% Copyright (c) 2007 Hartmut Henkel, Taco Hoekwater

% This file is part of luaTeX.

% luaTeX is free software; you can redistribute it and/or modify it under the
% terms of the GNU General Public License as published by the Free Software
% Foundation; either version 2 of the License, or (at your option) any later
% version.

% luaTeX is distributed in the hope that it will be useful, but WITHOUT ANY
% WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
% A PARTICULAR PURPOSE.  See the GNU General Public License for more details.

% You should have received a copy of the GNU General Public License
% along with luaTeX; if not, write to the Free Software Foundation, Inc.,
% 51 Franklin St, Fifth Floor, Boston, MA  02110-1301 USA

% pdfTeX is copyright (C) 1996-2006 Han The Thanh, <thanh@@pdftex.org>.
% e-TeX is copyright (C) 1994,98 by Peter Breitenlohner.

% This program is directly derived from Donald E. Knuth's TeX;
% the change history which follows and the reward offered for finders of
% bugs refer specifically to TeX; they should not be taken as referring
% to e-TeX, although the change history is relevant in that it
% demonstrates the evolutionary path followed.  This program is not TeX;
% that name is reserved strictly for the program which is the creation
% and sole responsibility of Professor Knuth.

% 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).


% Although considerable effort has been expended to make the luaTeX program
% correct and reliable, no warranty is implied; the authors disclaim 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 authors hope 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\pdfTeX{pdf\TeX}
\def\pdfeTeX{pdf\eTeX}
\def\PDF{PDF}
\def\Aleph{Aleph}
\def\eTeX{e\TeX}
\def\LuaTeX{Lua\TeX}
\def\THANH{H\`an Th\^e\llap{\raise 0.5ex\hbox{\'{}}} Th\`anh}
\def\ph{\hbox{Pascal-H}}
\def\pct!{{\char`\%}} % percent sign in ordinary text
\def\grp{\.{\char'173...\char'175}}
\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{LuaTeX}
\let\maybe=\iffalse % print only changed modules
\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 LuaTeX, a continuation of $\pdfTeX$ and $\Aleph$.  LuaTeX is a
document compiler intended to simplify high-quality typesetting for
many of the world's languages.  It is an extension of D. E. Knuth's
\TeX, which was designed essentially for the typesetting of languages
using the Latin alphabet.

The $\Aleph$ subsystem loosens many of the restrictions imposed by~\TeX:
register numbers are no longer limited to 8~bits;  fonts may have more
than 256~characters;  more than 256~fonts may be used;  etc.

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@>

This program contains code for various features extending \TeX,
therefore this program is called `\eTeX' and not
`\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].

A similar test suite called the ``\.{e-TRIP} test'' is available for
helping to determine whether a particular implementation deserves to be
known as `\eTeX'.

@d eTeX_version_string=="2.2" {current \eTeX\ version}
@d Omega_version_string=="1.15" { \.{\\OmegaVersion} }
@d Aleph_version_string=="0.0" { \.{\\AlephVersion} }
@d eTeX_version=2 { \.{\\eTeXversion} }
@d Omega_version=1 { \.{\\Omegaversion} }
@d Aleph_version=0 { \.{\\Alephversion} }
@d eTeX_minor_version=1 { \.{\\eTeXminorversion} }
@d Omega_minor_version=15 { \.{\\Omegaminorversion} }
@d Aleph_minor_version=0 { \.{\\Alephminorversion} }
@d eTeX_revision==".2" { \.{\\eTeXrevision} }
@d Omega_revision==".15" { \.{\\Omegarevision} }
@d Aleph_revision==".0" { \.{\\Alephrevision} }
@#
@d pdftex_version==200 { \.{\\pdftexversion} }
@d pdftex_revision=="0" { \.{\\pdftexrevision} }
@d pdftex_version_string=='-2.00.0' {current \pdfTeX\ version}
@#
@d luatex_version==25 { \.{\\luatexversion} }
@d luatex_revision=="4" { \.{\\luatexrevision} }
@d luatex_version_string=='snapshot-0.25.4' {current \LuaTeX\ version}
@d luatex_date_info==-extra_version_info { the compile date is negated }
@#
@d luaTeX_banner=='This is LuaTeX, Version ',luatex_version_string,extra_version_info
   {printed when \LuaTeX\ starts}
@#
@d banner==luaTeX_banner
@#
@d TEX==ETEX {change program name into |ETEX|}

@ 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
--- \eTeX, however, does use `\&{var}' parameters for the |reverse| function;
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...@>=
@!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}
@!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|}
@!dvi_buf_size=800; {size of the output buffer; must be a multiple of 8}
@!expand_depth=10000; {limits recursive calls of the |expand| procedure}
@!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@>
@!active_mem_size=50000; {number of words of |active_info| for active ocps}
@!ocp_maxint=@"10000000;


@ 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 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 |(fix_mem_max-fix_mem_min)/10|}
@d hash_prime=1777 {a prime number equal to about 85\pct! of |hash_size|}
@d ocp_base=0 {smallest internal ocp number; must not be less
  than |min_quarterword|}
@d ocp_biggest=32767 {the real biggest ocp}
@d number_ocps=ocp_biggest-ocp_base+1
@d ocp_list_base=0 {smallest internal ocp list number; must not be less
  than |min_quarterword|}
@d ocp_list_biggest=32727 {the real biggest ocp list}
@d number_ocp_lists=ocp_list_biggest-ocp_list_base+1
@d max_active_ocp_lists=32768
@d biggest_reg=65535 {the largest allowed register number; must be |<=max_quarterword|}
@d number_regs=65536 {|biggest_reg+1|}
@d number_attrs=65536 {total numbeer of attributes}
@d biggest_mark=65535 {the largest allowed marks class; must be |<=max_quarterword|}
@d number_marks=65536 {|biggest_mark+1|}
{using |2^20+2^16| characters instead of |2^21| saves 286MB on the virtual memory size
 of the running executable}
@d biggest_char=1114111 {2097151} {the largest allowed character number; must be |<=max_halfword|}
@d too_big_char=1114112 {2097152} {|biggest_char+1|}
@d special_char=1114113 {2097153} {|biggest_char+2|}
@d number_chars=1114112 {2097152} {|biggest_char+1|}
@d number_active_chars=65536+65536 {to reduce the memory req. only two planes }
@d string_offset=2097152
@d font_biggest=5535 {the real biggest font}
@d number_fonts=font_biggest-font_base+1
@d number_math_fonts=768
@d math_font_biggest=767
@d biggest_lang=32767
@d too_big_lang=32768
@d text_size=0 {size code for the largest size in a family}
@d script_size=256 {size code for the medium size in a family}
@d script_script_size=512 {size code for the smallest size in a family}


@ 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?}
@!luainit:boolean; {are we using lua for initializations }
@!tracefilenames:boolean; { print file open-close  info? }

@ Later on we will say `\ignorespaces|if X>=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 not luainit then  tracefilenames:=true;
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 hash_prime>hash_size then bad:=5;
if max_in_open>=128 then bad:=6;
{ |if null_list<256 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 not_found1=46 {like |not_found|, when there's more than one}
@d not_found2=47 {like |not_found|, when there's more than two}
@d not_found3=48 {like |not_found|, when there's more than three}
@d not_found4=49 {like |not_found|, when there's more than four}
@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 == pdfassert(1) {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
twenty-one-bit code that covers all of unicode, including 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..biggest_char; {eight-bit numbers}
@!BMP_code=0..65535; {sixteen-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...@>=
@!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 biggest_char do xchr[i]:=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...@>=

@* \[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..65535; {unsigned one-byte quantity}
@!real_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 real_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 |nameoffile| 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
|nameoffile|.
@^system dependencies@>

@<Glob...@>=
@!nameoffile:packed array[1..file_name_size] of char;@;@/
  {on some systems this may be a \&{record} variable}
@!namelength:0..file_name_size;@/{this many characters are actually
  relevant in |nameoffile| (the rest are blank)}
@!name_file_pointer:alpha_file;

@ 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
|nameoffile| 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,nameoffile,'/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,nameoffile,'/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,nameoffile,'/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,nameoffile,'/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,nameoffile,'/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,nameoffile,'/O'); w_open_out:=rewrite_OK(f);
end;

@ When input files are opened via a callback, they will also be read using
callbacks. for that purpose, the |open_read_file_callback| returns an
integer to uniquely identify a callback table. This id replaces the file
point |f| in this case, because the input does not have to be a file
in the traditional sense.

Signalling this fact is achieved by having two arrays of integers.

@<Glob...@>=
@!input_file_callback_id : ^integer;
@!read_file_callback_id : array[0..16] of integer;

@ 
@p function lua_a_open_in(var f:alpha_file; n:quarterword):boolean;
var k:integer; { a temporary value }
  fnam:str_number; { string returned by find callback }
  callback_id:integer;
  file_ok:boolean; { the status so far }
begin 
  file_ok:=true;
  if n=0 then begin
    texinputtype := 1; {Tell |open_input| we are \.{\\input}.}
    input_file_callback_id[index] := 0;
    end
  else begin
    texinputtype:=0; 
    read_file_callback_id[n] := 0;
    end;
  callback_id:=callback_defined(find_read_file_callback);
  if callback_id>0 then begin
    fnam:=0;
    file_ok:=run_callback(callback_id,'dS->s',n,stringcast(nameoffile+1),addressof(fnam));
    if (file_ok)and(fnam<>0)and(length(fnam)>0) then begin
      @<Fixup |nameoffile| after callback@>;
      end 
    else 
      file_ok:=false; {file not found}
    end;
  if file_ok then begin
    callback_id:=callback_defined(open_read_file_callback);
    if callback_id>0 then begin
      k := run_and_save_callback(callback_id,'S->',stringcast(nameoffile+1));
      if k>0 then begin
        lua_a_open_in := true;
        if n=0 then
          input_file_callback_id[index] := k
        else 
          read_file_callback_id[n] := k;
        end
      else 
        file_ok:=false; {read failed}
      end
    else begin {no read callback}
      if openinnameok(stringcast(nameoffile+1)) then begin
        lua_a_open_in := a_open_in(f,kpsetexformat);
        name_file_pointer := f;
        end
      else 
        file_ok:=false; {open failed}
      end;
    end;
  if not file_ok then begin
    lua_a_open_in := false;
    name_file_pointer := 0;
    end;
end;
@#
function lua_a_open_out(var f:alpha_file; n:quarterword):boolean;
var test:boolean;
  k:integer;
  fnam:str_number;
  callback_id:integer;
begin
  name_file_pointer := 0;
  callback_id:=callback_defined(find_write_file_callback);
  if callback_id>0 then begin
    fnam:=0;
    test:=run_callback(callback_id,'dS->s',n,stringcast(nameoffile+1),addressof(fnam));
    if (test)and(fnam<>0)and(length(fnam)>0) then begin
      @<Fixup |nameoffile| after callback@>;
      lua_a_open_out := do_a_open_out(f);
	  name_file_pointer := f;
      end
    else 
      lua_a_open_out := false;
    end 
  else begin
	if openoutnameok(stringcast(nameoffile+1)) then begin
      lua_a_open_out := a_open_out(f);
      name_file_pointer := f;
      end
    else
      lua_a_open_out := false;
   end;
end;
function lua_b_open_out(var f:alpha_file):boolean;
var test:boolean;
  k:integer;
  fnam:str_number;
  callback_id:integer;
begin
  name_file_pointer := 0;
  callback_id:=callback_defined(find_output_file_callback);
  if callback_id>0 then begin
    fnam:=0;
    test:=run_callback(callback_id,'S->s',stringcast(nameoffile+1),addressof(fnam));
    if (test)and(fnam<>0)and(length(fnam)>0) then begin
      @<Fixup |nameoffile| after callback@>;
      lua_b_open_out := do_b_open_out(f);
	  name_file_pointer := f;
      end
    else 
      lua_b_open_out := false;
    end 
  else begin
	if openoutnameok(stringcast(nameoffile+1)) then begin
      lua_b_open_out := b_open_out(f);
      name_file_pointer := f;
      end
    else
      lua_b_open_out := false;
   end;
end;

@ 
@<Fixup |nameoffile| after callback@>=
libcfree (nameoffile);
nameoffile := xmallocarray (packed_ASCII_code, length(fnam)+2);
for k:=str_start_macro(fnam) to str_start_macro(fnam+1)-1 do
  nameoffile[k-str_start_macro(fnam)+1] := str_pool[k];
nameoffile[length(fnam)+1]:=0;
namelength := length(fnam);
flush_string

@ 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;


@
 
@p procedure lua_a_close_in(var f:alpha_file; n:quarterword); {close a text file}
var ret:boolean;
    callback_id:integer;
begin
if n=0 then
  callback_id:=input_file_callback_id[index]
else
  callback_id:=read_file_callback_id[n];
if callback_id>0 then begin
  ret:=run_saved_callback(callback_id,'close','->');
  destroy_saved_callback(callback_id);
  if n=0 then
    input_file_callback_id[index] := 0
  else
    read_file_callback_id[n] := 0;
  end
else
  a_close(f);
end;
@#
procedure lua_a_close_out(var f:alpha_file); {close a text file}
begin
  a_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
|lua_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 packed_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 |lua_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 |lua_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 |lua_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 |lua_input_ln|.

If the |bypass_eoln| parameter is |true|, |lua_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 |lua_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]:=f^; get(f); incr(last);
    if buffer[last-1]<>" " then last_nonblank:=last;
    end;
  last:=last_nonblank; input_ln:=true;
  end;
end;

function lua_input_ln(var f:alpha_file;n:quarterword;@!bypass_eoln:boolean):boolean;
var lua_result:boolean;
	last_ptr:integer;
    callback_id:integer;
	bypass_p:boolean;
begin
if n=0 then
  callback_id:=input_file_callback_id[index]
else 
  callback_id:=read_file_callback_id[n];
if callback_id>0 then begin
    last:=first;
	last_ptr := first;
    lua_result := run_saved_callback(callback_id,'reader','->l', addressof(last_ptr));
	if (lua_result=true)and(last_ptr<>0) then begin
	  last := last_ptr;
	  if last>max_buf_stack then max_buf_stack:=last; 
	  lua_input_ln := true;
      @<Fix up the input buffer using callbacks@>; 
      end
    else 
      lua_input_ln := false;
    end
  else begin
    bypass_p := bypass_eoln; {this is for -Wextra}
    lua_result := input_ln(f,bypass_p);
	if lua_result=true then begin
      lua_input_ln := true;
      @<Fix up the input buffer using callbacks@>; 
      end
    else
      lua_input_ln := false;
    end
end;

@ 
@<Fix up the input buffer using callbacks@>=
if last>=first then begin
  callback_id := callback_defined(process_input_buffer_callback);
  if callback_id>0 then begin
    last_ptr := first;
    lua_result := run_callback(callback_id, 'l->l', (last-first), addressof(last_ptr)); 
    if (lua_result=true)and(last_ptr<>0) then begin
	  last := last_ptr;
	  if last>max_buf_stack then max_buf_stack:=last; 
      end;
    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 writeln(term_out,'Buffer size exceeded!'); goto final_end;
@.Buffer size exceeded@>
  end
else 
  check_buffer_overflow(buf_size+10) { need  a little bit more}

@ 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 writeln(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;
  writeln(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_macro(s)<=j<str_start_macro(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_macro(str_ptr)| are
ready for the next string to be allocated.

String numbers 0 to |biggest_char| are reserved for strings that correspond to single
UNICODE 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~|biggest_char|. 

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|}
@d str_start_macro(#) == str_start[(#) - string_offset]

@<Types...@>=
@!pool_pointer = integer; {for variables that point into |str_pool|}
@!str_number = integer; {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_macro(#+1)-str_start_macro(#)) {the number of characters
  in string number \#}

@ The length of the current string is called |cur_length|:

@d cur_length == (pool_ptr - str_start_macro(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(#) == check_pool_overflow((pool_ptr+#)) {test or grow the pool}

@p procedure string_room(t:integer);
begin
	str_room(t);
end;
@#
procedure append_pool_char(c:ASCII_code);
begin
	append_char(c);
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+string_offset) 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_macro(str_ptr):=pool_ptr;
make_string:=str_ptr-1;
end;

@ To destroy the most recently made string, we say |flush_string|.

The helper routines reads one utf sequence from the pool resp. the
buffer, and returns its character value. 

@d flush_string==begin decr(str_ptr); pool_ptr:=str_start_macro(str_ptr);
  end
@d test_sequence_byte(#)==if (#<@"80) or (#>=@"C0) then begin
  print_err("Text line contains an invalid utf-8 sequence");
@.Text line contains...@>
  help2("A funny symbol that I can't read has just been input.")@/
    ("Just continue, I'll change it to 0xFFFD.");@/
  deletions_allowed:=false; error; deletions_allowed:=true;
{the assigment before return is needed because web2c generates incorrect code}
  a:=@"FFFD; buffer_to_unichar:=a; return; end


@p function buffer_to_unichar(@!k:integer):integer;
label exit;
var a:@!integer; {a utf char}
b:@!integer; { a utf nibble}
begin
    b := buffer[k];
    if b<@"80 then
      a := b
    else if b>=@"F0 then begin
	  a := (b-@"F0) * 64;
	  b := buffer[k+1];
	  test_sequence_byte(b);
	  a := (a + (b-128)) * 64;
	  b := buffer[k+2];
	  test_sequence_byte(b);
	  a := (a + (b-128)) * 64;
	  b := buffer[k+3];
	  test_sequence_byte(b);
	  a := a + (b-128);
      end 
    else if b>=@"E0 then begin
	  a := (b-@"E0) * 64;
	  b := buffer[k+1];
	  test_sequence_byte(b);
	  a := (a + (b-128)) * 64;
	  b := buffer[k+2];
	  test_sequence_byte(b);
	  a := a + (b-128);
      end 
    else if b>=@"C0 then begin
	  a := (b-@"C0) * 64;
	  b := buffer[k+1];
	  test_sequence_byte(b);
	  a := a + (b-128);
      end
    else begin { NI: this is an encoding error }
	  print_err("Buffer contains an invalid utf-8 sequence");
@.Text line contains...@>
	  help2("A funny symbol somehow ended up in the input buffer.")@/
    	   ("Just continue, I'll change it to 0xFFFD.");@/
      deletions_allowed:=false; error; deletions_allowed:=true;
      a:=@"FFFD;
      end;
exit: 
  buffer_to_unichar := a;
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}
a: ASCII_code; {a unicode character }
@!result: boolean; {result of comparison}
begin result:=false; 
if s<string_offset then begin
  a := buffer_to_unichar(k); 
  if a<>s then goto not_found;
  end
else begin
j:=str_start_macro(s);
while j<str_start_macro(s+1) do
  begin if so(str_pool[j])<>buffer[k] then
    begin goto not_found;
    end;
  incr(j); incr(k);
  end;
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 found,not_found; {loop exit}
var j,@!k: pool_pointer; {running indices}
a: ASCII_code; {a utf char}
@!result: boolean; {result of comparison}
begin result:=false;
a:= 0;
if s<string_offset then begin
  if t>=string_offset then begin
    if s<=@"7F then
     if length(t)=1 then
       if str_pool[str_start_macro(t)]=s then
          goto found;
	a := pool_to_unichar(str_start_macro(t));
    if a<>s then goto not_found;
    end 
  else
    if t<>s then goto not_found;
  end
else if t<string_offset then begin
 if t<=@"7F then
   if length(s)=1 then
     if str_pool[str_start_macro(s)]=t then
       goto found;
  a := pool_to_unichar(str_start_macro(s));
  if a<>t then goto not_found;
  end 
else begin 
  if length(s)<>length(t) then goto not_found;
  j:=str_start_macro(s); k:=str_start_macro(t);
  while j<str_start_macro(s+1) do
    begin if str_pool[j]<>str_pool[k] then goto not_found;
    incr(j); incr(k);
    end;
  end;
found: 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@>

The first |string_offset| strings are single-characters strings matching
Unicode. There is no point in generating all of these. But |str_ptr| has
initialized properly, otherwise |print_char| cannot see the difference
between characters and strings.

@p @!init function get_strings_started:boolean; {initializes the string pool,
  but returns |false| if something goes wrong}
label done,exit;
var @!g:str_number; {garbage}
begin pool_ptr:=0; str_ptr:=string_offset; str_start[0]:=0;
@<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")

@ 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}.

Unprintable characters of codes 256--|65535| are, similarly, rendered
\.{\^\^\^\^0100}--\.{\^\^\^\^ffff}.

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@>

@ @<Read the other strings...@>=
  g := loadpoolstrings((pool_size-string_vacancies));
  if g=0 then begin
     wake_up_terminal; writeln(term_out,'! You have to increase POOLSIZE.');
     get_strings_started:=false;
     return;
  end;
  get_strings_started:=true;

@* \[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}
@!term_out_mode:halfword;
@!term_out_translation:halfword;
@!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 packed_ASCII_code; {circular buffer for
  pseudoprinting}
@!trick_count: integer; {threshold for pseudoprinting, explained later}
@!first_count: integer; {another variable for pseudoprinting}
@!inhibit_par_tokens:boolean; { for minor adjustments to |show_token_list| }

@ @<Initialize the output routines@>=
selector:=term_only; tally:=0; term_offset:=0; file_offset:=0;
inhibit_par_tokens:=false;

@ 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(#)==writeln(term_out,#)
@d wterm_cr==writeln(term_out)
@d wlog(#)==write(log_file,#)
@d wlog_ln(#)==writeln(log_file,#)
@d wlog_cr==writeln(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 writeln(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
|lua_input_ln|. All printing comes through |print_ln| or |print_char|.

@d wterm_char(#)==begin if (#>=@"20)or(#=@"0A)or(#=@"0D)or(#=@"09) then wterm(xchr[#])
                  else begin if term_offset+2>=max_print_line then begin
                     wterm_cr; term_offset:=0;
                     end;
                     incr(term_offset); wterm('^'); incr(term_offset); wterm('^'); 
                     wterm(xchr[#+64]);  
                 end; end
@d fix_term_offset(#)==
      if ((#>=@"C0) and (#<=@"DF) and (term_offset+2>=max_print_line)) or
         ((#>=@"E0) and (#<=@"EF) and (term_offset+3>=max_print_line)) or
         ((#>=@"F0) and (term_offset+4>=max_print_line)) then begin
        wterm_cr; term_offset:=0;
       end
@d fix_log_offset(#)==
      if ((#>=@"C0) and (#<=@"DF) and (file_offset+2>=max_print_line)) or
         ((#>=@"E0) and (#<=@"EF) and (file_offset+3>=max_print_line)) or
         ((#>=@"F0) and (file_offset+4>=max_print_line)) then begin
        wlog_cr; file_offset:=0;
       end

@<Basic print...@>=
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 
  fix_term_offset(s); fix_log_offset(s);
  wterm_char(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 
  fix_log_offset(s);
  wlog(xchr[s]); incr(file_offset);
  if file_offset=max_print_line then print_ln;
  end;
term_only: begin 
  fix_term_offset(s); 
  wterm_char(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@>

The first 256 entries above the 17th unicode plane are used for a
special trick: when \TeX\ has to print items in that range, it will
instead print the character that results from substracting @"110000
from that value. This allows byte-oriented output to things like
\.{\\specials} and \.{\\pdfliterals}. Todo: Perhaps it would be useful 
to do the same substraction while typesetting.
 
@d print_lc_hex(#)==l:=#;
   if l<10 then print_char(l+"0") else print_char(l-10+"a");

@<Basic print...@>=
function pool_to_unichar(@!t:pool_pointer):ASCII_code;
var a,result:@!ASCII_code; {a utf char}
b:@!quarterword; { a utf nibble}
begin
    b := str_pool[t];
    if b<=@"7F then
      a := b
    else if b>=@"F0 then begin
	  a := (b-@"F0) * 64;
	  b := str_pool[t+1];
	  a := (a + (b-128)) * 64;
	  b := str_pool[t+2];
	  a := (a + (b-128)) * 64;
	  b := str_pool[t+3];
	  a := a + (b-128);
      end
    else if b>=@"E0 then begin
	  a := (b-@"E0) * 64;
	  b := str_pool[t+1];
	  a := (a + (b-128)) * 64;
	  b := str_pool[t+2];
	  a := a + (b-128);
      end 
    else if b>=@"C0 then begin
	  a := (b-@"C0) * 64;
	  b := str_pool[t+1];
	  a := a + (b-128);
      end
    else begin  { NI: this is an encoding error }
	  wlog_ln('! Pool contains an invalid utf-8 sequence');
	  wterm_ln('! Pool contains an invalid utf-8 sequence');
@.Text line contains...@>
	  help2("A funny symbol somehow ended up in the string pool.")@/
    	   ("Just continue, I'll change it to 0xFFFD.");@/
      deletions_allowed:=false; error; deletions_allowed:=true;
      a:=@"FFFD;
      end;
result := a;
pool_to_unichar := result;
end ;

procedure print(@!s:integer); {prints string |s|}
label exit;
var j:pool_pointer; {current character code position}
@!v:integer; { a unicode char }
begin if s>=str_ptr then s:="???" {this can't happen}
@.???@>
else if s<string_offset then
  if s<0 then s:="???" {can't happen}
  else begin 
    {TH not sure about this, disabled for now!}
    if (false)and(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;
    if s<=@"7F then
      print_char(s)
    else if s<=@"7FF then begin
      print_char(@"C0 + (s div @"40));
      print_char(@"80 + (s mod @"40));
      end
    else if s<=@"FFFF then begin
      print_char(@"E0 + (s div @"1000));
      print_char(@"80 + ((s mod @"1000) div @"40));
      print_char(@"80 + ((s mod @"1000) mod @"40));
      end 
    else begin 
      if s>=@"110000 then 
	    print_char(s-@"110000)
      else begin
        print_char(@"F0 + (s div @"40000));
        print_char(@"80 + ((s mod @"40000) div @"1000));
        print_char(@"80 + (((s mod @"40000) mod @"1000) div @"40));
        print_char(@"80 + (((s mod @"40000) mod @"1000) mod @"40));
        end;
      end;
    return;
    end;
j:=str_start_macro(s);
while j<str_start_macro(s+1) do
  begin { 0x110000 in utf=8: 0xF4 0x90 0x80 0x80 }
    if (str_pool[j]=@"F4)and(j<str_start_macro(s+4))and(str_pool[j+1]=@"90) then begin
	  v := (((7*64+63)*64)+ (str_pool[j+2]-128))*64 +(str_pool[j+3]-128);
	  print_char(v-@"110000); j := j+4;
      end
    else begin
      print_char(str_pool[j]); incr(j);
    end;
  end;
exit:end;

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;

procedure print_nlp; {move to beginning of a line}
begin if ((term_offset>0)and(odd(selector)))or@|
  ((file_offset>0)and(selector>=log_only)) then print_ln;
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<string_offset) then print(s)
else begin j:=str_start_macro(s);
  while j<str_start_macro(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...@>=
print_banner;

@ The procedure |print_nl| is like |print|, but it makes sure that the
string appears at the beginning of a new line. (moved)

@<Basic print...@>=

@ 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<string_offset 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
@d print_font_name(#)==begin print(tex_font_name(#)); flush_string; end
 
@ 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_macro("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_macro(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|.

@<Basic print...@>=
procedure prompt_input(s:str_number); 
begin wake_up_terminal; print(s); term_input;
end;

@ 
@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(#);
  last_error:=#; end
@d print_warn(#)==begin if interaction=error_stop_mode then wake_up_terminal;
  if prepend_nl then begin print_nl(""); print_ln end;
  print_nl(#);
  end

@<Glob...@>=
@!interaction:batch_mode..error_stop_mode; {current level of interaction}
@!last_error:str_number;

@ @<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}

@p 
procedure dohelp5 (@!a,b,c,d,e:str_number);
begin
  help5(a)(b)(c)(d)(e);
end;
@#
procedure dohelp4 (@!a,b,c,d:str_number);
begin
  help4(a)(b)(c)(d);
end;
@#
procedure dohelp3 (@!a,b,c:str_number);
begin
  help3(a)(b)(c);
end;
@#
procedure dohelp2 (@!a,b:str_number);
begin
  help2(a)(b);
end;
@#
procedure dohelp1 (@!a:str_number);
begin
  help1(a);
end;
@#
procedure do_print_err (s:str_number);
begin
  print_err(s);
end;

@ @<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}
callback_id:integer;
@!s1,@!s2,@!s3,@!s4:integer;
  {used to save global variables when deleting tokens}
@!t:boolean;
begin if history<error_message_issued then history:=error_message_issued;
print_char("."); 
callback_id := callback_defined(show_error_hook_callback) ;
if callback_id>0 then t := run_callback(callback_id,'->');
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 lua_norm_error(@!s:str_number); {lua found a problem}
begin
print_err("LuaTeX error "); print(s);
help2("The lua interpreter ran into a problem, so the")@/
  ("remainder of this lua chunk will be ignored.");
error;
end;

procedure lua_fatal_error(@!s:str_number); {lua found a problem}
begin normalize_selector;
print_err("LuaTeX fatal error "); print(s);
succumb;
end;

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;

procedure overflow_ocp_buf_size;
begin
overflow("ocp_buf_size",ocp_buf_size);
end;

procedure overflow_ocp_stack_size;
begin
overflow("ocp_stack_size",ocp_stack_size);
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@>

@<Global...@>=
@!interrupt:integer; {should \TeX\ pause for instructions?}
@!OK_to_interrupt:boolean; {should interrupts be observed?}
@!detokenized_line:boolean; {indicates this is a 'detokenized' input line }
@!line_catcode_table:integer; {the used catcode table for input lines}
@!local_catcode_table:boolean; {the used catcode table for input lines}
@!static_int_base:integer; {C version of |int_base|}

@ @p procedure check_interrupt;
begin 
if interrupt<>0 then pause_for_instructions;
end;


@ @<Set init...@>=
interrupt:=0; OK_to_interrupt:=true; detokenized_line:=false;
line_catcode_table:=0; local_catcode_table:=false;

@ 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}

@* \[7b] Random numbers.

\font\tenlogo=logo10 % font used for the METAFONT logo
\def\MP{{\tenlogo META}\-{\tenlogo POST}}

This section is (almost) straight from MetaPost. I had to change
the types (use |integer| instead of |fraction|), but that should
not have any influence on the actual calculations (the original
comments refer to quantities like |fraction_four| ($2^{30}$), and
that is the same as the numeric representation of |maxdimen|).

I've copied the low-level variables and routines that are needed, but
only those (e.g. |m_log|), not the accompanying ones like |m_exp|. Most
of the following low-level numeric routines are only needed within the
calculation of |norm_rand|. I've been forced to rename |make_fraction|
to |make_frac| because TeX already has a routine by that name with
a wholly different function (it creates a |fraction_noad| for math
typesetting) -- Taco

And now let's complete our collection of numeric utility routines
by considering random number generation.
\MP\ generates pseudo-random numbers with the additive scheme recommended
in Section 3.6 of {\sl The Art of Computer Programming}; however, the
results are random fractions between 0 and |fraction_one-1|, inclusive.

There's an auxiliary array |randoms| that contains 55 pseudo-random
fractions. Using the recurrence $x_n=(x_{n-55}-x_{n-31})\bmod 2^{28}$,
we generate batches of 55 new $x_n$'s at a time by calling |new_randoms|.
The global variable |j_random| tells which element has most recently
been consumed.

@<Glob...@>=
@!randoms:array[0..54] of integer; {the last 55 random values generated}
@!j_random:0..54; {the number of unused |randoms|}
@!random_seed:scaled; {the default random seed}

@ A small bit of metafont is needed.

@d fraction_half==@'1000000000 {$2^{27}$, represents 0.50000000}
@d fraction_one==@'2000000000 {$2^{28}$, represents 1.00000000}
@d fraction_four==@'10000000000 {$2^{30}$, represents 4.00000000}
@d el_gordo == @'17777777777 {$2^{31}-1$, the largest value that \MP\ likes}
@d halfp(#)==(#) div 2
@d double(#) == #:=#+# {multiply a variable by two}

@ The |make_frac| routine produces the |fraction| equivalent of
|p/q|, given integers |p| and~|q|; it computes the integer
$f=\lfloor2^{28}p/q+{1\over2}\rfloor$, when $p$ and $q$ are
positive. If |p| and |q| are both of the same scaled type |t|,
the ``type relation'' |make_frac(t,t)=fraction| is valid;
and it's also possible to use the subroutine ``backwards,'' using
the relation |make_frac(t,fraction)=t| between scaled types.

If the result would have magnitude $2^{31}$ or more, |make_frac|
sets |arith_error:=true|. Most of \MP's internal computations have
been designed to avoid this sort of error.

If this subroutine were programmed in assembly language on a typical
machine, we could simply compute |(@t$2^{28}$@>*p)div q|, since a
double-precision product can often be input to a fixed-point division
instruction. But when we are restricted to \PASCAL\ arithmetic it
is necessary either to resort to multiple-precision maneuvering
or to use a simple but slow iteration. The multiple-precision technique
would be about three times faster than the code adopted here, but it
would be comparatively long and tricky, involving about sixteen
additional multiplications and divisions.

This operation is part of \MP's ``inner loop''; indeed, it will
consume nearly 10\pct! of the running time (exclusive of input and output)
if the code below is left unchanged. A machine-dependent recoding
will therefore make \MP\ run faster. The present implementation
is highly portable, but slow; it avoids multiplication and division
except in the initial stage. System wizards should be careful to
replace it with a routine that is guaranteed to produce identical
results in all cases.
@^system dependencies@>

As noted below, a few more routines should also be replaced by machine-dependent
code, for efficiency. But when a procedure is not part of the ``inner loop,''
such changes aren't advisable; simplicity and robustness are
preferable to trickery, unless the cost is too high.
@^inner loop@>

@p function make_frac(@!p,@!q:integer):integer;
var @!f:integer; {the fraction bits, with a leading 1 bit}
@!n:integer; {the integer part of $\vert p/q\vert$}
@!negative:boolean; {should the result be negated?}
@!be_careful:integer; {disables certain compiler optimizations}
begin if p>=0 then negative:=false
else  begin negate(p); negative:=true;
  end;
if q<=0 then
  begin debug if q=0 then confusion("/");@;@+gubed@;@/
@:this can't happen /}{\quad \./@>
  negate(q); negative:=not negative;
  end;
n:=p div q; p:=p mod q;
if n>=8 then
  begin arith_error:=true;
  if negative then make_frac:=-el_gordo@+else make_frac:=el_gordo;
  end
else  begin n:=(n-1)*fraction_one;
  @<Compute $f=\lfloor 2^{28}(1+p/q)+{1\over2}\rfloor$@>;
  if negative then make_frac:=-(f+n)@+else make_frac:=f+n;
  end;
end;

@ The |repeat| loop here preserves the following invariant relations
between |f|, |p|, and~|q|:
(i)~|0<=p<q|; (ii)~$fq+p=2^k(q+p_0)$, where $k$ is an integer and
$p_0$ is the original value of~$p$.

Notice that the computation specifies
|(p-q)+p| instead of |(p+p)-q|, because the latter could overflow.
Let us hope that optimizing compilers do not miss this point; a
special variable |be_careful| is used to emphasize the necessary
order of computation. Optimizing compilers should keep |be_careful|
in a register, not store it in memory.
@^inner loop@>

@<Compute $f=\lfloor 2^{28}(1+p/q)+{1\over2}\rfloor$@>=
f:=1;
repeat be_careful:=p-q; p:=be_careful+p;
if p>=0 then f:=f+f+1
else  begin double(f); p:=p+q;
  end;
until f>=fraction_one;
be_careful:=p-q;
if be_careful+p>=0 then incr(f)

@

@p function take_frac(@!q:integer;@!f:integer):integer;
var @!p:integer; {the fraction so far}
@!negative:boolean; {should the result be negated?}
@!n:integer; {additional multiple of $q$}
@!be_careful:integer; {disables certain compiler optimizations}
begin @<Reduce to the case that |f>=0| and |q>0|@>;
if f<fraction_one then n:=0
else  begin n:=f div fraction_one; f:=f mod fraction_one;
  if q<=el_gordo div n then n:=n*q
  else  begin arith_error:=true; n:=el_gordo;
    end;
  end;
f:=f+fraction_one;
@<Compute $p=\lfloor qf/2^{28}+{1\over2}\rfloor-q$@>;
be_careful:=n-el_gordo;
if be_careful+p>0 then
  begin arith_error:=true; n:=el_gordo-p;
  end;
if negative then take_frac:=-(n+p)
else take_frac:=n+p;
end;

@ @<Reduce to the case that |f>=0| and |q>0|@>=
if f>=0 then negative:=false
else  begin negate(f); negative:=true;
  end;
if q<0 then
  begin negate(q); negative:=not negative;
  end;

@ The invariant relations in this case are (i)~$\lfloor(qf+p)/2^k\rfloor
=\lfloor qf_0/2^{28}+{1\over2}\rfloor$, where $k$ is an integer and
$f_0$ is the original value of~$f$; (ii)~$2^k\L f<2^{k+1}$.
@^inner loop@>

@<Compute $p=\lfloor qf/2^{28}+{1\over2}\rfloor-q$@>=
p:=fraction_half; {that's $2^{27}$; the invariants hold now with $k=28$}
if q<fraction_four then
  repeat if odd(f) then p:=halfp(p+q)@+else p:=halfp(p);
  f:=halfp(f);
  until f=1
else  repeat if odd(f) then p:=p+halfp(q-p)@+else p:=halfp(p);
  f:=halfp(f);
  until f=1

@ The subroutines for logarithm and exponential involve two tables.
The first is simple: |two_to_the[k]| equals $2^k$. The second involves
a bit more calculation, which the author claims to have done correctly:
|spec_log[k]| is $2^{27}$ times $\ln\bigl(1/(1-2^{-k})\bigr)=
2^{-k}+{1\over2}2^{-2k}+{1\over3}2^{-3k}+\cdots\,$, rounded to the
nearest integer.

@<Glob...@>=
@!two_to_the:array[0..30] of integer; {powers of two}
@!spec_log:array[1..28] of integer; {special logarithms}


@ @<Set init...@>=
two_to_the[0]:=1;
for k:=1 to 30 do two_to_the[k]:=2*two_to_the[k-1];
spec_log[1]:=93032640;
spec_log[2]:=38612034;
spec_log[3]:=17922280;
spec_log[4]:=8662214;
spec_log[5]:=4261238;
spec_log[6]:=2113709;
spec_log[7]:=1052693;
spec_log[8]:=525315;
spec_log[9]:=262400;
spec_log[10]:=131136;
spec_log[11]:=65552;
spec_log[12]:=32772;
spec_log[13]:=16385;
for k:=14 to 27 do spec_log[k]:=two_to_the[27-k];
spec_log[28]:=1;

@

@p function m_log(@!x:integer):integer;
var @!y,@!z:integer; {auxiliary registers}
@!k:integer; {iteration counter}
begin if x<=0 then @<Handle non-positive logarithm@>
else  begin y:=1302456956+4-100; {$14\times2^{27}\ln2\approx1302456956.421063$}
  z:=27595+6553600; {and $2^{16}\times .421063\approx 27595$}
  while x<fraction_four do
    begin double(x); y:=y-93032639; z:=z-48782;
    end; {$2^{27}\ln2\approx 93032639.74436163$
      and $2^{16}\times.74436163\approx 48782$}
  y:=y+(z div unity); k:=2;
  while x>fraction_four+4 do
    @<Increase |k| until |x| can be multiplied by a
      factor of $2^{-k}$, and adjust $y$ accordingly@>;
  m_log:=y div 8;
  end;
end;

@ @<Increase |k| until |x| can...@>=
begin z:=((x-1) div two_to_the[k])+1; {$z=\lceil x/2^k\rceil$}
while x<fraction_four+z do
  begin z:=halfp(z+1); k:=k+1;
  end;
y:=y+spec_log[k]; x:=x-z;
end

@ @<Handle non-positive logarithm@>=
begin print_err("Logarithm of ");
@.Logarithm...replaced by 0@>
print_scaled(x); print(" has been replaced by 0");
help2("Since I don't take logs of non-positive numbers,")@/
  ("I'm zeroing this one. Proceed, with fingers crossed.");
error; m_log:=0;
end

@ The following somewhat different subroutine tests rigorously if $ab$ is
greater than, equal to, or less than~$cd$,
given integers $(a,b,c,d)$. In most cases a quick decision is reached.
The result is $+1$, 0, or~$-1$ in the three respective cases.

@d return_sign(#)==begin ab_vs_cd:=#; return;
  end

@p function ab_vs_cd(@!a,b,c,d:integer):integer;
label exit;
var @!q,@!r:integer; {temporary registers}
begin @<Reduce to the case that |a,c>=0|, |b,d>0|@>;
loop@+  begin q := a div d; r := c div b;
  if q<>r then
    if q>r then return_sign(1)@+else return_sign(-1);
  q := a mod d; r := c mod b;
  if r=0 then
    if q=0 then return_sign(0)@+else return_sign(1);
  if q=0 then return_sign(-1);
  a:=b; b:=q; c:=d; d:=r;
  end; {now |a>d>0| and |c>b>0|}
exit:end;

@ @<Reduce to the case that |a...@>=
if a<0 then
  begin negate(a); negate(b);
  end;
if c<0 then
  begin negate(c); negate(d);
  end;
if d<=0 then
  begin if b>=0 then
    if ((a=0)or(b=0))and((c=0)or(d=0)) then return_sign(0)
    else return_sign(1);
  if d=0 then
    if a=0 then return_sign(0)@+else return_sign(-1);
  q:=a; a:=c; c:=q; q:=-b; b:=-d; d:=q;
  end
else if b<=0 then
  begin if b<0 then if a>0 then return_sign(-1);
  if c=0 then return_sign(0) else return_sign(-1);
  end

@ To consume a random integer, the program below will say `|next_random|'
and then it will fetch |randoms[j_random]|.

@d next_random==if j_random=0 then new_randoms
  else decr(j_random)

@p procedure new_randoms;
var @!k:0..54; {index into |randoms|}
@!x:integer; {accumulator}
begin for k:=0 to 23 do
  begin x:=randoms[k]-randoms[k+31];
  if x<0 then x:=x+fraction_one;
  randoms[k]:=x;
  end;
for k:=24 to 54 do
  begin x:=randoms[k]-randoms[k-24];
  if x<0 then x:=x+fraction_one;
  randoms[k]:=x;
  end;
j_random:=54;
end;

@ To initialize the |randoms| table, we call the following routine.

@p procedure init_randoms(@!seed:integer);
var @!j,@!jj,@!k:integer; {more or less random integers}
@!i:0..54; {index into |randoms|}
begin j:=abs(seed);
while j>=fraction_one do j:=halfp(j);
k:=1;
for i:=0 to 54 do
  begin jj:=k; k:=j-k; j:=jj;
  if k<0 then k:=k+fraction_one;
  randoms[(i*21)mod 55]:=j;
  end;
new_randoms; new_randoms; new_randoms; {``warm up'' the array}
end;

@ To produce a uniform random number in the range |0<=u<x| or |0>=u>x|
or |0=u=x|, given a |scaled| value~|x|, we proceed as shown here.

Note that the call of |take_frac| will produce the values 0 and~|x|
with about half the probability that it will produce any other particular
values between 0 and~|x|, because it rounds its answers.

@p function unif_rand(@!x:integer):integer;
var @!y:integer; {trial value}
begin next_random; y:=take_frac(abs(x),randoms[j_random]);
if y=abs(x) then unif_rand:=0
else if x>0 then unif_rand:=y
else unif_rand:=-y;
end;

@ Finally, a normal deviate with mean zero and unit standard deviation
can readily be obtained with the ratio method (Algorithm 3.4.1R in
{\sl The Art of Computer Programming\/}).

@p function norm_rand:integer;
var @!x,@!u,@!l:integer; {what the book would call $2^{16}X$, $2^{28}U$,
  and $-2^{24}\ln U$}
begin repeat
  repeat next_random;
  x:=take_frac(112429,randoms[j_random]-fraction_half);
    {$2^{16}\sqrt{8/e}\approx 112428.82793$}
  next_random; u:=randoms[j_random];
  until abs(x)<u;
x:=make_frac(x,u);
l:=139548960-m_log(u); {$2^{24}\cdot12\ln2\approx139548959.6165$}
until ab_vs_cd(1024,l,x,x)>=0;
norm_rand:=x;
end;

@* \[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.

We are assuming 32-bit integers, a halfword must contain at least
32 bits, and a quarterword must contain at least 16 bits.
@^system dependencies@>

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.

We cannot use the full range of 32 bits in a halfword, because we have
to allow negative values for potential backend tricks like web2c's
dynamic allocation, a