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+%
+% \iffalse meta-comment
+%
+% Copyright (C) 1995, 1999 American Mathematical Society.
+% Copyright (C) 2016-2019 LaTeX3 Project and American Mathematical Society.
+%
+% This work may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3c
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+% https://www.latex-project.org/lppl.txt
+% and version 1.3c or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+%
+% This work has the LPPL maintenance status `maintained'.
+%
+% The Current Maintainer of this work is the LaTeX3 Project.
+%
+% \fi
+%
+% \iffalse
+%<*driver>
+\documentclass{amsdtx}
+\def\MaintainedByLaTeXTeam#1{%
+\begin{center}%
+\fbox{\fbox{\begin{tabular}{@{}l@{}}%
+This file is maintained by the \LaTeX{} Project team.\\%
+Bug reports can be opened (category \texttt{#1}) at\\%
+\url{https://latex-project.org/bugs/}.\end{tabular}}}\end{center}}
+\usepackage{amsgen}
+\GetFileInfo{amsgen.sty}
+\begin{document}
+\title{The \pkg{amsgen} package}
+\author{American Mathematical Society\\Michael Downes}
+\date{Version \fileversion, \filedate}
+\DocInput{amsgen.dtx}
+\end{document}
+%</driver>
+% \fi
+%
+% \maketitle
+% \MaintainedByLaTeXTeam{amslatex}
+%
+% \MakeShortVerb\|
+%
+% \section{Introduction}
+% This is an internal package for storing common functions
+% that are shared by more than one package in the \amslatex/
+% distribution. Some of these might eventually make it into the \latex/
+% kernel.
+%
+% \StopEventually{}
+%
+% Standard package info.
+% Using \cs{ProvidesFile} rather than \cs{ProvidesPackage} because
+% the latter, when input by, e.g, \cls{amsbook}, results in
+% \texttt{LaTeX warning: You have requested document class `amsbook',
+% but the document class provides `amsgen'.}
+% \begin{macrocode}
+\NeedsTeXFormat{LaTeX2e}% LaTeX 2.09 can't be used (nor non-LaTeX)
+[1994/12/01]% LaTeX date must December 1994 or later
+\ProvidesFile{amsgen.sty}[1999/11/30 v2.0 generic functions]
+% \end{macrocode}
+%
+% \section{Implementation}
+% Some general macros shared by \fn{amsart.dtx}, \fn{amsmath.dtx},
+% \fn{amsfonts.dtx}, \dots
+%
+% \begin{macro}{\@saveprimitive}
+% The \pkg{amsmath} package redefines a number of \tex/ primitives.
+% In case some preceding package also decided to redefine one of
+% those same primitives, we had better do some checking to make
+% sure that we are able to save the primitive meaning for internal
+% use. This is handled by the \cs{@saveprimitive} function. We
+% follow the example of \cs{@@input} where the primitive meaning is
+% stored in an internal control sequence with a |@@| prefix.
+% Primitive control sequences can be distinguished by the fact that
+% \cs{string} and \cs{meaning} return the same information.
+% \begin{macrocode}
+\providecommand{\@saveprimitive}[2]{\begingroup\escapechar`\\\relax
+ \edef\@tempa{\string#1}\edef\@tempb{\meaning#1}%
+ \ifx\@tempa\@tempb \global\let#2#1%
+ \else
+% \end{macrocode}
+% Check to see if \arg{2} was already given the desired primitive
+% meaning somewhere else.
+% \begin{macrocode}
+ \edef\@tempb{\meaning#2}%
+ \ifx\@tempa\@tempb
+ \else
+ \@latex@error{Unable to properly define \string#2; primitive
+ \noexpand#1no longer primitive}\@eha
+ \fi
+ \fi
+ \endgroup}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@xp}
+% \begin{macro}{\@nx}
+% Shorthands for long command names.
+% \begin{macrocode}
+\let\@xp=\expandafter
+\let\@nx=\noexpand
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\@emptytoks}
+% A token register companion for \cs{@empty}. Saves a little main mem and
+% probably makes initializations such as |\toks@{}| run faster too.
+% \begin{macrocode}
+\newtoks\@emptytoks
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@oparg}
+% Use of \cs{@oparg} simplifies some constructions where a macro
+% takes an optional argument in square brackets. We can't use
+% \cn{newcommand} here because this function might be previously
+% defined by the \pkg{amsmath} package in a loading sequence such as
+% \begin{verbatim}
+% \usepackage{amsmath,amsthm}
+% \end{verbatim}
+% \begin{macrocode}
+\def\@oparg#1[#2]{\@ifnextchar[{#1}{#1[#2]}}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@ifempty}
+% \begin{macro}{\@ifnotempty}
+% |\@ifnotempty| and |\@ifempty| use category 11 |@| characters to
+% test whether the argument is empty or not, since these are highly
+% unlikely to occur in the argument. As with \cn{@oparg}, there is a
+% possibility that these commands were defined previously in
+% \fn{amsmath.sty}.
+% \begin{macrocode}
+\long\def\@ifempty#1{\@xifempty#1@@..\@nil}
+\long\def\@xifempty#1#2@#3#4#5\@nil{%
+ \ifx#3#4\@xp\@firstoftwo\else\@xp\@secondoftwo\fi}
+% \end{macrocode}
+% \cs{@ifnotempty} is a shorthand that makes code read better when
+% no action is needed in the empty case. At a cost of double
+% argument-reading---so for often-executed code, avoiding
+% \cs{@ifnotempty} might be wise.
+% \begin{macrocode}
+\long\def\@ifnotempty#1{\@ifempty{#1}{}}
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% Some abbreviations to conserve token mem.
+% \begin{macrocode}
+\def\FN@{\futurelet\@let@token}
+\def\DN@{\def\next@}
+\def\RIfM@{\relax\ifmmode}
+\def\setboxz@h{\setbox\z@\hbox}
+\def\wdz@{\wd\z@}
+\def\boxz@{\box\z@}
+\def\relaxnext@{\let\@let@token\relax}
+% \end{macrocode}
+%
+% \begin{macro}{\new@ifnextchar}
+% This macro is a new version of \latex/'s \verb+\@ifnextchar+,
+% macro that does not skip over spaces.
+% \begin{macrocode}
+\long\def\new@ifnextchar#1#2#3{%
+% \end{macrocode}
+% By including the space after the equals sign, we make it possible
+% for \cs{new@ifnextchar} to do look-ahead for any token, including a
+% space!
+% \begin{macrocode}
+ \let\reserved@d= #1%
+ \def\reserved@a{#2}\def\reserved@b{#3}%
+ \futurelet\@let@token\new@ifnch
+}
+%
+\def\new@ifnch{%
+ \ifx\@let@token\reserved@d \let\reserved@b\reserved@a \fi
+ \reserved@b
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@ifstar}
+% There will essentially never be a space before the \qc{\*}, so
+% using \cs{@ifnextchar} is unnecessarily slow.
+% \begin{macrocode}
+\def\@ifstar#1#2{\new@ifnextchar *{\def\reserved@a*{#1}\reserved@a}{#2}}
+% \end{macrocode}
+% \end{macro}
+%
+% The hook \cs{every@size} was changed to \cs{every@math@size} in the
+% December 1994 release of \latex/ and its calling procedures changed.
+% If \cs{every@math@size} is undefined it means the user has an older
+% version of \latex/ so we had better define it and patch a couple of
+% functions (\cs{glb@settings} and \cs{set@fontsize}).
+% \begin{macrocode}
+\@ifundefined{every@math@size}{%
+% \end{macrocode}
+% Reuse the same token register; since it was never used except for
+% the purposes that are affected below, this is OK.
+% \begin{macrocode}
+\let\every@math@size=\every@size
+\def\glb@settings{%
+ \expandafter\ifx\csname S@\f@size\endcsname\relax
+ \calculate@math@sizes
+ \fi
+ \csname S@\f@size\endcsname
+ \ifmath@fonts
+% \ifnum \tracingfonts>\tw@
+% \@font@info{Setting up math fonts for
+% \f@size/\f@baselineskip}\fi
+ \begingroup
+ \escapechar\m@ne
+ \csname mv@\math@version \endcsname
+ \globaldefs\@ne
+ \let \glb@currsize \f@size
+ \math@fonts
+ \endgroup
+ \the\every@math@size
+ \else
+% \ifnum \tracingfonts>\tw@
+% \@font@info{No math setup for \f@size/\f@baselineskip}%
+% \fi
+ \fi
+}
+% \end{macrocode}
+% Remove |\the\every@size| from \cs{size@update}.
+% \begin{macrocode}
+\def\set@fontsize#1#2#3{%
+ \@defaultunits\@tempdimb#2pt\relax\@nnil
+ \edef\f@size{\strip@pt\@tempdimb}%
+ \@defaultunits\@tempskipa#3pt\relax\@nnil
+ \edef\f@baselineskip{\the\@tempskipa}%
+ \edef\f@linespread{#1}%
+ \let\baselinestretch\f@linespread
+ \def\size@update{%
+ \baselineskip\f@baselineskip\relax
+ \baselineskip\f@linespread\baselineskip
+ \normalbaselineskip\baselineskip
+ \setbox\strutbox\hbox{%
+ \vrule\@height.7\baselineskip
+ \@depth.3\baselineskip
+ \@width\z@}%
+%%% \the\every@size
+ \let\size@update\relax}%
+ }
+}{}% end \@ifundefined test
+% \end{macrocode}
+%
+% \begin{macro}{\ex@}
+% The \cs{ex@} variable provides a small unit of space for use in
+% math-mode constructions, that varies according to the current type
+% size. For example, the \cn{pmb} command uses \cs{ex@} units.
+% Since a macro or mu unit solution for the \meta{dimen} \cs{ex@} won't
+% work without changing a lot of current code in the \pkg{amsmath}
+% package, we set \cs{ex@} through the \cs{every@math@size} hook.
+% The value of \cs{ex@} is scaled nonlinearly in a range of roughly
+% 0.5pt to 1.5pt, by the function \cs{compute@ex@}.
+% \begin{macrocode}
+\newdimen\ex@
+\addto@hook\every@math@size{\compute@ex@}
+% \end{macrocode}
+% \end{macro}
+%
+% \cs{compute@ex@} computes \cs{ex@} as a nonlinear scaling from 10pt
+% to current font size (\cs{f@size}). Using .97 as the multiplier makes 1
+% |ex@| $\approx$ .9pt when the current type size is 8pt and 1 |ex@|
+% $\approx$ 1.1pt when the current type size is 12pt.
+%
+% The formula is essentially
+% \begin{displaymath}
+% \newcommand{\points}{\mbox{pt}}
+% \newcommand{\floor}[1]{\lfloor#1\rfloor}
+% 1\points \pm (1\points - (.97)^{\floor{\vert 10 - n\vert}})
+% \end{displaymath}
+% where $n$ = current type size, but adjusted to differentiate
+% half-point sizes as well as whole point sizes, and there is a
+% cutoff for extraordinarily large values of \cs{f@size} ($>$ 20pt)
+% so that the value of \cs{ex@} never exceeds 1.5pt.
+%
+% \begin{macrocode}
+\def\compute@ex@{%
+ \begingroup
+ \dimen@-\f@size\p@
+ \ifdim\dimen@<-20\p@
+% \end{macrocode}
+% Never make \cs{ex@} larger than 1.5pt.
+% \begin{macrocode}
+ \global\ex@ 1.5\p@
+ \else
+% \end{macrocode}
+% Adjust by the reference size and multiply by 2 to allow for
+% half-point sizes.
+% \begin{macrocode}
+ \advance\dimen@10\p@ \multiply\dimen@\tw@
+% \end{macrocode}
+% Save information about the current sign of \cs{dimen@}.
+% \begin{macrocode}
+ \edef\@tempa{\ifdim\dimen@>\z@ -\fi}%
+% \end{macrocode}
+% Get the absolute value of \cs{dimen@}.
+% \begin{macrocode}
+ \dimen@ \ifdim\dimen@<\z@ -\fi \dimen@
+ \advance\dimen@-\@m sp % fudge factor
+% \end{macrocode}
+% Here we use \cs{vfuzz} merely as a convenient scratch register
+% \begin{macrocode}
+ \vfuzz\p@
+% \end{macrocode}
+% Multiply in a loop.
+% \begin{macrocode}
+ \def\do{\ifdim\dimen@>\z@
+ \vfuzz=.97\vfuzz
+ \advance\dimen@ -\p@
+%\message{\vfuzz: \the\vfuzz, \dimen@: \the\dimen@}%
+ \@xp\do \fi}%
+ \do
+ \dimen@\p@ \advance\dimen@-\vfuzz
+ \global\ex@\p@
+ \global\advance\ex@ \@tempa\dimen@
+ \fi
+ \endgroup
+%\typeout{\string\f@size: \f@size}\showthe\ex@
+}
+% \end{macrocode}
+% Tests of the \cs{compute@ex@} function yield the following results:
+%
+% \begin{center}\begin{tabular}{rlrl}
+% \cs{f@size}& \cs{ex@}& \cs{f@size}& \cs{ex@}\\
+% 10& 1.0pt& 9& 0.94089pt\\
+% 11& 1.05911pt& 8.7& 0.91266pt\\
+% 12& 1.11473pt& 8.5& 0.91266pt\\
+% 14.4& 1.23982pt& 8.4& 0.88527pt\\
+% 17.28& 1.36684pt& 8& 0.88527pt\\
+% 20.74& 1.5pt& 7& 0.83293pt\\
+% 19.5& 1.4395pt& 6& 0.78369pt\\
+% && 5& 0.73737pt\\
+% && 1& 0.57785pt
+% \end{tabular}\end{center}
+%
+% \begin{macro}{\@addpunct}
+% Use of the \cs{@addpunct} function allows ending punctuation in
+% section headings and elsewhere to be intelligently omitted
+% when punctuation is already present.
+% \begin{macrocode}
+\def\@addpunct#1{\ifnum\spacefactor>\@m \else#1\fi}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\frenchspacing}
+% Change \cn{frenchspacing} to ensure that \cs{@addpunct} will
+% continue to work properly even when `french' spacing is in effect.
+% \begin{macrocode}
+\def\frenchspacing{\sfcode`\.1006\sfcode`\?1005\sfcode`\!1004%
+ \sfcode`\:1003\sfcode`\;1002\sfcode`\,1001 }
+% \end{macrocode}
+% \end{macro}
+%
+% \subsection{Miscellaneous}
+% \begin{macrocode}
+\def\nomath@env{\@amsmath@err{%
+ \string\begin{\@currenvir} allowed only in paragraph mode%
+}\@ehb% "You've lost some text"
+}
+% \end{macrocode}
+% A trade-off between main memory space and hash size; using
+% \verb+\Invalid@@+ saves 14 bytes of main memory for each use of
+% \verb+\Invalid@+, at the cost of one control sequence name.
+% \verb+\Invalid@+ is currently used about five times and
+% \verb+\Invalid@@+ is used by itself in some other instances,
+% which means that it saves us more memory than \verb+\FN@+,
+% \verb+\RIfM@+, and some of the other abbreviations above.
+% \begin{macrocode}
+\def\Invalid@@{Invalid use of \string}
+% \end{macrocode}
+%
+% The usual \cs{endinput} to ensure that random garbage at the end of
+% the file doesn't get copied by \fn{docstrip}.
+% \begin{macrocode}
+\endinput
+% \end{macrocode}
+%
+% \CheckSum{337}
+% \Finale