font_in_short_display:=null_font
+
+@ @<Clean...@>=
+q:=link(active);
+while q<>last_active do
+ begin cur_p:=link(q);
+ if type(q)=delta_node then free_node(q,delta_node_size)
+ else free_node(q,active_node_size);
+ q:=cur_p;
+ end;
+q:=passive;
+while q<>null do
+ begin cur_p:=link(q);
+ free_node(q,passive_node_size);
+ q:=cur_p;
+ end
+
+@ Here is the main switch in the |line_break| routine, where legal breaks
+are determined. As we move through the hlist, we need to keep the |active_width|
+array up to date, so that the badness of individual lines is readily calculated
+by |try_break|. It is convenient to use the short name |act_width| for
+the component of active width that represents real width as opposed to glue.
+
+@d act_width==active_width[1] {length from first active node to current node}
+@d kern_break==begin if not is_char_node(link(cur_p)) and auto_breaking then
+ if type(link(cur_p))=glue_node then try_break(0,unhyphenated);
+ act_width:=act_width+width(cur_p);
+ end
+
+@<Call |try_break| if |cur_p| is a legal breakpoint...@>=
+begin if is_char_node(cur_p) then
+ @<Advance \(c)|cur_p| to the node following the present
+ string of characters@>;
+case type(cur_p) of
+hlist_node,vlist_node,rule_node: act_width:=act_width+width(cur_p);
+whatsit_node: @<Advance \(p)past a whatsit node in the \(l)|line_break| loop@>;
+glue_node: begin @<If node |cur_p| is a legal breakpoint, call |try_break|;
+ then update the active widths by including the glue in |glue_ptr(cur_p)|@>;
+ if second_pass and auto_breaking then
+ @<Try to hyphenate the following word@>;
+ end;
+kern_node: if subtype(cur_p)=explicit then kern_break
+ else act_width:=act_width+width(cur_p);
+ligature_node: begin f:=font(lig_char(cur_p));
+ act_width:=act_width+char_width(f)(char_info(f)(character(lig_char(cur_p))));
+ end;
+disc_node: @<Try to break after a discretionary fragment, then |goto done5|@>;
+math_node: begin auto_breaking:=(subtype(cur_p)=after); kern_break;
+ end;
+penalty_node: try_break(penalty(cur_p),unhyphenated);
+mark_node,ins_node,adjust_node: do_nothing;
+othercases confusion("paragraph")
+@:this can't happen paragraph}{\quad paragraph@>
+endcases;@/
+prev_p:=cur_p; cur_p:=link(cur_p);
+done5:end
+
+@ The code that passes over the characters of words in a paragraph is
+part of \TeX's inner loop, so it has been streamlined for speed. We use
+the fact that `\.{\\parfillskip}' glue appears at the end of each paragraph;
+it is therefore unnecessary to check if |link(cur_p)=null| when |cur_p| is a
+character node.
+@^inner loop@>
+
+@<Advance \(c)|cur_p| to the node following the present string...@>=
+begin prev_p:=cur_p;
+repeat f:=font(cur_p);
+act_width:=act_width+char_width(f)(char_info(f)(character(cur_p)));
+cur_p:=link(cur_p);
+until not is_char_node(cur_p);
+end
+
+@ When node |cur_p| is a glue node, we look at |prev_p| to see whether or not
+a breakpoint is legal at |cur_p|, as explained above.
+
+@<If node |cur_p| is a legal breakpoint, call...@>=
+if auto_breaking then
+ begin if is_char_node(prev_p) then try_break(0,unhyphenated)
+ else if precedes_break(prev_p) then try_break(0,unhyphenated)
+ else if (type(prev_p)=kern_node)and(subtype(prev_p)<>explicit) then
+ try_break(0,unhyphenated);
+ end;
+check_shrinkage(glue_ptr(cur_p)); q:=glue_ptr(cur_p);
+act_width:=act_width+width(q);@|
+active_width[2+stretch_order(q)]:=@|
+ active_width[2+stretch_order(q)]+stretch(q);@/
+active_width[6]:=active_width[6]+shrink(q)
+
+@ The following code knows that discretionary texts contain
+only character nodes, kern nodes, box nodes, rule nodes, and ligature nodes.
+
+@<Try to break after a discretionary fragment...@>=
+begin s:=pre_break(cur_p); disc_width:=0;
+if s=null then try_break(ex_hyphen_penalty,hyphenated)
+else begin repeat @<Add the width of node |s| to |disc_width|@>;
+ s:=link(s);
+ until s=null;
+ act_width:=act_width+disc_width;
+ try_break(hyphen_penalty,hyphenated);
+ act_width:=act_width-disc_width;
+ end;
+r:=replace_count(cur_p); s:=link(cur_p);
+while r>0 do
+ begin @<Add the width of node |s| to |act_width|@>;
+ decr(r); s:=link(s);
+ end;
+prev_p:=cur_p; cur_p:=s; goto done5;
+end
+
+@ @<Add the width of node |s| to |disc_width|@>=
+if is_char_node(s) then
+ begin f:=font(s);
+ disc_width:=disc_width+char_width(f)(char_info(f)(character(s)));
+ end
+else case type(s) of
+ ligature_node: begin f:=font(lig_char(s));
+ disc_width:=disc_width+
+ char_width(f)(char_info(f)(character(lig_char(s))));
+ end;
+ hlist_node,vlist_node,rule_node,kern_node:
+ disc_width:=disc_width+width(s);
+ othercases confusion("disc3")
+@:this can't happen disc3}{\quad disc3@>
+ endcases
+
+@ @<Add the width of node |s| to |act_width|@>=
+if is_char_node(s) then
+ begin f:=font(s);
+ act_width:=act_width+char_width(f)(char_info(f)(character(s)));
+ end
+else case type(s) of
+ ligature_node: begin f:=font(lig_char(s));
+ act_width:=act_width+
+ char_width(f)(char_info(f)(character(lig_char(s))));
+ end;
+ hlist_node,vlist_node,rule_node,kern_node:
+ act_width:=act_width+width(s);
+ othercases confusion("disc4")
+@:this can't happen disc4}{\quad disc4@>
+ endcases
+
+@ The forced line break at the paragraph's end will reduce the list of
+breakpoints so that all active nodes represent breaks at |cur_p=null|.
+On the first pass, we insist on finding an active node that has the
+correct ``looseness.'' On the final pass, there will be at least one active
+node, and we will match the desired looseness as well as we can.
+
+The global variable |best_bet| will be set to the active node for the best
+way to break the paragraph, and a few other variables are used to
+help determine what is best.
+
+@<Glob...@>=
+@!best_bet:pointer; {use this passive node and its predecessors}
+@!fewest_demerits:integer; {the demerits associated with |best_bet|}
+@!best_line:halfword; {line number following the last line of the new paragraph}
+@!actual_looseness:integer; {the difference between |line_number(best_bet)|
+ and the optimum |best_line|}
+@!line_diff:integer; {the difference between the current line number and
+ the optimum |best_line|}
+
+@ @<Try the final line break at the end of the paragraph...@>=
+begin try_break(eject_penalty,hyphenated);
+if link(active)<>last_active then
+ begin @<Find an active node with fewest demerits@>;
+ if looseness=0 then goto done;
+ @<Find the best active node for the desired looseness@>;
+ if (actual_looseness=looseness)or final_pass then goto done;
+ end;
+end
+
+@ @<Find an active node...@>=
+r:=link(active); fewest_demerits:=awful_bad;
+repeat if type(r)<>delta_node then if total_demerits(r)<fewest_demerits then
+ begin fewest_demerits:=total_demerits(r); best_bet:=r;
+ end;
+r:=link(r);
+until r=last_active;
+best_line:=line_number(best_bet)
+
+@ The adjustment for a desired looseness is a slightly more complicated
+version of the loop just considered. Note that if a paragraph is broken
+into segments by displayed equations, each segment will be subject to the
+looseness calculation, independently of the other segments.
+
+@<Find the best active node...@>=
+begin r:=link(active); actual_looseness:=0;
+repeat if type(r)<>delta_node then
+ begin line_diff:=line_number(r)-best_line;
+ if ((line_diff<actual_looseness)and(looseness<=line_diff))or@|
+ ((line_diff>actual_looseness)and(looseness>=line_diff)) then
+ begin best_bet:=r; actual_looseness:=line_diff;
+ fewest_demerits:=total_demerits(r);
+ end
+ else if (line_diff=actual_looseness)and@|
+ (total_demerits(r)<fewest_demerits) then
+ begin best_bet:=r; fewest_demerits:=total_demerits(r);
+ end;
+ end;
+r:=link(r);
+until r=last_active;
+best_line:=line_number(best_bet);
+end
+
+@ Once the best sequence of breakpoints has been found (hurray), we call on the
+procedure |post_line_break| to finish the remainder of the work.
+(By introducing this subprocedure, we are able to keep |line_break|
+from getting extremely long.)
+
+@<Break the paragraph at the chosen...@>=
+post_line_break(final_widow_penalty)
+
+@ The total number of lines that will be set by |post_line_break|
+is |best_line-prev_graf-1|. The last breakpoint is specified by
+|break_node(best_bet)|, and this passive node points to the other breakpoints
+via the |prev_break| links. The finishing-up phase starts by linking the
+relevant passive nodes in forward order, changing |prev_break| to
+|next_break|. (The |next_break| fields actually reside in the same memory
+space as the |prev_break| fields did, but we give them a new name because
+of their new significance.) Then the lines are justified, one by one.
+
+@d next_break==prev_break {new name for |prev_break| after links are reversed}
+
+@<Declare subprocedures for |line_break|@>=
+procedure post_line_break(@!final_widow_penalty:integer);
+label done,done1;
+var q,@!r,@!s:pointer; {temporary registers for list manipulation}
+@!disc_break:boolean; {was the current break at a discretionary node?}
+@!post_disc_break:boolean; {and did it have a nonempty post-break part?}
+@!cur_width:scaled; {width of line number |cur_line|}
+@!cur_indent:scaled; {left margin of line number |cur_line|}
+@!t:quarterword; {used for replacement counts in discretionary nodes}
+@!pen:integer; {use when calculating penalties between lines}
+@!cur_line: halfword; {the current line number being justified}
+begin @<Reverse the links of the relevant passive nodes, setting |cur_p| to the
+ first breakpoint@>;
+cur_line:=prev_graf+1;
+repeat @<Justify the line ending at breakpoint |cur_p|, and append it to the
+ current vertical list, together with associated penalties and other
+ insertions@>;
+incr(cur_line); cur_p:=next_break(cur_p);
+if cur_p<>null then if not post_disc_break then
+ @<Prune unwanted nodes at the beginning of the next line@>;
+until cur_p=null;
+if (cur_line<>best_line)or(link(temp_head)<>null) then
+ confusion("line breaking");
+@:this can't happen line breaking}{\quad line breaking@>
+prev_graf:=best_line-1;
+end;
+
+@ The job of reversing links in a list is conveniently regarded as the job
+of taking items off one stack and putting them on another. In this case we
+take them off a stack pointed to by |q| and having |prev_break| fields;
+we put them on a stack pointed to by |cur_p| and having |next_break| fields.
+Node |r| is the passive node being moved from stack to stack.
+
+@<Reverse the links of the relevant passive nodes...@>=
+q:=break_node(best_bet); cur_p:=null;
+repeat r:=q; q:=prev_break(q); next_break(r):=cur_p; cur_p:=r;
+until q=null
+
+@ Glue and penalty and kern and math nodes are deleted at the beginning of
+a line, except in the anomalous case that the node to be deleted is actually
+one of the chosen breakpoints. Otherwise
+the pruning done here is designed to match
+the lookahead computation in |try_break|, where the |break_width| values
+are computed for non-discretionary breakpoints.
+
+@<Prune unwanted nodes at the beginning of the next line@>=
+begin r:=temp_head;
+loop@+ begin q:=link(r);
+ if q=cur_break(cur_p) then goto done1;
+ {|cur_break(cur_p)| is the next breakpoint}
+ {now |q| cannot be |null|}
+ if is_char_node(q) then goto done1;
+ if non_discardable(q) then goto done1;
+ if type(q)=kern_node then if subtype(q)<>explicit then goto done1;
+ r:=q; {now |type(q)=glue_node|, |kern_node|, |math_node| or |penalty_node|}
+ end;
+done1: if r<>temp_head then
+ begin link(r):=null; flush_node_list(link(temp_head));
+ link(temp_head):=q;
+ end;
+end
+
+@ The current line to be justified appears in a horizontal list starting
+at |link(temp_head)| and ending at |cur_break(cur_p)|. If |cur_break(cur_p)| is
+a glue node, we reset the glue to equal the |right_skip| glue; otherwise
+we append the |right_skip| glue at the right. If |cur_break(cur_p)| is a
+discretionary node, we modify the list so that the discretionary break
+is compulsory, and we set |disc_break| to |true|. We also append
+the |left_skip| glue at the left of the line, unless it is zero.
+
+@<Justify the line ending at breakpoint |cur_p|, and append it...@>=
+@<Modify the end of the line to reflect the nature of the break and to include
+ \.{\\rightskip}; also set the proper value of |disc_break|@>;
+@<Put the \(l)\.{\\leftskip} glue at the left and detach this line@>;
+@<Call the packaging subroutine, setting |just_box| to the justified box@>;
+@<Append the new box to the current vertical list, followed by the list of
+ special nodes taken out of the box by the packager@>;
+@<Append a penalty node, if a nonzero penalty is appropriate@>
+
+@ At the end of the following code, |q| will point to the final node on the
+list about to be justified.
+
+@<Modify the end of the line...@>=
+q:=cur_break(cur_p); disc_break:=false; post_disc_break:=false;
+if q<>null then {|q| cannot be a |char_node|}
+ if type(q)=glue_node then
+ begin delete_glue_ref(glue_ptr(q));
+ glue_ptr(q):=right_skip;
+ subtype(q):=right_skip_code+1; add_glue_ref(right_skip);
+ goto done;
+ end
+ else begin if type(q)=disc_node then
+ @<Change discretionary to compulsory and set
+ |disc_break:=true|@>
+ else if (type(q)=math_node)or(type(q)=kern_node) then width(q):=0;
+ end
+else begin q:=temp_head;
+ while link(q)<>null do q:=link(q);
+ end;
+@<Put the \(r)\.{\\rightskip} glue after node |q|@>;
+done:
+
+@ @<Change discretionary to compulsory...@>=
+begin t:=replace_count(q);
+@<Destroy the |t| nodes following |q|, and
+ make |r| point to the following node@>;
+if post_break(q)<>null then @<Transplant the post-break list@>;
+if pre_break(q)<>null then @<Transplant the pre-break list@>;
+link(q):=r; disc_break:=true;
+end
+
+@ @<Destroy the |t| nodes following |q|...@>=
+if t=0 then r:=link(q)
+else begin r:=q;
+ while t>1 do
+ begin r:=link(r); decr(t);
+ end;
+ s:=link(r);
+ r:=link(s); link(s):=null;
+ flush_node_list(link(q)); replace_count(q):=0;
+ end
+
+@ We move the post-break list from inside node |q| to the main list by
+re\-attaching it just before the present node |r|, then resetting |r|.
+
+@<Transplant the post-break list@>=
+begin s:=post_break(q);
+while link(s)<>null do s:=link(s);
+link(s):=r; r:=post_break(q); post_break(q):=null; post_disc_break:=true;
+end
+
+@ We move the pre-break list from inside node |q| to the main list by
+re\-attaching it just after the present node |q|, then resetting |q|.
+
+@<Transplant the pre-break list@>=
+begin s:=pre_break(q); link(q):=s;
+while link(s)<>null do s:=link(s);
+pre_break(q):=null; q:=s;
+end
+
+@ @<Put the \(r)\.{\\rightskip} glue after node |q|@>=
+r:=new_param_glue(right_skip_code); link(r):=link(q); link(q):=r; q:=r
+
+@ The following code begins with |q| at the end of the list to be
+justified. It ends with |q| at the beginning of that list, and with
+|link(temp_head)| pointing to the remainder of the paragraph, if any.
+
+@<Put the \(l)\.{\\leftskip} glue at the left...@>=
+r:=link(q); link(q):=null; q:=link(temp_head); link(temp_head):=r;
+if left_skip<>zero_glue then
+ begin r:=new_param_glue(left_skip_code);
+ link(r):=q; q:=r;
+ end
+
+@ @<Append the new box to the current vertical list...@>=
+append_to_vlist(just_box);
+if adjust_head<>adjust_tail then
+ begin link(tail):=link(adjust_head); tail:=adjust_tail;
+ end;
+adjust_tail:=null
+
+@ Now |q| points to the hlist that represents the current line of the
+paragraph. We need to compute the appropriate line width, pack the
+line into a box of this size, and shift the box by the appropriate
+amount of indentation.
+
+@<Call the packaging subroutine...@>=
+if cur_line>last_special_line then
+ begin cur_width:=second_width; cur_indent:=second_indent;
+ end
+else if par_shape_ptr=null then
+ begin cur_width:=first_width; cur_indent:=first_indent;
+ end
+else begin cur_width:=mem[par_shape_ptr+2*cur_line].sc;
+ cur_indent:=mem[par_shape_ptr+2*cur_line-1].sc;
+ end;
+adjust_tail:=adjust_head; just_box:=hpack(q,cur_width,exactly);
+shift_amount(just_box):=cur_indent
+
+@ Penalties between the lines of a paragraph come from club and widow lines,
+from the |inter_line_penalty| parameter, and from lines that end at
+discretionary breaks. Breaking between lines of a two-line paragraph gets
+both club-line and widow-line penalties. The local variable |pen| will
+be set to the sum of all relevant penalties for the current line, except
+that the final line is never penalized.
+
+@<Append a penalty node, if a nonzero penalty is appropriate@>=
+if cur_line+1<>best_line then
+ begin pen:=inter_line_penalty;
+ if cur_line=prev_graf+1 then pen:=pen+club_penalty;
+ if cur_line+2=best_line then pen:=pen+final_widow_penalty;
+ if disc_break then pen:=pen+broken_penalty;
+ if pen<>0 then
+ begin r:=new_penalty(pen);
+ link(tail):=r; tail:=r;
+ end;
+ end
+
+@* \[40] Pre-hyphenation.
+When the line-breaking routine is unable to find a feasible sequence of
+breakpoints, it makes a second pass over the paragraph, attempting to
+hyphenate the hyphenatable words. The goal of hyphenation is to insert
+discretionary material into the paragraph so that there are more
+potential places to break.
+
+The general rules for hyphenation are somewhat complex and technical,
+because we want to be able to hyphenate words that are preceded or
+followed by punctuation marks, and because we want the rules to work
+for languages other than English. We also must contend with the fact
+that hyphens might radically alter the ligature and kerning structure
+of a word.
+
+A sequence of characters will be considered for hyphenation only if it
+belongs to a ``potentially hyphenatable part'' of the current paragraph.
+This is a sequence of nodes $p_0p_1\ldots p_m$ where $p_0$ is a glue node,
+$p_1\ldots p_{m-1}$ are either character or ligature or whatsit or
+implicit kern nodes, and $p_m$ is a glue or penalty or insertion or adjust
+or mark or whatsit or explicit kern node. (Therefore hyphenation is
+disabled by boxes, math formulas, and discretionary nodes already inserted
+by the user.) The ligature nodes among $p_1\ldots p_{m-1}$ are effectively
+expanded into the original non-ligature characters; the kern nodes and
+whatsits are ignored. Each character |c| is now classified as either a
+nonletter (if |lc_code(c)=0|), a lowercase letter (if
+|lc_code(c)=c|), or an uppercase letter (otherwise); an uppercase letter
+is treated as if it were |lc_code(c)| for purposes of hyphenation. The
+characters generated by $p_1\ldots p_{m-1}$ may begin with nonletters; let
+$c_1$ be the first letter that is not in the middle of a ligature. Whatsit
+nodes preceding $c_1$ are ignored; a whatsit found after $c_1$ will be the
+terminating node $p_m$. All characters that do not have the same font as
+$c_1$ will be treated as nonletters. The |hyphen_char| for that font
+must be between 0 and 255, otherwise hyphenation will not be attempted.
+\TeX\ looks ahead for as many consecutive letters $c_1\ldots c_n$ as
+possible; however, |n| must be less than 64, so a character that would
+otherwise be $c_{64}$ is effectively not a letter. Furthermore $c_n$ must
+not be in the middle of a ligature. In this way we obtain a string of
+letters $c_1\ldots c_n$ that are generated by nodes $p_a\ldots p_b$, where
+|1<=a<=b+1<=m|. If |n>=l_hyf+r_hyf|, this string qualifies for hyphenation;
+however, |uc_hyph| must be positive, if $c_1$ is uppercase.
+
+The hyphenation process takes place in three stages. First, the candidate
+sequence $c_1\ldots c_n$ is found; then potential positions for hyphens
+are determined by referring to hyphenation tables; and finally, the nodes
+$p_a\ldots p_b$ are replaced by a new sequence of nodes that includes the
+discretionary breaks found.
+
+Fortunately, we do not have to do all this calculation very often, because
+of the way it has been taken out of \TeX's inner loop. For example, when
+the second edition of the author's 700-page book {\sl Seminumerical
+Algorithms} was typeset by \TeX, only about 1.2 hyphenations needed to be
+@^Knuth, Donald Ervin@>
+tried per paragraph, since the line breaking algorithm needed to use two
+passes on only about 5 per cent of the paragraphs.
+
+@<Initialize for hyphenating...@>=
+begin @!init if trie_not_ready then init_trie;@+tini@;@/
+cur_lang:=init_cur_lang; l_hyf:=init_l_hyf; r_hyf:=init_r_hyf;
+end
+
+@ The letters $c_1\ldots c_n$ that are candidates for hyphenation are placed
+into an array called |hc|; the number |n| is placed into |hn|; pointers to
+nodes $p_{a-1}$ and~$p_b$ in the description above are placed into variables
+|ha| and |hb|; and the font number is placed into |hf|.
+
+@<Glob...@>=
+@!hc:array[0..65] of 0..256; {word to be hyphenated}
+@!hn:small_number; {the number of positions occupied in |hc|}
+@!ha,@!hb:pointer; {nodes |ha..hb| should be replaced by the hyphenated result}
+@!hf:internal_font_number; {font number of the letters in |hc|}
+@!hu:array[0..63] of 0..256; {like |hc|, before conversion to lowercase}
+@!hyf_char:integer; {hyphen character of the relevant font}
+@!cur_lang,@!init_cur_lang:ASCII_code; {current hyphenation table of interest}
+@!l_hyf,@!r_hyf,@!init_l_hyf,@!init_r_hyf:integer; {limits on fragment sizes}
+@!hyf_bchar:halfword; {boundary character after $c_n$}
+
+@ Hyphenation routines need a few more local variables.
+
+@<Local variables for line...@>=
+@!j:small_number; {an index into |hc| or |hu|}
+@!c:0..255; {character being considered for hyphenation}
+
+@ When the following code is activated, the |line_break| procedure is in its
+second pass, and |cur_p| points to a glue node.
+
+@<Try to hyphenate...@>=
+begin prev_s:=cur_p; s:=link(prev_s);
+if s<>null then
+ begin @<Skip to node |ha|, or |goto done1| if no hyphenation
+ should be attempted@>;
+ if l_hyf+r_hyf>63 then goto done1;
+ @<Skip to node |hb|, putting letters into |hu| and |hc|@>;
+ @<Check that the nodes following |hb| permit hyphenation and that at least
+ |l_hyf+r_hyf| letters have been found, otherwise |goto done1|@>;
+ hyphenate;
+ end;
+done1: end
+
+@ @<Declare subprocedures for |line_break|@>=
+@t\4@>@<Declare the function called |reconstitute|@>
+procedure hyphenate;
+label common_ending,done,found,found1,found2,not_found,exit;
+var @<Local variables for hyphenation@>@;
+begin @<Find hyphen locations for the word in |hc|, or |return|@>;
+@<If no hyphens were found, |return|@>;
+@<Replace nodes |ha..hb| by a sequence of nodes that includes
+ the discretionary hyphens@>;
+exit:end;
+
+@ The first thing we need to do is find the node |ha| just before the
+first letter.
+
+@<Skip to node |ha|, or |goto done1|...@>=
+loop@+ begin if is_char_node(s) then
+ begin c:=qo(character(s)); hf:=font(s);
+ end
+ else if type(s)=ligature_node then
+ if lig_ptr(s)=null then goto continue
+ else begin q:=lig_ptr(s); c:=qo(character(q)); hf:=font(q);
+ end
+ else if (type(s)=kern_node)and(subtype(s)=normal) then goto continue
+ else if type(s)=whatsit_node then
+ begin @<Advance \(p)past a whatsit node in the \(p)pre-hyphenation loop@>;
+ goto continue;
+ end
+ else goto done1;
+ if lc_code(c)<>0 then
+ if (lc_code(c)=c)or(uc_hyph>0) then goto done2
+ else goto done1;
+continue: prev_s:=s; s:=link(prev_s);
+ end;
+done2: hyf_char:=hyphen_char[hf];
+if hyf_char<0 then goto done1;
+if hyf_char>255 then goto done1;
+ha:=prev_s
+
+@ The word to be hyphenated is now moved to the |hu| and |hc| arrays.
+
+@<Skip to node |hb|, putting letters...@>=
+hn:=0;
+loop@+ begin if is_char_node(s) then
+ begin if font(s)<>hf then goto done3;
+ hyf_bchar:=character(s); c:=qo(hyf_bchar);
+ if lc_code(c)=0 then goto done3;
+ if hn=63 then goto done3;
+ hb:=s; incr(hn); hu[hn]:=c; hc[hn]:=lc_code(c); hyf_bchar:=non_char;
+ end
+ else if type(s)=ligature_node then
+ @<Move the characters of a ligature node to |hu| and |hc|;
+ but |goto done3| if they are not all letters@>
+ else if (type(s)=kern_node)and(subtype(s)=normal) then
+ begin hb:=s;
+ hyf_bchar:=font_bchar[hf];
+ end
+ else goto done3;
+ s:=link(s);
+ end;
+done3:
+
+@ We let |j| be the index of the character being stored when a ligature node
+is being expanded, since we do not want to advance |hn| until we are sure
+that the entire ligature consists of letters. Note that it is possible
+to get to |done3| with |hn=0| and |hb| not set to any value.
+
+@<Move the characters of a ligature node to |hu| and |hc|...@>=
+begin if font(lig_char(s))<>hf then goto done3;
+j:=hn; q:=lig_ptr(s);@+if q>null then hyf_bchar:=character(q);
+while q>null do
+ begin c:=qo(character(q));
+ if lc_code(c)=0 then goto done3;
+ if j=63 then goto done3;
+ incr(j); hu[j]:=c; hc[j]:=lc_code(c);@/
+ q:=link(q);
+ end;
+hb:=s; hn:=j;
+if odd(subtype(s)) then hyf_bchar:=font_bchar[hf]@+else hyf_bchar:=non_char;
+end
+
+@ @<Check that the nodes following |hb| permit hyphenation...@>=
+if hn<l_hyf+r_hyf then goto done1; {|l_hyf| and |r_hyf| are |>=1|}
+loop@+ begin if not(is_char_node(s)) then
+ case type(s) of
+ ligature_node: do_nothing;
+ kern_node: if subtype(s)<>normal then goto done4;
+ whatsit_node,glue_node,penalty_node,ins_node,adjust_node,mark_node:
+ goto done4;
+ othercases goto done1
+ endcases;
+ s:=link(s);
+ end;
+done4:
+
+@* \[41] Post-hyphenation.
+If a hyphen may be inserted between |hc[j]| and |hc[j+1]|, the hyphenation
+procedure will set |hyf[j]| to some small odd number. But before we look
+at \TeX's hyphenation procedure, which is independent of the rest of the
+line-breaking algorithm, let us consider what we will do with the hyphens
+it finds, since it is better to work on this part of the program before
+forgetting what |ha| and |hb|, etc., are all about.
+
+@<Glob...@>=
+@!hyf:array [0..64] of 0..9; {odd values indicate discretionary hyphens}
+@!init_list:pointer; {list of punctuation characters preceding the word}
+@!init_lig:boolean; {does |init_list| represent a ligature?}
+@!init_lft:boolean; {if so, did the ligature involve a left boundary?}
+
+@ @<Local variables for hyphenation@>=
+@!i,@!j,@!l:0..65; {indices into |hc| or |hu|}
+@!q,@!r,@!s:pointer; {temporary registers for list manipulation}
+@!bchar:halfword; {right boundary character of hyphenated word, or |non_char|}
+
+@ \TeX\ will never insert a hyphen that has fewer than
+\.{\\lefthyphenmin} letters before it or fewer than
+\.{\\righthyphenmin} after it; hence, a short word has
+comparatively little chance of being hyphenated. If no hyphens have
+been found, we can save time by not having to make any changes to the
+paragraph.
+
+@<If no hyphens were found, |return|@>=
+for j:=l_hyf to hn-r_hyf do if odd(hyf[j]) then goto found1;
+return;
+found1:
+
+@ If hyphens are in fact going to be inserted, \TeX\ first deletes the
+subsequence of nodes between |ha| and~|hb|. An attempt is made to
+preserve the effect that implicit boundary characters and punctuation marks
+had on ligatures inside the hyphenated word, by storing a left boundary or
+preceding character in |hu[0]| and by storing a possible right boundary
+in |bchar|. We set |j:=0| if |hu[0]| is to be part of the reconstruction;
+otherwise |j:=1|.
+The variable |s| will point to the tail of the current hlist, and
+|q| will point to the node following |hb|, so that
+things can be hooked up after we reconstitute the hyphenated word.
+
+@<Replace nodes |ha..hb| by a sequence of nodes...@>=
+q:=link(hb); link(hb):=null; r:=link(ha); link(ha):=null; bchar:=hyf_bchar;
+if is_char_node(ha) then
+ if font(ha)<>hf then goto found2
+ else begin init_list:=ha; init_lig:=false; hu[0]:=qo(character(ha));
+ end
+else if type(ha)=ligature_node then
+ if font(lig_char(ha))<>hf then goto found2
+ else begin init_list:=lig_ptr(ha); init_lig:=true; init_lft:=(subtype(ha)>1);
+ hu[0]:=qo(character(lig_char(ha)));
+ if init_list=null then if init_lft then
+ begin hu[0]:=256; init_lig:=false;
+ end; {in this case a ligature will be reconstructed from scratch}
+ free_node(ha,small_node_size);
+ end
+else begin {no punctuation found; look for left boundary}
+ if not is_char_node(r) then if type(r)=ligature_node then
+ if subtype(r)>1 then goto found2;
+ j:=1; s:=ha; init_list:=null; goto common_ending;
+ end;
+s:=cur_p; {we have |cur_p<>ha| because |type(cur_p)=glue_node|}
+while link(s)<>ha do s:=link(s);
+j:=0; goto common_ending;
+found2: s:=ha; j:=0; hu[0]:=256; init_lig:=false; init_list:=null;
+common_ending: flush_node_list(r);
+@<Reconstitute nodes for the hyphenated word, inserting discretionary hyphens@>;
+flush_list(init_list)
+
+@ We must now face the fact that the battle is not over, even though the
+{\def\!{\kern-1pt}%
+hyphens have been found: The process of reconstituting a word can be nontrivial
+because ligatures might change when a hyphen is present. {\sl The \TeX book\/}
+discusses the difficulties of the word ``difficult'', and
+the discretionary material surrounding a
+hyphen can be considerably more complex than that. Suppose
+\.{abcdef} is a word in a font for which the only ligatures are \.{b\!c},
+\.{c\!d}, \.{d\!e}, and \.{e\!f}. If this word permits hyphenation
+between \.b and \.c, the two patterns with and without hyphenation are
+$\.a\,\.b\,\.-\,\.{c\!d}\,\.{e\!f}$ and $\.a\,\.{b\!c}\,\.{d\!e}\,\.f$.
+Thus the insertion of a hyphen might cause effects to ripple arbitrarily
+far into the rest of the word. A further complication arises if additional
+hyphens appear together with such rippling, e.g., if the word in the
+example just given could also be hyphenated between \.c and \.d; \TeX\
+avoids this by simply ignoring the additional hyphens in such weird cases.}
+
+Still further complications arise in the presence of ligatures that do not
+delete the original characters. When punctuation precedes the word being
+hyphenated, \TeX's method is not perfect under all possible scenarios,
+because punctuation marks and letters can propagate information back and forth.
+For example, suppose the original pre-hyphenation pair
+\.{*a} changes to \.{*y} via a \.{\?=:} ligature, which changes to \.{xy}
+via a \.{=:\?} ligature; if $p_{a-1}=\.x$ and $p_a=\.y$, the reconstitution
+procedure isn't smart enough to obtain \.{xy} again. In such cases the
+font designer should include a ligature that goes from \.{xa} to \.{xy}.
+
+@ The processing is facilitated by a subroutine called |reconstitute|. Given
+a string of characters $x_j\ldots x_n$, there is a smallest index $m\ge j$
+such that the ``translation'' of $x_j\ldots x_n$ by ligatures and kerning
+has the form $y_1\ldots y_t$ followed by the translation of $x_{m+1}\ldots x_n$,
+where $y_1\ldots y_t$ is some nonempty sequence of character, ligature, and
+kern nodes. We call $x_j\ldots x_m$ a ``cut prefix'' of $x_j\ldots x_n$.
+For example, if $x_1x_2x_3=\.{fly}$, and if the font contains `fl' as a
+ligature and a kern between `fl' and `y', then $m=2$, $t=2$, and $y_1$ will
+be a ligature node for `fl' followed by an appropriate kern node~$y_2$.
+In the most common case, $x_j$~forms no ligature with $x_{j+1}$ and we
+simply have $m=j$, $y_1=x_j$. If $m<n$ we can repeat the procedure on
+$x_{m+1}\ldots x_n$ until the entire translation has been found.
+
+The |reconstitute| function returns the integer $m$ and puts the nodes
+$y_1\ldots y_t$ into a linked list starting at |link(hold_head)|,
+getting the input $x_j\ldots x_n$ from the |hu| array. If $x_j=256$,
+we consider $x_j$ to be an implicit left boundary character; in this
+case |j| must be strictly less than~|n|. There is a
+parameter |bchar|, which is either 256 or an implicit right boundary character
+assumed to be present just following~$x_n$. (The value |hu[n+1]| is never
+explicitly examined, but the algorithm imagines that |bchar| is there.)
+
+If there exists an index |k| in the range $j\le k\le m$ such that |hyf[k]|
+is odd and such that the result of |reconstitute| would have been different
+if $x_{k+1}$ had been |hchar|, then |reconstitute| sets |hyphen_passed|
+to the smallest such~|k|. Otherwise it sets |hyphen_passed| to zero.
+
+A special convention is used in the case |j=0|: Then we assume that the
+translation of |hu[0]| appears in a special list of charnodes starting at
+|init_list|; moreover, if |init_lig| is |true|, then |hu[0]| will be
+a ligature character, involving a left boundary if |init_lft| is |true|.
+This facility is provided for cases when a hyphenated
+word is preceded by punctuation (like single or double quotes) that might
+affect the translation of the beginning of the word.
+
+@<Glob...@>=
+@!hyphen_passed:small_number; {first hyphen in a ligature, if any}
+
+@ @<Declare the function called |reconstitute|@>=
+function reconstitute(@!j,@!n:small_number;@!bchar,@!hchar:halfword):
+ small_number;
+label continue,done;
+var @!p:pointer; {temporary register for list manipulation}
+@!t:pointer; {a node being appended to}
+@!q:four_quarters; {character information or a lig/kern instruction}
+@!cur_rh:halfword; {hyphen character for ligature testing}
+@!test_char:halfword; {hyphen or other character for ligature testing}
+@!w:scaled; {amount of kerning}
+@!k:font_index; {position of current lig/kern instruction}
+begin hyphen_passed:=0; t:=hold_head; w:=0; link(hold_head):=null;
+ {at this point |ligature_present=lft_hit=rt_hit=false|}
+@<Set up data structures with the cursor following position |j|@>;
+continue:@<If there's a ligature or kern at the cursor position, update the data
+ structures, possibly advancing~|j|; continue until the cursor moves@>;
+@<Append a ligature and/or kern to the translation;
+ |goto continue| if the stack of inserted ligatures is nonempty@>;
+reconstitute:=j;
+end;
+
+@ The reconstitution procedure shares many of the global data structures
+by which \TeX\ has processed the words before they were hyphenated.
+There is an implied ``cursor'' between characters |cur_l| and |cur_r|;
+these characters will be tested for possible ligature activity. If
+|ligature_present| then |cur_l| is a ligature character formed from the
+original characters following |cur_q| in the current translation list.
+There is a ``ligature stack'' between the cursor and character |j+1|,
+consisting of pseudo-ligature nodes linked together by their |link| fields.
+This stack is normally empty unless a ligature command has created a new
+character that will need to be processed later. A pseudo-ligature is
+a special node having a |character| field that represents a potential
+ligature and a |lig_ptr| field that points to a |char_node| or is |null|.
+We have
+$$|cur_r|=\cases{|character(lig_stack)|,&if |lig_stack>null|;\cr
+ |qi(hu[j+1])|,&if |lig_stack=null| and |j<n|;\cr
+ bchar,&if |lig_stack=null| and |j=n|.\cr}$$
+
+@<Glob...@>=
+@!cur_l,@!cur_r:halfword; {characters before and after the cursor}
+@!cur_q:pointer; {where a ligature should be detached}
+@!lig_stack:pointer; {unfinished business to the right of the cursor}
+@!ligature_present:boolean; {should a ligature node be made for |cur_l|?}
+@!lft_hit,@!rt_hit:boolean; {did we hit a ligature with a boundary character?}
+
+@ @d append_charnode_to_t(#)== begin link(t):=get_avail; t:=link(t);
+ font(t):=hf; character(t):=#;
+ end
+@d set_cur_r==begin if j<n then cur_r:=qi(hu[j+1])@+else cur_r:=bchar;
+ if odd(hyf[j]) then cur_rh:=hchar@+else cur_rh:=non_char;
+ end
+
+@<Set up data structures with the cursor following position |j|@>=
+cur_l:=qi(hu[j]); cur_q:=t;
+if j=0 then
+ begin ligature_present:=init_lig; p:=init_list;
+ if ligature_present then lft_hit:=init_lft;
+ while p>null do
+ begin append_charnode_to_t(character(p)); p:=link(p);
+ end;
+ end
+else if cur_l<non_char then append_charnode_to_t(cur_l);
+lig_stack:=null; set_cur_r
+
+@ We may want to look at the lig/kern program twice, once for a hyphen
+and once for a normal letter. (The hyphen might appear after the letter
+in the program, so we'd better not try to look for both at once.)
+
+@<If there's a ligature or kern at the cursor position, update...@>=
+if cur_l=non_char then
+ begin k:=bchar_label[hf];
+ if k=non_address then goto done@+else q:=font_info[k].qqqq;
+ end
+else begin q:=char_info(hf)(cur_l);
+ if char_tag(q)<>lig_tag then goto done;
+ k:=lig_kern_start(hf)(q); q:=font_info[k].qqqq;
+ if skip_byte(q)>stop_flag then
+ begin k:=lig_kern_restart(hf)(q); q:=font_info[k].qqqq;
+ end;
+ end; {now |k| is the starting address of the lig/kern program}
+if cur_rh<non_char then test_char:=cur_rh@+else test_char:=cur_r;
+loop@+begin if next_char(q)=test_char then if skip_byte(q)<=stop_flag then
+ if cur_rh<non_char then
+ begin hyphen_passed:=j; hchar:=non_char; cur_rh:=non_char;
+ goto continue;
+ end
+ else begin if hchar<non_char then if odd(hyf[j]) then
+ begin hyphen_passed:=j; hchar:=non_char;
+ end;
+ if op_byte(q)<kern_flag then
+ @<Carry out a ligature replacement, updating the cursor structure
+ and possibly advancing~|j|; |goto continue| if the cursor doesn't
+ advance, otherwise |goto done|@>;
+ w:=char_kern(hf)(q); goto done; {this kern will be inserted below}
+ end;
+ if skip_byte(q)>=stop_flag then
+ if cur_rh=non_char then goto done
+ else begin cur_rh:=non_char; goto continue;
+ end;
+ k:=k+qo(skip_byte(q))+1; q:=font_info[k].qqqq;
+ end;
+done:
+
+@ @d wrap_lig(#)==if ligature_present then
+ begin p:=new_ligature(hf,cur_l,link(cur_q));
+ if lft_hit then
+ begin subtype(p):=2; lft_hit:=false;
+ end;
+ if # then if lig_stack=null then
+ begin incr(subtype(p)); rt_hit:=false;
+ end;
+ link(cur_q):=p; t:=p; ligature_present:=false;
+ end
+@d pop_lig_stack==begin if lig_ptr(lig_stack)>null then
+ begin link(t):=lig_ptr(lig_stack); {this is a charnode for |hu[j+1]|}
+ t:=link(t); incr(j);
+ end;
+ p:=lig_stack; lig_stack:=link(p); free_node(p,small_node_size);
+ if lig_stack=null then set_cur_r@+else cur_r:=character(lig_stack);
+ end {if |lig_stack| isn't |null| we have |cur_rh=non_char|}
+
+@<Append a ligature and/or kern to the translation...@>=
+wrap_lig(rt_hit);
+if w<>0 then
+ begin link(t):=new_kern(w); t:=link(t); w:=0;
+ end;
+if lig_stack>null then
+ begin cur_q:=t; cur_l:=character(lig_stack); ligature_present:=true;
+ pop_lig_stack; goto continue;
+ end
+
+@ @<Carry out a ligature replacement, updating the cursor structure...@>=
+begin if cur_l=non_char then lft_hit:=true;
+if j=n then if lig_stack=null then rt_hit:=true;
+check_interrupt; {allow a way out in case there's an infinite ligature loop}
+case op_byte(q) of
+qi(1),qi(5):begin cur_l:=rem_byte(q); {\.{=:\?}, \.{=:\?>}}
+ ligature_present:=true;
+ end;
+qi(2),qi(6):begin cur_r:=rem_byte(q); {\.{\?=:}, \.{\?=:>}}
+ if lig_stack>null then character(lig_stack):=cur_r
+ else begin lig_stack:=new_lig_item(cur_r);
+ if j=n then bchar:=non_char
+ else begin p:=get_avail; lig_ptr(lig_stack):=p;
+ character(p):=qi(hu[j+1]); font(p):=hf;
+ end;
+ end;
+ end;
+qi(3):begin cur_r:=rem_byte(q); {\.{\?=:\?}}
+ p:=lig_stack; lig_stack:=new_lig_item(cur_r); link(lig_stack):=p;
+ end;
+qi(7),qi(11):begin wrap_lig(false); {\.{\?=:\?>}, \.{\?=:\?>>}}
+ cur_q:=t; cur_l:=rem_byte(q); ligature_present:=true;
+ end;
+othercases begin cur_l:=rem_byte(q); ligature_present:=true; {\.{=:}}
+ if lig_stack>null then pop_lig_stack
+ else if j=n then goto done
+ else begin append_charnode_to_t(cur_r); incr(j); set_cur_r;
+ end;
+ end
+endcases;
+if op_byte(q)>qi(4) then if op_byte(q)<>qi(7) then goto done;
+goto continue;
+end
+
+@ Okay, we're ready to insert the potential hyphenations that were found.
+When the following program is executed, we want to append the word
+|hu[1..hn]| after node |ha|, and node |q| should be appended to the result.
+During this process, the variable |i| will be a temporary
+index into |hu|; the variable |j| will be an index to our current position
+in |hu|; the variable |l| will be the counterpart of |j|, in a discretionary
+branch; the variable |r| will point to new nodes being created; and
+we need a few new local variables:
+
+@<Local variables for hyph...@>=
+@!major_tail,@!minor_tail:pointer; {the end of lists in the main and
+ discretionary branches being reconstructed}
+@!c:ASCII_code; {character temporarily replaced by a hyphen}
+@!c_loc:0..63; {where that character came from}
+@!r_count:integer; {replacement count for discretionary}
+@!hyf_node:pointer; {the hyphen, if it exists}
+
+@ When the following code is performed, |hyf[0]| and |hyf[hn]| will be zero.
+
+@<Reconstitute nodes for the hyphenated word...@>=
+repeat l:=j; j:=reconstitute(j,hn,bchar,qi(hyf_char))+1;
+if hyphen_passed=0 then
+ begin link(s):=link(hold_head);
+ while link(s)>null do s:=link(s);
+ if odd(hyf[j-1]) then
+ begin l:=j; hyphen_passed:=j-1; link(hold_head):=null;
+ end;
+ end;
+if hyphen_passed>0 then
+ @<Create and append a discretionary node as an alternative to the
+ unhyphenated word, and continue to develop both branches until they
+ become equivalent@>;
+until j>hn;
+link(s):=q
+
+@ In this repeat loop we will insert another discretionary if |hyf[j-1]| is
+odd, when both branches of the previous discretionary end at position |j-1|.
+Strictly speaking, we aren't justified in doing this, because we don't know
+that a hyphen after |j-1| is truly independent of those branches. But in almost
+all applications we would rather not lose a potentially valuable hyphenation
+point. (Consider the word `difficult', where the letter `c' is in position |j|.)
+
+@d advance_major_tail==begin major_tail:=link(major_tail); incr(r_count);
+ end
+
+@<Create and append a discretionary node as an alternative...@>=
+repeat r:=get_node(small_node_size);
+link(r):=link(hold_head); type(r):=disc_node;
+major_tail:=r; r_count:=0;
+while link(major_tail)>null do advance_major_tail;
+i:=hyphen_passed; hyf[i]:=0;
+@<Put the \(c)characters |hu[l..i]| and a hyphen into |pre_break(r)|@>;
+@<Put the \(c)characters |hu[i+1..@,]| into |post_break(r)|, appending to this
+ list and to |major_tail| until synchronization has been achieved@>;
+@<Move pointer |s| to the end of the current list, and set |replace_count(r)|
+ appropriately@>;
+hyphen_passed:=j-1; link(hold_head):=null;
+until not odd(hyf[j-1])
+
+@ The new hyphen might combine with the previous character via ligature
+or kern. At this point we have |l-1<=i<j| and |i<hn|.
+
+@<Put the \(c)characters |hu[l..i]| and a hyphen into |pre_break(r)|@>=
+minor_tail:=null; pre_break(r):=null; hyf_node:=new_character(hf,hyf_char);
+if hyf_node<>null then
+ begin incr(i); c:=hu[i]; hu[i]:=hyf_char; free_avail(hyf_node);
+ end;
+while l<=i do
+ begin l:=reconstitute(l,i,font_bchar[hf],non_char)+1;
+ if link(hold_head)>null then
+ begin if minor_tail=null then pre_break(r):=link(hold_head)
+ else link(minor_tail):=link(hold_head);
+ minor_tail:=link(hold_head);
+ while link(minor_tail)>null do minor_tail:=link(minor_tail);
+ end;
+ end;
+if hyf_node<>null then
+ begin hu[i]:=c; {restore the character in the hyphen position}
+ l:=i; decr(i);
+ end
+
+@ The synchronization algorithm begins with |l=i+1<=j|.
+
+@<Put the \(c)characters |hu[i+1..@,]| into |post_break(r)|...@>=
+minor_tail:=null; post_break(r):=null; c_loc:=0;
+if bchar_label[hf]<>non_address then {put left boundary at beginning of new line}
+ begin decr(l); c:=hu[l]; c_loc:=l; hu[l]:=256;
+ end;
+while l<j do
+ begin repeat l:=reconstitute(l,hn,bchar,non_char)+1;
+ if c_loc>0 then
+ begin hu[c_loc]:=c; c_loc:=0;
+ end;
+ if link(hold_head)>null then
+ begin if minor_tail=null then post_break(r):=link(hold_head)
+ else link(minor_tail):=link(hold_head);
+ minor_tail:=link(hold_head);
+ while link(minor_tail)>null do minor_tail:=link(minor_tail);
+ end;
+ until l>=j;
+ while l>j do
+ @<Append characters of |hu[j..@,]| to |major_tail|, advancing~|j|@>;
+ end
+
+@ @<Append characters of |hu[j..@,]|...@>=
+begin j:=reconstitute(j,hn,bchar,non_char)+1;
+link(major_tail):=link(hold_head);
+while link(major_tail)>null do advance_major_tail;
+end
+
+@ Ligature insertion can cause a word to grow exponentially in size. Therefore
+we must test the size of |r_count| here, even though the hyphenated text
+was at most 63 characters long.
+
+@<Move pointer |s| to the end of the current list...@>=
+if r_count>127 then {we have to forget the discretionary hyphen}
+ begin link(s):=link(r); link(r):=null; flush_node_list(r);
+ end
+else begin link(s):=r; replace_count(r):=r_count;
+ end;
+s:=major_tail
+
+@* \[42] Hyphenation.
+When a word |hc[1..hn]| has been set up to contain a candidate for hyphenation,
+\TeX\ first looks to see if it is in the user's exception dictionary. If not,
+hyphens are inserted based on patterns that appear within the given word,
+using an algorithm due to Frank~M. Liang.
+@^Liang, Franklin Mark@>
+
+Let's consider Liang's method first, since it is much more interesting than the
+exception-lookup routine. The algorithm begins by setting |hyf[j]| to zero
+for all |j|, and invalid characters are inserted into |hc[0]|
+and |hc[hn+1]| to serve as delimiters. Then a reasonably fast method is
+used to see which of a given set of patterns occurs in the word
+|hc[0..(hn+1)]|. Each pattern $p_1\ldots p_k$ of length |k| has an associated
+sequence of |k+1| numbers $n_0\ldots n_k$; and if the pattern occurs in
+|hc[(j+1)..(j+k)]|, \TeX\ will set |hyf[j+i]:=@tmax@>(hyf[j+i],@t$n_i$@>)| for
+|0<=i<=k|. After this has been done for each pattern that occurs, a
+discretionary hyphen will be inserted between |hc[j]| and |hc[j+1]| when
+|hyf[j]| is odd, as we have already seen.
+
+The set of patterns $p_1\ldots p_k$ and associated numbers $n_0\ldots n_k$
+depends, of course, on the language whose words are being hyphenated, and
+on the degree of hyphenation that is desired. A method for finding
+appropriate |p|'s and |n|'s, from a given dictionary of words and acceptable
+hyphenations, is discussed in Liang's Ph.D. thesis (Stanford University,
+1983); \TeX\ simply starts with the patterns and works from there.
+
+@ The patterns are stored in a compact table that is also efficient for
+retrieval, using a variant of ``trie memory'' [cf.\ {\sl The Art of
+Computer Programming \bf3} (1973), 481--505]. We can find each pattern
+$p_1\ldots p_k$ by letting $z_0$ be one greater than the relevant language
+index and then, for |1<=i<=k|,
+setting |@t$z_i$@>:=trie_link@t$(z_{i-1})+p_i$@>|; the pattern will be
+identified by the number $z_k$. Since all the pattern information is
+packed together into a single |trie_link| array, it is necessary to
+prevent confusion between the data from inequivalent patterns, so another
+table is provided such that |trie_char@t$(z_i)=p_i$@>| for all |i|. There
+is also a table |trie_op|$(z_k)$ to identify the numbers $n_0\ldots n_k$
+associated with $p_1\ldots p_k$.
+
+Comparatively few different number sequences $n_0\ldots n_k$ actually occur,
+since most of the |n|'s are generally zero. Therefore the number sequences
+are encoded in such a way that |trie_op|$(z_k)$ is only one byte long.
+If |trie_op(@t$z_k$@>)<>min_quarterword|, when $p_1\ldots p_k$ has matched
+the letters in |hc[(l-k+1)..l@,]| of language |t|,
+we perform all of the required operations
+for this pattern by carrying out the following little program: Set
+|v:=trie_op(@t$z_k$@>)|. Then set |v:=v+op_start[t]|,
+|hyf[l-hyf_distance[v]]:=@tmax@>(hyf[l-hyf_distance[v]], hyf_num[v])|,
+and |v:=hyf_next[v]|; repeat, if necessary, until |v=min_quarterword|.
+
+@<Types...@>=
+@!trie_pointer=0..trie_size; {an index into |trie|}
+
+@ @d trie_link(#)==trie[#].rh {``downward'' link in a trie}
+@d trie_char(#)==trie[#].b1 {character matched at this trie location}
+@d trie_op(#)==trie[#].b0 {program for hyphenation at this trie location}
+
+@<Glob...@>=
+@!trie:array[trie_pointer] of two_halves; {|trie_link|, |trie_char|, |trie_op|}
+@!hyf_distance:array[1..trie_op_size] of small_number; {position |k-j| of $n_j$}
+@!hyf_num:array[1..trie_op_size] of small_number; {value of $n_j$}
+@!hyf_next:array[1..trie_op_size] of quarterword; {continuation code}
+@!op_start:array[ASCII_code] of 0..trie_op_size; {offset for current language}
+
+@ @<Local variables for hyph...@>=
+@!z:trie_pointer; {an index into |trie|}
+@!v:integer; {an index into |hyf_distance|, etc.}
+
+@ Assuming that these auxiliary tables have been set up properly, the
+hyphenation algorithm is quite short. In the following code we set |hc[hn+2]|
+to the impossible value 256, in order to guarantee that |hc[hn+3]| will
+never be fetched.
+
+@<Find hyphen locations for the word in |hc|...@>=
+for j:=0 to hn do hyf[j]:=0;
+@<Look for the word |hc[1..hn]| in the exception table, and |goto found| (with
+ |hyf| containing the hyphens) if an entry is found@>;
+if trie_char(cur_lang+1)<>qi(cur_lang) then return; {no patterns for |cur_lang|}
+hc[0]:=0; hc[hn+1]:=0; hc[hn+2]:=256; {insert delimiters}
+for j:=0 to hn-r_hyf+1 do
+ begin z:=trie_link(cur_lang+1)+hc[j]; l:=j;
+ while hc[l]=qo(trie_char(z)) do
+ begin if trie_op(z)<>min_quarterword then
+ @<Store \(m)maximum values in the |hyf| table@>;
+ incr(l); z:=trie_link(z)+hc[l];
+ end;
+ end;
+found: for j:=0 to l_hyf-1 do hyf[j]:=0;
+for j:=0 to r_hyf-1 do hyf[hn-j]:=0
+
+@ @<Store \(m)maximum values in the |hyf| table@>=
+begin v:=trie_op(z);
+repeat v:=v+op_start[cur_lang]; i:=l-hyf_distance[v];
+if hyf_num[v]>hyf[i] then hyf[i]:=hyf_num[v];
+v:=hyf_next[v];
+until v=min_quarterword;
+end
+
+@ The exception table that is built by \TeX's \.{\\hyphenation} primitive is
+organized as an ordered hash table [cf.\ Amble and Knuth, {\sl The Computer
+@^Amble, Ole@> @^Knuth, Donald Ervin@>
+Journal\/ \bf17} (1974), 135--142] using linear probing. If $\alpha$ and
+$\beta$ are words, we will say that $\alpha<\beta$ if $\vert\alpha\vert<
+\vert\beta\vert$ or if $\vert\alpha\vert=\vert\beta\vert$ and
+$\alpha$ is lexicographically smaller than $\beta$. (The notation $\vert
+\alpha\vert$ stands for the length of $\alpha$.) The idea of ordered hashing
+is to arrange the table so that a given word $\alpha$ can be sought by computing
+a hash address $h=h(\alpha)$ and then looking in table positions |h|, |h-1|,
+\dots, until encountering the first word $\L\alpha$. If this word is
+different from $\alpha$, we can conclude that $\alpha$ is not in the table.
+
+The words in the table point to lists in |mem| that specify hyphen positions
+in their |info| fields. The list for $c_1\ldots c_n$ contains the number |k| if
+the word $c_1\ldots c_n$ has a discretionary hyphen between $c_k$ and
+$c_{k+1}$.
+
+@<Types...@>=
+@!hyph_pointer=0..hyph_size; {an index into the ordered hash table}
+
+@ @<Glob...@>=
+@!hyph_word:array[hyph_pointer] of str_number; {exception words}
+@!hyph_list:array[hyph_pointer] of pointer; {list of hyphen positions}
+@!hyph_count:hyph_pointer; {the number of words in the exception dictionary}
+
+@ @<Local variables for init...@>=
+@!z:hyph_pointer; {runs through the exception dictionary}
+
+@ @<Set init...@>=
+for z:=0 to hyph_size do
+ begin hyph_word[z]:=0; hyph_list[z]:=null;
+ end;
+hyph_count:=0;
+
+@ The algorithm for exception lookup is quite simple, as soon as we have
+a few more local variables to work with.
+
+@<Local variables for hyph...@>=
+@!h:hyph_pointer; {an index into |hyph_word| and |hyph_list|}
+@!k:str_number; {an index into |str_start|}
+@!u:pool_pointer; {an index into |str_pool|}
+
+@ First we compute the hash code |h|, then we search until we either
+find the word or we don't. Words from different languages are kept
+separate by appending the language code to the string.
+
+@<Look for the word |hc[1...@>=
+h:=hc[1]; incr(hn); hc[hn]:=cur_lang;
+for j:=2 to hn do h:=(h+h+hc[j]) mod hyph_size;
+loop@+ begin @<If the string |hyph_word[h]| is less than \(hc)|hc[1..hn]|,
+ |goto not_found|; but if the two strings are equal,
+ set |hyf| to the hyphen positions and |goto found|@>;
+ if h>0 then decr(h)@+else h:=hyph_size;
+ end;
+not_found: decr(hn)
+
+@ @<If the string |hyph_word[h]| is less than \(hc)...@>=
+k:=hyph_word[h]; if k=0 then goto not_found;
+if length(k)<hn then goto not_found;
+if length(k)=hn then
+ begin j:=1; u:=str_start[k];
+ repeat if so(str_pool[u])<hc[j] then goto not_found;
+ if so(str_pool[u])>hc[j] then goto done;
+ incr(j); incr(u);
+ until j>hn;
+ @<Insert hyphens as specified in |hyph_list[h]|@>;
+ decr(hn); goto found;
+ end;
+done:
+
+@ @<Insert hyphens as specified...@>=
+s:=hyph_list[h];
+while s<>null do
+ begin hyf[info(s)]:=1; s:=link(s);
+ end
+
+@ @<Search |hyph_list| for pointers to |p|@>=
+for q:=0 to hyph_size do
+ begin if hyph_list[q]=p then
+ begin print_nl("HYPH("); print_int(q); print_char(")");
+ end;
+ end
+
+@ We have now completed the hyphenation routine, so the |line_break| procedure
+is finished at last. Since the hyphenation exception table is fresh in our
+minds, it's a good time to deal with the routine that adds new entries to it.
+
+When \TeX\ has scanned `\.{\\hyphenation}', it calls on a procedure named
+|new_hyph_exceptions| to do the right thing.
+
+@d set_cur_lang==if language<=0 then cur_lang:=0
+ else if language>255 then cur_lang:=0
+ else cur_lang:=language
+
+@p procedure new_hyph_exceptions; {enters new exceptions}
+label reswitch, exit, found, not_found;
+var n:0..64; {length of current word; not always a |small_number|}
+@!j:0..64; {an index into |hc|}
+@!h:hyph_pointer; {an index into |hyph_word| and |hyph_list|}
+@!k:str_number; {an index into |str_start|}
+@!p:pointer; {head of a list of hyphen positions}
+@!q:pointer; {used when creating a new node for list |p|}
+@!s,@!t:str_number; {strings being compared or stored}
+@!u,@!v:pool_pointer; {indices into |str_pool|}
+begin scan_left_brace; {a left brace must follow \.{\\hyphenation}}
+set_cur_lang;
+@<Enter as many hyphenation exceptions as are listed,
+until coming to a right brace; then |return|@>;
+exit:end;
+
+@ @<Enter as many...@>=
+n:=0; p:=null;
+loop@+ begin get_x_token;
+ reswitch: case cur_cmd of
+ letter,other_char,char_given:@<Append a new letter or hyphen@>;
+ char_num: begin scan_char_num; cur_chr:=cur_val; cur_cmd:=char_given;
+ goto reswitch;
+ end;
+ spacer,right_brace: begin if n>1 then @<Enter a hyphenation exception@>;
+ if cur_cmd=right_brace then return;
+ n:=0; p:=null;
+ end;
+ othercases @<Give improper \.{\\hyphenation} error@>
+ endcases;
+ end
+
+@ @<Give improper \.{\\hyph...@>=
+begin print_err("Improper "); print_esc("hyphenation");
+@.Improper \\hyphenation...@>
+ print(" will be flushed");
+help2("Hyphenation exceptions must contain only letters")@/
+ ("and hyphens. But continue; I'll forgive and forget.");
+error;
+end
+
+@ @<Append a new letter or hyphen@>=
+if cur_chr="-" then @<Append the value |n| to list |p|@>
+else begin if lc_code(cur_chr)=0 then
+ begin print_err("Not a letter");
+@.Not a letter@>
+ help2("Letters in \hyphenation words must have \lccode>0.")@/
+ ("Proceed; I'll ignore the character I just read.");
+ error;
+ end
+ else if n<63 then
+ begin incr(n); hc[n]:=lc_code(cur_chr);
+ end;
+ end
+
+@ @<Append the value |n| to list |p|@>=
+begin if n<63 then
+ begin q:=get_avail; link(q):=p; info(q):=n; p:=q;
+ end;
+end
+
+@ @<Enter a hyphenation exception@>=
+begin incr(n); hc[n]:=cur_lang; str_room(n); h:=0;
+for j:=1 to n do
+ begin h:=(h+h+hc[j]) mod hyph_size;
+ append_char(hc[j]);
+ end;
+s:=make_string;
+@<Insert the \(p)pair |(s,p)| into the exception table@>;
+end
+
+@ @<Insert the \(p)pair |(s,p)|...@>=
+if hyph_count=hyph_size then overflow("exception dictionary",hyph_size);
+@:TeX capacity exceeded exception dictionary}{\quad exception dictionary@>
+incr(hyph_count);
+while hyph_word[h]<>0 do
+ begin @<If the string |hyph_word[h]| is less than \(or)or equal to
+ |s|, interchange |(hyph_word[h],hyph_list[h])| with |(s,p)|@>;
+ if h>0 then decr(h)@+else h:=hyph_size;
+ end;
+hyph_word[h]:=s; hyph_list[h]:=p
+
+@ @<If the string |hyph_word[h]| is less than \(or)...@>=
+k:=hyph_word[h];
+if length(k)<length(s) then goto found;
+if length(k)>length(s) then goto not_found;
+u:=str_start[k]; v:=str_start[s];
+repeat if str_pool[u]<str_pool[v] then goto found;
+if str_pool[u]>str_pool[v] then goto not_found;
+incr(u); incr(v);
+until u=str_start[k+1];
+found:q:=hyph_list[h]; hyph_list[h]:=p; p:=q;@/
+t:=hyph_word[h]; hyph_word[h]:=s; s:=t;
+not_found:
+
+@* \[43] Initializing the hyphenation tables.
+The trie for \TeX's hyphenation algorithm is built from a sequence of
+patterns following a \.{\\patterns} specification. Such a specification
+is allowed only in \.{INITEX}, since the extra memory for auxiliary tables
+and for the initialization program itself would only clutter up the
+production version of \TeX\ with a lot of deadwood.
+
+The first step is to build a trie that is linked, instead of packed
+into sequential storage, so that insertions are readily made.
+After all patterns have been processed, \.{INITEX}
+compresses the linked trie by identifying common subtries. Finally the
+trie is packed into the efficient sequential form that the hyphenation
+algorithm actually uses.
+
+@<Declare subprocedures for |line_break|@>=
+@!init @<Declare procedures for preprocessing hyphenation patterns@>@;
+tini
+
+@ Before we discuss trie building in detail, let's consider the simpler
+problem of creating the |hyf_distance|, |hyf_num|, and |hyf_next| arrays.
+
+Suppose, for example, that \TeX\ reads the pattern `\.{ab2cde1}'. This is
+a pattern of length 5, with $n_0\ldots n_5=0\,0\,2\,0\,0\,1$ in the
+notation above. We want the corresponding |trie_op| code |v| to have
+|hyf_distance[v]=3|, |hyf_num[v]=2|, and |hyf_next[v]=@t$v^\prime$@>|,
+where the auxiliary |trie_op| code $v^\prime$ has
+|hyf_distance[@t$v^\prime$@>]=0|, |hyf_num[@t$v^\prime$@>]=1|, and
+|hyf_next[@t$v^\prime$@>]=min_quarterword|.
+
+\TeX\ computes an appropriate value |v| with the |new_trie_op| subroutine
+below, by setting
+$$\hbox{|@t$v^\prime$@>:=new_trie_op(0,1,min_quarterword)|,\qquad
+|v:=new_trie_op(3,2,@t$v^\prime$@>)|.}$$
+This subroutine looks up its three
+parameters in a special hash table, assigning a new value only if these
+three have not appeared before for the current language.
+
+The hash table is called |trie_op_hash|, and the number of entries it contains
+is |trie_op_ptr|.
+
+@<Glob...@>=
+@!init@! trie_op_hash:array[-trie_op_size..trie_op_size] of 0..trie_op_size;
+ {trie op codes for quadruples}
+@!trie_used:array[ASCII_code] of quarterword;
+ {largest opcode used so far for this language}
+@!trie_op_lang:array[1..trie_op_size] of ASCII_code;
+ {language part of a hashed quadruple}
+@!trie_op_val:array[1..trie_op_size] of quarterword;
+ {opcode corresponding to a hashed quadruple}
+@!trie_op_ptr:0..trie_op_size; {number of stored ops so far}
+tini
+
+@ It's tempting to remove the |overflow| stops in the following procedure;
+|new_trie_op| could return |min_quarterword| (thereby simply ignoring
+part of a hyphenation pattern) instead of aborting the job. However, that would
+lead to different hyphenation results on different installations of \TeX\
+using the same patterns. The |overflow| stops are necessary for portability
+of patterns.
+
+@<Declare procedures for preprocessing hyph...@>=
+function new_trie_op(@!d,@!n:small_number;@!v:quarterword):quarterword;
+label exit;
+var h:-trie_op_size..trie_op_size; {trial hash location}
+@!u:quarterword; {trial op code}
+@!l:0..trie_op_size; {pointer to stored data}
+begin h:=abs(n+313*d+361*v+1009*cur_lang) mod (trie_op_size+trie_op_size)
+ - trie_op_size;
+loop@+ begin l:=trie_op_hash[h];
+ if l=0 then {empty position found for a new op}
+ begin if trie_op_ptr=trie_op_size then
+ overflow("pattern memory ops",trie_op_size);
+ u:=trie_used[cur_lang];
+ if u=max_quarterword then
+ overflow("pattern memory ops per language",
+ max_quarterword-min_quarterword);
+ incr(trie_op_ptr); incr(u); trie_used[cur_lang]:=u;
+ hyf_distance[trie_op_ptr]:=d;
+ hyf_num[trie_op_ptr]:=n; hyf_next[trie_op_ptr]:=v;
+ trie_op_lang[trie_op_ptr]:=cur_lang; trie_op_hash[h]:=trie_op_ptr;
+ trie_op_val[trie_op_ptr]:=u; new_trie_op:=u; return;
+ end;
+ if (hyf_distance[l]=d)and(hyf_num[l]=n)and(hyf_next[l]=v)
+ and(trie_op_lang[l]=cur_lang) then
+ begin new_trie_op:=trie_op_val[l]; return;
+ end;
+ if h>-trie_op_size then decr(h)@+else h:=trie_op_size;
+ end;
+exit:end;
+
+@ After |new_trie_op| has compressed the necessary opcode information,
+plenty of information is available to unscramble the data into the
+final form needed by our hyphenation algorithm.
+
+@<Sort \(t)the hyphenation op tables into proper order@>=
+op_start[0]:=-min_quarterword;
+for j:=1 to 255 do op_start[j]:=op_start[j-1]+qo(trie_used[j-1]);
+for j:=1 to trie_op_ptr do
+ trie_op_hash[j]:=op_start[trie_op_lang[j]]+trie_op_val[j]; {destination}
+for j:=1 to trie_op_ptr do while trie_op_hash[j]>j do
+ begin k:=trie_op_hash[j];@/
+ t:=hyf_distance[k]; hyf_distance[k]:=hyf_distance[j]; hyf_distance[j]:=t;@/
+ t:=hyf_num[k]; hyf_num[k]:=hyf_num[j]; hyf_num[j]:=t;@/
+ t:=hyf_next[k]; hyf_next[k]:=hyf_next[j]; hyf_next[j]:=t;@/
+ trie_op_hash[j]:=trie_op_hash[k]; trie_op_hash[k]:=k;
+ end
+
+@ Before we forget how to initialize the data structures that have been
+mentioned so far, let's write down the code that gets them started.
+
+@<Initialize table entries...@>=
+for k:=-trie_op_size to trie_op_size do trie_op_hash[k]:=0;
+for k:=0 to 255 do trie_used[k]:=min_quarterword;
+trie_op_ptr:=0;
+
+@ The linked trie that is used to preprocess hyphenation patterns appears
+in several global arrays. Each node represents an instruction of the form
+``if you see character |c|, then perform operation |o|, move to the
+next character, and go to node |l|; otherwise go to node |r|.''
+The four quantities |c|, |o|, |l|, and |r| are stored in four arrays
+|trie_c|, |trie_o|, |trie_l|, and |trie_r|. The root of the trie
+is |trie_l[0]|, and the number of nodes is |trie_ptr|. Null trie
+pointers are represented by zero. To initialize the trie, we simply
+set |trie_l[0]| and |trie_ptr| to zero. We also set |trie_c[0]| to some
+arbitrary value, since the algorithm may access it.
+
+The algorithms maintain the condition
+$$\hbox{|trie_c[trie_r[z]]>trie_c[z]|\qquad
+whenever |z<>0| and |trie_r[z]<>0|};$$ in other words, sibling nodes are
+ordered by their |c| fields.
+
+@d trie_root==trie_l[0] {root of the linked trie}
+
+@<Glob...@>=
+@!init @!trie_c:packed array[trie_pointer] of packed_ASCII_code;
+ {characters to match}
+@t\hskip10pt@>@!trie_o:packed array[trie_pointer] of quarterword;
+ {operations to perform}
+@t\hskip10pt@>@!trie_l:packed array[trie_pointer] of trie_pointer;
+ {left subtrie links}
+@t\hskip10pt@>@!trie_r:packed array[trie_pointer] of trie_pointer;
+ {right subtrie links}
+@t\hskip10pt@>@!trie_ptr:trie_pointer; {the number of nodes in the trie}
+@t\hskip10pt@>@!trie_hash:packed array[trie_pointer] of trie_pointer;
+ {used to identify equivalent subtries}
+tini
+
+@ Let us suppose that a linked trie has already been constructed.
+Experience shows that we can often reduce its size by recognizing common
+subtries; therefore another hash table is introduced for this purpose,
+somewhat similar to |trie_op_hash|. The new hash table will be
+initialized to zero.
+
+The function |trie_node(p)| returns |p| if |p| is distinct from other nodes
+that it has seen, otherwise it returns the number of the first equivalent
+node that it has seen.
+
+Notice that we might make subtries equivalent even if they correspond to
+patterns for different languages, in which the trie ops might mean quite
+different things. That's perfectly all right.
+
+@<Declare procedures for preprocessing hyph...@>=
+function trie_node(@!p:trie_pointer):trie_pointer; {converts
+ to a canonical form}
+label exit;
+var h:trie_pointer; {trial hash location}
+@!q:trie_pointer; {trial trie node}
+begin h:=abs(trie_c[p]+1009*trie_o[p]+@|
+ 2718*trie_l[p]+3142*trie_r[p]) mod trie_size;
+loop@+ begin q:=trie_hash[h];
+ if q=0 then
+ begin trie_hash[h]:=p; trie_node:=p; return;
+ end;
+ if (trie_c[q]=trie_c[p])and(trie_o[q]=trie_o[p])and@|
+ (trie_l[q]=trie_l[p])and(trie_r[q]=trie_r[p]) then
+ begin trie_node:=q; return;
+ end;
+ if h>0 then decr(h)@+else h:=trie_size;
+ end;
+exit:end;
+
+@ A neat recursive procedure is now able to compress a trie by
+traversing it and applying |trie_node| to its nodes in ``bottom up''
+fashion. We will compress the entire trie by clearing |trie_hash| to
+zero and then saying `|trie_root:=compress_trie(trie_root)|'.
+@^recursion@>
+
+@<Declare procedures for preprocessing hyph...@>=
+function compress_trie(@!p:trie_pointer):trie_pointer;
+begin if p=0 then compress_trie:=0
+else begin trie_l[p]:=compress_trie(trie_l[p]);
+ trie_r[p]:=compress_trie(trie_r[p]);
+ compress_trie:=trie_node(p);
+ end;
+end;
+
+@ The compressed trie will be packed into the |trie| array using a
+``top-down first-fit'' procedure. This is a little tricky, so the reader
+should pay close attention: The |trie_hash| array is cleared to zero
+again and renamed |trie_ref| for this phase of the operation; later on,
+|trie_ref[p]| will be nonzero only if the linked trie node |p| is the
+smallest character
+in a family and if the characters |c| of that family have been allocated to
+locations |trie_ref[p]+c| in the |trie| array. Locations of |trie| that
+are in use will have |trie_link=0|, while the unused holes in |trie|
+will be doubly linked with |trie_link| pointing to the next larger vacant
+location and |trie_back| pointing to the next smaller one. This double
+linking will have been carried out only as far as |trie_max|, where
+|trie_max| is the largest index of |trie| that will be needed.
+To save time at the low end of the trie, we maintain array entries
+|trie_min[c]| pointing to the smallest hole that is greater than~|c|.
+Another array |trie_taken| tells whether or not a given location is
+equal to |trie_ref[p]| for some |p|; this array is used to ensure that
+distinct nodes in the compressed trie will have distinct |trie_ref|
+entries.
+
+@d trie_ref==trie_hash {where linked trie families go into |trie|}
+@d trie_back(#)==trie[#].lh {backward links in |trie| holes}
+
+@<Glob...@>=
+@!init@!trie_taken:packed array[1..trie_size] of boolean;
+ {does a family start here?}
+@t\hskip10pt@>@!trie_min:array[ASCII_code] of trie_pointer;
+ {the first possible slot for each character}
+@t\hskip10pt@>@!trie_max:trie_pointer; {largest location used in |trie|}
+@t\hskip10pt@>@!trie_not_ready:boolean; {is the trie still in linked form?}
+tini
+
+@ Each time \.{\\patterns} appears, it contributes further patterns to
+the future trie, which will be built only when hyphenation is attempted or
+when a format file is dumped. The boolean variable |trie_not_ready|
+will change to |false| when the trie is compressed; this will disable
+further patterns.
+
+@<Initialize table entries...@>=
+trie_not_ready:=true; trie_root:=0; trie_c[0]:=si(0); trie_ptr:=0;
+
+@ Here is how the trie-compression data structures are initialized.
+If storage is tight, it would be possible to overlap |trie_op_hash|,
+|trie_op_lang|, and |trie_op_val| with |trie|, |trie_hash|, and |trie_taken|,
+because we finish with the former just before we need the latter.
+
+@<Get ready to compress the trie@>=
+@<Sort \(t)the hyphenation...@>;
+for p:=0 to trie_size do trie_hash[p]:=0;
+trie_root:=compress_trie(trie_root); {identify equivalent subtries}
+for p:=0 to trie_ptr do trie_ref[p]:=0;
+for p:=0 to 255 do trie_min[p]:=p+1;
+trie_link(0):=1; trie_max:=0
+
+@ The |first_fit| procedure finds the smallest hole |z| in |trie| such that
+a trie family starting at a given node |p| will fit into vacant positions
+starting at |z|. If |c=trie_c[p]|, this means that location |z-c| must
+not already be taken by some other family, and that |z-c+@t$c^\prime$@>|
+must be vacant for all characters $c^\prime$ in the family. The procedure
+sets |trie_ref[p]| to |z-c| when the first fit has been found.
+
+@<Declare procedures for preprocessing hyph...@>=
+procedure first_fit(@!p:trie_pointer); {packs a family into |trie|}
+label not_found,found;
+var h:trie_pointer; {candidate for |trie_ref[p]|}
+@!z:trie_pointer; {runs through holes}
+@!q:trie_pointer; {runs through the family starting at |p|}
+@!c:ASCII_code; {smallest character in the family}
+@!l,@!r:trie_pointer; {left and right neighbors}
+@!ll:1..256; {upper limit of |trie_min| updating}
+begin c:=so(trie_c[p]);
+z:=trie_min[c]; {get the first conceivably good hole}
+loop@+ begin h:=z-c;@/
+ @<Ensure that |trie_max>=h+256|@>;
+ if trie_taken[h] then goto not_found;
+ @<If all characters of the family fit relative to |h|, then
+ |goto found|,\30\ otherwise |goto not_found|@>;
+ not_found: z:=trie_link(z); {move to the next hole}
+ end;
+found: @<Pack the family into |trie| relative to |h|@>;
+end;
+
+@ By making sure that |trie_max| is at least |h+256|, we can be sure that
+|trie_max>z|, since |h=z-c|. It follows that location |trie_max| will
+never be occupied in |trie|, and we will have |trie_max>=trie_link(z)|.
+
+@<Ensure that |trie_max>=h+256|@>=
+if trie_max<h+256 then
+ begin if trie_size<=h+256 then overflow("pattern memory",trie_size);
+@:TeX capacity exceeded pattern memory}{\quad pattern memory@>
+ repeat incr(trie_max); trie_taken[trie_max]:=false;
+ trie_link(trie_max):=trie_max+1; trie_back(trie_max):=trie_max-1;
+ until trie_max=h+256;
+ end
+
+@ @<If all characters of the family fit relative to |h|...@>=
+q:=trie_r[p];
+while q>0 do
+ begin if trie_link(h+so(trie_c[q]))=0 then goto not_found;
+ q:=trie_r[q];
+ end;
+goto found
+
+@ @<Pack the family into |trie| relative to |h|@>=
+trie_taken[h]:=true; trie_ref[p]:=h; q:=p;
+repeat z:=h+so(trie_c[q]); l:=trie_back(z); r:=trie_link(z);
+trie_back(r):=l; trie_link(l):=r; trie_link(z):=0;
+if l<256 then
+ begin if z<256 then ll:=z @+else ll:=256;
+ repeat trie_min[l]:=r; incr(l);
+ until l=ll;
+ end;
+q:=trie_r[q];
+until q=0
+
+@ To pack the entire linked trie, we use the following recursive procedure.
+@^recursion@>
+
+@<Declare procedures for preprocessing hyph...@>=
+procedure trie_pack(@!p:trie_pointer); {pack subtries of a family}
+var q:trie_pointer; {a local variable that need not be saved on recursive calls}
+begin repeat q:=trie_l[p];
+if (q>0)and(trie_ref[q]=0) then
+ begin first_fit(q); trie_pack(q);
+ end;
+p:=trie_r[p];
+until p=0;
+end;
+
+@ When the whole trie has been allocated into the sequential table, we
+must go through it once again so that |trie| contains the correct
+information. Null pointers in the linked trie will be represented by the
+value~0, which properly implements an ``empty'' family.
+
+@<Move the data into |trie|@>=
+h.rh:=0; h.b0:=min_quarterword; h.b1:=min_quarterword; {|trie_link:=0|,
+ |trie_op:=min_quarterword|, |trie_char:=qi(0)|}
+if trie_root=0 then {no patterns were given}
+ begin for r:=0 to 256 do trie[r]:=h;
+ trie_max:=256;
+ end
+else begin trie_fix(trie_root); {this fixes the non-holes in |trie|}
+ r:=0; {now we will zero out all the holes}
+ repeat s:=trie_link(r); trie[r]:=h; r:=s;
+ until r>trie_max;
+ end;
+trie_char(0):=qi("?"); {make |trie_char(c)<>c| for all |c|}
+
+@ The fixing-up procedure is, of course, recursive. Since the linked trie
+usually has overlapping subtries, the same data may be moved several
+times; but that causes no harm, and at most as much work is done as it
+took to build the uncompressed trie.
+@^recursion@>
+
+@<Declare procedures for preprocessing hyph...@>=
+procedure trie_fix(@!p:trie_pointer); {moves |p| and its siblings into |trie|}
+var q:trie_pointer; {a local variable that need not be saved on recursive calls}
+@!c:ASCII_code; {another one that need not be saved}
+@!z:trie_pointer; {|trie| reference; this local variable must be saved}
+begin z:=trie_ref[p];
+repeat q:=trie_l[p]; c:=so(trie_c[p]);
+trie_link(z+c):=trie_ref[q]; trie_char(z+c):=qi(c); trie_op(z+c):=trie_o[p];
+if q>0 then trie_fix(q);
+p:=trie_r[p];
+until p=0;
+end;
+
+@ Now let's go back to the easier problem, of building the linked
+trie. When \.{INITEX} has scanned the `\.{\\patterns}' control
+sequence, it calls on |new_patterns| to do the right thing.
+
+@<Declare procedures for preprocessing hyph...@>=
+procedure new_patterns; {initializes the hyphenation pattern data}
+label done, done1;
+var k,@!l:0..64; {indices into |hc| and |hyf|;
+ not always in |small_number| range}
+@!digit_sensed:boolean; {should the next digit be treated as a letter?}
+@!v:quarterword; {trie op code}
+@!p,@!q:trie_pointer; {nodes of trie traversed during insertion}
+@!first_child:boolean; {is |p=trie_l[q]|?}
+@!c:ASCII_code; {character being inserted}
+begin if trie_not_ready then
+ begin set_cur_lang; scan_left_brace; {a left brace must follow \.{\\patterns}}
+ @<Enter all of the patterns into a linked trie, until coming to a right
+ brace@>;
+ end
+else begin print_err("Too late for "); print_esc("patterns");
+ help1("All patterns must be given before typesetting begins.");
+ error; link(garbage):=scan_toks(false,false); flush_list(def_ref);
+ end;
+end;
+
+@ Novices are not supposed to be using \.{\\patterns}, so the error
+messages are terse. (Note that all error messages appear in \TeX's string
+pool, even if they are used only by \.{INITEX}.)
+
+@<Enter all of the patterns into a linked trie...@>=
+k:=0; hyf[0]:=0; digit_sensed:=false;
+loop@+ begin get_x_token;
+ case cur_cmd of
+ letter,other_char:@<Append a new letter or a hyphen level@>;
+ spacer,right_brace: begin if k>0 then
+ @<Insert a new pattern into the linked trie@>;
+ if cur_cmd=right_brace then goto done;
+ k:=0; hyf[0]:=0; digit_sensed:=false;
+ end;
+ othercases begin print_err("Bad "); print_esc("patterns");
+@.Bad \\patterns@>
+ help1("(See Appendix H.)"); error;
+ end
+ endcases;
+ end;
+done:
+
+@ @<Append a new letter or a hyphen level@>=
+if digit_sensed or(cur_chr<"0")or(cur_chr>"9") then
+ begin if cur_chr="." then cur_chr:=0 {edge-of-word delimiter}
+ else begin cur_chr:=lc_code(cur_chr);
+ if cur_chr=0 then
+ begin print_err("Nonletter");
+@.Nonletter@>
+ help1("(See Appendix H.)"); error;
+ end;
+ end;
+ if k<63 then
+ begin incr(k); hc[k]:=cur_chr; hyf[k]:=0; digit_sensed:=false;
+ end;
+ end
+else if k<63 then
+ begin hyf[k]:=cur_chr-"0"; digit_sensed:=true;
+ end
+
+@ When the following code comes into play, the pattern $p_1\ldots p_k$
+appears in |hc[1..k]|, and the corresponding sequence of numbers $n_0\ldots
+n_k$ appears in |hyf[0..k]|.
+
+@<Insert a new pattern into the linked trie@>=
+begin @<Compute the trie op code, |v|, and set |l:=0|@>;
+q:=0; hc[0]:=cur_lang;
+while l<=k do
+ begin c:=hc[l]; incr(l); p:=trie_l[q]; first_child:=true;
+ while (p>0)and(c>so(trie_c[p])) do
+ begin q:=p; p:=trie_r[q]; first_child:=false;
+ end;
+ if (p=0)or(c<so(trie_c[p])) then
+ @<Insert a new trie node between |q| and |p|, and
+ make |p| point to it@>;
+ q:=p; {now node |q| represents $p_1\ldots p_{l-1}$}
+ end;
+if trie_o[q]<>min_quarterword then
+ begin print_err("Duplicate pattern");
+@.Duplicate pattern@>
+ help1("(See Appendix H.)"); error;
+ end;
+trie_o[q]:=v;
+end
+
+@ @<Insert a new trie node between |q| and |p|...@>=
+begin if trie_ptr=trie_size then overflow("pattern memory",trie_size);
+@:TeX capacity exceeded pattern memory}{\quad pattern memory@>
+incr(trie_ptr); trie_r[trie_ptr]:=p; p:=trie_ptr; trie_l[p]:=0;
+if first_child then trie_l[q]:=p@+else trie_r[q]:=p;
+trie_c[p]:=si(c); trie_o[p]:=min_quarterword;
+end
+
+@ @<Compute the trie op code, |v|...@>=
+if hc[1]=0 then hyf[0]:=0;
+if hc[k]=0 then hyf[k]:=0;
+l:=k; v:=min_quarterword;
+loop@+ begin if hyf[l]<>0 then v:=new_trie_op(k-l,hyf[l],v);
+ if l>0 then decr(l)@+else goto done1;
+ end;
+done1:
+
+@ Finally we put everything together: Here is how the trie gets to its
+final, efficient form.
+The following packing routine is rigged so that the root of the linked
+tree gets mapped into location 1 of |trie|, as required by the hyphenation
+algorithm. This happens because the first call of |first_fit| will
+``take'' location~1.
+
+@<Declare procedures for preprocessing hyphenation patterns@>=
+procedure init_trie;
+var @!p:trie_pointer; {pointer for initialization}
+@!j,@!k,@!t:integer; {all-purpose registers for initialization}
+@!r,@!s:trie_pointer; {used to clean up the packed |trie|}
+@!h:two_halves; {template used to zero out |trie|'s holes}
+begin @<Get ready to compress the trie@>;
+if trie_root<>0 then
+ begin first_fit(trie_root); trie_pack(trie_root);
+ end;
+@<Move the data into |trie|@>;
+trie_not_ready:=false;
+end;
+
+@* \[44] Breaking vertical lists into pages.
+The |vsplit| procedure, which implements \TeX's \.{\\vsplit} operation,
+is considerably simpler than |line_break| because it doesn't have to
+worry about hyphenation, and because its mission is to discover a single
+break instead of an optimum sequence of breakpoints. But before we get
+into the details of |vsplit|, we need to consider a few more basic things.
+
+@ A subroutine called |prune_page_top| takes a pointer to a vlist and
+returns a pointer to a modified vlist in which all glue, kern, and penalty nodes
+have been deleted before the first box or rule node. However, the first
+box or rule is actually preceded by a newly created glue node designed so that
+the topmost baseline will be at distance |split_top_skip| from the top,
+whenever this is possible without backspacing.
+
+In this routine and those that follow, we make use of the fact that a
+vertical list contains no character nodes, hence the |type| field exists
+for each node in the list.
+@^data structure assumptions@>
+
+@p function prune_page_top(@!p:pointer):pointer; {adjust top after page break}
+var prev_p:pointer; {lags one step behind |p|}
+@!q:pointer; {temporary variable for list manipulation}
+begin prev_p:=temp_head; link(temp_head):=p;
+while p<>null do
+ case type(p) of
+ hlist_node,vlist_node,rule_node:@<Insert glue for |split_top_skip|
+ and set~|p:=null|@>;
+ whatsit_node,mark_node,ins_node: begin prev_p:=p; p:=link(prev_p);
+ end;
+ glue_node,kern_node,penalty_node: begin q:=p; p:=link(q); link(q):=null;
+ link(prev_p):=p; flush_node_list(q);
+ end;
+ othercases confusion("pruning")
+@:this can't happen pruning}{\quad pruning@>
+ endcases;
+prune_page_top:=link(temp_head);
+end;
+
+@ @<Insert glue for |split_top_skip|...@>=
+begin q:=new_skip_param(split_top_skip_code); link(prev_p):=q; link(q):=p;
+ {now |temp_ptr=glue_ptr(q)|}
+if width(temp_ptr)>height(p) then width(temp_ptr):=width(temp_ptr)-height(p)
+else width(temp_ptr):=0;
+p:=null;
+end
+
+@ The next subroutine finds the best place to break a given vertical list
+so as to obtain a box of height~|h|, with maximum depth~|d|.
+A pointer to the beginning of the vertical list is given,
+and a pointer to the optimum breakpoint is returned. The list is effectively
+followed by a forced break, i.e., a penalty node with the |eject_penalty|;
+if the best break occurs at this artificial node, the value |null| is returned.
+
+An array of six |scaled| distances is used to keep track of the height
+from the beginning of the list to the current place, just as in |line_break|.
+In fact, we use one of the same arrays, only changing its name to reflect
+its new significance.
+
+@d active_height==active_width {new name for the six distance variables}
+@d cur_height==active_height[1] {the natural height}
+@d set_height_zero(#)==active_height[#]:=0 {initialize the height to zero}
+@#
+@d update_heights=90 {go here to record glue in the |active_height| table}
+
+@p function vert_break(@!p:pointer; @!h,@!d:scaled):pointer;
+ {finds optimum page break}
+label done,not_found,update_heights;
+var prev_p:pointer; {if |p| is a glue node, |type(prev_p)| determines
+ whether |p| is a legal breakpoint}
+@!q,@!r:pointer; {glue specifications}
+@!pi:integer; {penalty value}
+@!b:integer; {badness at a trial breakpoint}
+@!least_cost:integer; {the smallest badness plus penalties found so far}
+@!best_place:pointer; {the most recent break that leads to |least_cost|}
+@!prev_dp:scaled; {depth of previous box in the list}
+@!t:small_number; {|type| of the node following a kern}
+begin prev_p:=p; {an initial glue node is not a legal breakpoint}
+least_cost:=awful_bad; do_all_six(set_height_zero); prev_dp:=0;
+loop@+ begin @<If node |p| is a legal breakpoint, check if this break is
+ the best known, and |goto done| if |p| is null or
+ if the page-so-far is already too full to accept more stuff@>;
+ prev_p:=p; p:=link(prev_p);
+ end;
+done: vert_break:=best_place;
+end;
+
+@ A global variable |best_height_plus_depth| will be set to the natural size
+of the box that corresponds to the optimum breakpoint found by |vert_break|.
+(This value is used by the insertion-splitting algorithm of the page builder.)
+
+@<Glob...@>=
+@!best_height_plus_depth:scaled; {height of the best box, without stretching or
+ shrinking}
+
+@ A subtle point to be noted here is that the maximum depth~|d| might be
+negative, so |cur_height| and |prev_dp| might need to be corrected even
+after a glue or kern node.
+
+@<If node |p| is a legal breakpoint, check...@>=
+if p=null then pi:=eject_penalty
+else @<Use node |p| to update the current height and depth measurements;
+ if this node is not a legal breakpoint, |goto not_found|
+ or |update_heights|,
+ otherwise set |pi| to the associated penalty at the break@>;
+@<Check if node |p| is a new champion breakpoint; then \(go)|goto done|
+ if |p| is a forced break or if the page-so-far is already too full@>;
+if (type(p)<glue_node)or(type(p)>kern_node) then goto not_found;
+update_heights: @<Update the current height and depth measurements with
+ respect to a glue or kern node~|p|@>;
+not_found: if prev_dp>d then
+ begin cur_height:=cur_height+prev_dp-d;
+ prev_dp:=d;
+ end;
+
+@ @<Use node |p| to update the current height and depth measurements...@>=
+case type(p) of
+hlist_node,vlist_node,rule_node: begin@t@>@;@/
+ cur_height:=cur_height+prev_dp+height(p); prev_dp:=depth(p);
+ goto not_found;
+ end;
+whatsit_node:@<Process whatsit |p| in |vert_break| loop, |goto not_found|@>;
+glue_node: if precedes_break(prev_p) then pi:=0
+ else goto update_heights;
+kern_node: begin if link(p)=null then t:=penalty_node
+ else t:=type(link(p));
+ if t=glue_node then pi:=0@+else goto update_heights;
+ end;
+penalty_node: pi:=penalty(p);
+mark_node,ins_node: goto not_found;
+othercases confusion("vertbreak")
+@:this can't happen vertbreak}{\quad vertbreak@>
+endcases
+
+@ @d deplorable==100000 {more than |inf_bad|, but less than |awful_bad|}
+
+@<Check if node |p| is a new champion breakpoint; then \(go)...@>=
+if pi<inf_penalty then
+ begin @<Compute the badness, |b|, using |awful_bad|
+ if the box is too full@>;
+ if b<awful_bad then
+ if pi<=eject_penalty then b:=pi
+ else if b<inf_bad then b:=b+pi
+ else b:=deplorable;
+ if b<=least_cost then
+ begin best_place:=p; least_cost:=b;
+ best_height_plus_depth:=cur_height+prev_dp;
+ end;
+ if (b=awful_bad)or(pi<=eject_penalty) then goto done;
+ end
+
+@ @<Compute the badness, |b|, using |awful_bad| if the box is too full@>=
+if cur_height<h then
+ if (active_height[3]<>0) or (active_height[4]<>0) or
+ (active_height[5]<>0) then b:=0
+ else b:=badness(h-cur_height,active_height[2])
+else if cur_height-h>active_height[6] then b:=awful_bad
+else b:=badness(cur_height-h,active_height[6])
+
+@ Vertical lists that are subject to the |vert_break| procedure should not
+contain infinite shrinkability, since that would permit any amount of
+information to ``fit'' on one page.
+
+@<Update the current height and depth measurements with...@>=
+if type(p)=kern_node then q:=p
+else begin q:=glue_ptr(p);
+ active_height[2+stretch_order(q)]:=@|
+ active_height[2+stretch_order(q)]+stretch(q);@/
+ active_height[6]:=active_height[6]+shrink(q);
+ if (shrink_order(q)<>normal)and(shrink(q)<>0) then
+ begin@t@>@;@/
+ print_err("Infinite glue shrinkage found in box being split");@/
+@.Infinite glue shrinkage...@>
+ help4("The box you are \vsplitting contains some infinitely")@/
+ ("shrinkable glue, e.g., `\vss' or `\vskip 0pt minus 1fil'.")@/
+ ("Such glue doesn't belong there; but you can safely proceed,")@/
+ ("since the offensive shrinkability has been made finite.");
+ error; r:=new_spec(q); shrink_order(r):=normal; delete_glue_ref(q);
+ glue_ptr(p):=r; q:=r;
+ end;
+ end;
+cur_height:=cur_height+prev_dp+width(q); prev_dp:=0
+
+@ Now we are ready to consider |vsplit| itself. Most of
+its work is accomplished by the two subroutines that we have just considered.
+
+Given the number of a vlist box |n|, and given a desired page height |h|,
+the |vsplit| function finds the best initial segment of the vlist and
+returns a box for a page of height~|h|. The remainder of the vlist, if
+any, replaces the original box, after removing glue and penalties and
+adjusting for |split_top_skip|. Mark nodes in the split-off box are used to
+set the values of |split_first_mark| and |split_bot_mark|; we use the
+fact that |split_first_mark=null| if and only if |split_bot_mark=null|.
+
+The original box becomes ``void'' if and only if it has been entirely
+extracted. The extracted box is ``void'' if and only if the original
+box was void (or if it was, erroneously, an hlist box).
+
+@p function vsplit(@!n:eight_bits; @!h:scaled):pointer;
+ {extracts a page of height |h| from box |n|}
+label exit,done;
+var v:pointer; {the box to be split}
+p:pointer; {runs through the vlist}
+q:pointer; {points to where the break occurs}
+begin v:=box(n);
+if split_first_mark<>null then
+ begin delete_token_ref(split_first_mark); split_first_mark:=null;
+ delete_token_ref(split_bot_mark); split_bot_mark:=null;
+ end;
+@<Dispense with trivial cases of void or bad boxes@>;
+q:=vert_break(list_ptr(v),h,split_max_depth);
+@<Look at all the marks in nodes before the break, and set the final
+ link to |null| at the break@>;
+q:=prune_page_top(q); p:=list_ptr(v); free_node(v,box_node_size);
+if q=null then box(n):=null {the |eq_level| of the box stays the same}
+else box(n):=vpack(q,natural);
+vsplit:=vpackage(p,h,exactly,split_max_depth);
+exit: end;
+
+@ @<Dispense with trivial cases of void or bad boxes@>=
+if v=null then
+ begin vsplit:=null; return;
+ end;
+if type(v)<>vlist_node then
+ begin print_err(""); print_esc("vsplit"); print(" needs a ");
+ print_esc("vbox");
+@:vsplit_}{\.{\\vsplit needs a \\vbox}@>
+ help2("The box you are trying to split is an \hbox.")@/
+ ("I can't split such a box, so I'll leave it alone.");
+ error; vsplit:=null; return;
+ end
+
+@ It's possible that the box begins with a penalty node that is the
+``best'' break, so we must be careful to handle this special case correctly.
+
+@<Look at all the marks...@>=
+p:=list_ptr(v);
+if p=q then list_ptr(v):=null
+else loop@+begin if type(p)=mark_node then
+ if split_first_mark=null then
+ begin split_first_mark:=mark_ptr(p);
+ split_bot_mark:=split_first_mark;
+ token_ref_count(split_first_mark):=@|
+ token_ref_count(split_first_mark)+2;
+ end
+ else begin delete_token_ref(split_bot_mark);
+ split_bot_mark:=mark_ptr(p);
+ add_token_ref(split_bot_mark);
+ end;
+ if link(p)=q then
+ begin link(p):=null; goto done;
+ end;
+ p:=link(p);
+ end;
+done:
+
+@* \[45] The page builder.
+When \TeX\ appends new material to its main vlist in vertical mode, it uses
+a method something like |vsplit| to decide where a page ends, except that
+the calculations are done ``on line'' as new items come in.
+The main complication in this process is that insertions must be put
+into their boxes and removed from the vlist, in a more-or-less optimum manner.
+
+We shall use the term ``current page'' for that part of the main vlist that
+is being considered as a candidate for being broken off and sent to the
+user's output routine. The current page starts at |link(page_head)|, and
+it ends at |page_tail|. We have |page_head=page_tail| if this list is empty.
+@^current page@>
+
+Utter chaos would reign if the user kept changing page specifications
+while a page is being constructed, so the page builder keeps the pertinent
+specifications frozen as soon as the page receives its first box or
+insertion. The global variable |page_contents| is |empty| when the
+current page contains only mark nodes and content-less whatsit nodes; it
+is |inserts_only| if the page contains only insertion nodes in addition to
+marks and whatsits. Glue nodes, kern nodes, and penalty nodes are
+discarded until a box or rule node appears, at which time |page_contents|
+changes to |box_there|. As soon as |page_contents| becomes non-|empty|,
+the current |vsize| and |max_depth| are squirreled away into |page_goal|
+and |page_max_depth|; the latter values will be used until the page has
+been forwarded to the user's output routine. The \.{\\topskip} adjustment
+is made when |page_contents| changes to |box_there|.
+
+Although |page_goal| starts out equal to |vsize|, it is decreased by the
+scaled natural height-plus-depth of the insertions considered so far, and by
+the \.{\\skip} corrections for those insertions. Therefore it represents
+the size into which the non-inserted material should fit, assuming that
+all insertions in the current page have been made.
+
+The global variables |best_page_break| and |least_page_cost| correspond
+respectively to the local variables |best_place| and |least_cost| in the
+|vert_break| routine that we have already studied; i.e., they record the
+location and value of the best place currently known for breaking the
+current page. The value of |page_goal| at the time of the best break is
+stored in |best_size|.
+
+@d inserts_only=1
+ {|page_contents| when an insert node has been contributed, but no boxes}
+@d box_there=2 {|page_contents| when a box or rule has been contributed}
+
+@<Glob...@>=
+@!page_tail:pointer; {the final node on the current page}
+@!page_contents:empty..box_there; {what is on the current page so far?}
+@!page_max_depth:scaled; {maximum box depth on page being built}
+@!best_page_break:pointer; {break here to get the best page known so far}
+@!least_page_cost:integer; {the score for this currently best page}
+@!best_size:scaled; {its |page_goal|}
+
+@ The page builder has another data structure to keep track of insertions.
+This is a list of four-word nodes, starting and ending at |page_ins_head|.
+That is, the first element of the list is node |r@t$_1$@>=link(page_ins_head)|;
+node $r_j$ is followed by |r@t$_{j+1}$@>=link(r@t$_j$@>)|; and if there are
+|n| items we have |r@t$_{n+1}$@>=page_ins_head|. The |subtype| field of
+each node in this list refers to an insertion number; for example, `\.{\\insert
+250}' would correspond to a node whose |subtype| is |qi(250)|
+(the same as the |subtype| field of the relevant |ins_node|). These |subtype|
+fields are in increasing order, and |subtype(page_ins_head)=
+qi(255)|, so |page_ins_head| serves as a convenient sentinel
+at the end of the list. A record is present for each insertion number that
+appears in the current page.
+
+The |type| field in these nodes distinguishes two possibilities that
+might occur as we look ahead before deciding on the optimum page break.
+If |type(r)=inserting|, then |height(r)| contains the total of the
+height-plus-depth dimensions of the box and all its inserts seen so far.
+If |type(r)=split_up|, then no more insertions will be made into this box,
+because at least one previous insertion was too big to fit on the current
+page; |broken_ptr(r)| points to the node where that insertion will be
+split, if \TeX\ decides to split it, |broken_ins(r)| points to the
+insertion node that was tentatively split, and |height(r)| includes also the
+natural height plus depth of the part that would be split off.
+
+In both cases, |last_ins_ptr(r)| points to the last |ins_node|
+encountered for box |qo(subtype(r))| that would be at least partially
+inserted on the next page; and |best_ins_ptr(r)| points to the last
+such |ins_node| that should actually be inserted, to get the page with
+minimum badness among all page breaks considered so far. We have
+|best_ins_ptr(r)=null| if and only if no insertion for this box should
+be made to produce this optimum page.
+
+The data structure definitions here use the fact that the |@!height| field
+appears in the fourth word of a box node.
+@^data structure assumptions@>
+
+@d page_ins_node_size=4 {number of words for a page insertion node}
+@d inserting=0 {an insertion class that has not yet overflowed}
+@d split_up=1 {an overflowed insertion class}
+@d broken_ptr(#)==link(#+1)
+ {an insertion for this class will break here if anywhere}
+@d broken_ins(#)==info(#+1) {this insertion might break at |broken_ptr|}
+@d last_ins_ptr(#)==link(#+2) {the most recent insertion for this |subtype|}
+@d best_ins_ptr(#)==info(#+2) {the optimum most recent insertion}
+
+@<Initialize the special list heads...@>=
+subtype(page_ins_head):=qi(255);
+type(page_ins_head):=split_up; link(page_ins_head):=page_ins_head;
+
+@ An array |page_so_far| records the heights and depths of everything
+on the current page. This array contains six |scaled| numbers, like the
+similar arrays already considered in |line_break| and |vert_break|; and it
+also contains |page_goal| and |page_depth|, since these values are
+all accessible to the user via |set_page_dimen| commands. The
+value of |page_so_far[1]| is also called |page_total|. The stretch
+and shrink components of the \.{\\skip} corrections for each insertion are
+included in |page_so_far|, but the natural space components of these
+corrections are not, since they have been subtracted from |page_goal|.
+
+The variable |page_depth| records the depth of the current page; it has been
+adjusted so that it is at most |page_max_depth|. The variable
+|last_glue| points to the glue specification of the most recent node
+contributed from the contribution list, if this was a glue node; otherwise
+|last_glue=max_halfword|. (If the contribution list is nonempty,
+however, the value of |last_glue| is not necessarily accurate.)
+The variables |last_penalty| and |last_kern| are similar. And
+finally, |insert_penalties| holds the sum of the penalties associated with
+all split and floating insertions.
+
+@d page_goal==page_so_far[0] {desired height of information on page being built}
+@d page_total==page_so_far[1] {height of the current page}
+@d page_shrink==page_so_far[6] {shrinkability of the current page}
+@d page_depth==page_so_far[7] {depth of the current page}
+
+@<Glob...@>=
+@!page_so_far:array [0..7] of scaled; {height and glue of the current page}
+@!last_glue:pointer; {used to implement \.{\\lastskip}}
+@!last_penalty:integer; {used to implement \.{\\lastpenalty}}
+@!last_kern:scaled; {used to implement \.{\\lastkern}}
+@!insert_penalties:integer; {sum of the penalties for held-over insertions}
+
+@ @<Put each...@>=
+primitive("pagegoal",set_page_dimen,0);
+@!@:page_goal_}{\.{\\pagegoal} primitive@>
+primitive("pagetotal",set_page_dimen,1);
+@!@:page_total_}{\.{\\pagetotal} primitive@>
+primitive("pagestretch",set_page_dimen,2);
+@!@:page_stretch_}{\.{\\pagestretch} primitive@>
+primitive("pagefilstretch",set_page_dimen,3);
+@!@:page_fil_stretch_}{\.{\\pagefilstretch} primitive@>
+primitive("pagefillstretch",set_page_dimen,4);
+@!@:page_fill_stretch_}{\.{\\pagefillstretch} primitive@>
+primitive("pagefilllstretch",set_page_dimen,5);
+@!@:page_filll_stretch_}{\.{\\pagefilllstretch} primitive@>
+primitive("pageshrink",set_page_dimen,6);
+@!@:page_shrink_}{\.{\\pageshrink} primitive@>
+primitive("pagedepth",set_page_dimen,7);
+@!@:page_depth_}{\.{\\pagedepth} primitive@>
+
+@ @<Cases of |print_cmd_chr|...@>=
+set_page_dimen: case chr_code of
+0: print_esc("pagegoal");
+1: print_esc("pagetotal");
+2: print_esc("pagestretch");
+3: print_esc("pagefilstretch");
+4: print_esc("pagefillstretch");
+5: print_esc("pagefilllstretch");
+6: print_esc("pageshrink");
+othercases print_esc("pagedepth")
+endcases;
+
+@ @d print_plus_end(#)==print(#);@+end
+@d print_plus(#)==if page_so_far[#]<>0 then
+ begin print(" plus "); print_scaled(page_so_far[#]); print_plus_end
+
+@p procedure print_totals;
+begin print_scaled(page_total);
+print_plus(2)("");
+print_plus(3)("fil");
+print_plus(4)("fill");
+print_plus(5)("filll");
+if page_shrink<>0 then
+ begin print(" minus "); print_scaled(page_shrink);
+ end;
+end;
+
+@ @<Show the status of the current page@>=
+if page_head<>page_tail then
+ begin print_nl("### current page:");
+ if output_active then print(" (held over for next output)");
+@.held over for next output@>
+ show_box(link(page_head));
+ if page_contents>empty then
+ begin print_nl("total height "); print_totals;
+@:total_height}{\.{total height}@>
+ print_nl(" goal height "); print_scaled(page_goal);
+@.goal height@>
+ r:=link(page_ins_head);
+ while r<>page_ins_head do
+ begin print_ln; print_esc("insert"); t:=qo(subtype(r));
+ print_int(t); print(" adds ");
+ t:=x_over_n(height(r),1000)*count(t); print_scaled(t);
+ if type(r)=split_up then
+ begin q:=page_head; t:=0;
+ repeat q:=link(q);
+ if (type(q)=ins_node)and(subtype(q)=subtype(r)) then incr(t);
+ until q=broken_ins(r);
+ print(", #"); print_int(t); print(" might split");
+ end;
+ r:=link(r);
+ end;
+ end;
+ end
+
+@ Here is a procedure that is called when the |page_contents| is changing
+from |empty| to |inserts_only| or |box_there|.
+
+@d set_page_so_far_zero(#)==page_so_far[#]:=0
+
+@p procedure freeze_page_specs(@!s:small_number);
+begin page_contents:=s;
+page_goal:=vsize; page_max_depth:=max_depth;
+page_depth:=0; do_all_six(set_page_so_far_zero);
+least_page_cost:=awful_bad;
+@!stat if tracing_pages>0 then
+ begin begin_diagnostic;
+ print_nl("%% goal height="); print_scaled(page_goal);
+@.goal height@>
+ print(", max depth="); print_scaled(page_max_depth);
+ end_diagnostic(false);
+ end;@;@+tats@;@/
+end;
+
+@ Pages are built by appending nodes to the current list in \TeX's
+vertical mode, which is at the outermost level of the semantic nest. This
+vlist is split into two parts; the ``current page'' that we have been
+talking so much about already, and the ``contribution list'' that receives
+new nodes as they are created. The current page contains everything that
+the page builder has accounted for in its data structures, as described
+above, while the contribution list contains other things that have been
+generated by other parts of \TeX\ but have not yet been
+seen by the page builder.
+The contribution list starts at |link(contrib_head)|, and it ends at the
+current node in \TeX's vertical mode.
+
+When \TeX\ has appended new material in vertical mode, it calls the procedure
+|build_page|, which tries to catch up by moving nodes from the contribution
+list to the current page. This procedure will succeed in its goal of
+emptying the contribution list, unless a page break is discovered, i.e.,
+unless the current page has grown to the point where the optimum next
+page break has been determined. In the latter case, the nodes after the
+optimum break will go back onto the contribution list, and control will
+effectively pass to the user's output routine.
+
+We make |type(page_head)=glue_node|, so that an initial glue node on
+the current page will not be considered a valid breakpoint.
+
+@<Initialize the special list...@>=
+type(page_head):=glue_node; subtype(page_head):=normal;
+
+@ The global variable |output_active| is true during the time the
+user's output routine is driving \TeX.
+
+@<Glob...@>=
+@!output_active:boolean; {are we in the midst of an output routine?}
+
+@ @<Set init...@>=
+output_active:=false; insert_penalties:=0;
+
+@ The page builder is ready to start a fresh page if we initialize
+the following state variables. (However, the page insertion list is initialized
+elsewhere.)
+
+@<Start a new current page@>=
+page_contents:=empty; page_tail:=page_head; link(page_head):=null;@/
+last_glue:=max_halfword; last_penalty:=0; last_kern:=0;
+page_depth:=0; page_max_depth:=0
+
+@ At certain times box 255 is supposed to be void (i.e., |null|),
+or an insertion box is supposed to be ready to accept a vertical list.
+If not, an error message is printed, and the following subroutine
+flushes the unwanted contents, reporting them to the user.
+
+@p procedure box_error(@!n:eight_bits);
+begin error; begin_diagnostic;
+print_nl("The following box has been deleted:");
+@.The following...deleted@>
+show_box(box(n)); end_diagnostic(true);
+flush_node_list(box(n)); box(n):=null;
+end;
+
+@ The following procedure guarantees that a given box register
+does not contain an \.{\\hbox}.
+
+@p procedure ensure_vbox(@!n:eight_bits);
+var p:pointer; {the box register contents}
+begin p:=box(n);
+if p<>null then if type(p)=hlist_node then
+ begin print_err("Insertions can only be added to a vbox");
+@.Insertions can only...@>
+ help3("Tut tut: You're trying to \insert into a")@/
+ ("\box register that now contains an \hbox.")@/
+ ("Proceed, and I'll discard its present contents.");
+ box_error(n);
+ end;
+end;
+
+@ \TeX\ is not always in vertical mode at the time |build_page|
+is called; the current mode reflects what \TeX\ should return to, after
+the contribution list has been emptied. A call on |build_page| should
+be immediately followed by `|goto big_switch|', which is \TeX's central
+control point.
+
+@d contribute=80 {go here to link a node into the current page}
+
+@p @t\4@>@<Declare the procedure called |fire_up|@>@;@/
+procedure build_page; {append contributions to the current page}
+label exit,done,done1,continue,contribute,update_heights;
+var p:pointer; {the node being appended}
+@!q,@!r:pointer; {nodes being examined}
+@!b,@!c:integer; {badness and cost of current page}
+@!pi:integer; {penalty to be added to the badness}
+@!n:min_quarterword..255; {insertion box number}
+@!delta,@!h,@!w:scaled; {sizes used for insertion calculations}
+begin if (link(contrib_head)=null)or output_active then return;
+repeat continue: p:=link(contrib_head);@/
+@<Update the values of |last_glue|, |last_penalty|, and |last_kern|@>;
+@<Move node |p| to the current page; if it is time for a page break,
+ put the nodes following the break back onto the contribution list,
+ and |return| to the user's output routine if there is one@>;
+until link(contrib_head)=null;
+@<Make the contribution list empty by setting its tail to |contrib_head|@>;
+exit:end;
+
+@ @d contrib_tail==nest[0].tail_field {tail of the contribution list}
+
+@<Make the contribution list empty...@>=
+if nest_ptr=0 then tail:=contrib_head {vertical mode}
+else contrib_tail:=contrib_head {other modes}
+
+@ @<Update the values of |last_glue|...@>=
+if last_glue<>max_halfword then delete_glue_ref(last_glue);
+last_penalty:=0; last_kern:=0;
+if type(p)=glue_node then
+ begin last_glue:=glue_ptr(p); add_glue_ref(last_glue);
+ end
+else begin last_glue:=max_halfword;
+ if type(p)=penalty_node then last_penalty:=penalty(p)
+ else if type(p)=kern_node then last_kern:=width(p);
+ end
+
+@ The code here is an example of a many-way switch into routines that
+merge together in different places. Some people call this unstructured
+programming, but the author doesn't see much wrong with it, as long as
+@^Knuth, Donald Ervin@>
+the various labels have a well-understood meaning.
+
+@<Move node |p| to the current page; ...@>=
+@<If the current page is empty and node |p| is to be deleted, |goto done1|;
+ otherwise use node |p| to update the state of the current page;
+ if this node is an insertion, |goto contribute|; otherwise if this node
+ is not a legal breakpoint, |goto contribute| or |update_heights|;
+ otherwise set |pi| to the penalty associated with this breakpoint@>;
+@<Check if node |p| is a new champion breakpoint; then \(if)if it is time for
+ a page break, prepare for output, and either fire up the user's
+ output routine and |return| or ship out the page and |goto done|@>;
+if (type(p)<glue_node)or(type(p)>kern_node) then goto contribute;
+update_heights:@<Update the current page measurements with respect to the
+ glue or kern specified by node~|p|@>;
+contribute: @<Make sure that |page_max_depth| is not exceeded@>;
+@<Link node |p| into the current page and |goto done|@>;
+done1:@<Recycle node |p|@>;
+done:
+
+@ @<Link node |p| into the current page and |goto done|@>=
+link(page_tail):=p; page_tail:=p;
+link(contrib_head):=link(p); link(p):=null; goto done
+
+@ @<Recycle node |p|@>=
+link(contrib_head):=link(p); link(p):=null; flush_node_list(p)
+
+@ The title of this section is already so long, it seems best to avoid
+making it more accurate but still longer, by mentioning the fact that a
+kern node at the end of the contribution list will not be contributed until
+we know its successor.
+
+@<If the current page is empty...@>=
+case type(p) of
+hlist_node,vlist_node,rule_node: if page_contents<box_there then
+ @<Initialize the current page, insert the \.{\\topskip} glue
+ ahead of |p|, and |goto continue|@>
+ else @<Prepare to move a box or rule node to the current page,
+ then |goto contribute|@>;
+whatsit_node: @<Prepare to move whatsit |p| to the current page,
+ then |goto contribute|@>;
+glue_node: if page_contents<box_there then goto done1
+ else if precedes_break(page_tail) then pi:=0
+ else goto update_heights;
+kern_node: if page_contents<box_there then goto done1
+ else if link(p)=null then return
+ else if type(link(p))=glue_node then pi:=0
+ else goto update_heights;
+penalty_node: if page_contents<box_there then goto done1@+else pi:=penalty(p);
+mark_node: goto contribute;
+ins_node: @<Append an insertion to the current page and |goto contribute|@>;
+othercases confusion("page")
+@:this can't happen page}{\quad page@>
+endcases
+
+@ @<Initialize the current page, insert the \.{\\topskip} glue...@>=
+begin if page_contents=empty then freeze_page_specs(box_there)
+else page_contents:=box_there;
+q:=new_skip_param(top_skip_code); {now |temp_ptr=glue_ptr(q)|}
+if width(temp_ptr)>height(p) then width(temp_ptr):=width(temp_ptr)-height(p)
+else width(temp_ptr):=0;
+link(q):=p; link(contrib_head):=q; goto continue;
+end
+
+@ @<Prepare to move a box or rule node to the current page...@>=
+begin page_total:=page_total+page_depth+height(p);
+page_depth:=depth(p);
+goto contribute;
+end
+
+@ @<Make sure that |page_max_depth| is not exceeded@>=
+if page_depth>page_max_depth then
+ begin page_total:=@|
+ page_total+page_depth-page_max_depth;@/
+ page_depth:=page_max_depth;
+ end;
+
+@ @<Update the current page measurements with respect to the glue...@>=
+if type(p)=kern_node then q:=p
+else begin q:=glue_ptr(p);
+ page_so_far[2+stretch_order(q)]:=@|
+ page_so_far[2+stretch_order(q)]+stretch(q);@/
+ page_shrink:=page_shrink+shrink(q);
+ if (shrink_order(q)<>normal)and(shrink(q)<>0) then
+ begin@t@>@;@/
+ print_err("Infinite glue shrinkage found on current page");@/
+@.Infinite glue shrinkage...@>
+ help4("The page about to be output contains some infinitely")@/
+ ("shrinkable glue, e.g., `\vss' or `\vskip 0pt minus 1fil'.")@/
+ ("Such glue doesn't belong there; but you can safely proceed,")@/
+ ("since the offensive shrinkability has been made finite.");
+ error;
+ r:=new_spec(q); shrink_order(r):=normal; delete_glue_ref(q);
+ glue_ptr(p):=r; q:=r;
+ end;
+ end;
+page_total:=page_total+page_depth+width(q); page_depth:=0
+
+@ @<Check if node |p| is a new champion breakpoint; then \(if)...@>=
+if pi<inf_penalty then
+ begin @<Compute the badness, |b|, of the current page,
+ using |awful_bad| if the box is too full@>;
+ if b<awful_bad then
+ if pi<=eject_penalty then c:=pi
+ else if b<inf_bad then c:=b+pi+insert_penalties
+ else c:=deplorable
+ else c:=b;
+ if insert_penalties>=10000 then c:=awful_bad;
+ @!stat if tracing_pages>0 then @<Display the page break cost@>;@+tats@;@/
+ if c<=least_page_cost then
+ begin best_page_break:=p; best_size:=page_goal;
+ least_page_cost:=c;
+ r:=link(page_ins_head);
+ while r<>page_ins_head do
+ begin best_ins_ptr(r):=last_ins_ptr(r);
+ r:=link(r);
+ end;
+ end;
+ if (c=awful_bad)or(pi<=eject_penalty) then
+ begin fire_up(p); {output the current page at the best place}
+ if output_active then return; {user's output routine will act}
+ goto done; {the page has been shipped out by default output routine}
+ end;
+ end
+
+@ @<Display the page break cost@>=
+begin begin_diagnostic; print_nl("%");
+print(" t="); print_totals;@/
+print(" g="); print_scaled(page_goal);@/
+print(" b=");
+if b=awful_bad then print_char("*")@+else print_int(b);
+@.*\relax@>
+print(" p="); print_int(pi);
+print(" c=");
+if c=awful_bad then print_char("*")@+else print_int(c);
+if c<=least_page_cost then print_char("#");
+end_diagnostic(false);
+end
+
+@ @<Compute the badness, |b|, of the current page...@>=
+if page_total<page_goal then
+ if (page_so_far[3]<>0) or (page_so_far[4]<>0) or@|
+ (page_so_far[5]<>0) then b:=0
+ else b:=badness(page_goal-page_total,page_so_far[2])
+else if page_total-page_goal>page_shrink then b:=awful_bad
+else b:=badness(page_total-page_goal,page_shrink)
+
+@ @<Append an insertion to the current page and |goto contribute|@>=
+begin if page_contents=empty then freeze_page_specs(inserts_only);
+n:=subtype(p); r:=page_ins_head;
+while n>=subtype(link(r)) do r:=link(r);
+n:=qo(n);
+if subtype(r)<>qi(n) then
+ @<Create a page insertion node with |subtype(r)=qi(n)|, and
+ include the glue correction for box |n| in the
+ current page state@>;
+if type(r)=split_up then insert_penalties:=insert_penalties+float_cost(p)
+else begin last_ins_ptr(r):=p;
+ delta:=page_goal-page_total-page_depth+page_shrink;
+ {this much room is left if we shrink the maximum}
+ if count(n)=1000 then h:=height(p)
+ else h:=x_over_n(height(p),1000)*count(n); {this much room is needed}
+ if ((h<=0)or(h<=delta))and(height(p)+height(r)<=dimen(n)) then
+ begin page_goal:=page_goal-h; height(r):=height(r)+height(p);
+ end
+ else @<Find the best way to split the insertion, and change
+ |type(r)| to |split_up|@>;
+ end;
+goto contribute;
+end
+
+@ We take note of the value of \.{\\skip} |n| and the height plus depth
+of \.{\\box}~|n| only when the first \.{\\insert}~|n| node is
+encountered for a new page. A user who changes the contents of \.{\\box}~|n|
+after that first \.{\\insert}~|n| had better be either extremely careful
+or extremely lucky, or both.
+
+@<Create a page insertion node...@>=
+begin q:=get_node(page_ins_node_size); link(q):=link(r); link(r):=q; r:=q;
+subtype(r):=qi(n); type(r):=inserting; ensure_vbox(n);
+if box(n)=null then height(r):=0
+else height(r):=height(box(n))+depth(box(n));
+best_ins_ptr(r):=null;@/
+q:=skip(n);
+if count(n)=1000 then h:=height(r)
+else h:=x_over_n(height(r),1000)*count(n);
+page_goal:=page_goal-h-width(q);@/
+page_so_far[2+stretch_order(q)]:=@|page_so_far[2+stretch_order(q)]+stretch(q);@/
+page_shrink:=page_shrink+shrink(q);
+if (shrink_order(q)<>normal)and(shrink(q)<>0) then
+ begin print_err("Infinite glue shrinkage inserted from "); print_esc("skip");
+@.Infinite glue shrinkage...@>
+ print_int(n);
+ help3("The correction glue for page breaking with insertions")@/
+ ("must have finite shrinkability. But you may proceed,")@/
+ ("since the offensive shrinkability has been made finite.");
+ error;
+ end;
+end
+
+@ Here is the code that will split a long footnote between pages, in an
+emergency. The current situation deserves to be recapitulated: Node |p|
+is an insertion into box |n|; the insertion will not fit, in its entirety,
+either because it would make the total contents of box |n| greater than
+\.{\\dimen} |n|, or because it would make the incremental amount of growth
+|h| greater than the available space |delta|, or both. (This amount |h| has
+been weighted by the insertion scaling factor, i.e., by \.{\\count} |n|
+over 1000.) Now we will choose the best way to break the vlist of the
+insertion, using the same criteria as in the \.{\\vsplit} operation.
+
+@<Find the best way to split the insertion...@>=
+begin if count(n)<=0 then w:=max_dimen
+else begin w:=page_goal-page_total-page_depth;
+ if count(n)<>1000 then w:=x_over_n(w,count(n))*1000;
+ end;
+if w>dimen(n)-height(r) then w:=dimen(n)-height(r);
+q:=vert_break(ins_ptr(p),w,depth(p));
+height(r):=height(r)+best_height_plus_depth;
+@!stat if tracing_pages>0 then @<Display the insertion split cost@>;@+tats@;@/
+if count(n)<>1000 then
+ best_height_plus_depth:=x_over_n(best_height_plus_depth,1000)*count(n);
+page_goal:=page_goal-best_height_plus_depth;
+type(r):=split_up; broken_ptr(r):=q; broken_ins(r):=p;
+if q=null then insert_penalties:=insert_penalties+eject_penalty
+else if type(q)=penalty_node then insert_penalties:=insert_penalties+penalty(q);
+end
+
+@ @<Display the insertion split cost@>=
+begin begin_diagnostic; print_nl("% split"); print_int(n);
+@.split@>
+print(" to "); print_scaled(w);
+print_char(","); print_scaled(best_height_plus_depth);@/
+print(" p=");
+if q=null then print_int(eject_penalty)
+else if type(q)=penalty_node then print_int(penalty(q))
+else print_char("0");
+end_diagnostic(false);
+end
+
+@ When the page builder has looked at as much material as could appear before
+the next page break, it makes its decision. The break that gave minimum
+badness will be used to put a completed ``page'' into box 255, with insertions
+appended to their other boxes.
+
+We also set the values of |top_mark|, |first_mark|, and |bot_mark|. The
+program uses the fact that |bot_mark<>null| implies |first_mark<>null|;
+it also knows that |bot_mark=null| implies |top_mark=first_mark=null|.
+
+The |fire_up| subroutine prepares to output the current page at the best
+place; then it fires up the user's output routine, if there is one,
+or it simply ships out the page. There is one parameter, |c|, which represents
+the node that was being contributed to the page when the decision to
+force an output was made.
+
+@<Declare the procedure called |fire_up|@>=
+procedure fire_up(@!c:pointer);
+label exit;
+var p,@!q,@!r,@!s:pointer; {nodes being examined and/or changed}
+@!prev_p:pointer; {predecessor of |p|}
+@!n:min_quarterword..255; {insertion box number}
+@!wait:boolean; {should the present insertion be held over?}
+@!save_vbadness:integer; {saved value of |vbadness|}
+@!save_vfuzz: scaled; {saved value of |vfuzz|}
+@!save_split_top_skip: pointer; {saved value of |split_top_skip|}
+begin @<Set the value of |output_penalty|@>;
+if bot_mark<>null then
+ begin if top_mark<>null then delete_token_ref(top_mark);
+ top_mark:=bot_mark; add_token_ref(top_mark);
+ delete_token_ref(first_mark); first_mark:=null;
+ end;
+@<Put the \(o)optimal current page into box 255, update |first_mark| and
+ |bot_mark|, append insertions to their boxes, and put the
+ remaining nodes back on the contribution list@>;
+if (top_mark<>null)and(first_mark=null) then
+ begin first_mark:=top_mark; add_token_ref(top_mark);
+ end;
+if output_routine<>null then
+ if dead_cycles>=max_dead_cycles then
+ @<Explain that too many dead cycles have occurred in a row@>
+ else @<Fire up the user's output routine and |return|@>;
+@<Perform the default output routine@>;
+exit:end;
+
+@ @<Set the value of |output_penalty|@>=
+if type(best_page_break)=penalty_node then
+ begin geq_word_define(int_base+output_penalty_code,penalty(best_page_break));
+ penalty(best_page_break):=inf_penalty;
+ end
+else geq_word_define(int_base+output_penalty_code,inf_penalty)
+
+@ As the page is finally being prepared for output,
+pointer |p| runs through the vlist, with |prev_p| trailing behind;
+pointer |q| is the tail of a list of insertions that
+are being held over for a subsequent page.
+
+@<Put the \(o)optimal current page into box 255...@>=
+if c=best_page_break then best_page_break:=null; {|c| not yet linked in}
+@<Ensure that box 255 is empty before output@>;
+insert_penalties:=0; {this will count the number of insertions held over}
+save_split_top_skip:=split_top_skip;
+if holding_inserts<=0 then
+ @<Prepare all the boxes involved in insertions to act as queues@>;
+q:=hold_head; link(q):=null; prev_p:=page_head; p:=link(prev_p);
+while p<>best_page_break do
+ begin if type(p)=ins_node then
+ begin if holding_inserts<=0 then
+ @<Either insert the material specified by node |p| into the
+ appropriate box, or hold it for the next page;
+ also delete node |p| from the current page@>;
+ end
+ else if type(p)=mark_node then @<Update the values of
+ |first_mark| and |bot_mark|@>;
+ prev_p:=p; p:=link(prev_p);
+ end;
+split_top_skip:=save_split_top_skip;
+@<Break the current page at node |p|, put it in box~255,
+ and put the remaining nodes on the contribution list@>;
+@<Delete \(t)the page-insertion nodes@>
+
+@ @<Ensure that box 255 is empty before output@>=
+if box(255)<>null then
+ begin print_err(""); print_esc("box"); print("255 is not void");
+@:box255}{\.{\\box255 is not void}@>
+ help2("You shouldn't use \box255 except in \output routines.")@/
+ ("Proceed, and I'll discard its present contents.");
+ box_error(255);
+ end
+
+@ @<Update the values of |first_mark| and |bot_mark|@>=
+begin if first_mark=null then
+ begin first_mark:=mark_ptr(p);
+ add_token_ref(first_mark);
+ end;
+if bot_mark<>null then delete_token_ref(bot_mark);
+bot_mark:=mark_ptr(p); add_token_ref(bot_mark);
+end
+
+@ When the following code is executed, the current page runs from node
+|link(page_head)| to node |prev_p|, and the nodes from |p| to |page_tail|
+are to be placed back at the front of the contribution list. Furthermore
+the heldover insertions appear in a list from |link(hold_head)| to |q|; we
+will put them into the current page list for safekeeping while the user's
+output routine is active. We might have |q=hold_head|; and |p=null| if
+and only if |prev_p=page_tail|. Error messages are suppressed within
+|vpackage|, since the box might appear to be overfull or underfull simply
+because the stretch and shrink from the \.{\\skip} registers for inserts
+are not actually present in the box.
+
+@<Break the current page at node |p|, put it...@>=
+if p<>null then
+ begin if link(contrib_head)=null then
+ if nest_ptr=0 then tail:=page_tail
+ else contrib_tail:=page_tail;
+ link(page_tail):=link(contrib_head);
+ link(contrib_head):=p;
+ link(prev_p):=null;
+ end;
+save_vbadness:=vbadness; vbadness:=inf_bad;
+save_vfuzz:=vfuzz; vfuzz:=max_dimen; {inhibit error messages}
+box(255):=vpackage(link(page_head),best_size,exactly,page_max_depth);
+vbadness:=save_vbadness; vfuzz:=save_vfuzz;
+if last_glue<>max_halfword then delete_glue_ref(last_glue);
+@<Start a new current page@>; {this sets |last_glue:=max_halfword|}
+if q<>hold_head then
+ begin link(page_head):=link(hold_head); page_tail:=q;
+ end
+
+@ If many insertions are supposed to go into the same box, we want to know
+the position of the last node in that box, so that we don't need to waste time
+when linking further information into it. The |last_ins_ptr| fields of the
+page insertion nodes are therefore used for this purpose during the
+packaging phase.
+
+@<Prepare all the boxes involved in insertions to act as queues@>=
+begin r:=link(page_ins_head);
+while r<>page_ins_head do
+ begin if best_ins_ptr(r)<>null then
+ begin n:=qo(subtype(r)); ensure_vbox(n);
+ if box(n)=null then box(n):=new_null_box;
+ p:=box(n)+list_offset;
+ while link(p)<>null do p:=link(p);
+ last_ins_ptr(r):=p;
+ end;
+ r:=link(r);
+ end;
+end
+
+@ @<Delete \(t)the page-insertion nodes@>=
+r:=link(page_ins_head);
+while r<>page_ins_head do
+ begin q:=link(r); free_node(r,page_ins_node_size); r:=q;
+ end;
+link(page_ins_head):=page_ins_head
+
+@ We will set |best_ins_ptr:=null| and package the box corresponding to
+insertion node~|r|, just after making the final insertion into that box.
+If this final insertion is `|split_up|', the remainder after splitting
+and pruning (if any) will be carried over to the next page.
+
+@<Either insert the material specified by node |p| into...@>=
+begin r:=link(page_ins_head);
+while subtype(r)<>subtype(p) do r:=link(r);
+if best_ins_ptr(r)=null then wait:=true
+else begin wait:=false; s:=last_ins_ptr(r); link(s):=ins_ptr(p);
+ if best_ins_ptr(r)=p then
+ @<Wrap up the box specified by node |r|, splitting node |p| if
+ called for; set |wait:=true| if node |p| holds a remainder after
+ splitting@>
+ else begin while link(s)<>null do s:=link(s);
+ last_ins_ptr(r):=s;
+ end;
+ end;
+@<Either append the insertion node |p| after node |q|, and remove it
+ from the current page, or delete |node(p)|@>;
+end
+
+@ @<Wrap up the box specified by node |r|, splitting node |p| if...@>=
+begin if type(r)=split_up then
+ if (broken_ins(r)=p)and(broken_ptr(r)<>null) then
+ begin while link(s)<>broken_ptr(r) do s:=link(s);
+ link(s):=null;
+ split_top_skip:=split_top_ptr(p);
+ ins_ptr(p):=prune_page_top(broken_ptr(r));
+ if ins_ptr(p)<>null then
+ begin temp_ptr:=vpack(ins_ptr(p),natural);
+ height(p):=height(temp_ptr)+depth(temp_ptr);
+ free_node(temp_ptr,box_node_size); wait:=true;
+ end;
+ end;
+best_ins_ptr(r):=null;
+n:=qo(subtype(r));
+temp_ptr:=list_ptr(box(n));
+free_node(box(n),box_node_size);
+box(n):=vpack(temp_ptr,natural);
+end
+
+@ @<Either append the insertion node |p|...@>=
+link(prev_p):=link(p); link(p):=null;
+if wait then
+ begin link(q):=p; q:=p; incr(insert_penalties);
+ end
+else begin delete_glue_ref(split_top_ptr(p));
+ free_node(p,ins_node_size);
+ end;
+p:=prev_p
+
+@ The list of heldover insertions, running from |link(page_head)| to
+|page_tail|, must be moved to the contribution list when the user has
+specified no output routine.
+
+@<Perform the default output routine@>=
+begin if link(page_head)<>null then
+ begin if link(contrib_head)=null then
+ if nest_ptr=0 then tail:=page_tail@+else contrib_tail:=page_tail
+ else link(page_tail):=link(contrib_head);
+ link(contrib_head):=link(page_head);
+ link(page_head):=null; page_tail:=page_head;
+ end;
+ship_out(box(255)); box(255):=null;
+end
+
+@ @<Explain that too many dead cycles have occurred in a row@>=
+begin print_err("Output loop---"); print_int(dead_cycles);
+@.Output loop...@>
+print(" consecutive dead cycles");
+help3("I've concluded that your \output is awry; it never does a")@/
+("\shipout, so I'm shipping \box255 out myself. Next time")@/
+("increase \maxdeadcycles if you want me to be more patient!"); error;
+end
+
+@ @<Fire up the user's output routine and |return|@>=
+begin output_active:=true;
+incr(dead_cycles);
+push_nest; mode:=-vmode; prev_depth:=ignore_depth; mode_line:=-line;
+begin_token_list(output_routine,output_text);
+new_save_level(output_group); normal_paragraph;
+scan_left_brace;
+return;
+end
+
+@ When the user's output routine finishes, it has constructed a vlist
+in internal vertical mode, and \TeX\ will do the following:
+
+@<Resume the page builder after an output routine has come to an end@>=
+begin if (loc<>null) or
+ ((token_type<>output_text)and(token_type<>backed_up)) then
+ @<Recover from an unbalanced output routine@>;
+end_token_list; {conserve stack space in case more outputs are triggered}
+end_graf; unsave; output_active:=false; insert_penalties:=0;@/
+@<Ensure that box 255 is empty after output@>;
+if tail<>head then {current list goes after heldover insertions}
+ begin link(page_tail):=link(head);
+ page_tail:=tail;
+ end;
+if link(page_head)<>null then {and both go before heldover contributions}
+ begin if link(contrib_head)=null then contrib_tail:=page_tail;
+ link(page_tail):=link(contrib_head);
+ link(contrib_head):=link(page_head);
+ link(page_head):=null; page_tail:=page_head;
+ end;
+pop_nest; build_page;
+end
+
+@ @<Recover from an unbalanced output routine@>=
+begin print_err("Unbalanced output routine");
+@.Unbalanced output routine@>
+help2("Your sneaky output routine has problematic {'s and/or }'s.")@/
+("I can't handle that very well; good luck."); error;
+repeat get_token;
+until loc=null;
+end {loops forever if reading from a file, since |null=min_halfword<=0|}
+
+@ @<Ensure that box 255 is empty after output@>=
+if box(255)<>null then
+ begin print_err("Output routine didn't use all of ");
+ print_esc("box"); print_int(255);
+@.Output routine didn't use...@>
+ help3("Your \output commands should empty \box255,")@/
+ ("e.g., by saying `\shipout\box255'.")@/
+ ("Proceed; I'll discard its present contents.");
+ box_error(255);
+ end
+
+@* \[46] The chief executive.
+We come now to the |main_control| routine, which contains the master
+switch that causes all the various pieces of \TeX\ to do their things,
+in the right order.
+
+In a sense, this is the grand climax of the program: It applies all the
+tools that we have worked so hard to construct. In another sense, this is
+the messiest part of the program: It necessarily refers to other pieces
+of code all over the place, so that a person can't fully understand what is
+going on without paging back and forth to be reminded of conventions that
+are defined elsewhere. We are now at the hub of the web, the central nervous
+system that touches most of the other parts and ties them together.
+@^brain@>
+
+The structure of |main_control| itself is quite simple. There's a label
+called |big_switch|, at which point the next token of input is fetched
+using |get_x_token|. Then the program branches at high speed into one of
+about 100 possible directions, based on the value of the current
+mode and the newly fetched command code; the sum |abs(mode)+cur_cmd|
+indicates what to do next. For example, the case `|vmode+letter|' arises
+when a letter occurs in vertical mode (or internal vertical mode); this
+case leads to instructions that initialize a new paragraph and enter
+horizontal mode.
+
+The big |case| statement that contains this multiway switch has been labeled
+|reswitch|, so that the program can |goto reswitch| when the next token
+has already been fetched. Most of the cases are quite short; they call
+an ``action procedure'' that does the work for that case, and then they
+either |goto reswitch| or they ``fall through'' to the end of the |case|
+statement, which returns control back to |big_switch|. Thus, |main_control|
+is not an extremely large procedure, in spite of the multiplicity of things
+it must do; it is small enough to be handled by \PASCAL\ compilers that put
+severe restrictions on procedure size.
+@!@^action procedure@>
+
+One case is singled out for special treatment, because it accounts for most
+of \TeX's activities in typical applications. The process of reading simple
+text and converting it into |char_node| records, while looking for ligatures
+and kerns, is part of \TeX's ``inner loop''; the whole program runs
+efficiently when its inner loop is fast, so this part has been written
+with particular care.
+
+@ We shall concentrate first on the inner loop of |main_control|, deferring
+consideration of the other cases until later.
+@^inner loop@>
+
+@d big_switch=60 {go here to branch on the next token of input}
+@d main_loop=70 {go here to typeset a string of consecutive characters}
+@d main_loop_wrapup=80 {go here to finish a character or ligature}
+@d main_loop_move=90 {go here to advance the ligature cursor}
+@d main_loop_move_lig=95 {same, when advancing past a generated ligature}
+@d main_loop_lookahead=100 {go here to bring in another character, if any}
+@d main_lig_loop=110 {go here to check for ligatures or kerning}
+@d append_normal_space=120 {go here to append a normal space between words}
+
+@p @t\4@>@<Declare action procedures for use by |main_control|@>@;
+@t\4@>@<Declare the procedure called |handle_right_brace|@>@;
+procedure main_control; {governs \TeX's activities}
+label big_switch,reswitch,main_loop,main_loop_wrapup,
+ main_loop_move,main_loop_move+1,main_loop_move+2,main_loop_move_lig,
+ main_loop_lookahead,main_loop_lookahead+1,
+ main_lig_loop,main_lig_loop+1,main_lig_loop+2,
+ append_normal_space,exit;
+var@!t:integer; {general-purpose temporary variable}
+begin if every_job<>null then begin_token_list(every_job,every_job_text);
+big_switch: get_x_token;@/
+reswitch: @<Give diagnostic information, if requested@>;
+case abs(mode)+cur_cmd of
+hmode+letter,hmode+other_char,hmode+char_given: goto main_loop;
+hmode+char_num: begin scan_char_num; cur_chr:=cur_val; goto main_loop;@+end;
+hmode+no_boundary: begin get_x_token;
+ if (cur_cmd=letter)or(cur_cmd=other_char)or(cur_cmd=char_given)or
+ (cur_cmd=char_num) then cancel_boundary:=true;
+ goto reswitch;
+ end;
+hmode+spacer: if space_factor=1000 then goto append_normal_space
+ else app_space;
+hmode+ex_space,mmode+ex_space: goto append_normal_space;
+@t\4@>@<Cases of |main_control| that are not part of the inner loop@>@;
+end; {of the big |case| statement}
+goto big_switch;
+main_loop:@<Append character |cur_chr| and the following characters (if~any)
+ to the current hlist in the current font; |goto reswitch| when
+ a non-character has been fetched@>;
+append_normal_space:@<Append a normal inter-word space to the current list,
+ then |goto big_switch|@>;
+exit:end;
+
+@ When a new token has just been fetched at |big_switch|, we have an
+ideal place to monitor \TeX's activity.
+@^debugging@>
+
+@<Give diagnostic information, if requested@>=
+if interrupt<>0 then if OK_to_interrupt then
+ begin back_input; check_interrupt; goto big_switch;
+ end;
+@!debug if panicking then check_mem(false);@+@;@+gubed
+if tracing_commands>0 then show_cur_cmd_chr
+
+@ The following part of the program was first written in a structured
+manner, according to the philosophy that ``premature optimization is
+the root of all evil.'' Then it was rearranged into pieces of
+spaghetti so that the most common actions could proceed with little or
+no redundancy.
+
+The original unoptimized form of this algorithm resembles the
+|reconstitute| procedure, which was described earlier in connection with
+hyphenation. Again we have an implied ``cursor'' between characters
+|cur_l| and |cur_r|. The main difference is that the |lig_stack| can now
+contain a charnode as well as pseudo-ligatures; that stack is now
+usually nonempty, because the next character of input (if any) has been
+appended to it. In |main_control| we have
+$$|cur_r|=\cases{|character(lig_stack)|,&if |lig_stack>null|;\cr
+ |font_bchar[cur_font]|,&otherwise;\cr}$$
+except when |character(lig_stack)=font_false_bchar[cur_font]|.
+Several additional global variables are needed.
+
+@<Glob...@>=
+@!main_f:internal_font_number; {the current font}
+@!main_i:four_quarters; {character information bytes for |cur_l|}
+@!main_j:four_quarters; {ligature/kern command}
+@!main_k:font_index; {index into |font_info|}
+@!main_p:pointer; {temporary register for list manipulation}
+@!main_s:integer; {space factor value}
+@!bchar:halfword; {right boundary character of current font, or |non_char|}
+@!false_bchar:halfword; {nonexistent character matching |bchar|, or |non_char|}
+@!cancel_boundary:boolean; {should the left boundary be ignored?}
+@!ins_disc:boolean; {should we insert a discretionary node?}
+
+@ The boolean variables of the main loop are normally false, and always reset
+to false before the loop is left. That saves us the extra work of initializing
+each time.
+
+@<Set init...@>=
+ligature_present:=false; cancel_boundary:=false; lft_hit:=false; rt_hit:=false;
+ins_disc:=false;
+
+@ We leave the |space_factor| unchanged if |sf_code(cur_chr)=0|; otherwise we
+set it equal to |sf_code(cur_chr)|, except that it should never change
+from a value less than 1000 to a value exceeding 1000. The most common
+case is |sf_code(cur_chr)=1000|, so we want that case to be fast.
+
+The overall structure of the main loop is presented here. Some program labels
+are inside the individual sections.
+
+@d adjust_space_factor==@t@>@;@/
+ main_s:=sf_code(cur_chr);
+ if main_s=1000 then space_factor:=1000
+ else if main_s<1000 then
+ begin if main_s>0 then space_factor:=main_s;
+ end
+ else if space_factor<1000 then space_factor:=1000
+ else space_factor:=main_s
+
+@<Append character |cur_chr|...@>=
+adjust_space_factor;@/
+main_f:=cur_font;
+bchar:=font_bchar[main_f]; false_bchar:=font_false_bchar[main_f];
+if mode>0 then if language<>clang then fix_language;
+fast_get_avail(lig_stack); font(lig_stack):=main_f; cur_l:=qi(cur_chr);
+character(lig_stack):=cur_l;@/
+cur_q:=tail;
+if cancel_boundary then
+ begin cancel_boundary:=false; main_k:=non_address;
+ end
+else main_k:=bchar_label[main_f];
+if main_k=non_address then goto main_loop_move+2; {no left boundary processing}
+cur_r:=cur_l; cur_l:=non_char;
+goto main_lig_loop+1; {begin with cursor after left boundary}
+@#
+main_loop_wrapup:@<Make a ligature node, if |ligature_present|;
+ insert a null discretionary, if appropriate@>;
+main_loop_move:@<If the cursor is immediately followed by the right boundary,
+ |goto reswitch|; if it's followed by an invalid character, |goto big_switch|;
+ otherwise move the cursor one step to the right and |goto main_lig_loop|@>;
+main_loop_lookahead:@<Look ahead for another character, or leave |lig_stack|
+ empty if there's none there@>;
+main_lig_loop:@<If there's a ligature/kern command relevant to |cur_l| and
+ |cur_r|, adjust the text appropriately; exit to |main_loop_wrapup|@>;
+main_loop_move_lig:@<Move the cursor past a pseudo-ligature, then
+ |goto main_loop_lookahead| or |main_lig_loop|@>
+
+@ If the current horizontal list is empty, the reference to |character(tail)|
+here is not strictly legal, since |tail| will be a node freshly returned by
+|get_avail|. But this should cause no problem on most implementations, and we
+do want the inner loop to be fast.
+@^dirty \PASCAL@>
+
+A discretionary break is not inserted for an explicit hyphen when we are in
+restricted horizontal mode. In particular, this avoids putting discretionary
+nodes inside of other discretionaries.
+
+@d pack_lig(#)== {the parameter is either |rt_hit| or |false|}
+ begin main_p:=new_ligature(main_f,cur_l,link(cur_q));
+ if lft_hit then
+ begin subtype(main_p):=2; lft_hit:=false;
+ end;
+ if # then if lig_stack=null then
+ begin incr(subtype(main_p)); rt_hit:=false;
+ end;
+ link(cur_q):=main_p; tail:=main_p; ligature_present:=false;
+ end
+
+@d wrapup(#)==if cur_l<non_char then
+ begin if character(tail)=qi(hyphen_char[main_f]) then if link(cur_q)>null then
+ ins_disc:=true;
+ if ligature_present then pack_lig(#);
+ if ins_disc then
+ begin ins_disc:=false;
+ if mode>0 then tail_append(new_disc);
+ end;
+ end
+
+@<Make a ligature node, if |ligature_present|;...@>=
+wrapup(rt_hit)
+
+@ @<If the cursor is immediately followed by the right boundary...@>=
+if lig_stack=null then goto reswitch;
+cur_q:=tail; cur_l:=character(lig_stack);
+main_loop_move+1:if not is_char_node(lig_stack) then goto main_loop_move_lig;
+main_loop_move+2:if(cur_chr<font_bc[main_f])or(cur_chr>font_ec[main_f]) then
+ begin char_warning(main_f,cur_chr); free_avail(lig_stack); goto big_switch;
+ end;
+main_i:=char_info(main_f)(cur_l);
+if not char_exists(main_i) then
+ begin char_warning(main_f,cur_chr); free_avail(lig_stack); goto big_switch;
+ end;
+tail_append(lig_stack) {|main_loop_lookahead| is next}
+
+@ Here we are at |main_loop_move_lig|.
+When we begin this code we have |cur_q=tail| and |cur_l=character(lig_stack)|.
+
+@<Move the cursor past a pseudo-ligature...@>=
+main_p:=lig_ptr(lig_stack);
+if main_p>null then tail_append(main_p);
+temp_ptr:=lig_stack; lig_stack:=link(temp_ptr);
+free_node(temp_ptr,small_node_size);
+main_i:=char_info(main_f)(cur_l); ligature_present:=true;
+if lig_stack=null then
+ if main_p>null then goto main_loop_lookahead
+ else cur_r:=bchar
+else cur_r:=character(lig_stack);
+goto main_lig_loop
+
+@ The result of \.{\\char} can participate in a ligature or kern, so we must
+look ahead for it.
+
+@<Look ahead for another character...@>=
+get_next; {set only |cur_cmd| and |cur_chr|, for speed}
+if cur_cmd=letter then goto main_loop_lookahead+1;
+if cur_cmd=other_char then goto main_loop_lookahead+1;
+if cur_cmd=char_given then goto main_loop_lookahead+1;
+x_token; {now expand and set |cur_cmd|, |cur_chr|, |cur_tok|}
+if cur_cmd=letter then goto main_loop_lookahead+1;
+if cur_cmd=other_char then goto main_loop_lookahead+1;
+if cur_cmd=char_given then goto main_loop_lookahead+1;
+if cur_cmd=char_num then
+ begin scan_char_num; cur_chr:=cur_val; goto main_loop_lookahead+1;
+ end;
+if cur_cmd=no_boundary then bchar:=non_char;
+cur_r:=bchar; lig_stack:=null; goto main_lig_loop;
+main_loop_lookahead+1: adjust_space_factor;
+fast_get_avail(lig_stack); font(lig_stack):=main_f;
+cur_r:=qi(cur_chr); character(lig_stack):=cur_r;
+if cur_r=false_bchar then cur_r:=non_char {this prevents spurious ligatures}
+
+@ Even though comparatively few characters have a lig/kern program, several
+of the instructions here count as part of \TeX's inner loop, since a
+@^inner loop@>
+potentially long sequential search must be performed. For example, tests with
+Computer Modern Roman showed that about 40 per cent of all characters
+actually encountered in practice had a lig/kern program, and that about four
+lig/kern commands were investigated for every such character.
+
+At the beginning of this code we have |main_i=char_info(main_f)(cur_l)|.
+
+@<If there's a ligature/kern command...@>=
+if char_tag(main_i)<>lig_tag then goto main_loop_wrapup;
+main_k:=lig_kern_start(main_f)(main_i); main_j:=font_info[main_k].qqqq;
+if skip_byte(main_j)<=stop_flag then goto main_lig_loop+2;
+main_k:=lig_kern_restart(main_f)(main_j);
+main_lig_loop+1:main_j:=font_info[main_k].qqqq;
+main_lig_loop+2:if next_char(main_j)=cur_r then
+ if skip_byte(main_j)<=stop_flag then
+ @<Do ligature or kern command, returning to |main_lig_loop|
+ or |main_loop_wrapup| or |main_loop_move|@>;
+if skip_byte(main_j)=qi(0) then incr(main_k)
+else begin if skip_byte(main_j)>=stop_flag then goto main_loop_wrapup;
+ main_k:=main_k+qo(skip_byte(main_j))+1;
+ end;
+goto main_lig_loop+1
+
+@ When a ligature or kern instruction matches a character, we know from
+|read_font_info| that the character exists in the font, even though we
+haven't verified its existence in the normal way.
+
+This section could be made into a subroutine, if the code inside
+|main_control| needs to be shortened.
+
+\chardef\?='174 % vertical line to indicate character retention
+
+@<Do ligature or kern command...@>=
+begin if op_byte(main_j)>=kern_flag then
+ begin wrapup(rt_hit);
+ tail_append(new_kern(char_kern(main_f)(main_j))); goto main_loop_move;
+ end;
+if cur_l=non_char then lft_hit:=true
+else if lig_stack=null then rt_hit:=true;
+check_interrupt; {allow a way out in case there's an infinite ligature loop}
+case op_byte(main_j) of
+qi(1),qi(5):begin cur_l:=rem_byte(main_j); {\.{=:\?}, \.{=:\?>}}
+ main_i:=char_info(main_f)(cur_l); ligature_present:=true;
+ end;
+qi(2),qi(6):begin cur_r:=rem_byte(main_j); {\.{\?=:}, \.{\?=:>}}
+ if lig_stack=null then {right boundary character is being consumed}
+ begin lig_stack:=new_lig_item(cur_r); bchar:=non_char;
+ end
+ else if is_char_node(lig_stack) then {|link(lig_stack)=null|}
+ begin main_p:=lig_stack; lig_stack:=new_lig_item(cur_r);
+ lig_ptr(lig_stack):=main_p;
+ end
+ else character(lig_stack):=cur_r;
+ end;
+qi(3):begin cur_r:=rem_byte(main_j); {\.{\?=:\?}}
+ main_p:=lig_stack; lig_stack:=new_lig_item(cur_r);
+ link(lig_stack):=main_p;
+ end;
+qi(7),qi(11):begin wrapup(false); {\.{\?=:\?>}, \.{\?=:\?>>}}
+ cur_q:=tail; cur_l:=rem_byte(main_j);
+ main_i:=char_info(main_f)(cur_l); ligature_present:=true;
+ end;
+othercases begin cur_l:=rem_byte(main_j); ligature_present:=true; {\.{=:}}
+ if lig_stack=null then goto main_loop_wrapup
+ else goto main_loop_move+1;
+ end
+endcases;
+if op_byte(main_j)>qi(4) then
+ if op_byte(main_j)<>qi(7) then goto main_loop_wrapup;
+if cur_l<non_char then goto main_lig_loop;
+main_k:=bchar_label[main_f]; goto main_lig_loop+1;
+end
+
+@ The occurrence of blank spaces is almost part of \TeX's inner loop,
+@^inner loop@>
+since we usually encounter about one space for every five non-blank characters.
+Therefore |main_control| gives second-highest priority to ordinary spaces.
+
+When a glue parameter like \.{\\spaceskip} is set to `\.{0pt}', we will
+see to it later that the corresponding glue specification is precisely
+|zero_glue|, not merely a pointer to some specification that happens
+to be full of zeroes. Therefore it is simple to test whether a glue parameter
+is zero or~not.
+
+@<Append a normal inter-word space...@>=
+if space_skip=zero_glue then
+ begin @<Find the glue specification, |main_p|, for
+ text spaces in the current font@>;
+ temp_ptr:=new_glue(main_p);
+ end
+else temp_ptr:=new_param_glue(space_skip_code);
+link(tail):=temp_ptr; tail:=temp_ptr;
+goto big_switch
+
+@ Having |font_glue| allocated for each text font saves both time and memory.
+If any of the three spacing parameters are subsequently changed by the
+use of \.{\\fontdimen}, the |find_font_dimen| procedure deallocates the
+|font_glue| specification allocated here.
+
+@<Find the glue specification...@>=
+begin main_p:=font_glue[cur_font];
+if main_p=null then
+ begin main_p:=new_spec(zero_glue); main_k:=param_base[cur_font]+space_code;
+ width(main_p):=font_info[main_k].sc; {that's |space(cur_font)|}
+ stretch(main_p):=font_info[main_k+1].sc; {and |space_stretch(cur_font)|}
+ shrink(main_p):=font_info[main_k+2].sc; {and |space_shrink(cur_font)|}
+ font_glue[cur_font]:=main_p;
+ end;
+end
+
+@ @<Declare act...@>=
+procedure app_space; {handle spaces when |space_factor<>1000|}
+var@!q:pointer; {glue node}
+begin if (space_factor>=2000)and(xspace_skip<>zero_glue) then
+ q:=new_param_glue(xspace_skip_code)
+else begin if space_skip<>zero_glue then main_p:=space_skip
+ else @<Find the glue specification...@>;
+ main_p:=new_spec(main_p);
+ @<Modify the glue specification in |main_p| according to the space factor@>;
+ q:=new_glue(main_p); glue_ref_count(main_p):=null;
+ end;
+link(tail):=q; tail:=q;
+end;
+
+@ @<Modify the glue specification in |main_p| according to the space factor@>=
+if space_factor>=2000 then width(main_p):=width(main_p)+extra_space(cur_font);
+stretch(main_p):=xn_over_d(stretch(main_p),space_factor,1000);
+shrink(main_p):=xn_over_d(shrink(main_p),1000,space_factor)
+
+@ Whew---that covers the main loop. We can now proceed at a leisurely
+pace through the other combinations of possibilities.
+
+@d any_mode(#)==vmode+#,hmode+#,mmode+# {for mode-independent commands}
+
+@<Cases of |main_control| that are not part of the inner loop@>=
+any_mode(relax),vmode+spacer,mmode+spacer,mmode+no_boundary:do_nothing;
+any_mode(ignore_spaces): begin @<Get the next non-blank non-call...@>;
+ goto reswitch;
+ end;
+vmode+stop: if its_all_over then return; {this is the only way out}
+@t\4@>@<Forbidden cases detected in |main_control|@>@+@,any_mode(mac_param):
+ report_illegal_case;
+@<Math-only cases in non-math modes, or vice versa@>: insert_dollar_sign;
+@t\4@>@<Cases of |main_control| that build boxes and lists@>@;
+@t\4@>@<Cases of |main_control| that don't depend on |mode|@>@;
+@t\4@>@<Cases of |main_control| that are for extensions to \TeX@>@;
+
+@ Here is a list of cases where the user has probably gotten into or out of math
+mode by mistake. \TeX\ will insert a dollar sign and rescan the current token.
+
+@d non_math(#)==vmode+#,hmode+#
+
+@<Math-only cases in non-math modes...@>=
+non_math(sup_mark), non_math(sub_mark), non_math(math_char_num),
+non_math(math_given), non_math(math_comp), non_math(delim_num),
+non_math(left_right), non_math(above), non_math(radical),
+non_math(math_style), non_math(math_choice), non_math(vcenter),
+non_math(non_script), non_math(mkern), non_math(limit_switch),
+non_math(mskip), non_math(math_accent),
+mmode+endv, mmode+par_end, mmode+stop, mmode+vskip, mmode+un_vbox,
+mmode+valign, mmode+hrule
+
+@ @<Declare action...@>=
+procedure insert_dollar_sign;
+begin back_input; cur_tok:=math_shift_token+"$";
+print_err("Missing $ inserted");
+@.Missing \$ inserted@>
+help2("I've inserted a begin-math/end-math symbol since I think")@/
+("you left one out. Proceed, with fingers crossed."); ins_error;
+end;
+
+@ When erroneous situations arise, \TeX\ usually issues an error message
+specific to the particular error. For example, `\.{\\noalign}' should
+not appear in any mode, since it is recognized by the |align_peek| routine
+in all of its legitimate appearances; a special error message is given
+when `\.{\\noalign}' occurs elsewhere. But sometimes the most appropriate
+error message is simply that the user is not allowed to do what he or she
+has attempted. For example, `\.{\\moveleft}' is allowed only in vertical mode,
+and `\.{\\lower}' only in non-vertical modes. Such cases are enumerated
+here and in the other sections referred to under `See also \dots.'
+
+@<Forbidden cases...@>=
+vmode+vmove,hmode+hmove,mmode+hmove,any_mode(last_item),
+
+@ The `|you_cant|' procedure prints a line saying that the current command
+is illegal in the current mode; it identifies these things symbolically.
+
+@<Declare action...@>=
+procedure you_cant;
+begin print_err("You can't use `");
+@.You can't use x in y mode@>
+print_cmd_chr(cur_cmd,cur_chr);
+print("' in "); print_mode(mode);
+end;
+
+@ @<Declare act...@>=
+procedure report_illegal_case;
+begin you_cant;
+help4("Sorry, but I'm not programmed to handle this case;")@/
+("I'll just pretend that you didn't ask for it.")@/
+("If you're in the wrong mode, you might be able to")@/
+("return to the right one by typing `I}' or `I$' or `I\par'.");@/
+error;
+end;
+
+@ Some operations are allowed only in privileged modes, i.e., in cases
+that |mode>0|. The |privileged| function is used to detect violations
+of this rule; it issues an error message and returns |false| if the
+current |mode| is negative.
+
+@<Declare act...@>=
+function privileged:boolean;
+begin if mode>0 then privileged:=true
+else begin report_illegal_case; privileged:=false;
+ end;
+end;
+
+@ Either \.{\\dump} or \.{\\end} will cause |main_control| to enter the
+endgame, since both of them have `|stop|' as their command code.
+
+@<Put each...@>=
+primitive("end",stop,0);@/
+@!@:end_}{\.{\\end} primitive@>
+primitive("dump",stop,1);@/
+@!@:dump_}{\.{\\dump} primitive@>
+
+@ @<Cases of |print_cmd_chr|...@>=
+stop:if chr_code=1 then print_esc("dump")@+else print_esc("end");
+
+@ We don't want to leave |main_control| immediately when a |stop| command
+is sensed, because it may be necessary to invoke an \.{\\output} routine
+several times before things really grind to a halt. (The output routine
+might even say `\.{\\gdef\\end\{...\}}', to prolong the life of the job.)
+Therefore |its_all_over| is |true| only when the current page
+and contribution list are empty, and when the last output was not a
+``dead cycle.''
+
+@<Declare act...@>=
+function its_all_over:boolean; {do this when \.{\\end} or \.{\\dump} occurs}
+label exit;
+begin if privileged then
+ begin if (page_head=page_tail)and(head=tail)and(dead_cycles=0) then
+ begin its_all_over:=true; return;
+ end;
+ back_input; {we will try to end again after ejecting residual material}
+ tail_append(new_null_box);
+ width(tail):=hsize;
+ tail_append(new_glue(fill_glue));
+ tail_append(new_penalty(-@'10000000000));@/
+ build_page; {append \.{\\hbox to \\hsize\{\}\\vfill\\penalty-'10000000000}}
+ end;
+its_all_over:=false;
+exit:end;
+
+@* \[47] Building boxes and lists.
+The most important parts of |main_control| are concerned with \TeX's
+chief mission of box-making. We need to control the activities that put
+entries on vlists and hlists, as well as the activities that convert
+those lists into boxes. All of the necessary machinery has already been
+developed; it remains for us to ``push the buttons'' at the right times.
+
+@ As an introduction to these routines, let's consider one of the simplest
+cases: What happens when `\.{\\hrule}' occurs in vertical mode, or
+`\.{\\vrule}' in horizontal mode or math mode? The code in |main_control|
+is short, since the |scan_rule_spec| routine already does most of what is
+required; thus, there is no need for a special action procedure.
+
+Note that baselineskip calculations are disabled after a rule in vertical
+mode, by setting |prev_depth:=ignore_depth|.
+
+@<Cases of |main_control| that build...@>=
+vmode+hrule,hmode+vrule,mmode+vrule: begin tail_append(scan_rule_spec);
+ if abs(mode)=vmode then prev_depth:=ignore_depth
+ else if abs(mode)=hmode then space_factor:=1000;
+ end;
+
+@ The processing of things like \.{\\hskip} and \.{\\vskip} is slightly
+more complicated. But the code in |main_control| is very short, since
+it simply calls on the action routine |append_glue|. Similarly, \.{\\kern}
+activates |append_kern|.
+
+@<Cases of |main_control| that build...@>=
+vmode+vskip,hmode+hskip,mmode+hskip,mmode+mskip: append_glue;
+any_mode(kern),mmode+mkern: append_kern;
+
+@ The |hskip| and |vskip| command codes are used for control sequences
+like \.{\\hss} and \.{\\vfil} as well as for \.{\\hskip} and \.{\\vskip}.
+The difference is in the value of |cur_chr|.
+
+@d fil_code=0 {identifies \.{\\hfil} and \.{\\vfil}}
+@d fill_code=1 {identifies \.{\\hfill} and \.{\\vfill}}
+@d ss_code=2 {identifies \.{\\hss} and \.{\\vss}}
+@d fil_neg_code=3 {identifies \.{\\hfilneg} and \.{\\vfilneg}}
+@d skip_code=4 {identifies \.{\\hskip} and \.{\\vskip}}
+@d mskip_code=5 {identifies \.{\\mskip}}
+
+@<Put each...@>=
+primitive("hskip",hskip,skip_code);@/
+@!@:hskip_}{\.{\\hskip} primitive@>
+primitive("hfil",hskip,fil_code);
+@!@:hfil_}{\.{\\hfil} primitive@>
+primitive("hfill",hskip,fill_code);@/
+@!@:hfill_}{\.{\\hfill} primitive@>
+primitive("hss",hskip,ss_code);
+@!@:hss_}{\.{\\hss} primitive@>
+primitive("hfilneg",hskip,fil_neg_code);@/
+@!@:hfil_neg_}{\.{\\hfilneg} primitive@>
+primitive("vskip",vskip,skip_code);@/
+@!@:vskip_}{\.{\\vskip} primitive@>
+primitive("vfil",vskip,fil_code);
+@!@:vfil_}{\.{\\vfil} primitive@>
+primitive("vfill",vskip,fill_code);@/
+@!@:vfill_}{\.{\\vfill} primitive@>
+primitive("vss",vskip,ss_code);
+@!@:vss_}{\.{\\vss} primitive@>
+primitive("vfilneg",vskip,fil_neg_code);@/
+@!@:vfil_neg_}{\.{\\vfilneg} primitive@>
+primitive("mskip",mskip,mskip_code);@/
+@!@:mskip_}{\.{\\mskip} primitive@>
+primitive("kern",kern,explicit);
+@!@:kern_}{\.{\\kern} primitive@>
+primitive("mkern",mkern,mu_glue);@/
+@!@:mkern_}{\.{\\mkern} primitive@>
+
+@ @<Cases of |print_cmd_chr|...@>=
+hskip: case chr_code of
+ skip_code:print_esc("hskip");
+ fil_code:print_esc("hfil");
+ fill_code:print_esc("hfill");
+ ss_code:print_esc("hss");
+ othercases print_esc("hfilneg")
+ endcases;
+vskip: case chr_code of
+ skip_code:print_esc("vskip");
+ fil_code:print_esc("vfil");
+ fill_code:print_esc("vfill");
+ ss_code:print_esc("vss");
+ othercases print_esc("vfilneg")
+ endcases;
+mskip: print_esc("mskip");
+kern: print_esc("kern");
+mkern: print_esc("mkern");
+
+@ All the work relating to glue creation has been relegated to the
+following subroutine. It does not call |build_page|, because it is
+used in at least one place where that would be a mistake.
+
+@<Declare action...@>=
+procedure append_glue;
+var s:small_number; {modifier of skip command}
+begin s:=cur_chr;
+case s of
+fil_code: cur_val:=fil_glue;
+fill_code: cur_val:=fill_glue;
+ss_code: cur_val:=ss_glue;
+fil_neg_code: cur_val:=fil_neg_glue;
+skip_code: scan_glue(glue_val);
+mskip_code: scan_glue(mu_val);
+end; {now |cur_val| points to the glue specification}
+tail_append(new_glue(cur_val));
+if s>=skip_code then
+ begin decr(glue_ref_count(cur_val));
+ if s>skip_code then subtype(tail):=mu_glue;
+ end;
+end;
+
+@ @<Declare act...@>=
+procedure append_kern;
+var s:quarterword; {|subtype| of the kern node}
+begin s:=cur_chr; scan_dimen(s=mu_glue,false,false);
+tail_append(new_kern(cur_val)); subtype(tail):=s;
+end;
+
+@ Many of the actions related to box-making are triggered by the appearance
+of braces in the input. For example, when the user says `\.{\\hbox}
+\.{to} \.{100pt\{$\langle\,\hbox{hlist}\,\rangle$\}}' in vertical mode,
+the information about the box size (100pt, |exactly|) is put onto |save_stack|
+with a level boundary word just above it, and |cur_group:=adjusted_hbox_group|;
+\TeX\ enters restricted horizontal mode to process the hlist. The right
+brace eventually causes |save_stack| to be restored to its former state,
+at which time the information about the box size (100pt, |exactly|) is
+available once again; a box is packaged and we leave restricted horizontal
+mode, appending the new box to the current list of the enclosing mode
+(in this case to the current list of vertical mode), followed by any
+vertical adjustments that were removed from the box by |hpack|.
+
+The next few sections of the program are therefore concerned with the
+treatment of left and right curly braces.
+
+@ If a left brace occurs in the middle of a page or paragraph, it simply
+introduces a new level of grouping, and the matching right brace will not have
+such a drastic effect. Such grouping affects neither the mode nor the
+current list.
+
+@<Cases of |main_control| that build...@>=
+non_math(left_brace): new_save_level(simple_group);
+any_mode(begin_group): new_save_level(semi_simple_group);
+any_mode(end_group): if cur_group=semi_simple_group then unsave
+ else off_save;
+
+@ We have to deal with errors in which braces and such things are not
+properly nested. Sometimes the user makes an error of commission by
+inserting an extra symbol, but sometimes the user makes an error of omission.
+\TeX\ can't always tell one from the other, so it makes a guess and tries
+to avoid getting into a loop.
+
+The |off_save| routine is called when the current group code is wrong. It tries
+to insert something into the user's input that will help clean off
+the top level.
+
+@<Declare act...@>=
+procedure off_save;
+var p:pointer; {inserted token}
+begin if cur_group=bottom_level then
+ @<Drop current token and complain that it was unmatched@>
+else begin back_input; p:=get_avail; link(temp_head):=p;
+ print_err("Missing ");
+ @<Prepare to insert a token that matches |cur_group|,
+ and print what it is@>;
+ print(" inserted"); ins_list(link(temp_head));
+ help5("I've inserted something that you may have forgotten.")@/
+ ("(See the <inserted text> above.)")@/
+ ("With luck, this will get me unwedged. But if you")@/
+ ("really didn't forget anything, try typing `2' now; then")@/
+ ("my insertion and my current dilemma will both disappear.");
+ error;
+ end;
+end;
+
+@ At this point, |link(temp_head)=p|, a pointer to an empty one-word node.
+
+@<Prepare to insert a token that matches |cur_group|...@>=
+case cur_group of
+semi_simple_group: begin info(p):=cs_token_flag+frozen_end_group;
+ print_esc("endgroup");
+@.Missing \\endgroup inserted@>
+ end;
+math_shift_group: begin info(p):=math_shift_token+"$"; print_char("$");
+@.Missing \$ inserted@>
+ end;
+math_left_group: begin info(p):=cs_token_flag+frozen_right; link(p):=get_avail;
+ p:=link(p); info(p):=other_token+"."; print_esc("right.");
+@.Missing \\right\hbox{.} inserted@>
+@^null delimiter@>
+ end;
+othercases begin info(p):=right_brace_token+"}"; print_char("}");
+@.Missing \} inserted@>
+ end
+endcases
+
+@ @<Drop current token and complain that it was unmatched@>=
+begin print_err("Extra "); print_cmd_chr(cur_cmd,cur_chr);
+@.Extra x@>
+help1("Things are pretty mixed up, but I think the worst is over.");@/
+error;
+end
+
+@ The routine for a |right_brace| character branches into many subcases,
+since a variety of things may happen, depending on |cur_group|. Some
+types of groups are not supposed to be ended by a right brace; error
+messages are given in hopes of pinpointing the problem. Most branches
+of this routine will be filled in later, when we are ready to understand
+them; meanwhile, we must prepare ourselves to deal with such errors.
+
+@<Cases of |main_control| that build...@>=
+any_mode(right_brace): handle_right_brace;
+
+@ @<Declare the procedure called |handle_right_brace|@>=
+procedure handle_right_brace;
+var p,@!q:pointer; {for short-term use}
+@!d:scaled; {holds |split_max_depth| in |insert_group|}
+@!f:integer; {holds |floating_penalty| in |insert_group|}
+begin case cur_group of
+simple_group: unsave;
+bottom_level: begin print_err("Too many }'s");
+@.Too many \}'s@>
+ help2("You've closed more groups than you opened.")@/
+ ("Such booboos are generally harmless, so keep going."); error;
+ end;
+semi_simple_group,math_shift_group,math_left_group: extra_right_brace;
+@t\4@>@<Cases of |handle_right_brace| where a |right_brace| triggers
+ a delayed action@>@;
+othercases confusion("rightbrace")
+@:this can't happen rightbrace}{\quad rightbrace@>
+endcases;
+end;
+
+@ @<Declare act...@>=
+procedure extra_right_brace;
+begin print_err("Extra }, or forgotten ");
+@.Extra \}, or forgotten x@>
+case cur_group of
+semi_simple_group: print_esc("endgroup");
+math_shift_group: print_char("$");
+math_left_group: print_esc("right");
+end;@/
+help5("I've deleted a group-closing symbol because it seems to be")@/
+("spurious, as in `$x}$'. But perhaps the } is legitimate and")@/
+("you forgot something else, as in `\hbox{$x}'. In such cases")@/
+("the way to recover is to insert both the forgotten and the")@/
+("deleted material, e.g., by typing `I$}'."); error;
+incr(align_state);
+end;
+
+@ Here is where we clear the parameters that are supposed to revert to their
+default values after every paragraph and when internal vertical mode is entered.
+
+@<Declare act...@>=
+procedure normal_paragraph;
+begin if looseness<>0 then eq_word_define(int_base+looseness_code,0);
+if hang_indent<>0 then eq_word_define(dimen_base+hang_indent_code,0);
+if hang_after<>1 then eq_word_define(int_base+hang_after_code,1);
+if par_shape_ptr<>null then eq_define(par_shape_loc,shape_ref,null);
+end;
+
+@ Now let's turn to the question of how \.{\\hbox} is treated. We actually
+need to consider also a slightly larger context, since constructions like
+`\.{\\setbox3=}\penalty0\.{\\hbox...}' and
+`\.{\\leaders}\penalty0\.{\\hbox...}' and
+`\.{\\lower3.8pt\\hbox...}'
+are supposed to invoke quite
+different actions after the box has been packaged. Conversely,
+constructions like `\.{\\setbox3=}' can be followed by a variety of
+different kinds of boxes, and we would like to encode such things in an
+efficient way.
+
+In other words, there are two problems: To represent the context of a box,
+and to represent its type.
+
+The first problem is solved by putting a ``context code'' on the |save_stack|,
+just below the two entries that give the dimensions produced by |scan_spec|.
+The context code is either a (signed) shift amount, or it is a large
+integer |>=box_flag|, where |box_flag=@t$2^{30}$@>|. Codes |box_flag| through
+|box_flag+255| represent `\.{\\setbox0}' through `\.{\\setbox255}';
+codes |box_flag+256| through |box_flag+511| represent `\.{\\global\\setbox0}'
+through `\.{\\global\\setbox255}';
+code |box_flag+512| represents `\.{\\shipout}'; and codes |box_flag+513|
+through |box_flag+515| represent `\.{\\leaders}', `\.{\\cleaders}',
+and `\.{\\xleaders}'.
+
+The second problem is solved by giving the command code |make_box| to all
+control sequences that produce a box, and by using the following |chr_code|
+values to distinguish between them: |box_code|, |copy_code|, |last_box_code|,
+|vsplit_code|, |vtop_code|, |vtop_code+vmode|, and |vtop_code+hmode|,
+where the latter two are used denote \.{\\vbox} and \.{\\hbox}, respectively.
+
+@d box_flag==@'10000000000 {context code for `\.{\\setbox0}'}
+@d ship_out_flag==box_flag+512 {context code for `\.{\\shipout}'}
+@d leader_flag==box_flag+513 {context code for `\.{\\leaders}'}
+@d box_code=0 {|chr_code| for `\.{\\box}'}
+@d copy_code=1 {|chr_code| for `\.{\\copy}'}
+@d last_box_code=2 {|chr_code| for `\.{\\lastbox}'}
+@d vsplit_code=3 {|chr_code| for `\.{\\vsplit}'}
+@d vtop_code=4 {|chr_code| for `\.{\\vtop}'}
+
+@<Put each...@>=
+primitive("moveleft",hmove,1);
+@!@:move_left_}{\.{\\moveleft} primitive@>
+primitive("moveright",hmove,0);@/
+@!@:move_right_}{\.{\\moveright} primitive@>
+primitive("raise",vmove,1);
+@!@:raise_}{\.{\\raise} primitive@>
+primitive("lower",vmove,0);
+@!@:lower_}{\.{\\lower} primitive@>
+@#
+primitive("box",make_box,box_code);
+@!@:box_}{\.{\\box} primitive@>
+primitive("copy",make_box,copy_code);
+@!@:copy_}{\.{\\copy} primitive@>
+primitive("lastbox",make_box,last_box_code);
+@!@:last_box_}{\.{\\lastbox} primitive@>
+primitive("vsplit",make_box,vsplit_code);
+@!@:vsplit_}{\.{\\vsplit} primitive@>
+primitive("vtop",make_box,vtop_code);@/
+@!@:vtop_}{\.{\\vtop} primitive@>
+primitive("vbox",make_box,vtop_code+vmode);
+@!@:vbox_}{\.{\\vbox} primitive@>
+primitive("hbox",make_box,vtop_code+hmode);@/
+@!@:hbox_}{\.{\\hbox} primitive@>
+primitive("shipout",leader_ship,a_leaders-1); {|ship_out_flag=leader_flag-1|}
+@!@:ship_out_}{\.{\\shipout} primitive@>
+primitive("leaders",leader_ship,a_leaders);
+@!@:leaders_}{\.{\\leaders} primitive@>
+primitive("cleaders",leader_ship,c_leaders);
+@!@:c_leaders_}{\.{\\cleaders} primitive@>
+primitive("xleaders",leader_ship,x_leaders);
+@!@:x_leaders_}{\.{\\xleaders} primitive@>
+
+@ @<Cases of |print_cmd_chr|...@>=
+hmove: if chr_code=1 then print_esc("moveleft")@+else print_esc("moveright");
+vmove: if chr_code=1 then print_esc("raise")@+else print_esc("lower");
+make_box: case chr_code of
+ box_code: print_esc("box");
+ copy_code: print_esc("copy");
+ last_box_code: print_esc("lastbox");
+ vsplit_code: print_esc("vsplit");
+ vtop_code: print_esc("vtop");
+ vtop_code+vmode: print_esc("vbox");
+ othercases print_esc("hbox")
+ endcases;
+leader_ship: if chr_code=a_leaders then print_esc("leaders")
+ else if chr_code=c_leaders then print_esc("cleaders")
+ else if chr_code=x_leaders then print_esc("xleaders")
+ else print_esc("shipout");
+
+@ Constructions that require a box are started by calling |scan_box| with
+a specified context code. The |scan_box| routine verifies
+that a |make_box| command comes next and then it calls |begin_box|.
+
+@<Cases of |main_control| that build...@>=
+vmode+hmove,hmode+vmove,mmode+vmove: begin t:=cur_chr;
+ scan_normal_dimen;
+ if t=0 then scan_box(cur_val)@+else scan_box(-cur_val);
+ end;
+any_mode(leader_ship): scan_box(leader_flag-a_leaders+cur_chr);
+any_mode(make_box): begin_box(0);
+
+@ The global variable |cur_box| will point to a newly-made box. If the box
+is void, we will have |cur_box=null|. Otherwise we will have
+|type(cur_box)=hlist_node| or |vlist_node| or |rule_node|; the |rule_node|
+case can occur only with leaders.
+
+@<Glob...@>=
+@!cur_box:pointer; {box to be placed into its context}
+
+@ The |box_end| procedure does the right thing with |cur_box|, if
+|box_context| represents the context as explained above.
+
+@<Declare act...@>=
+procedure box_end(@!box_context:integer);
+var p:pointer; {|ord_noad| for new box in math mode}
+begin if box_context<box_flag then @<Append box |cur_box| to the current list,
+ shifted by |box_context|@>
+else if box_context<ship_out_flag then @<Store \(c)|cur_box| in a box register@>
+else if cur_box<>null then
+ if box_context>ship_out_flag then @<Append a new leader node that
+ uses |cur_box|@>
+ else ship_out(cur_box);
+end;
+
+@ The global variable |adjust_tail| will be non-null if and only if the
+current box might include adjustments that should be appended to the
+current vertical list.
+
+@<Append box |cur_box| to the current...@>=
+begin if cur_box<>null then
+ begin shift_amount(cur_box):=box_context;
+ if abs(mode)=vmode then
+ begin append_to_vlist(cur_box);
+ if adjust_tail<>null then
+ begin if adjust_head<>adjust_tail then
+ begin link(tail):=link(adjust_head); tail:=adjust_tail;
+ end;
+ adjust_tail:=null;
+ end;
+ if mode>0 then build_page;
+ end
+ else begin if abs(mode)=hmode then space_factor:=1000
+ else begin p:=new_noad;
+ math_type(nucleus(p)):=sub_box;
+ info(nucleus(p)):=cur_box; cur_box:=p;
+ end;
+ link(tail):=cur_box; tail:=cur_box;
+ end;
+ end;
+end
+
+@ @<Store \(c)|cur_box| in a box register@>=
+if box_context<box_flag+256 then
+ eq_define(box_base-box_flag+box_context,box_ref,cur_box)
+else geq_define(box_base-box_flag-256+box_context,box_ref,cur_box)
+
+@ @<Append a new leader node ...@>=
+begin @<Get the next non-blank non-relax...@>;
+if ((cur_cmd=hskip)and(abs(mode)<>vmode))or@|
+ ((cur_cmd=vskip)and(abs(mode)=vmode))or@|
+ ((cur_cmd=mskip)and(abs(mode)=mmode)) then
+ begin append_glue; subtype(tail):=box_context-(leader_flag-a_leaders);
+ leader_ptr(tail):=cur_box;
+ end
+else begin print_err("Leaders not followed by proper glue");
+@.Leaders not followed by...@>
+ help3("You should say `\leaders <box or rule><hskip or vskip>'.")@/
+ ("I found the <box or rule>, but there's no suitable")@/
+ ("<hskip or vskip>, so I'm ignoring these leaders."); back_error;
+ flush_node_list(cur_box);
+ end;
+end
+
+@ Now that we can see what eventually happens to boxes, we can consider
+the first steps in their creation. The |begin_box| routine is called when
+|box_context| is a context specification, |cur_chr| specifies the type of
+box desired, and |cur_cmd=make_box|.
+
+@<Declare act...@>=
+procedure begin_box(@!box_context:integer);
+label exit, done;
+var @!p,@!q:pointer; {run through the current list}
+@!m:quarterword; {the length of a replacement list}
+@!k:halfword; {0 or |vmode| or |hmode|}
+@!n:eight_bits; {a box number}
+begin case cur_chr of
+box_code: begin scan_eight_bit_int; cur_box:=box(cur_val);
+ box(cur_val):=null; {the box becomes void, at the same level}
+ end;
+copy_code: begin scan_eight_bit_int; cur_box:=copy_node_list(box(cur_val));
+ end;
+last_box_code: @<If the current list ends with a box node, delete it from
+ the list and make |cur_box| point to it; otherwise set |cur_box:=null|@>;
+vsplit_code: @<Split off part of a vertical box, make |cur_box| point to it@>;
+othercases @<Initiate the construction of an hbox or vbox, then |return|@>
+endcases;@/
+box_end(box_context); {in simple cases, we use the box immediately}
+exit:end;
+
+@ Note that the condition |not is_char_node(tail)| implies that |head<>tail|,
+since |head| is a one-word node.
+
+@<If the current list ends with a box node, delete it...@>=
+begin cur_box:=null;
+if abs(mode)=mmode then
+ begin you_cant; help1("Sorry; this \lastbox will be void."); error;
+ end
+else if (mode=vmode)and(head=tail) then
+ begin you_cant;
+ help2("Sorry...I usually can't take things from the current page.")@/
+ ("This \lastbox will therefore be void."); error;
+ end
+else begin if not is_char_node(tail) then
+ if (type(tail)=hlist_node)or(type(tail)=vlist_node) then
+ @<Remove the last box, unless it's part of a discretionary@>;
+ end;
+end
+
+@ @<Remove the last box...@>=
+begin q:=head;
+repeat p:=q;
+if not is_char_node(q) then if type(q)=disc_node then
+ begin for m:=1 to replace_count(q) do p:=link(p);
+ if p=tail then goto done;
+ end;
+q:=link(p);
+until q=tail;
+cur_box:=tail; shift_amount(cur_box):=0;
+tail:=p; link(p):=null;
+done:end
+
+@ Here we deal with things like `\.{\\vsplit 13 to 100pt}'.
+
+@<Split off part of a vertical box, make |cur_box| point to it@>=
+begin scan_eight_bit_int; n:=cur_val;
+if not scan_keyword("to") then
+@.to@>
+ begin print_err("Missing `to' inserted");
+@.Missing `to' inserted@>
+ help2("I'm working on `\vsplit<box number> to <dimen>';")@/
+ ("will look for the <dimen> next."); error;
+ end;
+scan_normal_dimen;
+cur_box:=vsplit(n,cur_val);
+end
+
+@ Here is where we enter restricted horizontal mode or internal vertical
+mode, in order to make a box.
+
+@<Initiate the construction of an hbox or vbox, then |return|@>=
+begin k:=cur_chr-vtop_code; saved(0):=box_context;
+if k=hmode then
+ if (box_context<box_flag)and(abs(mode)=vmode) then
+ scan_spec(adjusted_hbox_group,true)
+ else scan_spec(hbox_group,true)
+else begin if k=vmode then scan_spec(vbox_group,true)
+ else begin scan_spec(vtop_group,true); k:=vmode;
+ end;
+ normal_paragraph;
+ end;
+push_nest; mode:=-k;
+if k=vmode then
+ begin prev_depth:=ignore_depth;
+ if every_vbox<>null then begin_token_list(every_vbox,every_vbox_text);
+ end
+else begin space_factor:=1000;
+ if every_hbox<>null then begin_token_list(every_hbox,every_hbox_text);
+ end;
+return;
+end
+
+@ @<Declare act...@>=
+procedure scan_box(@!box_context:integer);
+ {the next input should specify a box or perhaps a rule}
+begin @<Get the next non-blank non-relax...@>;
+if cur_cmd=make_box then begin_box(box_context)
+else if (box_context>=leader_flag)and((cur_cmd=hrule)or(cur_cmd=vrule)) then
+ begin cur_box:=scan_rule_spec; box_end(box_context);
+ end
+else begin@t@>@;@/
+ print_err("A <box> was supposed to be here");@/
+@.A <box> was supposed to...@>
+ help3("I was expecting to see \hbox or \vbox or \copy or \box or")@/
+ ("something like that. So you might find something missing in")@/
+ ("your output. But keep trying; you can fix this later."); back_error;
+ end;
+end;
+
+@ When the right brace occurs at the end of an \.{\\hbox} or \.{\\vbox} or
+\.{\\vtop} construction, the |package| routine comes into action. We might
+also have to finish a paragraph that hasn't ended.
+
+@<Cases of |handle...@>=
+hbox_group: package(0);
+adjusted_hbox_group: begin adjust_tail:=adjust_head; package(0);
+ end;
+vbox_group: begin end_graf; package(0);
+ end;
+vtop_group: begin end_graf; package(vtop_code);
+ end;
+
+@ @<Declare action...@>=
+procedure package(@!c:small_number);
+var h:scaled; {height of box}
+@!p:pointer; {first node in a box}
+@!d:scaled; {max depth}
+begin d:=box_max_depth; unsave; save_ptr:=save_ptr-3;
+if mode=-hmode then cur_box:=hpack(link(head),saved(2),saved(1))
+else begin cur_box:=vpackage(link(head),saved(2),saved(1),d);
+ if c=vtop_code then @<Readjust the height and depth of |cur_box|,
+ for \.{\\vtop}@>;
+ end;
+pop_nest; box_end(saved(0));
+end;
+
+@ The height of a `\.{\\vtop}' box is inherited from the first item on its list,
+if that item is an |hlist_node|, |vlist_node|, or |rule_node|; otherwise
+the \.{\\vtop} height is zero.
+
+
+@<Readjust the height...@>=
+begin h:=0; p:=list_ptr(cur_box);
+if p<>null then if type(p)<=rule_node then h:=height(p);
+depth(cur_box):=depth(cur_box)-h+height(cur_box); height(cur_box):=h;
+end
+
+@ A paragraph begins when horizontal-mode material occurs in vertical mode,
+or when the paragraph is explicitly started by `\.{\\indent}' or
+`\.{\\noindent}'.
+
+@<Put each...@>=
+primitive("indent",start_par,1);
+@!@:indent_}{\.{\\indent} primitive@>
+primitive("noindent",start_par,0);
+@!@:no_indent_}{\.{\\noindent} primitive@>
+
+@ @<Cases of |print_cmd_chr|...@>=
+start_par: if chr_code=0 then print_esc("noindent")@+ else print_esc("indent");
+
+@ @<Cases of |main_control| that build...@>=
+vmode+start_par: new_graf(cur_chr>0);
+vmode+letter,vmode+other_char,vmode+char_num,vmode+char_given,
+ vmode+math_shift,vmode+un_hbox,vmode+vrule,
+ vmode+accent,vmode+discretionary,vmode+hskip,vmode+valign,
+ vmode+ex_space,vmode+no_boundary:@t@>@;@/
+ begin back_input; new_graf(true);
+ end;
+
+@ @<Declare act...@>=
+function norm_min(@!h:integer):small_number;
+begin if h<=0 then norm_min:=1@+else if h>=63 then norm_min:=63@+
+else norm_min:=h;
+end;
+@#
+procedure new_graf(@!indented:boolean);
+begin prev_graf:=0;
+if (mode=vmode)or(head<>tail) then
+ tail_append(new_param_glue(par_skip_code));
+push_nest; mode:=hmode; space_factor:=1000; set_cur_lang; clang:=cur_lang;
+prev_graf:=(norm_min(left_hyphen_min)*@'100+norm_min(right_hyphen_min))
+ *@'200000+cur_lang;
+if indented then
+ begin tail:=new_null_box; link(head):=tail; width(tail):=par_indent;@+
+ end;
+if every_par<>null then begin_token_list(every_par,every_par_text);
+if nest_ptr=1 then build_page; {put |par_skip| glue on current page}
+end;
+
+@ @<Cases of |main_control| that build...@>=
+hmode+start_par,mmode+start_par: indent_in_hmode;
+
+@ @<Declare act...@>=
+procedure indent_in_hmode;
+var p,@!q:pointer;
+begin if cur_chr>0 then {\.{\\indent}}
+ begin p:=new_null_box; width(p):=par_indent;
+ if abs(mode)=hmode then space_factor:=1000
+ else begin q:=new_noad; math_type(nucleus(q)):=sub_box;
+ info(nucleus(q)):=p; p:=q;
+ end;
+ tail_append(p);
+ end;
+end;
+
+@ A paragraph ends when a |par_end| command is sensed, or when we are in
+horizontal mode when reaching the right brace of vertical-mode routines
+like \.{\\vbox}, \.{\\insert}, or \.{\\output}.
+
+@<Cases of |main_control| that build...@>=
+vmode+par_end: begin normal_paragraph;
+ if mode>0 then build_page;
+ end;
+hmode+par_end: begin if align_state<0 then off_save; {this tries to
+ recover from an alignment that didn't end properly}
+ end_graf; {this takes us to the enclosing mode, if |mode>0|}
+ if mode=vmode then build_page;
+ end;
+hmode+stop,hmode+vskip,hmode+hrule,hmode+un_vbox,hmode+halign: head_for_vmode;
+
+@ @<Declare act...@>=
+procedure head_for_vmode;
+begin if mode<0 then
+ if cur_cmd<>hrule then off_save
+ else begin print_err("You can't use `");
+ print_esc("hrule"); print("' here except with leaders");
+@.You can't use \\hrule...@>
+ help2("To put a horizontal rule in an hbox or an alignment,")@/
+ ("you should use \leaders or \hrulefill (see The TeXbook).");
+ error;
+ end
+else begin back_input; cur_tok:=par_token; back_input; token_type:=inserted;
+ end;
+end;
+
+@ @<Declare act...@>=
+procedure end_graf;
+begin if mode=hmode then
+ begin if head=tail then pop_nest {null paragraphs are ignored}
+ else line_break(widow_penalty);
+ normal_paragraph;
+ error_count:=0;
+ end;
+end;
+
+@ Insertion and adjustment and mark nodes are constructed by the following
+pieces of the program.
+
+@<Cases of |main_control| that build...@>=
+any_mode(insert),hmode+vadjust,mmode+vadjust: begin_insert_or_adjust;
+any_mode(mark): make_mark;
+
+@ @<Forbidden...@>=
+vmode+vadjust,
+
+@ @<Declare act...@>=
+procedure begin_insert_or_adjust;
+begin if cur_cmd=vadjust then cur_val:=255
+else begin scan_eight_bit_int;
+ if cur_val=255 then
+ begin print_err("You can't "); print_esc("insert"); print_int(255);
+@.You can't \\insert255@>
+ help1("I'm changing to \insert0; box 255 is special.");
+ error; cur_val:=0;
+ end;
+ end;
+saved(0):=cur_val; incr(save_ptr);
+new_save_level(insert_group); scan_left_brace; normal_paragraph;
+push_nest; mode:=-vmode; prev_depth:=ignore_depth;
+end;
+
+@ @<Cases of |handle...@>=
+insert_group: begin end_graf; q:=split_top_skip; add_glue_ref(q);
+ d:=split_max_depth; f:=floating_penalty; unsave; decr(save_ptr);
+ {now |saved(0)| is the insertion number, or 255 for |vadjust|}
+ p:=vpack(link(head),natural); pop_nest;
+ if saved(0)<255 then
+ begin tail_append(get_node(ins_node_size));
+ type(tail):=ins_node; subtype(tail):=qi(saved(0));
+ height(tail):=height(p)+depth(p); ins_ptr(tail):=list_ptr(p);
+ split_top_ptr(tail):=q; depth(tail):=d; float_cost(tail):=f;
+ end
+ else begin tail_append(get_node(small_node_size));
+ type(tail):=adjust_node;@/
+ subtype(tail):=0; {the |subtype| is not used}
+ adjust_ptr(tail):=list_ptr(p); delete_glue_ref(q);
+ end;
+ free_node(p,box_node_size);
+ if nest_ptr=0 then build_page;
+ end;
+output_group: @<Resume the page builder...@>;
+
+@ @<Declare act...@>=
+procedure make_mark;
+var p:pointer; {new node}
+begin p:=scan_toks(false,true); p:=get_node(small_node_size);
+type(p):=mark_node; subtype(p):=0; {the |subtype| is not used}
+mark_ptr(p):=def_ref; link(tail):=p; tail:=p;
+end;
+
+@ Penalty nodes get into a list via the |break_penalty| command.
+@^penalties@>
+
+@<Cases of |main_control| that build...@>=
+any_mode(break_penalty): append_penalty;
+
+@ @<Declare action...@>=
+procedure append_penalty;
+begin scan_int; tail_append(new_penalty(cur_val));
+if mode=vmode then build_page;
+end;
+
+@ The |remove_item| command removes a penalty, kern, or glue node if it
+appears at the tail of the current list, using a brute-force linear scan.
+Like \.{\\lastbox}, this command is not allowed in vertical mode (except
+internal vertical mode), since the current list in vertical mode is sent
+to the page builder. But if we happen to be able to implement it in
+vertical mode, we do.
+
+@<Cases of |main_control| that build...@>=
+any_mode(remove_item): delete_last;
+
+@ When |delete_last| is called, |cur_chr| is the |type| of node that
+will be deleted, if present.
+
+@<Declare action...@>=
+procedure delete_last;
+label exit;
+var @!p,@!q:pointer; {run through the current list}
+@!m:quarterword; {the length of a replacement list}
+begin if (mode=vmode)and(tail=head) then
+ @<Apologize for inability to do the operation now,
+ unless \.{\\unskip} follows non-glue@>
+else begin if not is_char_node(tail) then if type(tail)=cur_chr then
+ begin q:=head;
+ repeat p:=q;
+ if not is_char_node(q) then if type(q)=disc_node then
+ begin for m:=1 to replace_count(q) do p:=link(p);
+ if p=tail then return;
+ end;
+ q:=link(p);
+ until q=tail;
+ link(p):=null; flush_node_list(tail); tail:=p;
+ end;
+ end;
+exit:end;
+
+@ @<Apologize for inability to do the operation...@>=
+begin if (cur_chr<>glue_node)or(last_glue<>max_halfword) then
+ begin you_cant;
+ help2("Sorry...I usually can't take things from the current page.")@/
+ ("Try `I\vskip-\lastskip' instead.");
+ if cur_chr=kern_node then help_line[0]:=
+ ("Try `I\kern-\lastkern' instead.")
+ else if cur_chr<>glue_node then help_line[0]:=@|
+ ("Perhaps you can make the output routine do it.");
+ error;
+ end;
+end
+
+@ @<Put each...@>=
+primitive("unpenalty",remove_item,penalty_node);@/
+@!@:un_penalty_}{\.{\\unpenalty} primitive@>
+primitive("unkern",remove_item,kern_node);@/
+@!@:un_kern_}{\.{\\unkern} primitive@>
+primitive("unskip",remove_item,glue_node);@/
+@!@:un_skip_}{\.{\\unskip} primitive@>
+primitive("unhbox",un_hbox,box_code);@/
+@!@:un_hbox_}{\.{\\unhbox} primitive@>
+primitive("unhcopy",un_hbox,copy_code);@/
+@!@:un_hcopy_}{\.{\\unhcopy} primitive@>
+primitive("unvbox",un_vbox,box_code);@/
+@!@:un_vbox_}{\.{\\unvbox} primitive@>
+primitive("unvcopy",un_vbox,copy_code);@/
+@!@:un_vcopy_}{\.{\\unvcopy} primitive@>
+
+@ @<Cases of |print_cmd_chr|...@>=
+remove_item: if chr_code=glue_node then print_esc("unskip")
+ else if chr_code=kern_node then print_esc("unkern")
+ else print_esc("unpenalty");
+un_hbox: if chr_code=copy_code then print_esc("unhcopy")
+ else print_esc("unhbox");
+un_vbox: if chr_code=copy_code then print_esc("unvcopy")
+ else print_esc("unvbox");
+
+@ The |un_hbox| and |un_vbox| commands unwrap one of the 256 current boxes.
+
+@<Cases of |main_control| that build...@>=
+vmode+un_vbox,hmode+un_hbox,mmode+un_hbox: unpackage;
+
+@ @<Declare act...@>=
+procedure unpackage;
+label exit;
+var p:pointer; {the box}
+@!c:box_code..copy_code; {should we copy?}
+begin c:=cur_chr; scan_eight_bit_int; p:=box(cur_val);
+if p=null then return;
+if (abs(mode)=mmode)or((abs(mode)=vmode)and(type(p)<>vlist_node))or@|
+ ((abs(mode)=hmode)and(type(p)<>hlist_node)) then
+ begin print_err("Incompatible list can't be unboxed");
+@.Incompatible list...@>
+ help3("Sorry, Pandora. (You sneaky devil.)")@/
+ ("I refuse to unbox an \hbox in vertical mode or vice versa.")@/
+ ("And I can't open any boxes in math mode.");@/
+ error; return;
+ end;
+if c=copy_code then link(tail):=copy_node_list(list_ptr(p))
+else begin link(tail):=list_ptr(p); box(cur_val):=null;
+ free_node(p,box_node_size);
+ end;
+while link(tail)<>null do tail:=link(tail);
+exit:end;
+
+@ @<Forbidden...@>=vmode+ital_corr,
+
+@ Italic corrections are converted to kern nodes when the |ital_corr| command
+follows a character. In math mode the same effect is achieved by appending
+a kern of zero here, since italic corrections are supplied later.
+
+@<Cases of |main_control| that build...@>=
+hmode+ital_corr: append_italic_correction;
+mmode+ital_corr: tail_append(new_kern(0));
+
+@ @<Declare act...@>=
+procedure append_italic_correction;
+label exit;
+var p:pointer; {|char_node| at the tail of the current list}
+@!f:internal_font_number; {the font in the |char_node|}
+begin if tail<>head then
+ begin if is_char_node(tail) then p:=tail
+ else if type(tail)=ligature_node then p:=lig_char(tail)
+ else return;
+ f:=font(p);
+ tail_append(new_kern(char_italic(f)(char_info(f)(character(p)))));
+ subtype(tail):=explicit;
+ end;
+exit:end;
+
+@ Discretionary nodes are easy in the common case `\.{\\-}', but in the
+general case we must process three braces full of items.
+
+@<Put each...@>=
+primitive("-",discretionary,1);
+@!@:Single-character primitives -}{\quad\.{\\-}@>
+primitive("discretionary",discretionary,0);
+@!@:discretionary_}{\.{\\discretionary} primitive@>
+
+@ @<Cases of |print_cmd_chr|...@>=
+discretionary: if chr_code=1 then
+ print_esc("-")@+else print_esc("discretionary");
+
+@ @<Cases of |main_control| that build...@>=
+hmode+discretionary,mmode+discretionary: append_discretionary;
+
+@ The space factor does not change when we append a discretionary node,
+but it starts out as 1000 in the subsidiary lists.
+
+@<Declare act...@>=
+procedure append_discretionary;
+var c:integer; {hyphen character}
+begin tail_append(new_disc);
+if cur_chr=1 then
+ begin c:=hyphen_char[cur_font];
+ if c>=0 then if c<256 then pre_break(tail):=new_character(cur_font,c);
+ end
+else begin incr(save_ptr); saved(-1):=0; new_save_level(disc_group);
+ scan_left_brace; push_nest; mode:=-hmode; space_factor:=1000;
+ end;
+end;
+
+@ The three discretionary lists are constructed somewhat as if they were
+hboxes. A~subroutine called |build_discretionary| handles the transitions.
+(This is sort of fun.)
+
+@<Cases of |handle...@>=
+disc_group: build_discretionary;
+
+@ @<Declare act...@>=
+procedure build_discretionary;
+label done,exit;
+var p,@!q:pointer; {for link manipulation}
+@!n:integer; {length of discretionary list}
+begin unsave;
+@<Prune the current list, if necessary, until it contains only
+ |char_node|, |kern_node|, |hlist_node|, |vlist_node|, |rule_node|,
+ and |ligature_node| items; set |n| to the length of the list,
+ and set |q| to the list's tail@>;
+p:=link(head); pop_nest;
+case saved(-1) of
+0:pre_break(tail):=p;
+1:post_break(tail):=p;
+2:@<Attach list |p| to the current list, and record its length;
+ then finish up and |return|@>;
+end; {there are no other cases}
+incr(saved(-1)); new_save_level(disc_group); scan_left_brace;
+push_nest; mode:=-hmode; space_factor:=1000;
+exit:end;
+
+@ @<Attach list |p| to the current...@>=
+begin if (n>0)and(abs(mode)=mmode) then
+ begin print_err("Illegal math "); print_esc("discretionary");
+@.Illegal math \\disc...@>
+ help2("Sorry: The third part of a discretionary break must be")@/
+ ("empty, in math formulas. I had to delete your third part.");
+ flush_node_list(p); n:=0; error;
+ end
+else link(tail):=p;
+if n<=max_quarterword then replace_count(tail):=n
+else begin print_err("Discretionary list is too long");
+@.Discretionary list is too long@>
+ help2("Wow---I never thought anybody would tweak me here.")@/
+ ("You can't seriously need such a huge discretionary list?");
+ error;
+ end;
+if n>0 then tail:=q;
+decr(save_ptr); return;
+end
+
+@ During this loop, |p=link(q)| and there are |n| items preceding |p|.
+
+@<Prune the current list, if necessary...@>=
+q:=head; p:=link(q); n:=0;
+while p<>null do
+ begin if not is_char_node(p) then if type(p)>rule_node then
+ if type(p)<>kern_node then if type(p)<>ligature_node then
+ begin print_err("Improper discretionary list");
+@.Improper discretionary list@>
+ help1("Discretionary lists must contain only boxes and kerns.");@/
+ error;
+ begin_diagnostic;
+ print_nl("The following discretionary sublist has been deleted:");
+@.The following...deleted@>
+ show_box(p);
+ end_diagnostic(true);
+ flush_node_list(p); link(q):=null; goto done;
+ end;
+ q:=p; p:=link(q); incr(n);
+ end;
+done:
+
+@ We need only one more thing to complete the horizontal mode routines, namely
+the \.{\\accent} primitive.
+
+@<Cases of |main_control| that build...@>=
+hmode+accent: make_accent;
+
+@ The positioning of accents is straightforward but tedious. Given an accent
+of width |a|, designed for characters of height |x| and slant |s|;
+and given a character of width |w|, height |h|, and slant |t|: We will shift
+the accent down by |x-h|, and we will insert kern nodes that have the effect of
+centering the accent over the character and shifting the accent to the
+right by $\delta={1\over2}(w-a)+h\cdot t-x\cdot s$. If either character is
+absent from the font, we will simply use the other, without shifting.
+
+@<Declare act...@>=
+procedure make_accent;
+var s,@!t: real; {amount of slant}
+@!p,@!q,@!r:pointer; {character, box, and kern nodes}
+@!f:internal_font_number; {relevant font}
+@!a,@!h,@!x,@!w,@!delta:scaled; {heights and widths, as explained above}
+@!i:four_quarters; {character information}
+begin scan_char_num; f:=cur_font; p:=new_character(f,cur_val);
+if p<>null then
+ begin x:=x_height(f); s:=slant(f)/float_constant(65536);
+@^real division@>
+ a:=char_width(f)(char_info(f)(character(p)));@/
+ do_assignments;@/
+ @<Create a character node |q| for the next character,
+ but set |q:=null| if problems arise@>;
+ if q<>null then @<Append the accent with appropriate kerns,
+ then set |p:=q|@>;
+ link(tail):=p; tail:=p; space_factor:=1000;
+ end;
+end;
+
+@ @<Create a character node |q| for the next...@>=
+q:=null; f:=cur_font;
+if (cur_cmd=letter)or(cur_cmd=other_char)or(cur_cmd=char_given) then
+ q:=new_character(f,cur_chr)
+else if cur_cmd=char_num then
+ begin scan_char_num; q:=new_character(f,cur_val);
+ end
+else back_input
+
+@ The kern nodes appended here must be distinguished from other kerns, lest
+they be wiped away by the hyphenation algorithm or by a previous line break.
+
+The two kerns are computed with (machine-dependent) |real| arithmetic, but
+their sum is machine-independent; the net effect is machine-independent,
+because the user cannot remove these nodes nor access them via \.{\\lastkern}.
+
+@<Append the accent with appropriate kerns...@>=
+begin t:=slant(f)/float_constant(65536);
+@^real division@>
+i:=char_info(f)(character(q));
+w:=char_width(f)(i); h:=char_height(f)(height_depth(i));
+if h<>x then {the accent must be shifted up or down}
+ begin p:=hpack(p,natural); shift_amount(p):=x-h;
+ end;
+delta:=round((w-a)/float_constant(2)+h*t-x*s);
+@^real multiplication@>
+@^real addition@>
+r:=new_kern(delta); subtype(r):=acc_kern; link(tail):=r; link(r):=p;
+tail:=new_kern(-a-delta); subtype(tail):=acc_kern; link(p):=tail; p:=q;
+end
+
+@ When `\.{\\cr}' or `\.{\\span}' or a tab mark comes through the scanner
+into |main_control|, it might be that the user has foolishly inserted
+one of them into something that has nothing to do with alignment. But it is
+far more likely that a left brace or right brace has been omitted, since
+|get_next| takes actions appropriate to alignment only when `\.{\\cr}'
+or `\.{\\span}' or tab marks occur with |align_state=0|. The following
+program attempts to make an appropriate recovery.
+
+@<Cases of |main_control| that build...@>=
+any_mode(car_ret), any_mode(tab_mark): align_error;
+any_mode(no_align): no_align_error;
+any_mode(omit): omit_error;
+
+@ @<Declare act...@>=
+procedure align_error;
+begin if abs(align_state)>2 then
+ @<Express consternation over the fact that no alignment is in progress@>
+else begin back_input;
+ if align_state<0 then
+ begin print_err("Missing { inserted");
+@.Missing \{ inserted@>
+ incr(align_state); cur_tok:=left_brace_token+"{";
+ end
+ else begin print_err("Missing } inserted");
+@.Missing \} inserted@>
+ decr(align_state); cur_tok:=right_brace_token+"}";
+ end;
+ help3("I've put in what seems to be necessary to fix")@/
+ ("the current column of the current alignment.")@/
+ ("Try to go on, since this might almost work."); ins_error;
+ end;
+end;
+
+@ @<Express consternation...@>=
+begin print_err("Misplaced "); print_cmd_chr(cur_cmd,cur_chr);
+@.Misplaced \&@>
+@.Misplaced \\span@>
+@.Misplaced \\cr@>
+if cur_tok=tab_token+"&" then
+ begin help6("I can't figure out why you would want to use a tab mark")@/
+ ("here. If you just want an ampersand, the remedy is")@/
+ ("simple: Just type `I\&' now. But if some right brace")@/
+ ("up above has ended a previous alignment prematurely,")@/
+ ("you're probably due for more error messages, and you")@/
+ ("might try typing `S' now just to see what is salvageable.");
+ end
+else begin help5("I can't figure out why you would want to use a tab mark")@/
+ ("or \cr or \span just now. If something like a right brace")@/
+ ("up above has ended a previous alignment prematurely,")@/
+ ("you're probably due for more error messages, and you")@/
+ ("might try typing `S' now just to see what is salvageable.");
+ end;
+error;
+end
+
+@ The help messages here contain a little white lie, since \.{\\noalign}
+and \.{\\omit} are allowed also after `\.{\\noalign\{...\}}'.
+
+@<Declare act...@>=
+procedure no_align_error;
+begin print_err("Misplaced "); print_esc("noalign");
+@.Misplaced \\noalign@>
+help2("I expect to see \noalign only after the \cr of")@/
+ ("an alignment. Proceed, and I'll ignore this case."); error;
+end;
+procedure omit_error;
+begin print_err("Misplaced "); print_esc("omit");
+@.Misplaced \\omit@>
+help2("I expect to see \omit only after tab marks or the \cr of")@/
+ ("an alignment. Proceed, and I'll ignore this case."); error;
+end;
+
+@ We've now covered most of the abuses of \.{\\halign} and \.{\\valign}.
+Let's take a look at what happens when they are used correctly.
+
+@<Cases of |main_control| that build...@>=
+vmode+halign,hmode+valign:init_align;
+mmode+halign: if privileged then
+ if cur_group=math_shift_group then init_align
+ else off_save;
+vmode+endv,hmode+endv: do_endv;
+
+@ An |align_group| code is supposed to remain on the |save_stack|
+during an entire alignment, until |fin_align| removes it.
+
+A devious user might force an |endv| command to occur just about anywhere;
+we must defeat such hacks.
+
+@<Declare act...@>=
+procedure do_endv;
+begin base_ptr:=input_ptr; input_stack[base_ptr]:=cur_input;
+while (input_stack[base_ptr].index_field<>v_template) and
+ (input_stack[base_ptr].loc_field=null) and
+ (input_stack[base_ptr].state_field=token_list) do decr(base_ptr);
+if (input_stack[base_ptr].index_field<>v_template) or
+ (input_stack[base_ptr].loc_field<>null) or
+ (input_stack[base_ptr].state_field<>token_list) then
+ fatal_error("(interwoven alignment preambles are not allowed)");
+@.interwoven alignment preambles...@>
+ if cur_group=align_group then
+ begin end_graf;
+ if fin_col then fin_row;
+ end
+else off_save;
+end;
+
+@ @<Cases of |handle_right_brace|...@>=
+align_group: begin back_input; cur_tok:=cs_token_flag+frozen_cr;
+ print_err("Missing "); print_esc("cr"); print(" inserted");
+@.Missing \\cr inserted@>
+ help1("I'm guessing that you meant to end an alignment here.");
+ ins_error;
+ end;
+
+@ @<Cases of |handle_right_brace|...@>=
+no_align_group: begin end_graf; unsave; align_peek;
+ end;
+
+@ Finally, \.{\\endcsname} is not supposed to get through to |main_control|.
+
+@<Cases of |main_control| that build...@>=
+any_mode(end_cs_name): cs_error;
+
+@ @<Declare act...@>=
+procedure cs_error;
+begin print_err("Extra "); print_esc("endcsname");
+@.Extra \\endcsname@>
+help1("I'm ignoring this, since I wasn't doing a \csname.");
+error;
+end;
+
+@* \[48] Building math lists.
+The routines that \TeX\ uses to create mlists are similar to those we have
+just seen for the generation of hlists and vlists. But it is necessary to
+make ``noads'' as well as nodes, so the reader should review the
+discussion of math mode data structures before trying to make sense out of
+the following program.
+
+Here is a little routine that needs to be done whenever a subformula
+is about to be processed. The parameter is a code like |math_group|.
+
+@<Declare act...@>=
+procedure push_math(@!c:group_code);
+begin push_nest; mode:=-mmode; incompleat_noad:=null; new_save_level(c);
+end;
+
+@ We get into math mode from horizontal mode when a `\.\$' (i.e., a
+|math_shift| character) is scanned. We must check to see whether this
+`\.\$' is immediately followed by another, in case display math mode is
+called for.
+
+@<Cases of |main_control| that build...@>=
+hmode+math_shift:init_math;
+
+@ @<Declare act...@>=
+procedure init_math;
+label reswitch,found,not_found,done;
+var w:scaled; {new or partial |pre_display_size|}
+@!l:scaled; {new |display_width|}
+@!s:scaled; {new |display_indent|}
+@!p:pointer; {current node when calculating |pre_display_size|}
+@!q:pointer; {glue specification when calculating |pre_display_size|}
+@!f:internal_font_number; {font in current |char_node|}
+@!n:integer; {scope of paragraph shape specification}
+@!v:scaled; {|w| plus possible glue amount}
+@!d:scaled; {increment to |v|}
+begin get_token; {|get_x_token| would fail on \.{\\ifmmode}\thinspace!}
+if (cur_cmd=math_shift)and(mode>0) then @<Go into display math mode@>
+else begin back_input; @<Go into ordinary math mode@>;
+ end;
+end;
+
+@ @<Go into ordinary math mode@>=
+begin push_math(math_shift_group); eq_word_define(int_base+cur_fam_code,-1);
+if every_math<>null then begin_token_list(every_math,every_math_text);
+end
+
+@ We get into ordinary math mode from display math mode when `\.{\\eqno}' or
+`\.{\\leqno}' appears. In such cases |cur_chr| will be 0 or~1, respectively;
+the value of |cur_chr| is placed onto |save_stack| for safe keeping.
+
+@<Cases of |main_control| that build...@>=
+mmode+eq_no: if privileged then
+ if cur_group=math_shift_group then start_eq_no
+ else off_save;
+
+@ @<Put each...@>=
+primitive("eqno",eq_no,0);
+@!@:eq_no_}{\.{\\eqno} primitive@>
+primitive("leqno",eq_no,1);
+@!@:leq_no_}{\.{\\leqno} primitive@>
+
+@ When \TeX\ is in display math mode, |cur_group=math_shift_group|,
+so it is not necessary for the |start_eq_no| procedure to test for
+this condition.
+
+@<Declare act...@>=
+procedure start_eq_no;
+begin saved(0):=cur_chr; incr(save_ptr);
+@<Go into ordinary math mode@>;
+end;
+
+@ @<Cases of |print_cmd_chr|...@>=
+eq_no:if chr_code=1 then print_esc("leqno")@+else print_esc("eqno");
+
+@ @<Forbidden...@>=non_math(eq_no),
+
+@ When we enter display math mode, we need to call |line_break| to
+process the partial paragraph that has just been interrupted by the
+display. Then we can set the proper values of |display_width| and
+|display_indent| and |pre_display_size|.
+
+@<Go into display math mode@>=
+begin if head=tail then {`\.{\\noindent\$\$}' or `\.{\$\${ }\$\$}'}
+ begin pop_nest; w:=-max_dimen;
+ end
+else begin line_break(display_widow_penalty);@/
+ @<Calculate the natural width, |w|, by which the characters of the
+ final line extend to the right of the reference point,
+ plus two ems; or set |w:=max_dimen| if the non-blank information
+ on that line is affected by stretching or shrinking@>;
+ end;
+{now we are in vertical mode, working on the list that will contain the display}
+@<Calculate the length, |l|, and the shift amount, |s|, of the display lines@>;
+push_math(math_shift_group); mode:=mmode;
+eq_word_define(int_base+cur_fam_code,-1);@/
+eq_word_define(dimen_base+pre_display_size_code,w);
+eq_word_define(dimen_base+display_width_code,l);
+eq_word_define(dimen_base+display_indent_code,s);
+if every_display<>null then begin_token_list(every_display,every_display_text);
+if nest_ptr=1 then build_page;
+end
+
+@ @<Calculate the natural width, |w|, by which...@>=
+v:=shift_amount(just_box)+2*quad(cur_font); w:=-max_dimen;
+p:=list_ptr(just_box);
+while p<>null do
+ begin @<Let |d| be the natural width of node |p|;
+ if the node is ``visible,'' |goto found|;
+ if the node is glue that stretches or shrinks, set |v:=max_dimen|@>;
+ if v<max_dimen then v:=v+d;
+ goto not_found;
+ found: if v<max_dimen then
+ begin v:=v+d; w:=v;
+ end
+ else begin w:=max_dimen; goto done;
+ end;
+ not_found: p:=link(p);
+ end;
+done:
+
+@ @<Let |d| be the natural width of node |p|...@>=
+reswitch: if is_char_node(p) then
+ begin f:=font(p); d:=char_width(f)(char_info(f)(character(p)));
+ goto found;
+ end;
+case type(p) of
+hlist_node,vlist_node,rule_node: begin d:=width(p); goto found;
+ end;
+ligature_node:@<Make node |p| look like a |char_node|...@>;
+kern_node,math_node: d:=width(p);
+glue_node:@<Let |d| be the natural width of this glue; if stretching
+ or shrinking, set |v:=max_dimen|; |goto found| in the case of leaders@>;
+whatsit_node: @<Let |d| be the width of the whatsit |p|@>;
+othercases d:=0
+endcases
+
+@ We need to be careful that |w|, |v|, and |d| do not depend on any |glue_set|
+values, since such values are subject to system-dependent rounding.
+System-dependent numbers are not allowed to infiltrate parameters like
+|pre_display_size|, since \TeX82 is supposed to make the same decisions on all
+machines.
+
+@<Let |d| be the natural width of this glue...@>=
+begin q:=glue_ptr(p); d:=width(q);
+if glue_sign(just_box)=stretching then
+ begin if (glue_order(just_box)=stretch_order(q))and@|
+ (stretch(q)<>0) then
+ v:=max_dimen;
+ end
+else if glue_sign(just_box)=shrinking then
+ begin if (glue_order(just_box)=shrink_order(q))and@|
+ (shrink(q)<>0) then
+ v:=max_dimen;
+ end;
+if subtype(p)>=a_leaders then goto found;
+end
+
+@ A displayed equation is considered to be three lines long, so we
+calculate the length and offset of line number |prev_graf+2|.
+
+@<Calculate the length, |l|, ...@>=
+if par_shape_ptr=null then
+ if (hang_indent<>0)and@|
+ (((hang_after>=0)and(prev_graf+2>hang_after))or@|
+ (prev_graf+1<-hang_after)) then
+ begin l:=hsize-abs(hang_indent);
+ if hang_indent>0 then s:=hang_indent@+else s:=0;
+ end
+ else begin l:=hsize; s:=0;
+ end
+else begin n:=info(par_shape_ptr);
+ if prev_graf+2>=n then p:=par_shape_ptr+2*n
+ else p:=par_shape_ptr+2*(prev_graf+2);
+ s:=mem[p-1].sc; l:=mem[p].sc;
+ end
+
+@ Subformulas of math formulas cause a new level of math mode to be entered,
+on the semantic nest as well as the save stack. These subformulas arise in
+several ways: (1)~A left brace by itself indicates the beginning of a
+subformula that will be put into a box, thereby freezing its glue and
+preventing line breaks. (2)~A subscript or superscript is treated as a
+subformula if it is not a single character; the same applies to
+the nucleus of things like \.{\\underline}. (3)~The \.{\\left} primitive
+initiates a subformula that will be terminated by a matching \.{\\right}.
+The group codes placed on |save_stack| in these three cases are
+|math_group|, |math_group|, and |math_left_group|, respectively.
+
+Here is the code that handles case (1); the other cases are not quite as
+trivial, so we shall consider them later.
+
+@<Cases of |main_control| that build...@>=
+mmode+left_brace: begin tail_append(new_noad);
+ back_input; scan_math(nucleus(tail));
+ end;
+
+@ Recall that the |nucleus|, |subscr|, and |supscr| fields in a noad are
+broken down into subfields called |math_type| and either |info| or
+|(fam,character)|. The job of |scan_math| is to figure out what to place
+in one of these principal fields; it looks at the subformula that
+comes next in the input, and places an encoding of that subformula
+into a given word of |mem|.
+
+@d fam_in_range==((cur_fam>=0)and(cur_fam<16))
+
+@<Declare act...@>=
+procedure scan_math(@!p:pointer);
+label restart,reswitch,exit;
+var c:integer; {math character code}
+begin restart:@<Get the next non-blank non-relax...@>;
+reswitch:case cur_cmd of
+letter,other_char,char_given: begin c:=ho(math_code(cur_chr));
+ if c=@'100000 then
+ begin @<Treat |cur_chr| as an active character@>;
+ goto restart;
+ end;
+ end;
+char_num: begin scan_char_num; cur_chr:=cur_val; cur_cmd:=char_given;
+ goto reswitch;
+ end;
+math_char_num: begin scan_fifteen_bit_int; c:=cur_val;
+ end;
+math_given: c:=cur_chr;
+delim_num: begin scan_twenty_seven_bit_int; c:=cur_val div @'10000;
+ end;
+othercases @<Scan a subformula enclosed in braces and |return|@>
+endcases;@/
+math_type(p):=math_char; character(p):=qi(c mod 256);
+if (c>=var_code)and fam_in_range then fam(p):=cur_fam
+else fam(p):=(c div 256) mod 16;
+exit:end;
+
+@ An active character that is an |outer_call| is allowed here.
+
+@<Treat |cur_chr|...@>=
+begin cur_cs:=cur_chr+active_base;
+cur_cmd:=eq_type(cur_cs); cur_chr:=equiv(cur_cs);
+x_token; back_input;
+end
+
+@ The pointer |p| is placed on |save_stack| while a complex subformula
+is being scanned.
+
+@<Scan a subformula...@>=
+begin back_input; scan_left_brace;@/
+saved(0):=p; incr(save_ptr); push_math(math_group); return;
+end
+
+@ The simplest math formula is, of course, `\.{\${ }\$}', when no noads are
+generated. The next simplest cases involve a single character, e.g.,
+`\.{\$x\$}'. Even though such cases may not seem to be very interesting,
+the reader can perhaps understand how happy the author was when `\.{\$x\$}'
+was first properly typeset by \TeX. The code in this section was used.
+@^Knuth, Donald Ervin@>
+
+@<Cases of |main_control| that build...@>=
+mmode+letter,mmode+other_char,mmode+char_given:
+ set_math_char(ho(math_code(cur_chr)));
+mmode+char_num: begin scan_char_num; cur_chr:=cur_val;
+ set_math_char(ho(math_code(cur_chr)));
+ end;
+mmode+math_char_num: begin scan_fifteen_bit_int; set_math_char(cur_val);
+ end;
+mmode+math_given: set_math_char(cur_chr);
+mmode+delim_num: begin scan_twenty_seven_bit_int;
+ set_math_char(cur_val div @'10000);
+ end;
+
+@ The |set_math_char| procedure creates a new noad appropriate to a given
+math code, and appends it to the current mlist. However, if the math code
+is sufficiently large, the |cur_chr| is treated as an active character and
+nothing is appended.
+
+@<Declare act...@>=
+procedure set_math_char(@!c:integer);
+var p:pointer; {the new noad}
+begin if c>=@'100000 then
+ @<Treat |cur_chr|...@>
+else begin p:=new_noad; math_type(nucleus(p)):=math_char;
+ character(nucleus(p)):=qi(c mod 256);
+ fam(nucleus(p)):=(c div 256) mod 16;
+ if c>=var_code then
+ begin if fam_in_range then fam(nucleus(p)):=cur_fam;
+ type(p):=ord_noad;
+ end
+ else type(p):=ord_noad+(c div @'10000);
+ link(tail):=p; tail:=p;
+ end;
+end;
+
+@ Primitive math operators like \.{\\mathop} and \.{\\underline} are given
+the command code |math_comp|, supplemented by the noad type that they
+generate.
+
+@<Put each...@>=
+primitive("mathord",math_comp,ord_noad);
+@!@:math_ord_}{\.{\\mathord} primitive@>
+primitive("mathop",math_comp,op_noad);
+@!@:math_op_}{\.{\\mathop} primitive@>
+primitive("mathbin",math_comp,bin_noad);
+@!@:math_bin_}{\.{\\mathbin} primitive@>
+primitive("mathrel",math_comp,rel_noad);
+@!@:math_rel_}{\.{\\mathrel} primitive@>
+primitive("mathopen",math_comp,open_noad);
+@!@:math_open_}{\.{\\mathopen} primitive@>
+primitive("mathclose",math_comp,close_noad);
+@!@:math_close_}{\.{\\mathclose} primitive@>
+primitive("mathpunct",math_comp,punct_noad);
+@!@:math_punct_}{\.{\\mathpunct} primitive@>
+primitive("mathinner",math_comp,inner_noad);
+@!@:math_inner_}{\.{\\mathinner} primitive@>
+primitive("underline",math_comp,under_noad);
+@!@:underline_}{\.{\\underline} primitive@>
+primitive("overline",math_comp,over_noad);@/
+@!@:overline_}{\.{\\overline} primitive@>
+primitive("displaylimits",limit_switch,normal);
+@!@:display_limits_}{\.{\\displaylimits} primitive@>
+primitive("limits",limit_switch,limits);
+@!@:limits_}{\.{\\limits} primitive@>
+primitive("nolimits",limit_switch,no_limits);
+@!@:no_limits_}{\.{\\nolimits} primitive@>
+
+@ @<Cases of |print_cmd_chr|...@>=
+math_comp: case chr_code of
+ ord_noad: print_esc("mathord");
+ op_noad: print_esc("mathop");
+ bin_noad: print_esc("mathbin");
+ rel_noad: print_esc("mathrel");
+ open_noad: print_esc("mathopen");
+ close_noad: print_esc("mathclose");
+ punct_noad: print_esc("mathpunct");
+ inner_noad: print_esc("mathinner");
+ under_noad: print_esc("underline");
+ othercases print_esc("overline")
+ endcases;
+limit_switch: if chr_code=limits then print_esc("limits")
+ else if chr_code=no_limits then print_esc("nolimits")
+ else print_esc("displaylimits");
+
+@ @<Cases of |main_control| that build...@>=
+mmode+math_comp: begin tail_append(new_noad);
+ type(tail):=cur_chr; scan_math(nucleus(tail));
+ end;
+mmode+limit_switch: math_limit_switch;
+
+@ @<Declare act...@>=
+procedure math_limit_switch;
+label exit;
+begin if head<>tail then if type(tail)=op_noad then
+ begin subtype(tail):=cur_chr; return;
+ end;
+print_err("Limit controls must follow a math operator");
+@.Limit controls must follow...@>
+help1("I'm ignoring this misplaced \limits or \nolimits command."); error;
+exit:end;
+
+@ Delimiter fields of noads are filled in by the |scan_delimiter| routine.
+The first parameter of this procedure is the |mem| address where the
+delimiter is to be placed; the second tells if this delimiter follows
+\.{\\radical} or not.
+
+@<Declare act...@>=
+procedure scan_delimiter(@!p:pointer;@!r:boolean);
+begin if r then scan_twenty_seven_bit_int
+else begin @<Get the next non-blank non-relax...@>;
+ case cur_cmd of
+ letter,other_char: cur_val:=del_code(cur_chr);
+ delim_num: scan_twenty_seven_bit_int;
+ othercases cur_val:=-1
+ endcases;
+ end;
+if cur_val<0 then @<Report that an invalid delimiter code is being changed
+ to null; set~|cur_val:=0|@>;
+small_fam(p):=(cur_val div @'4000000) mod 16;
+small_char(p):=qi((cur_val div @'10000) mod 256);
+large_fam(p):=(cur_val div 256) mod 16;
+large_char(p):=qi(cur_val mod 256);
+end;
+
+@ @<Report that an invalid delimiter...@>=
+begin print_err("Missing delimiter (. inserted)");
+@.Missing delimiter...@>
+help6("I was expecting to see something like `(' or `\{' or")@/
+ ("`\}' here. If you typed, e.g., `{' instead of `\{', you")@/
+ ("should probably delete the `{' by typing `1' now, so that")@/
+ ("braces don't get unbalanced. Otherwise just proceed.")@/
+ ("Acceptable delimiters are characters whose \delcode is")@/
+ ("nonnegative, or you can use `\delimiter <delimiter code>'.");
+back_error; cur_val:=0;
+end
+
+@ @<Cases of |main_control| that build...@>=
+mmode+radical:math_radical;
+
+@ @<Declare act...@>=
+procedure math_radical;
+begin tail_append(get_node(radical_noad_size));
+type(tail):=radical_noad; subtype(tail):=normal;
+mem[nucleus(tail)].hh:=empty_field;
+mem[subscr(tail)].hh:=empty_field;
+mem[supscr(tail)].hh:=empty_field;
+scan_delimiter(left_delimiter(tail),true); scan_math(nucleus(tail));
+end;
+
+@ @<Cases of |main_control| that build...@>=
+mmode+accent,mmode+math_accent:math_ac;
+
+@ @<Declare act...@>=
+procedure math_ac;
+begin if cur_cmd=accent then
+ @<Complain that the user should have said \.{\\mathaccent}@>;
+tail_append(get_node(accent_noad_size));
+type(tail):=accent_noad; subtype(tail):=normal;
+mem[nucleus(tail)].hh:=empty_field;
+mem[subscr(tail)].hh:=empty_field;
+mem[supscr(tail)].hh:=empty_field;
+math_type(accent_chr(tail)):=math_char;
+scan_fifteen_bit_int;
+character(accent_chr(tail)):=qi(cur_val mod 256);
+if (cur_val>=var_code)and fam_in_range then fam(accent_chr(tail)):=cur_fam
+else fam(accent_chr(tail)):=(cur_val div 256) mod 16;
+scan_math(nucleus(tail));
+end;
+
+@ @<Complain that the user should have said \.{\\mathaccent}@>=
+begin print_err("Please use "); print_esc("mathaccent");
+print(" for accents in math mode");
+@.Please use \\mathaccent...@>
+help2("I'm changing \accent to \mathaccent here; wish me luck.")@/
+ ("(Accents are not the same in formulas as they are in text.)");
+error;
+end
+
+@ @<Cases of |main_control| that build...@>=
+mmode+vcenter: begin scan_spec(vcenter_group,false); normal_paragraph;
+ push_nest; mode:=-vmode; prev_depth:=ignore_depth;
+ if every_vbox<>null then begin_token_list(every_vbox,every_vbox_text);
+ end;
+
+@ @<Cases of |handle...@>=
+vcenter_group: begin end_graf; unsave; save_ptr:=save_ptr-2;
+ p:=vpack(link(head),saved(1),saved(0)); pop_nest;
+ tail_append(new_noad); type(tail):=vcenter_noad;
+ math_type(nucleus(tail)):=sub_box; info(nucleus(tail)):=p;
+ end;
+
+@ The routine that inserts a |style_node| holds no surprises.
+
+@<Put each...@>=
+primitive("displaystyle",math_style,display_style);
+@!@:display_style_}{\.{\\displaystyle} primitive@>
+primitive("textstyle",math_style,text_style);
+@!@:text_style_}{\.{\\textstyle} primitive@>
+primitive("scriptstyle",math_style,script_style);
+@!@:script_style_}{\.{\\scriptstyle} primitive@>
+primitive("scriptscriptstyle",math_style,script_script_style);
+@!@:script_script_style_}{\.{\\scriptscriptstyle} primitive@>
+
+@ @<Cases of |print_cmd_chr|...@>=
+math_style: print_style(chr_code);
+
+@ @<Cases of |main_control| that build...@>=
+mmode+math_style: tail_append(new_style(cur_chr));
+mmode+non_script: begin tail_append(new_glue(zero_glue));
+ subtype(tail):=cond_math_glue;
+ end;
+mmode+math_choice: append_choices;
+
+@ The routine that scans the four mlists of a \.{\\mathchoice} is very
+much like the routine that builds discretionary nodes.
+
+@<Declare act...@>=
+procedure append_choices;
+begin tail_append(new_choice); incr(save_ptr); saved(-1):=0;
+push_math(math_choice_group); scan_left_brace;
+end;
+
+@ @<Cases of |handle_right_brace|...@>=
+math_choice_group: build_choices;
+
+@ @<Declare act...@>=
+@t\4@>@<Declare the function called |fin_mlist|@>@t@>@;@/
+procedure build_choices;
+label exit;
+var p:pointer; {the current mlist}
+begin unsave; p:=fin_mlist(null);
+case saved(-1) of
+0:display_mlist(tail):=p;
+1:text_mlist(tail):=p;
+2:script_mlist(tail):=p;
+3:begin script_script_mlist(tail):=p; decr(save_ptr); return;
+ end;
+end; {there are no other cases}
+incr(saved(-1)); push_math(math_choice_group); scan_left_brace;
+exit:end;
+
+@ Subscripts and superscripts are attached to the previous nucleus by the
+@^superscripts@>@^subscripts@>
+action procedure called |sub_sup|. We use the facts that |sub_mark=sup_mark+1|
+and |subscr(p)=supscr(p)+1|.
+
+@<Cases of |main_control| that build...@>=
+mmode+sub_mark,mmode+sup_mark: sub_sup;
+
+@ @<Declare act...@>=
+procedure sub_sup;
+var t:small_number; {type of previous sub/superscript}
+@!p:pointer; {field to be filled by |scan_math|}
+begin t:=empty; p:=null;
+if tail<>head then if scripts_allowed(tail) then
+ begin p:=supscr(tail)+cur_cmd-sup_mark; {|supscr| or |subscr|}
+ t:=math_type(p);
+ end;
+if (p=null)or(t<>empty) then @<Insert a dummy noad to be sub/superscripted@>;
+scan_math(p);
+end;
+
+@ @<Insert a dummy...@>=
+begin tail_append(new_noad);
+p:=supscr(tail)+cur_cmd-sup_mark; {|supscr| or |subscr|}
+if t<>empty then
+ begin if cur_cmd=sup_mark then
+ begin print_err("Double superscript");
+@.Double superscript@>
+ help1("I treat `x^1^2' essentially like `x^1{}^2'.");
+ end
+ else begin print_err("Double subscript");
+@.Double subscript@>
+ help1("I treat `x_1_2' essentially like `x_1{}_2'.");
+ end;
+ error;
+ end;
+end
+
+@ An operation like `\.{\\over}' causes the current mlist to go into a
+state of suspended animation: |incompleat_noad| points to a |fraction_noad|
+that contains the mlist-so-far as its numerator, while the denominator
+is yet to come. Finally when the mlist is finished, the denominator will
+go into the incompleat fraction noad, and that noad will become the
+whole formula, unless it is surrounded by `\.{\\left}' and `\.{\\right}'
+delimiters.
+
+@d above_code=0 { `\.{\\above}' }
+@d over_code=1 { `\.{\\over}' }
+@d atop_code=2 { `\.{\\atop}' }
+@d delimited_code=3 { `\.{\\abovewithdelims}', etc.}
+
+@<Put each...@>=
+primitive("above",above,above_code);@/
+@!@:above_}{\.{\\above} primitive@>
+primitive("over",above,over_code);@/
+@!@:over_}{\.{\\over} primitive@>
+primitive("atop",above,atop_code);@/
+@!@:atop_}{\.{\\atop} primitive@>
+primitive("abovewithdelims",above,delimited_code+above_code);@/
+@!@:above_with_delims_}{\.{\\abovewithdelims} primitive@>
+primitive("overwithdelims",above,delimited_code+over_code);@/
+@!@:over_with_delims_}{\.{\\overwithdelims} primitive@>
+primitive("atopwithdelims",above,delimited_code+atop_code);
+@!@:atop_with_delims_}{\.{\\atopwithdelims} primitive@>
+
+@ @<Cases of |print_cmd_chr|...@>=
+above: case chr_code of
+ over_code:print_esc("over");
+ atop_code:print_esc("atop");
+ delimited_code+above_code:print_esc("abovewithdelims");
+ delimited_code+over_code:print_esc("overwithdelims");
+ delimited_code+atop_code:print_esc("atopwithdelims");
+ othercases print_esc("above")
+ endcases;
+
+@ @<Cases of |main_control| that build...@>=
+mmode+above: math_fraction;
+
+@ @<Declare act...@>=
+procedure math_fraction;
+var c:small_number; {the type of generalized fraction we are scanning}
+begin c:=cur_chr;
+if incompleat_noad<>null then
+ @<Ignore the fraction operation and complain about this ambiguous case@>
+else begin incompleat_noad:=get_node(fraction_noad_size);
+ type(incompleat_noad):=fraction_noad;
+ subtype(incompleat_noad):=normal;
+ math_type(numerator(incompleat_noad)):=sub_mlist;
+ info(numerator(incompleat_noad)):=link(head);
+ mem[denominator(incompleat_noad)].hh:=empty_field;
+ mem[left_delimiter(incompleat_noad)].qqqq:=null_delimiter;
+ mem[right_delimiter(incompleat_noad)].qqqq:=null_delimiter;@/
+ link(head):=null; tail:=head;
+ @<Use code |c| to distinguish between generalized fractions@>;
+ end;
+end;
+
+@ @<Use code |c|...@>=
+if c>=delimited_code then
+ begin scan_delimiter(left_delimiter(incompleat_noad),false);
+ scan_delimiter(right_delimiter(incompleat_noad),false);
+ end;
+case c mod delimited_code of
+above_code: begin scan_normal_dimen;
+ thickness(incompleat_noad):=cur_val;
+ end;
+over_code: thickness(incompleat_noad):=default_code;
+atop_code: thickness(incompleat_noad):=0;
+end {there are no other cases}
+
+@ @<Ignore the fraction...@>=
+begin if c>=delimited_code then
+ begin scan_delimiter(garbage,false); scan_delimiter(garbage,false);
+ end;
+if c mod delimited_code=above_code then scan_normal_dimen;
+print_err("Ambiguous; you need another { and }");
+@.Ambiguous...@>
+help3("I'm ignoring this fraction specification, since I don't")@/
+ ("know whether a construction like `x \over y \over z'")@/
+ ("means `{x \over y} \over z' or `x \over {y \over z}'.");
+error;
+end
+
+@ At the end of a math formula or subformula, the |fin_mlist| routine is
+called upon to return a pointer to the newly completed mlist, and to
+pop the nest back to the enclosing semantic level. The parameter to
+|fin_mlist|, if not null, points to a |right_noad| that ends the
+current mlist; this |right_noad| has not yet been appended.
+
+@<Declare the function called |fin_mlist|@>=
+function fin_mlist(@!p:pointer):pointer;
+var q:pointer; {the mlist to return}
+begin if incompleat_noad<>null then @<Compleat the incompleat noad@>
+else begin link(tail):=p; q:=link(head);
+ end;
+pop_nest; fin_mlist:=q;
+end;
+
+@ @<Compleat...@>=
+begin math_type(denominator(incompleat_noad)):=sub_mlist;
+info(denominator(incompleat_noad)):=link(head);
+if p=null then q:=incompleat_noad
+else begin q:=info(numerator(incompleat_noad));
+ if type(q)<>left_noad then confusion("right");
+@:this can't happen right}{\quad right@>
+ info(numerator(incompleat_noad)):=link(q);
+ link(q):=incompleat_noad; link(incompleat_noad):=p;
+ end;
+end
+
+@ Now at last we're ready to see what happens when a right brace occurs
+in a math formula. Two special cases are simplified here: Braces are effectively
+removed when they surround a single Ord without sub/superscripts, or when they
+surround an accent that is the nucleus of an Ord atom.
+
+@<Cases of |handle...@>=
+math_group: begin unsave; decr(save_ptr);@/
+ math_type(saved(0)):=sub_mlist; p:=fin_mlist(null); info(saved(0)):=p;
+ if p<>null then if link(p)=null then
+ if type(p)=ord_noad then
+ begin if math_type(subscr(p))=empty then
+ if math_type(supscr(p))=empty then
+ begin mem[saved(0)].hh:=mem[nucleus(p)].hh;
+ free_node(p,noad_size);
+ end;
+ end
+ else if type(p)=accent_noad then if saved(0)=nucleus(tail) then
+ if type(tail)=ord_noad then @<Replace the tail of the list by |p|@>;
+ end;
+
+@ @<Replace the tail...@>=
+begin q:=head; while link(q)<>tail do q:=link(q);
+link(q):=p; free_node(tail,noad_size); tail:=p;
+end
+
+@ We have dealt with all constructions of math mode except `\.{\\left}' and
+`\.{\\right}', so the picture is completed by the following sections of
+the program.
+
+@<Put each...@>=
+primitive("left",left_right,left_noad);
+@!@:left_}{\.{\\left} primitive@>
+primitive("right",left_right,right_noad);
+@!@:right_}{\.{\\right} primitive@>
+text(frozen_right):="right"; eqtb[frozen_right]:=eqtb[cur_val];
+
+@ @<Cases of |print_cmd_chr|...@>=
+left_right: if chr_code=left_noad then print_esc("left")
+else print_esc("right");
+
+@ @<Cases of |main_control| that build...@>=
+mmode+left_right: math_left_right;
+
+@ @<Declare act...@>=
+procedure math_left_right;
+var t:small_number; {|left_noad| or |right_noad|}
+@!p:pointer; {new noad}
+begin t:=cur_chr;
+if (t=right_noad)and(cur_group<>math_left_group) then
+ @<Try to recover from mismatched \.{\\right}@>
+else begin p:=new_noad; type(p):=t;
+ scan_delimiter(delimiter(p),false);
+ if t=left_noad then
+ begin push_math(math_left_group); link(head):=p; tail:=p;
+ end
+ else begin p:=fin_mlist(p); unsave; {end of |math_left_group|}
+ tail_append(new_noad); type(tail):=inner_noad;
+ math_type(nucleus(tail)):=sub_mlist;
+ info(nucleus(tail)):=p;
+ end;
+ end;
+end;
+
+@ @<Try to recover from mismatch...@>=
+begin if cur_group=math_shift_group then
+ begin scan_delimiter(garbage,false);
+ print_err("Extra "); print_esc("right");
+@.Extra \\right.@>
+ help1("I'm ignoring a \right that had no matching \left.");
+ error;
+ end
+else off_save;
+end
+
+@ Here is the only way out of math mode.
+
+@<Cases of |main_control| that build...@>=
+mmode+math_shift: if cur_group=math_shift_group then after_math
+ else off_save;
+
+@ @<Declare act...@>=
+procedure after_math;
+var l:boolean; {`\.{\\leqno}' instead of `\.{\\eqno}'}
+@!danger:boolean; {not enough symbol fonts are present}
+@!m:integer; {|mmode| or |-mmode|}
+@!p:pointer; {the formula}
+@!a:pointer; {box containing equation number}
+@<Local variables for finishing a displayed formula@>@;
+begin danger:=false;
+@<Check that the necessary fonts for math symbols are present;
+ if not, flush the current math lists and set |danger:=true|@>;
+m:=mode; l:=false; p:=fin_mlist(null); {this pops the nest}
+if mode=-m then {end of equation number}
+ begin @<Check that another \.\$ follows@>;
+ cur_mlist:=p; cur_style:=text_style; mlist_penalties:=false;
+ mlist_to_hlist; a:=hpack(link(temp_head),natural);
+ unsave; decr(save_ptr); {now |cur_group=math_shift_group|}
+ if saved(0)=1 then l:=true;
+ danger:=false;
+ @<Check that the necessary fonts for math symbols are present;
+ if not, flush the current math lists and set |danger:=true|@>;
+ m:=mode; p:=fin_mlist(null);
+ end
+else a:=null;
+if m<0 then @<Finish math in text@>
+else begin if a=null then @<Check that another \.\$ follows@>;
+ @<Finish displayed math@>;
+ end;
+end;
+
+@ @<Check that the necessary fonts...@>=
+if (font_params[fam_fnt(2+text_size)]<total_mathsy_params)or@|
+ (font_params[fam_fnt(2+script_size)]<total_mathsy_params)or@|
+ (font_params[fam_fnt(2+script_script_size)]<total_mathsy_params) then
+ begin print_err("Math formula deleted: Insufficient symbol fonts");@/
+@.Math formula deleted...@>
+ help3("Sorry, but I can't typeset math unless \textfont 2")@/
+ ("and \scriptfont 2 and \scriptscriptfont 2 have all")@/
+ ("the \fontdimen values needed in math symbol fonts.");
+ error; flush_math; danger:=true;
+ end
+else if (font_params[fam_fnt(3+text_size)]<total_mathex_params)or@|
+ (font_params[fam_fnt(3+script_size)]<total_mathex_params)or@|
+ (font_params[fam_fnt(3+script_script_size)]<total_mathex_params) then
+ begin print_err("Math formula deleted: Insufficient extension fonts");@/
+ help3("Sorry, but I can't typeset math unless \textfont 3")@/
+ ("and \scriptfont 3 and \scriptscriptfont 3 have all")@/
+ ("the \fontdimen values needed in math extension fonts.");
+ error; flush_math; danger:=true;
+ end
+
+@ The |unsave| is done after everything else here; hence an appearance of
+`\.{\\mathsurround}' inside of `\.{\$...\$}' affects the spacing at these
+particular \.\$'s. This is consistent with the conventions of
+`\.{\$\$...\$\$}', since `\.{\\abovedisplayskip}' inside a display affects the
+space above that display.
+
+@<Finish math in text@>=
+begin tail_append(new_math(math_surround,before));
+cur_mlist:=p; cur_style:=text_style; mlist_penalties:=(mode>0); mlist_to_hlist;
+link(tail):=link(temp_head);
+while link(tail)<>null do tail:=link(tail);
+tail_append(new_math(math_surround,after));
+space_factor:=1000; unsave;
+end
+
+@ \TeX\ gets to the following part of the program when the first `\.\$' ending
+a display has been scanned.
+
+@<Check that another \.\$ follows@>=
+begin get_x_token;
+if cur_cmd<>math_shift then
+ begin print_err("Display math should end with $$");
+@.Display math...with \$\$@>
+ help2("The `$' that I just saw supposedly matches a previous `$$'.")@/
+ ("So I shall assume that you typed `$$' both times.");
+ back_error;
+ end;
+end
+
+@ We have saved the worst for last: The fussiest part of math mode processing
+occurs when a displayed formula is being centered and placed with an optional
+equation number.
+
+@<Local variables for finishing...@>=
+@!b:pointer; {box containing the equation}
+@!w:scaled; {width of the equation}
+@!z:scaled; {width of the line}
+@!e:scaled; {width of equation number}
+@!q:scaled; {width of equation number plus space to separate from equation}
+@!d:scaled; {displacement of equation in the line}
+@!s:scaled; {move the line right this much}
+@!g1,@!g2:small_number; {glue parameter codes for before and after}
+@!r:pointer; {kern node used to position the display}
+@!t:pointer; {tail of adjustment list}
+
+@ At this time |p| points to the mlist for the formula; |a| is either
+|null| or it points to a box containing the equation number; and we are in
+vertical mode (or internal vertical mode).
+
+@<Finish displayed math@>=
+cur_mlist:=p; cur_style:=display_style; mlist_penalties:=false;
+mlist_to_hlist; p:=link(temp_head);@/
+adjust_tail:=adjust_head; b:=hpack(p,natural); p:=list_ptr(b);
+t:=adjust_tail; adjust_tail:=null;@/
+w:=width(b); z:=display_width; s:=display_indent;
+if (a=null)or danger then
+ begin e:=0; q:=0;
+ end
+else begin e:=width(a); q:=e+math_quad(text_size);
+ end;
+if w+q>z then
+ @<Squeeze the equation as much as possible; if there is an equation
+ number that should go on a separate line by itself,
+ set~|e:=0|@>;
+@<Determine the displacement, |d|, of the left edge of the equation, with
+ respect to the line size |z|, assuming that |l=false|@>;
+@<Append the glue or equation number preceding the display@>;
+@<Append the display and perhaps also the equation number@>;
+@<Append the glue or equation number following the display@>;
+resume_after_display
+
+@ @<Declare act...@>=
+procedure resume_after_display;
+begin if cur_group<>math_shift_group then confusion("display");
+@:this can't happen display}{\quad display@>
+unsave; prev_graf:=prev_graf+3;
+push_nest; mode:=hmode; space_factor:=1000; set_cur_lang; clang:=cur_lang;
+prev_graf:=(norm_min(left_hyphen_min)*@'100+norm_min(right_hyphen_min))
+ *@'200000+cur_lang;
+@<Scan an optional space@>;
+if nest_ptr=1 then build_page;
+end;
+
+@ The user can force the equation number to go on a separate line
+by causing its width to be zero.
+
+@<Squeeze the equation as much as possible...@>=
+begin if (e<>0)and((w-total_shrink[normal]+q<=z)or@|
+ (total_shrink[fil]<>0)or(total_shrink[fill]<>0)or
+ (total_shrink[filll]<>0)) then
+ begin free_node(b,box_node_size);
+ b:=hpack(p,z-q,exactly);
+ end
+else begin e:=0;
+ if w>z then
+ begin free_node(b,box_node_size);
+ b:=hpack(p,z,exactly);
+ end;
+ end;
+w:=width(b);
+end
+
+@ We try first to center the display without regard to the existence of
+the equation number. If that would make it too close (where ``too close''
+means that the space between display and equation number is less than the
+width of the equation number), we either center it in the remaining space
+or move it as far from the equation number as possible. The latter alternative
+is taken only if the display begins with glue, since we assume that the
+user put glue there to control the spacing precisely.
+
+@<Determine the displacement, |d|, of the left edge of the equation...@>=
+d:=half(z-w);
+if (e>0)and(d<2*e) then {too close}
+ begin d:=half(z-w-e);
+ if p<>null then if not is_char_node(p) then if type(p)=glue_node then d:=0;
+ end
+
+@ If the equation number is set on a line by itself, either before or
+after the formula, we append an infinite penalty so that no page break will
+separate the display from its number; and we use the same size and
+displacement for all three potential lines of the display, even though
+`\.{\\parshape}' may specify them differently.
+
+@<Append the glue or equation number preceding the display@>=
+tail_append(new_penalty(pre_display_penalty));@/
+if (d+s<=pre_display_size)or l then {not enough clearance}
+ begin g1:=above_display_skip_code; g2:=below_display_skip_code;
+ end
+else begin g1:=above_display_short_skip_code;
+ g2:=below_display_short_skip_code;
+ end;
+if l and(e=0) then {it follows that |type(a)=hlist_node|}
+ begin shift_amount(a):=s; append_to_vlist(a);
+ tail_append(new_penalty(inf_penalty));
+ end
+else tail_append(new_param_glue(g1))
+
+@ @<Append the display and perhaps also the equation number@>=
+if e<>0 then
+ begin r:=new_kern(z-w-e-d);
+ if l then
+ begin link(a):=r; link(r):=b; b:=a; d:=0;
+ end
+ else begin link(b):=r; link(r):=a;
+ end;
+ b:=hpack(b,natural);
+ end;
+shift_amount(b):=s+d; append_to_vlist(b)
+
+@ @<Append the glue or equation number following the display@>=
+if (a<>null)and(e=0)and not l then
+ begin tail_append(new_penalty(inf_penalty));
+ shift_amount(a):=s+z-width(a);
+ append_to_vlist(a);
+ g2:=0;
+ end;
+if t<>adjust_head then {migrating material comes after equation number}
+ begin link(tail):=link(adjust_head); tail:=t;
+ end;
+tail_append(new_penalty(post_display_penalty));
+if g2>0 then tail_append(new_param_glue(g2))
+
+@ When \.{\\halign} appears in a display, the alignment routines operate
+essentially as they do in vertical mode. Then the following program is
+activated, with |p| and |q| pointing to the beginning and end of the
+resulting list, and with |aux_save| holding the |prev_depth| value.
+
+@<Finish an alignment in a display@>=
+begin do_assignments;
+if cur_cmd<>math_shift then @<Pontificate about improper alignment in display@>
+else @<Check that another \.\$ follows@>;
+pop_nest;
+tail_append(new_penalty(pre_display_penalty));
+tail_append(new_param_glue(above_display_skip_code));
+link(tail):=p;
+if p<>null then tail:=q;
+tail_append(new_penalty(post_display_penalty));
+tail_append(new_param_glue(below_display_skip_code));
+prev_depth:=aux_save.sc; resume_after_display;
+end
+
+@ @<Pontificate...@>=
+begin print_err("Missing $$ inserted");
+@.Missing {\$\$} inserted@>
+help2("Displays can use special alignments (like \eqalignno)")@/
+ ("only if nothing but the alignment itself is between $$'s.");
+back_error;
+end
+
+@* \[49] Mode-independent processing.
+The long |main_control| procedure has now been fully specified, except for
+certain activities that are independent of the current mode. These activities
+do not change the current vlist or hlist or mlist; if they change anything,
+it is the value of a parameter or the meaning of a control sequence.
+
+Assignments to values in |eqtb| can be global or local. Furthermore, a
+control sequence can be defined to be `\.{\\long}' or `\.{\\outer}', and
+it might or might not be expanded. The prefixes `\.{\\global}', `\.{\\long}',
+and `\.{\\outer}' can occur in any order. Therefore we assign binary numeric
+codes, making it possible to accumulate the union of all specified prefixes
+by adding the corresponding codes. (\PASCAL's |set| operations could also
+have been used.)
+
+@<Put each...@>=
+primitive("long",prefix,1);
+@!@:long_}{\.{\\long} primitive@>
+primitive("outer",prefix,2);
+@!@:outer_}{\.{\\outer} primitive@>
+primitive("global",prefix,4);
+@!@:global_}{\.{\\global} primitive@>
+primitive("def",def,0);
+@!@:def_}{\.{\\def} primitive@>
+primitive("gdef",def,1);
+@!@:gdef_}{\.{\\gdef} primitive@>
+primitive("edef",def,2);
+@!@:edef_}{\.{\\edef} primitive@>
+primitive("xdef",def,3);
+@!@:xdef_}{\.{\\xdef} primitive@>
+
+@ @<Cases of |print_cmd_chr|...@>=
+prefix: if chr_code=1 then print_esc("long")
+ else if chr_code=2 then print_esc("outer")
+ else print_esc("global");
+def: if chr_code=0 then print_esc("def")
+ else if chr_code=1 then print_esc("gdef")
+ else if chr_code=2 then print_esc("edef")
+ else print_esc("xdef");
+
+@ Every prefix, and every command code that might or might not be prefixed,
+calls the action procedure |prefixed_command|. This routine accumulates
+a sequence of prefixes until coming to a non-prefix, then it carries out
+the command.
+
+@<Cases of |main_control| that don't...@>=
+any_mode(toks_register),
+any_mode(assign_toks),
+any_mode(assign_int),
+any_mode(assign_dimen),
+any_mode(assign_glue),
+any_mode(assign_mu_glue),
+any_mode(assign_font_dimen),
+any_mode(assign_font_int),
+any_mode(set_aux),
+any_mode(set_prev_graf),
+any_mode(set_page_dimen),
+any_mode(set_page_int),
+any_mode(set_box_dimen),
+any_mode(set_shape),
+any_mode(def_code),
+any_mode(def_family),
+any_mode(set_font),
+any_mode(def_font),
+any_mode(register),
+any_mode(advance),
+any_mode(multiply),
+any_mode(divide),
+any_mode(prefix),
+any_mode(let),
+any_mode(shorthand_def),
+any_mode(read_to_cs),
+any_mode(def),
+any_mode(set_box),
+any_mode(hyph_data),
+any_mode(set_interaction):prefixed_command;
+
+@ If the user says, e.g., `\.{\\global\\global}', the redundancy is
+silently accepted.
+
+@<Declare act...@>=
+@t\4@>@<Declare subprocedures for |prefixed_command|@>@t@>@;@/
+procedure prefixed_command;
+label done,exit;
+var a:small_number; {accumulated prefix codes so far}
+@!f:internal_font_number; {identifies a font}
+@!j:halfword; {index into a \.{\\parshape} specification}
+@!k:font_index; {index into |font_info|}
+@!p,@!q:pointer; {for temporary short-term use}
+@!n:integer; {ditto}
+@!e:boolean; {should a definition be expanded? or was \.{\\let} not done?}
+begin a:=0;
+while cur_cmd=prefix do
+ begin if not odd(a div cur_chr) then a:=a+cur_chr;
+ @<Get the next non-blank non-relax...@>;
+ if cur_cmd<=max_non_prefixed_command then
+ @<Discard erroneous prefixes and |return|@>;
+ end;
+@<Discard the prefixes \.{\\long} and \.{\\outer} if they are irrelevant@>;
+@<Adjust \(f)for the setting of \.{\\globaldefs}@>;
+case cur_cmd of
+@t\4@>@<Assignments@>@;
+othercases confusion("prefix")
+@:this can't happen prefix}{\quad prefix@>
+endcases;
+done: @<Insert a token saved by \.{\\afterassignment}, if any@>;
+exit:end;
+
+@ @<Discard erroneous...@>=
+begin print_err("You can't use a prefix with `");
+@.You can't use a prefix with x@>
+print_cmd_chr(cur_cmd,cur_chr); print_char("'");
+help1("I'll pretend you didn't say \long or \outer or \global.");
+back_error; return;
+end
+
+@ @<Discard the prefixes...@>=
+if (cur_cmd<>def)and(a mod 4<>0) then
+ begin print_err("You can't use `"); print_esc("long"); print("' or `");
+ print_esc("outer"); print("' with `");
+@.You can't use \\long...@>
+ print_cmd_chr(cur_cmd,cur_chr); print_char("'");
+ help1("I'll pretend you didn't say \long or \outer here.");
+ error;
+ end
+
+@ The previous routine does not have to adjust |a| so that |a mod 4=0|,
+since the following routines test for the \.{\\global} prefix as follows.
+
+@d global==(a>=4)
+@d define(#)==if global then geq_define(#)@+else eq_define(#)
+@d word_define(#)==if global then geq_word_define(#)@+else eq_word_define(#)
+
+@<Adjust \(f)for the setting of \.{\\globaldefs}@>=
+if global_defs<>0 then
+ if global_defs<0 then
+ begin if global then a:=a-4;
+ end
+ else begin if not global then a:=a+4;
+ end
+
+@ When a control sequence is to be defined, by \.{\\def} or \.{\\let} or
+something similar, the |get_r_token| routine will substitute a special
+control sequence for a token that is not redefinable.
+
+@<Declare subprocedures for |prefixed_command|@>=
+procedure get_r_token;
+label restart;
+begin restart: repeat get_token;
+until cur_tok<>space_token;
+if (cur_cs=0)or(cur_cs>frozen_control_sequence) then
+ begin print_err("Missing control sequence inserted");
+@.Missing control...@>
+ help5("Please don't say `\def cs{...}', say `\def\cs{...}'.")@/
+ ("I've inserted an inaccessible control sequence so that your")@/
+ ("definition will be completed without mixing me up too badly.")@/
+ ("You can recover graciously from this error, if you're")@/
+ ("careful; see exercise 27.2 in The TeXbook.");
+@:TeXbook}{\sl The \TeX book@>
+ if cur_cs=0 then back_input;
+ cur_tok:=cs_token_flag+frozen_protection; ins_error; goto restart;
+ end;
+end;
+
+@ @<Initialize table entries...@>=
+text(frozen_protection):="inaccessible";
+
+@ Here's an example of the way many of the following routines operate.
+(Unfortunately, they aren't all as simple as this.)
+
+@<Assignments@>=
+set_font: define(cur_font_loc,data,cur_chr);
+
+@ When a |def| command has been scanned,
+|cur_chr| is odd if the definition is supposed to be global, and
+|cur_chr>=2| if the definition is supposed to be expanded.
+
+@<Assignments@>=
+def: begin if odd(cur_chr)and not global and(global_defs>=0) then a:=a+4;
+ e:=(cur_chr>=2); get_r_token; p:=cur_cs;
+ q:=scan_toks(true,e); define(p,call+(a mod 4),def_ref);
+ end;
+
+@ Both \.{\\let} and \.{\\futurelet} share the command code |let|.
+
+@<Put each...@>=
+primitive("let",let,normal);@/
+@!@:let_}{\.{\\let} primitive@>
+primitive("futurelet",let,normal+1);@/
+@!@:future_let_}{\.{\\futurelet} primitive@>
+
+@ @<Cases of |print_cmd_chr|...@>=
+let: if chr_code<>normal then print_esc("futurelet")@+else print_esc("let");
+
+@ @<Assignments@>=
+let: begin n:=cur_chr;
+ get_r_token; p:=cur_cs;
+ if n=normal then
+ begin repeat get_token;
+ until cur_cmd<>spacer;
+ if cur_tok=other_token+"=" then
+ begin get_token;
+ if cur_cmd=spacer then get_token;
+ end;
+ end
+ else begin get_token; q:=cur_tok; get_token; back_input;
+ cur_tok:=q; back_input; {look ahead, then back up}
+ end; {note that |back_input| doesn't affect |cur_cmd|, |cur_chr|}
+ if cur_cmd>=call then add_token_ref(cur_chr);
+ define(p,cur_cmd,cur_chr);
+ end;
+
+@ A \.{\\chardef} creates a control sequence whose |cmd| is |char_given|;
+a \.{\\mathchardef} creates a control sequence whose |cmd| is |math_given|;
+and the corresponding |chr| is the character code or math code. A \.{\\countdef}
+or \.{\\dimendef} or \.{\\skipdef} or \.{\\muskipdef} creates a control
+sequence whose |cmd| is |assign_int| or \dots\ or |assign_mu_glue|, and the
+corresponding |chr| is the |eqtb| location of the internal register in question.
+
+@d char_def_code=0 {|shorthand_def| for \.{\\chardef}}
+@d math_char_def_code=1 {|shorthand_def| for \.{\\mathchardef}}
+@d count_def_code=2 {|shorthand_def| for \.{\\countdef}}
+@d dimen_def_code=3 {|shorthand_def| for \.{\\dimendef}}
+@d skip_def_code=4 {|shorthand_def| for \.{\\skipdef}}
+@d mu_skip_def_code=5 {|shorthand_def| for \.{\\muskipdef}}
+@d toks_def_code=6 {|shorthand_def| for \.{\\toksdef}}
+
+@<Put each...@>=
+primitive("chardef",shorthand_def,char_def_code);@/
+@!@:char_def_}{\.{\\chardef} primitive@>
+primitive("mathchardef",shorthand_def,math_char_def_code);@/
+@!@:math_char_def_}{\.{\\mathchardef} primitive@>
+primitive("countdef",shorthand_def,count_def_code);@/
+@!@:count_def_}{\.{\\countdef} primitive@>
+primitive("dimendef",shorthand_def,dimen_def_code);@/
+@!@:dimen_def_}{\.{\\dimendef} primitive@>
+primitive("skipdef",shorthand_def,skip_def_code);@/
+@!@:skip_def_}{\.{\\skipdef} primitive@>
+primitive("muskipdef",shorthand_def,mu_skip_def_code);@/
+@!@:mu_skip_def_}{\.{\\muskipdef} primitive@>
+primitive("toksdef",shorthand_def,toks_def_code);@/
+@!@:toks_def_}{\.{\\toksdef} primitive@>
+
+@ @<Cases of |print_cmd_chr|...@>=
+shorthand_def: case chr_code of
+ char_def_code: print_esc("chardef");
+ math_char_def_code: print_esc("mathchardef");
+ count_def_code: print_esc("countdef");
+ dimen_def_code: print_esc("dimendef");
+ skip_def_code: print_esc("skipdef");
+ mu_skip_def_code: print_esc("muskipdef");
+ othercases print_esc("toksdef")
+ endcases;
+char_given: begin print_esc("char"); print_hex(chr_code);
+ end;
+math_given: begin print_esc("mathchar"); print_hex(chr_code);
+ end;
+
+@ We temporarily define |p| to be |relax|, so that an occurrence of |p|
+while scanning the definition will simply stop the scanning instead of
+producing an ``undefined control sequence'' error or expanding the
+previous meaning. This allows, for instance, `\.{\\chardef\\foo=123\\foo}'.
+
+@<Assignments@>=
+shorthand_def: begin n:=cur_chr; get_r_token; p:=cur_cs; define(p,relax,256);
+ scan_optional_equals;
+ case n of
+ char_def_code: begin scan_char_num; define(p,char_given,cur_val);
+ end;
+ math_char_def_code: begin scan_fifteen_bit_int; define(p,math_given,cur_val);
+ end;
+ othercases begin scan_eight_bit_int;
+ case n of
+ count_def_code: define(p,assign_int,count_base+cur_val);
+ dimen_def_code: define(p,assign_dimen,scaled_base+cur_val);
+ skip_def_code: define(p,assign_glue,skip_base+cur_val);
+ mu_skip_def_code: define(p,assign_mu_glue,mu_skip_base+cur_val);
+ toks_def_code: define(p,assign_toks,toks_base+cur_val);
+ end; {there are no other cases}
+ end
+ endcases;
+ end;
+
+@ @<Assignments@>=
+read_to_cs: begin scan_int; n:=cur_val;
+ if not scan_keyword("to") then
+ begin print_err("Missing `to' inserted");
+@.Missing `to'...@>
+ help2("You should have said `\read<number> to \cs'.")@/
+ ("I'm going to look for the \cs now."); error;
+ end;
+ get_r_token;
+ p:=cur_cs; read_toks(n,p); define(p,call,cur_val);
+ end;
+
+@ The token-list parameters, \.{\\output} and \.{\\everypar}, etc., receive
+their values in the following way. (For safety's sake, we place an
+enclosing pair of braces around an \.{\\output} list.)
+
+@<Assignments@>=
+toks_register,assign_toks: begin q:=cur_cs;
+ if cur_cmd=toks_register then
+ begin scan_eight_bit_int; p:=toks_base+cur_val;
+ end
+ else p:=cur_chr; {|p=every_par_loc| or |output_routine_loc| or \dots}
+ scan_optional_equals;
+ @<Get the next non-blank non-relax non-call token@>;
+ if cur_cmd<>left_brace then @<If the right-hand side is a token parameter
+ or token register, finish the assignment and |goto done|@>;
+ back_input; cur_cs:=q; q:=scan_toks(false,false);
+ if link(def_ref)=null then {empty list: revert to the default}
+ begin define(p,undefined_cs,null); free_avail(def_ref);
+ end
+ else begin if p=output_routine_loc then {enclose in curlies}
+ begin link(q):=get_avail; q:=link(q);
+ info(q):=right_brace_token+"}";
+ q:=get_avail; info(q):=left_brace_token+"{";
+ link(q):=link(def_ref); link(def_ref):=q;
+ end;
+ define(p,call,def_ref);
+ end;
+ end;
+
+@ @<If the right-hand side is a token parameter...@>=
+begin if cur_cmd=toks_register then
+ begin scan_eight_bit_int; cur_cmd:=assign_toks; cur_chr:=toks_base+cur_val;
+ end;
+if cur_cmd=assign_toks then
+ begin q:=equiv(cur_chr);
+ if q=null then define(p,undefined_cs,null)
+ else begin add_token_ref(q); define(p,call,q);
+ end;
+ goto done;
+ end;
+end
+
+@ Similar routines are used to assign values to the numeric parameters.
+
+@<Assignments@>=
+assign_int: begin p:=cur_chr; scan_optional_equals; scan_int;
+ word_define(p,cur_val);
+ end;
+assign_dimen: begin p:=cur_chr; scan_optional_equals;
+ scan_normal_dimen; word_define(p,cur_val);
+ end;
+assign_glue,assign_mu_glue: begin p:=cur_chr; n:=cur_cmd; scan_optional_equals;
+ if n=assign_mu_glue then scan_glue(mu_val)@+else scan_glue(glue_val);
+ trap_zero_glue;
+ define(p,glue_ref,cur_val);
+ end;
+
+@ When a glue register or parameter becomes zero, it will always point to
+|zero_glue| because of the following procedure. (Exception: The tabskip
+glue isn't trapped while preambles are being scanned.)
+
+@<Declare subprocedures for |prefixed_command|@>=
+procedure trap_zero_glue;
+begin if (width(cur_val)=0)and(stretch(cur_val)=0)and(shrink(cur_val)=0) then
+ begin add_glue_ref(zero_glue);
+ delete_glue_ref(cur_val); cur_val:=zero_glue;
+ end;
+end;
+
+@ The various character code tables are changed by the |def_code| commands,
+and the font families are declared by |def_family|.
+
+@<Put each...@>=
+primitive("catcode",def_code,cat_code_base);
+@!@:cat_code_}{\.{\\catcode} primitive@>
+primitive("mathcode",def_code,math_code_base);
+@!@:math_code_}{\.{\\mathcode} primitive@>
+primitive("lccode",def_code,lc_code_base);
+@!@:lc_code_}{\.{\\lccode} primitive@>
+primitive("uccode",def_code,uc_code_base);
+@!@:uc_code_}{\.{\\uccode} primitive@>
+primitive("sfcode",def_code,sf_code_base);
+@!@:sf_code_}{\.{\\sfcode} primitive@>
+primitive("delcode",def_code,del_code_base);
+@!@:del_code_}{\.{\\delcode} primitive@>
+primitive("textfont",def_family,math_font_base);
+@!@:text_font_}{\.{\\textfont} primitive@>
+primitive("scriptfont",def_family,math_font_base+script_size);
+@!@:script_font_}{\.{\\scriptfont} primitive@>
+primitive("scriptscriptfont",def_family,math_font_base+script_script_size);
+@!@:script_script_font_}{\.{\\scriptscriptfont} primitive@>
+
+@ @<Cases of |print_cmd_chr|...@>=
+def_code: if chr_code=cat_code_base then print_esc("catcode")
+ else if chr_code=math_code_base then print_esc("mathcode")
+ else if chr_code=lc_code_base then print_esc("lccode")
+ else if chr_code=uc_code_base then print_esc("uccode")
+ else if chr_code=sf_code_base then print_esc("sfcode")
+ else print_esc("delcode");
+def_family: print_size(chr_code-math_font_base);
+
+@ The different types of code values have different legal ranges; the
+following program is careful to check each case properly.
+
+@<Assignments@>=
+def_code: begin @<Let |n| be the largest legal code value, based on |cur_chr|@>;
+ p:=cur_chr; scan_char_num; p:=p+cur_val; scan_optional_equals;
+ scan_int;
+ if ((cur_val<0)and(p<del_code_base))or(cur_val>n) then
+ begin print_err("Invalid code ("); print_int(cur_val);
+@.Invalid code@>
+ if p<del_code_base then print("), should be in the range 0..")
+ else print("), should be at most ");
+ print_int(n);
+ help1("I'm going to use 0 instead of that illegal code value.");@/
+ error; cur_val:=0;
+ end;
+ if p<math_code_base then define(p,data,cur_val)
+ else if p<del_code_base then define(p,data,hi(cur_val))
+ else word_define(p,cur_val);
+ end;
+
+@ @<Let |n| be the largest...@>=
+if cur_chr=cat_code_base then n:=max_char_code
+else if cur_chr=math_code_base then n:=@'100000
+else if cur_chr=sf_code_base then n:=@'77777
+else if cur_chr=del_code_base then n:=@'77777777
+else n:=255
+
+@ @<Assignments@>=
+def_family: begin p:=cur_chr; scan_four_bit_int; p:=p+cur_val;
+ scan_optional_equals; scan_font_ident; define(p,data,cur_val);
+ end;
+
+@ Next we consider changes to \TeX's numeric registers.
+
+@<Assignments@>=
+register,advance,multiply,divide: do_register_command(a);
+
+@ We use the fact that |register<advance<multiply<divide|.
+
+@<Declare subprocedures for |prefixed_command|@>=
+procedure do_register_command(@!a:small_number);
+label found,exit;
+var l,@!q,@!r,@!s:pointer; {for list manipulation}
+@!p:int_val..mu_val; {type of register involved}
+begin q:=cur_cmd;
+@<Compute the register location |l| and its type |p|; but |return| if invalid@>;
+if q=register then scan_optional_equals
+else if scan_keyword("by") then do_nothing; {optional `\.{by}'}
+arith_error:=false;
+if q<multiply then @<Compute result of |register| or
+ |advance|, put it in |cur_val|@>
+else @<Compute result of |multiply| or |divide|, put it in |cur_val|@>;
+if arith_error then
+ begin print_err("Arithmetic overflow");
+@.Arithmetic overflow@>
+ help2("I can't carry out that multiplication or division,")@/
+ ("since the result is out of range.");
+ error; return;
+ end;
+if p<glue_val then word_define(l,cur_val)
+else begin trap_zero_glue; define(l,glue_ref,cur_val);
+ end;
+exit: end;
+
+@ Here we use the fact that the consecutive codes |int_val...mu_val| and
+|assign_int..assign_mu_glue| correspond to each other nicely.
+
+@<Compute the register location |l| and its type |p|...@>=
+begin if q<>register then
+ begin get_x_token;
+ if (cur_cmd>=assign_int)and(cur_cmd<=assign_mu_glue) then
+ begin l:=cur_chr; p:=cur_cmd-assign_int; goto found;
+ end;
+ if cur_cmd<>register then
+ begin print_err("You can't use `"); print_cmd_chr(cur_cmd,cur_chr);
+@.You can't use x after ...@>
+ print("' after "); print_cmd_chr(q,0);
+ help1("I'm forgetting what you said and not changing anything.");
+ error; return;
+ end;
+ end;
+p:=cur_chr; scan_eight_bit_int;
+case p of
+int_val: l:=cur_val+count_base;
+dimen_val: l:=cur_val+scaled_base;
+glue_val: l:=cur_val+skip_base;
+mu_val: l:=cur_val+mu_skip_base;
+end; {there are no other cases}
+end;
+found:
+
+@ @<Compute result of |register| or |advance|...@>=
+if p<glue_val then
+ begin if p=int_val then scan_int@+else scan_normal_dimen;
+ if q=advance then cur_val:=cur_val+eqtb[l].int;
+ end
+else begin scan_glue(p);
+ if q=advance then @<Compute the sum of two glue specs@>;
+ end
+
+@ @<Compute the sum of two glue specs@>=
+begin q:=new_spec(cur_val); r:=equiv(l);
+delete_glue_ref(cur_val);
+width(q):=width(q)+width(r);
+if stretch(q)=0 then stretch_order(q):=normal;
+if stretch_order(q)=stretch_order(r) then stretch(q):=stretch(q)+stretch(r)
+else if (stretch_order(q)<stretch_order(r))and(stretch(r)<>0) then
+ begin stretch(q):=stretch(r); stretch_order(q):=stretch_order(r);
+ end;
+if shrink(q)=0 then shrink_order(q):=normal;
+if shrink_order(q)=shrink_order(r) then shrink(q):=shrink(q)+shrink(r)
+else if (shrink_order(q)<shrink_order(r))and(shrink(r)<>0) then
+ begin shrink(q):=shrink(r); shrink_order(q):=shrink_order(r);
+ end;
+cur_val:=q;
+end
+
+@ @<Compute result of |multiply| or |divide|...@>=
+begin scan_int;
+if p<glue_val then
+ if q=multiply then
+ if p=int_val then cur_val:=mult_integers(eqtb[l].int,cur_val)
+ else cur_val:=nx_plus_y(eqtb[l].int,cur_val,0)
+ else cur_val:=x_over_n(eqtb[l].int,cur_val)
+else begin s:=equiv(l); r:=new_spec(s);
+ if q=multiply then
+ begin width(r):=nx_plus_y(width(s),cur_val,0);
+ stretch(r):=nx_plus_y(stretch(s),cur_val,0);
+ shrink(r):=nx_plus_y(shrink(s),cur_val,0);
+ end
+ else begin width(r):=x_over_n(width(s),cur_val);
+ stretch(r):=x_over_n(stretch(s),cur_val);
+ shrink(r):=x_over_n(shrink(s),cur_val);
+ end;
+ cur_val:=r;
+ end;
+end
+
+@ The processing of boxes is somewhat different, because we may need
+to scan and create an entire box before we actually change the value of the old
+one.
+
+@<Assignments@>=
+set_box: begin scan_eight_bit_int;
+ if global then n:=256+cur_val@+else n:=cur_val;
+ scan_optional_equals;
+ if set_box_allowed then scan_box(box_flag+n)
+ else begin print_err("Improper "); print_esc("setbox");
+@.Improper \\setbox@>
+ help2("Sorry, \setbox is not allowed after \halign in a display,")@/
+ ("or between \accent and an accented character."); error;
+ end;
+ end;
+
+@ The |space_factor| or |prev_depth| settings are changed when a |set_aux|
+command is sensed. Similarly, |prev_graf| is changed in the presence of
+|set_prev_graf|, and |dead_cycles| or |insert_penalties| in the presence of
+|set_page_int|. These definitions are always global.
+
+When some dimension of a box register is changed, the change isn't exactly
+global; but \TeX\ does not look at the \.{\\global} switch.
+
+@<Assignments@>=
+set_aux:alter_aux;
+set_prev_graf:alter_prev_graf;
+set_page_dimen:alter_page_so_far;
+set_page_int:alter_integer;
+set_box_dimen:alter_box_dimen;
+
+@ @<Declare subprocedures for |prefixed_command|@>=
+procedure alter_aux;
+var c:halfword; {|hmode| or |vmode|}
+begin if cur_chr<>abs(mode) then report_illegal_case
+else begin c:=cur_chr; scan_optional_equals;
+ if c=vmode then
+ begin scan_normal_dimen; prev_depth:=cur_val;
+ end
+ else begin scan_int;
+ if (cur_val<=0)or(cur_val>32767) then
+ begin print_err("Bad space factor");
+@.Bad space factor@>
+ help1("I allow only values in the range 1..32767 here.");
+ int_error(cur_val);
+ end
+ else space_factor:=cur_val;
+ end;
+ end;
+end;
+
+@ @<Declare subprocedures for |prefixed_command|@>=
+procedure alter_prev_graf;
+var p:0..nest_size; {index into |nest|}
+begin nest[nest_ptr]:=cur_list; p:=nest_ptr;
+while abs(nest[p].mode_field)<>vmode do decr(p);
+scan_optional_equals; scan_int;
+if cur_val<0 then
+ begin print_err("Bad "); print_esc("prevgraf");
+@.Bad \\prevgraf@>
+ help1("I allow only nonnegative values here.");
+ int_error(cur_val);
+ end
+else begin nest[p].pg_field:=cur_val; cur_list:=nest[nest_ptr];
+ end;
+end;
+
+@ @<Declare subprocedures for |prefixed_command|@>=
+procedure alter_page_so_far;
+var c:0..7; {index into |page_so_far|}
+begin c:=cur_chr; scan_optional_equals; scan_normal_dimen;
+page_so_far[c]:=cur_val;
+end;
+
+@ @<Declare subprocedures for |prefixed_command|@>=
+procedure alter_integer;
+var c:0..1; {0 for \.{\\deadcycles}, 1 for \.{\\insertpenalties}}
+begin c:=cur_chr; scan_optional_equals; scan_int;
+if c=0 then dead_cycles:=cur_val
+else insert_penalties:=cur_val;
+end;
+
+@ @<Declare subprocedures for |prefixed_command|@>=
+procedure alter_box_dimen;
+var c:small_number; {|width_offset| or |height_offset| or |depth_offset|}
+@!b:eight_bits; {box number}
+begin c:=cur_chr; scan_eight_bit_int; b:=cur_val; scan_optional_equals;
+scan_normal_dimen;
+if box(b)<>null then mem[box(b)+c].sc:=cur_val;
+end;
+
+@ Paragraph shapes are set up in the obvious way.
+
+@<Assignments@>=
+set_shape: begin scan_optional_equals; scan_int; n:=cur_val;
+ if n<=0 then p:=null
+ else begin p:=get_node(2*n+1); info(p):=n;
+ for j:=1 to n do
+ begin scan_normal_dimen;
+ mem[p+2*j-1].sc:=cur_val; {indentation}
+ scan_normal_dimen;
+ mem[p+2*j].sc:=cur_val; {width}
+ end;
+ end;
+ define(par_shape_loc,shape_ref,p);
+ end;
+
+@ Here's something that isn't quite so obvious. It guarantees that
+|info(par_shape_ptr)| can hold any positive~|n| for which |get_node(2*n+1)|
+doesn't overflow the memory capacity.
+
+@<Check the ``constant''...@>=
+if 2*max_halfword<mem_top-mem_min then bad:=41;
+
+@ New hyphenation data is loaded by the |hyph_data| command.
+
+@<Put each...@>=
+primitive("hyphenation",hyph_data,0);
+@!@:hyphenation_}{\.{\\hyphenation} primitive@>
+primitive("patterns",hyph_data,1);
+@!@:patterns_}{\.{\\patterns} primitive@>
+
+@ @<Cases of |print_cmd_chr|...@>=
+hyph_data: if chr_code=1 then print_esc("patterns")
+ else print_esc("hyphenation");
+
+@ @<Assignments@>=
+hyph_data: if cur_chr=1 then
+ begin @!init new_patterns; goto done;@;@+tini@/
+ print_err("Patterns can be loaded only by INITEX");
+@.Patterns can be...@>
+ help0; error;
+ repeat get_token; until cur_cmd=right_brace; {flush the patterns}
+ return;
+ end
+ else begin new_hyph_exceptions; goto done;
+ end;
+
+@ All of \TeX's parameters are kept in |eqtb| except the font information,
+the interaction mode, and the hyphenation tables; these are strictly global.
+
+@<Assignments@>=
+assign_font_dimen: begin find_font_dimen(true); k:=cur_val;
+ scan_optional_equals; scan_normal_dimen; font_info[k].sc:=cur_val;
+ end;
+assign_font_int: begin n:=cur_chr; scan_font_ident; f:=cur_val;
+ scan_optional_equals; scan_int;
+ if n=0 then hyphen_char[f]:=cur_val@+else skew_char[f]:=cur_val;
+ end;
+
+@ @<Put each...@>=
+primitive("hyphenchar",assign_font_int,0);
+@!@:hyphen_char_}{\.{\\hyphenchar} primitive@>
+primitive("skewchar",assign_font_int,1);
+@!@:skew_char_}{\.{\\skewchar} primitive@>
+
+@ @<Cases of |print_cmd_chr|...@>=
+assign_font_int: if chr_code=0 then print_esc("hyphenchar")
+ else print_esc("skewchar");
+
+@ Here is where the information for a new font gets loaded.
+
+@<Assignments@>=
+def_font: new_font(a);
+
+@ @<Declare subprocedures for |prefixed_command|@>=
+procedure new_font(@!a:small_number);
+label common_ending;
+var u:pointer; {user's font identifier}
+@!s:scaled; {stated ``at'' size, or negative of scaled magnification}
+@!f:internal_font_number; {runs through existing fonts}
+@!t:str_number; {name for the frozen font identifier}
+@!old_setting:0..max_selector; {holds |selector| setting}
+@!flushable_string:str_number; {string not yet referenced}
+begin if job_name=0 then open_log_file;
+ {avoid confusing \.{texput} with the font name}
+@.texput@>
+get_r_token; u:=cur_cs;
+if u>=hash_base then t:=text(u)
+else if u>=single_base then
+ if u=null_cs then t:="FONT"@+else t:=u-single_base
+else begin old_setting:=selector; selector:=new_string;
+ print("FONT"); print(u-active_base); selector:=old_setting;
+@.FONTx@>
+ str_room(1); t:=make_string;
+ end;
+define(u,set_font,null_font); scan_optional_equals; scan_file_name;
+@<Scan the font size specification@>;
+@<If this font has already been loaded, set |f| to the internal
+ font number and |goto common_ending|@>;
+f:=read_font_info(u,cur_name,cur_area,s);
+common_ending: equiv(u):=f; eqtb[font_id_base+f]:=eqtb[u]; font_id_text(f):=t;
+end;
+
+@ @<Scan the font size specification@>=
+name_in_progress:=true; {this keeps |cur_name| from being changed}
+if scan_keyword("at") then @<Put the \(p)(positive) `at' size into |s|@>
+@.at@>
+else if scan_keyword("scaled") then
+@.scaled@>
+ begin scan_int; s:=-cur_val;
+ if (cur_val<=0)or(cur_val>32768) then
+ begin print_err("Illegal magnification has been changed to 1000");@/
+@.Illegal magnification...@>
+ help1("The magnification ratio must be between 1 and 32768.");
+ int_error(cur_val); s:=-1000;
+ end;
+ end
+else s:=-1000;
+name_in_progress:=false
+
+@ @<Put the \(p)(positive) `at' size into |s|@>=
+begin scan_normal_dimen; s:=cur_val;
+if (s<=0)or(s>=@'1000000000) then
+ begin print_err("Improper `at' size (");
+ print_scaled(s); print("pt), replaced by 10pt");
+@.Improper `at' size...@>
+ help2("I can only handle fonts at positive sizes that are")@/
+ ("less than 2048pt, so I've changed what you said to 10pt.");
+ error; s:=10*unity;
+ end;
+end
+
+@ When the user gives a new identifier to a font that was previously loaded,
+the new name becomes the font identifier of record. Font names `\.{xyz}' and
+`\.{XYZ}' are considered to be different.
+
+@<If this font has already been loaded...@>=
+flushable_string:=str_ptr-1;
+for f:=font_base+1 to font_ptr do
+ if str_eq_str(font_name[f],cur_name)and str_eq_str(font_area[f],cur_area) then
+ begin if cur_name=flushable_string then
+ begin flush_string; cur_name:=font_name[f];
+ end;
+ if s>0 then
+ begin if s=font_size[f] then goto common_ending;
+ end
+ else if font_size[f]=xn_over_d(font_dsize[f],-s,1000) then
+ goto common_ending;
+ end
+
+@ @<Cases of |print_cmd_chr|...@>=
+set_font:begin print("select font "); slow_print(font_name[chr_code]);
+ if font_size[chr_code]<>font_dsize[chr_code] then
+ begin print(" at "); print_scaled(font_size[chr_code]);
+ print("pt");
+ end;
+ end;
+
+@ @<Put each...@>=
+primitive("batchmode",set_interaction,batch_mode);
+@!@:batch_mode_}{\.{\\batchmode} primitive@>
+primitive("nonstopmode",set_interaction,nonstop_mode);
+@!@:nonstop_mode_}{\.{\\nonstopmode} primitive@>
+primitive("scrollmode",set_interaction,scroll_mode);
+@!@:scroll_mode_}{\.{\\scrollmode} primitive@>
+primitive("errorstopmode",set_interaction,error_stop_mode);
+@!@:error_stop_mode_}{\.{\\errorstopmode} primitive@>
+
+@ @<Cases of |print_cmd_chr|...@>=
+set_interaction: case chr_code of
+ batch_mode: print_esc("batchmode");
+ nonstop_mode: print_esc("nonstopmode");
+ scroll_mode: print_esc("scrollmode");
+ othercases print_esc("errorstopmode")
+ endcases;
+
+@ @<Assignments@>=
+set_interaction: new_interaction;
+
+@ @<Declare subprocedures for |prefixed_command|@>=
+procedure new_interaction;
+begin print_ln;
+interaction:=cur_chr;
+@<Initialize the print |selector| based on |interaction|@>;
+if log_opened then selector:=selector+2;
+end;
+
+@ The \.{\\afterassignment} command puts a token into the global
+variable |after_token|. This global variable is examined just after
+every assignment has been performed.
+
+@<Glob...@>=
+@!after_token:halfword; {zero, or a saved token}
+
+@ @<Set init...@>=
+after_token:=0;
+
+@ @<Cases of |main_control| that don't...@>=
+any_mode(after_assignment):begin get_token; after_token:=cur_tok;
+ end;
+
+@ @<Insert a token saved by \.{\\afterassignment}, if any@>=
+if after_token<>0 then
+ begin cur_tok:=after_token; back_input; after_token:=0;
+ end
+
+@ Here is a procedure that might be called `Get the next non-blank non-relax
+non-call non-assignment token'.
+
+@<Declare act...@>=
+procedure do_assignments;
+label exit;
+begin loop begin @<Get the next non-blank non-relax...@>;
+ if cur_cmd<=max_non_prefixed_command then return;
+ set_box_allowed:=false; prefixed_command; set_box_allowed:=true;
+ end;
+exit:end;
+
+@ @<Cases of |main_control| that don't...@>=
+any_mode(after_group):begin get_token; save_for_after(cur_tok);
+ end;
+
+@ Files for \.{\\read} are opened and closed by the |in_stream| command.
+
+@<Put each...@>=
+primitive("openin",in_stream,1);
+@!@:open_in_}{\.{\\openin} primitive@>
+primitive("closein",in_stream,0);
+@!@:close_in_}{\.{\\closein} primitive@>
+
+@ @<Cases of |print_cmd_chr|...@>=
+in_stream: if chr_code=0 then print_esc("closein")
+ else print_esc("openin");
+
+@ @<Cases of |main_control| that don't...@>=
+any_mode(in_stream): open_or_close_in;
+
+@ @<Declare act...@>=
+procedure open_or_close_in;
+var c:0..1; {1 for \.{\\openin}, 0 for \.{\\closein}}
+@!n:0..15; {stream number}
+begin c:=cur_chr; scan_four_bit_int; n:=cur_val;
+if read_open[n]<>closed then
+ begin a_close(read_file[n]); read_open[n]:=closed;
+ end;
+if c<>0 then
+ begin scan_optional_equals; scan_file_name;
+ if cur_ext="" then cur_ext:=".tex";
+ pack_cur_name;
+ if a_open_in(read_file[n]) then read_open[n]:=just_open;
+ end;
+end;
+
+@ The user can issue messages to the terminal, regardless of the
+current mode.
+
+@<Cases of |main_control| that don't...@>=
+any_mode(message):issue_message;
+
+@ @<Put each...@>=
+primitive("message",message,0);
+@!@:message_}{\.{\\message} primitive@>
+primitive("errmessage",message,1);
+@!@:err_message_}{\.{\\errmessage} primitive@>
+
+@ @<Cases of |print_cmd_chr|...@>=
+message: if chr_code=0 then print_esc("message")
+ else print_esc("errmessage");
+
+@ @<Declare act...@>=
+procedure issue_message;
+var old_setting:0..max_selector; {holds |selector| setting}
+@!c:0..1; {identifies \.{\\message} and \.{\\errmessage}}
+@!s:str_number; {the message}
+begin c:=cur_chr; link(garbage):=scan_toks(false,true);
+old_setting:=selector; selector:=new_string;
+token_show(def_ref); selector:=old_setting;
+flush_list(def_ref);
+str_room(1); s:=make_string;
+if c=0 then @<Print string |s| on the terminal@>
+else @<Print string |s| as an error message@>;
+flush_string;
+end;
+
+@ @<Print string |s| on the terminal@>=
+begin if term_offset+length(s)>max_print_line-2 then print_ln
+else if (term_offset>0)or(file_offset>0) then print_char(" ");
+slow_print(s); update_terminal;
+end
+
+@ If \.{\\errmessage} occurs often in |scroll_mode|, without user-defined
+\.{\\errhelp}, we don't want to give a long help message each time. So we
+give a verbose explanation only once.
+
+@<Glob...@>=
+@!long_help_seen:boolean; {has the long \.{\\errmessage} help been used?}
+
+@ @<Set init...@>=long_help_seen:=false;
+
+@ @<Print string |s| as an error message@>=
+begin print_err(""); slow_print(s);
+if err_help<>null then use_err_help:=true
+else if long_help_seen then help1("(That was another \errmessage.)")
+else begin if interaction<error_stop_mode then long_help_seen:=true;
+ help4("This error message was generated by an \errmessage")@/
+ ("command, so I can't give any explicit help.")@/
+ ("Pretend that you're Hercule Poirot: Examine all clues,")@/
+@^Poirot, Hercule@>
+ ("and deduce the truth by order and method.");
+ end;
+error; use_err_help:=false;
+end
+
+@ The |error| routine calls on |give_err_help| if help is requested from
+the |err_help| parameter.
+
+@p procedure give_err_help;
+begin token_show(err_help);
+end;
+
+@ The \.{\\uppercase} and \.{\\lowercase} commands are implemented by
+building a token list and then changing the cases of the letters in it.
+
+@<Cases of |main_control| that don't...@>=
+any_mode(case_shift):shift_case;
+
+@ @<Put each...@>=
+primitive("lowercase",case_shift,lc_code_base);
+@!@:lowercase_}{\.{\\lowercase} primitive@>
+primitive("uppercase",case_shift,uc_code_base);
+@!@:uppercase_}{\.{\\uppercase} primitive@>
+
+@ @<Cases of |print_cmd_chr|...@>=
+case_shift:if chr_code=lc_code_base then print_esc("lowercase")
+ else print_esc("uppercase");
+
+@ @<Declare act...@>=
+procedure shift_case;
+var b:pointer; {|lc_code_base| or |uc_code_base|}
+@!p:pointer; {runs through the token list}
+@!t:halfword; {token}
+@!c:eight_bits; {character code}
+begin b:=cur_chr; p:=scan_toks(false,false); p:=link(def_ref);
+while p<>null do
+ begin @<Change the case of the token in |p|, if a change is appropriate@>;
+ p:=link(p);
+ end;
+back_list(link(def_ref)); free_avail(def_ref); {omit reference count}
+end;
+
+@ When the case of a |chr_code| changes, we don't change the |cmd|.
+We also change active characters, using the fact that
+|cs_token_flag+active_base| is a multiple of~256.
+@^data structure assumptions@>
+
+@<Change the case of the token in |p|, if a change is appropriate@>=
+t:=info(p);
+if t<cs_token_flag+single_base then
+ begin c:=t mod 256;
+ if equiv(b+c)<>0 then info(p):=t-c+equiv(b+c);
+ end
+
+@ We come finally to the last pieces missing from |main_control|, namely the
+`\.{\\show}' commands that are useful when debugging.
+
+@<Cases of |main_control| that don't...@>=
+any_mode(xray): show_whatever;
+
+@ @d show_code=0 { \.{\\show} }
+@d show_box_code=1 { \.{\\showbox} }
+@d show_the_code=2 { \.{\\showthe} }
+@d show_lists=3 { \.{\\showlists} }
+
+@<Put each...@>=
+primitive("show",xray,show_code);
+@!@:show_}{\.{\\show} primitive@>
+primitive("showbox",xray,show_box_code);
+@!@:show_box_}{\.{\\showbox} primitive@>
+primitive("showthe",xray,show_the_code);
+@!@:show_the_}{\.{\\showthe} primitive@>
+primitive("showlists",xray,show_lists);
+@!@:show_lists_}{\.{\\showlists} primitive@>
+
+@ @<Cases of |print_cmd_chr|...@>=
+xray: case chr_code of
+ show_box_code:print_esc("showbox");
+ show_the_code:print_esc("showthe");
+ show_lists:print_esc("showlists");
+ othercases print_esc("show")
+ endcases;
+
+@ @<Declare act...@>=
+procedure show_whatever;
+label common_ending;
+var p:pointer; {tail of a token list to show}
+begin case cur_chr of
+show_lists: begin begin_diagnostic; show_activities;
+ end;
+show_box_code: @<Show the current contents of a box@>;
+show_code: @<Show the current meaning of a token, then |goto common_ending|@>;
+othercases @<Show the current value of some parameter or register,
+ then |goto common_ending|@>
+endcases;@/
+@<Complete a potentially long \.{\\show} command@>;
+common_ending: if interaction<error_stop_mode then
+ begin help0; decr(error_count);
+ end
+else if tracing_online>0 then
+ begin@t@>@;@/
+ help3("This isn't an error message; I'm just \showing something.")@/
+ ("Type `I\show...' to show more (e.g., \show\cs,")@/
+ ("\showthe\count10, \showbox255, \showlists).");
+ end
+else begin@t@>@;@/
+ help5("This isn't an error message; I'm just \showing something.")@/
+ ("Type `I\show...' to show more (e.g., \show\cs,")@/
+ ("\showthe\count10, \showbox255, \showlists).")@/
+ ("And type `I\tracingonline=1\show...' to show boxes and")@/
+ ("lists on your terminal as well as in the transcript file.");
+ end;
+error;
+end;
+
+@ @<Show the current meaning of a token...@>=
+begin get_token;
+if interaction=error_stop_mode then wake_up_terminal;
+print_nl("> ");
+if cur_cs<>0 then
+ begin sprint_cs(cur_cs); print_char("=");
+ end;
+print_meaning; goto common_ending;
+end
+
+@ @<Cases of |print_cmd_chr|...@>=
+undefined_cs: print("undefined");
+call: print("macro");
+long_call: print_esc("long macro");
+outer_call: print_esc("outer macro");
+long_outer_call: begin print_esc("long"); print_esc("outer macro");
+ end;
+end_template: print_esc("outer endtemplate");
+
+@ @<Show the current contents of a box@>=
+begin scan_eight_bit_int; begin_diagnostic;
+print_nl("> \box"); print_int(cur_val); print_char("=");
+if box(cur_val)=null then print("void")
+else show_box(box(cur_val));
+end
+
+@ @<Show the current value of some parameter...@>=
+begin p:=the_toks;
+if interaction=error_stop_mode then wake_up_terminal;
+print_nl("> "); token_show(temp_head);
+flush_list(link(temp_head)); goto common_ending;
+end
+
+@ @<Complete a potentially long \.{\\show} command@>=
+end_diagnostic(true); print_err("OK");
+@.OK@>
+if selector=term_and_log then if tracing_online<=0 then
+ begin selector:=term_only; print(" (see the transcript file)");
+ selector:=term_and_log;
+ end
+
+@* \[50] Dumping and undumping the tables.
+After \.{INITEX} has seen a collection of fonts and macros, it
+can write all the necessary information on an auxiliary file so
+that production versions of \TeX\ are able to initialize their
+memory at high speed. The present section of the program takes
+care of such output and input. We shall consider simultaneously
+the processes of storing and restoring,
+so that the inverse relation between them is clear.
+@.INITEX@>
+
+The global variable |format_ident| is a string that is printed right
+after the |banner| line when \TeX\ is ready to start. For \.{INITEX} this
+string says simply `\.{(INITEX)}'; for other versions of \TeX\ it says,
+for example, `\.{(preloaded format=plain 82.11.19)}', showing the year,
+month, and day that the format file was created. We have |format_ident=0|
+before \TeX's tables are loaded.
+
+@<Glob...@>=
+@!format_ident:str_number;
+
+@ @<Set init...@>=
+format_ident:=0;
+
+@ @<Initialize table entries...@>=
+format_ident:=" (INITEX)";
+
+@ @<Declare act...@>=
+@!init procedure store_fmt_file;
+label found1,found2,done1,done2;
+var j,@!k,@!l:integer; {all-purpose indices}
+@!p,@!q: pointer; {all-purpose pointers}
+@!x: integer; {something to dump}
+@!w: four_quarters; {four ASCII codes}
+begin @<If dumping is not allowed, abort@>;
+@<Create the |format_ident|, open the format file,
+ and inform the user that dumping has begun@>;
+@<Dump constants for consistency check@>;
+@<Dump the string pool@>;
+@<Dump the dynamic memory@>;
+@<Dump the table of equivalents@>;
+@<Dump the font information@>;
+@<Dump the hyphenation tables@>;
+@<Dump a couple more things and the closing check word@>;
+@<Close the format file@>;
+end;
+tini
+
+@ Corresponding to the procedure that dumps a format file, we have a function
+that reads one in. The function returns |false| if the dumped format is
+incompatible with the present \TeX\ table sizes, etc.
+
+@d bad_fmt=6666 {go here if the format file is unacceptable}
+@d too_small(#)==begin wake_up_terminal;
+ wterm_ln('---! Must increase the ',#);
+@.Must increase the x@>
+ goto bad_fmt;
+ end
+
+@p @t\4@>@<Declare the function called |open_fmt_file|@>@;
+function load_fmt_file:boolean;
+label bad_fmt,exit;
+var j,@!k:integer; {all-purpose indices}
+@!p,@!q: pointer; {all-purpose pointers}
+@!x: integer; {something undumped}
+@!w: four_quarters; {four ASCII codes}
+begin @<Undump constants for consistency check@>;
+@<Undump the string pool@>;
+@<Undump the dynamic memory@>;
+@<Undump the table of equivalents@>;
+@<Undump the font information@>;
+@<Undump the hyphenation tables@>;
+@<Undump a couple more things and the closing check word@>;
+load_fmt_file:=true; return; {it worked!}
+bad_fmt: wake_up_terminal;
+ wterm_ln('(Fatal format file error; I''m stymied)');
+@.Fatal format file error@>
+load_fmt_file:=false;
+exit:end;
+
+@ The user is not allowed to dump a format file unless |save_ptr=0|.
+This condition implies that |cur_level=level_one|, hence
+the |xeq_level| array is constant and it need not be dumped.
+
+@<If dumping is not allowed, abort@>=
+if save_ptr<>0 then
+ begin print_err("You can't dump inside a group");
+@.You can't dump...@>
+ help1("`{...\dump}' is a no-no."); succumb;
+ end
+
+@ Format files consist of |memory_word| items, and we use the following
+macros to dump words of different types:
+
+@d dump_wd(#)==begin fmt_file^:=#; put(fmt_file);@+end
+@d dump_int(#)==begin fmt_file^.int:=#; put(fmt_file);@+end
+@d dump_hh(#)==begin fmt_file^.hh:=#; put(fmt_file);@+end
+@d dump_qqqq(#)==begin fmt_file^.qqqq:=#; put(fmt_file);@+end
+
+@<Glob...@>=
+@!fmt_file:word_file; {for input or output of format information}
+
+@ The inverse macros are slightly more complicated, since we need to check
+the range of the values we are reading in. We say `|undump(a)(b)(x)|' to
+read an integer value |x| that is supposed to be in the range |a<=x<=b|.
+
+@d undump_wd(#)==begin get(fmt_file); #:=fmt_file^;@+end
+@d undump_int(#)==begin get(fmt_file); #:=fmt_file^.int;@+end
+@d undump_hh(#)==begin get(fmt_file); #:=fmt_file^.hh;@+end
+@d undump_qqqq(#)==begin get(fmt_file); #:=fmt_file^.qqqq;@+end
+@d undump_end_end(#)==#:=x;@+end
+@d undump_end(#)==(x>#) then goto bad_fmt@+else undump_end_end
+@d undump(#)==begin undump_int(x); if (x<#) or undump_end
+@d undump_size_end_end(#)==too_small(#)@+else undump_end_end
+@d undump_size_end(#)==if x># then undump_size_end_end
+@d undump_size(#)==begin undump_int(x);
+ if x<# then goto bad_fmt; undump_size_end
+
+@ The next few sections of the program should make it clear how we use the
+dump/undump macros.
+
+@<Dump constants for consistency check@>=
+dump_int(@$);@/
+dump_int(mem_bot);@/
+dump_int(mem_top);@/
+dump_int(eqtb_size);@/
+dump_int(hash_prime);@/
+dump_int(hyph_size)
+
+@ Sections of a \.{WEB} program that are ``commented out'' still contribute
+strings to the string pool; therefore \.{INITEX} and \TeX\ will have
+the same strings. (And it is, of course, a good thing that they do.)
+@.WEB@>
+@^string pool@>
+
+@<Undump constants for consistency check@>=
+x:=fmt_file^.int;
+if x<>@$ then goto bad_fmt; {check that strings are the same}
+undump_int(x);
+if x<>mem_bot then goto bad_fmt;
+undump_int(x);
+if x<>mem_top then goto bad_fmt;
+undump_int(x);
+if x<>eqtb_size then goto bad_fmt;
+undump_int(x);
+if x<>hash_prime then goto bad_fmt;
+undump_int(x);
+if x<>hyph_size then goto bad_fmt
+
+@ @d dump_four_ASCII==
+ w.b0:=qi(so(str_pool[k])); w.b1:=qi(so(str_pool[k+1]));
+ w.b2:=qi(so(str_pool[k+2])); w.b3:=qi(so(str_pool[k+3]));
+ dump_qqqq(w)
+
+@<Dump the string pool@>=
+dump_int(pool_ptr);
+dump_int(str_ptr);
+for k:=0 to str_ptr do dump_int(str_start[k]);
+k:=0;
+while k+4<pool_ptr do
+ begin dump_four_ASCII; k:=k+4;
+ end;
+k:=pool_ptr-4; dump_four_ASCII;
+print_ln; print_int(str_ptr); print(" strings of total length ");
+print_int(pool_ptr)
+
+@ @d undump_four_ASCII==
+ undump_qqqq(w);
+ str_pool[k]:=si(qo(w.b0)); str_pool[k+1]:=si(qo(w.b1));
+ str_pool[k+2]:=si(qo(w.b2)); str_pool[k+3]:=si(qo(w.b3))
+
+@<Undump the string pool@>=
+undump_size(0)(pool_size)('string pool size')(pool_ptr);
+undump_size(0)(max_strings)('max strings')(str_ptr);
+for k:=0 to str_ptr do undump(0)(pool_ptr)(str_start[k]);
+k:=0;
+while k+4<pool_ptr do
+ begin undump_four_ASCII; k:=k+4;
+ end;
+k:=pool_ptr-4; undump_four_ASCII;
+init_str_ptr:=str_ptr; init_pool_ptr:=pool_ptr
+
+@ By sorting the list of available spaces in the variable-size portion of
+|mem|, we are usually able to get by without having to dump very much
+of the dynamic memory.
+
+We recompute |var_used| and |dyn_used|, so that \.{INITEX} dumps valid
+information even when it has not been gathering statistics.
+
+@<Dump the dynamic memory@>=
+sort_avail; var_used:=0;
+dump_int(lo_mem_max); dump_int(rover);
+p:=mem_bot; q:=rover; x:=0;
+repeat for k:=p to q+1 do dump_wd(mem[k]);
+x:=x+q+2-p; var_used:=var_used+q-p;
+p:=q+node_size(q); q:=rlink(q);
+until q=rover;
+var_used:=var_used+lo_mem_max-p; dyn_used:=mem_end+1-hi_mem_min;@/
+for k:=p to lo_mem_max do dump_wd(mem[k]);
+x:=x+lo_mem_max+1-p;
+dump_int(hi_mem_min); dump_int(avail);
+for k:=hi_mem_min to mem_end do dump_wd(mem[k]);
+x:=x+mem_end+1-hi_mem_min;
+p:=avail;
+while p<>null do
+ begin decr(dyn_used); p:=link(p);
+ end;
+dump_int(var_used); dump_int(dyn_used);
+print_ln; print_int(x);
+print(" memory locations dumped; current usage is ");
+print_int(var_used); print_char("&"); print_int(dyn_used)
+
+@ @<Undump the dynamic memory@>=
+undump(lo_mem_stat_max+1000)(hi_mem_stat_min-1)(lo_mem_max);
+undump(lo_mem_stat_max+1)(lo_mem_max)(rover);
+p:=mem_bot; q:=rover;
+repeat for k:=p to q+1 do undump_wd(mem[k]);
+p:=q+node_size(q);
+if (p>lo_mem_max)or((q>=rlink(q))and(rlink(q)<>rover)) then goto bad_fmt;
+q:=rlink(q);
+until q=rover;
+for k:=p to lo_mem_max do undump_wd(mem[k]);
+if mem_min<mem_bot-2 then {make more low memory available}
+ begin p:=llink(rover); q:=mem_min+1;
+ link(mem_min):=null; info(mem_min):=null; {we don't use the bottom word}
+ rlink(p):=q; llink(rover):=q;@/
+ rlink(q):=rover; llink(q):=p; link(q):=empty_flag;
+ node_size(q):=mem_bot-q;
+ end;
+undump(lo_mem_max+1)(hi_mem_stat_min)(hi_mem_min);
+undump(null)(mem_top)(avail); mem_end:=mem_top;
+for k:=hi_mem_min to mem_end do undump_wd(mem[k]);
+undump_int(var_used); undump_int(dyn_used)
+
+@ @<Dump the table of equivalents@>=
+@<Dump regions 1 to 4 of |eqtb|@>;
+@<Dump regions 5 and 6 of |eqtb|@>;
+dump_int(par_loc); dump_int(write_loc);@/
+@<Dump the hash table@>
+
+@ @<Undump the table of equivalents@>=
+@<Undump regions 1 to 6 of |eqtb|@>;
+undump(hash_base)(frozen_control_sequence)(par_loc);
+par_token:=cs_token_flag+par_loc;@/
+undump(hash_base)(frozen_control_sequence)(write_loc);@/
+@<Undump the hash table@>
+
+@ The table of equivalents usually contains repeated information, so we dump it
+in compressed form: The sequence of $n+2$ values $(n,x_1,\ldots,x_n,m)$ in the
+format file represents $n+m$ consecutive entries of |eqtb|, with |m| extra
+copies of $x_n$, namely $(x_1,\ldots,x_n,x_n,\ldots,x_n)$.
+
+@<Dump regions 1 to 4 of |eqtb|@>=
+k:=active_base;
+repeat j:=k;
+while j<int_base-1 do
+ begin if (equiv(j)=equiv(j+1))and(eq_type(j)=eq_type(j+1))and@|
+ (eq_level(j)=eq_level(j+1)) then goto found1;
+ incr(j);
+ end;
+l:=int_base; goto done1; {|j=int_base-1|}
+found1: incr(j); l:=j;
+while j<int_base-1 do
+ begin if (equiv(j)<>equiv(j+1))or(eq_type(j)<>eq_type(j+1))or@|
+ (eq_level(j)<>eq_level(j+1)) then goto done1;
+ incr(j);
+ end;
+done1:dump_int(l-k);
+while k<l do
+ begin dump_wd(eqtb[k]); incr(k);
+ end;
+k:=j+1; dump_int(k-l);
+until k=int_base
+
+@ @<Dump regions 5 and 6 of |eqtb|@>=
+repeat j:=k;
+while j<eqtb_size do
+ begin if eqtb[j].int=eqtb[j+1].int then goto found2;
+ incr(j);
+ end;
+l:=eqtb_size+1; goto done2; {|j=eqtb_size|}
+found2: incr(j); l:=j;
+while j<eqtb_size do
+ begin if eqtb[j].int<>eqtb[j+1].int then goto done2;
+ incr(j);
+ end;
+done2:dump_int(l-k);
+while k<l do
+ begin dump_wd(eqtb[k]); incr(k);
+ end;
+k:=j+1; dump_int(k-l);
+until k>eqtb_size
+
+@ @<Undump regions 1 to 6 of |eqtb|@>=
+k:=active_base;
+repeat undump_int(x);
+if (x<1)or(k+x>eqtb_size+1) then goto bad_fmt;
+for j:=k to k+x-1 do undump_wd(eqtb[j]);
+k:=k+x;
+undump_int(x);
+if (x<0)or(k+x>eqtb_size+1) then goto bad_fmt;
+for j:=k to k+x-1 do eqtb[j]:=eqtb[k-1];
+k:=k+x;
+until k>eqtb_size
+
+@ A different scheme is used to compress the hash table, since its lower
+region is usually sparse. When |text(p)<>0| for |p<=hash_used|, we output
+two words, |p| and |hash[p]|. The hash table is, of course, densely packed
+for |p>=hash_used|, so the remaining entries are output in a~block.
+
+@<Dump the hash table@>=
+dump_int(hash_used); cs_count:=frozen_control_sequence-1-hash_used;
+for p:=hash_base to hash_used do if text(p)<>0 then
+ begin dump_int(p); dump_hh(hash[p]); incr(cs_count);
+ end;
+for p:=hash_used+1 to undefined_control_sequence-1 do dump_hh(hash[p]);
+dump_int(cs_count);@/
+print_ln; print_int(cs_count); print(" multiletter control sequences")
+
+@ @<Undump the hash table@>=
+undump(hash_base)(frozen_control_sequence)(hash_used); p:=hash_base-1;
+repeat undump(p+1)(hash_used)(p); undump_hh(hash[p]);
+until p=hash_used;
+for p:=hash_used+1 to undefined_control_sequence-1 do undump_hh(hash[p]);
+undump_int(cs_count)
+
+@ @<Dump the font information@>=
+dump_int(fmem_ptr);
+for k:=0 to fmem_ptr-1 do dump_wd(font_info[k]);
+dump_int(font_ptr);
+for k:=null_font to font_ptr do
+ @<Dump the array info for internal font number |k|@>;
+print_ln; print_int(fmem_ptr-7); print(" words of font info for ");
+print_int(font_ptr-font_base); print(" preloaded font");
+if font_ptr<>font_base+1 then print_char("s")
+
+@ @<Undump the font information@>=
+undump_size(7)(font_mem_size)('font mem size')(fmem_ptr);
+for k:=0 to fmem_ptr-1 do undump_wd(font_info[k]);
+undump_size(font_base)(font_max)('font max')(font_ptr);
+for k:=null_font to font_ptr do
+ @<Undump the array info for internal font number |k|@>
+
+@ @<Dump the array info for internal font number |k|@>=
+begin dump_qqqq(font_check[k]);
+dump_int(font_size[k]);
+dump_int(font_dsize[k]);
+dump_int(font_params[k]);@/
+dump_int(hyphen_char[k]);
+dump_int(skew_char[k]);@/
+dump_int(font_name[k]);
+dump_int(font_area[k]);@/
+dump_int(font_bc[k]);
+dump_int(font_ec[k]);@/
+dump_int(char_base[k]);
+dump_int(width_base[k]);
+dump_int(height_base[k]);@/
+dump_int(depth_base[k]);
+dump_int(italic_base[k]);
+dump_int(lig_kern_base[k]);@/
+dump_int(kern_base[k]);
+dump_int(exten_base[k]);
+dump_int(param_base[k]);@/
+dump_int(font_glue[k]);@/
+dump_int(bchar_label[k]);
+dump_int(font_bchar[k]);
+dump_int(font_false_bchar[k]);@/
+print_nl("\font"); print_esc(font_id_text(k)); print_char("=");
+print_file_name(font_name[k],font_area[k],"");
+if font_size[k]<>font_dsize[k] then
+ begin print(" at "); print_scaled(font_size[k]); print("pt");
+ end;
+end
+
+@ @<Undump the array info for internal font number |k|@>=
+begin undump_qqqq(font_check[k]);@/
+undump_int(font_size[k]);
+undump_int(font_dsize[k]);
+undump(min_halfword)(max_halfword)(font_params[k]);@/
+undump_int(hyphen_char[k]);
+undump_int(skew_char[k]);@/
+undump(0)(str_ptr)(font_name[k]);
+undump(0)(str_ptr)(font_area[k]);@/
+undump(0)(255)(font_bc[k]);
+undump(0)(255)(font_ec[k]);@/
+undump_int(char_base[k]);
+undump_int(width_base[k]);
+undump_int(height_base[k]);@/
+undump_int(depth_base[k]);
+undump_int(italic_base[k]);
+undump_int(lig_kern_base[k]);@/
+undump_int(kern_base[k]);
+undump_int(exten_base[k]);
+undump_int(param_base[k]);@/
+undump(min_halfword)(lo_mem_max)(font_glue[k]);@/
+undump(0)(fmem_ptr-1)(bchar_label[k]);
+undump(min_quarterword)(non_char)(font_bchar[k]);
+undump(min_quarterword)(non_char)(font_false_bchar[k]);
+end
+
+@ @<Dump the hyphenation tables@>=
+dump_int(hyph_count);
+for k:=0 to hyph_size do if hyph_word[k]<>0 then
+ begin dump_int(k); dump_int(hyph_word[k]); dump_int(hyph_list[k]);
+ end;
+print_ln; print_int(hyph_count); print(" hyphenation exception");
+if hyph_count<>1 then print_char("s");
+if trie_not_ready then init_trie;
+dump_int(trie_max);
+for k:=0 to trie_max do dump_hh(trie[k]);
+dump_int(trie_op_ptr);
+for k:=1 to trie_op_ptr do
+ begin dump_int(hyf_distance[k]);
+ dump_int(hyf_num[k]);
+ dump_int(hyf_next[k]);
+ end;
+print_nl("Hyphenation trie of length "); print_int(trie_max);
+@.Hyphenation trie...@>
+print(" has "); print_int(trie_op_ptr); print(" op");
+if trie_op_ptr<>1 then print_char("s");
+print(" out of "); print_int(trie_op_size);
+for k:=255 downto 0 do if trie_used[k]>min_quarterword then
+ begin print_nl(" "); print_int(qo(trie_used[k]));
+ print(" for language "); print_int(k);
+ dump_int(k); dump_int(qo(trie_used[k]));
+ end
+
+@ Only ``nonempty'' parts of |op_start| need to be restored.
+
+@<Undump the hyphenation tables@>=
+undump(0)(hyph_size)(hyph_count);
+for k:=1 to hyph_count do
+ begin undump(0)(hyph_size)(j);
+ undump(0)(str_ptr)(hyph_word[j]);
+ undump(min_halfword)(max_halfword)(hyph_list[j]);
+ end;
+undump_size(0)(trie_size)('trie size')(j); @+init trie_max:=j;@+tini
+for k:=0 to j do undump_hh(trie[k]);
+undump_size(0)(trie_op_size)('trie op size')(j); @+init trie_op_ptr:=j;@+tini
+for k:=1 to j do
+ begin undump(0)(63)(hyf_distance[k]); {a |small_number|}
+ undump(0)(63)(hyf_num[k]);
+ undump(min_quarterword)(max_quarterword)(hyf_next[k]);
+ end;
+init for k:=0 to 255 do trie_used[k]:=min_quarterword;@+tini@;@/
+k:=256;
+while j>0 do
+ begin undump(0)(k-1)(k); undump(1)(j)(x);@+init trie_used[k]:=qi(x);@+tini@;@/
+ j:=j-x; op_start[k]:=qo(j);
+ end;
+@!init trie_not_ready:=false @+tini
+
+@ We have already printed a lot of statistics, so we set |tracing_stats:=0|
+to prevent them from appearing again.
+
+@<Dump a couple more things and the closing check word@>=
+dump_int(interaction); dump_int(format_ident); dump_int(69069);
+tracing_stats:=0
+
+@ @<Undump a couple more things and the closing check word@>=
+undump(batch_mode)(error_stop_mode)(interaction);
+undump(0)(str_ptr)(format_ident);
+undump_int(x);
+if (x<>69069)or eof(fmt_file) then goto bad_fmt
+
+@ @<Create the |format_ident|...@>=
+selector:=new_string;
+print(" (preloaded format="); print(job_name); print_char(" ");
+print_int(year); print_char(".");
+print_int(month); print_char("."); print_int(day); print_char(")");
+if interaction=batch_mode then selector:=log_only
+else selector:=term_and_log;
+str_room(1);
+format_ident:=make_string;
+pack_job_name(format_extension);
+while not w_open_out(fmt_file) do
+ prompt_file_name("format file name",format_extension);
+print_nl("Beginning to dump on file ");
+@.Beginning to dump...@>
+slow_print(w_make_name_string(fmt_file)); flush_string;
+print_nl(""); slow_print(format_ident)
+
+@ @<Close the format file@>=
+w_close(fmt_file)
+
+@* \[51] The main program.
+This is it: the part of \TeX\ that executes all those procedures we have
+written.
+
+Well---almost. Let's leave space for a few more routines that we may
+have forgotten.
+
+@p @<Last-minute procedures@>
+
+@ We have noted that there are two versions of \TeX82. One, called \.{INITEX},
+@.INITEX@>
+has to be run first; it initializes everything from scratch, without
+reading a format file, and it has the capability of dumping a format file.
+The other one is called `\.{VIRTEX}'; it is a ``virgin'' program that needs
+@.VIRTEX@>
+to input a format file in order to get started. \.{VIRTEX} typically has
+more memory capacity than \.{INITEX}, because it does not need the space
+consumed by the auxiliary hyphenation tables and the numerous calls on
+|primitive|, etc.
+
+The \.{VIRTEX} program cannot read a format file instantaneously, of course;
+the best implementations therefore allow for production versions of \TeX\ that
+not only avoid the loading routine for \PASCAL\ object code, they also have
+a format file pre-loaded. This is impossible to do if we stick to standard
+\PASCAL; but there is a simple way to fool many systems into avoiding the
+initialization, as follows:\quad(1)~We declare a global integer variable
+called |ready_already|. The probability is negligible that this
+variable holds any particular value like 314159 when \.{VIRTEX} is first
+loaded.\quad(2)~After we have read in a format file and initialized
+everything, we set |ready_already:=314159|.\quad(3)~Soon \.{VIRTEX}
+will print `\.*', waiting for more input; and at this point we
+interrupt the program and save its core image in some form that the
+operating system can reload speedily.\quad(4)~When that core image is
+activated, the program starts again at the beginning; but now
+|ready_already=314159| and all the other global variables have
+their initial values too. The former chastity has vanished!
+
+In other words, if we allow ourselves to test the condition
+|ready_already=314159|, before |ready_already| has been
+assigned a value, we can avoid the lengthy initialization. Dirty tricks
+rarely pay off so handsomely.
+@^dirty \PASCAL@>
+@^system dependencies@>
+
+On systems that allow such preloading, the standard program called \.{TeX}
+should be the one that has \.{plain} format preloaded, since that agrees
+with {\sl The \TeX book}. Other versions, e.g., \.{AmSTeX}, should also
+@:TeXbook}{\sl The \TeX book@>
+@.AmSTeX@>
+@.plain@>
+be provided for commonly used formats.
+
+@<Glob...@>=
+@!ready_already:integer; {a sacrifice of purity for economy}
+
+@ Now this is really it: \TeX\ starts and ends here.
+
+The initial test involving |ready_already| should be deleted if the
+\PASCAL\ runtime system is smart enough to detect such a ``mistake.''
+@^system dependencies@>
+
+@p begin @!{|start_here|}
+history:=fatal_error_stop; {in case we quit during initialization}
+t_open_out; {open the terminal for output}
+if ready_already=314159 then goto start_of_TEX;
+@<Check the ``constant'' values...@>@;
+if bad>0 then
+ begin wterm_ln('Ouch---my internal constants have been clobbered!',
+ '---case ',bad:1);
+@.Ouch...clobbered@>
+ goto final_end;
+ end;
+initialize; {set global variables to their starting values}
+@!init if not get_strings_started then goto final_end;
+init_prim; {call |primitive| for each primitive}
+init_str_ptr:=str_ptr; init_pool_ptr:=pool_ptr; fix_date_and_time;
+tini@/
+ready_already:=314159;
+start_of_TEX: @<Initialize the output routines@>;
+@<Get the first line of input and prepare to start@>;
+history:=spotless; {ready to go!}
+main_control; {come to life}
+final_cleanup; {prepare for death}
+end_of_TEX: close_files_and_terminate;
+final_end: ready_already:=0;
+end.
+
+@ Here we do whatever is needed to complete \TeX's job gracefully on the
+local operating system. The code here might come into play after a fatal
+error; it must therefore consist entirely of ``safe'' operations that
+cannot produce error messages. For example, it would be a mistake to call
+|str_room| or |make_string| at this time, because a call on |overflow|
+might lead to an infinite loop.
+@^system dependencies@>
+
+Actually there's one way to get error messages, via |prepare_mag|;
+but that can't cause infinite recursion.
+@^recursion@>
+
+This program doesn't bother to close the input files that may still be open.
+
+@<Last-minute...@>=
+procedure close_files_and_terminate;
+var k:integer; {all-purpose index}
+begin @<Finish the extensions@>;
+@!stat if tracing_stats>0 then @<Output statistics about this job@>;@;@+tats@/
+wake_up_terminal; @<Finish the \.{DVI} file@>;
+if log_opened then
+ begin wlog_cr; a_close(log_file); selector:=selector-2;
+ if selector=term_only then
+ begin print_nl("Transcript written on ");
+@.Transcript written...@>
+ slow_print(log_name); print_char(".");
+ end;
+ end;
+end;
+
+@ The present section goes directly to the log file instead of using
+|print| commands, because there's no need for these strings to take
+up |str_pool| memory when a non-{\bf stat} version of \TeX\ is being used.
+
+@<Output statistics...@>=
+if log_opened then
+ begin wlog_ln(' ');
+ wlog_ln('Here is how much of TeX''s memory',' you used:');
+@.Here is how much...@>
+ wlog(' ',str_ptr-init_str_ptr:1,' string');
+ if str_ptr<>init_str_ptr+1 then wlog('s');
+ wlog_ln(' out of ', max_strings-init_str_ptr:1);@/
+ wlog_ln(' ',pool_ptr-init_pool_ptr:1,' string characters out of ',
+ pool_size-init_pool_ptr:1);@/
+ wlog_ln(' ',lo_mem_max-mem_min+mem_end-hi_mem_min+2:1,@|
+ ' words of memory out of ',mem_end+1-mem_min:1);@/
+ wlog_ln(' ',cs_count:1,' multiletter control sequences out of ',
+ hash_size:1);@/
+ wlog(' ',fmem_ptr:1,' words of font info for ',
+ font_ptr-font_base:1,' font');
+ if font_ptr<>font_base+1 then wlog('s');
+ wlog_ln(', out of ',font_mem_size:1,' for ',font_max-font_base:1);@/
+ wlog(' ',hyph_count:1,' hyphenation exception');
+ if hyph_count<>1 then wlog('s');
+ wlog_ln(' out of ',hyph_size:1);@/
+ wlog_ln(' ',max_in_stack:1,'i,',max_nest_stack:1,'n,',@|
+ max_param_stack:1,'p,',@|
+ max_buf_stack+1:1,'b,',@|
+ max_save_stack+6:1,'s stack positions out of ',@|
+ stack_size:1,'i,',
+ nest_size:1,'n,',
+ param_size:1,'p,',
+ buf_size:1,'b,',
+ save_size:1,'s');
+ end
+
+@ We get to the |final_cleanup| routine when \.{\\end} or \.{\\dump} has
+been scanned and |its_all_over|\kern-2pt.
+
+@<Last-minute...@>=
+procedure final_cleanup;
+label exit;
+var c:small_number; {0 for \.{\\end}, 1 for \.{\\dump}}
+begin c:=cur_chr;
+if job_name=0 then open_log_file;
+while input_ptr>0 do
+ if state=token_list then end_token_list@+else end_file_reading;
+while open_parens>0 do
+ begin print(" )"); decr(open_parens);
+ end;
+if cur_level>level_one then
+ begin print_nl("("); print_esc("end occurred ");
+ print("inside a group at level ");
+@:end_}{\.{(\\end occurred...)}@>
+ print_int(cur_level-level_one); print_char(")");
+ end;
+while cond_ptr<>null do
+ begin print_nl("("); print_esc("end occurred ");
+ print("when "); print_cmd_chr(if_test,cur_if);
+ if if_line<>0 then
+ begin print(" on line "); print_int(if_line);
+ end;
+ print(" was incomplete)");
+ if_line:=if_line_field(cond_ptr);
+ cur_if:=subtype(cond_ptr); temp_ptr:=cond_ptr;
+ cond_ptr:=link(cond_ptr); free_node(temp_ptr,if_node_size);
+ end;
+if history<>spotless then
+ if ((history=warning_issued)or(interaction<error_stop_mode)) then
+ if selector=term_and_log then
+ begin selector:=term_only;
+ print_nl("(see the transcript file for additional information)");
+@.see the transcript file...@>
+ selector:=term_and_log;
+ end;
+if c=1 then
+ begin @!init for c:=top_mark_code to split_bot_mark_code do
+ if cur_mark[c]<>null then delete_token_ref(cur_mark[c]);
+ store_fmt_file; return;@+tini@/
+ print_nl("(\dump is performed only by INITEX)"); return;
+@:dump_}{\.{\\dump...only by INITEX}@>
+ end;
+exit:end;
+
+@ @<Last-minute...@>=
+@!init procedure init_prim; {initialize all the primitives}
+begin no_new_control_sequence:=false;
+@<Put each...@>;
+no_new_control_sequence:=true;
+end;
+tini
+
+@ When we begin the following code, \TeX's tables may still contain garbage;
+the strings might not even be present. Thus we must proceed cautiously to get
+bootstrapped in.
+
+But when we finish this part of the program, \TeX\ is ready to call on the
+|main_control| routine to do its work.
+
+@<Get the first line...@>=
+begin @<Initialize the input routines@>;
+if (format_ident=0)or(buffer[loc]="&") then
+ begin if format_ident<>0 then initialize; {erase preloaded format}
+ if not open_fmt_file then goto final_end;
+ if not load_fmt_file then
+ begin w_close(fmt_file); goto final_end;
+ end;
+ w_close(fmt_file);
+ while (loc<limit)and(buffer[loc]=" ") do incr(loc);
+ end;
+if end_line_char_inactive then decr(limit)
+else buffer[limit]:=end_line_char;
+fix_date_and_time;@/
+@<Compute the magic offset@>;
+@<Initialize the print |selector|...@>;
+if (loc<limit)and(cat_code(buffer[loc])<>escape) then start_input;
+ {\.{\\input} assumed}
+end
+
+@* \[52] Debugging.
+Once \TeX\ is working, you should be able to diagnose most errors with
+the \.{\\show} commands and other diagnostic features. But for the initial
+stages of debugging, and for the revelation of really deep mysteries, you
+can compile \TeX\ with a few more aids, including the \PASCAL\ runtime
+checks and its debugger. An additional routine called |debug_help|
+will also come into play when you type `\.D' after an error message;
+|debug_help| also occurs just before a fatal error causes \TeX\ to succumb.
+@^debugging@>
+@^system dependencies@>
+
+The interface to |debug_help| is primitive, but it is good enough when used
+with a \PASCAL\ debugger that allows you to set breakpoints and to read
+variables and change their values. After getting the prompt `\.{debug \#}', you
+type either a negative number (this exits |debug_help|), or zero (this
+goes to a location where you can set a breakpoint, thereby entering into
+dialog with the \PASCAL\ debugger), or a positive number |m| followed by
+an argument |n|. The meaning of |m| and |n| will be clear from the
+program below. (If |m=13|, there is an additional argument, |l|.)
+@.debug \#@>
+
+@d breakpoint=888 {place where a breakpoint is desirable}
+
+@<Last-minute...@>=
+@!debug procedure debug_help; {routine to display various things}
+label breakpoint,exit;
+var k,@!l,@!m,@!n:integer;
+begin loop begin wake_up_terminal;
+ print_nl("debug # (-1 to exit):"); update_terminal;
+@.debug \#@>
+ read(term_in,m);
+ if m<0 then return
+ else if m=0 then
+ begin goto breakpoint;@\ {go to every label at least once}
+ breakpoint: m:=0; @{'BREAKPOINT'@}@\
+ end
+ else begin read(term_in,n);
+ case m of
+ @t\4@>@<Numbered cases for |debug_help|@>@;
+ othercases print("?")
+ endcases;
+ end;
+ end;
+exit:end;
+gubed
+
+@ @<Numbered cases...@>=
+1: print_word(mem[n]); {display |mem[n]| in all forms}
+2: print_int(info(n));
+3: print_int(link(n));
+4: print_word(eqtb[n]);
+5: print_word(font_info[n]);
+6: print_word(save_stack[n]);
+7: show_box(n);
+ {show a box, abbreviated by |show_box_depth| and |show_box_breadth|}
+8: begin breadth_max:=10000; depth_threshold:=pool_size-pool_ptr-10;
+ show_node_list(n); {show a box in its entirety}
+ end;
+9: show_token_list(n,null,1000);
+10: slow_print(n);
+11: check_mem(n>0); {check wellformedness; print new busy locations if |n>0|}
+12: search_mem(n); {look for pointers to |n|}
+13: begin read(term_in,l); print_cmd_chr(n,l);
+ end;
+14: for k:=0 to n do print(buffer[k]);
+15: begin font_in_short_display:=null_font; short_display(n);
+ end;
+16: panicking:=not panicking;
+
+@* \[53] Extensions.
+The program above includes a bunch of ``hooks'' that allow further
+capabilities to be added without upsetting \TeX's basic structure.
+Most of these hooks are concerned with ``whatsit'' nodes, which are
+intended to be used for special purposes; whenever a new extension to
+\TeX\ involves a new kind of whatsit node, a corresponding change needs
+to be made to the routines below that deal with such nodes,
+but it will usually be unnecessary to make many changes to the
+other parts of this program.
+
+In order to demonstrate how extensions can be made, we shall treat
+`\.{\\write}', `\.{\\openout}', `\.{\\closeout}', `\.{\\immediate}',
+`\.{\\special}', and `\.{\\setlanguage}' as if they were extensions.
+These commands are actually primitives of \TeX, and they should
+appear in all implementations of the system; but let's try to imagine
+that they aren't. Then the program below illustrates how a person
+could add them.
+
+Sometimes, of course, an extension will require changes to \TeX\ itself;
+no system of hooks could be complete enough for all conceivable extensions.
+The features associated with `\.{\\write}' are almost all confined to the
+following paragraphs, but there are small parts of the |print_ln| and
+|print_char| procedures that were introduced specifically to \.{\\write}
+characters. Furthermore one of the token lists recognized by the scanner
+is a |write_text|; and there are a few other miscellaneous places where we
+have already provided for some aspect of \.{\\write}. The goal of a \TeX\
+extender should be to minimize alterations to the standard parts of the
+program, and to avoid them completely if possible. He or she should also
+be quite sure that there's no easy way to accomplish the desired goals
+with the standard features that \TeX\ already has. ``Think thrice before
+extending,'' because that may save a lot of work, and it will also keep
+incompatible extensions of \TeX\ from proliferating.
+@^system dependencies@>
+@^extensions to \TeX@>
+
+@ First let's consider the format of whatsit nodes that are used to represent
+the data associated with \.{\\write} and its relatives. Recall that a whatsit
+has |type=whatsit_node|, and the |subtype| is supposed to distinguish
+different kinds of whatsits. Each node occupies two or more words; the
+exact number is immaterial, as long as it is readily determined from the
+|subtype| or other data.
+
+We shall introduce five |subtype| values here, corresponding to the
+control sequences \.{\\openout}, \.{\\write}, \.{\\closeout}, \.{\\special}, and
+\.{\\setlanguage}. The second word of I/O whatsits has a |write_stream| field
+that identifies the write-stream number (0 to 15, or 16 for out-of-range and
+positive, or 17 for out-of-range and negative).
+In the case of \.{\\write} and \.{\\special}, there is also a field that
+points to the reference count of a token list that should be sent. In the
+case of \.{\\openout}, we need three words and three auxiliary subfields
+to hold the string numbers for name, area, and extension.
+
+@d write_node_size=2 {number of words in a write/whatsit node}
+@d open_node_size=3 {number of words in an open/whatsit node}
+@d open_node=0 {|subtype| in whatsits that represent files to \.{\\openout}}
+@d write_node=1 {|subtype| in whatsits that represent things to \.{\\write}}
+@d close_node=2 {|subtype| in whatsits that represent streams to \.{\\closeout}}
+@d special_node=3 {|subtype| in whatsits that represent \.{\\special} things}
+@d language_node=4 {|subtype| in whatsits that change the current language}
+@d what_lang(#)==link(#+1) {language number, in the range |0..255|}
+@d what_lhm(#)==type(#+1) {minimum left fragment, in the range |1..63|}
+@d what_rhm(#)==subtype(#+1) {minimum right fragment, in the range |1..63|}
+@d write_tokens(#) == link(#+1) {reference count of token list to write}
+@d write_stream(#) == info(#+1) {stream number (0 to 17)}
+@d open_name(#) == link(#+1) {string number of file name to open}
+@d open_area(#) == info(#+2) {string number of file area for |open_name|}
+@d open_ext(#) == link(#+2) {string number of file extension for |open_name|}
+
+@ The sixteen possible \.{\\write} streams are represented by the |write_file|
+array. The |j|th file is open if and only if |write_open[j]=true|. The last
+two streams are special; |write_open[16]| represents a stream number
+greater than 15, while |write_open[17]| represents a negative stream number,
+and both of these variables are always |false|.
+
+@<Glob...@>=
+@!write_file:array[0..15] of alpha_file;
+@!write_open:array[0..17] of boolean;
+
+@ @<Set init...@>=
+for k:=0 to 17 do write_open[k]:=false;
+
+@ Extensions might introduce new command codes; but it's best to use
+|extension| with a modifier, whenever possible, so that |main_control|
+stays the same.
+
+@d immediate_code=4 {command modifier for \.{\\immediate}}
+@d set_language_code=5 {command modifier for \.{\\setlanguage}}
+
+@<Put each...@>=
+primitive("openout",extension,open_node);@/
+@!@:open_out_}{\.{\\openout} primitive@>
+primitive("write",extension,write_node); write_loc:=cur_val;@/
+@!@:write_}{\.{\\write} primitive@>
+primitive("closeout",extension,close_node);@/
+@!@:close_out_}{\.{\\closeout} primitive@>
+primitive("special",extension,special_node);@/
+@!@:special_}{\.{\\special} primitive@>
+primitive("immediate",extension,immediate_code);@/
+@!@:immediate_}{\.{\\immediate} primitive@>
+primitive("setlanguage",extension,set_language_code);@/
+@!@:set_language_}{\.{\\setlanguage} primitive@>
+
+@ The variable |write_loc| just introduced is used to provide an
+appropriate error message in case of ``runaway'' write texts.
+
+@<Glob...@>=
+@!write_loc:pointer; {|eqtb| address of \.{\\write}}
+
+@ @<Cases of |print_cmd_chr|...@>=
+extension: case chr_code of
+ open_node:print_esc("openout");
+ write_node:print_esc("write");
+ close_node:print_esc("closeout");
+ special_node:print_esc("special");
+ immediate_code:print_esc("immediate");
+ set_language_code:print_esc("setlanguage");
+ othercases print("[unknown extension!]")
+ endcases;
+
+@ When an |extension| command occurs in |main_control|, in any mode,
+the |do_extension| routine is called.
+
+@<Cases of |main_control| that are for extensions...@>=
+any_mode(extension):do_extension;
+
+@ @<Declare act...@>=
+@t\4@>@<Declare procedures needed in |do_extension|@>@;
+procedure do_extension;
+var i,@!j,@!k:integer; {all-purpose integers}
+@!p,@!q,@!r:pointer; {all-purpose pointers}
+begin case cur_chr of
+open_node:@<Implement \.{\\openout}@>;
+write_node:@<Implement \.{\\write}@>;
+close_node:@<Implement \.{\\closeout}@>;
+special_node:@<Implement \.{\\special}@>;
+immediate_code:@<Implement \.{\\immediate}@>;
+set_language_code:@<Implement \.{\\setlanguage}@>;
+othercases confusion("ext1")
+@:this can't happen ext1}{\quad ext1@>
+endcases;
+end;
+
+@ Here is a subroutine that creates a whatsit node having a given |subtype|
+and a given number of words. It initializes only the first word of the whatsit,
+and appends it to the current list.
+
+@<Declare procedures needed in |do_extension|@>=
+procedure new_whatsit(@!s:small_number;@!w:small_number);
+var p:pointer; {the new node}
+begin p:=get_node(w); type(p):=whatsit_node; subtype(p):=s;
+link(tail):=p; tail:=p;
+end;
+
+@ The next subroutine uses |cur_chr| to decide what sort of whatsit is
+involved, and also inserts a |write_stream| number.
+
+@<Declare procedures needed in |do_ext...@>=
+procedure new_write_whatsit(@!w:small_number);
+begin new_whatsit(cur_chr,w);
+if w<>write_node_size then scan_four_bit_int
+else begin scan_int;
+ if cur_val<0 then cur_val:=17
+ else if cur_val>15 then cur_val:=16;
+ end;
+write_stream(tail):=cur_val;
+end;
+
+@ @<Implement \.{\\openout}@>=
+begin new_write_whatsit(open_node_size);
+scan_optional_equals; scan_file_name;@/
+open_name(tail):=cur_name; open_area(tail):=cur_area; open_ext(tail):=cur_ext;
+end
+
+@ When `\.{\\write 12\{...\}}' appears, we scan the token list `\.{\{...\}}'
+without expanding its macros; the macros will be expanded later when this
+token list is rescanned.
+
+@<Implement \.{\\write}@>=
+begin k:=cur_cs; new_write_whatsit(write_node_size);@/
+cur_cs:=k; p:=scan_toks(false,false); write_tokens(tail):=def_ref;
+end
+
+@ @<Implement \.{\\closeout}@>=
+begin new_write_whatsit(write_node_size); write_tokens(tail):=null;
+end
+
+@ When `\.{\\special\{...\}}' appears, we expand the macros in the token
+list as in \.{\\xdef} and \.{\\mark}.
+
+@<Implement \.{\\special}@>=
+begin new_whatsit(special_node,write_node_size); write_stream(tail):=null;
+p:=scan_toks(false,true); write_tokens(tail):=def_ref;
+end
+
+@ Each new type of node that appears in our data structure must be capable
+of being displayed, copied, destroyed, and so on. The routines that we
+need for write-oriented whatsits are somewhat like those for mark nodes;
+other extensions might, of course, involve more subtlety here.
+
+@<Basic printing...@>=
+procedure print_write_whatsit(@!s:str_number;@!p:pointer);
+begin print_esc(s);
+if write_stream(p)<16 then print_int(write_stream(p))
+else if write_stream(p)=16 then print_char("*")
+@.*\relax@>
+else print_char("-");
+end;
+
+@ @<Display the whatsit...@>=
+case subtype(p) of
+open_node:begin print_write_whatsit("openout",p);
+ print_char("="); print_file_name(open_name(p),open_area(p),open_ext(p));
+ end;
+write_node:begin print_write_whatsit("write",p);
+ print_mark(write_tokens(p));
+ end;
+close_node:print_write_whatsit("closeout",p);
+special_node:begin print_esc("special");
+ print_mark(write_tokens(p));
+ end;
+language_node:begin print_esc("setlanguage");
+ print_int(what_lang(p)); print(" (hyphenmin ");
+ print_int(what_lhm(p)); print_char(",");
+ print_int(what_rhm(p)); print_char(")");
+ end;
+othercases print("whatsit?")
+endcases
+
+@ @<Make a partial copy of the whatsit...@>=
+case subtype(p) of
+open_node: begin r:=get_node(open_node_size); words:=open_node_size;
+ end;
+write_node,special_node: begin r:=get_node(write_node_size);
+ add_token_ref(write_tokens(p)); words:=write_node_size;
+ end;
+close_node,language_node: begin r:=get_node(small_node_size);
+ words:=small_node_size;
+ end;
+othercases confusion("ext2")
+@:this can't happen ext2}{\quad ext2@>
+endcases
+
+@ @<Wipe out the whatsit...@>=
+begin case subtype(p) of
+open_node: free_node(p,open_node_size);
+write_node,special_node: begin delete_token_ref(write_tokens(p));
+ free_node(p,write_node_size); goto done;
+ end;
+close_node,language_node: free_node(p,small_node_size);
+othercases confusion("ext3")
+@:this can't happen ext3}{\quad ext3@>
+endcases;@/
+goto done;
+end
+
+@ @<Incorporate a whatsit node into a vbox@>=do_nothing
+
+@ @<Incorporate a whatsit node into an hbox@>=do_nothing
+
+@ @<Let |d| be the width of the whatsit |p|@>=d:=0
+
+@ @d adv_past(#)==@+if subtype(#)=language_node then
+ begin cur_lang:=what_lang(#); l_hyf:=what_lhm(#); r_hyf:=what_rhm(#);@+end
+
+@<Advance \(p)past a whatsit node in the \(l)|line_break| loop@>=@+
+adv_past(cur_p)
+
+@ @<Advance \(p)past a whatsit node in the \(p)pre-hyphenation loop@>=@+
+adv_past(s)
+
+@ @<Prepare to move whatsit |p| to the current page, then |goto contribute|@>=
+goto contribute
+
+@ @<Process whatsit |p| in |vert_break| loop, |goto not_found|@>=
+goto not_found
+
+@ @<Output the whatsit node |p| in a vlist@>=
+out_what(p)
+
+@ @<Output the whatsit node |p| in an hlist@>=
+out_what(p)
+
+@ After all this preliminary shuffling, we come finally to the routines
+that actually send out the requested data. Let's do \.{\\special} first
+(it's easier).
+
+@<Declare procedures needed in |hlist_out|, |vlist_out|@>=
+procedure special_out(@!p:pointer);
+var old_setting:0..max_selector; {holds print |selector|}
+@!k:pool_pointer; {index into |str_pool|}
+begin synch_h; synch_v;@/
+old_setting:=selector; selector:=new_string;
+show_token_list(link(write_tokens(p)),null,pool_size-pool_ptr);
+selector:=old_setting;
+str_room(1);
+if cur_length<256 then
+ begin dvi_out(xxx1); dvi_out(cur_length);
+ end
+else begin dvi_out(xxx4); dvi_four(cur_length);
+ end;
+for k:=str_start[str_ptr] to pool_ptr-1 do dvi_out(so(str_pool[k]));
+pool_ptr:=str_start[str_ptr]; {erase the string}
+end;
+
+@ To write a token list, we must run it through \TeX's scanner, expanding
+macros and \.{\\the} and \.{\\number}, etc. This might cause runaways,
+if a delimited macro parameter isn't matched, and runaways would be
+extremely confusing since we are calling on \TeX's scanner in the middle
+of a \.{\\shipout} command. Therefore we will put a dummy control sequence as
+a ``stopper,'' right after the token list. This control sequence is
+artificially defined to be \.{\\outer}.
+@:end_write_}{\.{\\endwrite}@>
+
+@<Initialize table...@>=
+text(end_write):="endwrite"; eq_level(end_write):=level_one;
+eq_type(end_write):=outer_call; equiv(end_write):=null;
+
+@ @<Declare procedures needed in |hlist_out|, |vlist_out|@>=
+procedure write_out(@!p:pointer);
+var old_setting:0..max_selector; {holds print |selector|}
+@!old_mode:integer; {saved |mode|}
+@!j:small_number; {write stream number}
+@!q,@!r:pointer; {temporary variables for list manipulation}
+begin @<Expand macros in the token list
+ and make |link(def_ref)| point to the result@>;
+old_setting:=selector; j:=write_stream(p);
+if write_open[j] then selector:=j
+else begin {write to the terminal if file isn't open}
+ if (j=17)and(selector=term_and_log) then selector:=log_only;
+ print_nl("");
+ end;
+token_show(def_ref); print_ln;
+flush_list(def_ref); selector:=old_setting;
+end;
+
+@ The final line of this routine is slightly subtle; at least, the author
+didn't think about it until getting burnt! There is a used-up token list
+@^Knuth, Donald Ervin@>
+on the stack, namely the one that contained |end_write_token|. (We
+insert this artificial `\.{\\endwrite}' to prevent runaways, as explained
+above.) If it were not removed, and if there were numerous writes on a
+single page, the stack would overflow.
+
+@d end_write_token==cs_token_flag+end_write
+
+@<Expand macros in the token list and...@>=
+q:=get_avail; info(q):=right_brace_token+"}";@/
+r:=get_avail; link(q):=r; info(r):=end_write_token; ins_list(q);@/
+begin_token_list(write_tokens(p),write_text);@/
+q:=get_avail; info(q):=left_brace_token+"{"; ins_list(q);
+{now we're ready to scan
+ `\.\{$\langle\,$token list$\,\rangle$\.{\} \\endwrite}'}
+old_mode:=mode; mode:=0;
+ {disable \.{\\prevdepth}, \.{\\spacefactor}, \.{\\lastskip}, \.{\\prevgraf}}
+cur_cs:=write_loc; q:=scan_toks(false,true); {expand macros, etc.}
+get_token;@+if cur_tok<>end_write_token then
+ @<Recover from an unbalanced write command@>;
+mode:=old_mode;
+end_token_list {conserve stack space}
+
+@ @<Recover from an unbalanced write command@>=
+begin print_err("Unbalanced write command");
+@.Unbalanced write...@>
+help2("On this page there's a \write with fewer real {'s than }'s.")@/
+("I can't handle that very well; good luck."); error;
+repeat get_token;
+until cur_tok=end_write_token;
+end
+
+@ The |out_what| procedure takes care of outputting whatsit nodes for
+|vlist_out| and |hlist_out|\kern-.3pt.
+
+@<Declare procedures needed in |hlist_out|, |vlist_out|@>=
+procedure out_what(@!p:pointer);
+var j:small_number; {write stream number}
+begin case subtype(p) of
+open_node,write_node,close_node:@<Do some work that has been queued up
+ for \.{\\write}@>;
+special_node:special_out(p);
+language_node:do_nothing;
+othercases confusion("ext4")
+@:this can't happen ext4}{\quad ext4@>
+endcases;
+end;
+
+@ We don't implement \.{\\write} inside of leaders. (The reason is that
+the number of times a leader box appears might be different in different
+implementations, due to machine-dependent rounding in the glue calculations.)
+@^leaders@>
+
+@<Do some work that has been queued up...@>=
+if not doing_leaders then
+ begin j:=write_stream(p);
+ if subtype(p)=write_node then write_out(p)
+ else begin if write_open[j] then a_close(write_file[j]);
+ if subtype(p)=close_node then write_open[j]:=false
+ else if j<16 then
+ begin cur_name:=open_name(p); cur_area:=open_area(p);
+ cur_ext:=open_ext(p);
+ if cur_ext="" then cur_ext:=".tex";
+ pack_cur_name;
+ while not a_open_out(write_file[j]) do
+ prompt_file_name("output file name",".tex");
+ write_open[j]:=true;
+ end;
+ end;
+ end
+
+@ The presence of `\.{\\immediate}' causes the |do_extension| procedure
+to descend to one level of recursion. Nothing happens unless \.{\\immediate}
+is followed by `\.{\\openout}', `\.{\\write}', or `\.{\\closeout}'.
+@^recursion@>
+
+@<Implement \.{\\immediate}@>=
+begin get_x_token;
+if (cur_cmd=extension)and(cur_chr<=close_node) then
+ begin p:=tail; do_extension; {append a whatsit node}
+ out_what(tail); {do the action immediately}
+ flush_node_list(tail); tail:=p; link(p):=null;
+ end
+else back_input;
+end
+
+@ The \.{\\language} extension is somewhat different.
+We need a subroutine that comes into play when a character of
+a non-|clang| language is being appended to the current paragraph.
+
+@<Declare action...@>=
+procedure fix_language;
+var @!l:ASCII_code; {the new current language}
+begin if language<=0 then l:=0
+else if language>255 then l:=0
+else l:=language;
+if l<>clang then
+ begin new_whatsit(language_node,small_node_size);
+ what_lang(tail):=l; clang:=l;@/
+ what_lhm(tail):=norm_min(left_hyphen_min);
+ what_rhm(tail):=norm_min(right_hyphen_min);
+ end;
+end;
+
+@ @<Implement \.{\\setlanguage}@>=
+if abs(mode)<>hmode then report_illegal_case
+else begin new_whatsit(language_node,small_node_size);
+ scan_int;
+ if cur_val<=0 then clang:=0
+ else if cur_val>255 then clang:=0
+ else clang:=cur_val;
+ what_lang(tail):=clang;
+ what_lhm(tail):=norm_min(left_hyphen_min);
+ what_rhm(tail):=norm_min(right_hyphen_min);
+ end
+
+@ @<Finish the extensions@>=
+for k:=0 to 15 do if write_open[k] then a_close(write_file[k])
+
+@* \[54] System-dependent changes.
+This section should be replaced, if necessary, by any special
+modifications of the program
+that are necessary to make \TeX\ work at a particular installation.
+It is usually best to design your change file so that all changes to
+previous sections preserve the section numbering; then everybody's version
+will be consistent with the published program. More extensive changes,
+which introduce new sections, can be inserted here; then only the index
+itself will get a new section number.
+@^system dependencies@>
+
+@* \[55] Index.
+Here is where you can find all uses of each identifier in the program,
+with underlined entries pointing to where the identifier was defined.
+If the identifier is only one letter long, however, you get to see only
+the underlined entries. {\sl All references are to section numbers instead of
+page numbers.}
+
+This index also lists error messages and other aspects of the program
+that you might want to look up some day. For example, the entry
+for ``system dependencies'' lists all sections that should receive
+special attention from people who are installing \TeX\ in a new
+operating environment. A list of various things that can't happen appears
+under ``this can't happen''. Approximately 40 sections are listed under
+``inner loop''; these account for about 60\pct! of \TeX's running time,
+exclusive of input and output.