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-% \iffalse meta-comment
-%
-%% File: l3int.dtx
-%
-% Copyright (C) 1990-2024 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{l3int} module\\ Integers^^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}
-%
-% Calculation and comparison of integer values can be carried out
-% using literal numbers, \texttt{int} registers, constants and
-% integers stored in token list variables. The standard operators
-% \texttt{+}, \texttt{-}, \texttt{/} and \texttt{*} and
-% parentheses can be used within such expressions to carry
-% arithmetic operations. This module carries out these functions
-% on \emph{integer expressions} (\enquote{\meta{int expr}}).
-%
-% \section{Integer expressions}
-%
-% Throughout this module, (almost) all \texttt{n}-type argument allow
-% for an \meta{intexpr} argument with the following syntax. The
-% \meta{integer expression} should consist,
-% after expansion, of \texttt{+}, \texttt{-}, \texttt{*}, \texttt{/},
-% \texttt{(}, \texttt{)} and of course integer operands. The result
-% is calculated by applying standard mathematical rules with the
-% following peculiarities:
-% \begin{itemize}
-% \item \texttt{/} denotes division rounded to the closest integer with
-% ties rounded away from zero;
-% \item there is an error and the overall expression evaluates to zero
-% whenever the absolute value of any intermediate result exceeds
-% $2^{31}-1$, except in the case of scaling operations
-% $a$\texttt{*}$b$\texttt{/}$c$, for which $a$\texttt{*}$b$ may be
-% arbitrarily large (but the operands $a$, $b$, $c$ are still
-% constrained to an absolute value at most $2^{31}-1$);
-% \item parentheses may not appear after unary \texttt{+} or
-% \texttt{-}, namely placing \texttt{+(} or \texttt{-(} at the start
-% of an expression or after \texttt{+}, \texttt{-}, \texttt{*},
-% \texttt{/} or~\texttt{(} leads to an error.
-% \end{itemize}
-% Each integer operand can be either an integer variable (with no need
-% for \cs{int_use:N}) or an integer denotation. For example both
-% \begin{verbatim}
-% \int_show:n { 5 + 4 * 3 - ( 3 + 4 * 5 ) }
-% \end{verbatim}
-% and
-% \begin{verbatim}
-% \tl_new:N \l_my_tl
-% \tl_set:Nn \l_my_tl { 5 }
-% \int_new:N \l_my_int
-% \int_set:Nn \l_my_int { 4 }
-% \int_show:n { \l_my_tl + \l_my_int * 3 - ( 3 + 4 * 5 ) }
-% \end{verbatim}
-% show the same result $-6$ because \cs[no-index]{l_my_tl} expands to
-% the integer denotation~|5| while the integer variable \cs[no-index]{l_my_int}
-% takes the value~$4$. As the \meta{integer expression} is fully
-% expanded from left to right during evaluation, fully expandable and
-% restricted-expandable functions can both be used, and \cs{exp_not:n}
-% and its variants have no effect while \cs{exp_not:N} may incorrectly
-% interrupt the expression.
-% \begin{texnote}
-% Exactly two expansions are needed to evaluate \cs{int_eval:n}.
-% The result is \emph{not} an \meta{internal integer}, and therefore
-% should be terminated by a space if used in \cs{int_value:w} or in
-% a \TeX{}-style integer assignment.
-%
-% As all \TeX{} integers, integer operands can also be:
-% \tn{value}\Arg{\LaTeXe{} counter}; dimension or skip variables,
-% converted to integers in~\texttt{sp}; the character code of some
-% character given as \texttt{`}\meta{char} or
-% \texttt{`\textbackslash}\meta{char}; octal numbers given as
-% \texttt{'} followed by digits from \texttt{0} to \texttt{7}; or
-% hexadecimal numbers given as |"| followed by digits and upper case
-% letters from \texttt{A} to~\texttt{F}.
-% \end{texnote}
-%
-% \begin{function}[EXP]{\int_eval:n}
-% \begin{syntax}
-% \cs{int_eval:n} \Arg{int expr}
-% \end{syntax}
-% Evaluates the \meta{int expr} and leaves the result in the
-% input stream as an integer denotation: for positive results an
-% explicit sequence of decimal digits not starting with~\texttt{0},
-% for negative results \texttt{-}~followed by such a sequence, and
-% \texttt{0}~for zero. The \meta{int expr} should consist,
-% after expansion, of \texttt{+}, \texttt{-}, \texttt{*}, \texttt{/},
-% \texttt{(}, \texttt{)} and of course integer operands. The result
-% is calculated by applying standard mathematical rules with the
-% following peculiarities:
-% \begin{itemize}
-% \item \texttt{/} denotes division rounded to the closest integer with
-% ties rounded away from zero;
-% \item there is an error and the overall expression evaluates to zero
-% whenever the absolute value of any intermediate result exceeds
-% $2^{31}-1$, except in the case of scaling operations
-% $a$\texttt{*}$b$\texttt{/}$c$, for which $a$\texttt{*}$b$ may be
-% arbitrarily large;
-% \item parentheses may not appear after unary \texttt{+} or
-% \texttt{-}, namely placing \texttt{+(} or \texttt{-(} at the start
-% of an expression or after \texttt{+}, \texttt{-}, \texttt{*},
-% \texttt{/} or~\texttt{(} leads to an error.
-% \end{itemize}
-% Each integer operand can be either an integer variable (with no need
-% for \cs{int_use:N}) or an integer denotation. For example both
-% \begin{verbatim}
-% \int_eval:n { 5 + 4 * 3 - ( 3 + 4 * 5 ) }
-% \end{verbatim}
-% and
-% \begin{verbatim}
-% \tl_new:N \l_my_tl
-% \tl_set:Nn \l_my_tl { 5 }
-% \int_new:N \l_my_int
-% \int_set:Nn \l_my_int { 4 }
-% \int_eval:n { \l_my_tl + \l_my_int * 3 - ( 3 + 4 * 5 ) }
-% \end{verbatim}
-% evaluate to $-6$ because \cs[no-index]{l_my_tl} expands to the
-% integer denotation~|5|. As the \meta{int expr} is fully
-% expanded from left to right during evaluation, fully expandable and
-% restricted-expandable functions can both be used, and \cs{exp_not:n}
-% and its variants have no effect while \cs{exp_not:N} may incorrectly
-% interrupt the expression.
-% \begin{texnote}
-% Exactly two expansions are needed to evaluate \cs{int_eval:n}.
-% The result is \emph{not} an \meta{internal integer}, and therefore
-% requires suitable termination if used in a \TeX{}-style integer
-% assignment.
-%
-% As all \TeX{} integers, integer operands can also be dimension or
-% skip variables, converted to integers in~\texttt{sp}, or octal
-% numbers given as \texttt{'} followed by digits other than
-% \texttt{8} and \texttt{9}, or hexadecimal numbers given as
-% |"| followed by digits or upper case letters from
-% \texttt{A} to~\texttt{F}, or the character code of some character
-% or one-character control sequence, given as \texttt{`}\meta{char}.
-% \end{texnote}
-% \end{function}
-%
-% \begin{function}[EXP, added = 2018-03-30]{\int_eval:w}
-% \begin{syntax}
-% \cs{int_eval:w} \meta{int expr}
-% \end{syntax}
-% Evaluates the \meta{int expr} as described for
-% \cs{int_eval:n}. The end of the expression is the first token
-% encountered that cannot form part of such an expression. If that
-% token is \cs{scan_stop:} it is removed, otherwise not. Spaces do
-% \emph{not} terminate the expression. However, spaces terminate
-% explict integers, and this may terminate the expression: for
-% instance, \cs{int_eval:w} \verb*|1 + 1 9| (with explicit space
-% tokens inserted using |~| in a code setting) expands to \texttt{29}
-% since the digit~\texttt{9} is not part of the expression. Expansion
-% details, etc., are as given for \cs{int_eval:n}.
-% \end{function}
-%
-% \begin{function}[EXP, added = 2018-11-03]{\int_sign:n}
-% \begin{syntax}
-% \cs{int_sign:n} \Arg{int expr}
-% \end{syntax}
-% Evaluates the \meta{int expr} then leaves $1$ or $0$ or
-% $-1$ in the input stream according to the sign of the result.
-% \end{function}
-%
-% \begin{function}[EXP, updated = 2012-09-26]{\int_abs:n}
-% \begin{syntax}
-% \cs{int_abs:n} \Arg{int expr}
-% \end{syntax}
-% Evaluates the \meta{int expr} as described for
-% \cs{int_eval:n} and leaves the absolute value of the result in
-% the input stream as an \meta{integer denotation} after two
-% expansions.
-% \end{function}
-%
-% \begin{function}[EXP, updated = 2012-09-26]{\int_div_round:nn}
-% \begin{syntax}
-% \cs{int_div_round:nn} \Arg{int expr_1} \Arg{int expr_2}
-% \end{syntax}
-% Evaluates the two \meta{int expr}s as described earlier,
-% then divides the first value by the second, and rounds the result
-% to the closest integer. Ties are rounded away from zero.
-% Note that this is identical to using
-% |/| directly in an \meta{int expr}. The result is left in
-% the input stream as an \meta{integer denotation} after two expansions.
-% \end{function}
-%
-% \begin{function}[EXP, updated = 2012-02-09]{\int_div_truncate:nn}
-% \begin{syntax}
-% \cs{int_div_truncate:nn} \Arg{int expr_1} \Arg{int expr_2}
-% \end{syntax}
-% Evaluates the two \meta{int expr}s as described earlier,
-% then divides the first value by the second, and rounds the result
-% towards zero. Note that division using |/|
-% rounds to the closest integer instead.
-% The result is left in the input stream as an
-% \meta{integer denotation} after two expansions.
-% \end{function}
-%
-% \begin{function}[EXP, updated = 2012-09-26]{\int_max:nn, \int_min:nn}
-% \begin{syntax}
-% \cs{int_max:nn} \Arg{int expr_1} \Arg{int expr_2}
-% \cs{int_min:nn} \Arg{int expr_1} \Arg{int expr_2}
-% \end{syntax}
-% Evaluates the \meta{int expr}s as described for
-% \cs{int_eval:n} and leaves either the larger or smaller value
-% in the input stream as an \meta{integer denotation} after two
-% expansions.
-% \end{function}
-%
-% \begin{function}[EXP, updated = 2012-09-26]{\int_mod:nn}
-% \begin{syntax}
-% \cs{int_mod:nn} \Arg{int expr_1} \Arg{int expr_2}
-% \end{syntax}
-% Evaluates the two \meta{int expr}s as described earlier,
-% then calculates the integer remainder of dividing the first
-% expression by the second. This is obtained by subtracting
-% \cs{int_div_truncate:nn} \Arg{int expr_1} \Arg{int expr_2} times
-% \meta{int expr_2} from \meta{int expr_1}. Thus, the result has the
-% same sign as \meta{int expr_1} and its absolute value is strictly
-% less than that of \meta{int expr_2}. The result is left in the input
-% stream as an \meta{integer denotation} after two expansions.
-% \end{function}
-%
-% \section{Creating and initialising integers}
-%
-% \begin{function}{\int_new:N, \int_new:c}
-% \begin{syntax}
-% \cs{int_new:N} \meta{integer}
-% \end{syntax}
-% Creates a new \meta{integer} or raises an error if the name is
-% already taken. The declaration is global. The \meta{integer} is
-% initially equal to $0$.
-% \end{function}
-%
-% \begin{function}[updated = 2011-10-22]{\int_const:Nn, \int_const:cn}
-% \begin{syntax}
-% \cs{int_const:Nn} \meta{integer} \Arg{int expr}
-% \end{syntax}
-% Creates a new constant \meta{integer} or raises an error if the name
-% is already taken. The value of the \meta{integer} is set
-% globally to the \meta{int expr}.
-% \end{function}
-%
-% \begin{function}{\int_zero:N, \int_zero:c, \int_gzero:N, \int_gzero:c}
-% \begin{syntax}
-% \cs{int_zero:N} \meta{integer}
-% \end{syntax}
-% Sets \meta{integer} to $0$.
-% \end{function}
-%
-% \begin{function}[added = 2011-12-13]
-% {\int_zero_new:N, \int_zero_new:c, \int_gzero_new:N, \int_gzero_new:c}
-% \begin{syntax}
-% \cs{int_zero_new:N} \meta{integer}
-% \end{syntax}
-% Ensures that the \meta{integer} exists globally by applying
-% \cs{int_new:N} if necessary, then applies
-% \cs[index=int_zero:N]{int_(g)zero:N} to leave
-% the \meta{integer} set to zero.
-% \end{function}
-%
-% \begin{function}
-% {
-% \int_set_eq:NN, \int_set_eq:cN, \int_set_eq:Nc, \int_set_eq:cc,
-% \int_gset_eq:NN, \int_gset_eq:cN, \int_gset_eq:Nc, \int_gset_eq:cc
-% }
-% \begin{syntax}
-% \cs{int_set_eq:NN} \meta{integer_1} \meta{integer_2}
-% \end{syntax}
-% Sets the content of \meta{integer_1} equal to that of
-% \meta{integer_2}.
-% \end{function}
-%
-% \begin{function}[EXP, pTF, added=2012-03-03]
-% {\int_if_exist:N, \int_if_exist:c}
-% \begin{syntax}
-% \cs{int_if_exist_p:N} \meta{int}
-% \cs{int_if_exist:NTF} \meta{int} \Arg{true code} \Arg{false code}
-% \end{syntax}
-% Tests whether the \meta{int} is currently defined. This does not
-% check that the \meta{int} really is an integer variable.
-% \end{function}
-%
-% \section{Setting and incrementing integers}
-%
-% \begin{function}[updated = 2011-10-22]
-% {\int_add:Nn, \int_add:cn, \int_gadd:Nn, \int_gadd:cn}
-% \begin{syntax}
-% \cs{int_add:Nn} \meta{integer} \Arg{int expr}
-% \end{syntax}
-% Adds the result of the \meta{int expr} to the current
-% content of the \meta{integer}.
-% \end{function}
-%
-% \begin{function}{\int_decr:N, \int_decr:c, \int_gdecr:N, \int_gdecr:c}
-% \begin{syntax}
-% \cs{int_decr:N} \meta{integer}
-% \end{syntax}
-% Decreases the value stored in \meta{integer} by $1$.
-% \end{function}
-%
-% \begin{function}{\int_incr:N, \int_incr:c, \int_gincr:N, \int_gincr:c}
-% \begin{syntax}
-% \cs{int_incr:N} \meta{integer}
-% \end{syntax}
-% Increases the value stored in \meta{integer} by $1$.
-% \end{function}
-%
-% \begin{function}[updated = 2011-10-22]
-% {\int_set:Nn, \int_set:cn, \int_gset:Nn, \int_gset:cn}
-% \begin{syntax}
-% \cs{int_set:Nn} \meta{integer} \Arg{int expr}
-% \end{syntax}
-% Sets \meta{integer} to the value of \meta{int expr},
-% which must evaluate to an integer (as described for
-% \cs{int_eval:n}).
-% \end{function}
-%
-% \begin{function}[updated = 2011-10-22]
-% {\int_sub:Nn, \int_sub:cn, \int_gsub:Nn, \int_gsub:cn}
-% \begin{syntax}
-% \cs{int_sub:Nn} \meta{integer} \Arg{int expr}
-% \end{syntax}
-% Subtracts the result of the \meta{int expr} from the
-% current content of the \meta{integer}.
-% \end{function}
-%
-% \section{Using integers}
-%
-% \begin{function}[updated = 2011-10-22, EXP]{\int_use:N, \int_use:c}
-% \begin{syntax}
-% \cs{int_use:N} \meta{integer}
-% \end{syntax}
-% Recovers the content of an \meta{integer} 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 an
-% \meta{integer} is required (such as in the first and third arguments
-% of \cs{int_compare:nNnTF}).
-% \begin{texnote}
-% \cs{int_use:N} is the \TeX{} primitive \tn{the}: this is one of
-% several \LaTeX3 names for this primitive.
-% \end{texnote}
-% \end{function}
-%
-% \section{Integer expression conditionals}
-%
-% \begin{function}[EXP,pTF]{\int_compare:nNn}
-% \begin{syntax}
-% \cs{int_compare_p:nNn} \Arg{int expr_1} \meta{relation} \Arg{int expr_2} \\
-% \cs{int_compare:nNnTF}
-% ~~\Arg{int expr_1} \meta{relation} \Arg{int expr_2}
-% ~~\Arg{true code} \Arg{false code}
-% \end{syntax}
-% This function first evaluates each of the \meta{int expr}s
-% as described for \cs{int_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{int_compare:nTF} but around
-% $5$~times faster.
-% \end{function}
-%
-% \begin{function}[updated = 2013-01-13, EXP, pTF]{\int_compare:n}
-% \begin{syntax}
-% \cs{int_compare_p:n} \\
-% ~~\{ \\
-% ~~~~\meta{int expr_1} \meta{relation_1} \\
-% ~~~~\ldots{} \\
-% ~~~~\meta{int expr_N} \meta{relation_N} \\
-% ~~~~\meta{int expr_{N+1}} \\
-% ~~\} \\
-% \cs{int_compare:nTF}
-% ~~\{ \\
-% ~~~~\meta{int expr_1} \meta{relation_1} \\
-% ~~~~\ldots{} \\
-% ~~~~\meta{int expr_N} \meta{relation_N} \\
-% ~~~~\meta{int expr_{N+1}} \\
-% ~~\} \\
-% ~~\Arg{true code} \Arg{false code}
-% \end{syntax}
-% This function evaluates the \meta{int expr}s as described
-% for \cs{int_eval:n} and compares consecutive result using the
-% corresponding \meta{relation}, namely it compares \meta{int expr_1}
-% and \meta{int expr_2} using the \meta{relation_1}, then
-% \meta{int expr_2} and \meta{int expr_3} using the \meta{relation_2},
-% until finally comparing \meta{int expr_N} and \meta{int expr_{N+1}}
-% using the \meta{relation_N}. The test yields \texttt{true} if all
-% comparisons are \texttt{true}. Each \meta{int expr} is
-% evaluated only once, and the evaluation is lazy, in the sense that
-% if one comparison is \texttt{false}, then no other \meta{integer
-% expression} 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{int_compare:nNnTF} but
-% around $5$~times slower.
-% \end{function}
-%
-% \begin{function}[added = 2013-07-24, EXP, noTF]{\int_case:nn}
-% \begin{syntax}
-% \cs{int_case:nnTF} \Arg{test int expr} \\
-% ~~|{| \\
-% ~~~~\Arg{int expr case_1} \Arg{code case_1} \\
-% ~~~~\Arg{int expr case_2} \Arg{code case_2} \\
-% ~~~~\ldots \\
-% ~~~~\Arg{int expr case_n} \Arg{code case_n} \\
-% ~~|}| \\
-% ~~\Arg{true code}
-% ~~\Arg{false code}
-% \end{syntax}
-% This function evaluates the \meta{test int expr} and
-% compares this in turn to each of the
-% \meta{int 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{int_case:nn}, which does nothing if there is no match, is also
-% available. For example
-% \begin{verbatim}
-% \int_case:nnF
-% { 2 * 5 }
-% {
-% { 5 } { Small }
-% { 4 + 6 } { Medium }
-% { -2 * 10 } { Negative }
-% }
-% { No idea! }
-% \end{verbatim}
-% leaves \enquote{\texttt{Medium}} in the input stream.
-% \end{function}
-%
-% \begin{function}[EXP,pTF]{\int_if_even:n, \int_if_odd:n}
-% \begin{syntax}
-% \cs{int_if_odd_p:n} \Arg{int expr}
-% \cs{int_if_odd:nTF} \Arg{int expr}
-% ~~\Arg{true code} \Arg{false code}
-% \end{syntax}
-% This function first evaluates the \meta{int expr}
-% as described for \cs{int_eval:n}. It then evaluates if this
-% is odd or even, as appropriate.
-% \end{function}
-%
-% \begin{function}[EXP,pTF, added = 2023-05-17]{\int_if_zero:n}
-% \begin{syntax}
-% \cs{int_if_zero_p:n} \Arg{int expr}
-% \cs{int_if_zero:nTF} \Arg{int expr}
-% ~~\Arg{true code} \Arg{false code}
-% \end{syntax}
-% This function first evaluates the \meta{int expr}
-% as described for \cs{int_eval:n}. It then evaluates if this
-% is zero or not.
-% \end{function}
-%
-% \section{Integer expression loops}
-%
-% \begin{function}[rEXP]{\int_do_until:nNnn}
-% \begin{syntax}
-% \cs{int_do_until:nNnn} \Arg{int expr_1} \meta{relation} \Arg{int 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{int expr}s as described for \cs{int_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]{\int_do_while:nNnn}
-% \begin{syntax}
-% \cs{int_do_while:nNnn} \Arg{int expr_1} \meta{relation} \Arg{int 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{int expr}s as described for \cs{int_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]{\int_until_do:nNnn}
-% \begin{syntax}
-% \cs{int_until_do:nNnn} \Arg{int expr_1} \meta{relation} \Arg{int expr_2} \Arg{code}
-% \end{syntax}
-% Evaluates the relationship between the two \meta{int expr}s
-% as described for \cs{int_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]{\int_while_do:nNnn}
-% \begin{syntax}
-% \cs{int_while_do:nNnn} \Arg{int expr_1} \meta{relation} \Arg{int expr_2} \Arg{code}
-% \end{syntax}
-% Evaluates the relationship between the two \meta{int expr}s
-% as described for \cs{int_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]{\int_do_until:nn}
-% \begin{syntax}
-% \cs{int_do_until:nn} \Arg{integer relation} \Arg{code}
-% \end{syntax}
-% Places the \meta{code} in the input stream for \TeX{} to process, and
-% then evaluates the \meta{integer relation}
-% as described for \cs{int_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]{\int_do_while:nn}
-% \begin{syntax}
-% \cs{int_do_while:nn} \Arg{integer relation} \Arg{code}
-% \end{syntax}
-% Places the \meta{code} in the input stream for \TeX{} to process, and
-% then evaluates the \meta{integer relation}
-% as described for \cs{int_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]{\int_until_do:nn}
-% \begin{syntax}
-% \cs{int_until_do:nn} \Arg{integer relation} \Arg{code}
-% \end{syntax}
-% Evaluates the \meta{integer relation}
-% as described for \cs{int_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]{\int_while_do:nn}
-% \begin{syntax}
-% \cs{int_while_do:nn} \Arg{integer relation} \Arg{code}
-% \end{syntax}
-% Evaluates the \meta{integer relation}
-% as described for \cs{int_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{Integer step functions}
-%
-% \begin{function}[added = 2012-06-04, updated = 2018-04-22, rEXP]
-% {\int_step_function:nN, \int_step_function:nnN, \int_step_function:nnnN}
-% \begin{syntax}
-% \cs{int_step_function:nN} \Arg{final value} \meta{function}
-% \cs{int_step_function:nnN} \Arg{initial value} \Arg{final value} \meta{function}
-% \cs{int_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 integer 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 numerical argument. For example
-% \begin{verbatim}
-% \cs_set:Npn \my_func:n #1 { [I~saw~#1] \quad }
-% \int_step_function:nnnN { 1 } { 1 } { 5 } \my_func:n
-% \end{verbatim}
-% would print
-% \begin{quote}
-% [I saw 1] \quad
-% [I saw 2] \quad
-% [I saw 3] \quad
-% [I saw 4] \quad
-% [I saw 5] \quad
-% \end{quote}
-%
-% The functions \cs{int_step_function:nN} and \cs{int_step_function:nnN}
-% both use a fixed \meta{step} of $1$, and in the case of
-% \cs{int_step_function:nN} the \meta{initial value} is also fixed as
-% $1$. These functions are provided as simple short-cuts for code clarity.
-% \end{function}
-%
-% \begin{function}[added = 2012-06-04, updated = 2018-04-22]
-% {\int_step_inline:nn, \int_step_inline:nnn, \int_step_inline:nnnn}
-% \begin{syntax}
-% \cs{int_step_inline:nn} \Arg{final value} \Arg{code}
-% \cs{int_step_inline:nnn} \Arg{initial value} \Arg{final value} \Arg{code}
-% \cs{int_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 integer 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|).
-%
-% The functions \cs{int_step_inline:nn} and \cs{int_step_inline:nnn}
-% both use a fixed \meta{step} of $1$, and in the case of
-% \cs{int_step_inline:nn} the \meta{initial value} is also fixed as
-% $1$. These functions are provided as simple short-cuts for code clarity.
-% \end{function}
-%
-% \begin{function}[added = 2012-06-04, updated = 2018-04-22]
-% {\int_step_variable:nNn, \int_step_variable:nnNn, \int_step_variable:nnnNn}
-% \begin{syntax}
-% \cs{int_step_variable:nNn} \Arg{final value} \meta{tl~var} \Arg{code}
-% \cs{int_step_variable:nnNn} \Arg{initial value} \Arg{final value} \meta{tl~var} \Arg{code}
-% \cs{int_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 integer 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}.
-%
-% The functions \cs{int_step_variable:nNn} and \cs{int_step_variable:nnNn}
-% both use a fixed \meta{step} of $1$, and in the case of
-% \cs{int_step_variable:nNn} the \meta{initial value} is also fixed as
-% $1$. These functions are provided as simple short-cuts for code clarity.
-% \end{function}
-%
-% \section{Formatting integers}
-%
-% Integers can be placed into the output stream with formatting. These
-% conversions apply to any integer expressions.
-%
-% \begin{function}[updated = 2011-10-22, EXP]{\int_to_arabic:n, \int_to_arabic:v}
-% \begin{syntax}
-% \cs{int_to_arabic:n} \Arg{int expr}
-% \end{syntax}
-% Places the value of the \meta{int expr} in the input
-% stream as digits, with category code $12$ (other).
-% \end{function}
-%
-% \begin{function}[updated = 2011-09-17, EXP]{\int_to_alph:n, \int_to_Alph:n}
-% \begin{syntax}
-% \cs{int_to_alph:n} \Arg{int expr}
-% \end{syntax}
-% Evaluates the \meta{int expr} and converts the result
-% into a series of letters, which are then left in the input stream.
-% The conversion rule uses the $26$ letters of the English
-% alphabet, in order, adding letters when necessary to increase the total
-% possible range of representable numbers. Thus
-% \begin{verbatim}
-% \int_to_alph:n { 1 }
-% \end{verbatim}
-% places |a| in the input stream,
-% \begin{verbatim}
-% \int_to_alph:n { 26 }
-% \end{verbatim}
-% is represented as |z| and
-% \begin{verbatim}
-% \int_to_alph:n { 27 }
-% \end{verbatim}
-% is converted to |aa|. For conversions using other alphabets, use
-% \cs{int_to_symbols:nnn} to define an alphabet-specific
-% function. The basic \cs{int_to_alph:n} and \cs{int_to_Alph:n}
-% functions should not be modified.
-% The resulting tokens are digits with category code $12$ (other) and
-% letters with category code $11$ (letter).
-% \end{function}
-%
-% \begin{function}[updated = 2011-09-17, EXP]{\int_to_symbols:nnn}
-% \begin{syntax}
-% \cs{int_to_symbols:nnn}
-% ~~\Arg{int expr} \Arg{total symbols}
-% ~~\Arg{value to symbol mapping}
-% \end{syntax}
-% This is the low-level function for conversion of an
-% \meta{int expr} into a symbolic form (often
-% letters). The \meta{total symbols} available should be given
-% as an integer expression. Values are actually converted to symbols
-% according to the \meta{value to symbol mapping}. This should be given
-% as \meta{total symbols} pairs of entries, a number and the
-% appropriate symbol. Thus the \cs{int_to_alph:n} function is defined
-% as
-% \begin{verbatim}
-% \cs_new:Npn \int_to_alph:n #1
-% {
-% \int_to_symbols:nnn {#1} { 26 }
-% {
-% { 1 } { a }
-% { 2 } { b }
-% ...
-% { 26 } { z }
-% }
-% }
-% \end{verbatim}
-% \end{function}
-%
-% \begin{function}[added = 2014-02-11, EXP]{\int_to_bin:n}
-% \begin{syntax}
-% \cs{int_to_bin:n} \Arg{int expr}
-% \end{syntax}
-% Calculates the value of the \meta{int expr} and places
-% the binary representation of the result in the input stream.
-% \end{function}
-%
-% \begin{function}[added = 2014-02-11, EXP]{\int_to_hex:n, \int_to_Hex:n}
-% \begin{syntax}
-% \cs{int_to_hex:n} \Arg{int expr}
-% \end{syntax}
-% Calculates the value of the \meta{int expr} and places
-% the hexadecimal (base~$16$) representation of the result in the
-% input stream. Letters are used for digits beyond~$9$: lower
-% case letters for \cs{int_to_hex:n} and upper case ones for
-% \cs{int_to_Hex:n}.
-% The resulting tokens are digits with category code $12$ (other) and
-% letters with category code $11$ (letter).
-% \end{function}
-%
-% \begin{function}[added = 2014-02-11, EXP]{\int_to_oct:n}
-% \begin{syntax}
-% \cs{int_to_oct:n} \Arg{int expr}
-% \end{syntax}
-% Calculates the value of the \meta{int expr} and places
-% the octal (base~$8$) representation of the result in the input
-% stream.
-% The resulting tokens are digits with category code $12$ (other) and
-% letters with category code $11$ (letter).
-% \end{function}
-%
-% \begin{function}[updated = 2014-02-11, EXP]
-% {\int_to_base:nn, \int_to_Base:nn}
-% \begin{syntax}
-% \cs{int_to_base:nn} \Arg{int expr} \Arg{base}
-% \end{syntax}
-% Calculates the value of the \meta{int expr} and
-% converts it into the appropriate representation in the \meta{base};
-% the later may be given as an integer expression. For bases greater
-% than $10$ the higher \enquote{digits} are represented by
-% letters from the English alphabet: lower
-% case letters for \cs{int_to_base:n} and upper case ones for
-% \cs{int_to_Base:n}.
-% The maximum \meta{base} value is $36$.
-% The resulting tokens are digits with category code $12$ (other) and
-% letters with category code $11$ (letter).
-% \begin{texnote}
-% This is a generic version of \cs{int_to_bin:n}, \emph{etc.}
-% \end{texnote}
-% \end{function}
-%
-% \begin{function}[updated = 2011-10-22, rEXP]{\int_to_roman:n, \int_to_Roman:n}
-% \begin{syntax}
-% \cs{int_to_roman:n} \Arg{int expr}
-% \end{syntax}
-% Places the value of the \meta{int expr} in the input
-% stream as Roman numerals, either lower case (\cs{int_to_roman:n}) or
-% upper case (\cs{int_to_Roman:n}). If the value is negative or zero,
-% the output is empty. The Roman numerals are letters with category
-% code $11$ (letter). The letters used are |mdclxvi|, repeated as
-% needed: the notation with bars (such as $\bar{\mbox{v}}$ for $5000$)
-% is \emph{not} used. For instance \cs{int_to_roman:n} |{| 8249 |}|
-% expands to |mmmmmmmmccxlix|.
-% \end{function}
-%
-% \section{Converting from other formats to integers}
-%
-% \begin{function}[updated = 2014-08-25, EXP]{\int_from_alph:n}
-% \begin{syntax}
-% \cs{int_from_alph:n} \Arg{letters}
-% \end{syntax}
-% Converts the \meta{letters} into the integer (base~$10$)
-% representation and leaves this in the input stream. The
-% \meta{letters} are first converted to a string, with no expansion.
-% Lower and upper case letters from the English alphabet may be used,
-% with \enquote{a} equal to $1$ through to \enquote{z} equal to $26$.
-% The function also accepts a leading sign, made of |+| and~|-|. This
-% is the inverse function of \cs{int_to_alph:n} and
-% \cs{int_to_Alph:n}.
-% \end{function}
-%
-% \begin{function}[added = 2014-02-11, updated = 2014-08-25, EXP]
-% {\int_from_bin:n}
-% \begin{syntax}
-% \cs{int_from_bin:n} \Arg{binary number}
-% \end{syntax}
-% Converts the \meta{binary number} into the integer (base~$10$)
-% representation and leaves this in the input stream.
-% The \meta{binary number} is first converted to a string, with no
-% expansion. The function accepts a leading sign, made of |+|
-% and~|-|, followed by binary digits. This is the inverse function
-% of \cs{int_to_bin:n}.
-% \end{function}
-%
-% \begin{function}[added = 2014-02-11, updated = 2014-08-25, EXP]
-% {\int_from_hex:n}
-% \begin{syntax}
-% \cs{int_from_hex:n} \Arg{hexadecimal number}
-% \end{syntax}
-% Converts the \meta{hexadecimal number} into the integer (base~$10$)
-% representation and leaves this in the input stream. Digits greater
-% than $9$ may be represented in the \meta{hexadecimal number} by
-% upper or lower case letters. The \meta{hexadecimal number} is first
-% converted to a string, with no expansion. The function also accepts
-% a leading sign, made of |+| and~|-|. This is the inverse function
-% of \cs{int_to_hex:n} and \cs{int_to_Hex:n}.
-% \end{function}
-%
-% \begin{function}[added = 2014-02-11, updated = 2014-08-25, EXP]
-% {\int_from_oct:n}
-% \begin{syntax}
-% \cs{int_from_oct:n} \Arg{octal number}
-% \end{syntax}
-% Converts the \meta{octal number} into the integer (base~$10$)
-% representation and leaves this in the input stream.
-% The \meta{octal number} is first converted to a string, with no
-% expansion. The function accepts a leading sign, made of |+|
-% and~|-|, followed by octal digits. This is the inverse function
-% of \cs{int_to_oct:n}.
-% \end{function}
-%
-% \begin{function}[updated = 2014-08-25, updated = 2014-08-25, EXP]
-% {\int_from_roman:n}
-% \begin{syntax}
-% \cs{int_from_roman:n} \Arg{roman numeral}
-% \end{syntax}
-% Converts the \meta{roman numeral} into the integer (base~$10$)
-% representation and leaves this in the input stream. The \meta{roman
-% numeral} is first converted to a string, with no expansion. The
-% \meta{roman numeral} may be in upper or lower case; if the numeral
-% contains characters besides |mdclxvi| or |MDCLXVI| then the
-% resulting value is $-1$. This is the inverse function of
-% \cs{int_to_roman:n} and \cs{int_to_Roman:n}.
-% \end{function}
-%
-% \begin{function}[updated = 2014-08-25, EXP]{\int_from_base:nn}
-% \begin{syntax}
-% \cs{int_from_base:nn} \Arg{number} \Arg{base}
-% \end{syntax}
-% Converts the \meta{number} expressed in \meta{base} into the
-% appropriate value in base $10$. The \meta{number} is first
-% converted to a string, with no expansion. The \meta{number} should
-% consist of digits and letters (either lower or upper case), plus
-% optionally a leading sign. The maximum \meta{base} value is $36$.
-% This is the inverse function of \cs{int_to_base:nn} and
-% \cs{int_to_Base:nn}.
-% \end{function}
-%
-% \section{Random integers}
-%
-% \begin{function}[EXP, added = 2016-12-06, updated = 2018-04-27]{\int_rand:nn}
-% \begin{syntax}
-% \cs{int_rand:nn} \Arg{int expr_1} \Arg{int expr_2}
-% \end{syntax}
-% Evaluates the two \meta{int expr}s and produces a
-% pseudo-random number between the two (with bounds included).
-% This is not available in older versions of \XeTeX{}.
-% \end{function}
-%
-% \begin{function}[EXP, added = 2018-05-05]{\int_rand:n}
-% \begin{syntax}
-% \cs{int_rand:n} \Arg{int expr}
-% \end{syntax}
-% Evaluates the \meta{int expr} then produces a
-% pseudo-random number between $1$ and the \meta{int expr} (included).
-% This is not available in older versions of \XeTeX{}.
-% \end{function}
-%
-% \section{Viewing integers}
-%
-% \begin{function}{\int_show:N, \int_show:c}
-% \begin{syntax}
-% \cs{int_show:N} \meta{integer}
-% \end{syntax}
-% Displays the value of the \meta{integer} on the terminal.
-% \end{function}
-%
-% \begin{function}[added = 2011-11-22, updated = 2015-08-07]{\int_show:n}
-% \begin{syntax}
-% \cs{int_show:n} \Arg{int expr}
-% \end{syntax}
-% Displays the result of evaluating the \meta{int expr}
-% on the terminal.
-% \end{function}
-%
-% \begin{function}[added = 2014-08-22, updated = 2015-08-03]{\int_log:N, \int_log:c}
-% \begin{syntax}
-% \cs{int_log:N} \meta{integer}
-% \end{syntax}
-% Writes the value of the \meta{integer} in the log file.
-% \end{function}
-%
-% \begin{function}[added = 2014-08-22, updated = 2015-08-07]{\int_log:n}
-% \begin{syntax}
-% \cs{int_log:n} \Arg{int expr}
-% \end{syntax}
-% Writes the result of evaluating the \meta{int expr}
-% in the log file.
-% \end{function}
-%
-% \section{Constant integers}
-%
-% \begin{variable}[added = 2018-05-07]{\c_zero_int, \c_one_int}
-% Integer values used with primitive tests and assignments: their
-% self-terminating nature makes these more convenient and faster than
-% literal numbers.
-% \end{variable}
-%
-% \begin{variable}[module = int]{\c_max_int}
-% The maximum value that can be stored as an integer.
-% \end{variable}
-%
-% \begin{variable}[module = int]{\c_max_register_int}
-% Maximum number of registers.
-% \end{variable}
-%
-% \begin{variable}[module = int]{\c_max_char_int}
-% Maximum character code completely supported by the engine.
-% \end{variable}
-%
-% \section{Scratch integers}
-%
-% \begin{variable}{\l_tmpa_int, \l_tmpb_int}
-% Scratch integer 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_int, \g_tmpb_int}
-% Scratch integer 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{Direct number expansion}
-%
-% \begin{function}[EXP, added = 2018-03-27]{\int_value:w}
-% \begin{syntax}
-% \cs{int_value:w} \meta{integer}
-% \cs{int_value:w} \meta{integer denotation} \meta{optional space}
-% \end{syntax}
-% Expands the following tokens until an \meta{integer} is formed, and
-% leaves a normalized form (no leading sign except for negative
-% numbers, no leading digit~|0| except for zero) in the input stream
-% as category code $12$ (other) characters. The \meta{integer} can
-% consist of any number of signs (with intervening spaces) followed
-% by
-% \begin{itemize}
-% \item an integer variable (in fact, any \TeX{} register except
-% \tn{toks}) or
-% \item explicit digits (or by |'|\meta{octal digits} or |"|\meta{hexadecimal digits} or |`|\meta{character}).
-% \end{itemize}
-% In this last case expansion stops once a non-digit is found; if that is a
-% space it is removed as in \texttt{f}-expansion, and so \cs{exp_stop_f:}
-% may be employed as an end marker. Note that protected functions
-% \emph{are} expanded by this process.
-%
-% This function requires exactly one expansion to produce a value, and so
-% is suitable for use in cases where a number is required \enquote{directly}.
-% In general, \cs{int_eval:n} is the preferred approach to generating
-% numbers.
-% \begin{texnote}
-% This is the \TeX{} primitive \tn{number}.
-% \end{texnote}
-% \end{function}
-%
-% \section{Primitive conditionals}
-%
-% \begin{function}[EXP]{\if_int_compare:w}
-% \begin{syntax}
-% \cs{if_int_compare:w} \meta{integer_1} \meta{relation} \meta{integer_2}
-% ~~\meta{true code}
-% \cs{else:}
-% ~~\meta{false code}
-% \cs{fi:}
-% \end{syntax}
-% Compare two integers using \meta{relation}, which must be one of
-% |=|, |<| or |>| with category code $12$.
-% The \cs{else:} branch is optional.
-% \begin{texnote}
-% This is the \TeX{} primitive \tn{ifnum}.
-% \end{texnote}
-% \end{function}
-%
-% \begin{function}[EXP]{\if_case:w, \or:}
-% \begin{syntax}
-% \cs{if_case:w} \meta{integer} \meta{case_0}
-% ~~\cs{or:} \meta{case_1}
-% ~~\cs{or:} |...|
-% ~~\cs{else:} \meta{default}
-% \cs{fi:}
-% \end{syntax}
-% Selects a case to execute based on the value of the \meta{integer}. The
-% first case (\meta{case_0}) is executed if \meta{integer} is $0$, the second
-% (\meta{case_1}) if the \meta{integer} is $1$, \emph{etc.} The
-% \meta{integer} may be a literal, a constant or an integer
-% expression (\emph{e.g.}~using \cs{int_eval:n}).
-% \begin{texnote}
-% These are the \TeX{} primitives \tn{ifcase} and \tn{or}.
-% \end{texnote}
-% \end{function}
-%
-% \begin{function}[EXP]{\if_int_odd:w}
-% \begin{syntax}
-% \cs{if_int_odd:w} \meta{tokens} \meta{optional space}
-% ~~\meta{true code}
-% \cs{else:}
-% ~~\meta{true code}
-% \cs{fi:}
-% \end{syntax}
-% Expands \meta{tokens} until a non-numeric token or a space is found, and
-% tests whether the resulting \meta{integer} is odd. If so, \meta{true code}
-% is executed. The \cs{else:} branch is optional.
-% \begin{texnote}
-% This is the \TeX{} primitive \tn{ifodd}.
-% \end{texnote}
-% \end{function}
-%
-% \end{documentation}
-%
-% \begin{implementation}
-%
-% \section{\pkg{l3int} implementation}
-%
-% \begin{macrocode}
-%<*package>
-% \end{macrocode}
-%
-% \begin{macrocode}
-%<@@=int>
-% \end{macrocode}
-%
-% \TestFiles{m3int001,m3int002,m3int03}
-%
-% \begin{variable}{\c_max_register_int}
-% Done in \pkg{l3basics}.
-% \end{variable}
-%
-% \begin{macro}{\@@_to_roman:w}
-% \begin{macro}{\if_int_compare:w}
-% Done in \pkg{l3basics}.
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}{\or:}
-% Done in \pkg{l3basics}.
-% \end{macro}
-%
-% \begin{macro}{\int_value:w}
-% \begin{macro}{\@@_eval:w}
-% \begin{macro}{\@@_eval_end:}
-% \begin{macro}{\if_int_odd:w}
-% \begin{macro}{\if_case:w}
-% Here are the remaining primitives for number comparisons and
-% expressions.
-% \begin{macrocode}
-\cs_new_eq:NN \int_value:w \tex_number:D
-\cs_new_eq:NN \@@_eval:w \tex_numexpr:D
-\cs_new_eq:NN \@@_eval_end: \tex_relax:D
-\cs_new_eq:NN \if_int_odd:w \tex_ifodd:D
-\cs_new_eq:NN \if_case:w \tex_ifcase:D
-% \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-%
-% \begin{variable}{\s_@@_mark,\s_@@_stop}
-% Scan marks used throughout the module.
-% \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}
-% Function to gobble until a scan mark.
-% \begin{macrocode}
-\cs_new:Npn \@@_use_none_delimit_by_s_stop:w #1 \s_@@_stop { }
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{variable}{\q_@@_recursion_tail,\q_@@_recursion_stop}
-% Quarks for recursion.
-% \begin{macrocode}
-\quark_new:N \q_@@_recursion_tail
-\quark_new:N \q_@@_recursion_stop
-% \end{macrocode}
-% \end{variable}
-%
-% \begin{macro}[EXP]{\@@_if_recursion_tail_stop_do:Nn,\@@_if_recursion_tail_stop:N}
-% Functions to query quarks.
-% \begin{macrocode}
-\__kernel_quark_new_test:N \@@_if_recursion_tail_stop_do:Nn
-\__kernel_quark_new_test:N \@@_if_recursion_tail_stop:N
-% \end{macrocode}
-% \end{macro}
-%
-% \subsection{Integer expressions}
-%
-% \begin{macro}{\int_eval:n}
-% \begin{macro}{\int_eval:w}
-% Wrapper for \cs{@@_eval:w}: can be used in an integer expression or
-% directly in the input stream. It is very slightly faster to use
-% \tn{the} rather than \tn{number} to turn the expression to a number.
-% When debugging, we introduce parentheses to catch early termination (see \pkg{l3debug}).
-% \begin{macrocode}
-\cs_new:Npn \int_eval:n #1
- { \tex_the:D \@@_eval:w #1 \@@_eval_end: }
-\cs_new:Npn \int_eval:w { \tex_the:D \@@_eval:w }
-% \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}[EXP]{\int_sign:n, \@@_sign:Nw}
-% See \cs{int_abs:n}. Evaluate the expression once (and when
-% debugging is enabled, check that the expression is well-formed),
-% then test the first character to determine the sign. This is
-% wrapped in \cs{int_value:w} \ldots{} \cs{exp_stop_f:} to ensure a
-% fixed number of expansions and to avoid dealing with closing the
-% conditionals.
-% \begin{macrocode}
-\cs_new:Npn \int_sign:n #1
- {
- \int_value:w \exp_after:wN \@@_sign:Nw
- \int_value:w \@@_eval:w #1 \@@_eval_end: ;
- \exp_stop_f:
- }
-\cs_new:Npn \@@_sign:Nw #1#2 ;
- {
- \if_meaning:w 0 #1
- 0
- \else:
- \if_meaning:w - #1 - \fi: 1
- \fi:
- }
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}[EXP]{\int_abs:n}
-% \begin{macro}[EXP]{\@@_abs:N}
-% \UnitTested
-% \begin{macro}[EXP]{\int_max:nn}
-% \begin{macro}[EXP]{\int_min:nn}
-% \begin{macro}[EXP]{\@@_maxmin:wwN}
-% \UnitTested
-% \UnitTested
-% Functions for $\min$, $\max$, and absolute value with only one
-% evaluation. The absolute value is obtained by removing a leading
-% sign if any. All three functions expand in two steps.
-% \begin{macrocode}
-\cs_new:Npn \int_abs:n #1
- {
- \int_value:w \exp_after:wN \@@_abs:N
- \int_value:w \@@_eval:w #1 \@@_eval_end:
- \exp_stop_f:
- }
-\cs_new:Npn \@@_abs:N #1
- { \if_meaning:w - #1 \else: \exp_after:wN #1 \fi: }
-\cs_new:Npn \int_max:nn #1#2
- {
- \int_value:w \exp_after:wN \@@_maxmin:wwN
- \int_value:w \@@_eval:w #1 \exp_after:wN ;
- \int_value:w \@@_eval:w #2 ;
- >
- \exp_stop_f:
- }
-\cs_new:Npn \int_min:nn #1#2
- {
- \int_value:w \exp_after:wN \@@_maxmin:wwN
- \int_value:w \@@_eval:w #1 \exp_after:wN ;
- \int_value:w \@@_eval:w #2 ;
- <
- \exp_stop_f:
- }
-\cs_new:Npn \@@_maxmin:wwN #1 ; #2 ; #3
- {
- \if_int_compare:w #1 #3 #2 ~
- #1
- \else:
- #2
- \fi:
- }
-% \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}[EXP]{\int_div_truncate:nn}
-% \UnitTested
-% \begin{macro}[EXP]{\int_div_round:nn}
-% \UnitTested
-% \begin{macro}[EXP]{\int_mod:nn}
-% \UnitTested
-% \begin{macro}[EXP]{\@@_div_truncate:NwNw}
-% \begin{macro}[EXP]{\@@_mod:ww}
-% As \cs{@@_eval:w} rounds the result of a division we also provide a
-% version that truncates the result. We use an auxiliary to make sure
-% numerator and denominator are only evaluated once: this comes in
-% handy when those are more expressions are expensive to evaluate
-% (\emph{e.g.}, \cs{tl_count:n}). If the numerator |#1#2| is $0$,
-% then we divide $0$ by the denominator (this ensures that $0/0$ is
-% correctly reported as an error). Otherwise, shift the numerator
-% |#1#2| towards $0$ by $(\left\vert\texttt{\#3\#4}\right\vert-1)/2$, which we
-% round away from zero. It turns out that this quantity exactly
-% compensates the difference between \eTeX{}'s rounding and the
-% truncating behaviour that we want. The details are thanks to Heiko
-% Oberdiek: getting things right in all cases is not so easy.
-% \begin{macrocode}
-\cs_new:Npn \int_div_truncate:nn #1#2
- {
- \int_value:w \@@_eval:w
- \exp_after:wN \@@_div_truncate:NwNw
- \int_value:w \@@_eval:w #1 \exp_after:wN ;
- \int_value:w \@@_eval:w #2 ;
- \@@_eval_end:
- }
-\cs_new:Npn \@@_div_truncate:NwNw #1#2; #3#4;
- {
- \if_meaning:w 0 #1
- 0
- \else:
- (
- #1#2
- \if_meaning:w - #1 + \else: - \fi:
- ( \if_meaning:w - #3 - \fi: #3#4 - 1 ) / 2
- )
- \fi:
- / #3#4
- }
-% \end{macrocode}
-% For the sake of completeness:
-% \begin{macrocode}
-\cs_new:Npn \int_div_round:nn #1#2
- { \int_value:w \@@_eval:w ( #1 ) / ( #2 ) \@@_eval_end: }
-% \end{macrocode}
-% Finally there's the modulus operation.
-% \begin{macrocode}
-\cs_new:Npn \int_mod:nn #1#2
- {
- \int_value:w \@@_eval:w \exp_after:wN \@@_mod:ww
- \int_value:w \@@_eval:w #1 \exp_after:wN ;
- \int_value:w \@@_eval:w #2 ;
- \@@_eval_end:
- }
-\cs_new:Npn \@@_mod:ww #1; #2;
- { #1 - ( \@@_div_truncate:NwNw #1 ; #2 ; ) * #2 }
-% \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}[EXP]{\__kernel_int_add:nnn}
-% Equivalent to \cs{int_eval:n} |{#1+#2+#3}| except that overflow only
-% occurs if the final result overflows $[-2^{31}+1,2^{31}-1]$. The
-% idea is to choose the order in which the three numbers are added
-% together. If |#1| and |#2| have opposite signs (one is in
-% $[-2^{31}+1,-1]$ and the other in $[0,2^{31}-1]$) then |#1+#2|
-% cannot overflow so we compute the result as |#1+#2+#3|. If they
-% have the same sign, then either |#3| has the same sign and the order
-% does not matter, or |#3| has the opposite sign and any order in
-% which |#3| is not last will work. We use |#1+#3+#2|.
-% \begin{macrocode}
-\cs_new:Npn \__kernel_int_add:nnn #1#2#3
- {
- \int_value:w \@@_eval:w #1
- \if_int_compare:w #2 < \c_zero_int \exp_after:wN \reverse_if:N \fi:
- \if_int_compare:w #1 < \c_zero_int + #2 + #3 \else: + #3 + #2 \fi:
- \@@_eval_end:
- }
-% \end{macrocode}
-% \end{macro}
-%
-% \subsection{Creating and initialising integers}
-%
-% \begin{macro}{\int_new:N, \int_new:c}
-% \UnitTested
-% Two ways to do this: one for the format and one for the \LaTeXe{}
-% package. In plain \TeX{}, \cs{newcount} (and other allocators) are
-% \cs{outer}: to allow the code here to work in \enquote{generic} mode
-% this is therefore accessed by name. (The same applies to \cs{newbox},
-% \cs{newdimen} and so on.)
-% \begin{macrocode}
-\cs_new_protected:Npn \int_new:N #1
- {
- \__kernel_chk_if_free_cs:N #1
- \cs:w newcount \cs_end: #1
- }
-\cs_generate_variant:Nn \int_new:N { c }
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\int_const:Nn, \int_const:cn}
-% \begin{macro}{\@@_const:nN, \@@_const:eN}
-% \begin{macro}{\@@_constdef:Nw}
-% \begin{variable}{\c_@@_max_constdef_int}
-% \UnitTested
-% As stated, most constants can be defined as \tn{chardef} or
-% \tn{mathchardef} but that's engine dependent. As a result, there is some
-% set up code to determine what can be done. No full engine testing just yet
-% so everything is a little awkward.
-% We cannot use \cs{int_gset:Nn} because (when |check-declarations| is
-% enabled) this runs some checks that constants would fail.
-% \begin{macrocode}
-\cs_new_protected:Npn \int_const:Nn #1#2
- { \@@_const:eN { \int_eval:n {#2} } #1 }
-\cs_generate_variant:Nn \int_const:Nn { c }
-\cs_new_protected:Npn \@@_const:nN #1#2
- {
- \int_compare:nNnTF {#1} < \c_zero_int
- {
- \int_new:N #2
- \tex_global:D
- }
- {
- \int_compare:nNnTF {#1} > \c_@@_max_constdef_int
- {
- \int_new:N #2
- \tex_global:D
- }
- {
- \__kernel_chk_if_free_cs:N #2
- \tex_global:D \@@_constdef:Nw
- }
- }
- #2 = \@@_eval:w #1 \@@_eval_end:
- }
-\cs_generate_variant:Nn \@@_const:nN { e }
-\if_int_odd:w 0
- \cs_if_exist:NT \tex_luatexversion:D { 1 }
- \cs_if_exist:NT \tex_omathchardef:D { 1 }
- \cs_if_exist:NT \tex_XeTeXversion:D { 1 } ~
- \cs_if_exist:NTF \tex_omathchardef:D
- { \cs_new_eq:NN \@@_constdef:Nw \tex_omathchardef:D }
- { \cs_new_eq:NN \@@_constdef:Nw \tex_chardef:D }
- \tex_global:D \@@_constdef:Nw \c_@@_max_constdef_int 1114111 ~
-\else:
- \cs_new_eq:NN \@@_constdef:Nw \tex_mathchardef:D
- \tex_global:D \@@_constdef:Nw \c_@@_max_constdef_int 32767 ~
-\fi:
-% \end{macrocode}
-% \end{variable}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}{\int_zero:N, \int_zero:c}
-% \UnitTested
-% \begin{macro}{\int_gzero:N, \int_gzero:c}
-% \UnitTested
-% Functions that reset an \meta{integer} register to zero.
-% \begin{macrocode}
-\cs_new_protected:Npn \int_zero:N #1 { #1 = \c_zero_int }
-\cs_new_protected:Npn \int_gzero:N #1 { \tex_global:D #1 = \c_zero_int }
-\cs_generate_variant:Nn \int_zero:N { c }
-\cs_generate_variant:Nn \int_gzero:N { c }
-% \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}
-% {\int_zero_new:N, \int_zero_new:c, \int_gzero_new:N, \int_gzero_new:c}
-% Create a register if needed, otherwise clear it.
-% \begin{macrocode}
-\cs_new_protected:Npn \int_zero_new:N #1
- { \int_if_exist:NTF #1 { \int_zero:N #1 } { \int_new:N #1 } }
-\cs_new_protected:Npn \int_gzero_new:N #1
- { \int_if_exist:NTF #1 { \int_gzero:N #1 } { \int_new:N #1 } }
-\cs_generate_variant:Nn \int_zero_new:N { c }
-\cs_generate_variant:Nn \int_gzero_new:N { c }
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\int_set_eq:NN, \int_set_eq:cN, \int_set_eq:Nc, \int_set_eq:cc}
-% \UnitTested
-% \begin{macro}
-% {\int_gset_eq:NN, \int_gset_eq:cN, \int_gset_eq:Nc, \int_gset_eq:cc}
-% \UnitTested
-% Setting equal means using one integer inside the set function of
-% another. Check that assigned integer is local/global. No need to
-% check that the other one is defined as \TeX{} does it for us.
-% \begin{macrocode}
-\cs_new_protected:Npn \int_set_eq:NN #1#2 { #1 = #2 }
-\cs_generate_variant:Nn \int_set_eq:NN { c , Nc , cc }
-\cs_new_protected:Npn \int_gset_eq:NN #1#2 { \tex_global:D #1 = #2 }
-\cs_generate_variant:Nn \int_gset_eq:NN { c , Nc , cc }
-% \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}[pTF]{\int_if_exist:N, \int_if_exist:c}
-% Copies of the \texttt{cs} functions defined in \pkg{l3basics}.
-% \begin{macrocode}
-\prg_new_eq_conditional:NNn \int_if_exist:N \cs_if_exist:N
- { TF , T , F , p }
-\prg_new_eq_conditional:NNn \int_if_exist:c \cs_if_exist:c
- { TF , T , F , p }
-% \end{macrocode}
-% \end{macro}
-%
-% \subsection{Setting and incrementing integers}
-%
-% \begin{macro}{\int_add:Nn, \int_add:cn}
-% \UnitTested
-% \begin{macro}{\int_gadd:Nn, \int_gadd:cn}
-% \UnitTested
-% \begin{macro}{\int_sub:Nn, \int_sub:cn}
-% \UnitTested
-% \begin{macro}{\int_gsub:Nn, \int_gsub:cn}
-% \UnitTested
-% Adding and subtracting to and from a counter.
-% Including here the optional |by| would slow down these operations
-% by a few percent.
-% \begin{macrocode}
-\cs_new_protected:Npn \int_add:Nn #1#2
- { \tex_advance:D #1 \@@_eval:w #2 \@@_eval_end: }
-\cs_new_protected:Npn \int_sub:Nn #1#2
- { \tex_advance:D #1 - \@@_eval:w #2 \@@_eval_end: }
-\cs_new_protected:Npn \int_gadd:Nn #1#2
- { \tex_global:D \tex_advance:D #1 \@@_eval:w #2 \@@_eval_end: }
-\cs_new_protected:Npn \int_gsub:Nn #1#2
- { \tex_global:D \tex_advance:D #1 - \@@_eval:w #2 \@@_eval_end: }
-\cs_generate_variant:Nn \int_add:Nn { c }
-\cs_generate_variant:Nn \int_gadd:Nn { c }
-\cs_generate_variant:Nn \int_sub:Nn { c }
-\cs_generate_variant:Nn \int_gsub:Nn { c }
-% \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}{\int_incr:N, \int_incr:c}
-% \UnitTested
-% \begin{macro}{\int_gincr:N, \int_gincr:c}
-% \UnitTested
-% \begin{macro}{\int_decr:N, \int_decr:c}
-% \UnitTested
-% \begin{macro}{\int_gdecr:N, \int_gdecr:c}
-% \UnitTested
-% Incrementing and decrementing of integer registers is done with
-% the following functions.
-% \begin{macrocode}
-\cs_new_protected:Npn \int_incr:N #1
- { \tex_advance:D #1 \c_one_int }
-\cs_new_protected:Npn \int_decr:N #1
- { \tex_advance:D #1 - \c_one_int }
-\cs_new_protected:Npn \int_gincr:N #1
- { \tex_global:D \tex_advance:D #1 \c_one_int }
-\cs_new_protected:Npn \int_gdecr:N #1
- { \tex_global:D \tex_advance:D #1 - \c_one_int }
-\cs_generate_variant:Nn \int_incr:N { c }
-\cs_generate_variant:Nn \int_decr:N { c }
-\cs_generate_variant:Nn \int_gincr:N { c }
-\cs_generate_variant:Nn \int_gdecr:N { c }
-% \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}{\int_set:Nn, \int_set:cn}
-% \UnitTested
-% \begin{macro}{\int_gset:Nn, \int_gset:cn}
-% \UnitTested
-% As integers are register-based \TeX{} issues an error
-% if they are not defined. While the |=| sign is optional, this
-% version with |=| is slightly quicker than without, while adding the
-% optional space after |=| slows things down minutely.
-% \begin{macrocode}
-\cs_new_protected:Npn \int_set:Nn #1#2
- { #1 = \@@_eval:w #2 \@@_eval_end: }
-\cs_new_protected:Npn \int_gset:Nn #1#2
- { \tex_global:D #1 = \@@_eval:w #2 \@@_eval_end: }
-\cs_generate_variant:Nn \int_set:Nn { c }
-\cs_generate_variant:Nn \int_gset:Nn { c }
-% \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \subsection{Using integers}
-%
-% \begin{macro}{\int_use:N, \int_use:c}
-% \UnitTested
-% Here is how counters are accessed.
-% We hand-code the |c| variant for some speed gain.
-% \begin{macrocode}
-\cs_new_eq:NN \int_use:N \tex_the:D
-\cs_new:Npn \int_use:c #1 { \tex_the:D \cs:w #1 \cs_end: }
-% \end{macrocode}
-% \end{macro}
-%
-% \subsection{Integer expression conditionals}
-%
-% \begin{macro}[EXP]{\@@_compare_error:, \@@_compare_error:Nw}
-% Those functions are used for comparison tests which use a simple
-% syntax where only one set of braces is required and additional
-% operators such as |!=| and |>=| are supported. The tests first
-% evaluate their left-hand side, with a trailing
-% \cs{@@_compare_error:}. This marker is normally not expanded,
-% but if the relation symbol is missing from the test's argument, then
-% the marker inserts |=| (and itself) after triggering the relevant
-% \TeX{} error. If the first token which appears after evaluating and
-% removing the left-hand side is not a known relation symbol, then a
-% judiciously placed \cs{@@_compare_error:Nw} gets expanded,
-% cleaning up the end of the test and telling the user what the
-% problem was.
-% \begin{macrocode}
-\cs_new_protected:Npn \@@_compare_error:
- {
- \if_int_compare:w \c_zero_int \c_zero_int \fi:
- =
- \@@_compare_error:
- }
-\cs_new:Npn \@@_compare_error:Nw
- #1#2 \s_@@_stop
- {
- { }
- \c_zero_int \fi:
- \msg_expandable_error:nnn
- { kernel } { unknown-comparison } {#1}
- \prg_return_false:
- }
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}[pTF, EXP]{\int_compare:n}
-% \begin{macro}[EXP]
-% {\@@_compare:w, \@@_compare:Nw, \@@_compare:NNw, \@@_compare:nnN}
-% \begin{macro}[EXP]
-% {
-% \@@_compare_end_=:NNw,
-% \@@_compare_=:NNw,
-% \@@_compare_<:NNw,
-% \@@_compare_>:NNw,
-% \@@_compare_==:NNw,
-% \@@_compare_!=:NNw,
-% \@@_compare_<=:NNw,
-% \@@_compare_>=:NNw
-% }
-% Comparison tests using a simple syntax where only one set of braces
-% is required, additional operators such as |!=| and |>=| are
-% supported, and multiple comparisons can be performed at once, for
-% instance |0 < 5 <= 1|. The idea is to loop through the argument,
-% finding one operand at a time, and comparing it to the previous one.
-% The looping auxiliary \cs{@@_compare:Nw} reads one \meta{operand}
-% and one \meta{comparison} symbol, and leaves roughly
-% \begin{quote}
-% \meta{operand} \cs{prg_return_false:} \cs{fi:} \\
-% \cs{reverse_if:N} \cs{if_int_compare:w} \meta{operand} \meta{comparison} \\
-% \cs{@@_compare:Nw}
-% \end{quote}
-% in the input stream. Each call to this auxiliary provides the
-% second operand of the last call's \cs{if_int_compare:w}. If one of
-% the \meta{comparisons} is \texttt{false}, the \texttt{true} branch
-% of the \TeX{} conditional is taken (because of \cs{reverse_if:N}),
-% immediately returning \texttt{false} as the result of the test.
-% There is no \TeX{} conditional waiting the first operand, so we add
-% an \cs{if_false:} and expand by hand with \cs{int_value:w}, thus
-% skipping \cs{prg_return_false:} on the first iteration.
-%
-% Before starting the loop, the first step is to make sure that there
-% is at least one relation symbol. We first let \TeX{} evaluate this
-% left hand side of the (in)equality using \cs{@@_eval:w}. Since the
-% relation symbols |<|, |>|, |=| and |!| are not allowed in integer
-% expressions, they would terminate the expression. If the argument contains no
-% relation symbol, \cs{@@_compare_error:} is expanded,
-% inserting~|=| and itself after an error. In all cases,
-% \cs{@@_compare:w} receives as its argument an integer, a relation
-% symbol, and some more tokens. We then setup the loop, which is
-% ended by the two odd-looking items |e| and |{=nd_}|, with a trailing
-% \cs{s_@@_stop} used to grab the entire argument when necessary.
-% \begin{macrocode}
-\prg_new_conditional:Npnn \int_compare:n #1 { p , T , F , TF }
- {
- \exp_after:wN \@@_compare:w
- \int_value:w \@@_eval:w #1 \@@_compare_error:
- }
-\cs_new:Npn \@@_compare:w #1 \@@_compare_error:
- {
- \exp_after:wN \if_false: \int_value:w
- \@@_compare:Nw #1 e { = nd_ } \s_@@_stop
- }
-% \end{macrocode}
-% The goal here is to find an \meta{operand} and a \meta{comparison}.
-% The \meta{operand} is already evaluated, but we cannot yet grab it
-% as an argument. To access the following relation symbol, we remove
-% the number by applying \cs{@@_to_roman:w}, after making sure that
-% the argument becomes non-positive: its roman numeral representation
-% is then empty. Then probe the first two tokens with
-% \cs{@@_compare:NNw} to determine the relation symbol, building a
-% control sequence from it (\cs{token_to_str:N} gives better errors if
-% |#1| is not a character). All the extended forms have an extra |=|
-% hence the test for that as a second token. If the relation symbol
-% is unknown, then the control sequence is turned by \TeX{} into
-% \cs{scan_stop:}, ignored thanks to \tn{unexpanded}, and
-% \cs{@@_compare_error:Nw} raises an error.
-% \begin{macrocode}
-\cs_new:Npn \@@_compare:Nw #1#2 \s_@@_stop
- {
- \exp_after:wN \@@_compare:NNw
- \@@_to_roman:w - 0 #2 \s_@@_mark
- #1#2 \s_@@_stop
- }
-\cs_new:Npn \@@_compare:NNw #1#2#3 \s_@@_mark
- {
- \__kernel_exp_not:w
- \use:c
- {
- @@_compare_ \token_to_str:N #1
- \if_meaning:w = #2 = \fi:
- :NNw
- }
- \@@_compare_error:Nw #1
- }
-% \end{macrocode}
-% When the last \meta{operand} is seen, \cs{@@_compare:NNw} receives
-% |e| and |=nd_| as arguments, hence calling
-% \cs{@@_compare_end_=:NNw} to end the loop: return the result of the
-% last comparison (involving the operand that we just found). When a
-% normal relation is found, the appropriate auxiliary calls
-% \cs{@@_compare:nnN} where |#1| is \cs{if_int_compare:w} or
-% \cs{reverse_if:N} \cs{if_int_compare:w}, |#2| is the \meta{operand},
-% and |#3| is one of |<|, |=|, or~|>|. As announced earlier, we leave
-% the \meta{operand} for the previous conditional. If this
-% conditional is true the result of the test is known, so we remove
-% all tokens and return \texttt{false}. Otherwise, we apply the
-% conditional |#1| to the \meta{operand} |#2| and the comparison |#3|,
-% and call \cs{@@_compare:Nw} to look for additional operands, after
-% evaluating the following expression.
-% \begin{macrocode}
-\cs_new:cpn { @@_compare_end_=:NNw } #1#2#3 e #4 \s_@@_stop
- {
- {#3} \exp_stop_f:
- \prg_return_false: \else: \prg_return_true: \fi:
- }
-\cs_new:Npn \@@_compare:nnN #1#2#3
- {
- {#2} \exp_stop_f:
- \prg_return_false: \exp_after:wN \@@_use_none_delimit_by_s_stop:w
- \fi:
- #1 #2 #3 \exp_after:wN \@@_compare:Nw \int_value:w \@@_eval:w
- }
-% \end{macrocode}
-% The actual comparisons are then simple function calls, using the
-% relation as delimiter for a delimited argument and discarding
-% \cs{@@_compare_error:Nw} \meta{token} responsible for error
-% detection.
-% \begin{macrocode}
-\cs_new:cpn { @@_compare_=:NNw } #1#2#3 =
- { \@@_compare:nnN { \reverse_if:N \if_int_compare:w } {#3} = }
-\cs_new:cpn { @@_compare_<:NNw } #1#2#3 <
- { \@@_compare:nnN { \reverse_if:N \if_int_compare:w } {#3} < }
-\cs_new:cpn { @@_compare_>:NNw } #1#2#3 >
- { \@@_compare:nnN { \reverse_if:N \if_int_compare:w } {#3} > }
-\cs_new:cpn { @@_compare_==:NNw } #1#2#3 ==
- { \@@_compare:nnN { \reverse_if:N \if_int_compare:w } {#3} = }
-\cs_new:cpn { @@_compare_!=:NNw } #1#2#3 !=
- { \@@_compare:nnN { \if_int_compare:w } {#3} = }
-\cs_new:cpn { @@_compare_<=:NNw } #1#2#3 <=
- { \@@_compare:nnN { \if_int_compare:w } {#3} > }
-\cs_new:cpn { @@_compare_>=:NNw } #1#2#3 >=
- { \@@_compare:nnN { \if_int_compare:w } {#3} < }
-% \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}[pTF]{\int_compare:nNn}
-% \UnitTested
-% More efficient but less natural in typing.
-% \begin{macrocode}
-\prg_new_conditional:Npnn \int_compare:nNn #1#2#3 { p , T , F , TF }
- {
- \if_int_compare: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]{\int_if_zero:n}
-% \begin{macrocode}
-\prg_new_conditional:Npnn \int_if_zero:n #1 { p , T , F , TF }
- {
- \if_int_compare:w \@@_eval:w #1 = \c_zero_int
- \prg_return_true:
- \else:
- \prg_return_false:
- \fi:
- }
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}[EXP, noTF]{\int_case:nn}
-% \begin{macro}{\@@_case:nnTF}
-% \begin{macro}{\@@_case:nw, \@@_case_end:nw}
-% For integer 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{l3str}.
-% \begin{macrocode}
-\cs_new:Npn \int_case:nnTF #1
- {
- \exp:w
- \exp_args:Nf \@@_case:nnTF { \int_eval:n {#1} }
- }
-\cs_new:Npn \int_case:nnT #1#2#3
- {
- \exp:w
- \exp_args:Nf \@@_case:nnTF { \int_eval:n {#1} } {#2} {#3} { }
- }
-\cs_new:Npn \int_case:nnF #1#2
- {
- \exp:w
- \exp_args:Nf \@@_case:nnTF { \int_eval:n {#1} } {#2} { }
- }
-\cs_new:Npn \int_case:nn #1#2
- {
- \exp:w
- \exp_args:Nf \@@_case:nnTF { \int_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
- {
- \int_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}
-%
-% \begin{macro}[pTF]{\int_if_odd:n}
-% \UnitTested
-% \begin{macro}[pTF]{\int_if_even:n}
-% \UnitTested
-% A predicate function.
-% \begin{macrocode}
-\prg_new_conditional:Npnn \int_if_odd:n #1 { p , T , F , TF}
- {
- \if_int_odd:w \@@_eval:w #1 \@@_eval_end:
- \prg_return_true:
- \else:
- \prg_return_false:
- \fi:
- }
-\prg_new_conditional:Npnn \int_if_even:n #1 { p , T , F , TF}
- {
- \reverse_if:N \if_int_odd:w \@@_eval:w #1 \@@_eval_end:
- \prg_return_true:
- \else:
- \prg_return_false:
- \fi:
- }
-% \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \subsection{Integer expression loops}
-%
-% \begin{macro}{\int_while_do:nn}
-% \UnitTested
-% \TestMissing{Boundary cases}
-% \begin{macro}{\int_until_do:nn}
-% \UnitTested
-% \TestMissing{Boundary cases}
-% \begin{macro}{\int_do_while:nn}
-% \UnitTested
-% \TestMissing{Boundary cases}
-% \begin{macro}{\int_do_until:nn}
-% \UnitTested
-% \TestMissing{Boundary cases}
-% These are quite easy given the above functions. The |while| versions
-% test first and then execute the body. The |do_while| does it the
-% other way round.
-% \begin{macrocode}
-\cs_new:Npn \int_while_do:nn #1#2
- {
- \int_compare:nT {#1}
- {
- #2
- \int_while_do:nn {#1} {#2}
- }
- }
-\cs_new:Npn \int_until_do:nn #1#2
- {
- \int_compare:nF {#1}
- {
- #2
- \int_until_do:nn {#1} {#2}
- }
- }
-\cs_new:Npn \int_do_while:nn #1#2
- {
- #2
- \int_compare:nT {#1}
- { \int_do_while:nn {#1} {#2} }
- }
-\cs_new:Npn \int_do_until:nn #1#2
- {
- #2
- \int_compare:nF {#1}
- { \int_do_until:nn {#1} {#2} }
- }
-% \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}{\int_while_do:nNnn}
-% \begin{macro}{\int_until_do:nNnn}
-% \begin{macro}{\int_do_while:nNnn}
-% \begin{macro}{\int_do_until:nNnn}
-% As above but not using the more natural syntax.
-% \begin{macrocode}
-\cs_new:Npn \int_while_do:nNnn #1#2#3#4
- {
- \int_compare:nNnT {#1} #2 {#3}
- {
- #4
- \int_while_do:nNnn {#1} #2 {#3} {#4}
- }
- }
-\cs_new:Npn \int_until_do:nNnn #1#2#3#4
- {
- \int_compare:nNnF {#1} #2 {#3}
- {
- #4
- \int_until_do:nNnn {#1} #2 {#3} {#4}
- }
- }
-\cs_new:Npn \int_do_while:nNnn #1#2#3#4
- {
- #4
- \int_compare:nNnT {#1} #2 {#3}
- { \int_do_while:nNnn {#1} #2 {#3} {#4} }
- }
-\cs_new:Npn \int_do_until:nNnn #1#2#3#4
- {
- #4
- \int_compare:nNnF {#1} #2 {#3}
- { \int_do_until:nNnn {#1} #2 {#3} {#4} }
- }
-% \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-%
-% \subsection{Integer step functions}
-%
-% \begin{macro}{\int_step_function:nnnN}
-% \begin{macro}{\@@_step:wwwN, \@@_step:NwnnN}
-% \begin{macro}{\int_step_function:nN}
-% \begin{macro}{\int_step_function:nnN}
-% 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 \int_step_function:nnnN #1#2#3
- {
- \exp_after:wN \@@_step:wwwN
- \int_value:w \@@_eval:w #1 \exp_after:wN ;
- \int_value:w \@@_eval:w #2 \exp_after:wN ;
- \int_value:w \@@_eval:w #3 ;
- }
-\cs_new:Npn \@@_step:wwwN #1; #2; #3; #4
- {
- \int_compare:nNnTF {#2} > \c_zero_int
- { \@@_step:NwnnN > }
- {
- \int_compare:nNnTF {#2} = \c_zero_int
- {
- \msg_expandable_error:nnn
- { kernel } { zero-step } {#4}
- \prg_break:
- }
- { \@@_step:NwnnN < }
- }
- #1 ; {#2} {#3} #4
- \prg_break_point:
- }
-\cs_new:Npn \@@_step:NwnnN #1#2 ; #3#4#5
- {
- \if_int_compare:w #2 #1 #4 \exp_stop_f:
- \prg_break:n
- \fi:
- #5 {#2}
- \exp_after:wN \@@_step:NwnnN
- \exp_after:wN #1
- \int_value:w \@@_eval:w #2 + #3 ; {#3} {#4} #5
- }
-\cs_new:Npn \int_step_function:nN
- { \int_step_function:nnnN { 1 } { 1 } }
-\cs_new:Npn \int_step_function:nnN #1
- { \int_step_function:nnnN {#1} { 1 } }
-% \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}{\int_step_inline:nn, \int_step_inline:nnn, \int_step_inline:nnnn}
-% \begin{macro}{\int_step_variable:nNn, \int_step_variable:nnNn, \int_step_variable:nnnNn}
-% \UnitTested
-% \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{int_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 \int_step_inline:nn
- { \int_step_inline:nnnn { 1 } { 1 } }
-\cs_new_protected:Npn \int_step_inline:nnn #1
- { \int_step_inline:nnnn {#1} { 1 } }
-\cs_new_protected:Npn \int_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 \int_step_variable:nNn
- { \int_step_variable:nnnNn { 1 } { 1 } }
-\cs_new_protected:Npn \int_step_variable:nnNn #1
- { \int_step_variable:nnnNn {#1} { 1 } }
-\cs_new_protected:Npn \int_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}
- \int_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{Formatting integers}
-%
-% \begin{macro}{\int_to_arabic:n, \int_to_arabic:v}
-% \UnitTested
-% Nothing exciting here.
-% \begin{macrocode}
-\cs_new_eq:NN \int_to_arabic:n \int_eval:n
-\cs_generate_variant:Nn \int_to_arabic:n { v }
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\int_to_symbols:nnn}
-% \UnitTested
-% \begin{macro}{\@@_to_symbols:nnnn, \@@_to_symbols:ennn}
-% For conversion of integers to arbitrary symbols the method is in
-% general as follows. The input number (|#1|) is compared to the total
-% number of symbols available at each place (|#2|). If the input is larger
-% than the total number of symbols available then the modulus is needed,
-% with one added so that the positions don't have to number from
-% zero. Using an \texttt{f}-type expansion, this is done so that the system
-% is recursive. The actual conversion function therefore gets a `nice'
-% number at each stage. Of course, if the initial input was small enough
-% then there is no problem and everything is easy.
-% \begin{macrocode}
-\cs_new:Npn \int_to_symbols:nnn #1#2#3
- {
- \int_compare:nNnTF {#1} > {#2}
- {
- \@@_to_symbols:ennn
- {
- \int_case:nn
- { 1 + \int_mod:nn { #1 - 1 } {#2} }
- {#3}
- }
- {#1} {#2} {#3}
- }
- { \int_case:nn {#1} {#3} }
- }
-\cs_new:Npn \@@_to_symbols:nnnn #1#2#3#4
- {
- \exp_args:Nf \int_to_symbols:nnn
- { \int_div_truncate:nn { #2 - 1 } {#3} } {#3} {#4}
- #1
- }
-\cs_generate_variant:Nn \@@_to_symbols:nnnn { e }
-% \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}{\int_to_alph:n, \int_to_Alph:n}
-% \UnitTested
-% These both use the above function with input functions that make sense
-% for the alphabet in English.
-% \begin{macrocode}
-\cs_new:Npn \int_to_alph:n #1
- {
- \int_to_symbols:nnn {#1} { 26 }
- {
- { 1 } { a }
- { 2 } { b }
- { 3 } { c }
- { 4 } { d }
- { 5 } { e }
- { 6 } { f }
- { 7 } { g }
- { 8 } { h }
- { 9 } { i }
- { 10 } { j }
- { 11 } { k }
- { 12 } { l }
- { 13 } { m }
- { 14 } { n }
- { 15 } { o }
- { 16 } { p }
- { 17 } { q }
- { 18 } { r }
- { 19 } { s }
- { 20 } { t }
- { 21 } { u }
- { 22 } { v }
- { 23 } { w }
- { 24 } { x }
- { 25 } { y }
- { 26 } { z }
- }
- }
-\cs_new:Npn \int_to_Alph:n #1
- {
- \int_to_symbols:nnn {#1} { 26 }
- {
- { 1 } { A }
- { 2 } { B }
- { 3 } { C }
- { 4 } { D }
- { 5 } { E }
- { 6 } { F }
- { 7 } { G }
- { 8 } { H }
- { 9 } { I }
- { 10 } { J }
- { 11 } { K }
- { 12 } { L }
- { 13 } { M }
- { 14 } { N }
- { 15 } { O }
- { 16 } { P }
- { 17 } { Q }
- { 18 } { R }
- { 19 } { S }
- { 20 } { T }
- { 21 } { U }
- { 22 } { V }
- { 23 } { W }
- { 24 } { X }
- { 25 } { Y }
- { 26 } { Z }
- }
- }
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\int_to_base:nn, \int_to_Base:nn}
-% \UnitTested
-% \begin{macro}{\@@_to_base:nn, \@@_to_Base:nn,
-% \@@_to_base:nnN, \@@_to_Base:nnN, \@@_to_base:nnnN, \@@_to_Base:nnnN}
-% \begin{macro}{\@@_to_letter:n, \@@_to_Letter:n}
-% \UnitTested
-% Converting from base ten (|#1|) to a second base (|#2|) starts with
-% computing |#1|: if it is a complicated calculation, we shouldn't
-% perform it twice. Then check the sign, store it, either \texttt{-}
-% or \cs{c_empty_tl}, and feed the absolute value to the next auxiliary
-% function.
-% \begin{macrocode}
-\cs_new:Npn \int_to_base:nn #1
- { \exp_args:Nf \@@_to_base:nn { \int_eval:n {#1} } }
-\cs_new:Npn \int_to_Base:nn #1
- { \exp_args:Nf \@@_to_Base:nn { \int_eval:n {#1} } }
-\cs_new:Npn \@@_to_base:nn #1#2
- {
- \int_compare:nNnTF {#1} < 0
- { \exp_args:No \@@_to_base:nnN { \use_none:n #1 } {#2} - }
- { \@@_to_base:nnN {#1} {#2} \c_empty_tl }
- }
-\cs_new:Npn \@@_to_Base:nn #1#2
- {
- \int_compare:nNnTF {#1} < 0
- { \exp_args:No \@@_to_Base:nnN { \use_none:n #1 } {#2} - }
- { \@@_to_Base:nnN {#1} {#2} \c_empty_tl }
- }
-% \end{macrocode}
-% Here, the idea is to provide a recursive system to deal with the
-% input. The output is built up after the end of the function.
-% At each pass, the value in |#1| is checked to see if it is less
-% than the new base (|#2|). If it is, then it is converted directly,
-% putting the sign back in front.
-% On the other hand, if the value to convert is greater than or equal
-% to the new base then the modulus and remainder values are found. The
-% modulus is converted to a symbol and put on the right,
-% and the remainder is carried forward to the next round.
-% \begin{macrocode}
-\cs_new:Npn \@@_to_base:nnN #1#2#3
- {
- \int_compare:nNnTF {#1} < {#2}
- { \exp_last_unbraced:Nf #3 { \@@_to_letter:n {#1} } }
- {
- \exp_args:Nf \@@_to_base:nnnN
- { \@@_to_letter:n { \int_mod:nn {#1} {#2} } }
- {#1}
- {#2}
- #3
- }
- }
-\cs_new:Npn \@@_to_base:nnnN #1#2#3#4
- {
- \exp_args:Nf \@@_to_base:nnN
- { \int_div_truncate:nn {#2} {#3} }
- {#3}
- #4
- #1
- }
-\cs_new:Npn \@@_to_Base:nnN #1#2#3
- {
- \int_compare:nNnTF {#1} < {#2}
- { \exp_last_unbraced:Nf #3 { \@@_to_Letter:n {#1} } }
- {
- \exp_args:Nf \@@_to_Base:nnnN
- { \@@_to_Letter:n { \int_mod:nn {#1} {#2} } }
- {#1}
- {#2}
- #3
- }
- }
-\cs_new:Npn \@@_to_Base:nnnN #1#2#3#4
- {
- \exp_args:Nf \@@_to_Base:nnN
- { \int_div_truncate:nn {#2} {#3} }
- {#3}
- #4
- #1
- }
-% \end{macrocode}
-% Convert to a letter only if necessary, otherwise simply return the
-% value unchanged. It would be cleaner to use \cs{int_case:nn},
-% but in our case, the cases are contiguous, so it is forty times faster
-% to use the \cs{if_case:w} primitive. The first \cs{exp_after:wN}
-% expands the conditional, jumping to the correct case, the second one
-% expands after the resulting character to close the conditional.
-% Since |#1| might be an expression, and not directly a single digit,
-% we need to evaluate it properly, and expand the trailing \cs{fi:}.
-% \begin{macrocode}
-\cs_new:Npn \@@_to_letter:n #1
- {
- \exp_after:wN \exp_after:wN
- \if_case:w \@@_eval:w #1 - 10 \@@_eval_end:
- a
- \or: b
- \or: c
- \or: d
- \or: e
- \or: f
- \or: g
- \or: h
- \or: i
- \or: j
- \or: k
- \or: l
- \or: m
- \or: n
- \or: o
- \or: p
- \or: q
- \or: r
- \or: s
- \or: t
- \or: u
- \or: v
- \or: w
- \or: x
- \or: y
- \or: z
- \else: \int_value:w \@@_eval:w #1 \exp_after:wN \@@_eval_end:
- \fi:
- }
-\cs_new:Npn \@@_to_Letter:n #1
- {
- \exp_after:wN \exp_after:wN
- \if_case:w \@@_eval:w #1 - 10 \@@_eval_end:
- A
- \or: B
- \or: C
- \or: D
- \or: E
- \or: F
- \or: G
- \or: H
- \or: I
- \or: J
- \or: K
- \or: L
- \or: M
- \or: N
- \or: O
- \or: P
- \or: Q
- \or: R
- \or: S
- \or: T
- \or: U
- \or: V
- \or: W
- \or: X
- \or: Y
- \or: Z
- \else: \int_value:w \@@_eval:w #1 \exp_after:wN \@@_eval_end:
- \fi:
- }
-% \end{macrocode}
-%\end{macro}
-%\end{macro}
-%\end{macro}
-%
-% \begin{macro}{\int_to_bin:n, \int_to_hex:n, \int_to_Hex:n, \int_to_oct:n}
-% \UnitTested
-% Wrappers around the generic function.
-% \begin{macrocode}
-\cs_new:Npn \int_to_bin:n #1
- { \int_to_base:nn {#1} { 2 } }
-\cs_new:Npn \int_to_hex:n #1
- { \int_to_base:nn {#1} { 16 } }
-\cs_new:Npn \int_to_Hex:n #1
- { \int_to_Base:nn {#1} { 16 } }
-\cs_new:Npn \int_to_oct:n #1
- { \int_to_base:nn {#1} { 8 } }
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\int_to_roman:n, \int_to_Roman:n}
-% \UnitTested
-% \begin{macro}{\@@_to_roman:N, \@@_to_roman:N}
-% \begin{macro}
-% {
-% \@@_to_roman_i:w, \@@_to_roman_v:w, \@@_to_roman_x:w,
-% \@@_to_roman_l:w, \@@_to_roman_c:w, \@@_to_roman_d:w,
-% \@@_to_roman_m:w, \@@_to_roman_Q:w,
-% \@@_to_Roman_i:w, \@@_to_Roman_v:w, \@@_to_Roman_x:w,
-% \@@_to_Roman_l:w, \@@_to_Roman_c:w, \@@_to_Roman_d:w,
-% \@@_to_Roman_m:w, \@@_to_Roman_Q:w,
-% }
-% The \cs{@@_to_roman:w} primitive creates tokens of category
-% code $12$ (other). Usually, what is actually wanted is letters.
-% The approach here is to convert the output of the primitive into
-% letters using appropriate control sequence names. That keeps
-% everything expandable. The loop is terminated by the conversion
-% of the |Q|.
-% \begin{macrocode}
-\cs_new:Npn \int_to_roman:n #1
- {
- \exp_after:wN \@@_to_roman:N
- \@@_to_roman:w \int_eval:n {#1} Q
- }
-\cs_new:Npn \@@_to_roman:N #1
- {
- \use:c { @@_to_roman_ #1 :w }
- \@@_to_roman:N
- }
-\cs_new:Npn \int_to_Roman:n #1
- {
- \exp_after:wN \@@_to_Roman_aux:N
- \@@_to_roman:w \int_eval:n {#1} Q
- }
-\cs_new:Npn \@@_to_Roman_aux:N #1
- {
- \use:c { @@_to_Roman_ #1 :w }
- \@@_to_Roman_aux:N
- }
-\cs_new:Npn \@@_to_roman_i:w { i }
-\cs_new:Npn \@@_to_roman_v:w { v }
-\cs_new:Npn \@@_to_roman_x:w { x }
-\cs_new:Npn \@@_to_roman_l:w { l }
-\cs_new:Npn \@@_to_roman_c:w { c }
-\cs_new:Npn \@@_to_roman_d:w { d }
-\cs_new:Npn \@@_to_roman_m:w { m }
-\cs_new:Npn \@@_to_roman_Q:w #1 { }
-\cs_new:Npn \@@_to_Roman_i:w { I }
-\cs_new:Npn \@@_to_Roman_v:w { V }
-\cs_new:Npn \@@_to_Roman_x:w { X }
-\cs_new:Npn \@@_to_Roman_l:w { L }
-\cs_new:Npn \@@_to_Roman_c:w { C }
-\cs_new:Npn \@@_to_Roman_d:w { D }
-\cs_new:Npn \@@_to_Roman_m:w { M }
-\cs_new:Npn \@@_to_Roman_Q:w #1 { }
-% \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-%
-% \subsection{Converting from other formats to integers}
-%
-% \begin{macro}[rEXP]{\@@_pass_signs:wn, \@@_pass_signs_end:wn}
-% Called as \cs{@@_pass_signs:wn} \meta{signs and digits} \cs{s_@@_stop}
-% \Arg{code}, this function leaves in the input stream any sign it
-% finds, then inserts the \meta{code} before the first non-sign token
-% (and removes \cs{s_@@_stop}). More precisely, it deletes any~|+| and
-% passes any~|-| to the input stream, hence should be called in an
-% integer expression.
-% \begin{macrocode}
-\cs_new:Npn \@@_pass_signs:wn #1
- {
- \if:w + \if:w - \exp_not:N #1 + \fi: \exp_not:N #1
- \exp_after:wN \@@_pass_signs:wn
- \else:
- \exp_after:wN \@@_pass_signs_end:wn
- \exp_after:wN #1
- \fi:
- }
-\cs_new:Npn \@@_pass_signs_end:wn #1 \s_@@_stop #2 { #2 #1 }
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\int_from_alph:n}
-% \UnitTested
-% \begin{macro}{\@@_from_alph:nN, \@@_from_alph:N}
-% First take care of signs then loop through the input using the
-% \texttt{recursion} quarks. The \cs{@@_from_alph:nN} auxiliary
-% collects in its first argument the value obtained so far, and the
-% auxiliary \cs{@@_from_alph:N} converts one letter to an expression
-% which evaluates to the correct number.
-% \begin{macrocode}
-\cs_new:Npn \int_from_alph:n #1
- {
- \int_eval:n
- {
- \exp_after:wN \@@_pass_signs:wn \tl_to_str:n {#1}
- \s_@@_stop { \@@_from_alph:nN { 0 } }
- \q_@@_recursion_tail \q_@@_recursion_stop
- }
- }
-\cs_new:Npn \@@_from_alph:nN #1#2
- {
- \@@_if_recursion_tail_stop_do:Nn #2 {#1}
- \exp_args:Nf \@@_from_alph:nN
- { \int_eval:n { #1 * 26 + \@@_from_alph:N #2 } }
- }
-\cs_new:Npn \@@_from_alph:N #1
- { `#1 - \int_compare:nNnTF { `#1 } < { 91 } { 64 } { 96 } }
-% \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}{\int_from_base:nn}
-% \UnitTested
-% \begin{macro}{\@@_from_base:nnN, \@@_from_base:N}
-% Leave the signs into the integer expression, then loop through
-% characters, collecting the value found so far in the first argument
-% of \cs{@@_from_base:nnN}. To convert a single character,
-% \cs{@@_from_base:N} checks first for digits, then distinguishes
-% lower from upper case letters, turning them into the appropriate
-% number. Note that this auxiliary does not use \cs{int_eval:n},
-% hence is not safe for general use.
-% \begin{macrocode}
-\cs_new:Npn \int_from_base:nn #1#2
- {
- \int_eval:n
- {
- \exp_after:wN \@@_pass_signs:wn \tl_to_str:n {#1}
- \s_@@_stop { \@@_from_base:nnN { 0 } {#2} }
- \q_@@_recursion_tail \q_@@_recursion_stop
- }
- }
-\cs_new:Npn \@@_from_base:nnN #1#2#3
- {
- \@@_if_recursion_tail_stop_do:Nn #3 {#1}
- \exp_args:Nf \@@_from_base:nnN
- { \int_eval:n { #1 * #2 + \@@_from_base:N #3 } }
- {#2}
- }
-\cs_new:Npn \@@_from_base:N #1
- {
- \int_compare:nNnTF { `#1 } < { 58 }
- {#1}
- { `#1 - \int_compare:nNnTF { `#1 } < { 91 } { 55 } { 87 } }
- }
-% \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}{\int_from_bin:n, \int_from_hex:n, \int_from_oct:n}
-% \UnitTested
-% Wrappers around the generic function.
-% \begin{macrocode}
-\cs_new:Npn \int_from_bin:n #1
- { \int_from_base:nn {#1} { 2 } }
-\cs_new:Npn \int_from_hex:n #1
- { \int_from_base:nn {#1} { 16 } }
-\cs_new:Npn \int_from_oct:n #1
- { \int_from_base:nn {#1} { 8 } }
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{variable}
-% {
-% \c_@@_from_roman_i_int, \c_@@_from_roman_v_int,
-% \c_@@_from_roman_x_int, \c_@@_from_roman_l_int,
-% \c_@@_from_roman_c_int, \c_@@_from_roman_d_int,
-% \c_@@_from_roman_m_int,
-% \c_@@_from_roman_I_int, \c_@@_from_roman_V_int,
-% \c_@@_from_roman_X_int, \c_@@_from_roman_L_int,
-% \c_@@_from_roman_C_int, \c_@@_from_roman_D_int,
-% \c_@@_from_roman_M_int
-% }
-% Constants used to convert from Roman numerals to integers.
-% \begin{macrocode}
-\int_const:cn { c_@@_from_roman_i_int } { 1 }
-\int_const:cn { c_@@_from_roman_v_int } { 5 }
-\int_const:cn { c_@@_from_roman_x_int } { 10 }
-\int_const:cn { c_@@_from_roman_l_int } { 50 }
-\int_const:cn { c_@@_from_roman_c_int } { 100 }
-\int_const:cn { c_@@_from_roman_d_int } { 500 }
-\int_const:cn { c_@@_from_roman_m_int } { 1000 }
-\int_const:cn { c_@@_from_roman_I_int } { 1 }
-\int_const:cn { c_@@_from_roman_V_int } { 5 }
-\int_const:cn { c_@@_from_roman_X_int } { 10 }
-\int_const:cn { c_@@_from_roman_L_int } { 50 }
-\int_const:cn { c_@@_from_roman_C_int } { 100 }
-\int_const:cn { c_@@_from_roman_D_int } { 500 }
-\int_const:cn { c_@@_from_roman_M_int } { 1000 }
-% \end{macrocode}
-% \end{variable}
-%
-% \begin{macro}{\int_from_roman:n}
-% \UnitTested
-% \TestMissing{boundary cases / wrong input?}
-% \begin{macro}{\@@_from_roman:NN}
-% \begin{macro}{\@@_from_roman_error:w}
-% The method here is to iterate through the input, finding the
-% appropriate value for each letter and building up a sum. This is
-% then evaluated by \TeX{}. If any unknown letter is found, skip to
-% the closing parenthesis and insert |*0-1| afterwards, to replace the
-% value by $-1$.
-% \begin{macrocode}
-\cs_new:Npn \int_from_roman:n #1
- {
- \int_eval:n
- {
- (
- 0
- \exp_after:wN \@@_from_roman:NN \tl_to_str:n {#1}
- \q_@@_recursion_tail \q_@@_recursion_tail \q_@@_recursion_stop
- )
- }
- }
-\cs_new:Npn \@@_from_roman:NN #1#2
- {
- \@@_if_recursion_tail_stop:N #1
- \int_if_exist:cF { c_@@_from_roman_ #1 _int }
- { \@@_from_roman_error:w }
- \@@_if_recursion_tail_stop_do:Nn #2
- { + \use:c { c_@@_from_roman_ #1 _int } }
- \int_if_exist:cF { c_@@_from_roman_ #2 _int }
- { \@@_from_roman_error:w }
- \int_compare:nNnTF
- { \use:c { c_@@_from_roman_ #1 _int } }
- <
- { \use:c { c_@@_from_roman_ #2 _int } }
- {
- + \use:c { c_@@_from_roman_ #2 _int }
- - \use:c { c_@@_from_roman_ #1 _int }
- \@@_from_roman:NN
- }
- {
- + \use:c { c_@@_from_roman_ #1 _int }
- \@@_from_roman:NN #2
- }
- }
-\cs_new:Npn \@@_from_roman_error:w #1 \q_@@_recursion_stop #2
- { #2 * 0 - 1 }
-% \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-%
-% \subsection{Viewing integer}
-%
-% \begin{macro}{\int_show:N, \int_show:c}
-% \UnitTested
-% \begin{macro}{\@@_show:nN}
-% Diagnostics.
-% \begin{macrocode}
-\cs_new_eq:NN \int_show:N \__kernel_register_show:N
-\cs_generate_variant:Nn \int_show:N { c }
-% \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}{\int_show:n}
-% \UnitTested
-% We don't use the \TeX{} primitive \tn{showthe} to show integer
-% expressions: this gives a more unified output.
-% \begin{macrocode}
-\cs_new_protected:Npn \int_show:n
- { \__kernel_msg_show_eval:Nn \int_eval:n }
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\int_log:N, \int_log:c}
-% Diagnostics.
-% \begin{macrocode}
-\cs_new_eq:NN \int_log:N \__kernel_register_log:N
-\cs_generate_variant:Nn \int_log:N { c }
-% \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\int_log:n}
-% Similar to \cs{int_show:n}.
-% \begin{macrocode}
-\cs_new_protected:Npn \int_log:n
- { \__kernel_msg_log_eval:Nn \int_eval:n }
-% \end{macrocode}
-% \end{macro}
-%
-%\subsection{Random integers}
-%
-% \begin{macro}{\int_rand:nn}
-% Defined in \pkg{l3fp-random}.
-% \end{macro}
-%
-% \subsection{Constant integers}
-%
-% \begin{variable}{\c_zero_int, \c_one_int}
-% The zero is defined in \pkg{l3basics}.
-% \begin{macrocode}
-\int_const:Nn \c_one_int { 1 }
-% \end{macrocode}
-% \end{variable}
-%
-% \begin{variable}{\c_max_int}
-% The largest number allowed is $2^{31}-1$
-% \begin{macrocode}
-\int_const:Nn \c_max_int { 2 147 483 647 }
-% \end{macrocode}
-% \end{variable}
-%
-% \begin{variable}{\c_max_char_int}
-% The largest character code is $1114111$ (hexadecimal |10FFFF|) in
-% \XeTeX{} and \LuaTeX{} and $255$ in other engines. In many places
-% \pTeX{} and \upTeX{} support larger character codes but for instance
-% the values of \tn{lccode} are restricted to $[0,255]$.
-% \begin{macrocode}
-\int_const:Nn \c_max_char_int
- {
- \if_int_odd:w 0
- \cs_if_exist:NT \tex_luatexversion:D { 1 }
- \cs_if_exist:NT \tex_XeTeXversion:D { 1 } ~
- "10FFFF
- \else:
- "FF
- \fi:
- }
-% \end{macrocode}
-% \end{variable}
-%
-% \subsection{Scratch integers}
-%
-% \begin{variable}{\l_tmpa_int, \l_tmpb_int}
-% \begin{variable}{\g_tmpa_int, \g_tmpb_int}
-% We provide two local and two global scratch counters, maybe we
-% need more or less.
-% \begin{macrocode}
-\int_new:N \l_tmpa_int
-\int_new:N \l_tmpb_int
-\int_new:N \g_tmpa_int
-\int_new:N \g_tmpb_int
-% \end{macrocode}
-% \end{variable}
-% \end{variable}
-%
-% \subsection{Integers for earlier modules}
-%
-%<@@=seq>
-%
-% \begin{variable}{\l_@@_internal_a_int, \l_@@_internal_b_int}
-% \begin{macrocode}
-\int_new:N \l_@@_internal_a_int
-\int_new:N \l_@@_internal_b_int
-% \end{macrocode}
-% \end{variable}
-%
-% \begin{macrocode}
-%</package>
-% \end{macrocode}
-%
-% \end{implementation}
-%
-% \PrintIndex