Message-Id: <199312130900.AA17663@mail.cs.tu-berlin.de>
Reply-To: Mailing list for the LaTeX3 project <LATEX-L@DHDURZ1.BITNET>
Date:         Fri, 10 Dec 93 19:24:21 +0100
From: Frank Mittelbach <MITTELBACH@mzdmza.zdv.uni-mainz.de>
Sender: Mailing list for the LaTeX3 project <LATEX-L@DHDURZ1.BITNET>
To: Multiple Recipients of <LATEX-L@DHDURZ1.BITNET>
Subject:      deferred loading of math fonts
Status: R


Some time ago we had a discussion on the amount of fonts used by NFSS
in different sizes. Below is a piece of code that could be described
as being partly the result of this discussion. I can't claim that this
is tested and i don't have the time to do it right now but perhaps
some of you running NFSS2 might be interested in doing this.

enjoy

frank

--------------- a driver file for 2.09:   mdisplay.drv

\documentstyle[doc]{article}

\CodelineIndex
\MakeShortVerb{\|}

\input{mdisplay.dtx}  % to test it on itself

\begin{document}
\DocInput{mdisplay.dtx}
\end{document}

--------------- the code: mdisplay.dtx

% \CheckSum{131}
%
% \section{Introduction}
%
% As suggested by \meta{name?} the math font handling of NFSS2 could
% be improved by avoiding a global change of all math fonts whenever
% the current text size is changed. Instead, the math font setup could
% be deferred until it is actually needed, i.e., until a formula is
% encountered in the new size.
%
% This file implements his suggestion. The amount of code change is
% not very high but there are a few subtle points.
%
% This code is by no means tested, I can only claim that it works
% correctly for the example below; but I think the algorithm is
% basically sound.
%
% I believe that for most type of applications NFSS will slightly gain
% in speed, however it is trivial to show that this is not true for
% all possible applications.
%
%
% \section{Outline of algorithm}
%
% \TeX{} uses the the math fonts that are current when the end of a
% formula is reached. If we don't want to keep font setups local to
% every formula (which would result in an enormous overhead, we have
% to be careful not to end up with the wrong setup in case formulas
% are nested, e.g., we need to be able to handle
% \begin{verbatim}
% $ a=b+c \mbox{ \small for all $b$ and $c\in Z$}$
%\end{verbatim}
% Here the inner formulae |b| and |c\in Z| are typeset in |\small| but
% we have to return to |\normalsize| before we reach the closing |$|
% of the outer formula.
%
% This is handled in the following way:
% \begin{enumerate}
% \item At any point in the document the global variable
%   |\gbl@currsize| contains the point size for which the math fonts
%   currently are set up.
%
% \item \label{it:everymath} Whenever we start a formula we compare
%   its value with the local variable |\f@size| that describes the
%   current text font size.
%
% \item If both are the same we assume that we can use the current
%   math font setup without adjustment.
%
% \item \label{it:everymathend} If they differ we call |\gbl@settings|
%   which changes the math font setup and updates |\gbl@settings|.
%   \begin{enumerate}
% \item If we are recursivly inside another formula (|\if@inmath|) we
%      ensure that |\gbl@settings| is executed again in the outer
%      formula, so that the old setup is automatically restored.
% \item Otherwise, we set the switch |@inmath| locally to |true| so
%      that all nested formulae will be able to detect that they are
%      nested in some outer formula.
%   \end{enumerate}
% \end{enumerate}
%
%
% The above algorithm has the following features:
% \begin{itemize}
% \item For sizes which are not containing any formula no math setup
%   is done. Compared to the original algorithm of NFSS this results
%   in the following savings:
%   \begin{itemize}
%   \item No unnecessary loading of math fonts for sizes that are not
%      used to typeset any math formulae (explict or implicit ones).
%   \item No time overhead due to unnecessary changes of the math font
%      setup on entrance and exit of the text font size.
%   \end{itemize}
%
% \item Math font setup changes for top-level formulae will survive
%   (there is% no restauration after the formula) thus any following
%   formula in the same size will be directly typsetable. Compared to
%   NFSS2 the new algorithm has the overhead of one test per formula
%   to see if the current math setup is valid (in the original
%   algorithm the setup was always valid, thus no test was necessary).
%
% \item In nested formulae the math font setup is restored in the
%   outer formula by a series of |\aftergroup| commands and checks.
%   Compared to the original algorithm this involves additional checks
%   ($2 \times \langle\mbox{non-math levels}\rangle$ per inner
%   formula).
%
% \end{itemize}
%
% \StopEventually{}
%
% \section{The Code}
%
%    \begin{macrocode}
\makeatletter
%    \end{macrocode}
%
% If \TeX{} would support a hook just before the end of a formula
% (opposite of |\everymath| so to speak) the implementation of the
% algorithm would be much simpler because in that case we would set up
% the correct math fonts at this point without having to worry about
% incorrect settings due to nesting. The same would be true if in
% \LaTeX{} the use of |$| (as the primitive \TeX{} command) would be
% impossible and instead only a higher-level interface would be
% available. Note that this does not mean that a |$| couldn't be the
% short-hand for starting and stopping that higher-level interface, it
% only means that the direct \TeX{} function must be hidden.
%
% Anyway, since we don't have this and won't have it in \LaTeXe{} we
% need to implement it in a somewhat slower way.
%
% We test for the current setup on entry of a formula, i.e., on the
% hooks |\everymath| and |\everydisplay|. But since these hooks may
% contain user data we provide ourselves with an internal version of
% these hooks which stays frozen.
%
% \begin{macro}{\frozen@everymath}
% \begin{macro}{\frozen@everydisplay}
%    New internal names for |\everymath| and |\everydisplay|.
%    \begin{macrocode}
\let\frozen@everymath\everymath
\let\frozen@everydisplay\everydisplay
%    \end{macrocode}
% \end{macro}
% \end{macro}
%
% \begin{macro}{\everymath}
% \begin{macro}{\everydisplay}
%    Now we provide now user hooks that will be called in the frozen
%    internals.
%    \begin{macrocode}
\newtoks\everymath
\newtoks\everydisplay
%    \end{macrocode}
% \end{macro}
% \end{macro}
%
%
% \begin{macro}{\frozen@everymath}
%    Now we define the behaviour of the frozen hooks: first check the
%    math setup then call the user hook.
%    \begin{macrocode}
\frozen@everymath = {\check@mathfonts
                     \the\everymath}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\frozen@everydisplay}
%    Ditto for the display hook.
%    \begin{macrocode}
\frozen@everydisplay = {\check@mathfonts
                        \the\everydisplay}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\if@inmath}
%    To detect nested formulae we need a switch.
%    \begin{macrocode}
\newif\if@inmath
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\check@mathfonts}
%    In the |\check@mathfonts| macros we implement the steps
%    \ref{it:everymath} to \ref{it:everymathend}.
%    \begin{macrocode}
\def\check@mathfonts{%
  \ifx \glb@currsize \f@size
  \else
     \glb@settings
  \fi
%    \end{macrocode}
%    If we are recursivly inside another formula we issue
%    |\resglb@settings| to restore the setup on the other level.
%    \begin{macrocode}
  \if@inmath
     \aftergroup\restglb@settings
  \else
     \@inmathtrue
  \fi
}
%    \end{macrocode}
% \end{macro}
%
%
% \begin{macro}{\restglb@settings}
%    This macro will be executed the first time after the current
%    formula. However, its real work must be done one or more levels
%    later when we have reached the next math mode. Thus, we just
%    check for math mode and as long as we are outside of it we simply
%    issue another |\restglb@settings| to be executed after this
%    group.
%    \begin{macrocode}
\def\restglb@settings{%
  \ifmmode
%    \end{macrocode}
%    Once we have reached the next outer math mode we restore the math
%    fonts.  Due to the fact that we might have more than one such
%    execution on the same level (there is one such macro for every
%    inner formula, for example, two from the two formulae inside the
%    |\mbox| in the above example) we have a quick test if the setup
%    is already correct.
%    \begin{macrocode}
    \ifx \glb@currsize \f@size
    \else
       \glb@settings
    \fi
  \else
     \aftergroup\restglb@settings
  \fi
}
%    \end{macrocode}
% \end{macro}
%
%
% \begin{macro}{\p@selectfont}
%    The |\p@selectfont| becomes simpler since it doesn't have to deal
%    with math font size changes any longer. So now we only set the
%    parts dealing with the current text font.
%    \begin{macrocode}
\def\p@selectfont{%
    \xdef\font@name{%
      \csname\curr@fontshape/\f@size\endcsname}%
    \pickup@font
    \font@name
      \@tempskipa \f@baselineskip\relax
      \baselineskip \baselinestretch\@tempskipa
    \setbox\strutbox\hbox{\vrule\@height.7\baselineskip
        \@depth.3\baselineskip \@width\z@}%
    \normalbaselineskip\baselineskip
    }
%    \end{macrocode}
% \end{macro}
%
%
%
% \begin{macro}{\glb@settings}
%    The |\glb@settings| macro is unchanged except that I have moved
%    the hook |\every@size| into it
%    \begin{macrocode}
\def\glb@settings{%
  \begingroup
     \expandafter\ifx\csname S@\f@size\endcsname\relax
       \calculate@math@sizes
     \fi
     \csname S@\f@size\endcsname
      \ifmath@fonts
        \escapechar\m@ne
        \csname mv@\math@version \endcsname
      \else
        \math@fontstrue
      \fi
    \globaldefs\@ne
    \math@fonts
    \let \glb@currsize \f@size
  \endgroup
  \the\every@size
  }
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\mathversion}
% \begin{macro}{\setup@mathversion}
%    Finally we better not forget a version change, something that
%    also results in the need to change and reset the math font setup.
%    Rather than keeping track of the math version that was current
%    when the last setup occured and comparing this to
%    |\math@version|; we simply set |\glb@currsize| to an impossible
%    value and thus automatically forcing a new setup for the next
%    formula. By using |\aftergroup| the same is enforced after the
%    current group, i.e., at the point where the scope of the
%    |\mathversion| ends.
%    \begin{macrocode}
\def\mathversion#1{\@nomath\mathversion
          \expandafter\ifx\csname mv@#1\endcsname\relax
          \@latexerr{Math version `#1' is not defined}\@eha\else
          \edef\math@version{#1}%
	  \setup@mathversion\aftergroup\setup@mathversion
          \fi}
\def\setup@mathversion{\gdef\glb@currsize{}}
%    \end{macrocode}
% \end{macro}
% \end{macro}
%
%    \begin{macrocode}
  \makeatother
%    \end{macrocode}
%
% \Finale
%
\endinput