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-% \iffalse meta-comment
-%
-%% File: l3skip.dtx
-%
-% Copyright (C) 2004-2011 Frank Mittelbach, The LaTeX Project
-% (C) 2012-2024 The LaTeX Project
-%
-% It may be distributed and/or modified under the conditions of the
-% LaTeX Project Public License (LPPL), either version 1.3c of this
-% license or (at your option) any later version. The latest version
-% of this license is in the file
-%
-% https://www.latex-project.org/lppl.txt
-%
-% This file is part of the "l3kernel bundle" (The Work in LPPL)
-% and all files in that bundle must be distributed together.
-%
-% -----------------------------------------------------------------------
-%
-% The development version of the bundle can be found at
-%
-% https://github.com/latex3/latex3
-%
-% for those people who are interested.
-%
-%<*driver>
-\documentclass[full,kernel]{l3doc}
-\begin{document}
- \DocInput{\jobname.dtx}
-\end{document}
-%</driver>
-% \fi
-%
-% \title{^^A
-% The \pkg{l3skip} module\\ Dimensions and skips^^A
-% }
-%
-% \author{^^A
-% The \LaTeX{} Project\thanks
-% {^^A
-% E-mail:
-% \href{mailto:latex-team@latex-project.org}
-% {latex-team@latex-project.org}^^A
-% }^^A
-% }
-%
-% \date{Released 2024-03-14}
-%
-% \maketitle
-%
-% \begin{documentation}
-%
-% \LaTeX3 provides two general length variables: \texttt{dim} and
-% \texttt{skip}. Lengths stored as \texttt{dim} variables have a fixed
-% length, whereas \texttt{skip} lengths have a rubber (stretch/shrink)
-% component. In addition, the \texttt{muskip} type is available for
-% use in math mode: this is a special form of \texttt{skip} where the
-% lengths involved are determined by the current math font (in
-% \texttt{mu)}. There are common features in the creation and setting of
-% length variables, but for clarity the functions are grouped by variable
-% type.
-%
-% Many functions take
-% \emph{dimension expressions} (\enquote{\meta{dim expr}}) or
-% \emph{skip expressions} (\enquote{\meta{skip expr}}) as arguments.
-%
-%
-% \section{Creating and initialising \texttt{dim} variables}
-%
-% \begin{function}{\dim_new:N, \dim_new:c}
-% \begin{syntax}
-% \cs{dim_new:N} \meta{dimension}
-% \end{syntax}
-% Creates a new \meta{dimension} or raises an error if the name is
-% already taken. The declaration is global. The \meta{dimension}
-% is initially equal to $0$\,pt.
-% \end{function}
-%
-% \begin{function}[added = 2012-03-05]{\dim_const:Nn, \dim_const:cn}
-% \begin{syntax}
-% \cs{dim_const:Nn} \meta{dimension} \Arg{dim expr}
-% \end{syntax}
-% Creates a new constant \meta{dimension} or raises an error if the
-% name is already taken. The value of the \meta{dimension} is set
-% globally to the \meta{dim expr}.
-% \end{function}
-%
-% \begin{function}{\dim_zero:N, \dim_zero:c, \dim_gzero:N, \dim_gzero:c}
-% \begin{syntax}
-% \cs{dim_zero:N} \meta{dimension}
-% \end{syntax}
-% Sets \meta{dimension} to $0$\,pt.
-% \end{function}
-%
-% \begin{function}[added = 2012-01-07]
-% {\dim_zero_new:N, \dim_zero_new:c, \dim_gzero_new:N, \dim_gzero_new:c}
-% \begin{syntax}
-% \cs{dim_zero_new:N} \meta{dimension}
-% \end{syntax}
-% Ensures that the \meta{dimension} exists globally by applying
-% \cs{dim_new:N} if necessary, then applies
-% \cs[index=dim_zero:N]{dim_(g)zero:N} to leave
-% the \meta{dimension} set to zero.
-% \end{function}
-%
-% \begin{function}[EXP, pTF, added=2012-03-03]{\dim_if_exist:N, \dim_if_exist:c}
-% \begin{syntax}
-% \cs{dim_if_exist_p:N} \meta{dimension}
-% \cs{dim_if_exist:NTF} \meta{dimension} \Arg{true code} \Arg{false code}
-% \end{syntax}
-% Tests whether the \meta{dimension} is currently defined. This does
-% not check that the \meta{dimension} really is a dimension variable.
-% \end{function}
-%
-% \section{Setting \texttt{dim} variables}
-%
-% \begin{function}[updated = 2011-10-22]
-% {\dim_add:Nn, \dim_add:cn, \dim_gadd:Nn, \dim_gadd:cn}
-% \begin{syntax}
-% \cs{dim_add:Nn} \meta{dimension} \Arg{dim expr}
-% \end{syntax}
-% Adds the result of the \meta{dim expr} to the current
-% content of the \meta{dimension}.
-% \end{function}
-%
-% \begin{function}[updated = 2011-10-22]
-% {\dim_set:Nn, \dim_set:cn, \dim_gset:Nn, \dim_gset:cn}
-% \begin{syntax}
-% \cs{dim_set:Nn} \meta{dimension} \Arg{dim expr}
-% \end{syntax}
-% Sets \meta{dimension} to the value of \meta{dim expr}, which
-% must evaluate to a length with units.
-% \end{function}
-%
-% \begin{function}
-% {
-% \dim_set_eq:NN, \dim_set_eq:cN, \dim_set_eq:Nc, \dim_set_eq:cc,
-% \dim_gset_eq:NN, \dim_gset_eq:cN, \dim_gset_eq:Nc, \dim_gset_eq:cc
-% }
-% \begin{syntax}
-% \cs{dim_set_eq:NN} \meta{dimension_1} \meta{dimension_2}
-% \end{syntax}
-% Sets the content of \meta{dimension_1} equal to that of
-% \meta{dimension_2}.
-% \end{function}
-%
-% \begin{function}[updated = 2011-10-22]
-% {\dim_sub:Nn, \dim_sub:cn, \dim_gsub:Nn, \dim_gsub:cn}
-% \begin{syntax}
-% \cs{dim_sub:Nn} \meta{dimension} \Arg{dim expr}
-% \end{syntax}
-% Subtracts the result of the \meta{dim expr} from the
-% current content of the \meta{dimension}.
-% \end{function}
-%
-% \section{Utilities for dimension calculations}
-%
-% \begin{function}[updated = 2012-09-26, EXP]{\dim_abs:n}
-% \begin{syntax}
-% \cs{dim_abs:n} \Arg{dim expr}
-% \end{syntax}
-% Converts the \meta{dim expr} to its absolute value, leaving the result
-% in the input stream as a \meta{dimension denotation}.
-% \end{function}
-%
-% \begin{function}[added = 2012-09-09, updated = 2012-09-26, EXP]
-% {\dim_max:nn, \dim_min:nn}
-% \begin{syntax}
-% \cs{dim_max:nn} \Arg{dim expr_1} \Arg{dim expr_2}
-% \cs{dim_min:nn} \Arg{dim expr_1} \Arg{dim expr_2}
-% \end{syntax}
-% Evaluates the two \meta{dim exprs} and leaves either the
-% maximum or minimum value in the input stream as appropriate, as a
-% \meta{dimension denotation}.
-% \end{function}
-%
-% \begin{function}[updated = 2011-10-22, rEXP]{\dim_ratio:nn}
-% \begin{syntax}
-% \cs{dim_ratio:nn} \Arg{dim expr_1} \Arg{dim expr_2}
-% \end{syntax}
-% Parses the two \meta{dim exprs} and converts the ratio of
-% the two to a form suitable for use inside a \meta{dim expr}.
-% This ratio is then left in the input stream, allowing syntax such as
-% \begin{verbatim}
-% \dim_set:Nn \l_my_dim
-% { 10 pt * \dim_ratio:nn { 5 pt } { 10 pt } }
-% \end{verbatim}
-% The output of \cs{dim_ratio:nn} on full expansion is a ratio expression
-% between two integers, with all distances converted to scaled points.
-% Thus
-% \begin{verbatim}
-% \tl_set:Ne \l_my_tl { \dim_ratio:nn { 5 pt } { 10 pt } }
-% \tl_show:N \l_my_tl
-% \end{verbatim}
-% displays |327680/655360| on the terminal.
-% \end{function}
-%
-% \section{Dimension expression conditionals}
-%
-% \begin{function}[EXP,pTF]{\dim_compare:nNn}
-% \begin{syntax}
-% \cs{dim_compare_p:nNn} \Arg{dim expr_1} \meta{relation} \Arg{dim expr_2} \\
-% \cs{dim_compare:nNnTF}
-% ~~\Arg{dim expr_1} \meta{relation} \Arg{dim expr_2}
-% ~~\Arg{true code} \Arg{false code}
-% \end{syntax}
-% This function first evaluates each of the \meta{dim exprs}
-% as described for \cs{dim_eval:n}. The two results are then
-% compared using the \meta{relation}:
-% \begin{center}
-% \begin{tabular}{ll}
-% Equal & |=| \\
-% Greater than & |>| \\
-% Less than & |<| \\
-% \end{tabular}
-% \end{center}
-% This function is less flexible than \cs{dim_compare:nTF} but around
-% $5$~times faster.
-% \end{function}
-%
-% \begin{function}[updated = 2013-01-13, EXP, pTF]{\dim_compare:n}
-% \begin{syntax}
-% \cs{dim_compare_p:n} \\
-% ~~\{ \\
-% ~~~~\meta{dim expr_1} \meta{relation_1} \\
-% ~~~~\ldots{} \\
-% ~~~~\meta{dim expr_N} \meta{relation_N} \\
-% ~~~~\meta{dim expr_{N+1}} \\
-% ~~\} \\
-% \cs{dim_compare:nTF}
-% ~~\{ \\
-% ~~~~\meta{dim expr_1} \meta{relation_1} \\
-% ~~~~\ldots{} \\
-% ~~~~\meta{dim expr_N} \meta{relation_N} \\
-% ~~~~\meta{dim expr_{N+1}} \\
-% ~~\} \\
-% ~~\Arg{true code} \Arg{false code}
-% \end{syntax}
-% This function evaluates the \meta{dim exprs} as
-% described for \cs{dim_eval:n} and compares consecutive result using
-% the corresponding \meta{relation}, namely it compares
-% \meta{dim expr_1} and \meta{dim expr_2} using the \meta{relation_1},
-% then \meta{dim expr_2} and \meta{dim expr_3} using the
-% \meta{relation_2}, until finally comparing \meta{dim expr_N} and
-% \meta{dim expr_{N+1}} using the \meta{relation_N}. The test yields
-% \texttt{true} if all comparisons are \texttt{true}. Each
-% \meta{dim expr} is evaluated only once, and the
-% evaluation is lazy, in the sense that if one comparison is
-% \texttt{false}, then no other \meta{dim expr} is
-% evaluated and no other comparison is performed. The
-% \meta{relations} can be any of the following:
-% \begin{center}
-% \begin{tabular}{ll}
-% Equal & |=| or |==| \\
-% Greater than or equal to & |>=| \\
-% Greater than & |>| \\
-% Less than or equal to & |<=| \\
-% Less than & |<| \\
-% Not equal & |!=| \\
-% \end{tabular}
-% \end{center}
-% This function is more flexible than \cs{dim_compare:nNnTF} but
-% around $5$~times slower.
-% \end{function}
-%
-% \begin{function}[added = 2013-07-24, EXP, noTF]{\dim_case:nn}
-% \begin{syntax}
-% \cs{dim_case:nnTF} \Arg{test dim expr} \\
-% ~~|{| \\
-% ~~~~\Arg{dim expr case_1} \Arg{code case_1} \\
-% ~~~~\Arg{dim expr case_2} \Arg{code case_2} \\
-% ~~~~\ldots \\
-% ~~~~\Arg{dim expr case_n} \Arg{code case_n} \\
-% ~~|}| \\
-% ~~\Arg{true code}
-% ~~\Arg{false code}
-% \end{syntax}
-% This function evaluates the \meta{test dim expr} and
-% compares this in turn to each of the
-% \meta{dim expr cases}. If the two are equal then the
-% associated \meta{code} is left in the input stream
-% and other cases are discarded. If any of the
-% cases are matched, the \meta{true code} is also inserted into the
-% input stream (after the code for the appropriate case), while if none
-% match then the \meta{false code} is inserted. The function
-% \cs{dim_case:nn}, which does nothing if there is no match, is also
-% available. For example
-% \begin{verbatim}
-% \dim_set:Nn \l_tmpa_dim { 5 pt }
-% \dim_case:nnF
-% { 2 \l_tmpa_dim }
-% {
-% { 5 pt } { Small }
-% { 4 pt + 6 pt } { Medium }
-% { - 10 pt } { Negative }
-% }
-% { No idea! }
-% \end{verbatim}
-% leaves \enquote{\texttt{Medium}} in the input stream.
-% \end{function}
-%
-% \section{Dimension expression loops}
-%
-% \begin{function}[rEXP]{\dim_do_until:nNnn}
-% \begin{syntax}
-% \cs{dim_do_until:nNnn} \Arg{dim expr_1} \meta{relation} \Arg{dim expr_2} \Arg{code}
-% \end{syntax}
-% Places the \meta{code} in the input stream for \TeX{} to process, and
-% then evaluates the relationship between the two
-% \meta{dim exprs} as described for \cs{dim_compare:nNnTF}.
-% If the test is \texttt{false} then the \meta{code} is inserted
-% into the input stream again and a loop occurs until the
-% \meta{relation} is \texttt{true}.
-% \end{function}
-%
-% \begin{function}[rEXP]{\dim_do_while:nNnn}
-% \begin{syntax}
-% \cs{dim_do_while:nNnn} \Arg{dim expr_1} \meta{relation} \Arg{dim expr_2} \Arg{code}
-% \end{syntax}
-% Places the \meta{code} in the input stream for \TeX{} to process, and
-% then evaluates the relationship between the two
-% \meta{dim exprs} as described for \cs{dim_compare:nNnTF}.
-% If the test is \texttt{true} then the \meta{code} is inserted
-% into the input stream again and a loop occurs until the
-% \meta{relation} is \texttt{false}.
-% \end{function}
-%
-% \begin{function}[rEXP]{\dim_until_do:nNnn}
-% \begin{syntax}
-% \cs{dim_until_do:nNnn} \Arg{dim expr_1} \meta{relation} \Arg{dim expr_2} \Arg{code}
-% \end{syntax}
-% Evaluates the relationship between the two \meta{dim exprs}
-% as described for \cs{dim_compare:nNnTF}, and then places the
-% \meta{code} in the input stream if the \meta{relation} is
-% \texttt{false}. After the \meta{code} has been processed by \TeX{} the
-% test is repeated, and a loop occurs until the test is
-% \texttt{true}.
-% \end{function}
-%
-% \begin{function}[rEXP]{\dim_while_do:nNnn}
-% \begin{syntax}
-% \cs{dim_while_do:nNnn} \Arg{dim expr_1} \meta{relation} \Arg{dim expr_2} \Arg{code}
-% \end{syntax}
-% Evaluates the relationship between the two \meta{dim exprs}
-% as described for \cs{dim_compare:nNnTF}, and then places the
-% \meta{code} in the input stream if the \meta{relation} is
-% \texttt{true}. After the \meta{code} has been processed by \TeX{} the
-% test is repeated, and a loop occurs until the test is
-% \texttt{false}.
-% \end{function}
-%
-% \begin{function}[updated = 2013-01-13, rEXP]{\dim_do_until:nn}
-% \begin{syntax}
-% \cs{dim_do_until:nn} \Arg{dimension relation} \Arg{code}
-% \end{syntax}
-% Places the \meta{code} in the input stream for \TeX{} to process, and
-% then evaluates the \meta{dimension relation}
-% as described for \cs{dim_compare:nTF}.
-% If the test is \texttt{false} then the \meta{code} is inserted
-% into the input stream again and a loop occurs until the
-% \meta{relation} is \texttt{true}.
-% \end{function}
-%
-% \begin{function}[updated = 2013-01-13, rEXP]{\dim_do_while:nn}
-% \begin{syntax}
-% \cs{dim_do_while:nn} \Arg{dimension relation} \Arg{code}
-% \end{syntax}
-% Places the \meta{code} in the input stream for \TeX{} to process, and
-% then evaluates the \meta{dimension relation}
-% as described for \cs{dim_compare:nTF}.
-% If the test is \texttt{true} then the \meta{code} is inserted
-% into the input stream again and a loop occurs until the
-% \meta{relation} is \texttt{false}.
-% \end{function}
-%
-% \begin{function}[updated = 2013-01-13, rEXP]{\dim_until_do:nn}
-% \begin{syntax}
-% \cs{dim_until_do:nn} \Arg{dimension relation} \Arg{code}
-% \end{syntax}
-% Evaluates the \meta{dimension relation}
-% as described for \cs{dim_compare:nTF}, and then places the
-% \meta{code} in the input stream if the \meta{relation} is
-% \texttt{false}. After the \meta{code} has been processed by \TeX{} the
-% test is repeated, and a loop occurs until the test is
-% \texttt{true}.
-% \end{function}
-%
-% \begin{function}[updated = 2013-01-13, rEXP]{\dim_while_do:nn}
-% \begin{syntax}
-% \cs{dim_while_do:nn} \Arg{dimension relation} \Arg{code}
-% \end{syntax}
-% Evaluates the \meta{dimension relation}
-% as described for \cs{dim_compare:nTF}, and then places the
-% \meta{code} in the input stream if the \meta{relation} is
-% \texttt{true}. After the \meta{code} has been processed by \TeX{} the
-% test is repeated, and a loop occurs until the test is
-% \texttt{false}.
-% \end{function}
-%
-% \section{Dimension step functions}
-%
-% \begin{function}[added = 2018-02-18, rEXP]
-% {\dim_step_function:nnnN}
-% \begin{syntax}
-% \cs{dim_step_function:nnnN} \Arg{initial value} \Arg{step} \Arg{final value} \meta{function}
-% \end{syntax}
-% This function first evaluates the \meta{initial value}, \meta{step}
-% and \meta{final value}, all of which should be dimension expressions.
-% The \meta{function} is then placed in front of each \meta{value}
-% from the \meta{initial value} to the \meta{final value} in turn
-% (using \meta{step} between each \meta{value}). The \meta{step} must
-% be non-zero. If the \meta{step} is positive, the loop stops when
-% the \meta{value} becomes larger than the \meta{final value}. If the
-% \meta{step} is negative, the loop stops when the \meta{value}
-% becomes smaller than the \meta{final value}. The \meta{function}
-% should absorb one argument.
-% \end{function}
-%
-% \begin{function}[added = 2018-02-18]
-% {\dim_step_inline:nnnn}
-% \begin{syntax}
-% \cs{dim_step_inline:nnnn} \Arg{initial value} \Arg{step} \Arg{final value} \Arg{code}
-% \end{syntax}
-% This function first evaluates the \meta{initial value}, \meta{step}
-% and \meta{final value}, all of which should be dimension expressions.
-% Then for each \meta{value} from the \meta{initial value} to the
-% \meta{final value} in turn (using \meta{step} between each
-% \meta{value}), the \meta{code} is inserted into the input stream
-% with |#1| replaced by the current \meta{value}. Thus the
-% \meta{code} should define a function of one argument~(|#1|).
-% \end{function}
-%
-% \begin{function}[added = 2018-02-18]
-% {\dim_step_variable:nnnNn}
-% \begin{syntax}
-% \cs{dim_step_variable:nnnNn} \\
-% ~~\Arg{initial value} \Arg{step} \Arg{final value} \meta{tl~var} \Arg{code}
-% \end{syntax}
-% This function first evaluates the \meta{initial value}, \meta{step}
-% and \meta{final value}, all of which should be dimension expressions.
-% Then for each \meta{value} from the \meta{initial value} to the
-% \meta{final value} in turn (using \meta{step} between each
-% \meta{value}), the \meta{code} is inserted into the input stream,
-% with the \meta{tl~var} defined as the current \meta{value}. Thus
-% the \meta{code} should make use of the \meta{tl~var}.
-% \end{function}
-%
-% \section{Using \texttt{dim} expressions and variables}
-%
-% \begin{function}[updated = 2011-10-22, EXP]{\dim_eval:n}
-% \begin{syntax}
-% \cs{dim_eval:n} \Arg{dim expr}
-% \end{syntax}
-% Evaluates the \meta{dim expr}, expanding any
-% dimensions and token list variables within the \meta{expression}
-% to their content (without requiring \cs{dim_use:N}/\cs{tl_use:N})
-% and applying the standard mathematical rules. The result of the
-% calculation is left in the input stream as a
-% \meta{dimension denotation} after two expansions. This is
-% expressed in points (\texttt{pt}), and requires suitable
-% termination if used in a \TeX{}-style assignment as it is \emph{not}
-% an \meta{internal dimension}.
-% \end{function}
-%
-% \begin{function}[EXP, added = 2018-11-03]{\dim_sign:n}
-% \begin{syntax}
-% \cs{dim_sign:n} \Arg{dim expr}
-% \end{syntax}
-% Evaluates the \meta{dim expr} then leaves $1$ or $0$ or $-1$ in the
-% input stream according to the sign of the result.
-% \end{function}
-%
-% \begin{function}[EXP]{\dim_use:N, \dim_use:c}
-% \begin{syntax}
-% \cs{dim_use:N} \meta{dimension}
-% \end{syntax}
-% Recovers the content of a \meta{dimension} and places it directly
-% in the input stream. An error is raised if the variable does
-% not exist or if it is invalid. Can be omitted in places where a
-% \meta{dimension} is required (such as in the argument of
-% \cs{dim_eval:n}).
-% \begin{texnote}
-% \cs{dim_use:N} is the \TeX{} primitive \tn{the}: this is one of
-% several \LaTeX3 names for this primitive.
-% \end{texnote}
-% \end{function}
-%
-% \begin{function}[added = 2014-07-15, EXP]{\dim_to_decimal:n}
-% \begin{syntax}
-% \cs{dim_to_decimal:n} \Arg{dim expr}
-% \end{syntax}
-% Evaluates the \meta{dim expr}, and leaves the result,
-% expressed in points (\texttt{pt}) in the input stream, with \emph{no
-% units}. The result is rounded by \TeX{} to at most five decimal
-% places. If the decimal part of the result is zero, it is omitted,
-% together with the decimal marker.
-%
-% For example
-% \begin{verbatim}
-% \dim_to_decimal:n { 1bp }
-% \end{verbatim}
-% leaves |1.00374| in the input stream, \emph{i.e.}~the magnitude of
-% one \enquote{big point} when converted to (\TeX{}) points.
-% \end{function}
-%
-% \begin{function}[added = 2014-07-15, updated = 2023-05-20, EXP]
-% {\dim_to_decimal_in_bp:n}
-% \begin{syntax}
-% \cs{dim_to_decimal_in_bp:n} \Arg{dim expr}
-% \end{syntax}
-% Evaluates the \meta{dim expr}, and leaves the result,
-% expressed in big points (\texttt{bp}) in the input stream, with \emph{no
-% units}. The result is rounded by \TeX{} to at most five decimal
-% places. If the decimal part of the result is zero, it is omitted,
-% together with the decimal marker.
-%
-% For example
-% \begin{verbatim}
-% \dim_to_decimal_in_bp:n { 1pt }
-% \end{verbatim}
-% leaves |0.99628| in the input stream, \emph{i.e.}~the magnitude of
-% one (\TeX{}) point when converted to big points.
-% \begin{texnote}
-% The implementation of this function is re-entrant: the result of
-% \begin{verbatim}
-% \dim_compare:nNnTF
-% { <x>bp } =
-% { \dim_to_decimal_in_bp:n { <x>bp } bp }
-% \end{verbatim}
-% will be logically \texttt{true}. The decimal representations may
-% differ provided they produce the same \TeX{} dimension.
-% \end{texnote}
-% \end{function}
-%
-% \begin{function}[added = 2023-05-20, EXP]
-% {
-% \dim_to_decimal_in_cc:n ,
-% \dim_to_decimal_in_cm:n ,
-% \dim_to_decimal_in_dd:n ,
-% \dim_to_decimal_in_in:n ,
-% \dim_to_decimal_in_mm:n ,
-% \dim_to_decimal_in_pc:n
-% }
-% \begin{syntax}
-% \cs{dim_to_decimal_in_cm:n} \Arg{dim expr}
-% \end{syntax}
-% Evaluates the \meta{dim expr}, and leaves the result,
-% expressed with the appropriate scaling in the input stream, with
-% \emph{no units}. If the decimal part of the result is zero, it is omitted,
-% together with the decimal marker. The precisions of the result is limited
-% to a maximum of five decimal places with trailing zeros omitted.
-%
-% The maximum \TeX{} allowable dimension value (available as
-% \tn{maxdimen} in plain \TeX{} and \LaTeX{} and \cs{c_max_dim} in
-% \pkg{expl3}) can only be expressed exactly in the units
-% \texttt{pt}, \texttt{bp} and \texttt{sp}. The maximum allowable
-% input values to five decimal places are\\
-% \begin{center}
-% \begin{tabular}{@{}>{$}r<{$}@{\,}l@{}}
-% 1276.00215 & cc \\
-% 575.83174 & cm \\
-% 15312.02584 & dd \\
-% 226.70540 & in \\
-% 5758.31742 & mm \\
-% 1365.33333 & pc \\
-% \end{tabular}
-% \end{center}
-% (Note that these are not all equal, but rather any larger value will overflow
-% due to the way \TeX{} converts to \texttt{sp}.)
-% Values given to five decimal places larger that these will result in \TeX{}
-% errors; the behavior if additional decimal places are given depends on the
-% \TeX{} internals and thus larger values are \emph{not} supported by
-% \pkg{expl3}.
-% \begin{texnote}
-% The implementation of these functions is re-entrant: the result of
-% \begin{verbatim}
-% \dim_compare:nNnTF
-% { <x><unit> } =
-% { \dim_to_decimal_in_<unit>:n { <x><unit> } <unit> }
-% \end{verbatim}
-% will be logically \texttt{true}. The decimal representations may
-% differ provided they produce the same \TeX{} dimension.
-% \end{texnote}
-% \end{function}
-%
-% \begin{function}[added = 2015-05-18, EXP]{\dim_to_decimal_in_sp:n}
-% \begin{syntax}
-% \cs{dim_to_decimal_in_sp:n} \Arg{dim expr}
-% \end{syntax}
-% Evaluates the \meta{dim expr}, and leaves the result,
-% expressed in scaled points (\texttt{sp}) in the input stream, with \emph{no
-% units}. The result is necessarily an integer.
-% \end{function}
-%
-% \begin{function}[added = 2014-07-15, updated = 2023-05-20, EXP]
-% {\dim_to_decimal_in_unit:nn}
-% \begin{syntax}
-% \cs{dim_to_decimal_in_unit:nn} \Arg{dim expr_1} \Arg{dim expr_2}
-% \end{syntax}
-% Evaluates the \meta{dim exprs}, and leaves the value of
-% \meta{dim expr_1}, expressed in a unit given by \meta{dim expr_2}, in
-% the input stream. If the decimal part of the result
-% is zero, it is omitted, together with the decimal marker.
-% The precisions of the result is limited
-% to a maximum of five decimal places with trailing zeros omitted.
-%
-% For example
-% \begin{verbatim}
-% \dim_to_decimal_in_unit:nn { 1bp } { 1mm }
-% \end{verbatim}
-% leaves |0.35278| in the input stream, \emph{i.e.}~the magnitude of
-% one big point when expressed in millimetres. The conversions do
-% \emph{not} guarantee that \TeX{} would yield identical results
-% for the direct input in an equality test, thus for instance
-% \begin{verbatim}
-% \dim_compare:nNnTF
-% { 1bp } =
-% { \dim_to_decimal_in_unit:nn { 1bp } { 1mm } mm }
-% \end{verbatim}
-% will take the \texttt{false} branch.
-% \end{function}
-%
-% \begin{function}[EXP, added = 2012-05-08, tested = m3fp-convert002]
-% {\dim_to_fp:n}
-% \begin{syntax}
-% \cs{dim_to_fp:n} \Arg{dim expr}
-% \end{syntax}
-% Expands to an internal floating point number equal to the value of
-% the \meta{dim expr} in \texttt{pt}. Since dimension expressions are
-% evaluated much faster than their floating point equivalent,
-% \cs{dim_to_fp:n} can be used to speed up parts of a computation
-% where a low precision and a smaller range are acceptable.
-% \end{function}
-%
-% \section{Viewing \texttt{dim} variables}
-%
-% \begin{function}{\dim_show:N, \dim_show:c}
-% \begin{syntax}
-% \cs{dim_show:N} \meta{dimension}
-% \end{syntax}
-% Displays the value of the \meta{dimension} on the terminal.
-% \end{function}
-%
-% \begin{function}[added = 2011-11-22, updated = 2015-08-07]{\dim_show:n}
-% \begin{syntax}
-% \cs{dim_show:n} \Arg{dim expr}
-% \end{syntax}
-% Displays the result of evaluating the \meta{dim expr}
-% on the terminal.
-% \end{function}
-%
-% \begin{function}[added = 2014-08-22, updated = 2015-08-03]{\dim_log:N, \dim_log:c}
-% \begin{syntax}
-% \cs{dim_log:N} \meta{dimension}
-% \end{syntax}
-% Writes the value of the \meta{dimension} in the log file.
-% \end{function}
-%
-% \begin{function}[added = 2014-08-22, updated = 2015-08-07]{\dim_log:n}
-% \begin{syntax}
-% \cs{dim_log:n} \Arg{dim expr}
-% \end{syntax}
-% Writes the result of evaluating the \meta{dim expr}
-% in the log file.
-% \end{function}
-%
-% \section{Constant dimensions}
-%
-% \begin{variable}{\c_max_dim}
-% The maximum value that can be stored as a dimension. This can also
-% be used as a component of a skip.
-% \end{variable}
-%
-% \begin{variable}{\c_zero_dim}
-% A zero length as a dimension. This can also be used as a component
-% of a skip.
-% \end{variable}
-%
-% \section{Scratch dimensions}
-%
-% \begin{variable}{\l_tmpa_dim, \l_tmpb_dim}
-% Scratch dimension for local assignment. These are never used by
-% the kernel code, and so are safe for use with any \LaTeX3-defined
-% function. However, they may be overwritten by other non-kernel
-% code and so should only be used for short-term storage.
-% \end{variable}
-%
-% \begin{variable}{\g_tmpa_dim, \g_tmpb_dim}
-% Scratch dimension for global assignment. These are never used by
-% the kernel code, and so are safe for use with any \LaTeX3-defined
-% function. However, they may be overwritten by other non-kernel
-% code and so should only be used for short-term storage.
-% \end{variable}
-%
-% \section{Creating and initialising \texttt{skip} variables}
-%
-% \begin{function}{\skip_new:N, \skip_new:c}
-% \begin{syntax}
-% \cs{skip_new:N} \meta{skip}
-% \end{syntax}
-% Creates a new \meta{skip} or raises an error if the name is
-% already taken. The declaration is global. The \meta{skip}
-% is initially equal to $0$\,pt.
-% \end{function}
-%
-% \begin{function}[added = 2012-03-05]{\skip_const:Nn, \skip_const:cn}
-% \begin{syntax}
-% \cs{skip_const:Nn} \meta{skip} \Arg{skip expr}
-% \end{syntax}
-% Creates a new constant \meta{skip} or raises an error if the
-% name is already taken. The value of the \meta{skip} is set
-% globally to the \meta{skip expr}.
-% \end{function}
-%
-% \begin{function}{\skip_zero:N, \skip_zero:c, \skip_gzero:N, \skip_gzero:c}
-% \begin{syntax}
-% \cs{skip_zero:N} \meta{skip}
-% \end{syntax}
-% Sets \meta{skip} to $0$\,pt.
-% \end{function}
-%
-% \begin{function}[added = 2012-01-07]
-% {\skip_zero_new:N, \skip_zero_new:c, \skip_gzero_new:N, \skip_gzero_new:c}
-% \begin{syntax}
-% \cs{skip_zero_new:N} \meta{skip}
-% \end{syntax}
-% Ensures that the \meta{skip} exists globally by applying
-% \cs{skip_new:N} if necessary, then applies
-% \cs[index=skip_zero:N]{skip_(g)zero:N} to leave
-% the \meta{skip} set to zero.
-% \end{function}
-%
-% \begin{function}[EXP, pTF, added=2012-03-03]
-% {\skip_if_exist:N, \skip_if_exist:c}
-% \begin{syntax}
-% \cs{skip_if_exist_p:N} \meta{skip}
-% \cs{skip_if_exist:NTF} \meta{skip} \Arg{true code} \Arg{false code}
-% \end{syntax}
-% Tests whether the \meta{skip} is currently defined. This does not
-% check that the \meta{skip} really is a skip variable.
-% \end{function}
-%
-% \section{Setting \texttt{skip} variables}
-%
-% \begin{function}[updated = 2011-10-22]
-% {\skip_add:Nn, \skip_add:cn, \skip_gadd:Nn, \skip_gadd:cn}
-% \begin{syntax}
-% \cs{skip_add:Nn} \meta{skip} \Arg{skip expr}
-% \end{syntax}
-% Adds the result of the \meta{skip expr} to the current
-% content of the \meta{skip}.
-% \end{function}
-%
-% \begin{function}[updated = 2011-10-22]
-% {\skip_set:Nn, \skip_set:cn, \skip_gset:Nn, \skip_gset:cn}
-% \begin{syntax}
-% \cs{skip_set:Nn} \meta{skip} \Arg{skip expr}
-% \end{syntax}
-% Sets \meta{skip} to the value of \meta{skip expr}, which
-% must evaluate to a length with units and may include a rubber
-% component (for example |1 cm plus 0.5 cm|.
-% \end{function}
-%
-% \begin{function}
-% {
-% \skip_set_eq:NN, \skip_set_eq:cN, \skip_set_eq:Nc, \skip_set_eq:cc,
-% \skip_gset_eq:NN, \skip_gset_eq:cN, \skip_gset_eq:Nc, \skip_gset_eq:cc
-% }
-% \begin{syntax}
-% \cs{skip_set_eq:NN} \meta{skip_1} \meta{skip_2}
-% \end{syntax}
-% Sets the content of \meta{skip_1} equal to that of \meta{skip_2}.
-% \end{function}
-%
-% \begin{function}[updated = 2011-10-22]
-% {\skip_sub:Nn, \skip_sub:cn, \skip_gsub:Nn, \skip_gsub:cn}
-% \begin{syntax}
-% \cs{skip_sub:Nn} \meta{skip} \Arg{skip expr}
-% \end{syntax}
-% Subtracts the result of the \meta{skip expr} from the
-% current content of the \meta{skip}.
-% \end{function}
-%
-% \section{Skip expression conditionals}
-%
-% \begin{function}[EXP,pTF]{\skip_if_eq:nn}
-% \begin{syntax}
-% \cs{skip_if_eq_p:nn} \Arg{skip expr_1} \Arg{skip expr_2}
-% \cs{skip_if_eq:nnTF}
-% ~~\Arg{skip expr_1} \Arg{skip expr_2}
-% ~~\Arg{true code} \Arg{false code}
-% \end{syntax}
-% This function first evaluates each of the
-% \meta{skip exprs} as described for \cs{skip_eval:n}.
-% The two results are then compared for exact equality,
-% \emph{i.e.}~both the fixed and rubber components must be the same
-% for the test to be true.
-% \end{function}
-%
-% \begin{function}[EXP, pTF, added = 2012-03-05]{\skip_if_finite:n}
-% \begin{syntax}
-% \cs{skip_if_finite_p:n} \Arg{skip expr}
-% \cs{skip_if_finite:nTF} \Arg{skip expr} \Arg{true code} \Arg{false code}
-% \end{syntax}
-% Evaluates the \meta{skip expr} as described for \cs{skip_eval:n},
-% and then tests if all of its components are finite.
-% \end{function}
-%
-% \section{Using \texttt{skip} expressions and variables}
-%
-% \begin{function}[updated = 2011-10-22, EXP]{\skip_eval:n}
-% \begin{syntax}
-% \cs{skip_eval:n} \Arg{skip expr}
-% \end{syntax}
-% Evaluates the \meta{skip expr}, expanding any skips
-% and token list variables within the \meta{expression}
-% to their content (without requiring \cs{skip_use:N}/\cs{tl_use:N})
-% and applying the standard mathematical rules. The result of the
-% calculation is left in the input stream as a \meta{glue denotation}
-% after two expansions. This is expressed in points (\texttt{pt}),
-% and requires suitable termination if used in a \TeX{}-style
-% assignment as it is \emph{not} an \meta{internal glue}.
-% \end{function}
-%
-% \begin{function}[EXP]{\skip_use:N, \skip_use:c}
-% \begin{syntax}
-% \cs{skip_use:N} \meta{skip}
-% \end{syntax}
-% Recovers the content of a \meta{skip} and places it directly
-% in the input stream. An error is raised if the variable does
-% not exist or if it is invalid. Can be omitted in places where a
-% \meta{dimension} or \meta{skip} is required (such as in the argument of
-% \cs{skip_eval:n}).
-% \begin{texnote}
-% \cs{skip_use:N} is the \TeX{} primitive \tn{the}: this is one of
-% several \LaTeX3 names for this primitive.
-% \end{texnote}
-% \end{function}
-%
-% \section{Viewing \texttt{skip} variables}
-%
-% \begin{function}[updated = 2015-08-03]{\skip_show:N, \skip_show:c}
-% \begin{syntax}
-% \cs{skip_show:N} \meta{skip}
-% \end{syntax}
-% Displays the value of the \meta{skip} on the terminal.
-% \end{function}
-%
-% \begin{function}[added = 2011-11-22, updated = 2015-08-07]{\skip_show:n}
-% \begin{syntax}
-% \cs{skip_show:n} \Arg{skip expr}
-% \end{syntax}
-% Displays the result of evaluating the \meta{skip expr}
-% on the terminal.
-% \end{function}
-%
-% \begin{function}[added = 2014-08-22, updated = 2015-08-03]{\skip_log:N, \skip_log:c}
-% \begin{syntax}
-% \cs{skip_log:N} \meta{skip}
-% \end{syntax}
-% Writes the value of the \meta{skip} in the log file.
-% \end{function}
-%
-% \begin{function}[added = 2014-08-22, updated = 2015-08-07]{\skip_log:n}
-% \begin{syntax}
-% \cs{skip_log:n} \Arg{skip expr}
-% \end{syntax}
-% Writes the result of evaluating the \meta{skip expr}
-% in the log file.
-% \end{function}
-%
-% \section{Constant skips}
-%
-% \begin{variable}[updated = 2012-11-02]{\c_max_skip}
-% The maximum value that can be stored as a skip (equal to
-% \cs{c_max_dim} in length), with no stretch nor shrink component.
-% \end{variable}
-%
-% \begin{variable}[updated = 2012-11-01]{\c_zero_skip}
-% A zero length as a skip, with no stretch nor shrink component.
-% \end{variable}
-%
-% \section{Scratch skips}
-%
-% \begin{variable}{\l_tmpa_skip, \l_tmpb_skip}
-% Scratch skip for local assignment. These are never used by
-% the kernel code, and so are safe for use with any \LaTeX3-defined
-% function. However, they may be overwritten by other non-kernel
-% code and so should only be used for short-term storage.
-% \end{variable}
-%
-% \begin{variable}{\g_tmpa_skip, \g_tmpb_skip}
-% Scratch skip for global assignment. These are never used by
-% the kernel code, and so are safe for use with any \LaTeX3-defined
-% function. However, they may be overwritten by other non-kernel
-% code and so should only be used for short-term storage.
-% \end{variable}
-%
-% \section{Inserting skips into the output}
-%
-% \begin{function}[updated = 2011-10-22]
-% {\skip_horizontal:N, \skip_horizontal:c, \skip_horizontal:n}
-% \begin{syntax}
-% \cs{skip_horizontal:N} \meta{skip}
-% \cs{skip_horizontal:n} \Arg{skip expr}
-% \end{syntax}
-% Inserts a horizontal \meta{skip} into the current list.
-% The argument can also be a \meta{dim}.
-% \begin{texnote}
-% \cs{skip_horizontal:N} is the \TeX{} primitive \tn{hskip}.
-% \end{texnote}
-% \end{function}
-%
-% \begin{function}[updated = 2011-10-22]
-% {\skip_vertical:N, \skip_vertical:c, \skip_vertical:n}
-% \begin{syntax}
-% \cs{skip_vertical:N} \meta{skip}
-% \cs{skip_vertical:n} \Arg{skip expr}
-% \end{syntax}
-% Inserts a vertical \meta{skip} into the current list.
-% The argument can also be a \meta{dim}.
-% \begin{texnote}
-% \cs{skip_vertical:N} is the \TeX{} primitive \tn{vskip}.
-% \end{texnote}
-% \end{function}
-%
-% \section{Creating and initialising \texttt{muskip} variables}
-%
-% \begin{function}{\muskip_new:N, \muskip_new:c}
-% \begin{syntax}
-% \cs{muskip_new:N} \meta{muskip}
-% \end{syntax}
-% Creates a new \meta{muskip} or raises an error if the name is
-% already taken. The declaration is global. The \meta{muskip}
-% is initially equal to $0$\,mu.
-% \end{function}
-%
-% \begin{function}[added = 2012-03-05]{\muskip_const:Nn, \muskip_const:cn}
-% \begin{syntax}
-% \cs{muskip_const:Nn} \meta{muskip} \Arg{muskip expr}
-% \end{syntax}
-% Creates a new constant \meta{muskip} or raises an error if the
-% name is already taken. The value of the \meta{muskip} is set
-% globally to the \meta{muskip expr}.
-% \end{function}
-%
-% \begin{function}
-% {\muskip_zero:N, \muskip_zero:c, \muskip_gzero:N, \muskip_gzero:c}
-% \begin{syntax}
-% \cs{skip_zero:N} \meta{muskip}
-% \end{syntax}
-% Sets \meta{muskip} to $0$\,mu.
-% \end{function}
-%
-% \begin{function}[added = 2012-01-07]
-% {
-% \muskip_zero_new:N, \muskip_zero_new:c,
-% \muskip_gzero_new:N, \muskip_gzero_new:c
-% }
-% \begin{syntax}
-% \cs{muskip_zero_new:N} \meta{muskip}
-% \end{syntax}
-% Ensures that the \meta{muskip} exists globally by applying
-% \cs{muskip_new:N} if necessary, then applies
-% \cs[index=muskip_zero:N]{muskip_(g)zero:N}
-% to leave the \meta{muskip} set to zero.
-% \end{function}
-%
-% \begin{function}[EXP, pTF, added=2012-03-03]
-% {\muskip_if_exist:N, \muskip_if_exist:c}
-% \begin{syntax}
-% \cs{muskip_if_exist_p:N} \meta{muskip}
-% \cs{muskip_if_exist:NTF} \meta{muskip} \Arg{true code} \Arg{false code}
-% \end{syntax}
-% Tests whether the \meta{muskip} is currently defined. This does not
-% check that the \meta{muskip} really is a muskip variable.
-% \end{function}
-%
-% \section{Setting \texttt{muskip} variables}
-%
-% \begin{function}[updated = 2011-10-22]
-% {\muskip_add:Nn, \muskip_add:cn, \muskip_gadd:Nn, \muskip_gadd:cn}
-% \begin{syntax}
-% \cs{muskip_add:Nn} \meta{muskip} \Arg{muskip expr}
-% \end{syntax}
-% Adds the result of the \meta{muskip expr} to the current
-% content of the \meta{muskip}.
-% \end{function}
-%
-% \begin{function}[updated = 2011-10-22]
-% {\muskip_set:Nn, \muskip_set:cn, \muskip_gset:Nn, \muskip_gset:cn}
-% \begin{syntax}
-% \cs{muskip_set:Nn} \meta{muskip} \Arg{muskip expr}
-% \end{syntax}
-% Sets \meta{muskip} to the value of \meta{muskip expr}, which
-% must evaluate to a math length with units and may include a rubber
-% component (for example |1 mu plus 0.5 mu|.
-% \end{function}
-%
-% \begin{function}
-% {
-% \muskip_set_eq:NN, \muskip_set_eq:cN,
-% \muskip_set_eq:Nc, \muskip_set_eq:cc,
-% \muskip_gset_eq:NN, \muskip_gset_eq:cN,
-% \muskip_gset_eq:Nc, \muskip_gset_eq:cc
-% }
-% \begin{syntax}
-% \cs{muskip_set_eq:NN} \meta{muskip_1} \meta{muskip_2}
-% \end{syntax}
-% Sets the content of \meta{muskip_1} equal to that of
-% \meta{muskip_2}.
-% \end{function}
-%
-% \begin{function}[updated = 2011-10-22]
-% {\muskip_sub:Nn, \muskip_sub:cn, \muskip_gsub:Nn, \muskip_gsub:cn}
-% \begin{syntax}
-% \cs{muskip_sub:Nn} \meta{muskip} \Arg{muskip expr}
-% \end{syntax}
-% Subtracts the result of the \meta{muskip expr} from the
-% current content of the \meta{muskip}.
-% \end{function}
-%
-% \section{Using \texttt{muskip} expressions and variables}
-%
-% \begin{function}[updated = 2011-10-22, EXP]{\muskip_eval:n}
-% \begin{syntax}
-% \cs{muskip_eval:n} \Arg{muskip expr}
-% \end{syntax}
-% Evaluates the \meta{muskip expr}, expanding any skips
-% and token list variables within the \meta{expression}
-% to their content (without requiring \cs{muskip_use:N}/\cs{tl_use:N})
-% and applying the standard mathematical rules. The result of the
-% calculation is left in the input stream as a \meta{muglue denotation}
-% after two expansions. This is expressed in \texttt{mu},
-% and requires suitable termination if used in a \TeX{}-style
-% assignment as it is \emph{not} an \meta{internal muglue}.
-% \end{function}
-%
-% \begin{function}[EXP]{\muskip_use:N, \muskip_use:c}
-% \begin{syntax}
-% \cs{muskip_use:N} \meta{muskip}
-% \end{syntax}
-% Recovers the content of a \meta{skip} and places it directly
-% in the input stream. An error is raised if the variable does
-% not exist or if it is invalid. Can be omitted in places where a
-% \meta{dimension} is required (such as in the argument of
-% \cs{muskip_eval:n}).
-% \begin{texnote}
-% \cs{muskip_use:N} is the \TeX{} primitive \tn{the}: this is one of
-% several \LaTeX3 names for this primitive.
-% \end{texnote}
-% \end{function}
-%
-% \section{Viewing \texttt{muskip} variables}
-%
-% \begin{function}[updated = 2015-08-03]{\muskip_show:N, \muskip_show:c}
-% \begin{syntax}
-% \cs{muskip_show:N} \meta{muskip}
-% \end{syntax}
-% Displays the value of the \meta{muskip} on the terminal.
-% \end{function}
-%
-% \begin{function}[added = 2011-11-22, updated = 2015-08-07]{\muskip_show:n}
-% \begin{syntax}
-% \cs{muskip_show:n} \Arg{muskip expr}
-% \end{syntax}
-% Displays the result of evaluating the \meta{muskip expr}
-% on the terminal.
-% \end{function}
-%
-% \begin{function}[added = 2014-08-22, updated = 2015-08-03]{\muskip_log:N, \muskip_log:c}
-% \begin{syntax}
-% \cs{muskip_log:N} \meta{muskip}
-% \end{syntax}
-% Writes the value of the \meta{muskip} in the log file.
-% \end{function}
-%
-% \begin{function}[added = 2014-08-22, updated = 2015-08-07]{\muskip_log:n}
-% \begin{syntax}
-% \cs{muskip_log:n} \Arg{muskip expr}
-% \end{syntax}
-% Writes the result of evaluating the \meta{muskip expr}
-% in the log file.
-% \end{function}
-%
-% \section{Constant muskips}
-%
-% \begin{variable}{\c_max_muskip}
-% The maximum value that can be stored as a muskip, with no stretch
-% nor shrink component.
-% \end{variable}
-%
-% \begin{variable}{\c_zero_muskip}
-% A zero length as a muskip, with no stretch nor shrink component.
-% \end{variable}
-%
-% \section{Scratch muskips}
-%
-% \begin{variable}{\l_tmpa_muskip, \l_tmpb_muskip}
-% Scratch muskip for local assignment. These are never used by
-% the kernel code, and so are safe for use with any \LaTeX3-defined
-% function. However, they may be overwritten by other non-kernel
-% code and so should only be used for short-term storage.
-% \end{variable}
-%
-% \begin{variable}{\g_tmpa_muskip, \g_tmpb_muskip}
-% Scratch muskip for global assignment. These are never used by
-% the kernel code, and so are safe for use with any \LaTeX3-defined
-% function. However, they may be overwritten by other non-kernel
-% code and so should only be used for short-term storage.
-% \end{variable}
-%
-% \section{Primitive conditional}
-%
-% \begin{function}[EXP]{\if_dim:w}
-% \begin{syntax}
-% \cs{if_dim:w} \meta{dimen_1} \meta{relation} \meta{dimen_2}
-% ~~\meta{true code}
-% \cs{else:}
-% ~~\meta{false}
-% \cs{fi:}
-% \end{syntax}
-% Compare two dimensions. The \meta{relation} is one of
-% |<|, |=| or |>| with category code $12$.
-% \begin{texnote}
-% This is the \TeX{} primitive \tn{ifdim}.
-% \end{texnote}
-% \end{function}
-%
-% \end{documentation}
-%
-% \begin{implementation}
-%
-% \section{\pkg{l3skip} implementation}
-%
-% \begin{macrocode}
-%<*package>
-% \end{macrocode}
-%
-% \begin{macrocode}
-%<@@=dim>
-% \end{macrocode}
-%
-% \subsection{Length primitives renamed}
-%
-% \begin{macro}{\if_dim:w}
-% \begin{macro}{\@@_eval:w}
-% \begin{macro}{\@@_eval_end:}
-% Primitives renamed.
-% \begin{macrocode}
-\cs_new_eq:NN \if_dim:w \tex_ifdim:D
-\cs_new_eq:NN \@@_eval:w \tex_dimexpr:D
-\cs_new_eq:NN \@@_eval_end: \tex_relax:D
-% \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-%
-% \subsection{Internal auxiliaries}
-%
-% \begin{variable}{\s_@@_mark,\s_@@_stop}
-% Internal scan marks.
-% \begin{macrocode}
-\scan_new:N \s_@@_mark
-\scan_new:N \s_@@_stop
-% \end{macrocode}
-% \end{variable}
-%
-% \begin{macro}[EXP]{\@@_use_none_delimit_by_s_stop:w}
-% Functions to gobble up to a scan mark.
-% \begin{macrocode}
-\cs_new:Npn \@@_use_none_delimit_by_s_stop:w #1 \s_@@_stop { }
-% \end{macrocode}
-% \end{macro}
-%
-% \subsection{Creating and initialising \texttt{dim} variables}
-%
-% \begin{macro}{\dim_new:N, \dim_new:c}
-% Allocating \meta{dim} registers \ldots
-% \begin{macrocode}
-\cs_new_protected:Npn \dim_new:N #1
- {
- \__kernel_chk_if_free_cs:N #1
- \cs:w newdimen \cs_end: #1
- }
-\cs_generate_variant:Nn \dim_new:N { c }
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\dim_const:Nn, \dim_const:cn}
-% Contrarily to integer constants, we cannot avoid using a register,
-% even for constants. We cannot use \cs{dim_gset:Nn} because
-% debugging code would complain that the constant is not a global
-% variable. Since \cs{dim_const:Nn} does not need to be fast, use
-% \cs{dim_eval:n} to avoid needing a debugging patch that wraps the
-% expression in checking code.
-% \begin{macrocode}
-\cs_new_protected:Npn \dim_const:Nn #1#2
- {
- \dim_new:N #1
- \tex_global:D #1 = \dim_eval:n {#2} \scan_stop:
- }
-\cs_generate_variant:Nn \dim_const:Nn { c }
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\dim_zero:N, \dim_zero:c}
-% \begin{macro}{\dim_gzero:N, \dim_gzero:c}
-% Reset the register to zero. Using \cs{c_zero_skip} deals with the
-% case where the variable passed is incorrectly a skip (for example a
-% \LaTeXe{} length). Besides, these functions are then simply copied
-% for \cs{skip_zero:N} and related functions.
-% \begin{macrocode}
-\cs_new_protected:Npn \dim_zero:N #1 { #1 = \c_zero_skip }
-\cs_new_protected:Npn \dim_gzero:N #1
- { \tex_global:D #1 = \c_zero_skip }
-\cs_generate_variant:Nn \dim_zero:N { c }
-\cs_generate_variant:Nn \dim_gzero:N { c }
-% \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}
-% {\dim_zero_new:N, \dim_zero_new:c, \dim_gzero_new:N, \dim_gzero_new:c}
-% Create a register if needed, otherwise clear it.
-% \begin{macrocode}
-\cs_new_protected:Npn \dim_zero_new:N #1
- { \dim_if_exist:NTF #1 { \dim_zero:N #1 } { \dim_new:N #1 } }
-\cs_new_protected:Npn \dim_gzero_new:N #1
- { \dim_if_exist:NTF #1 { \dim_gzero:N #1 } { \dim_new:N #1 } }
-\cs_generate_variant:Nn \dim_zero_new:N { c }
-\cs_generate_variant:Nn \dim_gzero_new:N { c }
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}[pTF]{\dim_if_exist:N, \dim_if_exist:c}
-% Copies of the \texttt{cs} functions defined in \pkg{l3basics}.
-% \begin{macrocode}
-\prg_new_eq_conditional:NNn \dim_if_exist:N \cs_if_exist:N
- { TF , T , F , p }
-\prg_new_eq_conditional:NNn \dim_if_exist:c \cs_if_exist:c
- { TF , T , F , p }
-% \end{macrocode}
-% \end{macro}
-%
-% \subsection{Setting \texttt{dim} variables}
-%
-% \begin{macro}{\dim_set:Nn, \dim_set:cn}
-% \begin{macro}{\dim_gset:Nn, \dim_gset:cn}
-% Setting dimensions is easy enough but when debugging we want both to
-% check that the variable is correctly local/global and to wrap the
-% expression in some code. The \cs{scan_stop:} deals with the case
-% where the variable passed is a skip (for example a \LaTeXe{}
-% length).
-% \begin{macrocode}
-\cs_new_protected:Npn \dim_set:Nn #1#2
- { #1 = \@@_eval:w #2 \@@_eval_end: \scan_stop: }
-\cs_new_protected:Npn \dim_gset:Nn #1#2
- { \tex_global:D #1 = \@@_eval:w #2 \@@_eval_end: \scan_stop: }
-\cs_generate_variant:Nn \dim_set:Nn { c }
-\cs_generate_variant:Nn \dim_gset:Nn { c }
-% \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}{\dim_set_eq:NN, \dim_set_eq:cN, \dim_set_eq:Nc, \dim_set_eq:cc}
-% \begin{macro}
-% {\dim_gset_eq:NN, \dim_gset_eq:cN, \dim_gset_eq:Nc, \dim_gset_eq:cc}
-% All straightforward, with a \cs{scan_stop:} to deal with the case
-% where |#1| is (incorrectly) a skip.
-% \begin{macrocode}
-\cs_new_protected:Npn \dim_set_eq:NN #1#2
- { #1 = #2 \scan_stop: }
-\cs_generate_variant:Nn \dim_set_eq:NN { c , Nc , cc }
-\cs_new_protected:Npn \dim_gset_eq:NN #1#2
- { \tex_global:D #1 = #2 \scan_stop: }
-\cs_generate_variant:Nn \dim_gset_eq:NN { c , Nc , cc }
-% \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}{\dim_add:Nn, \dim_add:cn}
-% \begin{macro}{\dim_gadd:Nn, \dim_gadd:cn}
-% \begin{macro}{\dim_sub:Nn, \dim_sub:cn}
-% \begin{macro}{\dim_gsub:Nn, \dim_gsub:cn}
-% Using |by| here would slow things down just to detect nonsensical
-% cases such as passing |\dimen 123| as the first argument.
-% Using \cs{scan_stop:} deals with skip variables. Since
-% debugging checks that the variable is correctly local/global, the
-% global versions cannot be defined as \cs{tex_global:D} followed by
-% the local versions.
-% \begin{macrocode}
-\cs_new_protected:Npn \dim_add:Nn #1#2
- { \tex_advance:D #1 \@@_eval:w #2 \@@_eval_end: \scan_stop: }
-\cs_new_protected:Npn \dim_gadd:Nn #1#2
- {
- \tex_global:D \tex_advance:D #1
- \@@_eval:w #2 \@@_eval_end: \scan_stop:
- }
-\cs_generate_variant:Nn \dim_add:Nn { c }
-\cs_generate_variant:Nn \dim_gadd:Nn { c }
-\cs_new_protected:Npn \dim_sub:Nn #1#2
- { \tex_advance:D #1 - \@@_eval:w #2 \@@_eval_end: \scan_stop: }
-\cs_new_protected:Npn \dim_gsub:Nn #1#2
- {
- \tex_global:D \tex_advance:D #1
- -\@@_eval:w #2 \@@_eval_end: \scan_stop:
- }
-\cs_generate_variant:Nn \dim_sub:Nn { c }
-\cs_generate_variant:Nn \dim_gsub:Nn { c }
-% \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-%
-% \subsection{Utilities for dimension calculations}
-%
-% \begin{macro}[EXP]{\dim_abs:n}
-% \begin{macro}[EXP]{\@@_abs:N}
-% \UnitTested
-% \begin{macro}[EXP]{\dim_max:nn}
-% \begin{macro}[EXP]{\dim_min:nn}
-% \begin{macro}[EXP]{\@@_maxmin:wwN}
-% \UnitTested
-% \UnitTested
-% Functions for $\min$, $\max$, and absolute value with only one evaluation.
-% The absolute value is evaluated by removing a leading~|-| if present.
-% \begin{macrocode}
-\cs_new:Npn \dim_abs:n #1
- {
- \exp_after:wN \@@_abs:N
- \dim_use:N \@@_eval:w #1 \@@_eval_end:
- }
-\cs_new:Npn \@@_abs:N #1
- { \if_meaning:w - #1 \else: \exp_after:wN #1 \fi: }
-\cs_new:Npn \dim_max:nn #1#2
- {
- \dim_use:N \@@_eval:w \exp_after:wN \@@_maxmin:wwN
- \dim_use:N \@@_eval:w #1 \exp_after:wN ;
- \dim_use:N \@@_eval:w #2 ;
- >
- \@@_eval_end:
- }
-\cs_new:Npn \dim_min:nn #1#2
- {
- \dim_use:N \@@_eval:w \exp_after:wN \@@_maxmin:wwN
- \dim_use:N \@@_eval:w #1 \exp_after:wN ;
- \dim_use:N \@@_eval:w #2 ;
- <
- \@@_eval_end:
- }
-\cs_new:Npn \@@_maxmin:wwN #1 ; #2 ; #3
- {
- \if_dim:w #1 #3 #2 ~
- #1
- \else:
- #2
- \fi:
- }
-% \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}{\dim_ratio:nn}
-% \begin{macro}{\@@_ratio:n}
-% With dimension expressions, something like |10 pt * ( 5 pt / 10 pt )| does
-% not work. Instead, the ratio part needs to be converted to an integer
-% expression. Using \cs{int_value:w} forces everything into |sp|, avoiding
-% any decimal parts.
-% \begin{macrocode}
-\cs_new:Npn \dim_ratio:nn #1#2
- { \@@_ratio:n {#1} / \@@_ratio:n {#2} }
-\cs_new:Npn \@@_ratio:n #1
- { \int_value:w \@@_eval:w (#1) \@@_eval_end: }
-% \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \subsection{Dimension expression conditionals}
-%
-% \begin{macro}[pTF, EXP]{\dim_compare:nNn}
-% Simple comparison.
-% \begin{macrocode}
-\prg_new_conditional:Npnn \dim_compare:nNn #1#2#3 { p , T , F , TF }
- {
- \if_dim:w \@@_eval:w #1 #2 \@@_eval:w #3 \@@_eval_end:
- \prg_return_true: \else: \prg_return_false: \fi:
- }
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}[pTF, EXP]{\dim_compare:n}
-% \begin{macro}[EXP]{\@@_compare:w, \@@_compare:wNN}
-% \begin{macro}[EXP]
-% {
-% \@@_compare_=:w,
-% \@@_compare_!:w,
-% \@@_compare_<:w,
-% \@@_compare_>:w
-% }
-% \begin{macro}{\@@_compare_error:}
-% This code is adapted from the \cs{int_compare:nTF} function. First
-% make sure that there is at least one relation operator, by
-% evaluating a dimension expression with a trailing
-% \cs{@@_compare_error:}. Just like for integers, the looping
-% auxiliary \cs{@@_compare:wNN} closes a primitive conditional and
-% opens a new one. It is actually easier to grab a dimension operand
-% than an integer one, because once evaluated, dimensions all end with
-% \texttt{pt} (with category other). Thus we do not need specific
-% auxiliaries for the three \enquote{simple} relations |<|, |=|,
-% and~|>|.
-% \begin{macrocode}
-\prg_new_conditional:Npnn \dim_compare:n #1 { p , T , F , TF }
- {
- \exp_after:wN \@@_compare:w
- \dim_use:N \@@_eval:w #1 \@@_compare_error:
- }
-\cs_new:Npn \@@_compare:w #1 \@@_compare_error:
- {
- \exp_after:wN \if_false: \exp:w \exp_end_continue_f:w
- \@@_compare:wNN #1 ? { = \@@_compare_end:w \else: } \s_@@_stop
- }
-\exp_args:Nno \use:nn
- { \cs_new:Npn \@@_compare:wNN #1 } { \tl_to_str:n {pt} #2#3 }
- {
- \if_meaning:w = #3
- \use:c { @@_compare_#2:w }
- \fi:
- #1 pt \exp_stop_f:
- \prg_return_false:
- \exp_after:wN \@@_use_none_delimit_by_s_stop:w
- \fi:
- \reverse_if:N \if_dim:w #1 pt #2
- \exp_after:wN \@@_compare:wNN
- \dim_use:N \@@_eval:w #3
- }
-\cs_new:cpn { @@_compare_ ! :w }
- #1 \reverse_if:N #2 ! #3 = { #1 #2 = #3 }
-\cs_new:cpn { @@_compare_ = :w }
- #1 \@@_eval:w = { #1 \@@_eval:w }
-\cs_new:cpn { @@_compare_ < :w }
- #1 \reverse_if:N #2 < #3 = { #1 #2 > #3 }
-\cs_new:cpn { @@_compare_ > :w }
- #1 \reverse_if:N #2 > #3 = { #1 #2 < #3 }
-\cs_new:Npn \@@_compare_end:w #1 \prg_return_false: #2 \s_@@_stop
- { #1 \prg_return_false: \else: \prg_return_true: \fi: }
-\cs_new_protected:Npn \@@_compare_error:
- {
- \if_int_compare:w \c_zero_int \c_zero_int \fi:
- =
- \@@_compare_error:
- }
-% \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}[EXP, noTF]{\dim_case:nn}
-% \begin{macro}{\@@_case:nnTF}
-% \begin{macro}{\@@_case:nw, \@@_case_end:nw}
-% For dimension cases, the first task to fully expand the check
-% condition. The over all idea is then much the same as for
-% \cs{str_case:nnTF} as described in \pkg{l3basics}.
-% \begin{macrocode}
-\cs_new:Npn \dim_case:nnTF #1
- {
- \exp:w
- \exp_args:Nf \@@_case:nnTF { \dim_eval:n {#1} }
- }
-\cs_new:Npn \dim_case:nnT #1#2#3
- {
- \exp:w
- \exp_args:Nf \@@_case:nnTF { \dim_eval:n {#1} } {#2} {#3} { }
- }
-\cs_new:Npn \dim_case:nnF #1#2
- {
- \exp:w
- \exp_args:Nf \@@_case:nnTF { \dim_eval:n {#1} } {#2} { }
- }
-\cs_new:Npn \dim_case:nn #1#2
- {
- \exp:w
- \exp_args:Nf \@@_case:nnTF { \dim_eval:n {#1} } {#2} { } { }
- }
-\cs_new:Npn \@@_case:nnTF #1#2#3#4
- { \@@_case:nw {#1} #2 {#1} { } \s_@@_mark {#3} \s_@@_mark {#4} \s_@@_stop }
-\cs_new:Npn \@@_case:nw #1#2#3
- {
- \dim_compare:nNnTF {#1} = {#2}
- { \@@_case_end:nw {#3} }
- { \@@_case:nw {#1} }
- }
-\cs_new:Npn \@@_case_end:nw #1#2#3 \s_@@_mark #4#5 \s_@@_stop
- { \exp_end: #1 #4 }
-% \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-%
-% \subsection{Dimension expression loops}
-%
-% \begin{macro}{\dim_while_do:nn}
-% \begin{macro}{\dim_until_do:nn}
-% \begin{macro}{\dim_do_while:nn}
-% \begin{macro}{\dim_do_until:nn}
-% |while_do| and |do_while| functions for dimensions. Same as for the
-% |int| type only the names have changed.
-% \begin{macrocode}
-\cs_new:Npn \dim_while_do:nn #1#2
- {
- \dim_compare:nT {#1}
- {
- #2
- \dim_while_do:nn {#1} {#2}
- }
- }
-\cs_new:Npn \dim_until_do:nn #1#2
- {
- \dim_compare:nF {#1}
- {
- #2
- \dim_until_do:nn {#1} {#2}
- }
- }
-\cs_new:Npn \dim_do_while:nn #1#2
- {
- #2
- \dim_compare:nT {#1}
- { \dim_do_while:nn {#1} {#2} }
- }
-\cs_new:Npn \dim_do_until:nn #1#2
- {
- #2
- \dim_compare:nF {#1}
- { \dim_do_until:nn {#1} {#2} }
- }
-% \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}{\dim_while_do:nNnn}
-% \begin{macro}{\dim_until_do:nNnn}
-% \begin{macro}{\dim_do_while:nNnn}
-% \begin{macro}{\dim_do_until:nNnn}
-% |while_do| and |do_while| functions for dimensions. Same as for the
-% |int| type only the names have changed.
-% \begin{macrocode}
-\cs_new:Npn \dim_while_do:nNnn #1#2#3#4
- {
- \dim_compare:nNnT {#1} #2 {#3}
- {
- #4
- \dim_while_do:nNnn {#1} #2 {#3} {#4}
- }
- }
-\cs_new:Npn \dim_until_do:nNnn #1#2#3#4
- {
- \dim_compare:nNnF {#1} #2 {#3}
- {
- #4
- \dim_until_do:nNnn {#1} #2 {#3} {#4}
- }
- }
-\cs_new:Npn \dim_do_while:nNnn #1#2#3#4
- {
- #4
- \dim_compare:nNnT {#1} #2 {#3}
- { \dim_do_while:nNnn {#1} #2 {#3} {#4} }
- }
-\cs_new:Npn \dim_do_until:nNnn #1#2#3#4
- {
- #4
- \dim_compare:nNnF {#1} #2 {#3}
- { \dim_do_until:nNnn {#1} #2 {#3} {#4} }
- }
-% \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-%
-% \subsection{Dimension step functions}
-%
-% \begin{macro}{\dim_step_function:nnnN}
-% \begin{macro}{\@@_step:wwwN, \@@_step:NnnnN}
-% Before all else, evaluate the initial value, step, and final value.
-% Repeating a function by steps first needs a check on the direction
-% of the steps. After that, do the function for the start value then
-% step and loop around. It would be more symmetrical to test for a
-% step size of zero before checking the sign, but we optimize for the
-% most frequent case (positive step).
-% \begin{macrocode}
-\cs_new:Npn \dim_step_function:nnnN #1#2#3
- {
- \exp_after:wN \@@_step:wwwN
- \tex_the:D \@@_eval:w #1 \exp_after:wN ;
- \tex_the:D \@@_eval:w #2 \exp_after:wN ;
- \tex_the:D \@@_eval:w #3 ;
- }
-\cs_new:Npn \@@_step:wwwN #1; #2; #3; #4
- {
- \dim_compare:nNnTF {#2} > \c_zero_dim
- { \@@_step:NnnnN > }
- {
- \dim_compare:nNnTF {#2} = \c_zero_dim
- {
- \msg_expandable_error:nnn { kernel } { zero-step } {#4}
- \use_none:nnnn
- }
- { \@@_step:NnnnN < }
- }
- {#1} {#2} {#3} #4
- }
-\cs_new:Npn \@@_step:NnnnN #1#2#3#4#5
- {
- \dim_compare:nNnF {#2} #1 {#4}
- {
- #5 {#2}
- \exp_args:NNf \@@_step:NnnnN
- #1 { \dim_eval:n { #2 + #3 } } {#3} {#4} #5
- }
- }
-% \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}{\dim_step_inline:nnnn}
-% \begin{macro}{\dim_step_variable:nnnNn}
-% \begin{macro}{\@@_step:NNnnnn}
-% The approach here is to build a function, with a global integer
-% required to make the nesting safe (as seen in other in line
-% functions), and map that function using \cs{dim_step_function:nnnN}.
-% We put a \cs{prg_break_point:Nn} so that \texttt{map_break}
-% functions from other modules correctly decrement \cs{g__kernel_prg_map_int}
-% before looking for their own break point. The first argument is
-% \cs{scan_stop:}, so that no breaking function recognizes this break
-% point as its own.
-% \begin{macrocode}
-\cs_new_protected:Npn \dim_step_inline:nnnn
- {
- \int_gincr:N \g__kernel_prg_map_int
- \exp_args:NNc \@@_step:NNnnnn
- \cs_gset_protected:Npn
- { @@_map_ \int_use:N \g__kernel_prg_map_int :w }
- }
-\cs_new_protected:Npn \dim_step_variable:nnnNn #1#2#3#4#5
- {
- \int_gincr:N \g__kernel_prg_map_int
- \exp_args:NNc \@@_step:NNnnnn
- \cs_gset_protected:Npe
- { @@_map_ \int_use:N \g__kernel_prg_map_int :w }
- {#1}{#2}{#3}
- {
- \tl_set:Nn \exp_not:N #4 {##1}
- \exp_not:n {#5}
- }
- }
-\cs_new_protected:Npn \@@_step:NNnnnn #1#2#3#4#5#6
- {
- #1 #2 ##1 {#6}
- \dim_step_function:nnnN {#3} {#4} {#5} #2
- \prg_break_point:Nn \scan_stop: { \int_gdecr:N \g__kernel_prg_map_int }
- }
-% \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-%
-% \subsection{Using \texttt{dim} expressions and variables}
-%
-% \begin{macro}{\dim_eval:n}
-% Evaluating a dimension expression expandably.
-% \begin{macrocode}
-\cs_new:Npn \dim_eval:n #1
- { \dim_use:N \@@_eval:w #1 \@@_eval_end: }
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}[EXP]{\dim_sign:n, \@@_sign:Nw}
-% See \cs{dim_abs:n}. Contrarily to \cs{int_sign:n} the case of a
-% zero dimension cannot be distinguished from a positive dimension by
-% looking only at the first character, since |0.2pt| and |0pt| start
-% the same way. We need explicit comparisons. We start by
-% distinguishing the most common case of a positive dimension.
-% \begin{macrocode}
-\cs_new:Npn \dim_sign:n #1
- {
- \int_value:w \exp_after:wN \@@_sign:Nw
- \dim_use:N \@@_eval:w #1 \@@_eval_end: ;
- \exp_stop_f:
- }
-\cs_new:Npn \@@_sign:Nw #1#2 ;
- {
- \if_dim:w #1#2 > \c_zero_dim
- 1
- \else:
- \if_meaning:w - #1
- -1
- \else:
- 0
- \fi:
- \fi:
- }
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\dim_use:N, \dim_use:c}
-% Accessing a \meta{dim}. We hand-code the |c| variant for some speed gain.
-% \begin{macrocode}
-\cs_new_eq:NN \dim_use:N \tex_the:D
-\cs_new:Npn \dim_use:c #1 { \tex_the:D \cs:w #1 \cs_end: }
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}[EXP]{\dim_to_decimal:n}
-% \begin{macro}[EXP]{\@@_to_decimal:w}
-% A function which comes up often enough to deserve a place in the
-% kernel. Evaluate the dimension expression~|#1| then remove the
-% trailing \texttt{pt}. When debugging is enabled, the argument is
-% put in parentheses as this prevents the dimension expression from
-% terminating early and leaving extra tokens lying around. This is
-% used a lot by low-level manipulations.
-% \begin{macrocode}
-\cs_new:Npn \dim_to_decimal:n #1
- {
- \exp_after:wN
- \@@_to_decimal:w \dim_use:N \@@_eval:w #1 \@@_eval_end:
- }
-\use:e
- {
- \cs_new:Npn \exp_not:N \@@_to_decimal:w
- #1 . #2 \tl_to_str:n { pt }
- }
- {
- \int_compare:nNnTF {#2} > \c_zero_int
- { #1 . #2 }
- { #1 }
- }
-% \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}[EXP]{\dim_to_fp:n}
-% Defined in \pkg{l3fp-convert}, documented here.
-% \end{macro}
-%
-% \subsection{Conversion of \texttt{dim} to other units}
-%
-% The conversion from \texttt{pt} or \texttt{sp} to other units is complicated
-% by the fact that \TeX{}'s conversion to \texttt{sp} involves rounding and
-% hard-coded ratios. In order to give re-entrant outcomes, we therefore need
-% to do quite a bit of work: see
-% \url{https://github.com/latex3/latex3/issues/954} for detailed discussion.
-% After dealing with the trivial case, we therefore have some work to do.
-% The code to do this is contributed by Ruixi Zhang.
-%
-% \begin{macro}[EXP]{\dim_to_decimal_in_sp:n}
-% The one easy case: the only requirement here is that we avoid an
-% overflow.
-% \begin{macrocode}
-\cs_new:Npn \dim_to_decimal_in_sp:n #1
- { \int_value:w \@@_eval:w #1 \@@_eval_end: }
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}[EXP]
-% {
-% \dim_to_decimal_in_bp:n ,
-% \dim_to_decimal_in_cc:n ,
-% \dim_to_decimal_in_cm:n ,
-% \dim_to_decimal_in_dd:n ,
-% \dim_to_decimal_in_in:n ,
-% \dim_to_decimal_in_mm:n ,
-% \dim_to_decimal_in_pc:n
-% }
-% \begin{macro}[EXP]{\@@_to_decimal_aux:w}
-% We first set up a helper macro \cs[no-index]{@@_tmp:w} which takes two
-% arguments. The first argument is one of the following engine-defined
-% units: |in|,~|pc|, |cm|, |mm|, |bp|, |dd|, |cc|, |nd|, and~|nc|.
-% The second argument is $\frac{1}{2}\delta^{-1}$ in reduced fraction,
-% where $\delta>1$~is the engine-defined conversion factor for each unit.
-% Note that $\delta$~must be strictly larger than~$1$ for the following
-% algorithm to work.
-%
-% Here is how the algorithm works: Suppose that a user inputs a
-% non-negative dimension in a unit that has conversion factor~$\delta>1$.
-% Then this dimension is internally represented as $X$\,sp, where
-% $X=\lfloor N\delta\rfloor$ for some integer $N\ge0$. We then seek a
-% formula to express this $N$ using~$X$.
-% The \cs[no-index]{dim_to_decimal_in_<unit>:n} functions shall return
-% the number $N/2^{16}$ in decimal. This way, we guarantee the returned
-% decimal followed by the original unit will parse to exactly~$X$\,sp.
-%
-% So how do we get $N$ from~$X$? Well, since $X=\lfloor N\delta\rfloor$,
-% we have $X\le N\delta<X+1$ and $X\delta^{-1}\le N<(X+1)\delta^{-1}$.
-% Let's focus on the midpoint of this bounding interval for~$N$. The
-% midpoint is $(X+\frac{1}{2})\delta^{-1}$. The fact $\delta>1$ implies
-% that the bounding interval is shorter than~$1$ in length. Thus,
-% (1)~$\hbox{midpoint}+\frac{1}{2}>N$ and
-% (2)~$\hbox{midpoint}+\frac{1}{2}<N+1$. In other words,
-% $N=\lfloor\hbox{midpoint}+\frac{1}{2}\rfloor$. As long as we can
-% rewrite the midpoint as the result of a \enquote{scaling operation} of \eTeX,
-% the $\lfloor\ldots+\frac{1}{2}\rfloor$ part will follow naturally.
-% Indeed we can: $\hbox{midpoint}=(2X+1)\times(\frac{1}{2}\delta^{-1})$.
-%
-% Addendum: If $\delta\ge2$, then the bounding interval for~$N$ is at
-% most~$\frac{1}{2}$ wide in length. In this case, the leftpoint
-% $X\delta^{-1}$ suffices as $N=\lfloor X\delta^{-1}+\frac{1}{2}\rfloor$.
-% Six out of the nine units listed above can be handled in this way,
-% which is much simpler than using midpoint. But three remaining units
-% have $1<\delta<2$; they are |bp|~($\delta=7227/7200$),
-% |nd|~($\delta=685/642$), and |dd|~($\delta=1238/1157$),
-% and these three must be handled using midpoint.
-% For consistency, we shall use the midpoint approach for all nine units.
-% \begin{macrocode}
-\group_begin:
- \cs_set_protected:Npn \@@_tmp:w #1#2
- {
- \cs_new:cpn { dim_to_decimal_in_ #1 :n } ##1
- {
- \exp_after:wN \@@_to_decimal_aux:w
- \int_value:w \@@_eval:w ##1 \@@_eval_end: ; #2 ;
- }
- }
-% \end{macrocode}
-% Conversions to other units are now coded.
-% Consult the pdf\/\TeX{} source for each conversion factor~$\delta$.
-% Each factor $\frac{1}{2}\delta^{-1}$ is hand-coded
-% for accuracy (and speed). As the units \texttt{nc} and \texttt{nd}
-% are not supported by \XeTeX{} or (u)p\TeX{}, they are not included
-% here.
-% \begin{macrocode}
- \@@_tmp:w { in } { 50 / 7227 } % delta = 7227/100
- \@@_tmp:w { pc } { 1 / 24 } % delta = 12/1
- \@@_tmp:w { cm } { 127 / 7227 } % delta = 7227/254
- \@@_tmp:w { mm } { 1270 / 7227 } % delta = 7227/2540
- \@@_tmp:w { bp } { 400 / 803 } % delta = 7227/7200
- \@@_tmp:w { dd } { 1157 / 2476 } % delta = 1238/1157
- \@@_tmp:w { cc } { 1157 / 29712 } % delta = 14856/1157
-\group_end:
-% \end{macrocode}
-% The tokens after \cs{@@_to_decimal_aux:w} shall have the following form:
-% |<number>;<half of delta inverse>;|, where |<number>| represents the
-% input dimension in |sp| unit.
-% If |<number>| is positive, then |#1| is its leading digit and |#2|
-% (possibly empty) is all the remaining digits;
-% If |<number>| is zero, then |#1| is~|0|$_{12}$ and |#2| is empty;
-% If |<number>| is negative, then |#1| is its sign~|-|$_{12}$ and |#2|
-% is all its digits.
-% In all three cases, |#1#2| is the original |<number>|. We can use |#1|
-% to decide whether to use the |-1| formula or the |+1| formula.
-% \begin{macrocode}
-\cs_new:Npn \@@_to_decimal_aux:w #1#2 ; #3 ;
- {
- \dim_to_decimal:n
- {
-% \end{macrocode}
-% We need different formulae depending on whether the user input dimension
-% is negative or not.
-% For negative dimension (internally represented as $X$\,sp), the formula
-% is $(2X-1)\times(\frac{1}{2}\delta^{-1})$.
-% For non-negative dimension, the formula
-% is $(2X+1)\times(\frac{1}{2}\delta^{-1})$.
-% The intermediate step doubles the dimension~$X$.
-% To avoid overflow, we must invoke \cs[no-index]{int_eval:n}.
-% \begin{macrocode}
- \int_eval:n
- { ( 2 * #1#2 \if:w #1 - - \else: + \fi: 1 ) * #3 }
-% \end{macrocode}
-% Now we append~|sp| to finish the dimension specification.
-% \begin{macrocode}
- sp
- }
- }
-% \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}[EXP]{\dim_to_decimal_in_unit:nn}
-% \begin{macrocode}
-\cs_new:Npn \dim_to_decimal_in_unit:nn #1#2
- {
- \exp_after:wN \@@_chk_unit:w
- \int_value:w \@@_eval:w #2 \@@_eval_end: ; {#1}
- }
-% \end{macrocode}
-% \end{macro}
-% \begin{macro}[EXP]{\@@_chk_unit:w}
-% The tokens after \cs{@@_chk_unit:w} shall have the following form:
-% |<number2>;{<dimexpr1>}|, where |<number2>| represents |<dimexpr2>| in
-% |sp| unit.
-% If |#1| is~|0|$_{12}$, the \enquote{unit} |<dimexpr2>| must also be zero.
-% So we throw out a \enquote{division by zero} error message at this point.
-% Otherwise, if |#1| is~|-|$_{12}$, we shall negate both |<dimexpr1>| and
-% |<dimexpr2>| for later procedures.
-% \begin{macrocode}
-\cs_new:Npn \@@_chk_unit:w #1#2;#3
- {
- \token_if_eq_charcode:NNTF #1 0
- { \msg_expandable_error:nn { dim } { zero-unit } }
- {
- \exp_after:wN \@@_branch_unit:w
- \int_value:w \if:w #1 - - \fi: \@@_eval:w #3 \exp_after:wN ;
- \int_value:w \if:w #1 - - \fi: #1#2 ;
- }
- }
-% \end{macrocode}
-% \end{macro}
-% \begin{macro}[EXP]{\@@_branch_unit:w}
-% The tokens after \cs{@@_branch_unit:w} shall have the following form:
-% |<number1>;<number2>;|, where |<number1>| represents |<dimexpr1>| in
-% |sp| unit (whose sign is taken care of) and |<number2>| represents the
-% absolute value of |<dimexpr2>| in |sp| unit (which is strictly positive).
-%
-% As explained, the formulae $(2X\pm1)\times(\frac{1}{2}\delta^{-1})$ work
-% if and only if $\delta=|<number2>|/65536>1$. This corresponds to
-% |<dimexpr2>| strictly larger than 1\,pt in absolute value.
-% In this case, we simply call \cs{@@_to_decimal_aux:w} and supply
-% $\frac{1}{2}\delta^{-1}=32768/|<number2>|$ as |<half of delta inverse>|.
-%
-% Otherwise if $|<number2>|=65536$, then |<dimexpr2>| is 1\,pt in absolute
-% value and we call \cs{dim_to_decimal:n} directly.
-%
-% Otherwise $0<|<number2>|<65536$ and we shall proceed differently.
-%
-% For unit less than 1\,pt, write $n=|<number2>|$, then $\delta=n/65536<1$.
-% The midpoint formulae are not optimal. Let's go back to the inequalities
-% $X\delta^{-1}\le N<(X+1)\delta^{-1}$. Since now $\delta<1$, the bounding
-% interval is wider than~$1$ in length. Consider the ceiling integer
-% $M=\lceil X\delta^{-1}\rceil$, then $X\delta^{-1}\le M<(X+1)\delta^{-1}$,
-% or equivalently $X\le M\delta<X+1$, and thus $\lfloor M\delta\rfloor=X$.
-% The key point here is that we \emph{don't} need to solve for~$N$;
-% in fact, any integer that can reproduce~$X$ (such as~$M$) is good enough.
-% So the algorithm goes like this: (1)~Compute rounding of $X\delta^{-1}$,
-% i.e., $M'=\lfloor X\delta^{-1}+\frac{1}{2}\rfloor$; this $M'$ could be
-% either $M$ or $M-1$. (2)~Check if $\lfloor M'\delta\rfloor=X$, i.e.,
-% whether our candidate $M'$ can reproduce~$X$. If so, then this $M'$ is
-% good enough; if not, then we add one to~$M'$.
-%
-% But when $0<n<65536$, we cannot delay the problem of overflow any more.
-% For $X\delta^{-1}=X\times65536/n$, where $X$ can go up to $2^{30}-1$ and
-% $n$ can be as small as~$1$, the result is well over $2^{31}-1$ (largest
-% integer allowed within |\numexpr|).
-% For example, |\dim_to_decimal_in_unit:nn { \maxdimen } { 1sp }|.
-% Here, all inputs are legal, so we should be able to output |1073741823|
-% \emph{without} causing arithmetic overflow.
-%
-% As a workaround, let's write $X=qn+r$ with some $q\ge0$ and $0\le r<n$.
-% Then $X\delta^{-1}=65536q+65536r/n$, and so
-% $M'=65536q+\lfloor65536r/n+\frac{1}{2}\rfloor=65536q+R'$.
-% Computing $R'$ will never overflow. If this $R'$ can reproduce~$r$, then
-% it is good enough; otherwise we add one to~$R'$. In the end, we shall
-% output $q+R'/65536$ in decimal.
-%
-% Note: $q=\lfloor X/n\rfloor=\lfloor\frac{2X-n}{2n}+\frac{1}{2}\rfloor$
-% represents the \enquote{integer} part, while $0\le R'\le65536$ represents the
-% \enquote{fractional} part. (Can $R'=65536$ really happen? Didn't investigate.)
-% \begin{macrocode}
-\cs_new:Npn \@@_branch_unit:w #1;#2;
- {
- \int_compare:nNnTF {#2} > { 65536 }
- { \@@_to_decimal_aux:w #1 ; 32768 / #2 ; }
- {
- \int_compare:nNnTF {#2} = { 65536 }
- { \dim_to_decimal:n { #1sp } }
- { \@@_get_quotient:w #1 ; #2 ; }
- }
- }
-% \end{macrocode}
-% \end{macro}
-% \begin{macro}[EXP]{\@@_get_quotient:w}
-% We wish to get the quotient $q$ via rounding of $\frac{2X-n}{2n}$.
-% When $0\le X<n/2$, we have $\frac{2X-n}{2n}<0$. So, strictly speaking,
-% |\numexpr| performs its rounding as
-% $\lceil\frac{2X-n}{2n}-\frac{1}{2}\rceil$, not exactly what we want.
-% However, lucky for us, only $X=0$ makes
-% $\lceil\frac{2X-n}{2n}-\frac{1}{2}\rceil=-1\neq0$ (we want~$0$);
-% all other $0<X<n/2$ make $\lceil\frac{2X-n}{2n}-\frac{1}{2}\rceil=0=q$.
-% Thus, let's filter out $X=0$ early.
-% If $X\neq0$, we extract its sign and leave the sign to the back.
-% The sign does not participate in any calculations (also the code works
-% with positive integers only). The sign is used at the last stages when
-% we parse the decimal output.
-%
-% After \cs{@@_get_quotient:w} has done its job, either we have the
-% decimal~|0|, or we have \cs{@@_get_remainder:w} followed by
-% $q$|;|$\lvert X\rvert$|;|$n$|;<sign of X>;|.
-% \begin{macrocode}
-\cs_new:Npn \@@_get_quotient:w #1#2;#3;
- {
- \token_if_eq_charcode:NNTF #1 0
- { 0 }
- {
- \token_if_eq_charcode:NNTF #1 -
- {
- \exp_after:wN \exp_after:wN \exp_after:wN \@@_get_remainder:w
- \int_eval:n { ( 2 * #2 - #3 ) / ( 2 * #3 ) } ;
- #2 ; #3 ; - ;
- }
- {
- \exp_after:wN \exp_after:wN \exp_after:wN \@@_get_remainder:w
- \int_eval:n { ( 2 * #1#2 - #3 ) / ( 2 * #3 ) } ;
- #1#2 ; #3 ; ;
- }
- }
- }
-% \end{macrocode}
-% \end{macro}
-% \begin{macro}[EXP]{\@@_get_remainder:w}
-% \cs{@@_get_remainder:w} does not need to read the sign.
-% After finding the remainder~$r$, the number~$\lvert X\rvert$ is no longer
-% needed. We should then have \cs{@@_convert_remainder:w} followed by
-% $r$|;|$n$|;|$q$|;<sign of X>;|.
-% \begin{macrocode}
-\cs_new:Npn \@@_get_remainder:w #1;#2;#3;
- {
- \exp_after:wN \exp_after:wN \exp_after:wN \@@_convert_remainder:w
- \int_eval:n { #2 - #1 * #3 } ;
- #3 ; #1 ;
- }
-% \end{macrocode}
-% \end{macro}
-% \begin{macro}[EXP]{\@@_convert_remainder:w}
-% This is trivial. We compute $R'=\lfloor65536r/n+\frac{1}{2}\rfloor$,
-% then leave \cs{@@_test_candidate:w} followed by
-% $R'$|;|$r$|;|$n$|;|$q$|;<sign of X>;|.
-% \begin{macrocode}
-\cs_new:Npn \@@_convert_remainder:w #1;#2;
- {
- \exp_after:wN \exp_after:wN \exp_after:wN \@@_test_candidate:w
- \int_eval:n { #1 * 65536 / #2 } ;
- #1 ; #2 ;
- }
-% \end{macrocode}
-% \end{macro}
-% \begin{macro}[EXP]{\@@_test_candidate:w}
-% Now the fun part: We take $R'$, $r$ and~$n$ to test whether
-% $r=\lfloor R'\delta\rfloor$. This is done as a dimension comparison.
-% The left-hand side, $r$, is simply |r sp|. The right-hand side,
-% $\lfloor R'\delta\rfloor$, is exactly |<R' as decimal><dimen = n sp>|.
-% If the result is true, then we've found~$R'$;
-% otherwise we add one to~$R'$.
-% After this step, $r$ and~$n$ are no longer needed. We should then have
-% \cs{@@_parse_decimal:w} followed by $R'$|;|$q$|;<sign of X>;|.
-% \begin{macrocode}
-\cs_new:Npn \@@_test_candidate:w #1;#2;#3;
- {
- \dim_compare:nNnTF { #2sp } =
- { \dim_to_decimal:n { #1sp } \@@_eval:w #3sp \@@_eval_end: }
- { \@@_parse_decimal:w #1 ; }
- {
- \@@_parse_decimal:w \int_eval:n { #1 + 1 } ;
- }
- }
-% \end{macrocode}
-% \end{macro}
-% \begin{macro}[EXP]{\@@_parse_decimal:w, \@@_parse_decimal_aux:w}
-% The Grand Finale: We sum $q$ and $R'/65536$ together, and negate the
-% result if necessary. These are all done expandably.
-% If $0<R'/65536<1$, the integer summation is naturally terminated at the
-% decimal point. If $R'/65536=0$ (or~$1$?), the summation is terminated
-% at the semicolon. The auxiliary function \cs{@@_parse_decimal_aux:w}
-% takes care of both cases.
-% \begin{macrocode}
-\cs_new:Npn \@@_parse_decimal:w #1;#2;#3;
- {
- \exp_after:wN \@@_parse_decimal_aux:w
- \int_value:w #3 \int_eval:w #2 + \dim_to_decimal:n { #1sp } ;
- }
-\cs_new:Npn \@@_parse_decimal_aux:w #1 ; {#1}
-% \end{macrocode}
-% \end{macro}
-%
-% \subsection{Viewing \texttt{dim} variables}
-%
-% \begin{macro}{\dim_show:N, \dim_show:c}
-% Diagnostics.
-% \begin{macrocode}
-\cs_new_eq:NN \dim_show:N \__kernel_register_show:N
-\cs_generate_variant:Nn \dim_show:N { c }
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\dim_show:n}
-% Diagnostics. We don't use the \TeX{} primitive \tn{showthe} to show
-% dimension expressions: this gives a more unified output.
-% \begin{macrocode}
-\cs_new_protected:Npn \dim_show:n
- { \__kernel_msg_show_eval:Nn \dim_eval:n }
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\dim_log:N, \dim_log:c, \dim_log:n}
-% Diagnostics. Redirect output of \cs{dim_show:n} to the log.
-% \begin{macrocode}
-\cs_new_eq:NN \dim_log:N \__kernel_register_log:N
-\cs_new_eq:NN \dim_log:c \__kernel_register_log:c
-\cs_new_protected:Npn \dim_log:n
- { \__kernel_msg_log_eval:Nn \dim_eval:n }
-% \end{macrocode}
-% \end{macro}
-%
-% \subsection{Constant dimensions}
-%
-% \begin{variable}{\c_zero_dim, \c_max_dim}
-% Constant dimensions.
-% \begin{macrocode}
-\dim_const:Nn \c_zero_dim { 0 pt }
-\dim_const:Nn \c_max_dim { 16383.99999 pt }
-% \end{macrocode}
-% \end{variable}
-%
-% \subsection{Scratch dimensions}
-%
-% \begin{variable}{\l_tmpa_dim, \l_tmpb_dim}
-% \begin{variable}{\g_tmpa_dim, \g_tmpb_dim}
-% We provide two local and two global scratch registers, maybe we
-% need more or less.
-% \begin{macrocode}
-\dim_new:N \l_tmpa_dim
-\dim_new:N \l_tmpb_dim
-\dim_new:N \g_tmpa_dim
-\dim_new:N \g_tmpb_dim
-% \end{macrocode}
-% \end{variable}
-% \end{variable}
-%
-% \subsection{Creating and initialising \texttt{skip} variables}
-%
-% \begin{macrocode}
-%<@@=skip>
-% \end{macrocode}
-%
-% \begin{variable}{\s_@@_stop}
-% Internal scan marks.
-% \begin{macrocode}
-\scan_new:N \s_@@_stop
-% \end{macrocode}
-% \end{variable}
-%
-% \begin{macro}{\skip_new:N, \skip_new:c}
-% Allocation of a new internal registers.
-% \begin{macrocode}
-\cs_new_protected:Npn \skip_new:N #1
- {
- \__kernel_chk_if_free_cs:N #1
- \cs:w newskip \cs_end: #1
- }
-\cs_generate_variant:Nn \skip_new:N { c }
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\skip_const:Nn, \skip_const:cn}
-% Contrarily to integer constants, we cannot avoid using a register,
-% even for constants. See \cs{dim_const:Nn} for why we cannot use
-% \cs{skip_gset:Nn}.
-% \begin{macrocode}
-\cs_new_protected:Npn \skip_const:Nn #1#2
- {
- \skip_new:N #1
- \tex_global:D #1 = \skip_eval:n {#2} \scan_stop:
- }
-\cs_generate_variant:Nn \skip_const:Nn { c }
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\skip_zero:N, \skip_zero:c}
-% \begin{macro}{\skip_gzero:N, \skip_gzero:c}
-% Reset the register to zero.
-% \begin{macrocode}
-\cs_new_eq:NN \skip_zero:N \dim_zero:N
-\cs_new_eq:NN \skip_gzero:N \dim_gzero:N
-\cs_generate_variant:Nn \skip_zero:N { c }
-\cs_generate_variant:Nn \skip_gzero:N { c }
-% \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}
-% {\skip_zero_new:N, \skip_zero_new:c, \skip_gzero_new:N, \skip_gzero_new:c}
-% Create a register if needed, otherwise clear it.
-% \begin{macrocode}
-\cs_new_protected:Npn \skip_zero_new:N #1
- { \skip_if_exist:NTF #1 { \skip_zero:N #1 } { \skip_new:N #1 } }
-\cs_new_protected:Npn \skip_gzero_new:N #1
- { \skip_if_exist:NTF #1 { \skip_gzero:N #1 } { \skip_new:N #1 } }
-\cs_generate_variant:Nn \skip_zero_new:N { c }
-\cs_generate_variant:Nn \skip_gzero_new:N { c }
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}[pTF]{\skip_if_exist:N, \skip_if_exist:c}
-% Copies of the \texttt{cs} functions defined in \pkg{l3basics}.
-% \begin{macrocode}
-\prg_new_eq_conditional:NNn \skip_if_exist:N \cs_if_exist:N
- { TF , T , F , p }
-\prg_new_eq_conditional:NNn \skip_if_exist:c \cs_if_exist:c
- { TF , T , F , p }
-% \end{macrocode}
-% \end{macro}
-%
-% \subsection{Setting \texttt{skip} variables}
-%
-% \begin{macro}{\skip_set:Nn, \skip_set:cn}
-% \begin{macro}{\skip_gset:Nn, \skip_gset:cn}
-% Much the same as for dimensions.
-% \begin{macrocode}
-\cs_new_protected:Npn \skip_set:Nn #1#2
- { #1 = \tex_glueexpr:D #2 \scan_stop: }
-\cs_new_protected:Npn \skip_gset:Nn #1#2
- { \tex_global:D #1 = \tex_glueexpr:D #2 \scan_stop: }
-\cs_generate_variant:Nn \skip_set:Nn { c }
-\cs_generate_variant:Nn \skip_gset:Nn { c }
-% \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}
-% {\skip_set_eq:NN, \skip_set_eq:cN, \skip_set_eq:Nc, \skip_set_eq:cc}
-% \begin{macro}
-% {\skip_gset_eq:NN, \skip_gset_eq:cN, \skip_gset_eq:Nc, \skip_gset_eq:cc}
-% All straightforward.
-% \begin{macrocode}
-\cs_new_protected:Npn \skip_set_eq:NN #1#2 { #1 = #2 }
-\cs_generate_variant:Nn \skip_set_eq:NN { c , Nc , cc }
-\cs_new_protected:Npn \skip_gset_eq:NN #1#2 { \tex_global:D #1 = #2 }
-\cs_generate_variant:Nn \skip_gset_eq:NN { c , Nc , cc }
-% \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}{\skip_add:Nn, \skip_add:cn}
-% \begin{macro}{\skip_gadd:Nn, \skip_gadd:cn}
-% \begin{macro}{\skip_sub:Nn, \skip_sub:cn}
-% \begin{macro}{\skip_gsub:Nn, \skip_gsub:cn}
-% Using |by| here deals with the (incorrect) case |\skip123|.
-% \begin{macrocode}
-\cs_new_protected:Npn \skip_add:Nn #1#2
- { \tex_advance:D #1 \tex_glueexpr:D #2 \scan_stop: }
-\cs_new_protected:Npn \skip_gadd:Nn #1#2
- { \tex_global:D \tex_advance:D #1 \tex_glueexpr:D #2 \scan_stop: }
-\cs_generate_variant:Nn \skip_add:Nn { c }
-\cs_generate_variant:Nn \skip_gadd:Nn { c }
-\cs_new_protected:Npn \skip_sub:Nn #1#2
- { \tex_advance:D #1 - \tex_glueexpr:D #2 \scan_stop: }
-\cs_new_protected:Npn \skip_gsub:Nn #1#2
- { \tex_global:D \tex_advance:D #1 - \tex_glueexpr:D #2 \scan_stop: }
-\cs_generate_variant:Nn \skip_sub:Nn { c }
-\cs_generate_variant:Nn \skip_gsub:Nn { c }
-% \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-%
-% \subsection{Skip expression conditionals}
-%
-% \begin{macro}[pTF]{\skip_if_eq:nn}
-% Comparing skips means doing two expansions to make strings, and then
-% testing them. As a result, only equality is tested.
-% \begin{macrocode}
-\prg_new_conditional:Npnn \skip_if_eq:nn #1#2 { p , T , F , TF }
- {
- \str_if_eq:eeTF { \skip_eval:n {#1} } { \skip_eval:n {#2} }
- { \prg_return_true: }
- { \prg_return_false: }
- }
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}[EXP,pTF]{\skip_if_finite:n}
-% \begin{macro}[EXP]{\@@_if_finite:wwNw}
-% With \eTeX{}, we have an easy access to the order of infinities of
-% the stretch and shrink components of a skip. However, to access
-% both, we either need to evaluate the expression twice, or evaluate
-% it, then call an auxiliary to extract both pieces of information
-% from the result. Since we are going to need an auxiliary anyways,
-% it is quicker to make it search for the string \texttt{fil} which
-% characterizes infinite glue.
-% \begin{macrocode}
-\cs_set_protected:Npn \@@_tmp:w #1
- {
- \prg_new_conditional:Npnn \skip_if_finite:n ##1 { p , T , F , TF }
- {
- \exp_after:wN \@@_if_finite:wwNw
- \skip_use:N \tex_glueexpr:D ##1 ; \prg_return_false:
- #1 ; \prg_return_true: \s_@@_stop
- }
- \cs_new:Npn \@@_if_finite:wwNw ##1 #1 ##2 ; ##3 ##4 \s_@@_stop {##3}
- }
-\exp_args:No \@@_tmp:w { \tl_to_str:n { fil } }
-% \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \subsection{Using \texttt{skip} expressions and variables}
-%
-% \begin{macro}{\skip_eval:n}
-% Evaluating a skip expression expandably.
-% \begin{macrocode}
-\cs_new:Npn \skip_eval:n #1
- { \skip_use:N \tex_glueexpr:D #1 \scan_stop: }
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\skip_use:N, \skip_use:c}
-% Accessing a \meta{skip}.
-% \begin{macrocode}
-\cs_new_eq:NN \skip_use:N \dim_use:N
-\cs_new_eq:NN \skip_use:c \dim_use:c
-% \end{macrocode}
-% \end{macro}
-%
-% \subsection{Inserting skips into the output}
-%
-% \begin{macro}{\skip_horizontal:N, \skip_horizontal:c, \skip_horizontal:n}
-% \begin{macro}{\skip_vertical:N, \skip_vertical:c, \skip_vertical:n}
-% Inserting skips.
-% \begin{macrocode}
-\cs_new_eq:NN \skip_horizontal:N \tex_hskip:D
-\cs_new:Npn \skip_horizontal:n #1
- { \skip_horizontal:N \tex_glueexpr:D #1 \scan_stop: }
-\cs_new_eq:NN \skip_vertical:N \tex_vskip:D
-\cs_new:Npn \skip_vertical:n #1
- { \skip_vertical:N \tex_glueexpr:D #1 \scan_stop: }
-\cs_generate_variant:Nn \skip_horizontal:N { c }
-\cs_generate_variant:Nn \skip_vertical:N { c }
-% \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \subsection{Viewing \texttt{skip} variables}
-%
-% \begin{macro}{\skip_show:N, \skip_show:c}
-% Diagnostics.
-% \begin{macrocode}
-\cs_new_eq:NN \skip_show:N \__kernel_register_show:N
-\cs_generate_variant:Nn \skip_show:N { c }
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\skip_show:n}
-% Diagnostics. We don't use the \TeX{} primitive \tn{showthe} to show
-% skip expressions: this gives a more unified output.
-% \begin{macrocode}
-\cs_new_protected:Npn \skip_show:n
- { \__kernel_msg_show_eval:Nn \skip_eval:n }
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\skip_log:N, \skip_log:c, \skip_log:n}
-% Diagnostics. Redirect output of \cs{skip_show:n} to the log.
-% \begin{macrocode}
-\cs_new_eq:NN \skip_log:N \__kernel_register_log:N
-\cs_new_eq:NN \skip_log:c \__kernel_register_log:c
-\cs_new_protected:Npn \skip_log:n
- { \__kernel_msg_log_eval:Nn \skip_eval:n }
-% \end{macrocode}
-% \end{macro}
-%
-% \subsection{Constant skips}
-%
-% \begin{macro}{\c_zero_skip, \c_max_skip}
-% Skips with no rubber component are just dimensions but need to terminate
-% correctly.
-% \begin{macrocode}
-\skip_const:Nn \c_zero_skip { \c_zero_dim }
-\skip_const:Nn \c_max_skip { \c_max_dim }
-% \end{macrocode}
-% \end{macro}
-%
-% \subsection{Scratch skips}
-%
-% \begin{variable}{\l_tmpa_skip, \l_tmpb_skip}
-% \begin{variable}{\g_tmpa_skip, \g_tmpb_skip}
-% We provide two local and two global scratch registers, maybe we
-% need more or less.
-% \begin{macrocode}
-\skip_new:N \l_tmpa_skip
-\skip_new:N \l_tmpb_skip
-\skip_new:N \g_tmpa_skip
-\skip_new:N \g_tmpb_skip
-% \end{macrocode}
-% \end{variable}
-% \end{variable}
-%
-% \subsection{Creating and initialising \texttt{muskip} variables}
-%
-% \begin{macro}{\muskip_new:N, \muskip_new:c}
-% And then we add muskips.
-% \begin{macrocode}
-\cs_new_protected:Npn \muskip_new:N #1
- {
- \__kernel_chk_if_free_cs:N #1
- \cs:w newmuskip \cs_end: #1
- }
-\cs_generate_variant:Nn \muskip_new:N { c }
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\muskip_const:Nn, \muskip_const:cn}
-% See \cs{skip_const:Nn}.
-% \begin{macrocode}
-\cs_new_protected:Npn \muskip_const:Nn #1#2
- {
- \muskip_new:N #1
- \tex_global:D #1 = \muskip_eval:n {#2} \scan_stop:
- }
-\cs_generate_variant:Nn \muskip_const:Nn { c }
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\muskip_zero:N, \muskip_zero:c}
-% \begin{macro}{\muskip_gzero:N, \muskip_gzero:c}
-% Reset the register to zero.
-% \begin{macrocode}
-\cs_new_protected:Npn \muskip_zero:N #1
- { #1 = \c_zero_muskip }
-\cs_new_protected:Npn \muskip_gzero:N #1
- { \tex_global:D #1 = \c_zero_muskip }
-\cs_generate_variant:Nn \muskip_zero:N { c }
-\cs_generate_variant:Nn \muskip_gzero:N { c }
-% \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}
-% {
-% \muskip_zero_new:N, \muskip_zero_new:c,
-% \muskip_gzero_new:N, \muskip_gzero_new:c
-% }
-% Create a register if needed, otherwise clear it.
-% \begin{macrocode}
-\cs_new_protected:Npn \muskip_zero_new:N #1
- { \muskip_if_exist:NTF #1 { \muskip_zero:N #1 } { \muskip_new:N #1 } }
-\cs_new_protected:Npn \muskip_gzero_new:N #1
- { \muskip_if_exist:NTF #1 { \muskip_gzero:N #1 } { \muskip_new:N #1 } }
-\cs_generate_variant:Nn \muskip_zero_new:N { c }
-\cs_generate_variant:Nn \muskip_gzero_new:N { c }
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}[pTF]{\muskip_if_exist:N, \muskip_if_exist:c}
-% Copies of the \texttt{cs} functions defined in \pkg{l3basics}.
-% \begin{macrocode}
-\prg_new_eq_conditional:NNn \muskip_if_exist:N \cs_if_exist:N
- { TF , T , F , p }
-\prg_new_eq_conditional:NNn \muskip_if_exist:c \cs_if_exist:c
- { TF , T , F , p }
-% \end{macrocode}
-% \end{macro}
-%
-% \subsection{Setting \texttt{muskip} variables}
-%
-% \begin{macro}{\muskip_set:Nn, \muskip_set:cn}
-% \begin{macro}{\muskip_gset:Nn, \muskip_gset:cn}
-% This should be pretty familiar.
-% \begin{macrocode}
-\cs_new_protected:Npn \muskip_set:Nn #1#2
- { #1 = \tex_muexpr:D #2 \scan_stop: }
-\cs_new_protected:Npn \muskip_gset:Nn #1#2
- { \tex_global:D #1 = \tex_muexpr:D #2 \scan_stop: }
-\cs_generate_variant:Nn \muskip_set:Nn { c }
-\cs_generate_variant:Nn \muskip_gset:Nn { c }
-% \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}
-% {
-% \muskip_set_eq:NN, \muskip_set_eq:cN,
-% \muskip_set_eq:Nc, \muskip_set_eq:cc
-% }
-% \begin{macro}
-% {
-% \muskip_gset_eq:NN, \muskip_gset_eq:cN,
-% \muskip_gset_eq:Nc, \muskip_gset_eq:cc
-% }
-% All straightforward.
-% \begin{macrocode}
-\cs_new_protected:Npn \muskip_set_eq:NN #1#2 { #1 = #2 }
-\cs_generate_variant:Nn \muskip_set_eq:NN { c , Nc , cc }
-\cs_new_protected:Npn \muskip_gset_eq:NN #1#2 { \tex_global:D #1 = #2 }
-\cs_generate_variant:Nn \muskip_gset_eq:NN { c , Nc , cc }
-% \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}{\muskip_add:Nn, \muskip_add:cn}
-% \begin{macro}{\muskip_gadd:Nn, \muskip_gadd:cn}
-% \begin{macro}{\muskip_sub:Nn, \muskip_sub:cn}
-% \begin{macro}{\muskip_gsub:Nn, \muskip_gsub:cn}
-% Using |by| here deals with the (incorrect) case |\muskip123|.
-% \begin{macrocode}
-\cs_new_protected:Npn \muskip_add:Nn #1#2
- { \tex_advance:D #1 \tex_muexpr:D #2 \scan_stop: }
-\cs_new_protected:Npn \muskip_gadd:Nn #1#2
- { \tex_global:D \tex_advance:D #1 \tex_muexpr:D #2 \scan_stop: }
-\cs_generate_variant:Nn \muskip_add:Nn { c }
-\cs_generate_variant:Nn \muskip_gadd:Nn { c }
-\cs_new_protected:Npn \muskip_sub:Nn #1#2
- { \tex_advance:D #1 - \tex_muexpr:D #2 \scan_stop: }
-\cs_new_protected:Npn \muskip_gsub:Nn #1#2
- { \tex_global:D \tex_advance:D #1 - \tex_muexpr:D #2 \scan_stop: }
-\cs_generate_variant:Nn \muskip_sub:Nn { c }
-\cs_generate_variant:Nn \muskip_gsub:Nn { c }
-% \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-%
-% \subsection{Using \texttt{muskip} expressions and variables}
-%
-% \begin{macro}{\muskip_eval:n}
-% Evaluating a muskip expression expandably.
-% \begin{macrocode}
-\cs_new:Npn \muskip_eval:n #1
- { \muskip_use:N \tex_muexpr:D #1 \scan_stop: }
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\muskip_use:N, \muskip_use:c}
-% Accessing a \meta{muskip}.
-% \begin{macrocode}
-\cs_new_eq:NN \muskip_use:N \dim_use:N
-\cs_new_eq:NN \muskip_use:c \dim_use:c
-% \end{macrocode}
-% \end{macro}
-%
-% \subsection{Viewing \texttt{muskip} variables}
-%
-% \begin{macro}{\muskip_show:N, \muskip_show:c}
-% Diagnostics.
-% \begin{macrocode}
-\cs_new_eq:NN \muskip_show:N \__kernel_register_show:N
-\cs_generate_variant:Nn \muskip_show:N { c }
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\muskip_show:n}
-% Diagnostics. We don't use the \TeX{} primitive \tn{showthe} to show
-% muskip expressions: this gives a more unified output.
-% \begin{macrocode}
-\cs_new_protected:Npn \muskip_show:n
- { \__kernel_msg_show_eval:Nn \muskip_eval:n }
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\muskip_log:N, \muskip_log:c, \muskip_log:n}
-% Diagnostics. Redirect output of \cs{muskip_show:n} to the log.
-% \begin{macrocode}
-\cs_new_eq:NN \muskip_log:N \__kernel_register_log:N
-\cs_new_eq:NN \muskip_log:c \__kernel_register_log:c
-\cs_new_protected:Npn \muskip_log:n
- { \__kernel_msg_log_eval:Nn \muskip_eval:n }
-% \end{macrocode}
-% \end{macro}
-%
-% \subsection{Constant muskips}
-%
-% \begin{macro}{\c_zero_muskip}
-% \begin{macro}{\c_max_muskip}
-% Constant muskips given by their value.
-% \begin{macrocode}
-\muskip_const:Nn \c_zero_muskip { 0 mu }
-\muskip_const:Nn \c_max_muskip { 16383.99999 mu }
-% \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \subsection{Scratch muskips}
-%
-% \begin{variable}{\l_tmpa_muskip, \l_tmpb_muskip}
-% \begin{variable}{\g_tmpa_muskip, \g_tmpb_muskip}
-% We provide two local and two global scratch registers, maybe we
-% need more or less.
-% \begin{macrocode}
-\muskip_new:N \l_tmpa_muskip
-\muskip_new:N \l_tmpb_muskip
-\muskip_new:N \g_tmpa_muskip
-\muskip_new:N \g_tmpb_muskip
-% \end{macrocode}
-% \end{variable}
-% \end{variable}
-%
-% \begin{macrocode}
-%</package>
-% \end{macrocode}
-%
-% \end{implementation}
-%
-% \PrintIndex