The amsgen package

American Mathematical Society Michael Downes

Version 1.2a, 1995/02/01

1 Introduction

This is an internal package for storing common functions that are shared by more than one package in the AMS-L^{A}TEX distribution. Some of these might eventually make it into the L^{A}TEX kernel.

Standard package identification.

  \ProvidesFile{amsgen.sty}[1995/02/01 v1.2a]

2 Implementation

Some general macros shared by amsart.dtx, amsmath.dtx, amsfonts.dtx, . . .

\@saveprimitive The 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 \@saveprimitive function. We follow the example of \@@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 \string and \meaning return the same information.

  \providecommand{\@saveprimitive}[2]{\begingroup\escapechar`\\\relax
    \edef\@tempa{\string#1}\edef\@tempb{\meaning#1}%
    \ifx\@tempa\@tempb \global\let#2#1%
    \else

Check to see if #2 was already given the desired primitive meaning somewhere else.

      \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}

{\@xp \atop \@nx} Shorthands for long command names.

  \let\@xp=\expandafter
  \let\@nx=\noexpand

\@emptytoks A token register companion for \@empty. Saves a little main mem and probably makes initializations such as \toks@{} run faster too.

  \newtoks\@emptytoks

\@oparg Use of \@oparg simplifies some constructions where a macro takes an optional argument in square brackets. We can’t use \newcommand here because this function might be previously defined by the amstex package in a loading sequence such as

 \usepackage{amstex,amsthm}

  \def\@oparg#1[#2]{\@ifnextchar[{#1}{#1[#2]}}
\@ifempty \@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 \@oparg, there is a possibility that these commands were defined previously in amstex.sty.

  \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}

\@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 oftenexecuted code, avoiding \@ifnotempty might be wise.

  \long\def\@ifnotempty#1{\@ifempty{#1}{}}

Some abbreviations to conserve token mem.

  \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}

\new@ifnextchar This macro is a new version of L^{A}TEX’s \@ifnextchar, macro that does not skip over spaces.

  \def\new@ifnextchar#1#2#3{%
    \let\@tempe #1\def\@tempa{#2}\def\@tempb{#3}\futurelet
      \@tempc\new@ifnch}
  %
  \def\new@ifnch{\ifx\@tempc \@tempe \let\@tempd\@tempa
               \else\let\@tempd\@tempb\fi\@tempd}

2. IMPLEMENTATION 3

\@ifstar There will essentially never be a space before the *, so using \@ifnextchar is

unnecessarily slow.

\def\@ifstar#1#2{\new@ifnextchar *{\def\@tempa*{#1}\@tempa}{#2}}

The hook \every@size was changed to \every@math@size in the December 1994 release of L^{A}TEX and its calling procedures changed. If \every@math@size is undefined it means the user has an older version of L^{A}TEX so we had better define it and patch a couple of functions (\glb@settings and \set@fontsize).

\@ifundefined{every@math@size}{%

Reuse the same token register; since it was never used except for the purposes that are affected below, this is OK.

\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
}
Remove \the\every@size from \size@update.
\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

\ex@ The \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 \pmb command uses \ex@ units. Since a macro or mu unit solution for the ⟨dimen⟩ \ex@ won’t work without changing a lot of current code in the amstex package, we set \ex@ through the \every@math@size hook. The value of \ex@ is scaled nonlinearly in a range of roughly 0.5pt to 1.5pt, by the function \compute@ex@.

  \newdimen\ex@
  \addto@hook\every@math@size{\compute@ex@}

\compute@ex@ computes \ex@ as a nonlinear scaling from 10pt to current font size (\f@size). Using .97 as the multiplier makes 1 ex@ ≈ .9pt when the current type size is 8pt and 1 ex@ ≈ 1.1pt when the current type size is 12pt.

The formula is essentially

1pt ± (1pt − (.97)^{⌊|10−n|⌋})

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 \f@size (> 20pt) so that the value of \ex@ never exceeds 1.5pt.

  \def\compute@ex@{%
    \begingroup
    \dimen@-\f@size\p@
    \ifdim\dimen@<-20\p@

Never make \ex@ larger than 1.5pt.

      \global\ex@ 1.5\p@
    \else

Adjust by the reference size and multiply by 2 to allow for half-point sizes.

      \advance\dimen@10\p@ \multiply\dimen@\tw@

Save information about the current sign of \dimen@.

      \edef\@tempa{\ifdim\dimen@>\z@ -\fi}%

Get the absolute value of \dimen@.

      \dimen@ \ifdim\dimen@<\z@ -\fi \dimen@
      \advance\dimen@-\@m sp % fudge factor

Here we use \vfuzz merely as a convenient scratch register

      \vfuzz\p@

Multiply in a loop.

      \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@
  }

Tests of the \compute@ex@ function yield the following results:

              \f@size  \ex@      \f@size  \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

\@addpunct Use of the \@addpunct allows ending punctuation in section headings and else-

where to be intelligently omitted when punctuation is already present

  \def\@addpunct#1{\ifnum\spacefactor>\@m \else#1\fi}

\frenchspacing Change \frenchspacing to ensure that \@addpunct will continue to work prop-

erly even when ‘french’ spacing is in effect.

  \def\frenchspacing{\sfcode`\.1006\sfcode`\?1005\sfcode`\!1004%
    \sfcode`\:1003\sfcode`\;1002\sfcode`\,1001 }

\@mathmeasure The function \@mathmeasure takes three arguments; the third arg is typeset as a math formula in an hbox, using arg #2 as the mathstyle, and the result is left in the box named by the first arg. It is assumed that we are already in math mode, so we can turn off \everymath (in particular, \check@mathfonts).

  \def\@mathmeasure#1#2#3{\setbox#1\hbox{\frozen@everymath\@emptytoks
    \m@th$#2#3$}}

2.1 Miscellaneous

  \def\nomath@env{\@amsmath@err{%
    \string\begin{\@currenvir} allowed only in paragraph mode%
  }\@ehb% "You've lost some text"
  }

A trade-off between main memory space and hash size; using \Invalid@@ saves 14 bytes of main memory for each use of \Invalid@, at the cost of one control sequence name. \Invalid@ is currently used about five times and \Invalid@@ is used by itself in some other instances, which means that it saves us more memory than \FN@, \RIfM@, and some of the other abbreviations above.

  \def\Invalid@@{Invalid use of \string}

The usual \endinput to ensure that random garbage at the end of the file doesn’t get copied by docstrip.

  \endinput