head 1.1; access; symbols; locks; comment @# @; 1.1 date 95.07.12.22.05.45; author WB; state Exp; branches; next ; desc @@ 1.1 log @Initial revision @ text @%%%-*- compile-command: "notangle plain.tw > plain.sty" -*- %%%===================================================================== %%% @@Noweb-file{ %%% author = "W\l{}odek Bzyl", %%% version = "$Id: plain.tw,v 4.12 1995/07/10 21:32:25 web Exp $", %%% date = "25 April 1995", %%% time = "22:05:47 MET", %%% filename = "plain.tw", %%% checksum = "45702 2586 10926 101053", %%% address = "Instytut Matematyki, %%% Uniwersytet Gda\'nski %%% Wita Stwosza 57 %%% 80--952 Gda\'nsk, Poland", %%% email = "matwb@@halina.univ.gda.pl (Internet)", %%% abstract = "", %%% } %%%===================================================================== \title{PLAIN.TW}{W\l{}odek Bzyl\hfil matwb@@halina.univ.gda.pl} \printcontents @@ \chapter{Introduction} {\it However, we will not include a verbatim description, because some parts of that file are too boring, and because the actual macros have been ``optimized'' with respect to memory space and running time.} \hfill {\sl D.E.~Knuth about\/ [[plain.tex]] format.} \bigskip \bigskip \noindent What follows is devoted to the details of the plain \TeX\ format. This file serves two purposes: \medskip \item{(1)} As a documentation of the [[plain.tex]] format. Weaving and texing this document should produce a handy reference. \item{(2)} The division of this web source into `chunks' should ease creation of other formats tailored to particular applications. Chunks could be easily modified, removed, added, or replaced. \medskip \noindent The change file mechanism is not needed in case of \TeX\ language. Change files are used to incorporate system dependent code into source file, but \TeX\ code is already system independent. \TeX\ code could be only `format dependent' and here change files could be used. Another feature of format file is that it evolves with time, yet some intermediate versions are used for preparation of books, articles etc. All these versions and configurations must be kept well organized, otherwise you are lost. The Revision Control System is the tool that assists with these tasks. With the RCS it is possible, with small overhead, to preserve \stress{all revisions} which evolved from given text document, merge changes made by others, compare different versions, keep log of changes. This document consists mainly of excerpts from the {\sl \TeX Book}, but it is organised around the macros as they appear in the [[plain.tex]] rather than around the topics as in a user manual. Therefore this document is not a \stress{user manual}, although many definitions are contained here. @@ \chapter{The layout of the format} <<*>>= <> \catcode`@@ = 11 <> <> <> <> <> <> <> <> <> <> <> \catcode`@@ = 12 <> @@ There are 256 characters that \TeX\ might encounter at each step, in a file or in a line of text typed directly on your terminal. These 256~characters are classified into 16 categories numbered 0 to 15: \begindisplay \def\\{\hfill} \hfil\hidewidth\it Category\hidewidth&\it \qquad Meaning\hidewidth&% \it Default\hfil\cr \noalign{\smallskip} \\0&Escape character&[[\]]\cr \\1&Beginning of group&[[{]]\cr \\2&End of group&[[}]]\cr \\3&Math shift&[[$]]\cr \\4&Alignment tab&[[&]]\cr \\5&End of line&\\cr \\6&Parameter&[[#]]\cr \\7&Superscript&[[^]]\cr \\8&Subscript&[[_]]\cr \\9&Ignored character&\\cr 10&Space&\ttt{\char"20}\cr 11&Letter&[[A]], \dots, [[Z]] and [[a]], \dots, [[z]]\cr 12&Other character&none of the above or below\cr 13&Active character&[[~]]\cr 14&Comment character&[[%]]\cr 15&Invalid character&\\cr \enddisplay When [[INITEX]] begins, category 12 (other) has been assigned to all~256 possible characters, except that the 52~letters [[A...Z]] and [[a...z]] are category~11 (letter), and assignments equivalent to the following have been made: \begindisplay \def\\{\hfill} [[\catcode `\\ = 0]]&\cr [[\catcode `\^^M = 5]]&\cr [[\catcode `\^^@@ = 9]]&\cr [[\catcode `\ = 10]]&\cr [[\catcode `\% = 14]]&\cr [[\catcode `\^^? = 15]]&\cr \enddisplay Thus `[[\]]' is already an escape character, `[[\char"20]]' is a space, and `[[%]]' is available for comments on the first line of the file; ASCII \ is ignored, ASCII \ is an end-of-line character, and ASCII \ is invalid. \medskip Furthermore \ is given category space, \ becomes an active character that will detect runaways on files that have been divided into ``file pages'' by \ characters. Finally the control sequence [[\active]] is defined to yield the constant~13. To re-catcode these special characters---not counting ASCII \begindisplay \def\\{\hfill} \\\& [[^^@@]]\cr \\\& [[^^I]]\cr \\\& [[^^J]]\cr \\\& [[^^L]]\cr \\\& [[^^M]]\cr \\\& [[^^?]]\cr \enddisplay ---use the control sequence [[\dospecials]] that lists all the characters whose catcodes should probably be changed to~12 (other) when copying things verbatim. Each symbol in the list is preceded by [[\do]], which can be defined if you want to do something to every item in the list. <>= \catcode`\{=1 \catcode`\}=2 \catcode`\$=3 \catcode`\&=4 \catcode`\#=6 \catcode`\^=7 \catcode`\^^K=7 % uparrow is for superscripts \catcode`\_=8 \catcode`\^^A=8 % downarrow are for subscripts \catcode`\^^I=10 \chardef\active=13 \catcode`\~=\active % tilde is active \catcode`\^^L=\active \outer\def^^L{\par} % ascii form-feed is "\outer\par" \def\dospecials{\do\ \do\\\do\{\do\}\do\$\do\&% \do\#\do\^\do\^^K\do\_\do\^^A\do\%\do\~} @@ To make the plain macros more efficient in time and space, several constant values are declared as control sequences. \stress{If they were changed, anything could happen.} So be careful! <>= \chardef\@@ne=1 \chardef\tw@@=2 \chardef\thr@@@@=3 \chardef\sixt@@@@n=16 \chardef\@@cclv=255 \mathchardef\@@cclvi=256 \mathchardef\@@m=1000 \mathchardef\@@M=10000 \mathchardef\@@MM=20000 @@ \section{Text fonts} <>= <> <> <> <> <> <> @@ Fonts assigned to [[\preloaded]] are not part of the format, but they are preloaded so that other format packages can use them. For example, if another set of macros says [[\font\ninerm=cmr9]], \TeX\ will not have to reload the font metric information for [[cmr9]]. <>= \font\tenrm=cmr10 % roman text \font\preloaded=cmr9 \font\preloaded=cmr8 \font\sevenrm=cmr7 \font\preloaded=cmr6 \font\fiverm=cmr5 \font\preloaded=cmss10 % sans serif \font\preloaded=cmssq8 \font\preloaded=cmssi10 % sans serif italic \font\preloaded=cmssqi8 \font\tenbf=cmbx10 % boldface extended \font\preloaded=cmbx9 \font\preloaded=cmbx8 \font\sevenbf=cmbx7 \font\preloaded=cmbx6 \font\fivebf=cmbx5 \font\tentt=cmtt10 % typewriter \font\preloaded=cmtt9 \font\preloaded=cmtt8 \font\preloaded=cmsltt10 % slanted typewriter \font\tensl=cmsl10 % slanted roman \font\preloaded=cmsl9 \font\preloaded=cmsl8 \font\tenit=cmti10 % text italic \font\preloaded=cmti9 \font\preloaded=cmti8 \font\preloaded=cmti7 \font\preloaded=cmu10 % unslanted text italic \font\preloaded=cmcsc10 % caps and small caps \font\preloaded=cmssbx10 % sans serif bold extended \font\preloaded=cmdunh10 % Dunhill style \font\preloaded=cmr7 scaled \magstep4 % for titles \font\preloaded=cmtt10 scaled \magstep2 \font\preloaded=cmssbx10 scaled \magstep2 \font\preloaded=manfnt % METAFONT logo and dragon curve and special symbols @@ Additional [[\preloaded]] fonts can be specified here. (And those that were [[\preloaded]] above can be eliminated.) <>= \let\preloaded=\undefined % preloaded fonts must be declared anew later. @@ <>= \def\magstephalf{1095 } \def\magstep#1{\ifcase#1 \@@m\or 1200\or 1440\or 1728\or 2074\or 2488\fi\relax} \def\magnification{\afterassignment\m@@g\count@@} \def\m@@g{\mag\count@@ \hsize6.5truein\vsize8.9truein\dimen\footins8truein} @@ \subsection{Font encoding} We usually think of text files as containing characters. It doesn't cause any problems most of the time when we use plain ASCII characters---letters A--Z, a--z, the numerals 0--9 and some of punctuation characters. This illusion is broken down when we start using characters that do not belong to this limited set, for example, accented characters / mathematical symbols. Then what we see on screen may not match what we key in. What gets printed may not match what we see on screen. Moreover, what gets shown on screen and what gets printed depends on what machine we are on and how the fonts that we are using are set up. In reality text files contain just numeric codes (in range 0--255) stored in 8-bit bytes, and the mapping between `character' and numeric code is quite arbitrary. This is because there are very many more characters than the 256 numeric codes possible with 8-bits. Consequently, there will be a need for more than one possible mapping or `font encoding', or in other words, there would not be a `standard' encoding that suits all purposes. \medskip When a symbol is built up by forming a box, the [[\leavevmode]] macro is called first; this starts a new paragraph, if \TeX\ is in vertical mode, but does nothing if \TeX\ is in horizontal mode or math mode. [[\chardef]] positions are taken from the fonts [[cmr10]] and [[cmsy10]]. <>= \chardef\%=`\% \chardef\&=`\& \chardef\#=`\# \chardef\$=`\$ \chardef\ss="19 \chardef\ae="1A \chardef\oe="1B \chardef\o="1C \chardef\AE="1D \chardef\OE="1E \chardef\O="1F \chardef\i="10 \chardef\j="11 % dotless letters \def\aa{\accent23a} \def\l{\char32l} \def\L{\leavevmode\setbox0\hbox{L}\hbox to\wd0{\hss\char32L}} \def\leavevmode{\unhbox\voidb@@x} % begins a paragraph, if necessary \def\_{\leavevmode \kern.06em \vbox{\hrule width.3em}} \def\AA{\leavevmode\setbox0\hbox{h}\dimen@@\ht0\advance\dimen@@-1ex% \rlap{\raise.67\dimen@@\hbox{\char'27}}A} \def\mathhexbox#1#2#3{\leavevmode \hbox{$\m@@th \mathchar"#1#2#3$}} \def\dag{\mathhexbox279} \def\ddag{\mathhexbox27A} \def\S{\mathhexbox278} \def\P{\mathhexbox27B} @@ The accent positions are taken from Computer Modern font family. We are about to `hard-wire' CM accent encoding into the format. Different encoding will be necessary if other styles of type are used. Three alternative control-symbol accents are defined, suitable for keyboards with extended character sets: [[\let\^^_=\v]], [[\let\^^S=\u]], [[\let\^^D=\^]]. <>= \def\oalign#1{\leavevmode\vtop{\baselineskip\z@@skip \lineskip.25ex% \ialign{##\crcr#1\crcr}}} \def\o@@lign{\lineskiplimit\z@@ \oalign} \def\ooalign{\lineskiplimit-\maxdimen \oalign} % chars over each other \def\sh@@ft#1{\dimen\z@@.00#1ex\multiply\dimen\z@@\fontdimen1\font \kern-.0156\dimen\z@@} % compensate for slant in lowered accents \def\d#1{{\o@@lign{\relax#1\crcr\hidewidth\sh@@ft{10}.\hidewidth}}} \def\b#1{{\o@@lign{\relax#1\crcr\hidewidth\sh@@ft{29}% \vbox to.2ex{\hbox{\char22}\vss}\hidewidth}}} \def\c#1{\setbox\z@@\hbox{#1}\ifdim\ht\z@@=1ex\accent24 #1% \else{\ooalign{\unhbox\z@@\crcr\hidewidth\char24\hidewidth}}\fi} \def\copyright{{\ooalign{\hfil\raise.07ex\hbox{c}\hfil\crcr\mathhexbox20D}}} \def\dots{\relax\ifmmode\ldots\else$\m@@th\ldots\,$\fi} \def\TeX{T\kern-.1667em\lower.5ex\hbox{E}\kern-.125emX} \def\`#1{{\accent18 #1}} \def\'#1{{\accent19 #1}} \def\v#1{{\accent20 #1}} \let\^^_=\v \def\u#1{{\accent21 #1}} \let\^^S=\u \def\=#1{{\accent22 #1}} \def\^#1{{\accent94 #1}} \let\^^D=\^ \def\.#1{{\accent95 #1}} \def\H#1{{\accent"7D #1}} \def\~#1{{\accent"7E #1}} \def\"#1{{\accent"7F #1}} \def\t#1{{\edef\next{\the\font}\the\textfont1\accent"7F\next#1}} @@ [[INITEX]] sets [[\uccode]]$\,`x=`X$ and [[\uccode]]$\,`X=`X$ for all letters $x$, and [[\lccode]]$\,`x=`x$, [[\lccode]]$\,`X=`x$; all other values are zero. <>= %%% Thats all for English language. @@ Space factor code affects setting of interword glue. The space factor is normally 1000, which means that the interword glue should not be modified. If the space factor $f$ is different from 1000, the interword glue is computed as follows: Take the normal space glue for the current font, and add the extra space if $f\ge2000$. Then the stretch component is multiplied by $f/1000$, while the shrink component is multiplied by $1000/f$. (Look up the Appendix for the values of normal space, normal stretch, normal shrink, and extra space for some of CM fonts.) [[INITEX]] sets space factor codes: [[\sfcode]]$\,x=1000$ for all $x$, except that [[\sfcode]]$\,`X=999$ for uppercase letters. The characters `[[)]]', `[[']]', and `[[]]]' does not change space factor. <>= \sfcode`\)=0 \sfcode`\'=0 \sfcode`\]=0 @@ \section{Math fonts} <>= <> <> <> <> <> <> @@ As was said earlier, the font metric information about preloaded font will be build into the format. But, if another set of macros says [[\font\fiftyfiverm = cmr9 at 55pt]], \TeX\ will \stress{have to reload again} the font metric information for [[cmr9]]. <>= \font\teni=cmmi10 % math italic \font\preloaded=cmmi9 \font\preloaded=cmmi8 \font\seveni=cmmi7 \font\preloaded=cmmi6 \font\fivei=cmmi5 \font\tensy=cmsy10 % math symbols \font\preloaded=cmsy9 \font\preloaded=cmsy8 \font\sevensy=cmsy7 \font\preloaded=cmsy6 \font\fivesy=cmsy5 \font\tenex=cmex10 % math extension \font\preloaded=cmmib10 % bold math italic \font\preloaded=cmbsy10 % bold math symbols @@ \subsection{Mathematical spacing} Spacing around mathematical object is measured in [[mu]]---`math units.' [[1mu]] is equal to $1/18\,$th part of [[\fontdimen 6]] of the font in family 2. [[\quad]] spacing does not change with the style of formula, nor does it depend on the math font families that are being used. But thin spaces, medium spaces, and thick spaces do get bigger and smaller as the size of type gets bigger and smaller; this is because they are defined in terms of \. According to these specifications, thin spaces in plain \TeX\ do not stretch or shrink; medium spaces can stretch a little, and they can shrink to zero; thick spaces can stretch a lot, but they never shrink. \medskip The following table gives the complete definition of muglue between mathematical objects. A formula is converted to a math list, and the math list consists chiefly of ``atoms'' of eight basic types: Ord~(ordinary), Op~(large operator), Bin~(binary operation), Rel~(relation), Open~(opening), Close~(closing), Punct~(punctuation), and Inner~(a delimited subformula). Other kinds of atoms, which arise from commands like [[\overline]] or [[\mathaccent]] or [[\vcenter]], etc., are all treated as type~Ord; fractions are treated as type~Inner. The following (non-symmetric) table is used to determine the spacing between pairs of adjacent atoms: \medbreak $$\baselineskip0pt\lineskip0pt \halign to\hsize {\strut\hbox to1.5\parindent{\it#\hfil}& % for the legend "Left atom" #\hfil\quad& % for the row labels #\hfil\tabskip 0pt plus 20pt& % for the rule at the left \hbox to 25pt{\tt\hss#\hss}& % for column 1 \hbox to 25pt{\tt\hss#\hss}& % for column 2 \hbox to 25pt{\tt\hss#\hss}& % for column 3 \hbox to 25pt{\tt\hss#\hss}& % for column 4 \hbox to 25pt{\tt\hss#\hss}& % for column 5 \hbox to 25pt{\tt\hss#\hss}& % for column 6 \hbox to 25pt{\tt\hss#\hss}& % for column 7 \hbox to 25pt{\tt\hss#\hss}& % for column 8 #\hfil\tabskip0pt\cr % for the rule at the right \noalign{\vskip-6pt} % it just happens that there's extra white space &&&&\multispan7\hss\it Right atom\hss\cr \noalign{\vskip3pt} &&&\rm Ord&\rm Op&\rm Bin&\rm Rel&\rm Open&\rm Close&\rm Punct&\rm Inner\cr \noalign{\vskip2pt} \omit&&\multispan{10}\leaders\hrule\hfil\cr \omit\vbox to 2pt{}&&\vrule&&&&&&&&&\vrule\cr &Ord&\vrule&0&1&(2)&(3)&0&0&0&(1)&\vrule\cr &Op&\vrule&1&1&*&(3)&0&0&0&(1)&\vrule\cr &Bin&\vrule&(2)&(2)&*&*&(2)&*&*&(2)&\vrule\cr Left&Rel&\vrule&(3)&(3)&*&0&(3)&0&0&(3)&\vrule\cr atom&Open&\vrule&0&0&*&0&0&0&0&0&\vrule\cr &Close&\vrule&0&1&(2)&(3)&0&0&0&(1)&\vrule\cr &Punct&\vrule&(1)&(1)&*&(1)&(1)&(1)&(1)&(1)&\vrule\cr &Inner&\vrule&(1)&1&(2)&(3)&(1)&0&(1)&(1)&\vrule\cr \omit\vbox to 2pt{}&&\vrule&&&&&&&&&\vrule\cr \omit&&\multispan{10}\leaders\hrule\hfil\cr}$$ \medbreak Here [[0]], [[1]], [[2]], and [[3]] stand for no space, thin space, medium space, and thick space, respectively. Thin space, medium space, and thin space are equal to values of [[\thinmuskim]], [[\medmuskip]], [[\thickmuskip]] parameters, respectively. The table entry is parenthesized if the space is to be inserted only in display and text styles, not in script and scriptscript styles. For example, many of the entries in the Rel row and the Rel column are `{\tt(3)}'; this means that thick spaces are normally inserted before and after relational symbols like `=', but not in subscripts. Some of the entries in the table are `{\tt*}'; such cases never arise, because Bin atoms must be preceded and followed by atoms compatible with the nature of binary operations. The conversion of math lists to horizontal lists is done whenever \TeX\ is about to leave math mode, and the inter-atomic spacing is inserted at that time. <>= \thinmuskip=3mu \medmuskip=4mu plus 2mu minus 4mu \thickmuskip=5mu plus 5mu @@ For the positioning of accents over single character the width of [[\skewchar]] is used. For most of fonts the default value of [[\skewchar]] is [[-1]]; but the math italic (family 1) and math symbol fonts (family 2) have special [[\skewchar]] values equal to [['177]] and [['60]], respectively. These are characters `{\teni\char'177\/}' and `{\tensy\char'60}'. <>= \skewchar\teni='177 \skewchar\seveni='177 \skewchar\fivei='177 \skewchar\tensy='60 \skewchar\sevensy='60 \skewchar\fivesy='60 @@ A math code is relevant only when the corresponding category code is 11 or~12. When processing in math mode characters of categories~11 and~12, [[\char]] and [[\chardef]] characters are replaced by their math code. If we denote 15-bit number by [["uvwz]], then math codes are assigned by \medskip [[\mathcode]] \<8-bit number> = [["uvwz]],\quad where \medskip \itemitem{[[u]]} --- the class code (see below for the list) \itemitem{[[v]]} --- the font family number (see the font tables at the end of this document) \itemitem{[[wz]]} --- the position of the character in the font $$\halign{\indent#\hfil&\quad#\hfil&\quad#\hfil& \hskip4em#\hfil&\quad#\hfil&\quad#\hfil\cr \it \kern-2pt Class&\it Meaning&\kern-2pt\it Example& \it \kern-2pt Class&\it Meaning&\kern-2pt\it Example\cr \noalign{\vskip2pt} 0&Ordinary&[[/]]& 4&Opening&[[(]]\cr 1&Large operator&[[\sum]]& 5&Closing&[[)]]\cr 2&Binary operation&[[+]]& 6&Punctuation&[[,]]\cr 3&Relation&[[=]]& 7&Variable family&[[x]]\cr }$$ A [[\mathcode]] can also have the special value \hex{8000}, which causes the character to behave as if it has catcode~13 (active). This feature makes [[']] apostrophe expand to [[\prime]]. The mathcode of [[']] does not interfere with the use of [[']] in octal constants. The mathcode of [["8000]] is also assigned to space and underscore. [[INITEX]] sets up [[\mathcode]]$\,x=x$ for $x=0..255$, except that [[\mathcode]]$\,x=x+\hex{7000}$ for each of the ten digits $x={}$[[`0]] to [[`9]]; [[\mathcode]]$\,x=x+\hex{7100}$ for each of the 52~letters. \TeX\ looks at the mathcode only when it is typesetting a character whose catcode is 11~(letter) or 12~(other), or when it encounters a character that is given explicitly as [[\char]]\. Class 7 is a special case that allows math symbols to change families. It behaves exactly like class~0, except that the specified family is replaced by the current value of an integer parameter called [[\fam]], provided that [[\fam]] is a legal family number (i.e., if it lies between 0 and~15). \TeX\ automatically sets [[\fam=-1]] whenever math mode is entered; therefore class~7 and class~0 are equivalent unless [[\fam]] has been given a new value. Plain \TeX\ changes [[\fam]] to~0 when the user types `[[\rm]]'; this makes it convenient to get roman letters in formulas, since letters belong to class~7. The control sequence [[\rm]] is an abbreviation for `[[\fam=0 \tenrm]]'; thus, [[\rm]] causes [[\fam]] to become zero, and it makes [[\tenrm]] the ``current font.'' In horizontal mode, the [[\fam]] value is irrelevant and the current font governs the typesetting of letters; but in math mode, the current font is irrelevant and the [[\fam]] value governs the letters. The current font affects math mode only if control space ([[\ ]]) is used or if dimensions are given in [[ex]] or [[em]] units; it also has an effect if an [[\hbox]] appears inside a formula, since the contents of an hbox are typeset in horizontal mode. <>= \mathcode`\^^@@="2201 % \cdot \mathcode`\^^A="3223 % \downarrow \mathcode`\^^B="010B % \alpha \mathcode`\^^C="010C % \beta \mathcode`\^^D="225E % \land \mathcode`\^^E="023A % \lnot \mathcode`\^^F="3232 % \in \mathcode`\^^G="0119 % \pi \mathcode`\^^H="0115 % \lambda \mathcode`\^^I="010D % \gamma \mathcode`\^^J="010E % \delta \mathcode`\^^K="3222 % \uparrow \mathcode`\^^L="2206 % \pm \mathcode`\^^M="2208 % \oplus \mathcode`\^^N="0231 % \infty \mathcode`\^^O="0140 % \partial \mathcode`\^^P="321A % \subset \mathcode`\^^Q="321B % \supset \mathcode`\^^R="225C % \cap \mathcode`\^^S="225B % \cup \mathcode`\^^T="0238 % \forall \mathcode`\^^U="0239 % \exists \mathcode`\^^V="220A % \otimes \mathcode`\^^W="3224 % \leftrightarrow \mathcode`\^^X="3220 % \leftarrow \mathcode`\^^Y="3221 % \rightarrow \mathcode`\^^Z="8000 % \ne \mathcode`\^^[="2205 % \diamond \mathcode`\^^\="3214 % \le \mathcode`\^^]="3215 % \ge \mathcode`\^^^="3211 % \equiv \mathcode`\^^_="225F % \lor \mathcode`\ ="8000 % \space \mathcode`\!="5021 \mathcode`\'="8000 % ^\prime \mathcode`\(="4028 \mathcode`\)="5029 \mathcode`\*="2203 % \ast \mathcode`\+="202B \mathcode`\,="613B \mathcode`\-="2200 \mathcode`\.="013A \mathcode`\/="013D \mathcode`\:="303A \mathcode`\;="603B \mathcode`\<="313C \mathcode`\=="303D \mathcode`\>="313E \mathcode`\?="503F \mathcode`\[="405B \mathcode`\\="026E % \backslash \mathcode`\]="505D \mathcode`\_="8000 % \_ \mathcode`\{="4266 \mathcode`\|="026A \mathcode`\}="5267 \mathcode`\^^?="1273 % \smallint @@ Delimiter codes are used after [[\left]] and [[\right]] commands, when \TeX\ is looking for a delimiter. If we denote 24-bit number by [["qrstuv]], then delimiter codes are assigned by \medskip [[\delcode]] \<8-bit number> = [["qrstuv]],\quad where \medskip \itemitem{[[q]]} --- the font family number of \itemitem{[[rs]]} --- the position of the the small variant of the delimiter \itemitem{[[t]]} --- the font family number of \itemitem{[[uv]]} --- the position of the the large variant of the delimiter \medskip %%% Assigning delimiters codes to characters completes coding. %%% The full list consists of: %%% [[\catcode]], [[\lccode]], [[\uccode]], [[\mathcode]], [[\delcode]]. [[INITEX]] sets all [[\delcode]] values to [[-1]], which means that no characters are recognized as delimiters in math formulas, except [[\delcode]]$\,`.=0$, so that `[[.]]' stands for ``null delimiter''. [[{]] and [[}]] should \stress{not get} delcodes; otherwise parameter grouping fails! <>= \delcode`\(="028300 \delcode`\)="029301 \delcode`\[="05B302 \delcode`\]="05D303 \delcode`\<="26830A \delcode`\>="26930B \delcode`\/="02F30E \delcode`\|="26A30C \delcode`\\="26E30F @@ All characters that are typeset in math mode belong to one of sixteen {\sl families} of fonts, numbered internally from 0 to~15. Each of these families consists of three fonts: one for text size, one for script size, and one for scriptscriptsize. The commands [[\textfont]], [[\scriptfont]], and [[\scriptscriptfont]] are used to specify the members of each family. Since there are up to 256~characters per font, and 3~fonts per family, and 16~families, \TeX\ can access up to 12,288 characters in any one formula (4096 in~each of the three sizes). The [[plain.tex]] format uses family~1 for math italic letters, family~2 for ordinary math symbols, and family~3 for large symbols. Text italic is put in family~4, slanted roman in family~5, bold roman in family~6, and typewriter type in family~7. A macro [[\newfam]] will assign symbolic names to families that aren't already used. [[INITEX]] initializes the mathcodes of all letters [[A]] to~[[Z]] and [[a]] to~[[z]] so that they are symbols of class~7 and family~1; that's why it is natural to use family~1 for math italics. Similarly, the digits [[0]] to~[[9]] are class~7 and family~0. None of the other families is treated in any special way by \TeX. \TeX\ doesn't check to see if the families are sensibly organized. The only constraint is that the fonts in families 2 and~3 have special [[\fontdimen]] parameters, which govern mathematical spacing (see Appendix). In Computer Modern only [[cmsy]] and [[cmex]] have these parameters, so their assignment to families 2 and~3 is almost mandatory. During the time that a math formula is being read, \TeX\ remembers each symbol as being ``character position so-and-so in family number such-and-such,'' but it does not take note of what fonts are actually in the families until reaching the end of the formula. <>= \textfont0=\tenrm \scriptfont0=\sevenrm \scriptscriptfont0=\fiverm \def\rm{\fam\z@@\tenrm} \textfont1=\teni \scriptfont1=\seveni \scriptscriptfont1=\fivei \def\mit{\fam\@@ne} \def\oldstyle{\fam\@@ne\teni} \textfont2=\tensy \scriptfont2=\sevensy \scriptscriptfont2=\fivesy \def\cal{\fam\tw@@} \textfont3=\tenex \scriptfont3=\tenex \scriptscriptfont3=\tenex \newfam\itfam \def\it{\fam\itfam\tenit} % \it is family 4 \textfont\itfam=\tenit \newfam\slfam \def\sl{\fam\slfam\tensl} % \sl is family 5 \textfont\slfam=\tensl \newfam\bffam \def\bf{\fam\bffam\tenbf} % \bf is family 6 \textfont\bffam=\tenbf \scriptfont\bffam=\sevenbf \scriptscriptfont\bffam=\fivebf \newfam\ttfam \def\tt{\fam\ttfam\tentt} % \tt is family 7 \textfont\ttfam=\tentt @@ \section{Registers allocation} Here are macros for the automatic allocation of [[\count]], [[\box]], [[\dimen]], [[\skip]], [[\muskip]], and [[\toks]] registers, as well as [[\read]] and [[\write]] stream numbers, [[\fam]] codes, [[\language]] codes, and [[\insert]] numbers. The main use of these macros is for registers that are defined by one macro and used by others, possibly at different nesting levels. The following counters are reserved: \begindisplay 0--9& page numbering\cr 10& count allocation\cr 11& dimen allocation\cr 12& skip allocation\cr 13& muskip allocation\cr 14& box allocation\cr 15& toks allocation\cr 16& read file allocation\cr 17& write file allocation\cr 18& math family allocation\cr 19& language allocation\cr 20& insert allocation\cr 21& the most recently allocated number\cr 22& constant -1\cr \enddisplay New counters are allocated starting with 23, 24, etc. Other registers are allocated starting with 10. This leaves 0 through 9 for the user to play with safely, except that counts 0 to 9 are considered to be the page and subpage numbers (since they are displayed during output). In this scheme, [[\count]] 10 always contains the number of the highest-numbered counter that has been allocated, [[\count 14]] the highest-numbered box, etc. Inserts are given numbers 254, 253, etc., since they require a [[\count]], [[\dimen]], [[\skip]], and [[\box]] all with the same number; [[\count]] 20 contains the lowest-numbered insert that has been allocated. [[\box255]] is reserved for [[\output]]; [[\count255]], [[\dimen255]], and [[\skip255]] can be used freely. It is recommended that macro designers always use global assignments with respect to registers numbered 1, 3, 5, 7, 9, and always non-global assignments with respect to registers 0, 2, 4, 6, 8, 255. This will prevent ``save stack buildup'' that might otherwise occur. <>= \count10=22 % allocates \count registers 23, 24, ... \count11=9 % allocates \dimen registers 10, 11, ... \count12=9 % allocates \skip registers 10, 11, ... \count13=9 % allocates \muskip registers 10, 11, ... \count14=9 % allocates \box registers 10, 11, ... \count15=9 % allocates \toks registers 10, 11, ... \count16=-1 % allocates input streams 0, 1, ... \count17=-1 % allocates output streams 0, 1, ... \count18=3 % allocates math families 4, 5, ... \count19=0 % allocates \language codes 1, 2, ... \count20=255 % allocates insertions 254, 253, ... \countdef\insc@@unt=20 % the insertion counter \countdef\allocationnumber=21 % the most recent allocation \countdef\m@@ne=22 \m@@ne=-1 % a handy constant \def\wlog{\immediate\write\m@@ne} % write on log file (only) <> <> <> <> @@ Here are abbreviations for the names of scratch registers that don't need to be allocated. <>= \countdef\count@@=255 \dimendef\dimen@@=0 \dimendef\dimen@@i=1 % global only \dimendef\dimen@@ii=2 \skipdef\skip@@=0 \toksdef\toks@@=0 @@ Now, we define [[\newcount]], [[\newbox]], etc. so that you can say [[\newcount\foo]] and [[\foo]] will be defined (with [[\countdef]]) to be the next counter. To find out which counter [[\foo]] is, you can look at [[\allocationnumber]]. Since there's no [[\boxdef]] command, [[\chardef]] is used to define a [[\newbox]], [[\newinsert]], [[\newfam]], and so on. <>= \outer\def\newcount{\alloc@@0\count\countdef\insc@@unt} \outer\def\newdimen{\alloc@@1\dimen\dimendef\insc@@unt} \outer\def\newskip{\alloc@@2\skip\skipdef\insc@@unt} \outer\def\newmuskip{\alloc@@3\muskip\muskipdef\@@cclvi} \outer\def\newbox{\alloc@@4\box\chardef\insc@@unt} \let\newtoks=\relax % we do this to allow plain.tex to be read in twice \outer\def\newhelp#1#2{\newtoks#1#1\expandafter{\csname#2\endcsname}} \outer\def\newtoks{\alloc@@5\toks\toksdef\@@cclvi} \outer\def\newread{\alloc@@6\read\chardef\sixt@@@@n} \outer\def\newwrite{\alloc@@7\write\chardef\sixt@@@@n} \outer\def\newfam{\alloc@@8\fam\chardef\sixt@@@@n} \outer\def\newlanguage{\alloc@@9\language\chardef\@@cclvi} @@ <>= \def\alloc@@#1#2#3#4#5{\global\advance\count1#1by\@@ne \ch@@ck#1#4#2% make sure there's still room \allocationnumber=\count1#1% \global#3#5=\allocationnumber \wlog{\string#5=\string#2\the\allocationnumber}} \outer\def\newinsert#1{\global\advance\insc@@unt by\m@@ne \ch@@ck0\insc@@unt\count \ch@@ck1\insc@@unt\dimen \ch@@ck2\insc@@unt\skip \ch@@ck4\insc@@unt\box \allocationnumber=\insc@@unt \global\chardef#1=\allocationnumber \wlog{\string#1=\string\insert\the\allocationnumber}} \def\ch@@ck#1#2#3{\ifnum\count1#1<#2% \else\errmessage{No room for a new #3}\fi} @@ We finish with the initalization of some constants. <>= \newdimen\maxdimen \maxdimen=16383.99999pt % the largest legal \newskip\hideskip \hideskip=-1000pt plus 1fill % negative but can grow \newskip\centering \centering=0pt plus 1000pt minus 1000pt \newdimen\p@@ \p@@=1pt % this saves macro space and time \newdimen\z@@ \z@@=0pt % can be used both for 0pt and 0 \newskip\z@@skip \z@@skip=0pt plus0pt minus0pt \newbox\voidb@@x % permanently void box register @@ \section{Parameters} Let's turn now to \TeX's parameters, which the previous chapters have introduced one at a time; it will be convenient to assemble them all together. \bigskip An \ is one of the following tokens: \begindisplay\belowdisplayskip=3pt plus 6pt \abovedisplayskip=3pt plus 1pt% \openup.15pt [[\pretolerance]]\qquad badness tolerance before hyphenation\cr [[\tolerance]]\qquad badness tolerance after hyphenation\cr [[\hbadness]]\qquad badness above which bad hboxes will be shown\cr [[\vbadness]]\qquad badness above which bad vboxes will be shown\cr [[\linepenalty]]\qquad amount added to badness of every line in a paragraph\cr [[\hyphenpenalty]]\qquad penalty for line break after discretionary hyphen\cr [[\exhyphenpenalty]]\qquad penalty for line break after explicit hyphen\cr [[\binoppenalty]]\qquad penalty for line break after binary operation\cr [[\relpenalty]]\qquad penalty for line break after math relation\cr [[\clubpenalty]]\qquad penalty for creating a club line at bottom of page\cr [[\widowpenalty]]\qquad penalty for creating a widow line at top of page\cr [[\displaywidowpenalty]]\qquad ditto, before a display\cr [[\brokenpenalty]]\qquad penalty for page break after a hyphenated line\cr [[\predisplaypenalty]]\qquad penalty for page break just before a display\cr [[\postdisplaypenalty]]\qquad penalty for page break just after a display\cr [[\interlinepenalty]]\qquad additional penalty for page break between lines\cr [[\floatingpenalty]]\qquad penalty for insertions that are split\cr [[\outputpenalty]]\qquad penalty at the current page break\cr [[\doublehyphendemerits]]\qquad demerits for consecutive broken lines\cr [[\finalhyphendemerits]]\qquad demerits for a penultimate broken line\cr [[\adjdemerits]]\qquad demerits for adjacent incompatible lines\cr [[\looseness]]\qquad change to the number of lines in a paragraph\cr [[\pausing]]\qquad positive if pausing after each line is read from a file\cr [[\holdinginserts]]\qquad positive if insertions remain dormant in output box\cr [[\tracingonline]]\qquad positive if showing diagnostic info on the terminal\cr [[\tracingmacros]]\qquad positive if showing macros as they are expanded\cr [[\tracingstats]]\qquad positive if showing statistics about memory usage\cr [[\tracingparagraphs]]\qquad positive if showing line-break calculations\cr [[\tracingpages]]\qquad positive if showing page-break calculations\cr [[\tracingoutput]]\qquad positive if showing boxes that are shipped out\cr [[\tracinglostchars]]\qquad positive if showing characters not in the font\cr [[\tracingcommands]]\qquad positive if showing commands before they are executed\cr [[\tracingrestores]]\qquad positive if showing deassignments when groups end\cr [[\language]]\qquad the current set of hyphenation rules\cr [[\uchyph]]\qquad positive if hyphenating words beginning with capital letters\cr [[\lefthyphenmin]]\qquad smallest fragment at beginning of hyphenated word\cr [[\righthyphenmin]]\qquad smallest fragment at end of hyphenated word\cr [[\globaldefs]]\qquad nonzero if overriding [[\global]] specifications\cr [[\defaulthyphenchar]]\qquad [[\hyphenchar]] value when a font is loaded\cr [[\defaultskewchar]]\qquad [[\skewchar]] value when a font is loaded\cr [[\escapechar]]\qquad escape character in the output of control sequence tokens\cr [[\endlinechar]]\qquad character placed at the right end of an input line\cr [[\newlinechar]]\qquad character that starts a new output line\cr [[\maxdeadcycles]]\qquad upper bound on [[\deadcycles]]\cr [[\hangafter]]\qquad hanging indentation changes after this many lines\cr [[\fam]]\qquad the current family number\cr [[\mag]]\qquad magnification ratio, times 1000\cr [[\delimiterfactor]]\qquad ratio for variable delimiters, times 1000\cr [[\time]]\qquad current time of day in minutes since midnight\cr [[\day]]\qquad current day of the month\cr [[\month]]\qquad current month of the year\cr [[\year]]\qquad current year of our Lord\cr [[\showboxbreadth]]\qquad maximum items per level when boxes are shown\cr [[\showboxdepth]]\qquad maximum level when boxes are shown\cr [[\errorcontextlines]]\qquad maximum extra context shown when errors occur\cr \enddisplay The first few of these parameters have values in units of ``badness'' and ``penalties'' that affect line breaking and page breaking. Then come demerit-oriented parameters; demerits are essentially given in units of ``badness squared,'' so those parameters tend to have larger values. By contrast, the next few parameters ([[\looseness]], [[\pausing]], etc.)\ generally have quite small values (either $-1$ or 0 or 1 or~2). Miscellaneous parameters complete the set. \bigskip A \ is one of the following: \begindisplay\openup.15pt [[\hfuzz]]\qquad maximum overrun before overfull hbox messages occur\cr [[\vfuzz]]\qquad maximum overrun before overfull vbox messages occur\cr [[\overfullrule]]\qquad width of rules appended to overfull boxes\cr [[\emergencystretch]]\qquad reduces badnesses on final pass of line-breaking\cr [[\hsize]]\qquad line width in horizontal mode\cr [[\vsize]]\qquad page height in vertical mode\cr [[\maxdepth]]\qquad maximum depth of boxes on main pages\cr [[\splitmaxdepth]]\qquad maximum depth of boxes on split pages\cr [[\boxmaxdepth]]\qquad maximum depth of boxes on explicit pages\cr [[\lineskiplimit]]\qquad threshold where [[\baselineskip]] changes to [[\lineskip]]\cr [[\delimitershortfall]]\qquad maximum space not covered by a delimiter\cr [[\nulldelimiterspace]]\qquad width of a null delimiter\cr [[\scriptspace]]\qquad extra space after subscript or superscript\cr [[\mathsurround]]\qquad kerning before and after math in text\cr [[\predisplaysize]]\qquad length of text preceding a display\cr [[\displaywidth]]\qquad length of line for displayed equation\cr [[\displayindent]]\qquad indentation of line for displayed equation\cr [[\parindent]]\qquad width of\/ [[\indent]]\cr [[\hangindent]]\qquad amount of hanging indentation\cr [[\hoffset]]\qquad horizontal offset in [[\shipout]]\cr [[\voffset]]\qquad vertical offset in [[\shipout]]\cr \enddisplay Before typesetting a delimiter \TeX\ determines the size $f$ of the formula to be covered as twice the maximum of the height and the depth of the formula. The size $d$ of the delimiter should be $$ \min\big\{ f - \hbox{[[\delimitershortfall]]},\> \hbox{[[\delimiterfactor]]} \cdot {f \over 1000} \big\} \leq d $$ \medskip And the possibilities for \ are: \begindisplay\openup.15pt [[\baselineskip]]\qquad desired glue between baselines\cr [[\lineskip]]\qquad interline glue if\/ [[\baselineskip]] isn't feasible\cr [[\parskip]]\qquad extra glue just above paragraphs\cr [[\abovedisplayskip]]\qquad extra glue just above displays\cr [[\abovedisplayshortskip]]\qquad ditto, following short lines\cr [[\belowdisplayskip]]\qquad extra glue just below displays\cr [[\belowdisplayshortskip]]\qquad ditto, following short lines\cr [[\leftskip]]\qquad glue at left of justified lines\cr [[\rightskip]]\qquad glue at right of justified lines\cr [[\topskip]]\qquad glue at top of main pages\cr [[\splittopskip]]\qquad glue at top of split pages\cr [[\tabskip]]\qquad glue between aligned entries\cr [[\spaceskip]]\qquad glue between words, if nonzero\cr [[\xspaceskip]]\qquad glue between sentences, if nonzero\cr [[\parfillskip]]\qquad additional [[\rightskip]] at end of paragraphs\cr \enddisplay To above parameters (except [[\parfillskip]]) are assigned values appropriate for CM family typeset at 12$\,$pt baseline. \medskip Finally, there are three permissible \ tokens: \begindisplay\openup.15pt [[\thinmuskip]]\qquad thin space in math formulas\cr [[\medmuskip]]\qquad medium space in math formulas\cr [[\thickmuskip]]\qquad thick space in math formulas\cr \enddisplay \bigskip \TeX\ also has parameters that are token lists. Such parameters do not enter into the definitions of \ and such things. A \ is any of: \begindisplay\openup.15pt [[\output]]\qquad the user's output routine\cr [[\everypar]]\qquad tokens to insert when a paragraph begins\cr [[\everymath]]\qquad tokens to insert when math in text begins\cr [[\everydisplay]]\qquad tokens to insert when display math begins\cr [[\everyhbox]]\qquad tokens to insert when an hbox begins\cr [[\everyvbox]]\qquad tokens to insert when a vbox begins\cr [[\everyjob]]\qquad tokens to insert when the job begins\cr [[\everycr]]\qquad tokens to insert after every [[\cr]] or nonredundant [[\crcr]]\cr [[\errhelp]]\qquad tokens that supplement an [[\errmessage]]\cr \enddisplay \bigskip All of numeric parameters are listed below, but the code is commented out if no special value needs to be set. [[INITEX]] makes all parameters zero except where noted. <>= <> <> <> <> @@ <>= \pretolerance=100 \tolerance=200 % INITEX sets this to 10000 \hbadness=1000 \vbadness=1000 \linepenalty=10 \hyphenpenalty=50 \exhyphenpenalty=50 \binoppenalty=700 \relpenalty=500 \clubpenalty=150 \widowpenalty=150 \displaywidowpenalty=50 \brokenpenalty=100 \predisplaypenalty=10000 % \postdisplaypenalty=0 % \interlinepenalty=0 % \floatingpenalty=0, set during \insert % \outputpenalty=0, set before TeX enters \output \doublehyphendemerits=10000 \finalhyphendemerits=5000 \adjdemerits=10000 % \looseness=0, cleared by TeX after each paragraph % \pausing=0 % \holdinginserts=0 % \tracingonline=0 % \tracingmacros=0 % \tracingstats=0 % \tracingparagraphs=0 % \tracingpages=0 % \tracingoutput=0 \tracinglostchars=1 % \tracingcommands=0 % \tracingrestores=0 % \language=0 \uchyph=1 % \lefthyphenmin=2 \righthyphenmin=3 set below % \globaldefs=0 % \maxdeadcycles=25 % INITEX does this % \hangafter=1 % INITEX does this, also TeX after each paragraph % \fam=0 % \mag=1000 % INITEX does this % \escapechar=`\\ % INITEX does this \defaulthyphenchar=`\- \defaultskewchar=-1 % \endlinechar=`\^^M % INITEX does this \newlinechar=-1 \delimiterfactor=901 % \time=now % TeX does this at beginning of job % \day=now % TeX does this at beginning of job % \month=now % TeX does this at beginning of job % \year=now % TeX does this at beginning of job \showboxbreadth=5 \showboxdepth=3 \errorcontextlines=5 @@ <>= \hfuzz=0.1pt \vfuzz=0.1pt \overfullrule=5pt \hsize=6.5in \vsize=8.9in \maxdepth=4pt \splitmaxdepth=\maxdimen \boxmaxdepth=\maxdimen % \lineskiplimit=0pt, changed by \normalbaselines \delimitershortfall=5pt \nulldelimiterspace=1.2pt \scriptspace=0.5pt % \mathsurround=0pt % \predisplaysize=0pt, set before TeX enters $$ % \displaywidth=0pt, set before TeX enters $$ % \displayindent=0pt, set before TeX enters $$ \parindent=20pt % \hangindent=0pt, zeroed by TeX after each paragraph % \hoffset=0pt % \voffset=0pt @@ <>= % \baselineskip=0pt, changed by \normalbaselines % \lineskip=0pt, changed by \normalbaselines \parskip=0pt plus 1pt \abovedisplayskip=12pt plus 3pt minus 9pt \abovedisplayshortskip=0pt plus 3pt \belowdisplayskip=12pt plus 3pt minus 9pt \belowdisplayshortskip=7pt plus 3pt minus 4pt % \leftskip=0pt % \rightskip=0pt \topskip=10pt \splittopskip=10pt % \tabskip=0pt % \spaceskip=0pt % \xspaceskip=0pt \parfillskip=0pt plus 1fil @@ We also define special registers that function like parameters: <>= \newskip\smallskipamount \smallskipamount=3pt plus 1pt minus 1pt \newskip\medskipamount \medskipamount=6pt plus 2pt minus 2pt \newskip\bigskipamount \bigskipamount=12pt plus 4pt minus 4pt \newskip\normalbaselineskip \normalbaselineskip=12pt \newskip\normallineskip \normallineskip=1pt \newdimen\normallineskiplimit \normallineskiplimit=0pt \newdimen\jot \jot=3pt \newcount\interdisplaylinepenalty \interdisplaylinepenalty=100 \newcount\interfootnotelinepenalty \interfootnotelinepenalty=100 \def\normalbaselines{\lineskip\normallineskip \baselineskip\normalbaselineskip \lineskiplimit\normallineskiplimit} @@ \section{Macros for text} Here we introduce macros that are used for basic formatting unrelated to mathematics. <>= <> <> <> <> <> <> <> <> <> <> <> <> @@ [[\]]\ and [[\]]\ are defined so that they expand to [[\]]\; this helps to prevent confusion, since all three cases look identical when displayed on most computer terminals. <>= \def\^^M{\ } % control = control \def\^^I{\ } % same for @@ The control sequences [[\endgraf]] and [[\endline]] are made equivalent to \TeX's primitive [[\par]] and~[[\cr]] operations, since it is often useful to redefine the meanings of [[\par]] and~[[\cr]] themselves. Then come the definitions of [[\space]] (a blank space), [[\empty]] (a~list of no tokens), and [[\null]] (an~empty hbox). [[\bgroup]] and [[\egroup]] are made to provide ``implicit'' grouping characters that turn out to be especially useful in macro definitions. <>= \let\endgraf=\par \let\endline=\cr \def\space{ } \def\empty{} \def\null{\hbox{}} \let\bgroup={ \let\egroup=} @@ The [[\obeylines]] macro says `[[\let^^M=\par]]' instead of `[[\def^^M{\par}]]' because the [[\let]] technique allows constructions such as `[[\let\par=\cr]] [[\obeylines]] [[\halign||{...}]]' in which [[\cr]]'s need not be given within the alignment. <>= {\catcode`\^^M=\active % these lines must end with % \gdef\obeylines{\catcode`\^^M\active \let^^M\par}% \global\let^^M\par} % this is in case ^^M appears in a \write \def\obeyspaces{\catcode`\ \active} {\obeyspaces\global\let =\space} @@ The macros [[\lq]], [[\rq]], [[\lbrack]], and [[\rbrack]] are defined, for people who have difficulty typing quotation marks and/or brackets. <>= \def\lq{`} \def\rq{'} \def\lbrack{[} \def\rbrack{]} @@ The macros [[\enskip]], [[\quad]], and [[\qquad]] provide spaces that are legitimate breakpoints within a paragraph; [[\enspace]], [[\thinspace]], and [[\negthinspace]] produce space that cannot cause a break (although the space will disappear if it occurs just next to certain kinds of breaks). All six of these spaces are relative to the current font. You can get horizontal space that never disappears by saying `[[\hglue]]\'; this space is able to stretch or shrink. Similarly, there's a vertical analog, `[[\vglue]]\'. The [[\nointerlineskip]] macro suppresses interline glue that would ordinarily be inserted before the next box in vertical mode; this is a ``one shot'' macro, but [[\offinterlineskip]] is more drastic---it sets things up so that future interline glue will be present, but zero. There also are macros for potentially breakable vertical spaces: [[\smallskip]], [[\medskip]], and [[\bigskip]]. <>= \def\thinspace{\kern .16667em } \def\negthinspace{\kern-.16667em } \def\enspace{\kern.5em } \def\enskip{\hskip.5em\relax} \def\quad{\hskip1em\relax} \def\qquad{\hskip2em\relax} \def\smallskip{\vskip\smallskipamount} \def\medskip{\vskip\medskipamount} \def\bigskip{\vskip\bigskipamount} \def\nointerlineskip{\prevdepth-1000\p@@} \def\offinterlineskip{\baselineskip-1000\p@@ \lineskip\z@@ \lineskiplimit\maxdimen} \def\topglue{\nointerlineskip\vglue-\topskip\vglue} % for top of page \def\vglue{\afterassignment\vgl@@\skip@@=} \def\vgl@@{\par \dimen@@\prevdepth \hrule height\z@@ \nobreak\vskip\skip@@ \prevdepth\dimen@@} \def\hglue{\afterassignment\hgl@@\skip@@=} \def\hgl@@{\leavevmode \count@@\spacefactor \vrule width\z@@ \nobreak\hskip\skip@@ \spacefactor\count@@} @@ The following macros introduce penalty markers that make breaking less, or more, desirable. The [[\break]], [[\nobreak]], and [[\allowbreak]] macros are intended for use in any mode; the [[~]]~(tie) and [[\slash]] (hyphen-like~`/') macros are intended for horizontal mode. The others are intended only for vertical mode, i.e., between paragraphs, so they begin with [[\par]]. <>= \def~{\penalty\@@M \ } % tie \def\slash{/\penalty\exhyphenpenalty} % a `/' that acts like a `-' \def\break{\penalty-\@@M} \def\nobreak{\penalty \@@M} \def\allowbreak{\penalty \z@@} \def\filbreak{\par\vfil\penalty-200\vfilneg} \def\goodbreak{\par\penalty-500 } \def\eject{\par\break} \def\supereject{\par\penalty-\@@MM} \def\removelastskip{\ifdim\lastskip=\z@@\else\vskip-\lastskip\fi} \def\smallbreak{\par\ifdim\lastskip<\smallskipamount \removelastskip\penalty-50\smallskip\fi} \def\medbreak{\par\ifdim\lastskip<\medskipamount \removelastskip\penalty-100\medskip\fi} \def\bigbreak{\par\ifdim\lastskip<\bigskipamount \removelastskip\penalty-200\bigskip\fi} @@ [[\line]], [[\leftline]], [[\rightline]], and [[\centerline]] produce boxes of the full line width, while [[\llap]] and [[\rlap]] make boxes whose effective width is zero. The [[\underbar]] macro puts its argument into an hbox with a straight line at a fixed distance under it. [[\underbar]] uses math mode to do its job, although the operation is essentially non-mathematical in nature. A few of the other macros below use math mode in similar ways; thus, \TeX's mathematical abilities prove to be useful even when no mathematical typesetting is actually being done. A special control sequence [[\m@@th]] is used to ``turn off'' [[\mathsurround]] when such constructions are being performed.) <>= \def\line{\hbox to\hsize} \def\leftline#1{\line{#1\hss}} \def\rightline#1{\line{\hss#1}} \def\centerline#1{\line{\hss#1\hss}} \def\rlap#1{\hbox to\z@@{#1\hss}} \def\llap#1{\hbox to\z@@{\hss#1}} \def\m@@th{\mathsurround\z@@} \def\underbar#1{$\setbox\z@@\hbox{#1}\dp\z@@\z@@ \m@@th \underline{\box\z@@}$} @@ A [[\strut]] is implemented here as a rule of width zero. The `[[\relax]]' in this macro and in others below is necessary in case |\strut| appears first in an alignment entry, because \TeX\ is in a somewhat unpredictable mode at such times. <>= \newbox\strutbox \setbox\strutbox=\hbox{\vrule height8.5pt depth3.5pt width\z@@} \def\strut{\relax\ifmmode\copy\strutbox\else\unhcopy\strutbox\fi} @@ The [[\ialign]] macro provides for alignments when it is necessary to be sure that [[\tabskip]] is initially zero. The [[\hidewidth]] macro can be used essentially as [[\hfill]] in alignment entries that are permitted to ``stick out'' of their column. There's also [[\multispan]], which permits alignment entries to span one or more columns. <>= \def\hidewidth{\hskip\hideskip} % for alignment entries that can stick out \def\ialign{\everycr{}\tabskip\z@@skip\halign} % initialized \halign \newcount\mscount \def\multispan#1{\omit \mscount#1\relax \loop\ifnum\mscount>\@@ne \sp@@n\repeat} \def\sp@@n{\span\omit\advance\mscount\m@@ne} @@ Now we get to the ``tabbing'' macros. They keep track of the tab positions by maintaining boxes full of empty boxes having the specified widths. The macro [[\+]] has been declared `[[\outer]]' here, so that \TeX\ will be better able to detect runaway arguments and definitions. A non-[[\outer]] version, called [[\tabalign]], has also been provided in case it is necessary to use [[\+]] in some ``inner'' place. You can use [[\tabalign]] just like [[\+]], except after [[\settabs]]. <>= \newif\ifus@@ \newif\if@@cr \newbox\tabs \newbox\tabsyet \newbox\tabsdone \def\cleartabs{\global\setbox\tabsyet\null \setbox\tabs\null} \def\settabs{\setbox\tabs\null \futurelet\next\sett@@b} \let\+=\relax % in case this file is being read in twice \def\sett@@b{\ifx\next\+\def\nxt{\afterassignment\s@@tt@@b\let\nxt}% \else\let\nxt\s@@tcols\fi \let\next\relax \nxt} \def\s@@tt@@b{\let\nxt\relax \us@@false\m@@ketabbox} \def\tabalign{\us@@true\m@@ketabbox} % non-\outer version of \+ \outer\def\+{\tabalign} \def\s@@tcols#1\columns{\count@@#1\dimen@@\hsize \loop\ifnum\count@@>\z@@ \@@nother \repeat} \def\@@nother{\dimen@@ii\dimen@@ \divide\dimen@@ii\count@@ \setbox\tabs\hbox{\hbox to\dimen@@ii{}\unhbox\tabs}% \advance\dimen@@-\dimen@@ii \advance\count@@\m@@ne} \def\m@@ketabbox{\begingroup \global\setbox\tabsyet\copy\tabs \global\setbox\tabsdone\null \def\cr{\@@crtrue\crcr\egroup\egroup \ifus@@\unvbox\z@@\lastbox\fi\endgroup \setbox\tabs\hbox{\unhbox\tabsyet\unhbox\tabsdone}}% \setbox\z@@\vbox\bgroup\@@crfalse \ialign\bgroup&\t@@bbox##\t@@bb@@x\crcr} \def\t@@bbox{\setbox\z@@\hbox\bgroup} \def\t@@bb@@x{\if@@cr\egroup % now \box\z@@ holds the column \else\hss\egroup \global\setbox\tabsyet\hbox{\unhbox\tabsyet \global\setbox\@@ne\lastbox}% now \box\@@ne holds its size \ifvoid\@@ne\global\setbox\@@ne\hbox to\wd\z@@{}% \else\setbox\z@@\hbox to\wd\@@ne{\unhbox\z@@}\fi \global\setbox\tabsdone\hbox{\box\@@ne\unhbox\tabsdone}\fi \box\z@@} @@ Paragraph shapes of a limited but important kind are provided by [[\item]], [[\itemitem]], and [[\narrower]]. A macro [[\hang]] causes hanging indentation by the normal amount of [[\parindent]], after the first line; thus, the entire paragraph will be indented by the same amount (unless it began with [[\noindent]]). [[\textindent]][[{stuff}]] is like [[\indent]], but it puts the `[[stuff]]' into the indentation, flush right except for an en~space; it also removes spaces that might follow the right brace in `[[{stuff}]]'. <>= \def\hang{\hangindent\parindent} \def\textindent#1{\indent\llap{#1\enspace}\ignorespaces} \def\item{\par\hang\textindent} \def\itemitem{\par\indent \hangindent2\parindent \textindent} \def\narrower{\advance\leftskip\parindent \advance\rightskip\parindent} @@ The [[\beginsection]] macro is intended to mark the beginning of a new major subdivision in a document; to use it, you say `[[\beginsection]]\
' followed by a blank line (or~[[\par]]). The macro first emits glue and penalties, designed to start a new page if the present page is nearly full; then it makes a [[\bigskip]] and puts the section title flush left on a line by itself, in boldface type. The section title is also displayed on the terminal. After a [[\smallskip]], with page break prohibited, a [[\noindent]] command is given; this suppresses indentation in the next paragraph, i.e., in the first paragraph of the new section. (However, the next ``paragraph'' will be empty if vertical mode material immediately follows the [[\beginsection]] command.) Special statements in a mathematical paper are often called theorems, lemmas, definitions, axioms, postulates, remarks, corollaries, algorithms, facts, conjectures, or some such things, and they generally are given special typographic treatment. The [[\proclaim]] macro puts the title of the proclamation in boldface, then sets the rest of the paragraph in slanted type. The paragraph is followed by something similar to [[\medbreak]], except that the amount of penalty is different so that page breaks are discouraged: <>= \outer\def\beginsection#1\par{\vskip\z@@ plus.3\vsize\penalty-250 \vskip\z@@ plus-.3\vsize\bigskip\vskip\parskip \message{#1}\leftline{\bf#1}\nobreak\smallskip\noindent} \outer\def\proclaim #1. #2\par{\medbreak \noindent{\bf#1.\enspace}{\sl#2\par}% \ifdim\lastskip<\medskipamount \removelastskip\penalty55\medskip\fi} @@ Ragged-right setting is initiated by restricting the spaces between words to have a fixed width, and by putting variable space at the right of each line. You should not call [[\raggedright]] until your text font has already been specified. It is assumed that the ragged-right material will not be in a variety of different sizes. If this assumption is not valid, a different approach should be used: [[\fontdimen]] parameters 3 and~4 of the fonts you will be using should be set to zero, by saying, e.g., `[[\fontdimen3\tenrm=0pt]]'. These parameters specify the stretchability and shrinkability of interword spaces. A special macro [[\ttraggedright]] should be used for ragged-right setting in [[typewriter type]], since the spaces between words are generally bigger in that style. (Spaces are already unstretchable and unshrinkable in font~|cmtt|.) <>= \def\raggedright {\rightskip\z@@ plus2em \spaceskip.3333em \xspaceskip.5em\relax} \def\ttraggedright {\tt\rightskip\z@@ plus2em\relax} % for use with \tt only @@ The [[\nonfrenchspacing]] macro is be used to change the default sfcodes (set by [[INITEX]]) of punctuation marks. This macro, when called, affects spacing after punctuation marks. <>= \def\frenchspacing{\sfcode`\.\@@m \sfcode`\?\@@m \sfcode`\!\@@m \sfcode`\:\@@m \sfcode`\;\@@m \sfcode`\,\@@m} \def\nonfrenchspacing{\sfcode`\.3000\sfcode`\?3000\sfcode`\!3000% \sfcode`\:2000\sfcode`\;1500\sfcode`\,1250 } @@ [[\rightarrowfill]] and [[\leftarrowfill]] macros use [[\cleaders]] with a repeatable box consisting of the middle 10 units of a minus sign, where one unit is ${1\over18}\em$. The leaders are preceded and followed by $-$ and~$\to$; there's enough backspacing to compensate for up to 5~units of extra space, fore and aft, that |\cleaders| might leave blank. In this way a macro is obtained such that [[\hbox to 100pt{\rightarrowfill}]] yields `\hbox to 100pt{\rightarrowfill}'. The [[\overbrace]] and [[\underbrace]] macros of plain \TeX\ are constructed by combining characters with rules. Font [[cmex10]] contains four symbols $\bracelu\;\braceld\;\bracerd\;\braceru$, each of which has depth zero and height equal to the thickness of a rule that joins them properly. Therefore it's easy to define [[\upbracefill]] and [[\downbracefill]] macros so that you can obtain, e.g., \begindisplay \vbox{\kern4pt \hbox to 100pt{\downbracefill}\hbox to 50pt{\upbracefill} } \enddisplay by saying `[[\hbox to 100pt{\downbracefill}\hbox to 50pt{\upbracefill}]]' in vertical mode. <>= \def\hrulefill{\leaders\hrule\hfill} \def\dotfill{\cleaders\hbox{$\m@@th \mkern1.5mu.\mkern1.5mu$}\hfill} \def\rightarrowfill{$\m@@th\smash-\mkern-6mu% \cleaders\hbox{$\mkern-2mu\smash-\mkern-2mu$}\hfill \mkern-6mu\mathord\rightarrow$} \def\leftarrowfill{$\m@@th\mathord\leftarrow\mkern-6mu% \cleaders\hbox{$\mkern-2mu\smash-\mkern-2mu$}\hfill \mkern-6mu\smash-$} \mathchardef\braceld="37A \mathchardef\bracerd="37B \mathchardef\bracelu="37C \mathchardef\braceru="37D \def\downbracefill{$\m@@th \setbox\z@@\hbox{$\braceld$}% \braceld\leaders\vrule height\ht\z@@ depth\z@@\hfill\braceru \bracelu\leaders\vrule height\ht\z@@ depth\z@@\hfill\bracerd$} \def\upbracefill{$\m@@th \setbox\z@@\hbox{$\braceld$}% \bracelu\leaders\vrule height\ht\z@@ depth\z@@\hfill\bracerd \braceld\leaders\vrule height\ht\z@@ depth\z@@\hfill\braceru$} @@ If you want to see all of the hyphens that plain \TeX\ will find in some random text, you can say `[[\showhyphens{]]\[[}]]' and the results will appear on your terminal (and in the log file). The [[\showhyphens]] macro creates an hbox that is intentionally underfull. <>= \def\showhyphens#1{\setbox0\vbox{\parfillskip\z@@skip\hsize\maxdimen\tenrm \pretolerance\m@@ne\tolerance\m@@ne\hbadness0\showboxdepth0\ #1}} @@ At the end of a \TeX\ manuscript it's usually best to finish everything off by typing `[[\bye]]'. The `[[\vfill\supereject]]' gets \TeX\ to flush out all remaining insertions, with blank space filling the bottom of incomplete pages, and `[[\end]]' sends the computer into its endgame routine. <>= \outer\def\bye{\par\vfill\supereject\end} @@ \section{Macros for math} Most of this section consists of long listings of special symbols together with their font locations. <>= <> <> <> <> <> <> <> <> <> <> <> <> <> @@ \TeX\ does automatic spacing of math formulas so that they look right, and this is almost true. But occasionally you must give \TeX\ some help. The number of possible math formulas is vast, and \TeX's spacing rules are rather simple, so it is natural that exceptions should arise. The basic elements of space that \TeX\ puts into formulas are called: thin spaces, medium spaces, thick spaces. The normal space between words of a paragraph is approximately equal to two thin spaces. \bigskip \noindent You can add your own spacing whenever you want to, by using the control sequences $$\halign{\indent#\hfil&\quad#\hfil\cr |\,|&thin space \ (normally 1/6 of a quad);\cr |\>|&medium space \ (normally 2/9 of a quad);\cr |\;|&thick space \ (normally 5/18 of a quad);\cr |\!|&negative thin space \ (normally $-1/6$ of a quad).\cr}$$ <>= \def\,{\mskip\thinmuskip} \def\>{\mskip\medmuskip} \def\;{\mskip\thickmuskip} \def\!{\mskip-\thinmuskip} @@ The next job is to define Greek letters and other symbols of type Ord. Uppercase Greek letters are assigned hexadecimal codes of the form \hex{7xxx}, so that they will change families when [[\fam]] changes. [[\mathchardef]] defines a control sequence to be a synonym for a math character (check [[\mathchar]] for the meaning of hex number). <>= \mathchardef\alpha="010B \mathchardef\beta="010C \mathchardef\gamma="010D \mathchardef\delta="010E \mathchardef\epsilon="010F \mathchardef\zeta="0110 \mathchardef\eta="0111 \mathchardef\theta="0112 \mathchardef\iota="0113 \mathchardef\kappa="0114 \mathchardef\lambda="0115 \mathchardef\mu="0116 \mathchardef\nu="0117 \mathchardef\xi="0118 \mathchardef\pi="0119 \mathchardef\rho="011A \mathchardef\sigma="011B \mathchardef\tau="011C \mathchardef\upsilon="011D \mathchardef\phi="011E \mathchardef\chi="011F \mathchardef\psi="0120 \mathchardef\omega="0121 \mathchardef\varepsilon="0122 \mathchardef\vartheta="0123 \mathchardef\varpi="0124 \mathchardef\varrho="0125 \mathchardef\varsigma="0126 \mathchardef\varphi="0127 \mathchardef\Gamma="7000 \mathchardef\Delta="7001 \mathchardef\Theta="7002 \mathchardef\Lambda="7003 \mathchardef\Xi="7004 \mathchardef\Pi="7005 \mathchardef\Sigma="7006 \mathchardef\Upsilon="7007 \mathchardef\Phi="7008 \mathchardef\Psi="7009 \mathchardef\Omega="700A @@ <>= \mathchardef\aleph="0240 \def\hbar{{\mathchar'26\mkern-9muh}} \mathchardef\imath="017B \mathchardef\jmath="017C \mathchardef\ell="0160 \mathchardef\wp="017D \mathchardef\Re="023C \mathchardef\Im="023D \mathchardef\partial="0140 \mathchardef\infty="0231 \mathchardef\prime="0230 \mathchardef\emptyset="023B \mathchardef\nabla="0272 \def\surd{{\mathchar"1270}} \mathchardef\top="023E \mathchardef\bot="023F \def\angle{{\vbox{\ialign{$\m@@th\scriptstyle##$\crcr \not\mathrel{\mkern14mu}\crcr \noalign{\nointerlineskip} \mkern2.5mu\leaders\hrule height.34pt\hfill\mkern2.5mu\crcr}}}} \mathchardef\triangle="0234 \mathchardef\forall="0238 \mathchardef\exists="0239 \mathchardef\neg="023A \let\lnot=\neg \mathchardef\flat="015B \mathchardef\natural="015C \mathchardef\sharp="015D \mathchardef\clubsuit="027C \mathchardef\diamondsuit="027D \mathchardef\heartsuit="027E \mathchardef\spadesuit="027F @@ Integral signs get special treatment so that their limits won't be set above and below. <>= \mathchardef\coprod="1360 \mathchardef\bigvee="1357 \mathchardef\bigwedge="1356 \mathchardef\biguplus="1355 \mathchardef\bigcap="1354 \mathchardef\bigcup="1353 \mathchardef\intop="1352 \def\int{\intop\nolimits} \mathchardef\prod="1351 \mathchardef\sum="1350 \mathchardef\bigotimes="134E \mathchardef\bigoplus="134C \mathchardef\bigodot="134A \mathchardef\ointop="1348 \def\oint{\ointop\nolimits} \mathchardef\bigsqcup="1346 \mathchardef\smallint="1273 @@ <>= \mathchardef\triangleleft="212F \mathchardef\triangleright="212E \mathchardef\bigtriangleup="2234 \mathchardef\bigtriangledown="2235 \mathchardef\wedge="225E \let\land=\wedge \mathchardef\vee="225F \let\lor=\vee \mathchardef\cap="225C \mathchardef\cup="225B \mathchardef\ddagger="227A \mathchardef\dagger="2279 \mathchardef\sqcap="2275 \mathchardef\sqcup="2274 \mathchardef\uplus="225D \mathchardef\amalg="2271 \mathchardef\diamond="2205 \mathchardef\bullet="220F \mathchardef\wr="226F \mathchardef\div="2204 \mathchardef\odot="220C \mathchardef\oslash="220B \mathchardef\otimes="220A \mathchardef\ominus="2209 \mathchardef\oplus="2208 \mathchardef\mp="2207 \mathchardef\pm="2206 \mathchardef\circ="220E \mathchardef\bigcirc="220D \mathchardef\setminus="226E % for set difference A\setminus B \mathchardef\cdot="2201 \mathchardef\ast="2203 \mathchardef\times="2202 \mathchardef\star="213F @@ Relations are also fairly straightforward, except for the ones that are constructed from other characters. The [[\mapstochar]] is a character `$\mapstochar\mskip5mu$' of width zero that is quite useless by itself, but it combines with right arrows to make [[\mapsto]] `$\mapsto$' and [[\longmapsto]] `$\longmapsto$'. Similarly, [[\not]] is a relation character of width zero that puts a slash over the character that follows. When two relations are adjacent in a math formula, \TeX\ puts no space between them. <>= \mathchardef\propto="322F \mathchardef\sqsubseteq="3276 \mathchardef\sqsupseteq="3277 \mathchardef\parallel="326B \mathchardef\mid="326A \mathchardef\dashv="3261 \mathchardef\vdash="3260 \mathchardef\nearrow="3225 \mathchardef\searrow="3226 \mathchardef\nwarrow="322D \mathchardef\swarrow="322E \mathchardef\Leftrightarrow="322C \mathchardef\Leftarrow="3228 \mathchardef\Rightarrow="3229 \def\neq{\not=} \let\ne=\neq \mathchardef\leq="3214 \let\le=\leq \mathchardef\geq="3215 \let\ge=\geq \mathchardef\succ="321F \mathchardef\prec="321E \mathchardef\approx="3219 \mathchardef\succeq="3217 \mathchardef\preceq="3216 \mathchardef\supset="321B \mathchardef\subset="321A \mathchardef\supseteq="3213 \mathchardef\subseteq="3212 \mathchardef\in="3232 \mathchardef\ni="3233 \let\owns=\ni \mathchardef\gg="321D \mathchardef\ll="321C \mathchardef\not="3236 \mathchardef\leftrightarrow="3224 \mathchardef\leftarrow="3220 \let\gets=\leftarrow \mathchardef\rightarrow="3221 \let\to=\rightarrow \mathchardef\mapstochar="3237 \def\mapsto{\mapstochar\rightarrow} \mathchardef\sim="3218 \mathchardef\simeq="3227 \mathchardef\perp="323F \mathchardef\equiv="3211 \mathchardef\asymp="3210 \mathchardef\smile="315E \mathchardef\frown="315F \mathchardef\leftharpoonup="3128 \mathchardef\leftharpoondown="3129 \mathchardef\rightharpoonup="312A \mathchardef\rightharpoondown="312B \def\joinrel{\mathrel{\mkern-3mu}} \def\relbar{\mathrel{\smash-}} % \smash, because - has the same height as + \def\Relbar{\mathrel=} \mathchardef\lhook="312C \def\hookrightarrow{\lhook\joinrel\rightarrow} \mathchardef\rhook="312D \def\hookleftarrow{\leftarrow\joinrel\rhook} \def\bowtie{\mathrel\triangleright\joinrel\mathrel\triangleleft} \def\models{\mathrel|\joinrel=} \def\Longrightarrow{\Relbar\joinrel\Rightarrow} \def\longrightarrow{\relbar\joinrel\rightarrow} \def\longleftarrow{\leftarrow\joinrel\relbar} \def\Longleftarrow{\Leftarrow\joinrel\Relbar} \def\longmapsto{\mapstochar\longrightarrow} \def\longleftrightarrow{\leftarrow\joinrel\rightarrow} \def\Longleftrightarrow{\Leftarrow\joinrel\Rightarrow} \def\iff{\;\Longleftrightarrow\;} @@ After defining characters [[\ldotp]] and [[\cdotp]] that act as math punctuation, [[\ldots]] and [[\cdots]] macros are defined that give the proper spacing in most circumstances. Vertical and diagonal dots ([[\vdots]] and [[\ddots]]) are also provided here: <>= \mathchardef\ldotp="613A % ldot as a punctuation mark \mathchardef\cdotp="6201 % cdot as a punctuation mark \mathchardef\colon="603A % colon as a punctuation mark \def\ldots{\mathinner{\ldotp\ldotp\ldotp}} \def\cdots{\mathinner{\cdotp\cdotp\cdotp}} \def\vdots{\vbox{\baselineskip4\p@@ \lineskiplimit\z@@ \kern6\p@@\hbox{.}\hbox{.}\hbox{.}}} \def\ddots{\mathinner{\mkern1mu\raise7\p@@\vbox{\kern7\p@@\hbox{.}}\mkern2mu \raise4\p@@\hbox{.}\mkern2mu\raise\p@@\hbox{.}\mkern1mu}} @@ Most of the math accents are handled entirely by the [[\mathaccent]] primitive, but a few of the variable-width ones are constructed the hard way. <>= \def\acute{\mathaccent"7013 } \def\grave{\mathaccent"7012 } \def\ddot{\mathaccent"707F } \def\tilde{\mathaccent"707E } \def\bar{\mathaccent"7016 } \def\breve{\mathaccent"7015 } \def\check{\mathaccent"7014 } \def\hat{\mathaccent"705E } \def\vec{\mathaccent"017E } \def\dot{\mathaccent"705F } \def\widetilde{\mathaccent"0365 } \def\widehat{\mathaccent"0362 } \def\overrightarrow#1{\vbox{\m@@th\ialign{##\crcr \rightarrowfill\crcr\noalign{\kern-\p@@\nointerlineskip} $\hfil\displaystyle{#1}\hfil$\crcr}}} \def\overleftarrow#1{\vbox{\m@@th\ialign{##\crcr \leftarrowfill\crcr\noalign{\kern-\p@@\nointerlineskip} $\hfil\displaystyle{#1}\hfil$\crcr}}} \def\overbrace#1{\mathop{\vbox{\m@@th\ialign{##\crcr\noalign{\kern3\p@@} \downbracefill\crcr\noalign{\kern3\p@@\nointerlineskip} $\hfil\displaystyle{#1}\hfil$\crcr}}}\limits} \def\underbrace#1{\mathop{\vtop{\m@@th\ialign{##\crcr $\hfil\displaystyle{#1}\hfil$\crcr\noalign{\kern3\p@@\nointerlineskip} \upbracefill\crcr\noalign{\kern3\p@@}}}}\limits} \def\skew#1#2#3{{\muskip\z@@#1mu\divide\muskip\z@@\tw@@ \mkern\muskip\z@@ #2{\mkern-\muskip\z@@{#3}\mkern\muskip\z@@}\mkern-\muskip\z@@}{}} @@ Now we come to 24 delimiters that can change their size. These are denoted explicitly by a \<27-bit number>. If we denote 27-bit number by [["cqrstuv]], then delimiter codes are assigned by \medskip [[\delimiter "cqrstuv]],\quad where \medskip \itemitem{[[c]]} --- the class \itemitem{[[q]]} --- the font family number of \itemitem{[[rs]]} --- the position of the the small variant of the delimiter \itemitem{[[t]]} --- the font family number of \itemitem{[[uv]]} --- the position of the the large variant of the delimiter \medskip After [[\left]] and [[\right]] commands the class digit is ignored. When \TeX\ is not looking for a delimiter the righmost three digits [[tuv]] are ignored, and the remaining four [[cqrs]] are treated as a [[\mathchar]]. <>= \def\lmoustache{\delimiter"437A340 } % top from (, bottom from ) \def\rmoustache{\delimiter"537B341 } % top from ), bottom from ( \def\lgroup{\delimiter"462833A } % extensible ( with sharper tips \def\rgroup{\delimiter"562933B } % extensible ) with sharper tips \def\arrowvert{\delimiter"26A33C } % arrow without arrowheads \def\Arrowvert{\delimiter"26B33D } % double arrow without arrowheads \def\bracevert{\delimiter"77C33E } % the vertical bar that extends braces \def\Vert{\delimiter"26B30D } \let\|=\Vert \def\vert{\delimiter"26A30C } \def\uparrow{\delimiter"3222378 } \def\downarrow{\delimiter"3223379 } \def\updownarrow{\delimiter"326C33F } \def\Uparrow{\delimiter"322A37E } \def\Downarrow{\delimiter"322B37F } \def\Updownarrow{\delimiter"326D377 } \def\backslash{\delimiter"26E30F } % for double coset G\backslash H \def\rangle{\delimiter"526930B } \def\langle{\delimiter"426830A } \def\rbrace{\delimiter"5267309 } \let\}=\rbrace \def\lbrace{\delimiter"4266308 } \let\{=\lbrace \def\rceil{\delimiter"5265307 } \def\lceil{\delimiter"4264306 } \def\rfloor{\delimiter"5263305 } \def\lfloor{\delimiter"4262304 } @@ In the [[plain.tex]] format and in the Computer Modern math fonts there is only one radical---the square root. The meaning of [[\radical]] is analogous to the [[\delimiter]] commands. Only the class number is dropped. Joining the radical character and the horizontal rule is done by leeting the radical character have a large depth, and the height which is equal to the rule thickness. The rule is placed on the baseline and the radical character is placed below. Then the whole is centered around math axis. <>= \def\choose{\atopwithdelims()} \def\brack{\atopwithdelims[]} \def\brace{\atopwithdelims\{\}} \def\sqrt{\radical"270370 } @@ These macros depend on actual sizes of delimiters. <>= \def\bigl{\mathopen\big} \def\bigm{\mathrel\big} \def\bigr{\mathclose\big} \def\Bigl{\mathopen\Big} \def\Bigm{\mathrel\Big} \def\Bigr{\mathclose\Big} \def\biggl{\mathopen\bigg} \def\biggm{\mathrel\bigg} \def\biggr{\mathclose\bigg} \def\Biggl{\mathopen\Bigg} \def\Biggm{\mathrel\Bigg} \def\Biggr{\mathclose\Bigg} \def\big#1{{\hbox{$\left#1\vbox to8.5\p@@{}\right.\n@@space$}}} \def\Big#1{{\hbox{$\left#1\vbox to11.5\p@@{}\right.\n@@space$}}} \def\bigg#1{{\hbox{$\left#1\vbox to14.5\p@@{}\right.\n@@space$}}} \def\Bigg#1{{\hbox{$\left#1\vbox to17.5\p@@{}\right.\n@@space$}}} \def\n@@space{\nulldelimiterspace\z@@ \m@@th} @@ The [[\mathpalette]] operation constructs a formula in all four styles; it is applied here in the implementation of [[\phantom]], [[\smash]], [[\root]], and other operations. (Actually [[\phantom]] and [[\smash]] are not perfect: They assume that the current style is uncramped.) These definitions illustrate how other built-up symbol combinations could be defined to work in all four styles. The control sequences [[\sp]] and [[\sb]] are provided for people who can't easily type [[^]] and [[_]]; a ``discretionary times sign'' [[\*]] is defined. <>= \def\mathpalette#1#2{\mathchoice{#1\displaystyle{#2}}% {#1\textstyle{#2}}{#1\scriptstyle{#2}}{#1\scriptscriptstyle{#2}}} \newbox\rootbox \def\root#1\of{\setbox\rootbox\hbox{$\m@@th\scriptscriptstyle{#1}$} \mathpalette\r@@@@t} \def\r@@@@t#1#2{\setbox\z@@\hbox{$\m@@th#1\sqrt{#2}$} \dimen@@\ht\z@@ \advance\dimen@@-\dp\z@@ \mkern5mu\raise.6\dimen@@\copy\rootbox \mkern-10mu \box\z@@} \newif\ifv@@ \newif\ifh@@ \def\vphantom{\v@@true\h@@false\ph@@nt} \def\hphantom{\v@@false\h@@true\ph@@nt} \def\phantom{\v@@true\h@@true\ph@@nt} \def\ph@@nt{\ifmmode\def\next{\mathpalette\mathph@@nt}% \else\let\next\makeph@@nt\fi\next} \def\makeph@@nt#1{\setbox\z@@\hbox{#1}\finph@@nt} \def\mathph@@nt#1#2{\setbox\z@@\hbox{$\m@@th#1{#2}$}\finph@@nt} \def\finph@@nt{\setbox\tw@@\null \ifv@@ \ht\tw@@\ht\z@@ \dp\tw@@\dp\z@@\fi \ifh@@ \wd\tw@@\wd\z@@\fi \box\tw@@} \def\mathstrut{\vphantom(} \def\smash{\relax % \relax, in case this comes first in \halign \ifmmode\def\next{\mathpalette\mathsm@@sh}\else\let\next\makesm@@sh \fi\next} \def\makesm@@sh#1{\setbox\z@@\hbox{#1}\finsm@@sh} \def\mathsm@@sh#1#2{\setbox\z@@\hbox{$\m@@th#1{#2}$}\finsm@@sh} \def\finsm@@sh{\ht\z@@\z@@ \dp\z@@\z@@ \box\z@@} \def\cong{\mathrel{\mathpalette\@@vereq\sim}} % congruence sign \def\@@vereq#1#2{\lower.5\p@@\vbox{\lineskiplimit\maxdimen\lineskip-.5\p@@ \ialign{$\m@@th#1\hfil##\hfil$\crcr#2\crcr=\crcr}}} \def\notin{\mathrel{\mathpalette\c@@ncel\in}} \def\c@@ncel#1#2{\m@@th\ooalign{$\hfil#1\mkern1mu/\hfil$\crcr$#1#2$}} \def\rightleftharpoons{\mathrel{\mathpalette\rlh@@{}}} \def\rlh@@#1{\vcenter{\m@@th\hbox{\ooalign{\raise2pt \hbox{$#1\rightharpoonup$}\crcr $#1\leftharpoondown$}}}} \def\buildrel#1\over#2{\mathrel{\mathop{\kern\z@@#2}\limits^{#1}}} \def\doteq{\buildrel\textstyle.\over=} \let\sp=^ \let\sb=_ \def\*{\discretionary{\thinspace\the\textfont2\char2}{}{}} @@ The 32 common functions whose names generally appear in roman letters. <>= \def\log{\mathop{\rm log}\nolimits} \def\lg{\mathop{\rm lg}\nolimits} \def\ln{\mathop{\rm ln}\nolimits} \def\lim{\mathop{\rm lim}} \def\limsup{\mathop{\rm lim\,sup}} \def\liminf{\mathop{\rm lim\,inf}} \def\sin{\mathop{\rm sin}\nolimits} \def\arcsin{\mathop{\rm arcsin}\nolimits} \def\sinh{\mathop{\rm sinh}\nolimits} \def\cos{\mathop{\rm cos}\nolimits} \def\arccos{\mathop{\rm arccos}\nolimits} \def\cosh{\mathop{\rm cosh}\nolimits} \def\tan{\mathop{\rm tan}\nolimits} \def\arctan{\mathop{\rm arctan}\nolimits} \def\tanh{\mathop{\rm tanh}\nolimits} \def\cot{\mathop{\rm cot}\nolimits} \def\coth{\mathop{\rm coth}\nolimits} \def\sec{\mathop{\rm sec}\nolimits} \def\csc{\mathop{\rm csc}\nolimits} \def\max{\mathop{\rm max}} \def\min{\mathop{\rm min}} \def\sup{\mathop{\rm sup}} \def\inf{\mathop{\rm inf}} \def\arg{\mathop{\rm arg}\nolimits} \def\ker{\mathop{\rm ker}\nolimits} \def\dim{\mathop{\rm dim}\nolimits} \def\hom{\mathop{\rm hom}\nolimits} \def\det{\mathop{\rm det}} \def\exp{\mathop{\rm exp}\nolimits} \def\Pr{\mathop{\rm Pr}} \def\gcd{\mathop{\rm gcd}} \def\deg{\mathop{\rm deg}\nolimits} \def\bmod{\nonscript\mskip-\medmuskip\mkern5mu \mathbin{\rm mod}\penalty900\mkern5mu\nonscript\mskip-\medmuskip} \def\pmod#1{\allowbreak\mkern18mu({\rm mod}\,\,#1)} @@ The definition of [[\matrix]] goes to some pains to ensure that two $n$-rowed matrices will have the same height and the same depth, unless at least one of their rows is unusually big. The definition of [[\bordermatrix]] is even more complicated, but it seems to work reasonably well; it uses a constant [[\p@@renwd]] that represents the width of a big extensible left parenthesis. <>= \def\cases#1{\left\{\,\vcenter{\normalbaselines\m@@th \ialign{$##\hfil$&\quad##\hfil\crcr#1\crcr}}\right.} \def\matrix#1{\null\,\vcenter{\normalbaselines\m@@th \ialign{\hfil$##$\hfil&&\quad\hfil$##$\hfil\crcr \mathstrut\crcr\noalign{\kern-\baselineskip} #1\crcr\mathstrut\crcr\noalign{\kern-\baselineskip}}}\,} \def\pmatrix#1{\left(\matrix{#1}\right)} \newdimen\p@@renwd \setbox0=\hbox{\tenex B} \p@@renwd=\wd0 % width of the big left ( \def\bordermatrix#1{\begingroup \m@@th \setbox\z@@\vbox{\def\cr{\crcr\noalign{\kern2\p@@\global\let\cr\endline}}% \ialign{$##$\hfil\kern2\p@@\kern\p@@renwd&\thinspace\hfil$##$\hfil &&\quad\hfil$##$\hfil\crcr \omit\strut\hfil\crcr\noalign{\kern-\baselineskip}% #1\crcr\omit\strut\cr}}% \setbox\tw@@\vbox{\unvcopy\z@@\global\setbox\@@ne\lastbox}% \setbox\tw@@\hbox{\unhbox\@@ne\unskip\global\setbox\@@ne\lastbox}% \setbox\tw@@\hbox{$\kern\wd\@@ne\kern-\p@@renwd\left(\kern-\wd\@@ne \global\setbox\@@ne\vbox{\box\@@ne\kern2\p@@}% \vcenter{\kern-\ht\@@ne\unvbox\z@@\kern-\baselineskip}\,\right)$}% \null\;\vbox{\kern\ht\@@ne\box\tw@@}\endgroup} @@ The value of [[\lineskiplimit]] is assumed to be [[\normallineskiplimit]] plus the accumulated amount of ``opening up.'' Thus, the [[\vskip]] instructions in [[\displ@@y]] will compensate for the fact that the first baseline of an alignment is separated by an opened-up baselineskip from the last line preceding the display. <>= \def\openup{\afterassignment\@@penup\dimen@@=} \def\@@penup{\advance\lineskip\dimen@@ \advance\baselineskip\dimen@@ \advance\lineskiplimit\dimen@@} \def\eqalign#1{\null\,\vcenter{\openup\jot\m@@th \ialign{\strut\hfil$\displaystyle{##}$&$\displaystyle{{}##}$\hfil \crcr#1\crcr}}\,} \newif\ifdt@@p \def\displ@@y{\global\dt@@ptrue\openup\jot\m@@th \everycr{\noalign{\ifdt@@p \global\dt@@pfalse \ifdim\prevdepth>-1000\p@@ \vskip-\lineskiplimit \vskip\normallineskiplimit \fi \else \penalty\interdisplaylinepenalty \fi}}} \def\@@lign{\tabskip\z@@skip\everycr{}} % restore inside \displ@@y \def\displaylines#1{\displ@@y \tabskip\z@@skip \halign{\hbox to\displaywidth{$\@@lign\hfil\displaystyle##\hfil$}\crcr #1\crcr}} \def\eqalignno#1{\displ@@y \tabskip\centering \halign to\displaywidth{\hfil$\@@lign\displaystyle{##}$\tabskip\z@@skip &$\@@lign\displaystyle{{}##}$\hfil\tabskip\centering &\llap{$\@@lign##$}\tabskip\z@@skip\crcr #1\crcr}} \def\leqalignno#1{\displ@@y \tabskip\centering \halign to\displaywidth{\hfil$\@@lign\displaystyle{##}$\tabskip\z@@skip &$\@@lign\displaystyle{{}##}$\hfil\tabskip\centering &\kern-\displaywidth\rlap{$\@@lign##$}\tabskip\displaywidth\crcr #1\crcr}} @@ Below we have an interesting set of macros that convert [[f''']] into [[f^{\prime\prime\prime}]]. <>= {\catcode`\'=\active \gdef'{^\bgroup\prim@@s}} \def\prim@@s{\prime\futurelet\next\pr@@m@@s} \def\pr@@m@@s{\ifx'\next\let\nxt\pr@@@@@@s \else\ifx^\next\let\nxt\pr@@@@@@t \else\let\nxt\egroup\fi\fi \nxt} \def\pr@@@@@@s#1{\prim@@s} \def\pr@@@@@@t#1#2{#2\egroup} {\catcode`\^^Z=\active \gdef^^Z{\not=}} % ^^Z is like \ne in math {\catcode`\_=\active \global\let_=\_} % _ in math is either subscript or \_ @@ \section{Macros for output} <>= <> <> <> <> <> @@ The [[\makeheadline]] macro constructs a vbox of height and depth zero. The magic constant $-22.5\pt$ is equal to $$ \hbox{[[\topskip]]} -\hbox{\}-2\,\hbox{[[\baselineskip]]} $$ i.e., $10\pt-8.5\pt-24\pt$ (assuming default values of [[\topskip]] and the height of the strut); this places the reference point of the headline exactly $24\pt$ above the reference point of the top line on the page, unless the headline or the top line are excessively large. The [[\advancepageno]] macro normally advances [[\pageno]] by~$+1$; but if [[\pageno]] is negative (for roman numerals), the advance is by~$-1$. The new value of [[\pageno]] will be appropriate for the next time the output routine is called into action. <>= \countdef\pageno=0 \pageno=1 % first page is number 1 \newtoks\headline \headline={\hfil} % headline is normally blank \newtoks\footline \footline={\hss\tenrm\folio\hss} % footline is normally a centered page number in font \tenrm % \def\makeheadline{\vbox to\z@@{\vskip-22.5\p@@ \line{\vbox to8.5\p@@{}\the\headline}\vss}\nointerlineskip} \def\makefootline{\baselineskip24\p@@\line{\the\footline}} % \def\folio{\ifnum\pageno<\z@@ \romannumeral-\pageno \else\number\pageno \fi} \def\nopagenumbers{\footline{\hfil}} % blank out the footline \def\advancepageno{\ifnum\pageno<\z@@ \global\advance\pageno\m@@ne \else\global\advance\pageno\@@ne \fi} % increase |pageno| @@ Ragged-bottom setting is achieved by inserting infinite glue, which overpowers the stretchability of [[\topskip]]. This macros assume that [[\topskip = 10pt]] <>= \newif\ifr@@ggedbottom \def\raggedbottom{\topskip 10\p@@ plus60\p@@ \r@@ggedbottomtrue} \def\normalbottom{\topskip 10\p@@ \r@@ggedbottomfalse} % undoes \raggedbottom @@ There are 255 classes of insertions, [[\insert0]] to [[\insert254]], and they are tied to other registers of the same number. For example, [[\insert100]] is connected with [[\count100]], [[\dimen100]], [[\skip100]], and [[\box100]]. \def\n{\thinspace$n$} For our purposes let's consider a particular class of insertions called class $n$; we will then be dealing with \TeX's primitive command \begindisplay [[\insert]]\n[[{]]\[[}]] \enddisplay which puts an insertion item into a horizontal or vertical list. For this class of insertions \begindisplay [[\box]]\n\qquad is where the material appears when a page is output;\cr [[\count]]\n\qquad is the magnification factor for page breaking;\cr [[\dimen]]\n\qquad is the maximum insertion size per page;\cr [[\skip]]\n\qquad is the extra space to allocate on a page.\cr \enddisplay For example, material inserted with [[\insert100]] will eventually appear in [[\box100]]. @@ [[\footnote]] macro depends on the value of [[\bigskipamount]], and [[\parindent]]. Because the value of [[\vsize]] ($8.9\in$) is greater than [[\dimen\footins]] ($8\in$), footnotes never fill up the whole page. <>= \newinsert\footins \def\footnote#1{\let\@@sf\empty % parameter #2 (the text) is read later \ifhmode\edef\@@sf{\spacefactor\the\spacefactor}\/\fi #1\@@sf\vfootnote{#1}} \def\vfootnote#1{\insert\footins\bgroup \interlinepenalty\interfootnotelinepenalty \splittopskip\ht\strutbox % top baseline for broken footnotes \splitmaxdepth\dp\strutbox \floatingpenalty\@@MM \leftskip\z@@skip \rightskip\z@@skip \spaceskip\z@@skip \xspaceskip\z@@skip \textindent{#1}\footstrut\futurelet\next\fo@@t} \def\fo@@t{\ifcat\bgroup\noexpand\next \let\next\f@@@@t \else\let\next\f@@t\fi \next} \def\f@@@@t{\bgroup\aftergroup\@@foot\let\next} \def\f@@t#1{#1\@@foot} \def\@@foot{\strut\egroup} \def\footstrut{\vbox to\splittopskip{}} \skip\footins=\bigskipamount % space added when footnote is present \count\footins=1000 % footnote magnification factor (1 to 1) \dimen\footins=8in % maximum footnotes per page \def\footnoterule{\kern-3\p@@ \hrule width 2truein \kern 2.6\p@@} % the \hrule is .4pt high @@ Here the constant [[12\p@@ = 12pt]] is hard coded into the format. <>= \newinsert\topins \newif\ifp@@ge \newif\if@@mid \def\topinsert{\@@midfalse\p@@gefalse\@@ins} \def\midinsert{\@@midtrue\@@ins} \def\pageinsert{\@@midfalse\p@@getrue\@@ins} \skip\topins=\z@@skip % no space added when a topinsert is present \count\topins=1000 % magnification factor (1 to 1) \dimen\topins=\maxdimen % no limit per page \def\@@ins{\par\begingroup\setbox\z@@\vbox\bgroup} % start a \vbox \def\endinsert{\egroup % finish the \vbox \if@@mid \dimen@@\ht\z@@ \advance\dimen@@\dp\z@@ \advance\dimen@@12\p@@ \advance\dimen@@\pagetotal \advance\dimen@@-\pageshrink \ifdim\dimen@@>\pagegoal\@@midfalse\p@@gefalse\fi\fi \if@@mid \bigskip\box\z@@\bigbreak \else\insert\topins{\penalty100 % floating insertion \splittopskip\z@@skip \splitmaxdepth\maxdimen \floatingpenalty\z@@ \ifp@@ge \dimen@@\dp\z@@ \vbox to\vsize{\unvbox\z@@\kern-\dimen@@}% depth is zero \else \box\z@@\nobreak\bigskip\fi}\fi\endgroup} @@ The value of [[\boxmaxdepth]] is set to [[\maxdepth]] so that the vbox will be constructed under the assumptions that \TeX's page builder has used to set up [[\box255]]. The [[\pagecontents]] macro produces a vertical list for everything that belongs on the main body of the page, namely the contents of [[\box255]] together with illustrations (inserted at the top) and footnotes (inserted at the bottom). [[\topins]] and [[\footins]] are the insertion class numbers for the two kinds of insertions used in plain \TeX; if more classes of insertions are added, [[\pagecontents]] should be changed accordingly. Notice that the boxes are unboxed so that the glue coming from insertions can help out the glue on the main page. The [[\footnoterule]] macro places a dividing line between the page and its footnotes; it makes a net contribution of $0\pt$ to the height of the vertical list. The [[\dosupereject]] macro is designed to clear out any insertions that have been held over, whether they are illustrations or footnotes or both. The negative [[\kern]] here cancels out the natural space of the [[\topskip]] glue that goes above the empty [[\line]]; that empty line box prevents the [[\vfill]] from disappearing into a page break. The vertical list that results from [[\dosupereject]] is placed on \TeX's list of things to put out next, just after the straggling insertions have been reconsidered. Hence another super-eject will occur, and the process will continue until no insertions remain. <>= \output{\plainoutput} \def\plainoutput{\shipout\vbox{\makeheadline\pagebody\makefootline}% \advancepageno \ifnum\outputpenalty>-\@@MM \else\dosupereject\fi} \def\pagebody{\vbox to\vsize{\boxmaxdepth\maxdepth \pagecontents}} \def\dosupereject{\ifnum\insertpenalties>\z@@ % something is being held over \line{}\kern-\topskip\nobreak\vfill\supereject\fi} \def\pagecontents{\ifvoid\topins\else\unvbox\topins\fi \dimen@@=\dp\@@cclv \unvbox\@@cclv % open up \box255 \ifvoid\footins\else % footnote info is present \vskip\skip\footins \footnoterule \unvbox\footins\fi \ifr@@ggedbottom \kern-\dimen@@ \vfil \fi} @@ \section{Hyphenation} A discretionary break consists of three sequences of characters called the {\sl pre-break}, {\sl post-break}, and {\sl no-break\/} texts. The idea is that if a line break occurs here, the pre-break text will appear at the end of the current line and the post-break text will occur at the beginning of the next line; but if no break occurs, the no-break text will appear in the current line. The discretionary are specified by writing \begindisplay |\discretionary{|\|}{|\|}{|\|}| \enddisplay where the three texts consist entirely of characters, boxes, and kerns. If a word contains discretionary breaks \TeX\ will not hyphenate it. Hyphenation exceptions are specified with the statements like \begindisplay [[\hyphenation{gal-axy iso-peri-met-ric}]] \enddisplay which gives to \TeX\ locations where these words may be hyphenated. The default values of [[\hyphenchar]] is [[`-]]. Sometimes the typewriter fonts are given [[\hyphenchar]]\[[=-1]] which value inhibits hyphenation. <>= \lefthyphenmin=2 \righthyphenmin=3 % disallow x- or -xx breaks \input hyphen @@ \section{Initalization} <>= \normalbaselines\rm % select roman font \nonfrenchspacing % punctuation affects the spacing @@ \section{Programming support} <>= <> <> @@ The [[\loop...\repeat]] macro provides for iterative operations. In this macro and several others, the control sequence `[[\next]]' is given a temporary value that is not going to be needed later; thus, [[\next]] acts like a ``scratch control sequence.'' The macro [[\newif]] to be used for definitions of new conditionals. For example, [[\newif\iffoo]] creates [[\footrue]], [[\foofalse]] to go with [[\iffoo]]. <>= \def\loop#1\repeat{\def\body{#1}\iterate} \def\iterate{\body \let\next\iterate \else\let\next\relax\fi \next} \let\repeat=\fi % this makes \loop...\if...\repeat skippable \outer\def\newif#1{\count@@\escapechar \escapechar\m@@ne \expandafter\expandafter\expandafter \edef\@@if#1{true}{\let\noexpand#1=\noexpand\iftrue}% \expandafter\expandafter\expandafter \edef\@@if#1{false}{\let\noexpand#1=\noexpand\iffalse}% \@@if#1{false}\escapechar\count@@} % the condition starts out false \def\@@if#1#2{\csname\expandafter\if@@\string#1#2\endcsname} {\uccode`1=`i \uccode`2=`f \uppercase{\gdef\if@@12{}}} % `if' is required @@ <>= \def\tracingall{\tracingonline\@@ne\tracingcommands\tw@@\tracingstats\tw@@ \tracingpages\@@ne\tracingoutput\@@ne\tracinglostchars\@@ne \tracingmacros\tw@@\tracingparagraphs\@@ne\tracingrestores\@@ne \showboxbreadth\maxdimen\showboxdepth\maxdimen\errorstopmode} @@ The format name and version number are recorded in control sequences, in order to help the people who might have to explain why something doesn't work. <>= \def\fmtname{plain+W}\def\fmtversion{3.14159+W} @@ \chapter{Appendices} \section{Efficiency and memory-space considerations} One difficulty with large sets of macros is that they take up space. It would be nice to preload every macro that every \TeX\ user has ever dreamed up; but there might not be enough room, because \TeX's memory capacity is finite. You might find it necessary to hold back and to load only the macros that are really needed. \medskip How much memory space does a macro require? \medskip \noindent There are four kinds of memory involved: token memory, name memory, string memory, and character memory. (If any of these becomes too full, it will be necessary to increase what \TeX\ calls the macro memory size, the hash size, the number of strings, and/or the pool size, respectively. The token memory is most important; a macro takes one cell of token memory for each token in its definition, including the `|{|' and the `|}|'. For example, the comparatively short definition \medskip [[\def\example#1\two{\four}]] \medskip \noindent takes five tokens: |#1|, [[\two]], |{|$_1$, [[\four]], and |}|$_2$. Each control sequence also takes up one cell of name memory, one cell of string memory, and as many cells of character memory as there are characters in the name (seven in the case of |\example|). Character memory is comparatively cheap; four characters, or in some cases five, will fit in the same number of bits as a single cell of token memory, inside the machine. Therefore you don't save much by choosing short macro names. \TeX\ will tell you how close you come to exceeding its current memory capacity if you say [[\tracingstats=1]]. \TeX\ governs fourteen kinds of memory: \begindisplay |number of strings|\qquad(names of control sequences and files)\cr |pool size|\qquad(the characters in such names)\cr |main memory size|\qquad(boxes, glue, breakpoints, token lists, characters, etc.)\cr |hash size|\qquad(control sequence names)\cr |font memory|\qquad(font metric data)\cr |exception dictionary|\qquad(hyphenation exceptions)\cr |input stack size|\qquad(simultaneous input sources)\cr |semantic nest size|\qquad(unfinished lists being constructed)\cr |parameter stack size|\qquad(macro parameters)\cr |buffer size|\qquad(characters in lines being read from files)\cr |save size|\qquad(values to restore at group ends)\cr |text input levels|\qquad(|\input| files and error insertions)\cr |grouping levels|\qquad(unfinished groups)\cr |pattern memory|\qquad(hyphenation pattern data)\cr \enddisplay The current amount of memory available will also be shown. One obvious way to keep from loading too many macros is to keep the macro files short and to |\input| only the ones that you need. \section{Extensible delimiters} \TeX\ builds large delimiters by using ``extensible'' characters, which are specified by giving top, midle, bottom, and repeatable characters in an \bold{extensible} command. For example, the extensible left parentheses in [[cmex10]] are defined by (see Figure~4) \medskip [[extensible oct"060": oct"060", 0, oct"100", oct"102";]] \medskip \noindent this says that character code [[oct"060"]] specifies an extensible delimiter constructed from itself as the top piece, from character number [[oct"100"]] as the bottom piece, and from character number [[oct"102"]] as the piece which should be repeated as often as necessary to reach a desired size. In this particular example there is no middle piece, but characters like curly braces have a middle piece as well. A zero value in the top, middle, or bottom position means that no character should be used in that part of the construction; but a zero value in the final position means that character number zero is the repeater. The width of an extensible character is taken to be the width of the repeater. Also several characters of various sizes can be linked together in a series by means of a \bold{charlist} command. For example (see Figure~4), \medskip [[charlist oct"000": oct"020": oct"022": oct"040";]] \medskip \noindent is used in the font [[cmex10]] to specify the left parentheses that \TeX\ uses in displayed math formulas. \TeX\ follows charlist to make variable-size delimiters and variable-size accents, as well to link [[\textstyle]] and the [[\displaystyle]] operators. \section{Font dimensions} The main information about font consists of the dimensions of the characters. These numbers \TeX\ finds in the font metric files. Except character dimensions, font metric files contain: values for [[\fontdimen]] parameters, italic correction of characters, ligature and kerning programs for characters. We change the fontdimen parameters with the (global) assignment: \begindisplay [[\fontdimen]]\\\\, \enddisplay for example, the assignment [[\fontdimen8\tenex = 0.6pt]] changes width of the fraction bar from default $0.4\pt$ to $0.6\pt$. \bigskip \noindent The first seven fontdimen parameters have the following meaning: \medskip \item{1.} the slant per point \item{2.} the interword space; that is used unless [[\spaceskip]] is specified \item{3.} interword stretch \item{4.} interword shrink \item{5.} the x-height \item{6.} the quad width (for the font in family 2, $1/18\,$th quad width is equal to $1\,$mu) \item{7.} the extra space; that value is added to the interword space used whenever [[\spacefactor]]${}\geq 2000$, unless [[\xspaceskip]] is specified. \bigskip \noindent For the font in family 2 attributes 8--19 specify positioning of fractions, subscripts, superscripts. \medskip \noindent \stress{fraction numerator attributes: minimum shift up, from the main baseline, of the baseline of the numerator of a generalized fraction} \medskip \item{8.} num1: for display style \item{9.} num2: for text style or smaller if a fraction bar is present \item{10.} num3: for text style or smaller if no a fraction bar is present \medskip \noindent \stress{fraction denominator attributes: minimum shift down, from the main baseline, of the baseline of the denominator of a generalized fraction} \medskip \item{11.} denom1: for display style \item{12.} denom2: for text style or smaller \medskip \noindent \stress{superscript attributes: minimum shift up, from the main baseline, of the baseline of the superscript} \medskip \item{13.} sup1: for display style \item{14.} sup2: for text style or smaller, non-cramped \item{15.} sup3: for text style or smaller, cramped \medskip \noindent \stress{subscript attributes: minimum shift down, from the main baseline, of the baseline of a subscript} \medskip \item{16.} sub1: when no superscript is present \item{17.} sub2: when superscript is present \medskip \noindent \stress{script adjustment attributes: for use only with non-glyph, that is, composite objects} \medskip \item{18.} sup\_drop: maximum distance of superscript baseline below top of nucleus \item{19.} sub\_drop: minimum distance of subscript baseline below bottom of nucleus \medskip \noindent Delimiter span attributes: height plus depth of delimiter enclosing a generalized fraction. \medskip \item{20.} delim1: in display style \item{21.} delim2: in text style or smaller \medskip \noindent The last parameter, the height of the math axis, specifies the height above the baseline of the fraction bar, and the centre of large delimiters and most operators and relations. This position is used in vertical centering. \medskip \item{22.} axis\_height. \bigbreak \noindent For the font in family 3 attributes 9--12 determine extra space added when limits are attached to operators. The attribute 8 specifies thickness of the rule used for overlines, underlines, radical extenders, and fraction bars. From that dimension are derived `clearances' around fraction bar. The attribute 13 specifies extra space added above and below attached limits. \medskip \item{8.} default\_rule\_thickness \item{9.} big\_op\_spacing1 \item{10.} big\_op\_spacing2 \item{11.} big\_op\_spacing3 \item{12.} big\_op\_spacing4 \item{13.} big\_op\_spacing5 \medskip \noindent We have: big\_op\_spacing1(2) $\leq$ space between upper (lower) limit and top (bottom) of large operator $\leq$ big\_op\_spacing3(4) \bigskip \begingroup \def \loop #1\repeat% {\global\def\body{#1}\iterate} \newcount \dno \def \?#1% {\ifdim\the\fontdimen\dno#1<10pt \hphantom{0}\fi% \the\fontdimen\dno#1} \ialign{\global\advance \dno by 1\relax#& \hfil\number\dno.#\quad&& \quad\tentt#\cr \omit&\omit\tensl fontdimen&cmsy10&cmex10&cmtt10&cmr10&cmti10&cmbx10 \cr\noalign{\bigskip} \loop&& \?\tensy& \?\tenex& \?\tentt& \?\tenrm& \?\tenit& \?\tenbf&\cr \ifnum\dno<7\repeat\cr} \advance \dno by -1 \vskip-\baselineskip \ialign{\global\advance \dno by 1\relax#& \hfil\number\dno.#\quad&& \quad\tentt#\cr \omit&\omit\hphantom{\tensl fontdimen}&\cr \loop&& \?\tensy& \?\tenex&\cr \ifnum\dno<13\repeat\cr} \advance \dno by -1 \vskip-\baselineskip \ialign{\global\advance \dno by 1\relax#& \hfil\number\dno.#\quad&& \quad\tentt#\cr \omit&\omit\hphantom{\tensl fontdimen}&\cr \loop&& \?\tensy&\cr \ifnum\dno<22\repeat\cr} \endgroup @@ \section{Font tables} \noindent {\bf Figure 1.\enspace}[[cmr10]]---family 0 \beginchart\tenrm \normalchart \endchart \medskip\vfill \noindent {\bf Figure 2.\enspace}[[cmmi10]]---family 1 \beginchart\teni \normalchart \endchart \medskip\vfill \noindent {\bf Figure 3.\enspace}[[cmsy10]]---family 2 \beginchart\tensy \normalchart \endchart \medskip\vfill \noindent {\bf Figure 4.\enspace}[[cmex10]]---family 3 \beginchart\tenex \normalchart \endchart @